Design of a static micro-cell for phase equilibrium measurements: measurements and modelling

Transcription

1 Desgn of a statc mcro-cell for phase equlbrum measurements: measurements and modellng Caleb Narasgadu To cte ths verson: Caleb Narasgadu. Desgn of a statc mcro-cell for phase equlbrum measurements: measurements and modellng. Chemcal and Process Engneerng. École Natonale Supéreure des Mnes de Pars; Unversty of KwaZulu-Natal - Afrque du Sud, 20. Englsh. <NNT : 20ENMP007>. <pastel > HAL Id: pastel Submtted on 5 Mar 202 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not. The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers. L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés.

2 N : 2009 ENAM XXXX École doctorale n 432 : Scences des Méters de l lngéneur Doctorat ParsTech T H È S E pour obtenr le grade de docteur délvré par l École natonale supéreure des mnes de Pars Spécalté «Géne des Procédés» présentée et soutenue publquement par Caleb NARASIGADU le 06 septembre 20 Concepton ďune Mcro-Cellule pour Mesures d Équlbres de Phases : Mesures et Modélsaton Desgn of a Statc Mcro-Cell for Phase Equlbrum Measurements : Measurements and Modellng Drecteurs de thèse : Domnque RICHON et Deresh RAMJUGERNATH Co-encadrements de la thèse : Chrstophe COQUELET et Paramespr NAIDOO Jury M. Jean-Nöel JAUBERT, Professeur, Insttut Natonal Polytechnque de Lorrane Rapporteur M. Serge LAUGIER, Matre de Conférence, E.N.S.C.B.P. Rapporteur M. Johan Davd RAAL, Professeur Emerte, Unversty of KwaZulu-Natal Examnateur M. Pascal MOUGIN, Ingéneur de Recherche, Insttut franças du pétrole Examnateur M. Deresh RAMJUGERNATH, Professeur, Unversty of KwaZulu-Natal Examnateur M. Domnque RICHON, Drecteur de Recherche, MINES ParsTech Examnateur M. Chrstophe COQUELET, Matre Assstant, MINES ParsTech Examnateur T H È S E MINES ParsTech Centre Énergétque et Procédés Laboratore CEP/TEP 35, rue Sant Honoré, Fontanebleau cedex, France

3 DESIGN OF A STATIC MICRO-CELL FOR PHASE EQUILIBRIUM MEASUREMENTS: MEASUREMENTS AND MODELLING by CALEB NARASIGADU [MSc. (Eng)] Unversty of KwaZulu Natal Submtted n fulfllment of the academc requrements for the degree of Doctor of Phlosophy n Engneerng at the School of Chemcal Engneerng, Unversty of KwaZulu Natal and L Ecole Natonale Supéreure des Mnes de Pars as agreed n the conventon for nternatonal jont doctorate supervson entered nto by these two nsttutons Durban 20

4 ABSTRACT ABSTRACT Vapour-Lqud Equlbrum (VLE), Lqud-Lqud Equlbrum (LLE) and Vapour-Lqud-Lqud Equlbrum (VLLE) are of specal nterest n chemcal engneerng as these types of data form the bass for the desgn and optmzaton of separaton processes such as dstllaton and extracton, whch nvolve phase contactng. Of recent, chemcal companes/ndustres have requred thermodynamc data (especally phase equlbrum data) for chemcals that are expensve or costly to synthesze. Phase equlbrum data for such chemcals are scarce n the open lterature snce most apparatus used for phase equlbrum measurements requre large volumes (on average 20 ) of chemcals. Therefore, new technques and equpment have to be developed to measure phase equlbrum for small volumes across reasonable temperature and pressure ranges. Ths study covers the desgn of a new apparatus that enables relable vapour pressure and equlbra measurements for multple lqud and vapour phases of small volumes (a maxmum of 8 ). These phase equlbra measurements nclude: VLE, LLE and VLLE. The operatng temperature of the apparatus ranges from 253 to 473 K and the operatng pressure ranges from absolute vacuum to 600 kpa. The samplng of the phases are accomplshed usng a sngle Rapd-OnLne-Sampler- Injector ( ) that s capable of wthdrawng as lttle as μl of sample from each phase. Ths ensures that the equlbrum condton s not dsturbed durng the samplng and analyss process. As an added advantage, a short equlbrum tme s generally assocated wth a small volume apparatus. Ths enables rapd measurement of multple phase equlbra. A novel technque s used to acheve samplng for each phase. The technque made use of a metallc rod (smlar n dmenson to the capllary of the ) n an arrangement to compensate for volume changes durng samplng. As part of ths study, vapour pressure and phase equlbrum data were measured to test the operaton of the newly developed apparatus that nclude the followng systems: VLE for 2-methoxy-2-methylpropane + ethyl acetate at K LLE for methanol + heptane at 350 kpa LLE for hexane + acetontrle at 350 kpa VLLE for hexane + acetontrle at K New expermental vapour pressure and VLE data were also measured for systems of nterest to petrochemcal companes. These measurements nclude: VLE for methanol + butan-2-one at , and K

5 ABSTRACT VLE for ethanol + butan-2-one at , and 43.2 K VLE for ethanol + 2-methoxy-2-methylbutane at and 43.9 K VLE for ethanol + 2-methylpent-2-ene at K These measurements were undertaken to understand the thermodynamc nteractons of lght alcohols and carbonyls as part of a number of dstllaton systems n synthetc fuel refnng processes whch are currently not well descrbed. Two of these above mentoned systems nclude expensve chemcals: 2-methoxy-2-methylbutane and 2-methylpent-2-ene. The expermental vapour pressure data obtaned were regressed usng the extended Antone and Wagner equatons. The expermental VLE data measured were regressed wth thermodynamc models usng the drect and combned methods. For the drect method the Soave-Redlch-Kwong and Peng-Robnson equatons of state were used wth the temperature dependent functon (α) of Mathas and Copeman (983). For the combned method, the Vral equaton of state wth the second Vral coeffcent correlaton of Tsonopoulos (974) was used together wth one of the followng lqud-phase actvty coeffcent model: TK-Wlson, NRTL and modfed UNIQUAC. Thermodynamc consstency testng was also performed for all the VLE expermental data measured where almost all the systems measured showed good thermodynamc consstency for the pont test of Van Ness et al. (973) and drect test of Van Ness (995). v

6 PREFACE PREFACE The work presented n ths thess was performed at the Unversty of KwaZulu-Natal and L Ecole Natonale Supéreure des Mnes de Pars from January 2008 to March 20 as stpulated n the conventon for nternatonal jont doctorate supervson entered nto by these two nsttutons. The work was supervsed by Professor D. Ramjugernath and Doctor P. Nadoo at the Unversty of KwaZulu-Natal and Prof. D. Rchon and Doctor C. Coquelet at L Ecole Natonale Supéreure des Mnes de Pars. Ths thess s submtted as the full requrement for the degree PhD n chemcal engneerng. I, Caleb Narasgadu declare that: ) The research n ths dssertaton, except where otherwse stated, s my orgnal work. ) Ths thess has not been submtted for any degree or examnaton at any other unversty. ) Ths thess does not contan other persons data, pctures, graphs or other nformaton, unless specfcally acknowledged as beng sourced from other persons. v) Ths thess does not contan other persons wrtng, unless specfcally acknowledged as beng sourced from other researchers. Where other wrtten sources have been quoted then: a) Ther words have been re-wrtten but the general nformaton attrbuted to them has been referenced; b) Where ther exact words have been used, ther wrtng has been placed nsde quotaton marks and referenced. v) Ths thess does not contan text, graphcs or tables coped and pasted from the nternet, unless specfcally acknowledged and the source beng detaled n the thess and n the References secton. C. Narasgadu As supervsor of ths canddate, I approve ths dssertaton for submsson: Professor D. Ramjugernath Doctor P. Nadoo Professor D. Rchon Doctor C. Coquelet v

7 ACKNOWLEDGEMENTS ACKNOWLEDGEMENTS I would lke to take ths opportunty to acknowledge and thank the followng who have made a tremendous contrbuton to ths work: Frstly, my Lord and Savour, Jesus Chrst, Who has made my tertary educaton a realty. Lord, I am eternally grateful to You. My supervsors, Professor D. Ramjugernath, Doctor P. Nadoo, Doctor C. Coquelet and Professor D. Rchon for ther expert knowledge, gudance and support. SASOL Ltd. for ther fnancal assstance. The techncal staff at the School of Chemcal Engneerng Unversty of KwaZulu Natal, n partcular Kelly Robertson for hs nvaluable contrbuton to ths work n terms of constructon work. Alan Raymond Foster and Warren Errol Sheahan for ther assstance wth the schematc drawngs. My mum, Lnda, my sster, Lsa, and my uncle and aunt, Jva and Sylva, for ther many years of wholehearted support, prayer, encouragement, love and motvaton. My extended famly, fellow postgraduate colleagues, frends and especally the congregaton of Chrstan Revval Centre Tongaat church for ther nvaluable advce, prayer, support and frendshp. v

8 DEDICATION DEDICATION To my Lord and Savour, Jesus Chrst But wthout fath t s mpossble to please and be satsfactory to Hm. For whoever would come near to God must [necessarly] beleve that God exsts and that He s the rewarder of those who earnestly and dlgently seek Hm [out]. HEBREWS :6 (AMPLIFIED BIBLE) v

9 TABLE OF CONTENTS TABLE OF CONTENTS ABSTRACT... PREFACE..... v ACKNOWLEDGEMENTS... v TABLE OF CONTENTS... v LIST OF FIGURES.... xv LIST OF PHOTOGRAPHS... xxv LIST OF TABLES... xxv NOMENCLATURE... xxx CHAPTER : FRENCH SUMMARY... INTRODUCTION...2 CHAPTER 2: FRENCH SUMMARY... 4 LITERATURE REVIEW The Statc Method Cell Desgn Materal of Constructon Thermal Envronment Agtaton of Cell Contents. 2.3 Samplng Technques Degassng of Components v

10 TABLE OF CONTENTS CHAPTER 3: FRENCH SUMMARY THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Fugacty and Fugacty Coeffcents Fugacty Coeffcents from the Vral Equaton of State Fugacty Coeffcents from a Cubc Equaton of State The Soave-Redlch-Kwong (SRK) Cubc Equaton of State The Peng-Robnson (PR) Cubc Equaton of State The Alpha Correlaton of Mathas and Copeman. (983) Mxng Rules for Cubc Equatons of State Actvty and Actvty Coeffcent Lqud Phase Actvty Coeffcent Models The Tsuboka-Katayama-Wlson (TK-Wlson) Equaton The NRTL (Non-Random Two Lqud) Equaton The Modfed UNIQUAC (UNIversal QUas-Chemcal) Equaton Vapour-Lqud Equlbrum (VLE) VLE Data Regresson The Combned (γ-ф) Method The Drect (Ф-Ф) Method Lqud-Lqud Equlbrum (LLE) Bnary Systems Theoretcal Treatment of LLE Bnary LLE Data Regresson Vapour-Lqud-Lqud Equlbrum (VLLE) VLLE Data Regresson Thermodynamc Consstency Tests The Pont Test The Drect Test CHAPTER 4: FRENCH SUMMARY... 7 x

11 TABLE OF CONTENTS EQUIPMENT DESCRIPTION Descrpton of the Equlbrum Cell and ts Housng Samplng Technque and Assembly Method of Agtaton wthn the Equlbrum Cell Isothermal Envronment for the Equlbrum Cell Temperature and Pressure Measurement Temperature Measurement Pressure Measurement Composton Analyss Data Loggng Degassng Apparatus Compresson Devce for Cell Loadng Safety Features Overvew. 9 CHAPTER 5: FRENCH SUMMARY EXPERIMENTAL PROCEDURE Degassng Apparatus Preparaton Cleanng of the Degassng Apparatus Operatng Procedure of the Degassng Apparatus Compresson Devce Preparaton and Cleanng Chargng the Compresson Devce Phase Equlbrum Apparatus Preparaton Leak Detecton Cleanng the Equlbrum Cell Calbraton Temperature Probe Calbraton Pressure Transmtter Calbraton 03 x

12 TABLE OF CONTENTS Gas Chromatograph Calbraton Operatng Procedures for Phase Equlbrum Measurements In-Stu Degassng Vapour Pressure Measurement Bnary Vapour-Lqud Equlbrum (VLE) Measurement Bnary Lqud-Lqud Equlbrum (LLE) Measurement Bnary Vapour-Lqud-Lqud Equlbrum (VLLE) Measurement CHAPTER 6: FRENCH SUMMARY... 7 EXPERIMENTAL RESULTS Chemcal Purty Expermental Uncertantes Vapour Pressure Data Phase Equlbra of Test Systems Vapour-Lqud Equlbrum (VLE) Result Methoxy-2-Methylpropane () + Ethyl Acetate (2) Lqud-Lqud Equlbrum (LLE) Results Hexane () + Acetontrle (2) Methanol () + Heptane (2) Phase Equlbra of New Systems Vapour-Lqud Equlbrum (VLE) Methanol () + Butan-2-one (2) Ethanol () + Butan-2-one (2) Ethanol () + 2-Methoxy-2-Methylbutane (2) Methylpent-2-ene () + Ethanol (2) Vapour-Lqud-Lqud Equlbrum (VLLE) Hexane () + Acetontrle (2) CHAPTER 7: FRENCH SUMMARY.. 42 DATA ANALYSIS AND DISCUSSION Pure Component Propertes 43 x

13 TABLE OF CONTENTS 7.2 Expermental Vapour Pressure Data Comparson of Expermental and Lterature Vapour Pressure Regresson usng Emprcal Correlatons Regresson usng Equatons of State Thermodynamc Consstency Testng for Vapour Pressure Data Expermental Actvty Coeffcents VLE/VLLE Systems Expermental VLE Data Reducton Methoxy-2-Methylpropane () + Ethyl Acetate (2) Methanol () + Butan-2-one (2) Ethanol () + Butan-2-one (2) Ethanol () + 2-Methoxy-2-Methylbutane (2) Methylpent-2-ene () + Ethanol (2) Expermental LLE Data Reducton Hexane () + Acetontrle (2) Methanol () + Heptane (2) Expermental VLLE Data Reducton Hexane () + Acetontrle (2) Thermodynamc Consstency Testng for VLE Systems Methoxy-2-Methylpropane () + Ethyl Acetate (2) Methanol () + Butan-2-one (2) Ethanol () + Butan-2-one (2) Ethanol () + 2-Methoxy-2-Methylbutane (2) Methylpent-2-ene () + Ethanol () Concludng Remarks. 26 CHAPTER 8: FRENCH SUMMARY CONCLUSION CHAPTER 9: FRENCH SUMMARY RECOMMENDATIONS. 223 x

14 TABLE OF CONTENTS REFERENCES APPENDIX A: CRITERION FOR PHASE EQUILIBRIUM APPENDIX B: PHYSICAL PROPERTIES OF CHEMICALS APPENDIX C: CALIBRATIONS C. Temperature Calbratons C.2 Pressure Calbratons C.3 Gas Chromatograph Condtons. 26 C.4 Gas Chromatograph Calbratons C.4. VLE Systems 263 C.4.2 LLE and VLLE Systems. 272 APPENDIX D: USER-INTERFACE OF SOFTWARE APPENDIX E: APPARATUS FLOW DIAGRAM 278 APPENDIX F: COMMUNICATIONS F. Publcatons F.2 Conferences FRENCH & ENGLISH ABSTRACTS x

15 LIST OF FIGURES LIST OF FIGURES Chapter 2 Fgure 2-: Schematc llustraton of the statc analytcal method (Raal and Mühlbauer, 998)...8 Fgure 2-2: Schematc of the expermental apparatus of Outcalt and Lee (2004).. 0 Fgure 2-3: Equlbrum cell and agtator of Bae et al. (98) 2 Fgure 2-4: Schematc llustraton of the equlbrum cell and auxllary equpment of Huang et al. (985)...3 Fgure 2-5: Equlbrum cell of Ashcroft et al. (983) 4 Fgure 2-6: Schematc of the acoustc nterferometer used for bubble pont pressure measurements by Takag et al. (2003)..4 Fgure 2-7: (a) Equlbrum cell assembly of Fguere et al. (980); (b) carrer gas crculaton through the cell to sweep samples (cross secton -).6 Fgure 2-8: Equlbrum cell of Legret et al. (98) 7 Fgure 2-9: Samplng mcrocell of Legret et al. (98)..7 Fgure 2-0: Equlbrum cell and samplng system of Rogers and Prausntz (970)..8 Fgure 2-: Samplng confguraton of the sx-port gas chromatograph valve used by Ramjugernath (2000) (Raal and Mühlbauer, 998).9 Fgure 2-2: Electromagnetc verson of sampler ( Evoluton IV) 9 Fgure 2-3: Schematc of the degassng apparatus of Van Ness and Abbott (978)...2 Fgure 2-4: Purfcaton and degassng apparatus of Fscher and Gmehlng (994)...2 Chapter 3 Fgure 3-: Fgure 3-2: Fgure 3-3: The three common types of bnary phase dagrams for T-x-y, P-x-y and x-y plots: (a) ntermedate-bolng; (b) mnmum bolng azeotrope; (c) maxmum bolng azeotrope (Raal and Mühlbauer, 998) Calculaton flow dagram for the bubble pont pressure procedure of the combned method to obtan the parameters for the lqud phase actvty coeffcent model (Smth et al., 200)...54 Calculaton flow dagram for the bubble pont pressure teraton for the drect method to obtan parameters for the mxng rule used (Smth et al., 200).58 xv

16 LIST OF FIGURES Fgure 3-4: Fgure 3-5: Fgure 3-6: Fgure 3-7: Three types of constant pressure bnary LLE phase dagrams: (a) an sland curve, (b) a convex curve and (c) a concave curve, where α and β refer to the two lqud phases (Smth et al., 200)...60 Molar Gbbs energy of mxng for a partally mscble bnary system at constant temperature and pressure (Prausntz et al., 999).6 A common T-x-y dagram at constant pressure for a bnary system exhbtng VLLE (Smth et al., 200)...64 A common P-x-y dagram at constant temperature for a bnary system exhbtng VLLE (Smth et al., 200) 65 Chapter 4 Fgure 4-: Fgure 4-2: Fgure 4-3: Fgure 4-4: Schematc of the equlbrum cell assembly.79 Postons of the GC samplng valve durng operaton for (a) flushng and (b) samplng...85 Schematc of the (a) total condenser and (b) the degassng unt assembly..87 Schematc of the compresson devce...89 Chapter 5 Fgure 5-: Schematc of the set-up for chargng the compresson devce Fgure 5-2: Schematc of the set-up for chargng the equlbrum cell wth degassed lqud from the bolng flask.. 08 Fgure 5-3: Schematc of the set-up for chargng the second component nto the equlbrum cell..0 Chapter 6 Fgure 6-: Vapour pressure plots for the ethers used n ths study, 2-methoxy-2-methylbutane and 2-methoxy-2-methylpropane, compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature.24 xv

17 LIST OF FIGURES Fgure 6-2: Vapour pressure plots for the alcohols used n ths study, ethanol and methanol, compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature.25 Fgure 6-3: Vapour pressure plots for the ketone (butan-2-one) and ester (ethyl acetate) used n ths study compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature...25 Fgure 6-4: Vapour pressure plots for the alkanes used n ths study, heptane and hexane, compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature.26 Fgure 6-5: Vapour pressure plots for the alkene (2-methylpent-2-ene) and ntrle (acetontrle) used n ths study compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature.26 Fgure 6-6: The x-y plot for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K, error bars show 2% error for and..28 Fgure 6-7: The P-x- y plot for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K, error bars show % error for pressure and 2% error for and 28 Fgure 6-8: The T-- plot for the hexane () + acetontrle (2) system at 350 kpa, error bars show 0.3% error for temperature and 2% error for and..29 Fgure 6-9: The T-- plot for the methanol () + heptane (2) system at 350 kpa, error bars show 0.3% error for temperature and 2% error for and..30 Fgure 6-0: The x-y plot for the methanol () + butan-2-one (2) system, error bars show 2% error for and Fgure 6-: The P-x-y plot for the methanol () + butan-2-one (2) system, error bars show % error for pressure and 2% error for and.33 Fgure 6-2: The x-y plot for the ethanol () + butan-2-one (2) system, error bars show 2% error for and 34 Fgure 6-3: The P-x-y plot for the ethanol () + butan-2-one (2) system, error bars show % error for pressure and 2% error for and.35 Fgure 6-4: The x-y plot for the ethanol () + 2-methoxy-2-methylbutane (2) system, error bars show 2% error for and 36 Fgure 6-5: The P-x-y plot for the ethanol () + 2-methoxy-2-methylbutane (2) system, error bars show % error for pressure and 2% error for and..37 Fgure 6-6: The x-y plot for the 2-methylpent-2-ene () + ethanol (2) system at K, error bars show 2% error for and 38 xv

18 LIST OF FIGURES Fgure 6-7: The P-x-y plot for the 2-methylpent-2-ene () + ethanol (2) system at K, error bars show % error for pressure and 2% error for and.39 Fgure 6-8: The --y plot for the hexane () + acetontrle (2) system at K, error bars show 2% error for, and 40 Fgure 6-9: The P---y plot for the hexane () + acetontrle (2) system at K, error bars show % error for pressure and 2% error for, and..4 Chapter 7 Fgure 7-: Fgure 7-2: Fgure 7-3: Fgure 7-4: Fgure 7-5: Fgure 7-6: Fgure 7-7: Fgure 7-8: Vapour pressure devaton plots for the comparson of expermental data wth Aspen Plus (2004) for 2-methoxy-2-methylbutane and expermental data wth Red et al. (988) for 2-methoxy-2-methylpropane 45 Vapour pressure devaton plots for the comparson of expermental data wth Red et al. (988) for ethanol and expermental data wth Aspen Plus (2004) for methanol Vapour pressure devaton plots for the comparson of expermental data wth Red et al. (988) for butan-2-one and expermental data wth Aspen Plus (2004) for ethyl acetate Vapour pressure devaton plots for the comparson of expermental data wth Red et al. (988) for heptane and hexane..47 Vapour pressure devaton plots for the comparson of expermental data wth Aspen Plus (2004) for 2-methylpent-2-ene and expermental data wth Red et al. (988) for acetontrle...47 Vapour pressure plots for the ethers used n ths study, 2-methoxy-2-methylbutane and 2-methoxy-2-methylpropane, wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature...52 Vapour pressure plots for the alcohols used n ths study, ethanol and methanol, wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature...54 Vapour pressure plots for the ketone (butan-2-one) and ester (ethyl acetate) used n ths study wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature.54 xv

19 LIST OF FIGURES Fgure 7-9: Vapour pressure plots for the alkanes used n ths study, heptane and hexane, wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature 55 Fgure 7-0: Vapour pressure plots for the alkene (2-methylpent-2-ene) and ntrle (acetontrle) used n ths study wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature 55 Fgure 7-: Ft of the TS-NRTL model combnaton to the x-y plot of the methoxy-2- methylpropane () + ethyl acetate (2) system at K for the combned method 64 Fgure 7-2: Ft of the TS-NRTL model combnaton to the P-x-y plot of the methoxy-2- methylpropane () + ethyl acetate (2) system at K for the combned method 64 Fgure 7-3: Comparson of the expermental actvty coeffcents and those calculated from the TS-NRTL model combnaton for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K for the combned method..65 Fgure 7-4: Ft of the PR-MC-WS-NRTL model combnaton to the x-y plot of the 2-methoxy- 2-methylpropane () + ethyl acetate (2) system at K for the drect method 66 Fgure 7-5: Ft of the PR-MC-WS-NRTL model combnaton to the P-x-y plot of the 2- methoxy-2-methylpropane () + ethyl acetate (2) system at K for the drect method 66 Fgure 7-6: Best ft model combnaton for the x-y plot of the methanol () + butan-2-one (2) system wth the combned method.69 Fgure 7-7: Best ft model combnaton ( K: TS-TKWILSON; K: TS-NRTL; K: TS-TKWILSON) to the P-x-y plot of the methanol () + butan-2-one (2) system wth the combned method.70 Fgure 7-8: Comparson of the expermental actvty coeffcents and those calculated from the best ft model combnaton for the methanol () + butan-2-one (2) system wth the combned method...70 Fgure 7-9: Best ft model combnaton for the x-y plot of the methanol () + butan-2-one (2) system wth the drect method 7 Fgure 7-20: Best ft model combnaton ( K: PR-MC-WS-NRTL; K: SRK-MC- WS-NRTL; K: PR-MC-WS-NRTL) to the P-x-y plot of the methanol () + butan-2-one (2) system wth the drect method..72 xv

20 LIST OF FIGURES Fgure 7-2: Best ft model combnaton for the x-y plot of the ethanol () + butan-2-one (2) system wth the combned method.74 Fgure 7-22: Best ft model combnaton ( K: TS-UNIQUAC; K: TS-UNIQUAC; K: TS-NRTL) to the P-x-y plot of the ethanol () + butan-2-one (2) system wth the combned method.75 Fgure 7-23: Comparson of the expermental actvty coeffcents and those calculated from the best ft model combnaton for the ethanol () + butan-2-one (2) system wth the combned method...75 Fgure 7-24: Best ft model combnaton for the x-y plot of the ethanol () + butan-2-one (2) system wth the drect method 76 Fgure 7-25: Best ft model combnaton (383.26, and 43.2 K: SRK-MC-WS-NRTL) to the P-x-y plot of the ethanol () + butan-2-one (2) system wth the drect method 77 Fgure 7-26: Best ft model combnaton for the x-y plot of the ethanol () + 2-methoxy-2- methylbutane (2) system wth the combned method.79 Fgure 7-27: Best ft model combnaton ( and 43.9 K: TS-NRTL) to the P-x-y plot of the ethanol () + 2-methoxy-2-methylbutane (2) system wth the combned method 80 Fgure 7-28: Comparson of the expermental actvty coeffcents and those calculated from the best ft model combnaton for the ethanol () + 2-methoxy-2-methylbutane (2) system wth the combned method.80 Fgure 7-29: Best ft model combnaton for the x-y plot of the ethanol () + 2-methoxy-2- methylbutane (2) system wth the drect method...8 Fgure 7-30: Best ft model combnaton ( K: PR-MC-WS-NRTL and 43.2 K: SRK- MC-WS-NRTL) to the P-x-y plot of the ethanol () + 2-methoxy-2-methylbutane (2) system wth the drect method..82 Fgure 7-3: Ft of the TS-NRTL model combnaton to the x-y plot of the 2-methylpent-2-ene () + ethanol (2) system at K for the combned method.84 Fgure 7-32: Ft of the TS-NRTL model combnaton to the P-x-y plot of the 2-methylpent-2-ene () + ethanol (2) system at K for the combned method.84 Fgure 7-33: Comparson of the expermental actvty coeffcents and those calculated from the TS-NRTL model combnaton for the 2-methylpent-2-ene () + ethanol (2) system at K for the combned method 85 xx

21 LIST OF FIGURES Fgure 7-34: Comparson of the vapour pressures of ethanol and 2-methylpent-2-ene showng the Bancroft pont 85 Fgure 7-35: Ft of the PR-MC-WS-NRTL model combnaton to the x-y plot of the 2- methylpent-2-ene () + ethanol (2) system at K for the drect method..87 Fgure 7-36: Ft of the PR-MC-WS-NRTL model combnaton to the P-x-y plot of the 2- methylpent-2-ene () + ethanol (2) system at K for the drect method..87 Fgure 7-37: Temperature dependence of the TK-Wlson model parameters for the hexane () + acetontrle (2) system 89 Fgure 7-38: Temperature dependence of the NRTL model parameters for the hexane () + acetontrle (2) system 90 Fgure 7-39: Temperature dependence of the modfed UNIQUAC model parameters for the hexane () + acetontrle (2) system...90 Fgure 7-40: Temperature dependence of the TK-Wlson model parameters for the methanol () + heptane (2) system...92 Fgure 7-4: Temperature dependence of the NRTL model parameters for the methanol () + heptane (2) system..93 Fgure 7-42: Temperature dependence of the modfed UNIQUAC parameters for the methanol () + heptane (2) system.93 Fgure 7-43: Ft of the TS-TKWILSON model combnaton to the x-y plot of the hexane () + acetontrle (2) system at K for the combned method...96 Fgure 7-44: Ft of the TS-TKWILSON model combnaton to the P-x-y plot of the hexane () + acetontrle (2) system at K for the combned method...96 Fgure 7-45: Comparson of the P-x-y predcton plot usng the parameters regressed from LLE and VLLE data wth the TK-Wlson model for the hexane () + acetontrle (2) system at K.97 Fgure 7-46: Comparson of the molar Gbbs energy of mxng usng the parameters regressed from LLE and VLLE data wth the TK-Wlson model for the hexane () + acetontrle (2) system at K.97 Fgure 7-47: P plot for the TS-NRTL and PR-MC-WS-NRTL model combnatons for the 2- methoxy-2-methylpropane () + ethyl acetate (2) system at K 200 Fgure 7-48: plot for the TS-NRTL and PR-MC-WS-NRTL model combnatons for the 2- methoxy-2-methylpropane () + ethyl acetate (2) system at K..20 Fgure 7-49: ln (γ/γ) plot for the TS-NRTL model combnaton for the 2-methoxy-2- methylpropane () + ethyl acetate (2) system at K.20 xx

22 LIST OF FIGURES Fgure 7-50: P plot for the best ft drect method model combnatons of the methanol () + butan-2-one (2) system at , and K Fgure 7-5: plot for the best ft drect method model combnatons of the methanol () + butan-2-one (2) system at , and K Fgure 7-52: P plot for the best ft combned method model combnatons of the methanol () + butan-2-one (2) system at , and K Fgure 7-53: plot for the best ft combned method model combnatons of the methanol () + butan-2-one (2) system at , and K 204 Fgure 7-54: ln (γ/γ) plot for the combned method best ft model combnatons of the methanol () + butan-2-one (2) system at , and K Fgure 7-55: P plot for the best ft drect method model combnatons of the ethanol () + butan-2-one (2) system at , and 43.2 K Fgure 7-56: plot for the best ft drect method model combnatons of the ethanol () + butan- 2-one (2) system at , and 43.2 K Fgure 7-57: P plot for the best ft combned method model combnatons of the ethanol () + butan-2-one (2) system at , and 43.2 K Fgure 7-58: plot for the best ft combned method model combnatons of the ethanol () + butan-2-one (2) system at , and 43.2 K Fgure 7-59: ln (γ/γ) plot for the combned method best ft model combnatons of the ethanol () + butan-2-one (2) system at , and 43.2 K Fgure 7-60: P plot for the best ft drect method model combnatons of the ethanol () + 2- methoxy-2-methylbutane (2) system at and 43.9 K...20 Fgure 7-6: plot for the best ft drect method model combnatons of the ethanol () + 2- methoxy-2-methylbutane (2) system at and 43.9 K...2 Fgure 7-62: P plot for the best ft combned method model combnatons of the ethanol () + 2-methoxy-2-methylbutane (2) system at and 43.9 K 2 Fgure 7-63: plot for the best ft combned method model combnatons of the ethanol () + 2- methoxy-2-methylbutane (2) system at and 43.9 K 22 Fgure 7-64: ln (γ/γ) plot for the combned method best ft model combnatons of the ethanol () + 2-methoxy-2-methylbutane (2) system at and 43.9 K...23 Fgure 7-65: P plot for the TS-NRTL and PR-MC-WS-NRTL model combnatons for the 2- methylpent-2-ene () + ethanol (2) system at K.24 Fgure 7-66: plot for the TS-NRTL and PR-MC-WS-NRTL model combnatons for the 2- methylpent-2-ene () + ethanol (2) system at K.24 xx

23 LIST OF FIGURES Fgure 7-67: ln (γ/γ) plot for the TS-NRTL model combnaton for the 2-methylpent-2-ene () + ethanol (2) system at K..25 Appendx C Fgure C-: Fgure C-2: Fgure C-3: Fgure C-4: Fgure C-5: Fgure C-6: Fgure C-7: Fgure C-8: Fgure C-9: Fgure C-0: Fgure C-: Fgure C-2: Fgure C-3: Fgure C-4: Temperature calbraton plot for the probe of the upper 36 SS flange of the equlbrum cell (low temperature range) Temperature devaton plot for the probe of the upper 36 SS flange of the equlbrum cell (low temperature range) Temperature calbraton plot for the probe of the upper 36 SS flange of the equlbrum cell (hgh temperature range) Temperature devaton plot for the probe of the upper 36 SS flange of the equlbrum cell (hgh temperature range) Temperature calbraton plot for the probe of the lower 36 SS flange of the equlbrum cell (low temperature range) Temperature devaton plot for the probe of the lower 36 SS flange of the equlbrum cell (low temperature range) Temperature calbraton plot for the probe of the lower 36 SS flange of the equlbrum cell (hgh temperature range) Temperature devaton plot for the probe of the lower 36 SS flange of the equlbrum cell (hgh temperature range) Temperature calbraton plot for the probe of the upper 36 SS flange of the equlbrum cell used to control the heater cartrdge.. 25 Temperature devaton plot for the probe of the upper 36 SS flange of the equlbrum cell used to control the heater cartrdge.. 25 Temperature calbraton plot for the sensor on the low pressure transmtter alumnum block Temperature devaton plot for the sensor on the low pressure transmtter alumnum block Temperature calbraton plot for the sensor on the hgh pressure transmtter alumnum block Temperature devaton plot for the sensor on the hgh pressure transmtter alumnum block xx

24 LIST OF FIGURES Fgure C-5: Temperature calbraton plot for the sensor n the expanson chamber Fgure C-6: Temperature devaton plot for the sensor n the expanson chamber Fgure C-7: Temperature calbraton plot for the sensor n the lnes between the and the 6-port GC valve Fgure C-8: Temperature devaton plot for the sensor n the lnes between the and the 6-port GC valve Fgure C-9: Temperature calbraton plot for the sensor n the lnes between the 6-port GC valve and the GC. 256 Fgure C-20: Temperature devaton plot for the sensor n the lnes between the 6-port GC valve and the GC Fgure C-2: Temperature calbraton plot for the sensor n the lnes between the pressure transmtters and the equlbrum cell Fgure C-22: Temperature devaton plot for the sensor n the lnes between the pressure transmtters and the equlbrum cell Fgure C-23: Temperature calbraton plot for the sensor n the alumnum block for the GC valve Fgure C-24: Temperature devaton plot for the sensor n the alumnum block for the GC valve Fgure C-25: Pressure calbraton plot for the low pressure transmtter Fgure C-26: Pressure devaton plot for the low pressure transmtter 260 Fgure C-27: Pressure calbraton plot for the moderate pressure transmtter. 260 Fgure C-28: Pressure devaton plot for the moderate pressure transmtter Fgure C-29: GC calbraton graph for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system (2-methoxy-2-methylpropane dlute regon) Fgure C-30: GC calbraton graph for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system (ethyl acetate dlute regon) 265 Fgure C-3: Composton devaton plot for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system Fgure C-32: GC calbraton graph for the methanol () + butan-2-one (2) system (methanol dlute regon) Fgure C-33: GC calbraton graph for the methanol () + butan-2-one (2) system (butan-2-one dlute regon) xx

25 LIST OF FIGURES Fgure C-34: Composton devaton plot for the methanol () + butan-2-one (2) system. 267 Fgure C-35: GC calbraton graph for the ethanol () + butan-2-one (2) system (ethanol dlute regon).268 Fgure C-36: GC calbraton graph for the ethanol () + butan-2-one (2) system (butan-2-one dlute regon) Fgure C-37: Composton devaton plot for the ethanol () + butan-2-one (2) system. 269 Fgure C-38: GC calbraton graph for the ethanol () + 2-methoxy-2-methylbutane (2) system (ethanol dlute regon) 269 Fgure C-39: GC calbraton graph for the ethanol () + 2-methoxy-2-methylbutane (2) system (2-methoxy-2-methylbutane dlute regon) 270 Fgure C-40: Composton devaton plot for the ethanol () + 2-methoxy-2-methylbutane (2) system. 270 Fgure C-4: GC calbraton graph for the 2-methylpent-2-ene () + ethanol (2) system (2- methylpent-2-ene dlute regon). 27 Fgure C-42: GC calbraton graph for the 2-methylpent-2-ene () + ethanol (2) system (ethanol dlute regon).. 27 Fgure C-43: Composton devaton plot for the 2-methylpent-2-ene () + ethanol (2) system. 272 Fgure C-44: GC calbraton graph for the hexane () + acetontrle (2) system (hexane calbraton, second order polynomal ft) Fgure C-45: GC calbraton graph for the hexane () + acetontrle (2) system (acetontrle calbraton, second order polynomal ft) Fgure C-46: Composton devaton plot for the hexane () + acetontrle (2) system Fgure C-47: GC calbraton graph for the methanol () + heptane (2) system (methanol calbraton, second order polynomal ft) Fgure C-48: GC calbraton graph for the methanol () + heptane (2) system (heptane calbraton, second order polynomal ft) Fgure C-49: Composton devaton plot for the methanol () + heptane (2) system. 275 Appendx D Fgure D-: User-nterface of the software for the 34970A Aglent data acquston unt 276 Fgure D-2: User-nterface of the software for the 34970A Aglent data acquston unt, showng the scan control optons xxv

26 LIST OF FIGURES Fgure D-3: User-nterface of the GC Solutons software used for the equlbrum phase composton analyss Fgure D-4: User-nterface for the ntegraton of the peak areas Appendx E Fgure E-: Flow dagram for the entre apparatus set-up. 278 xxv

27 LIST OF PHOTOGRAPHS LIST OF PHOTOGRAPHS Chapter 4 Photograph 4-: (a) The sapphre equlbrum cell and (b) the cell housed wthn two 36 stanless steel flanges...75 Photograph 4-2: The O-rngs n the upper 36 stanless steel flange that seal the equlbrum cell...76 Photograph 4-3: The ron framework for the ol bath and fxed poston of the equlbrum cell wth the mechancal jack used to (a) lower the ol bath and (b) to rase the ol bath...8 Photograph 4-4: The compresson devce (a) cover-ld and (b) pston assembly..89 Photograph 4-5: Expermental set-up n the laboratory.9 xxv

28 LIST OF TABLES LIST OF TABLES Chapter 3 Table 3-: Table 3-2: Advantages and dsadvantages of cubc equatons of state (Valderrama, 2003).56 Consstency ndex for the drect test of Van Ness (995) wth the root mean square values (RMSD).70 Chapter 6 Table 6-: Chemcal purtes and refractve ndces for all reagents used n ths study..20 Table 6-2: Expermental uncertantes for temperature and pressure measurements..2 Table 6-3: Expermental uncertantes for mole fracton compostons of VLE systems 2 Table 6-4: Expermental vapour pressure data 23 Table 6-5: Expermental vapour-lqud equlbrum data for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K..27 Table 6-6: Expermental lqud-lqud equlbrum data for the hexane () + acetontrle (2) system at 350 kpa...29 Table 6-7: Expermental lqud-lqud equlbrum data for the methanol () + heptane (2) system at 350 kpa...3 Table 6-8: Expermental vapour-lqud equlbrum data for the methanol () + butan-2-one (2) system.32 Table 6-9: Expermental vapour-lqud equlbrum data for the ethanol () + butan-2-one (2) system.34 Table 6-0: Expermental vapour-lqud equlbrum data for the ethanol () + 2-methoxy-2- methylbutane (2) system.36 Table 6-: Expermental vapour-lqud equlbrum data for 2-methylpent-2-ene () + ethanol (2) at K 38 Table 6-2: Expermental vapour-lqud-lqud equlbrum data for hexane () + acetontrle (2) at K.40 Chapter 7 Table 7-: Average absolute devatons (AAD) for the vapour pressures...48 xxv

29 LIST OF TABLES Table 7-2: Regressed pure component parameters for the extended Antone equaton...5 Table 7-3: Regressed pure component parameters for the Wagner equaton..5 Table 7-4: Regressed pure component parameters for the α functon of Mathas and Copeman (983) wth the SRK EoS...53 Table 7-5: Regressed pure component parameters for the α functon of Mathas and Copeman (983) wth the PR EoS..53 Table 7-6: Expermental lqud-phase actvty coeffcents for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K..57 Table 7-7: Expermental lqud-phase actvty coeffcents for the methanol () + butan-2-one (2) system...57 Table 7-8: Expermental lqud-phase actvty coeffcents for the ethanol () + butan-2-one (2) system.58 Table 7-9: Expermental lqud-phase actvty coeffcents for the ethanol () + 2-methoxy-2- methylbutane (2) system.58 Table 7-0: Expermental lqud-phase actvty coeffcents for the 2-methylpent-2-ene () + ethanol (2) system at K...59 Table 7-: Expermental lqud-phase actvty coeffcents for the hexane () + acetontrle (2) system at K.59 Table 7-2: The regresson combnatons used for the combned method 60 Table 7-3: The regresson combnatons used for the drect method...6 Table 7-4: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the 2-methoxy-2- methylpropane () + ethyl acetate (2) system at K..63 Table 7-5: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method of the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K..65 Table 7-6: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the methanol () + butan-2-one (2) system..68 Table 7-7: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method appled to the methanol () + butan- 2-one (2) system.7 xxv

30 LIST OF TABLES Table 7-8: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the ethanol () + butan-2-one (2) system..73 Table 7-9: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method of the ethanol () + butan-2-one (2) system.76 Table 7-20: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the ethanol () + 2- methoxy-2-methylbutane (2) system..78 Table 7-2: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method of the ethanol () + 2-methoxy-2- methylbutane (2) system.8 Table 7-22: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the 2-methylpent-2- ene () + ethanol (2) system at K.83 Table 7-23: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method of the 2-methylpent-2-ene () + ethanol (2) system at K...86 Table 7-24: Model parameters from mutual solublty data for the hexane () + acetontrle (2) system.89 Table 7-25: Ftted equatons for the actvty coeffcent models used n the LLE data reducton for the hexane () + acetontrle (2) system 9 Table 7-26: Model parameters from mutual solublty data for the methanol () + heptane (2) system.92 Table 7-27: Ftted equatons for the actvty coeffcent models used n the LLE data reducton for the methanol () + heptane (2) system..94 Table 7-28: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the hexane () + acetontrle (2) system at K 95 Table 7-29: Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K.200 xxx

31 LIST OF TABLES Table 7-30: Table 7-3: Table 7-32: Table 7-33: Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the methanol () + butan-2-one (2) system at , and K.205 Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the ethanol () + butan-2-one (2) system at , and 43.2 K.209 Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the ethanol () + 2-methoxy-2-methylbutane (2) system at and 43.9 K.22 Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the 2-methylpent-2-ene () + ethanol (2) system at K...25 Appendx B Table B-: Physcal propertes of chemcals used n ths study Table B-2: Pure component constants for the modfed UNIQUAC model. 245 Appendx C Table C-: Calbraton results for temperature probes/sensors used n ths study Table C-2: Calbraton results for pressure transmtters used n ths study Table C3: Specfcatons of the gas chromatograph capllary columns used n ths study Table C4: Gas chromatograph (GC) operatng condtons for the systems studed n ths work 262 Table C-5: Gas chromatograph calbraton results for all VLE systems used n ths study Table C-6: Gas chromatograph calbraton results for all LLE and VLLE systems used n ths study xxx

32 NOMENCLATURE NOMENCLATURE Englsh Letters ' A '' A Parameter n the extended Antone vapour pressure equaton Parameter n the Wagner vapour pressure equaton E A Excess Helmholtz free energy at nfnte pressure [J.mol - ] A m Mxture parameter n a cubc equaton of state * A AVD a Peak area for speces obtaned from the gas chromatograph Average absolute devaton of a property Intermolecular attracton force parameter n a cubc equaton of state a j TK-Wlson model energy nteracton parameter of Tsuboka and Katayama (975) a m [J.mol - ] Mxture ntermolecular attracton force parameter n a cubc equaton of state a t Polar contrbuton parameter n correlaton of Tsonopoulos (974) ' B Parameter n the extended Antone vapour pressure equaton '' B Parameter n the Wagner vapour pressure equaton B j Interacton second Vral coeffcent [.mol - ] B m Mxture parameter n a cubc equaton of state B mxture Second Vral coeffcent of a mxture, defned by Equaton (3-27) [.mol - ] B vral Second Vral coeffcent, densty expanson [.mol - ] b b m Molecular sze parameter n a cubc equaton of state Mxture ntermolecular attracton force parameter n a cubc equaton of state b t Polar contrbuton parameter n correlaton of Tsonopoulos (974) ' C Parameter n the extended Antone vapour pressure equaton '' C Parameter n the Wagner vapour pressure equaton c Parameter n the mxng rule of Wong and Sandler (992) D Summaton term n the mxng rule of Wong and Sandler (992) ' D '' D Parameter n the extended Antone vapour pressure equaton Parameter n the Wagner vapour pressure equaton xxx

33 NOMENCLATURE ' E F F f Parameter n the extended Antone vapour pressure equaton Objectve functon n an teraton scheme Response factor of speces from gas chromatograph Fugacty, pure speces [kpa] fˆ Fugacty, speces n soluton [kpa] ( 0) f Term n correlaton of Tsonopoulos (974), defned by Equaton (3-3) ( ) f Term n correlaton of Tsonopoulos (974), defned by Equaton (3-32) ( 2) f Term n correlaton of Tsonopoulos (974), defned by Equaton (3-34) G Molar Gbbs energy [J.mol - ] G j Parameter n the NRTL model of Renon and Prausntz (968) G Partal Gbbs energy, speces G Gbbs energy change of mxng [J.mol - ] g j NRTL model energy nteracton parameter of Renon and Prausntz (968) [J.mol - ] H Molar enthalpy [J.mol - ] H K k j Partal enthalpy, speces n soluton Vapour-lqud equlbrum rato for speces Bnary nteracton parameter l Parameter n the UNIQUAC model of Abrams and Prausntz (975) N n n Number of chemcal speces Number of moles Number of moles, speces n T P Total number of moles n a system Absolute pressure [kpa] sat P Saturaton vapour pressure, speces [kpa] Q Quadratc summaton term n the mxng rule of Wong and Sandler (992) q Area parameter for UNIQUAC model of Abrams and Prausntz (975) ' q Area parameter for modfed UNIQUAC model of Anderson and Prausntz (978) R Unversal gas constant [J.mol -.K - ] RMSD Root mean squared devaton xxx

34 NOMENCLATURE r Volume parameter for UNIQUAC model of Abrams and Prausntz (975) S Molar entropy [J.mol -.K - ] T Absolute temperature [K] u j Energy nteracton parameter of UNIQUAC model of Abrams and Prausntz (975) [J.mol - ] V Molar volume [.mol - ] V Partal molar volume, speces n soluton ' x Term used n the Wagner vapour pressure equaton, defned by Equaton (7-4) x y Z z Mole fracton, speces, lqud phase Mole fracton, speces, vapour phase Compressblty factor Overall mole fracton Greek Letters α Scalng factor functon n a cubc equaton of state α j Non-randomness parameter n the NRTL model of Renon and Prausntz (968) β Parameter n the TK-Wlson model of Tsuboka and Katayama (975) β v Parameter n the TK-Wlson model of Tsuboka and Katayama (975) Φ Rato of fugacty coeffcents, defned by Equaton (3-24) * Φ Volume fracton n the UNIQUAC model of Abrams and Prausntz (975) φ φˆ Γ γ δ Fugacty coeffcent, pure speces Fugacty coeffcent, speces n soluton Integraton constant Actvty coeffcent, speces n soluton Denotes a resdual for a property δ j Parameter that relates second Vral coeffcents, defned by Equaton (3-29) ε, ε A, ε B Tolerances used for objectve functons * * *, ε P, ε T ε Constant terms n the drect test of Van Ness (995) κ Characterstc constant n a cubc equaton of state xxx

35 NOMENCLATURE κ, κ κ Parameters n the scalng factor functon of Mathas and Copeman (983) 2, 3 Λ j Parameter n the TK-Wlson model of Tsuboka and Katayama (975) λ j Parameter n the TK-Wlson model of Tsuboka and Katayama (975) µ Chemcal potental, speces θ Area fracton n the UNIQUAC model of Abrams and Prausntz (975) ' θ Area fracton n the modfed UNIQUAC model of Anderson and Prausntz (978) τ j Parameter n the NRTL model of Renon and Prausntz (968) ω Acentrc factor Subscrpt c Denotes a crtcal property cal Denotes a calculated value from a model exp Denotes an expermental value Denotes speces j Denotes speces j new Denotes the current value of a property n an teraton scheme old Denotes the prevous value of a property n an teraton scheme r Denotes a reduced property Denotes speces 2 Denotes speces 2 Superscrpt E d g l sat v α β Denotes an excess property Denotes value for an deal soluton Denotes value for an deal gas Denotes lqud phase Denotes a saturated value Denotes vapour phase Denotes a phase Denotes a phase xxxv

36 NOMENCLATURE π Number of phases Denotes a value at nfnte dluton Notes Dfference operator xxxv

37 CHAPTER FRENCH SUMMARY Les ndustres chmques ont un beson constant de données d'équlbre de phase (dagrammes de phases) précses (partculèrement pour les nouveaux produts chmques dont la synthèse est coûteuse pour) afn concevor avec succès des procédés de séparaton effcaces et économes facle à mettre en œuvre. Pour détermner ces dagrammes de phases, l est nécessare de dsposer d un apparellage fable assocé à une méthodologe expérmentale ben adaptée. Ben qu l sot facle de trouver dans la lttérature de nombreux types d apparellages destnés à la mesure d'équlbres de phase, seulement peu d'entre eux ont été conçus pour travaller sur de petts volumes de produts chmques (nféreurs à 20 ). Cette étude concerne donc une prse de recul face à l exstant, une réflexon crtque et enfn la concepton et le développement d'un nouvel équpement expérmental de mesure de tenson de vapeur et des équlbres multphasques sur de petts volumes de l ordre de 8. La température de fonctonnement de cet équpement expérmental s'étend de 253 à 473 K et la presson de fonctonnement s'étend du vde à 6000 kpa. En complément de cette étude, de nouvelles données expérmentales d'équlbre de phase ont été obtenues, sur des systèmes bnares comprenant un alcool léger et un composé carbonylé, pour le compte d une compagne pétrochmque Sud-Afrcane.

38 CHAPTER INTRODUCTION CHAPTER ONE INTRODUCTION Phase equlbrum s of specal nterest n chemcal engneerng as ths type of data forms the bass for the desgn of separaton processes such as dstllaton and extracton, whch nvolve phase contactng. In the lght of chemcal companes/ndustres manufacturng new chemcals, there s an mportant need for thermodynamc data, especally phase equlbrum measurements. These new chemcals are extremely costly to synthesze or commercally unavalable. There s a varety of expermental equpment and technques desgned to perform phase equlbrum measurements, but such equpment usually requre a large volume of the chemcal speces to undertake measurements. As a result, new technques and equpment have to be developed to measure phase equlbrum for small volumes (say 20 ) across reasonable temperature and pressure ranges. Ths study covers the desgn of a new apparatus that enables relable vapour pressure and equlbra measurements for multple lqud and vapour phases of small volumes (a maxmum of 8 ). These phase equlbra measurements nclude: vapour-lqud equlbrum (VLE), lqudlqud equlbrum (LLE) and vapour-lqud-lqud equlbrum (VLLE). The operatng temperature of the apparatus ranges from 253 to 473 K and the operatng pressure ranges from absolute vacuum to 6000 kpa. The samplng of the phases are accomplshed usng a Rapd- OnLne-Sampler-Injector ( ) that s capable of wthdrawng as lttle as μl of sample from each phase (Gulbot et al., 2000). The use of a also does not dsturb the equlbrum under study snce approxmately only a μl of sample s wthdrawn. As an added advantage, a short equlbrum tme s generally assocated wth a small volume apparatus. Ths enables rapd measurement of multple phase equlbra. As part of ths study, vapour pressure and phase equlbrum data were measured to test the operaton of the newly developed apparatus that nclude the followng systems: VLE for 2-methoxy-2-methylpropane + ethyl acetate at K LLE for methanol + heptane at 350 kpa 2

39 CHAPTER INTRODUCTION LLE for hexane + acetontrle at 350 kpa VLLE for hexane + acetontrle at K New expermental vapour pressure and VLE data were also measured for systems of nterest to petrochemcal companes. These measurements nclude: VLE for methanol + butan-2-one at , and K VLE for ethanol + butan-2-one at , and 43.2 K VLE for ethanol + 2-methoxy-2-methylbutane at and 43.9 K VLE for ethanol + 2-methylpent-2-ene at K These measurements were undertaken to understand the thermodynamc nteractons of lght alcohols and carbonyls as part of a number of dstllaton systems n synthetc fuel processes whch are currently not well descrbed. Two of these above mentoned systems nclude expensve chemcals: 2-methoxy-2-methylbutane and 2-methylpent-2-ene. A quotaton obtaned from Captal Lab Supplers CC on 22 Aprl 200 showed a cost of R5 50 for 500 ml of 2- methoxy-2-methylbutane wth purty greater than 97% and R2 605 for 50 ml of 2-methylpent- 2-ene wth a mnmum purty of 98%. Overall, ths study focuses on: the desgn and development of a new phase equlbra apparatus for small volumes (a maxmum of 8 ), measurement of new vapour pressure and phase equlbra data and thermodynamc modelng of the measured data. Novel features of ths apparatus ncludes: a small equlbrum cell volume (8 ) and a new technque that uses a sngle movable for the samplng of equlbrum phases. 3

40 CHAPTER 2 FRENCH SUMMARY La mesure d'équlbre de phase concerne classquement la mesure de la température, de la presson et des compostons des phases en présence. La lttérature fournt les nformatons nécessares pour une grande sére d équpements ans que sur les technques dsponbles afn de permettre des mesures d'équlbres de phase. La méthode statque est l'une des méthodes les plus utlsées à ce jour pour les équlbres «lqude-vapeur» (ELV) à moyennes et hautes pressons. Elle a donc tout naturellement été au cœur de nos préoccupatons pour notre concepton et son développement. Notre revue bblographque, objet du chaptre 2 est focalsée sur : le matérel de constructon de la cellule d'équlbre; les méthodes de régulaton de température pour un équlbre de température unforme autour de la cellule d'équlbre; le dégazage des composés avant leur ntroducton dans la cellule d équlbre; les méthodes d'agtaton effcaces à l ntéreur des cellules d'équlbre; les méthodes d'échantllonnage des phases lqudes et des phases vapeurs et les méthodes de vaporsaton et d'homogénésaton des échantllons. Les cellules d'équlbre sont habtuellement construtes en acer noxydable, verre boroslcaté ou saphr dépendant des condtons opératores (nveau de presson, corrosons possbles etc ). Le saphr est ben connu pour ses proprétés optques, ses résstances mécanque et chmque. L'acer noxydable (type 36) est habtuellement chos comme matérau de constructon prncpal pour dverses pèces d'équpement expérmental en rason de ses proprétés mécanques (résstance en partculer), la faclté à le souder et à l usner. Des thermostats à ar, (Legret et al., 98, Galca- Luna et al., 2000, etc ), ou à azote (Rogers et Prausntz, 970), ou des thermostats à eau (Katayama et al., 975, Wu et al., 200, etc ) ou encore à hule (Legret et al., 980, Park et al., 2007, etc ) sont généralement utlsés comme envronnement thermque pour la cellule d'équlbre selon la température ambante requse et les condtons d utlsaton (le nettoyage fréquent de pèces plongées dans un ban d hule peut s avérer une contrante dffcle à accepter.). Le chauffage électrque est un autre autres moyen de réalser l'équlbre thermque (Besserer et Robnson, 97 ; Konrad et al., 983 et Corazza et al., 2003). L'équlbre est réalsé dans un temps rédut dans la mesure où le contenu de la cellule d'équlbre est convenablement agté. Parm les méthodes d'agtaton on trouve : l utlsaton d'un barreau magnétque en rotaton dans un champ magnétque extéreur (Legret et a.., 98) ; le bullage de la vapeur au travers du lqude (Outcalt et Lee, 2004), l utlsaton d'un pston commandé par un champ électromagnétque (Gómez-Neto et Thodos, 978), l oscllaton de la cellule d'équlbre autour d un axe horzontal (Huang et autres, 985) et même l utlsaton des ultrasons (Takag et al., 2003). Les technques employées pour prélever les phases à l'équlbre ncluent : l'utlsaton d électrovannes pneumatque ou électromagnétque à 4

41 CHAPTER 2 FRENCH SUMMARY acton rapde (Fguère et al., 980) ; une mcrocellule détachable (Legret et autres, 98) ; l'utlsaton d un axe percé transversalement agssant comme un tror (Rogers et Prausntz, 970) ; l'utlsaton de capllares (Wagner et Wchterle, 987 et Matos et al., 989) ; une vanne 6 voes pour chromatographe en phase gazeuse (Ramjugernath, 2000) et l échantllonneur breveté : Rapd- On-Lne-Sample-Injector ( ) (Gulbot et al., 2000). On trouve dans la lttérature beaucoup de procédures pour dégazer les lqudes, tels que le chauffage avec reflux de lqude et retrat pérodque de phase vapeur, congélaton et décongélaton sous vde poussé, et auss sublmaton et dstllaton sous vde. Parm toutes ces méthodes, Van Ness et Abbott (978) préfèrent la dstllaton sous vde qu ls jugent comme mons pénble et plus rapde. 5

42 CHAPTER 2 LITERATURE REVIEW 2 CHAPTER TWO LITERATURE REVIEW The measurement of phase equlbra nvolves the measurements of temperature, pressure and phase compostons. Accordng to Walas (985), care must be taken to ensure that the temperature and pressure are measured at the pont where equlbrum really exsts and that the wthdrawal of samples for analyss does not dsturb the equlbrum apprecably. It s however practcally dffcult to obtan expermental data of hgh accuracy. Lterature ndcates a varety of phase equlbrum equpment developments made n order to acheve relable and apprecably accurate measurements. These nclude revews by Hála et al. (967), Malanowsk (982), Abbott (986), Schneder (998), Chrstov and Dohrn (2002) and Dohrn et al. (200) to name a few. Accordng to Hála et al. (967), low pressure vapour-lqud equlbrum (VLE) can be classfed nto the followng categores:. Dstllaton Methods 2. Dynamc Methods 3. Statc Methods 4. Flow Methods 5. Dew and Bubble Pont Methods The purpose of ths chapter s not to present an exhaustve revew of all expermental technques for phase equlbra, rather t wll focus on the statc method for low to moderately hgh pressure VLE, whch s one of the most commonly used methods today. For an excellent revew of the other methods n phase equlbra measurement, the reader s referred to Robnson and Gllland (950), Hála et al. (967), Raal and Mühlbauer (998), Chrstov and Dohrn (2002) and Dohrn et al. (200). 6

43 CHAPTER 2 LITERATURE REVIEW 2. The Statc Method Accordng to Kolbe and Gmehlng (985), the measurement of VLE usng statc methods have become ncreasngly mportant n recent years, where an mportant step n ths drecton was made by Gbbs and Van Ness (972). The major advantage of the statc method s ts smplcty. A lqud mxture s charged nto an evacuated equlbrum cell mmersed n a constant temperature bath and one wats as long as needed untl equlbrum s reached. Usually, an nternal strrng mechansm s added to the equlbrum cell to promote the establshment of equlbrum n a shorter tme. The statc method can be subdvded nto analytcal methods or the synthetc method. In analytcal methods, one or both the lqud and vapour compostons are sampled and analyzed, whle n the synthetc method no samplng of the phases s requred. Ths study was concerned wth the development of a statc analytcal apparatus and wll therefore focus on ths method. Fgure 2- shows a schematc llustraton of the statc analytcal method. The statc synthetc method, on the other hand, has been studed by many researchers whch nclude Gbbs and Van Ness (972), Am (978), Maher and Smth (979), Kolbe and Gmehlng (985), Rarey and Gmehlng (993), Fscher and Gmehlng (994), Takag et al. (2003), Francesch et al. (2004), Outcalt and Lee (2004) and Dohrn et al. (2007) to name a few. The reader s thus referred to the publcatons mentoned above n regards to the development of a statc synthetc apparatus. For mxtures wth more than two components, the nformaton that can be obtaned usng the statc synthetc method s very lmted. Furthermore, thermodynamc consstency testng of the data cannot be carred out when the statc synthetc method s used (Raal and Mühlbauer, 998). Hence, the expermental apparatus for the statc analytcal method has been studed by many other researchers whch nclude: Rgas et al. (958), Kalra et al. (978), Ng and Robnson (978), Fguere et al. (980), Gullevc et al. (983), Zmmerman and Keller (989), Mühlbauer and Raal (99), Laursen et al. (2002), Secuanu et al. (2003) and Garmrood et al. (2004) to name a few. The man dfferences n these studes were the: materal of constructon for the equlbrum cell, methods of creatng a unform equlbrum cell temperature, methods of agtatng the equlbrum cell contents, methods of samplng the lqud and vapour phases, methods of vapoursng and homogenzng the samples, method of n-stu analyss of the lqud and vapour phases, 7

44 CHAPTER 2 LITERATURE REVIEW and the degassng of components pror to measurements. Fgure 2-: Schematc llustraton of the statc analytcal method (Raal and Mühlbauer, 998). The above mentoned ponts can be classfed nto three man features; cell desgn, samplng technques and degassng of components. These features wll now be dscussed n detal as they form the core for the development of the new expermental apparatus for ths study. 2.2 Cell Desgn Lterature descrbes a varety of equpment, where each s desgned for a specfc applcaton as the desgn of a unversal phase equlbrum apparatus for all temperatures, pressures and chemcal nature s an mpossble task. Over the years, there has been good progress made on broadenng exstng notons for equpment development wth new deas formed for new applcatons/purposes. The desgns depend on expermental condtons, e.g. temperature and pressure, and on the physcal propertes of the components studed, whch nclude corrosveness, densty, vscosty, toxcty, etc. It s rather dffcult and even unproftable to propose an apparatus that could be used ndscrmnately. Instead, the desgn of a new apparatus should be as smple as possble wthout compromsng a sgnfcant loss for the qualty of the data to be measured. 8

45 CHAPTER 2 LITERATURE REVIEW 2.2. Materal of Constructon Over the number of years, researchers have used varous materals to construct the equlbrum cell, whch s the heart of the apparatus. Some of the most commonly used materals nclude; stanless steel (Fguere et al., 980), chromum-nckel-molybdenum steel (Reff et al., 987), duran glass (Holldorff and Knapp, 988), manganese steel (Ashcroft et al., 983), brass (Zabaloy et al., 994) and sapphre (Ng et al., 985). The choce of materal depends on several factors, most of whch are already mentoned above. Apart from these factors, vsual observaton of the cell n operaton s also consdered mportant. Ths mportance s evdent where the phase separaton needs to be vewed pror to samplng especally f a sngle movable samplng devce s employed. Strength and chemcal resstance propertes of the materal must also be consdered. Sapphre s well-known as a strong and tough optcal materal that also offers excellent chemcal resstance (General Ruby and Sapphre Company). In addton to the materal of constructon propertes for the equlbrum cell, the strength and chemcal resstance propertes for the materal of constructon of the varous equpment parts also used to desgn the phase equlbra apparatus must be carefully consdered. Stanless steel (SS) s known to succumb to pttng and crevce corroson n warm chlorde envronments, however, the addton of 2% molybdenum to 304 SS to produce 36 SS offers a sgnfcant ncrease n resstance to pttng (Fontana and Greene, 967). Another remarkable property of 36 SS s ts mechancal strength (such as hgh tensle and yeld strength) and the ablty to retan these propertes for long perods of tme under extreme hgh or low temperatures (Snnott, 2005). The 36 SS materal also has very good weldng and machnng propertes makng t sutable to use n the constructon of varous equpment parts. Hence, 36 SS s usually chosen as the prncpal materal of constructon for the varous parts n the desgn of a phase equlbra apparatus Thermal Envronment For sothermal measurements, t s essental to ensure that the equlbrum cell s housed n a temperature controlled envronment. To acheve ths, researchers used dfferent types of temperature controlled envronments; ar bath (Legret et al., 98 and Galca-Luna et al., 2000), ntrogen bath (Rogers and Prausntz, 970), water bath (Katayama et al., 975 and Wu et al., 200) and ol bath (Legret et al., 980 and Park et al., 2007). These baths are usually lned wth varous materals. These nclude; alumnum (Ng and Robnson, 978), copper (Konrad et al., 983) or jackets. Researchers also use a varaton of the above mentoned thermostats e.g. a 9

46 CHAPTER 2 LITERATURE REVIEW two-stage water bath thermostat was used by Am (978), were an nternal thermostat served as a thermal capacty to smooth temperature fluctuatons. Ng and Robnson (978) used an entrely dfferent approach by makng use of a 25 mm thck alumnum shroud contanng eght vertcally mounted and unformly spaced pencl-type 250 W electrcal heaters, to mantan the equlbrum cell temperature. Other researchers that used electrcal heatng nclude Besserer and Robnson (97), Konrad et al. (983) and Corazza et al. (2003) were n each case thermostattng jackets were electrcally heated to mantan the equlbrum temperature. Besserer and Robnson (97) were able to control the equlbrum temperature to wthn 0.5 K of the set-pont by makng use of a thermocouple proportonal-band temperature controller. Ths temperature controller controlled the heaters n the alumnum shroud whch was placed over the ends of the equlbrum cell. Konrad et al. (983) was able to reduce the axal temperature gradents to smaller than 0.2 K by makng use of addtonal head and bottom heaters whlst Corazza et al. (2003) report a temperature accuracy of 0. K. On the other hand, Outcalt and Lee (2004) made use of flud crculaton n conjuncton wth computer-controlled electrc heatng to control the temperature of the system, where the equlbrum cell was housed wthn an alumnum block (see Fgure 2-2). The flud crculaton provded a rough temperature control were flow channels were bored through the sdes of the alumnum block and sx thn-flm heaters were used for the fne temperature control. The outsde of the alumnum block was also covered wth nsulaton. Fgure 2-2: Schematc of the expermental apparatus of Outcalt and Lee (2004). 0

47 CHAPTER 2 LITERATURE REVIEW The presence of temperature gradents can lead to consderable error on sample representatvty. Nadoo (2004) notes some ponts wth regards to temperature gradents: The measurement of temperature at dfferent ponts wthn the bath and n the walls of the equlbrum cell allows one to detect temperature gradents. The occurrence of local hot or cold spots should be avoded. These local hot or cold spots can occur when energy s exchanged drectly from a heater or cooler to the equlbrum cell. The use of strrers n lqud baths and deflecton shelds n ar or ntrogen baths can help n the preventon of these local spots. Conductve paths to and from the equlbrum cell, such as fttngs, attachments or samplng devces must be avoded. Ths problem can be overcome by placng the fttngs and attachments wthn the temperature regulated bath n addton to the equlbrum cell. Insulaton should be used n-between the nner and outer lnng of baths to mnmze heat exchange wth the surroundng envronment. Fbrefrax Duraback and polyurethane foam are typcally used for ths purpose. A large thermal capacty asssts to smooth temperature fluctuatons Agtaton of Cell Contents An nternal strrng mechansm s usually added to the equlbrum cell to promote the establshment of equlbrum n a shorter tme. Lterature reports varous methods avalable for the agtaton of the equlbrum cell contents. The most common method employed makes use of nternal magnetc strrers. Kalra and Robnson (975) made use of a Teflon-coated magnetc strrer n the equlbrum cell that was drven by a magnetc ple externally mounted to the equlbrum cell. The magnetc ple was made-up of three magnets encased n an alumnum housng and mounted on a varable speed DC motor. Kalra and Robnson (975) reported that equlbrum between the phases was acheved n hours whch was dependant on the condtons and the mxture beng studed. Ng and Robnson (978), Nakayama et al. (987) and Galca-Luna et al. (2000) also used smlar agtaton methods. Fguere et al. (980), Legret et al. (98), Gullevc et al. (983) and Konrad et al. (983) also made use of an nternal strrer to ad the mxng of phases. However n ths case the magnetc strrers were rotated n an orentable magnetc feld that was nduced by cols located outsde the equlbrum cell. Legret et al. (98) reported a pressure equlbraton tme of 0 mnutes. On the other hand, Secuanu et al. (2003) made use of a varable speed strrer wth mpellers mounted nto the equlbrum cell.

48 CHAPTER 2 LITERATURE REVIEW Fgure 2-3: Equlbrum cell and agtator of Bae et al. (98). A: charge valve; B: agtator; C: lqud wthdrawal poston; D: fttng to pressure measurement system; E: glass wndow; F: Teflon packng. Interestngly, Bae et al. (98) made use of a unque magnetcally drven nternally vaned mpeller mounted on a hollow shaft to acheve mxng of the equlbrum cell phases. Vapour entered the small holes on the upper part of the shaft then descended down the hollow shaft and fnally dspersed nto the underlyng lqud phase (see Fgure 2-3). On the other hand, Huang et al. (985) made use of another unconventonal technque to mx the cell contents by external oscllatng movement of the equlbrum cell assembly (see Fgure 2-4). Other researchers such as Gómez-Neto and Thodos (978) made use of a pston devce to assst n the mxng of the phases. A magnetc agtator was actuated by an electromagnetc feld whch was generated externally near the top of the equlbrum cell. The magnetc agtator conssted of a thn hollow ron cylnder that was forced to rse nto the vapour phase and then fall nto the lqud phase once every 30 s controlled by the magnetc feld. Measurements frst requred at least 8 hours to reach thermal equlbrum wth an ar-bath and once agtaton was acheved, the system was then allowed up to 2 hours to ensure that the system pressure acheved equlbrum. Ashcroft et al. (983) acheved agtaton by mechancally rockng the equlbrum cell for approxmately 3 hours. Ther desgn conssted of swvel jonts for ol and mercury lnes leadng to the equlbrum cell to enable contnuous rotaton (see Fgure 2-5). 2

49 CHAPTER 2 LITERATURE REVIEW Fgure 2-4: Schematc llustraton of the equlbrum cell and auxllary equpment of Huang et al. (985). Outcalt and Lee (2004) made use of a vapour crculaton pump to bubble the vapour through the lqud phase n order to acheve mxng (see Fgure 2-2). The pston of the pump was a magnet that was controlled by pulsng power to a solenod that was wound around the outsde of the pump shaft. Takag et al. (2003) used an acoustc nterferometer that acheves mxng by means of ultrasonc speed for bubble pont pressure measurements (see Fgure 2-6). A sng-around technque operated at 2 MHz was employed to create the ultrasonc speed. Conclusvely, whatever the method used, t s mportant to acheve homogenety nsde the cell. 3

50 CHAPTER 2 LITERATURE REVIEW Fgure 2-5: Equlbrum cell of Ashcroft et al. (983). A: cell body; B: end caps; C: pston; D: wndow assembles; E: glass capllary; F: toughened glass wndows; G: pston ndcatng rod; H: samplng valve. Fgure 2-6: Schematc of the acoustc nterferometer used for bubble pont pressure measurements by Takag et al. (2003). 4

51 CHAPTER 2 LITERATURE REVIEW 2.3 Samplng Technques The lmt of analytcal methods s the technque of analyss tself, whch controls the precson that wll result for the compostons of the equlbrum phases measured. The samplng technque used has a drect nfluence on the qualty of the results obtaned. Some of the varous optons avalable for analyses n relaton to analytc methods nclude: Physochemcal methods of analyss, e.g., spectroscopy (Kaser et al., 992 and da Cruz Francsco et al., 2004), photometry (Andersen et al., 200), absorpton and fluorescence phenomena (Azawa et al., 2004), small angle x-ray scatterng (Sheh, et al., 2004) and refractve ndces. These are some of the methods avalable for n-stu composton analyss (no samplng requred). External analyses, where a samplng devce for both the lqud and vapour phases s requred. The wthdrawn samples may be analysed by gas chromatography, mass spectrometry or by ttraton methods, etc. The dfferences n the varous methods usually results from the manner n whch the samples are taken and how the samples are analysed. It s essental that the samplng procedure does not perturb the equlbrum and that the sample s representatve of the studed coexstng phases. When samples are wthdrawn from an equlbrum cell, a change n the volume of the equlbrum cell s experenced. Ths consequently results n a change of the cell pressure. There are two contrbutng factors assocated wth the volume change by sample wthdrawal:. The sze of the wthdrawn sample, whch s determned by the analytcal devce employed. Generally, the smaller the sze of the sample wthdrawn, the smaller the pressure drop. 2. The nteror cell volume. The bgger the cell volume, the smaller the pressure drop for a constant sample sze. Hence, an excellent samplng devce s one that wthdraws the smallest sample volume possble wth respect to the nteror cell volume. If a moble samplng devce s used, one has to consder the volume dsplaced by the movement of the samplng devce, especally for a small nteror cell volume, as ths would affect the pressure drop. Furthermore, the samplng devce should have the smallest dead volume. Dead volume can cause the thermodynamc condton of the sampled mxture to dffer from the thermodynamc equlbrum condton n the cell. Ths consequently would lead to ncorrect determnaton of phase compostons. To meet these 5

52 CHAPTER 2 LITERATURE REVIEW objectves, and mantan mnmal dsturbances to equlbrum, several procedures n lterature have been proposed. Nadoo (2004) provdes a good summary of these procedures: Researchers such as Klnk et al. (975) and Mühlbauer (990) used a large equlbrum cell to dampen the effects of both the wthdrawn sample volume and the volume changes assocated wth the samplng method employed. However, a large equlbrum cell requres an ncreased consumpton of chemcals. Fguere et al. (980), Danesh and Todd (990) and Lauret et al. (994) made use of fast-actng pneumatc or electromagnetc valves, whch helped mnmze the wthdrawn volume of the sample. In addton, measurements were made more rapdly snce there was no rotaton valve. However, the volumes of the samples taken are not constant, snce frcton s not completely reproducble. Fgure 2-7 shows the equlbrum cell and samplng system of Fguere et al. (980). (a) (b) Fgure 2-7: (a) Equlbrum cell assembly of Fguere et al. (980); (b) carrer gas crculaton through the cell to sweep samples (cross secton -). A: cell cap; B: pressure transducer; C: equlbrum compartment; D: magnetc strrer; E: valve; F: cell body; G: heatng resstance place; H: coolng col space; I: Teflon thermal sheld; J: Vton O-rng; K: sprng washers; L: copper gasket; M: channel; N: thermocouple well; O: valve pusher. 6

53 CHAPTER 2 LITERATURE REVIEW Nasr et al. (98) and Staby and Mollerup (99) made use of a varablevolume equlbrum cell to compensate for pressure changes. Legret et al. (98) made use of a detachable samplng devce or mcrocell (see Fgures 2-8 and 2-9). Ths helped avod changes n pressure by takng the sample very close to the equlbrum cell, wth practcally no dead volume. Fgure 2-8: Equlbrum cell of Legret et al. (98). A: cell body; B: samplng valve wth packng jont; C: thermocouple well; D: pressure transducer; E: magnetc strrer; F: connecton to fllng crcut; G: mcrocell bearer fxng-pn; H: mcrocell set-screw; I: mcrocell; J: valve fxng pn; K: seat of samplng valve stem. Fgure 2-9: Samplng mcrocell of Legret et al. (98). A: stem; B: mcrocell body; C: drvng screw; D,G: jonts; E,F: antfrcton rngs. 7

54 CHAPTER 2 LITERATURE REVIEW Rogers and Prausntz (970) desgned an equlbrum cell wth pstons movng nsde the equlbrum cell (see Fgure 2-0). Ths system s theoretcally good as the sample s taken well nsde the equlbrum phase and s extracted wthout a change of pressure. However, t s practcally dffcult to acheve the necessary tghtness of the pston and hence, the rapd wear of the seals makes ths technque unrelable. Fgure 2-0: Equlbrum cell and samplng system of Rogers and Prausntz (970). Wagner and Wchterle (987) and Matos et al. (989) used capllares to wthdraw small samples. However, accordng to Brunner et al. (994), samplng through capllares can lead to dfferental vapoursaton and scattered result, caused by a pressure drop along the capllary. Ths effect s more pronounced for mxtures of lght and heavy hydrocarbons. Ramjugernath (2000) used a novel samplng technque wth a sx-port gas chromatograph valve. Ths technque avoded volume changes by the analytc devce as the equlbrum sample was contnuously crculated (by mpeller nduced flow) through the port s loops. Snce the sample loop was solated, there was no change n nteror condtons despte the sample wthdrawal. Galca-Luna et al. (2000) made use of a compressed ar-montored sampler njector whch conssted of a movable capllary adjusted by a dfferental screw. Samples less than mg were wthdrawn. The njector contaned an expanson 8

55 CHAPTER 2 LITERATURE REVIEW chamber whch was heated by a heatng resstance n order to rapdly vapourse lqud samples for good chromatographc analyses. Fgure 2-: Samplng confguraton of the sx-port gas chromatograph valve used by Ramjugernath (2000) (Raal and Mühlbauer, 998). Fgure 2-2: Electromagnetc verson of the ( Evoluton IV). A: carrer gas nlet; B: capllary; C: body; D: carrer gas outlet; E: movng part set n moton by the electromagnet; F: electromagnet; G: return sprng; H: power supply coupled wth a tmer; I: soft ron core; J: coolng fns. 9

56 CHAPTER 2 LITERATURE REVIEW Baba-Ahmed et al. (999) and Gulbot et al. (2000) made use of a Rapd-On- Lne-Sample-Injector ( ). The allows for measurements up to 000 bar and 850 K, for corrosve chemcals and samples from μg to a few mg (Rchon, 2003). The sampler used by Galca-Luna et al. (2000) s a pneumatc sampler of the. Of recent an electromagnetc verson of the has been developed ( Evoluton IV). The electromagnetc verson of the s shown n Fgure 2-2. Samplng wth the electromagnetc verson s acheved by promptng the electromagnet whch attracts the movng part and generates a break n the seal between the fxed capllary and the movng part. The sze of the samples wthdrawn, under gven pressure and temperature condtons, s drectly proportonal to the sealbreakng tme. Ths tme can be controlled by means of a tmer coupled wth the electromagnet s power supply. 2.4 Degassng of Components Degassng s the removal of hghly volatle components (or dssolved gases) from a relatvely non-volatle lqud. Accordng to Am (978), degassng s crucal as the presence of resdual gases dssolved n the nvestgated soluton may lead to large errors n pressure determnaton. Hence, degassng cannot be gnored as ts omsson may result n measured pressures that wll not correspond to the expected mxture. Ths s evdent especally at low pressures and low volatle component concentratons, as the dssolved gases may compete wth the more volatle component n the lqud phase. Degassng can be acheved ether n-stu or external to the equlbrum cell. Lterature ndcates many procedures for degassng lquds, such as lqud refluxng wth perodc vapour wthdrawal, alternate freezng and pumpng to hgh vacuum, vacuum sublmaton and vacuum dstllaton. Of all these methods, Van Ness and Abbott (978) found that vacuum dstllaton s least tedous and requres the least amount of tme. Accordng to Van Ness and Abbott (978), when a flask contanng a certan thoroughly degassed lqud s rapdly nverted, a sharp metallc clck s heard. Van Ness and Abbott (978) presume ths results from a sudden collapse of trapped vapour under the lqud head. However, Van Ness and Abbott (978) also menton that a postve result from a clck test s evdently suffcent but not necessary evdence of thorough degassng. Fscher and Gmehlng (994) used the vacuum dstllaton method of Van Ness and Abbott (978) but found that wthout further separaton, less volatle mpurtes are enrched n the degassed lqud n the reboler. Fscher and Gmehlng (994) therefore developed a modfed vacuum dstllaton degassng unt that allowed chemcal reactons to be carred out before degassng and the desred compound to be separated by further dstllaton after degassng. 20

57 CHAPTER 2 LITERATURE REVIEW Fgure 2-3: Schematc of the degassng apparatus of Van Ness and Abbott (978). A: stll pot; B: rectfyng column; C: condenser; D: surge vessel. Fgure 2-4: Purfcaton and degassng apparatus of Fscher and Gmehlng (994). A: heater; B: thermometer; C: bulb; D: Vgreux column; E: reflux condenser; F: Lebg condenser; G: bulb for pure and degassed product; H: vacuum pump; I: vacuum ndcator; J: capllary; K: strrer. 2

58 CHAPTER 3 FRENCH SUMMARY Il y a dfférents types d'équlbres de phases, toutefos les tros les plus courants sont: les équlbres lqude-vapeur (ELV), équlbres lqude-lqude (ELL) et équlbres lqude-vapeur-lqude (ELLV). L'équlbre de phases thermodynamque mplque que la température, la presson, le potentel chmque (fugacté) de chaque consttuant sont dentques dans chaque phase. La fugacté de mélange content un coeffcent qu exprme la non-déalté dans le mélange. Dans le cas des équlbres lqude-vapeur, le coeffcent de fugacté peut être employé pour décrre la non-déalté des phases lqude et vapeur. La fugacté de mélange en phase lqude pourrat également être décrte par un coeffcent d'actvté qu lu auss tent compte de la non- déalté en phase lqude. Les calculs des équlbres de phase font appel à l'utlsaton de modèles thermodynamques. Les deux méthodes les plus utlsées pour la régresson des données d équlbres lqude-vapeur (ELV) sont les méthodes drectes et combnées. La méthode drecte se sert d'une même équaton d'état (EdE), parm bon nombre d équatons cubques, pour calculer les coeffcents de fugacté pour chacune des phases, phase lqude et phase vapeur. De telles équatons ncluent l'ede de Soave- Redlch-Kwong et l'ede de Peng-Robnson. Ces équatons peuvent s applquer à des composés polares et non polares et offrr des résultats satsfasants. La méthode drecte exge l emplo d'une règle de mélange afn de représenter au meux les proprétés de mélange. La règle de mélange la plus utlsée est celle de Wong et Sandler (992). En ce qu concerne la méthode combnée, on fat appel à deux modèles pour une représentaton séparée des phases lqude et vapeur. Une EdE est employée pour représenter la non-déalté en phase vapeur tands qu'un modèle de soluton lqude (utlsaton du coeffcent d'actvté) est employé pour représenter le non-déalté en phase lqude. Souvent dans la méthode combnée on fat appel à l EdE du vrel (avec des corrélatons pour calculer les coeffcents du vrel) pour tenr compte de la non-déalté en phase vapeur. Les modèles de solutons lqudes avec des expressons pour les coeffcents d'actvté de phase ncluent : le modèle de Tsuboka-Katayama-Wlson (TK- Wlson), Le modèle Non-Random Two Lquds (NRTL) et le modèle Unversal Quas- Chemcal (UNIQUAC). Ces modèles sont basés sur la théore de composton locale et offrent des résultats satsfasants pour des travaux de VLE et de LLE régresson de données ELV et ELL de systèmes fortement non-déaux. Quand toutes les températures, pressons et compostons dans chacune des phases ont été détermnées expérmentalement pour un équlbre de phase, ces données peuvent et dovent être examnées pour s assurer de leur cohérence thermodynamque. La méthode du test par «pont» 22

59 CHAPTER 3 FRENCH SUMMARY exge que la dévaton moyenne absolue ne dépasse pas 0.0 pour la fracton molare en phase vapeur et que la dsperson (erreurs sur la fracton molare en phase vapeur (Δy) en foncton de la fracton molare en vapeur ( )) sot centrée sur zéro. Le test appelé «drect» se sert de ľéquaton de Gbbs-Duhem ďune part et des résdus sur les coeffcents ďactvté des composants bnares. Cet essa exge que les résdus des rapports des coeffcents ďactvté soent dspersés de manère équlbrée autour de zéro dans un graphque en foncton de la fracton molare en phase lqud ( ). Ce test fat appel également comme crtère quanttatf de ľndex ďunformté élaboré par Van Ness (995). 23

60 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES 3 CHAPTER THREE THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Thermodynamc data on chemcal compounds and ther mxtures play an mportant role for phase separaton processes n chemcal ndustres as they are needed for effcent desgn and operaton of chemcal processng plants. Phase equlbrum s of specal nterest n chemcal engneerng as ths type of data forms the bass for the desgn and optmzaton of separaton processes such as dstllaton and extracton, whch nvolve phase contactng. The separaton of mxtures by phase contactng operatons s made possble snce the equlbrum compostons of two phases are usually very dfferent from one another (Prausntz et al., 999). In chemcal ndustres, separaton processes generally occur for mult-component systems. Hence n order to desgn and optmze such separaton processes one requres the nformaton of multcomponent phase equlbrum propertes. However, obtanng mult-component phase equlbrum propertes by measurements s generally dffcult and commonly mpractcal. Raal and Mühlbauer (998) menton that mult-component phase equlbrum propertes can be predcted from the measurement of bnary phase equlbrum data, whch nclude vapour-lqud equlbrum (VLE) and lqud-lqud equlbrum (LLE). Ths nvolves the theoretcal treatment of bnary phase equlbrum data to calculate such varables as temperature, pressure and Gbbs excess energy and also to enable extrapolaton and nterpolaton to expermentally dffcult condtons. The use of chemcal thermodynamcs enables one to perform such tasks. Ths chapter attempts to provde a revew of the thermodynamc fundamentals and prncples requred to undertake theoretcal treatment of phase equlbrum data obtaned from measurements. Ths nvolves a dscusson on the evaluaton of the fugacty and actvty coeffcents together wth the analyss, regresson and correlaton of the expermental data. The two most well known methods of VLE data regresson vz. the γ Ф (combned) method and Ф Ф (drect) method are also 24

61 (T) CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES examned along wth the assocated actvty coeffcent models and equatons of state. The chapter fnally dscusses some thermodynamc consstency tests carred out on the expermental VLE data. Walas (985) and Raal and Mühlbauer (998) offer a more detaled dscusson on thermodynamc fundamentals and the reader s referred to such texts for further nformaton. 3. Fugacty and Fugacty Coeffcents Smth et al. (200) state that equlbrum s a statc condton where no changes occur n the macroscopc propertes of the system wth tme and that n engneerng practce, the assumpton of equlbrum s consdered justfed when t leads to results of satsfactory accuracy. The crteron for phase equlbrum s outlned n Appendx A, where the chemcal potental (μ ) serves as the fundamental crteron for phase equlbrum. However, chemcal potental s defned n relaton to quanttes that are mmeasurable where absolute values are unknown. Ths therefore mples that the chemcal potental has no absolute values. G. N. Lews ntroduced a quantty known as fugacty ( ), wth unts of pressure, whch could be related to chemcal potental: G ( T ) + RT ln f = Γ (3-) where Г s the ntegraton constant at temperature T (Smth et al., 200). The partal molar Gbbs energy s defned as: G ( ng) = (3-2) n T, P, n j Usng Equaton (A-6) for the defnton of chemcal potental mples: µ = G (3-3) Now comparson of Equatons (3-) and (3-3) shows the followng relaton of chemcal potental and fugacty: 25

62 (T) CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES ( T ) + RT ln f µ = Γ (3-4) Substtuton of Equaton (3-4) nto Equaton (A-4) for a closed system at equlbrum wth all phases present at the same temperature results n: f = f =... = f (3-5) α β π for =, 2,, N. The followng equaton holds for an deal gas: G g ( T ) + RT ln P = Γ (3-6) wth Г beng the same ntegraton constant as n Equaton (3-) at temperature T. The theory of fugacty for a real flud s gven by: G ( T ) + RT ln f = Γ (3-7) Subtractng Equaton (3-6) from Equaton (3-7) at constant temperature and pressure: G g f G = RT ln (3-8) P The left-hand sde of Equaton (3-8) s defned as the resdual Gbbs energy () and the rato / P s termed the fugacty coeffcent of component, symbolzed asφ. Equatons (3-6) to (3-8) are only applcable to pure speces. An equaton smlar to Equaton (3-4) can also be wrtten for a speces n soluton: ( T ) + RT ln fˆ µ = Γ (3-9) where fˆ s the fugacty of speces n soluton. Smlar to Equaton (3-5): 26

63 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES f ˆ = fˆ =... = fˆ (3-0) α β π where α, β and π denote phases. In terms of VLE, Equaton (3-0) becomes: fˆ = fˆ (3-) v l where =, 2,, N and v and l denote vapour and lqud phases respectvely. The relaton of the vapour and lqud fugactes to measurable quanttes such as temperature, pressure and composton s acheved by extendng the defnton of the fugacty coeffcent to nclude the fugacty coeffcent of speces n soluton ( φˆ ) and another dmensonless varable, γ, known as the actvty coeffcent of speces n soluton. The actvty coeffcent s dscussed n Secton 3.2. For bnary VLE, the relaton s descrbed by Equatons (3-2) and (3-3): f ˆ v = y φˆ P (3-2) f ˆ = x γ f (3-3) l where and are the lqud and vapour compostons respectvely of speces. If one consders a phase change of a pure flud from a saturated lqud to a saturated vapour at saturated pressure and temperature, the followng relaton can be found as a result of Equaton (3-5): f = f = f (3-4) v l sat where sat f s the saturated fugacty of speces. The saturated fugacty coeffcent of pure flud speces ( φ sat ) at saturated pressure s: sat f φ = (3-5) P sat sat Ths therefore leads to: 27

64 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES φ = φ = φ (3-6) v l sat When Equaton (3-7) s dfferentated, one obtans: dg = RTd ln (3-7) f Usng the property relaton for Gbbs energy, dg = VdP SdT, for a speces n soluton at constant composton and temperature yelds: dg = VdP (3-8) Equatons (3-7) and (3-8) are then used to elmnate : V d ln f = dp (3-9) RT Integratng Equaton (3-9) from the ntal state of saturated lqud to a fnal state of compressed lqud at constant pressure (P), results n: P f ln = sat VdP (3-20) f RT sat P where s the lqud molar volume of speces whch s consdered a weak functon of pressure for temperatures much lower than the crtcal temperature ( ). Therefore, can be assumed approxmately constant at the saturated lqud molar volume ( V ). Evaluaton of the ntegral n Equaton (3-20) yelds: sat ( P P ) l l f V ln = sat (3-2) f RT Usng Equaton (3-5) to elmnate sat f, results n: 28

65 and are CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES f sat ( P P ) l sat sat V = φ P exp (3-22) RT The exponental term n Equaton (3-22) s known as the Poyntng correcton factor. Ths factor provdes the correcton for the lqud phase fugacty from the vapour pressure of speces to the system pressure. The combnaton of Equatons (3-2), (3-3) and (3-22) results n: y Φ P = x γ P (3-23) sat where Φ = ˆ φ φ sat V exp l sat ( P P ) RT (3-24) The equaton proposed by Rackett (970) can be used to evaluate the saturated lqud molar volume ( V ): l V l ( T ) ( V ) ( Z ) r ( ) = (3-25) c c where Z s the compressblty factor, subscrpt c ndcates the crtcal pont and ( T temperature defned as T / ( T. ) c r ) s the reduced Equaton (3-23) provdes a useful relaton for the vapour and lqud phases at equlbrum. In the case of an deal system, the vapour phase s represented by an deal gas and the lqud phase by an deal soluton. The deal system s the smplest possble relaton for VLE and s commonly known as Raoult s Law (Smth et al., 200). Equaton (3-24) reduces to Raoult s Law when Ф γ both set to a value of one. Smth et al. (200) menton that the Poyntng factor dffers from unt by only a few parts per thousand at low to moderate pressures and therefore ts omsson ntroduces neglgble error. Ths assumpton s reasonable for non-polar components at low pressures but the error becomes sgnfcant for mxtures that contan polar or assocatng components (Prausntz et al., 980). 29

66 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES 3.. Fugacty Coeffcents from the Vral Equaton of State The determnaton of the fugacty coeffcent of a speces n soluton s made possble by a number of methods avalable. One such method that has ts theoretcal bass n statstcal mechancs s known as the vral equaton of state whch s represented by the Taylor seres expanson. The vral equaton of state can be used at low to moderate pressures to evaluate the fugacty coeffcents n order to adequately descrbe the non-dealty of the vapour phase n VLE. However, the Taylor seres expanson s an nfnte seres and thus cannot be appled to practcal calculatons. Hence, a truncated form of the vral equaton s usually employed where the degree of truncaton s controlled by the temperature and pressure. Accordng to Perry and Green (998), the pressure explct form of the vral equaton of state truncated to the second term s sutable for descrbng the vapour phase at sub-crtcal temperatures and pressures up to 5 bar: Z BvralP = + (3-26) RT where Z s the compressblty factor and s defned as PV/RT. For an deal gas the compressblty factor equals unty. The nomenclature s known as the second vral coeffcent and s a functon of temperature and composton (for mxtures). For a mxture, the composton dependence for the second vral coeffcent s based on statstcal mechancs: B mxture y y jbj (3-27) = j where y s the vapour mole fracton of a mxture and the subscrpts and j dentfy the speces. s known as the cross vral coeffcent that represents both pure and component mxture coeffcents and typfes a bmolecular nteracton between speces and j wth =. When the vral equaton of state, truncated to the second term for a bnary system, s used to descrbe the vapour phase, the fugacty coeffcent (Φ ) of Equaton (3-24) becomes: Φ l sat ( B V )( P P ) 2 + Py δ j = exp (3-28) RT where 30

67 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES δ = 2B B B (3-29) j j jj The pure component second vral coeffcents ( and ) and that for the mxtures ( ) can be expermentally determned by varous technques. Ramjugernath (2000) dscusses one such technque that nvolves the calculaton of volume n a hgh pressure VLE cell. Dymond and Smth (980) and Cholnsk et al. (986) have compled a lst of expermental second and thrd vral coeffcents for varous gases and some mxtures at specfed temperatures. Snce the second vral coeffcent s dependent on temperature, t s rather dffcult to obtan expermental values of the second vral coeffcent at desred temperatures. Hence, correlatons were developed to enable calculaton of the second vral coeffcent for both pure components and ther mxtures. Accordng to Hayden and O Connell (975), the second vral coeffcents can be related to the equlbrum constant n a smple way and therefore f a correlaton for the second vral coeffcent can yeld accurate values for substances whch assocate very strongly (e.g. carboxylc acds), t can be used for all systems. The correlaton proposed by Tsonopoulos (974) s one of the most wdely used correlatons for evaluatng the second vral coeffcents for both pure components and mxtures of non-polar and polar systems. The correlaton of Tsonopoulos (974) also accounts for speces (such as water and alcohols) that exhbt hydrogen bondng. For non-polar gases, Tsonopoulos (974) proposed that: B vral Pc (0) ) f r RTc ( ( T ) + ω f ( T ) = (3-30) r where f ( 0) ( Tr ) = (3-3) T T T T r r r r and f ( ) ( Tr ) = (3-32) T T T r r r Polar components however contan a non-zero dpole moment that expresses the effect of electrostatc forces between molecules. Tsonopoulos (974) therefore proposed an addtonal parameter n Equaton (3-30): 3

68 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES B vral Pc (0) ) f r r RTc () (2 ( T ) + f ( T ) + f ( T ) = ω (3-33) r where a T t ( Tr ) 6 (2) f = (3-34) r In the case of components that exhbt hydrogen bondng, the effect of dmerzaton makes the temperature dependence of the polar effect more complex for the second vral coeffcent. Tsonopoulos (974) therefore proposed a second addtonal parameter to account for ths effect: t t ( Tr ) 6 8 (2) f + a b = (3-35) T T r r The parameters and are functons of the dpole moment and are determned by regresson of expermental data for smlar compounds. The second vral cross coeffcents can be determned usng Equatons (3-33) to (3-35) but wth the followng parameters: ( P c, ω j, ( a t and ) j c T, ( ) j ( b t ) j. The mxng rules as suggested by Tsonopoulos (974) are used to determne these parameters: ) j ( T ) ( T ) ( T ) ( k ) c j = (3-36) c c j j ( P ) c j = 4 ( T ) c j ( P ) ( ) ( ) ( ) c V Pc V c j c + ( Tc ) ( c ) T j / 3 ( V ) + ( V ) / 3 ( ) 3 c c j j (3-37) and ω + ω j ωj = (3-38) 2 The parameter n Equaton (3-36) s an emprcal bnary nteracton parameter whch s set to a value of zero when speces and j are very smlar n sze and chemcal nature. When speces and j 32

69 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES are not smlar n sze or chemcal nature, the gudelnes of Tarakad and Danner (977) are used to determne the value of. For polar/non-polar systems, t s assumed that has no polar term and hence ( both set to a value of zero. However for polar/polar systems, s found by assumng: t ) j a and ( t ) j b are ( a ) t j ( b ) t j ( a ) + ( a ) t t j = (3-39) 2 ( b ) + ( b ) t t j = (3-40) Fugacty Coeffcents from a Cubc Equaton of State A cubc equaton of state (EoS) s also commonly used to evaluate fugacty coeffcents. The smplest cubc EoS that accounted for devatons from the deal gas law and based on ntermolecular forces was developed by Van der Waals (873). In hs work, Van der Waals (873) amed to develop a smple and generalzed sem-emprcal EoS that accounted for the behavour of fluds both above and below the crtcal pont. However the parameters n the equaton developed by van der Waals (873) were not temperature dependent and therefore the equaton was lmted n ts applcaton to descrbe hghly non-deal systems (Anderko, 990). Numerous modfcatons were proposed to the van der Waals (873) EoS but only the modfcatons developed by Redlch and Kwong (949) and Soave (972) were recognzed as the most successful. Later Peng and Robnson (976) also proposed a modfcaton that was wdely accepted. Only the equaton of Soave (972) and that of Peng and Robnson (976) were used n ths study and wll therefore be further dscussed The Soave-Redlch-Kwong (SRK) Cubc Equaton of State The cubc EoS of Redlch and Kwong (949) was not able to offer a satsfactory representaton of the lqud phase non-dealty. Hence the equaton could not be used to perform accurate calculatons for VLE. Soave (972) therefore modfed ths equaton and proposed that: 33

70 n CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES ( V b) a( T ) ( V + b) RT P = (3-4) V The constant a s related to the ntermolecular attracton force of molecules and s consdered temperature dependent whlst the constant b accounts for the molecular sze of the molecule and s temperature ndependent. They are determned from the followng equatons: a ( T ) a {( T ) } α {( T ), ω } = (3-42) c r ( T ) b ( T c ) b = (3-43) where a ( T ) c 2 2 ( Tc ) ( P c ) R = (3-44) c ( c ) ( P c ) R T b ( T ) = (3-45) [ ( )] {( T ) ω } = + κ ( T ) c, r α (3-46) The parameter κ Equaton (3-46) s a constant characterstc of each component. Soave (972) proposed a correlaton of ths constant wth respect to the acentrc factor: κ = ω 0.76ω 2 (3-47) In order to assst wth computatonal calculatons, Equaton (3-4) can also be expressed n terms of the compressblty factor (Z) for a mxture: ( A B { B } ) 2 A B = Z Z + (3-48) m m m m m 34

71 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES where ( T ) am P Am = (3-49) R 2 T 2 bm P Bm = RT (3-50) where and from Equatons (3-5) to (3-53) are obtaned from mxng rules, whch are dscussed n Secton However, Soave (972) employed the followng mxng rules: a m z z jaj (3-5) = j b m = zb (3-52) where j ( )( a a ) 0. 5 a = k (3-53) j j The use of z n Equatons (3-5), (3-52) and (3-54) can be used to represent the lqud mole fracton (x) or the vapour mole fracton (y). The parameter k j s known as the bnary nteracton parameter that s unque to each bnary system and found from the regresson of expermental VLE data. It should be noted that k = k. j j In the case of a bnary system, the largest real root of Equaton (3-48) corresponds to the vapour phase compressblty factor whlst the smallest real root corresponds to that of the lqud phase compressblty factor. The fugacty coeffcent of speces n a mxture for each phase s then found from: n z k ak ˆ b Am b k = B = ( ) ( ) + + m lnφ Z ln Z Bm 2 ln (3-54) bm Bm bm am Z 35

72 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Usually, more theoretcally correct mxng rules such as those by Wong and Sandler (992) and Twu and Coon (996) are employed as they offer a greater degree of flexblty and accuracy. The mxng rule of Wong and Sandler (992) s dscussed further n Secton The SRK EoS offers a better calculaton of vapour pressures for several hydrocarbons and correlaton of VLE behavour for systems consstng of non-polar and slghtly polar fluds when compared to the Redlch-Kwong EoS. Soave (993) later modfed the temperature dependence on the attracton term n the SRK EoS to ncorporate both polar and non-polar fluds n order to mprove vapour pressure calculatons. However the calculaton of lqud phase specfc volume wth the SRK EoS s consderably larger (as hgh as 27 %) than lterature values (Peng and Robnson, 976) The Peng-Robnson (PR) Cubc Equaton of State Accordng to Peng and Robnson (976), there were stll some shortcomngs wth the equaton proposed by Redlch and Kwong (949) and the modfcaton by Soave (972). One such shortcomng was concerned wth the falure to predct satsfactory lqud densty values. Peng and Robnson (976) also amed to mprove the accuracy of the equaton near the crtcal pont. The proposed equaton of Peng and Robnson (976) s: a( T ) ( V + b) + b( V b) RT P = (3-55) V b V The constants a and b are the same as descrbed for the SRK EoS except where Equatons (3-44), (3-45) and (3-47) were modfed as follows: a ( T ) c 2 2 ( Tc ) ( P c ) R = (3-56) c ( c ) ( P c ) R T b ( T ) = (3-57) κ = + ω ω (3-58)

73 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES The correspondng relaton for Equaton (3-55) n terms of the compressblty factor for a mxture s: ( B ) Z + ( A 3B 2B ) Z ( A B B B ) = 0 3 Z (3-59) m m m m m m m m,,, and are the same for the Peng-Robnson (PR) EoS as descrbed for the SRK EoS n Equatons (3-49) to (3-53) respectvely. Also, n smlar manner the largest and smallest real roots of Equaton (3-59) correspond to the vapour and lqud compressblty factor respectvely. The expresson for the fugacty coeffcent of speces n a mxture becomes: b lnφ ˆ = b m + ( + ) ( ) ( ) ( ) 2 zk ak Am k b Z 2 Bm Z ln Z Bm ln 2 2Bm am bm Z + 2 Bm (3-60) The SRK and PR EoS are most wdely used n ndustry snce they requre only crtcal propertes and acentrc parameters for the generalsed parameters as nput nformaton, a short computaton tme and they produce reasonably good VLE predctons for hydrocarbon systems. However, the dsadvantages of the SRK and PR EoS nclude poor lqud densty calculatons, naccurate generalsed parameters for polar and assocatng fluds whch cannot be used for extrapolaton, poor phase behavour correlaton for long-chan molecules, naccurate calculatons n the crtcal regon and naccurate vapour pressure calculatons for pressures below.3 kpa. Abbott (979) and Martn (979) provde a detaled revew concernng the shortcomngs of tradtonal forms of cubc EoS The Alpha Correlaton of Mathas and Copeman (983) Twu et al. (99) mentoned that n order for a cubc EoS to accurately correlate phase equlbra of mxtures, the vapour pressure of the pure components and the propertes of the mxture must be accurately predcted. The temperature dependent attracton term, also known as the α functon, sgnfcantly contrbutes to the accurate predcton of vapour pressure whlst the mxng rule employed greatly nfluences the mxture propertes. Mathas and Copeman (983) proposed an α functon wth adjustable parameters expressed n the form of a seres to be used n any cubc EoS. In the lterature, researchers such as Kang et al. (2002), Valtz et al. (2002) and Horstmann et al. (2005) have found that truncatng the seres to three adjustable parameters was suffcent to provde good accuracy. The use of the three adjustable parameters renders the α functon more flexble, where these parameters are found from the regresson of expermental vapour pressure data. Ths α 37

74 and are CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES functon of Mathas and Copeman (983) was used n ths study wth both the SRK and PR EoS and catered for non-polar and polar components: {( T ), ω } + κ ( T ) 2 ( ) + κ ( ( T ) ) + κ ( ( T ) ) 3 α 2 3 c = r r r (3-6) 2 where κ, κ κ the adjustable parameters that are unque to each component and are determned from the regresson of expermental vapour pressure data. Snce the α functon can be appled to any EoS, the adjustable parameters would dffer from one EoS to another Mxng Rules for Cubc Equatons of State Mxng rules are used to accurately represent the phase equlbra of mxtures when usng an EoS to regress VLE data, where t characterzes the nteracton of molecules n a mxture. The mxng rules used by Soave (972) and Peng and Robnson (976) are known as the van der Waals one-fludtheory classcal mxng rules. Lterature shows numerous mxng rules wth dfferent classfcatons that were developed over the years. Raal and Mühlbauer (998) provdes an excellent detaled revew of these mxng rules. Accordng to Hernández-Gaduza et al. (200), the extrapolaton of many mxng rules to mult-component mxtures s ncoherent due to the nvarance problem and the dluton effect. Mchelsen and Kstenmacher (990) noted these shortcomngs n ther fndngs as the Mchelsen-Kstenmacher-Syndrome. One such mxng rule that dd not suffer these shortcomngs was the mxng rule of Wong and Sandler (992) whch was also consdered n ths study. The mxture parameters and from the Wong and Sandler (992) mxng s found from: a m RT b m QD = (3-62) ( D) Q = (3-63) ( D) where Q and D are defned as: a Q = x x j b (3-64) RT j j 38

75 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES E a A D = x + (3-65) b RT crt and E A s the excess Helmholtz free energy calculated at nfnte pressure. The mxng rule also makes use of the partal molar dervatves of and wth respectve to the number of moles to evaluate the fugacty coeffcents obtaned from an EoS: RT n n a n 2 m nb = D n m + b m nd n (3-66) nb n m = n Q 2 nd ( ) ( ) 2 D n n D n Q (3-67) and the correspondng partal dervatves of Q and D are gven by: 2 n Q = 2 n n j x j b a RT j (3-68) nd n a = b RT lnγ + c (3-69) and E na = RT n lnγ (3-70) The parameter c s dependent on the EoS used. Equatons (3-7a) and (3-7b) show the value of c used n the SRK and PR EoS respectvely: c = ln(2) (3-7a) ( 2 ) c = ln (3-7b) 2 39

76 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Wong and Sandler (992) made use of the excess Helmholtz free energy nstead of the excess Gbbs free energy as the former s much less pressure dependent and thus the correct behavour was obtaned at both low and nfnte pressure. In ths study the NRTL actvty coeffcent model (dscussed n Secton ) was used to descrbe the excess Helmholtz free energy at nfnte pressure and the nfnte dluton actvty coeffcents (lnγ ): E A RT = x j k x τ g j x k j g k j (3-72) x jτ jg j x lτ ljglj j x jgj l ln γ = + τ j (3-73) xk gk j xk gk xk gkj k k k Equaton (3-64) s calculated wth the ad of the followng: a a j b + b j a RT RT b = RT 2 j ( k ) j (3-74) Expermental bnary VLE data are regressed to obtan the bnary nteracton parameter k j. 3.2 Actvty and Actvty Coeffcent The actvty coeffcent was ntroduced earler n Secton 3. as a factor that accounts for the nondealty of the lqud phase n VLE. For the actvty coeffcent to be completely defned, the standard-state fugacty must be specfed (Prausntz et al., 980). The standard-state fugacty of speces s taken as the fugacty of speces at the same temperature as that of the mxture and at some specfed pressure and composton. Accordng to Gess et al. (99) the concept of excess propertes must be ntroduced n order to obtan some physcal sense of the actvty coeffcent. The excess property s defned as the dfference between the actual property value and that of an deal soluton at the same temperature, pressure and composton. The actvty coeffcent for speces s: 40

77 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES fˆ γ = (3-75) x f and n terms of the Gbbs energy s: G ( T ) + RT ln fˆ = Γ (3-76) The deal soluton behavour can be adequately represented by the Lews/Randall rule (Smth et al., 200): f ˆ = x f (3-77) d Equaton (3-76) wrtten for an deal soluton s: G d ( T ) + RT ln x f = Γ (3-78) Usng the excess property defnton for Equatons (3-76) and (3-78): G E = RT lnγ (3-79) Van Ness (959) derved the fundamental excess-property relaton to show the nter-relaton and sgnfcance of varous excess thermodynamc propertes: E E E E ng nv nh G d = dp dt + dn 2 (3-80) RT RT RT RT The combnaton of Equatons (3-79) and (3-80) provdes an alternatve form of the fundamental excess property relaton n terms of the actvty coeffcent: ng d RT E E nv = RT E nh dp dt + lnγ dn 2 (3-8) RT Inspecton of Equatons (3-80) and (3-8) show that: 4

78 may CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES ln = E ( ng RT ) γ (3-82) n P, T, n j For a bnary system and usng the propertes of a partal molar quantty: ln ln G x d E ( G RT ) E 2 γ = + (3-83) RT dx G x d E ( G RT ) E γ 2 = + (3-84) RT dx2 The partal molar property of G E RT s γ, therefore: E G RT = x ln γ (3-85) Propertes such as, and γ all be accessed expermentally thus renderng the excess property equatons qute useful. It should also be noted that the molar excess Gbbs energy s a functon of measurable system propertes; temperature, pressure and composton. The excess propertes are related to the actvty coeffcent by the Gbbs-Duhem equaton: E E V H xd lnγ = dp dt (3-86) 2 RT RT and at constant pressure and temperature, Equaton (3-85) becomes: xd ln γ = 0 (3-87) The Gbbs-Duhem equaton s the bass used for thermodynamc consstency testng of VLE data. 42

79 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES 3.2. Lqud Phase Actvty Coeffcent Models The lqud phase actvty coeffcent models are used to account for the non-dealty of the lqud phase n phase equlbra calculatons. The models are generally functons of lqud compostons, expressed as mole fractons, volume fractons or molecular surface fractons and temperature (Walas, 985). Usually the volume or molecular surface fractons are used when molecules dffer substantally n sze and chemcal nature. The smplest lqud phase actvty model s the two-suffx Margules equaton (Smth et al., 200). Over the years, many researchers have proposed numerous lqud phase actvty coeffcent models to mprove representaton of the lqud phase non-dealty. Some of these models whch have receved much attenton nclude: the TK-Wlson (Tsuboka- Katayama-Wlson), NRTL (Non-Random Two Lqud) and modfed UNIQUAC (UNIversal QUAs-Chemcal) models. These models were consdered n ths study and expressed n the form of excess Gbbs energy as a functon of lqud mole fractons and temperature. The actvty coeffcents were then calculated for each component usng Equaton (3-82) The Tsuboka-Katayama-Wlson (TK-Wlson) Equaton The TK-Wlson equaton s a modfcaton of the equaton developed by Wlson (964). Wlson (964) based hs equaton on the concept of local composton whch occurs wthn a lqud soluton. Accordng to Smth et al. (200), models whch are based on ths concept are presumed to account for short-range order and non-random molecular orentatons that result from dfferences n molecular sze and ntermolecular forces. Prausntz et al. (999) found that the Wlson equaton appeared to provde a good representaton for a wde range of mscble mxtures, partcularly for solutons of polar or assocatng components n non-polar solvents. The Wlson equaton can also be readly generalzed to mult-component systems wthout ntroducng further parameters other than that of the bnary consttuents. However, there were two major dsadvantages wth the Wlson equaton. One was that the equaton could not predct lqud mmscblty and hence could not be used to represent systems that dsplayed mmscblty. Secondly, the equaton could not be used for systems whch showed a maxmum or mnmum when the natural logarthms of the actvty coeffcents was plotted aganst the lqud mole fracton. Therefore Tsuboka and Katayama (975) modfed the Wlson equaton to meet these shortcomngs. The modfcaton was based on an excess energy equaton wth the Wlson s local volume fractons and the Gbbs-Helmholtz correlaton. The TK-Wlson equaton for a bnary system s expressed as: 43

80 and are CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES E G RT x + V x V V x + x l l l l = x ln + x2 ln (3-88) x + Λ2 x2 Λ 2x + x2 V where l V Λ = 2 λ l 2 2 exp V RT (3-89) and l V Λ = λ l 2 2 exp V RT 2 (3-90) 2 = a2 a λ (3-9) λ (3-92) 2 = a2 a22 The parameters λ λ actvty coeffcents are gven as: the adjustable parameters for the TK-Wlson equaton. The correspondng x + V x V lnγ ln x + Λ x l l = (3-93) 2 2 ( β β v ) x 2 where x + V x V lnγ 2 ln x + Λ x l l = 2 2 (3-94) 2 2 ( β β v ) x Λ Λ = x + Λ x Λ x + x 2 2 β (3-95) l l V V V V2 β v = (3-96) x + V x V x + x V l 2 l 2 2 l 2 l l V l 2 44

81 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES The Wlson and TK-Wlson equatons are generally n very good agreement when the molar volume ratos V V are close to unty. Care must be taken when usng the regressed VLE parameters of l l j TK-Wlson to predct LLE as the latter s very senstve to the parameters (Walas, 985) The NRTL (Non-Random Two Lqud) Equaton The NRTL equaton proposed by Renon and Prausntz (968) was based on the local composton model as well as the two-lqud model of Scott (956) together wth an assumpton of nonrandomness smlar to that used by Wlson (964). The NRTL equaton has a major advantage when compared to the orgnal Wlson equaton n that both partally mscble and completely mscble systems could be satsfactorly represented. Lke the TK-Wlson equaton, the NRTL equaton s applcable to mult-component mxtures wth only the bnary parameters. Moreover the NRTL equaton can be appled to hghly non-deal systems to yeld a good representaton of phase equlbra (Raal and Mühlbauer, 998). For a bnary system, the NRTL equaton s: G E RT = x x 2 τ 2G x + G 2 2 x 2 τ 2G2 + G x + x 2 2 (3-97) where ( α ) G (3-98) 2 = exp 2τ 2 ( α ) G (3-99) 2 = exp 2τ 2 g2 g 22 τ 2 = (3-00) RT g 2 g τ 2 = (3-0) RT The correspondng actvty coeffcents are gven by: 45

82 α and are should = and and outsde CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES 2 ( ) 2 G2 τ 2G2 lnγ + = x2 τ 2 2 (3-02) x + x2g2 x2 + xg2 2 ( ) 2 G2 τ 2G2 lnγ + 2 = x τ 2 2 (3-03) x2 + xg2 x + x2g2 The NRTL equaton conssts of the followng adjustable parameters: ( ), ( ), α α. The ( ) and ( ) parameters represent the nteracton between speces components and 2. The parameters α characterstc of the randomness of the mxture where a value of zero ndcates that the mxture s completely random. Renon and Prausntz (986) note that α α provde gudelnes for sutable values for α. However, over the years many researchers have found that the gudelnes provded by Renon and Prausntz (986) were too restrctve and that values of α these gudelnes gave better predctons for phase equlbra. Walas (985) notes that f an estmate for α has to be made; t should be 0.3 for non-aqueous mxtures and about 0.4 for aqueous organc mxtures. On the other hand, Raal and Mühlbauer (998) have found these suggestons to be nconclusve and mentons that a sutable value for α expermental data. be found from the reducton of The NRTL model can provde very good representaton of hghly non-deal systems especally for partally mscble systems and can accurately represent systems whch show a maxmum or mnmum when the natural logarthms of the actvty coeffcents s plotted aganst the lqud mole fracton (Walas, 985). However n the range of very low molar concentratons, the NRTL model s nferor to the Wlson model n treatng strongly asymmetrc systems (Vetere, 2000). In hs study, Vetere (2000) provdes an explanaton for ths behavour and a smple modfcaton of the NRTL model ncorporatng molar volume ratos. The NRTL model has been successfully used to model smlar VLE systems that were nvestgated n ths study. Wen and Tu (2007) and Martínez et al. (2008) reported that the NRTL model was capable of correlatng data for the ethanol + butan-2-one system. Arce et al. (996, 997, and 998) have also reported satsfactory modelng wth the NRTL model for the ethanol + 2-methoxy-2- methylbutane system. 46

83 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES The Modfed UNIQUAC (UNIversal QUAs-Chemcal) Equaton Abrams and Prausntz (975) sem-theoretcally developed the UNIQUAC equaton usng the twolqud model and the theory of local composton. The proposed equaton was made up of two parts: a combnatoral part to account for the dfferences n the sze and shape of the molecules and the resdual part to account for the ntermolecular nteractons between the molecules. Anderson and Prausntz (978) later modfed the UNIQUAC equaton to obtan better agreement for systems contanng water or lower alcohols by determnng optmum values for the surface nteracton parameter (q') usng a varety of systems contanng water and/or alcohols. Smlar to the TK- Wlson and NRTL equatons, the modfed UNIQUAC equaton can also be readly extended to mult-component mxtures n terms of the bnary parameters only. The modfed UNIQUAC equaton can also be used to represent systems that exhbt partal mscblty for phase equlbra. The modfed UNIQUAC equaton for a bnary system s presented as: G E Φ = x ln RT x + x 2 Φ ln x * 2 2 * qz θ + ln * 2 Φ q2 z θ 2 + ln * 2 Φ 2 q q ln ' 2 ln ' ' ' ( θ + θ τ ) ' ' ( θ τ + θ ) (3-04) where z s the co-ordnaton number that s usually set to a value of ten. The volume fracton, Ф *, and the area fractons θ and θ' are found from: * r x Φ = 2 r x j= j j (3-05) θ = 2 q x j= q j x j (3-06) θ ' = 2 q x j= ' q ' j x j (3-07) 47

84 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES The parameter r s a pure component volume parameter that accounts for the sze of the molecules, whlst the parameters q accounts for the geometrc external surface of the molecules and q' for the surface of nteracton of the molecules. The parameter q' was ntroduced by Anderson and Prausntz (978) to obtan better agreement for systems contanng water or lower alcohols. In ther work, Anderson and Prausntz (978) found that the values of q' were smaller than q, ndcatve that for alcohols the ntermolecular attracton s determned prmarly by the OH group. To revert to the orgnal formulaton of the UNIQUAC equaton, q' s set equal to q. These pure component structural parameters are evaluated from molecular structure contrbutons for varous groups and subgroups and are outlned n Raal and Mühlbauer (998). The adjustable parameters ( ) and ( ) are found from: u2 u22 τ 2 = exp (3-08) RT u2 u τ 2 = exp (3-09) RT The correspondng actvty coeffcents are gven by: Φ lnγ = ln x q ln ' lnγ q 2 ' 2 * z + q 2 θ ln * Φ * r + Φ 2 l l r2 ' ' ' ' τ ( ) 2 τ 2 θ + + θ 2τ 2 θ 2q2 ' ' ' ' θ + θ 2τ 2 θτ 2 + θ 2 Φ = ln x ln * 2 2 z + q 2 2 θ 2 ln * Φ 2 * + Φ l r r ' ' ' ' τ ( ) 2 τ 2 θ θτ 2 θq ' ' ' ' θ 2 + θτ 2 θ 2τ 2 + θ l (3-0) (3-) where z l = ( r q ) ( r ) (3-2) 2 48

85 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES The UNIQUAC equaton s applcable to a wde varety of non-electrolyte lqud mxtures contanng polar or non-polar fluds. The man dsadvantage of the UNIQUAC equaton s ts greater algebrac complexty and the need for pure component structural parameters. The modfed UNIQUAC equaton was consdered n ths study snce systems that contaned lower alcohols were measured as part of ths study. However, even wth ts greater algebrac complexty, the UNIQUAC model on average s less satsfactory n correlatng VLE data of moderately non-deal systems when compared to the Wlson and NRTL models (Malanowsk and Anderko,992). Smlar to the NRTL model, the UNIQUAC model was also found to satsfactorly model smlar VLE systems nvestgated n ths study. For the ethanol + butan-2-one system, Ohta et al. (98), Wen and Tu (2007) and Martínez et al. (2008) acheved satsfactory modelng wth the UNIQUAC model. For the ethanol + 2-methoxy-2-methylbutane, Arce et al. (996, 997, and 998) reported that the UNIQUAC model was sutable for such a system. 3.3 Vapour-Lqud Equlbrum (VLE) Phase dagrams provde a good summary for VLE data. Some of the most commonly used phase dagrams nclude the x-y plot wth ether a T-x-y plot for an sobar or P-x-y plot for an sotherm. There are fve types that are used to categorze the VLE behavour of bnary systems (Raal and Mühlbauer, 998). Systems for whch all compostons have bolng ponts between those of the pure components are classfed as type I. Type I s also more commonly known as ntermedatebolng systems. Types II and III are used to classfy systems that contan homogeneous azeotropes, where type II descrbes mnmum bolng homogenous azeotropes and type III descrbes maxmum bolng homogenous azeotropes. Azeotropes descrbe a state at whch the vapour composton s exactly the same as the lqud composton; hence at ths state no phase separaton s possble by conventonal dstllaton. A complaton of data for such states s provded by Gmehlng and Onken ( ). The type IV classfcaton descrbes systems wth partally mscble lqud phases and a sngle heterogeneous azeotrope. The temperature of the azeotrope provdes a sub-classfcaton to type IV; (a) the temperature of the azeotrope s below the pure component bolng temperatures or (b) the temperature of the azeotrope s ntermedate between the pure component bolng temperatures. The type V classfcaton descrbes systems wth partal lqud mscblty and both a homogenous and heterogenous azeotrope whch rarely occurs. Of all the classfcatons, the frst three types are the most commonly encountered and are dsplayed n Fgure

86 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Fgure 3-: The three common types of bnary phase dagrams for T-x-y, P-x-y and x-y plots: (a) ntermedate-bolng; (b) mnmum bolng azeotrope; (c) maxmum bolng azeotrope (Raal and Mühlbauer, 998) VLE Data Regresson In order to successfully mplement a desgn method for separaton processes, quanttatve estmates of flud phase equlbra are requred. Sometmes phase equlbrum data are readly avalable and thus quanttatve estmates can be obtaned wthout much effort. However, n most cases phase equlbrum data are unavalable and thus t becomes rather dffcult to make rough estmates on a ratonal bass. In such cases, predctve models have been developed to assst n the desgn of 50

87 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES chemcal processes. For phase separaton processes, these models nclude the use of cubc equatons of state wth mxng rules and lqud phase actvty coeffcent models. Phase equlbrum data are regressed usng these models to yeld a set of parameters that are unque to each system studed and the model employed. The model parameters are mportant as t allows predcton of phase equlbrum to expermentally dffcult condtons. The two most wdely used methods for the regresson of VLE data nclude: the γ Ф method or combned method and the Ф Ф method also known as the drect method. In the combned method, the fugacty coeffcent from an EoS (such as the vral EoS) s used to descrbe the non-dealtes of the vapour phase whlst an actvty coeffcent model s used to descrbe the non-dealtes of the lqud phase. For the drect method, the fugacty coeffcents from an EoS (such as a cubc EoS) are used to descrbe the non-dealtes n both the vapour and lqud phase where a mxng rule s employed to descrbe the mxture propertes. For each method, the calculaton procedure depends on the nature of the VLE data (sothermal or sobarc). In the case of each expermental pont n an sothermal VLE data set, the pressure and vapour composton are calculated by a bubble pont pressure computaton or the pressure and lqud composton are calculated by a dew pont pressure calculaton. The computaton scheme depends on whether the VLE data are fully determned by the measurement of temperature, pressure, vapour and lqud compostons or partally determned where only one of the phase composton or the overall composton s known. Smlarly n the case of each expermental pont n an sobarc VLE data set, the temperature and vapour composton are calculated by a bubble pont temperature calculaton or the temperature and lqud composton are calculated by a dew pont temperature calculaton. Accordng to Smth et al. (200), the vapour composton measurements are the most susceptble to error. Therefore the bubble pont computaton s generally favoured over the dew pont computaton for a fully determned VLE data set. The measurement of VLE to obtan a fully determned VLE data set s encouraged by Smth et al. (200) snce ths allows for thermodynamc consstency testng to be carred out. In the case where a statc analytcal apparatus s used to carry out measurements, sothermal VLE data are much more easly measured as opposed to sobarc VLE data. Furthermore, regresson of sothermal VLE data s less tedous as the model parameters can be treated as constants snce the temperature s constant. These model parameters are known to have strong temperature but weak pressure dependence (Raal and Mühlbauer, 998). The combned and drect methods are now dscussed n greater detal below. 5

88 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES The Combned (γ Ф) Method Ths method combnes the use of two dfferent equatons to regress VLE data, where one equaton descrbes the non-dealty of the vapour phase and the other descrbes the non-dealty of the lqud phase. In ths study, the vral EoS wth the second vral coeffcent correlaton of Tsonopoulos (974) was used to descrbe the non-dealty of the vapour phase and an actvty coeffcent model was used to descrbe the lqud phase non-dealty. Usually, more than one lqud phase actvty coeffcent model s used for VLE data regresson, as a comparson can be made to check whch model fts the expermental data best. For ths study, the TK-Wlson, NRTL and modfed UNIQUAC lqud phase actvty coeffcent models (descrbed n Secton 3.2.) were used. The parameters for the lqud phase actvty coeffcent models are obtaned by usng a sutable algorthm to perform the VLE data regresson. Snce only sothermal bnary VLE data were measured n ths study, a procedure adapted from Smth et al. (200) for the regresson of an sothermal set of expermental bnary VLE data usng the combned method follows:. The temperature, lqud phase compostons and the pure component propertes are selected as nputs for the regresson algorthm. A sutable lqud phase actvty coeffcent model s then chosen. 2. Intal estmates for the parameters of the lqud phase actvty coeffcent model are then chosen. The actvty coeffcents are then calculated usng Equatons (3-83) and (3-84). Intally the vapour phase s assumed deal and therefore the fugacty coeffcents (Ф ) are ntally set to unty to enable an ntal calculaton of the system pressure. The saturated pressures ( P sat ) are then evaluated from a sutable vapour pressure correlaton (such as the extended Antone or Wagner equaton). 3. From the law of mass conservaton, = =. Therefore the system pressure s determned from the manpulaton of Equaton (3-23): P = x γ P Φ sat + x2γ 2P Φ 2 sat 2 (3-3) 4. The vapour mole fractons are then determned from: 52

89 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES y sat x P = γ (3-4) Φ P 5. Wth the vapour mole fractons calculated, the fugacty coeffcents are then evaluated from Equaton (3-28) usng the correlaton of Tsonopoulos (974) for the second vral coeffcents. The system pressure s now recalculated usng Equaton (3-3) and compared to the prevous value: δ P = P new P old (3-5) If the dfference s wthn a specfed tolerance, the next step s followed; otherwse step 4 s repeated wth the new pressure value calculated. Sometmes the specfed tolerance s not acheved or dvergence occurs n ths step. When ths occurs, new ntal estmates of the model parameters must be chosen n step above. 6. Once all the pressure values for each expermental pont of the VLE data set are determned, the model parameters are then optmzed by an optmzaton method wth a sutable objectve functon to yeld the best ft to the expermental P-x data for the entre composton range. 53

90 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Read T, x and pure component propertes. Set a tolerance, ε, for the pressure dfference. Choose ntal estmates for model parameters Set all Evaluate Φ = for ntal teraton. sat P and γ Use optmsaton method to get next estmate of model parameters No Dsplay the model s pressure, P, and the set of y values Yes Is objectve functon at mnmum? Calculate the overall pressure, P, from Equaton (3-24). Yes No Is δp < ε? Calculate the set of y values from Equaton (3-25) and evaluate the set of Φ values from Equaton (3-28) Recalculate the overall pressure, P Fgure 3-2: Calculaton flow dagram for the bubble pont pressure procedure of the combned method to obtan the parameters for the lqud phase actvty coeffcent model (Smth et al., 200). The regresson algorthm for sobarc VLE data s same as outlned above, except that the temperature s not constant and ts varaton must be consdered. In the sxth step above, an 54

91 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES objectve functon was requred. For ths study, the followng objectve functon was used to optmze for the model parameters: F = n P exp, P P = exp, cal, (3-6) Other objectve functons are also possble but accordng to Van Ness et al. (973), Equaton (3-6) s at least as good as any other and s the most smplest and drect objectve functon. Accordng to Van Ness and Abbott (982), Equaton (3-6) s successful n the regresson of sothermal VLE data and may also even be superor to any other maxmum lkelhood method. Optmsaton algorthms developed by Marquardt (963) and Gess et al. (99) make use of Equaton (3-6) for the regresson of expermental VLE data. However, software programmes such as MATLAB have bult-n algorthms whch enable such calculatons to be performed wth much ease. For ths study, the fmnsearch functon n MATLAB whch uses the Nelder-Mead smplex method for optmzaton was employed (Lagaras et al., 998). The regresson procedure for sothermal VLE data s summarzed as a calculaton flow dagram n Fgure The Drect (Ф Ф) Method Ths method makes use of a cubc EoS to calculate the fugacty coeffcents that descrbe both the vapour and lqud phase non-dealtes. Usng Equaton (3-): fˆ l l v v = x ˆ φ P = fˆ = y ˆ φ P (3-7) where the fugacty coeffcents are obtaned from: l l P RT PV ln ˆ φ = dv ln l RT l n V V T V n nt RT,, j (3-8) v v P RT PV ln ˆ φ = dv ln v RT v n V V T V n nt RT,, j (3-9) 55

92 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES where refers to the total number of moles n the system. The terms on the rght hand sde of the equaton are evaluated usng a sutable EoS. Often the equlbrum rato ( ), defned as the rato of the vapour composton to the lqud composton, s used to smplfy calculatons when usng the drect method of VLE data regresson. Usng Equaton (3-7): K = y x Φˆ = Φˆ v l (3-20) Valderrama (2003) notes some of the advantages and dsadvantages of cubc equatons of state, shown n Table 3-. Table 3-: Advantages and dsadvantages of cubc equatons of state (Valderrama, 2003). Advantages Dsadvantages Equatons of state are applcable to both low and hgh pressure systems. Actual pressure, volume and temperature data tend to follow a fourth degree equaton nstead of a cubc equaton. Due to ther cubc nature n volume, calculatons are relatvely smple to perform. Cubc equatons of state cannot represent all propertes of a flud n all dfferent ranges of temperature and pressure. The equaton can be tuned wth the adjustable parameters of the temperature attracton (α) functon to gve accurate values for any Mxng rules used for equatons of state are emprcal n nature snce the nteractons between unlke molecules are unknown. Ths volumetrc or thermodynamc property for most means nteracton parameters are usually applcatons. requred. Furthermore, applcaton of mxng rules to complex mxtures mght actually requre several nteracton parameters even wth the use of modern mxng rules. The equatons can be easly extended to mxtures by use of mxng rules of any complexty. Raal and Mühlbauer (998) provdes a good summary of the challenges assocated wth usng the drect method: 56

93 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES. The EoS selected must be able to adequately descrbe both the vapour and lqud phase non-dealtes. More mportantly, the EoS must be flexble enough to fully descrbe the pressure, volume and temperature behavour of a pure substance for both phases n the temperature and pressure range of study. 2. An approprate mxng rule must be carefully selected to correctly descrbe the propertes of the mxture. Most mxng rules are somewhat emprcal n nature and tend to be system specfc. 3. If a hgher than cubc order EoS s used, care must be taken to locate the approprate roots for lqud and vapour denstes. The nteracton parameters of the mxng rule used are determned from the regresson of expermental VLE data. Ths regresson technque s smlar to that of the combned method dscussed n Secton wth the same objectve functon used. Fgure 3-3 shows the calculaton flow dagram for the regresson of sothermal VLE data. 57

94 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Read T, x and pure component propertes. Set ntal estmates for mxng rule parameters. Set tolerances, ε A and ε B for the pressure teratons. Input ntal pressure guess: P= xp or sat Pk+ = Pk Dsplay the model s pressure, P, and the set of y values Use optmsaton method to get next estmate of mxng rule parameters No Evaluate ˆl φ and ˆv φ to obtan ˆl / ˆv K = φ φ Is objecton functon at mnmum? Yes Calculate: Kx = Kx and y Kx = Kx Obtan new estmate for overall pressure, P, usng an teraton procedure Recalculate ˆv φ, K, K x and Kx No No Kxk+ < ε B Kx k+ Kx < k ε A Yes Yes Fgure 3-3: Calculaton flow dagram for the bubble pont pressure teraton for the drect method to obtan parameters for the mxng rule used (Smth et al., 200). 58

95 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES 3.4 Lqud-Lqud Equlbrum (LLE) Lqud-lqud equlbrum (LLE) s a phenomenon that results when pars of chemcal speces are mxed n a certan composton range and allowed to reach thermodynamc equlbrum, do not form a sngle homogenous phase (Smth et al., 200). Systems that exhbt LLE form two lqud phases of dfferent compostons. The splttng phenomenon occurs because of a crteron that exts for phase equlbrum n a closed system (Smth et al., 200). Ths crteron s satsfed when the Gbbs energy s a mnmum wth respect to all possble changes at a gven temperature and pressure (dscussed n more detal n Secton 3.4.2). The splttng thus occurs snce the system can acheve a lower Gbbs energy by dong so than compared to formng a sngle homogenous phase. Temperature has a strong nfluence on LLE but the effect of pressure s only sgnfcant at very hgh pressures or near the crtcal pont (Walas, 985). Bnary and ternary systems are the two most common types of LLE systems dscussed n lterature. Bnary LLE systems are encountered n an azeotropc dstllaton column where the condensed dstllate forms two lqud phases. A ternary LLE system fnds ts use n lqud-lqud extracton. Snce only bnary systems were measured n ths study, a short descrpton of bnary LLE systems wll be presented. The reader s referred to Treybal (963) and Novák et al. (987), who dscuss ternary LLE systems n detal Bnary LLE Phase dagrams for bnary LLE systems are smply presented n the form of T-x-x dagrams. Some types of bnary LLE systems are shown n Fgure 3-4. The phase dagram n Fgure 3-4 (a) s known as the sland curve that conssts of an upper crtcal soluton temperature (UCST), symbolzed as and a lower crtcal soluton temperature (LCST), symbolzed as. Ths type of phase dagram s qute rare and thus seldom encountered as LLE s only possble at temperatures between and. Fgure 3-4 (b) shows LLE bnary systems that exhbt an UCST only. For ths type of systems, the UCST may however not exst f the mxture bubble pont s lower than the UCST. Fgure 3-4 (c) shows LLE bnary systems that exhbt a LCST only. It should be noted that n ths case, the LCST may not exst f freezng occurs at a temperature hgher than the LCST. Phase dagrams of Fgure 3-4 (b) and 3-4 (c) are commonly encountered. The curves of the phase dagrams shown n Fgure 3-6 are also known as solublty or bnodal curves. For any specfc temperature wthn the solublty curve, A and B denote the equlbrum ponts wth compostons α x and β x respectvely. When the 59

96 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES solublty curve ntersects both the bubble and freezng pont curves, a fourth type of behavour s observed (Sørensen et al., 979 and 980). Fgure 3-4: Three types of constant pressure bnary LLE phase dagrams: (a) an sland curve, (b) a convex curve and (c) a concave curve, where α and β refer to the two lqud phases (Smth et al., 200) Theoretcal Treatment of LLE At equlbrum a stable system tends towards achevng a mnmum Gbbs energy at a fxed temperature and pressure. The stablty crteron ndcates that a lqud mxture wll splt nto separate lqud phases f t can lower ts Gbbs energy by dong so (Smth et al., 200). A typcal curve showng the Gbbs energy of mxng for a bnary partally mscble lqud at constant temperature and pressure s llustrated n Fgure 3-5. The Gbbs energy of mxng s defned as G = G x G, where G s the mxture Gbbs energy and the pure component Gbbs energy. 60

97 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Fgure 3-5: Molar Gbbs energy of mxng for a partally mscble bnary system at constant temperature and pressure (Prausntz et al., 999). In Fgure 3-5, a mxture wth composton correspondng to pont a wll splt nto separate phases wth compostons ' x and '' x accordng to the stablty crteron. Pont b represents the molar Gbbs energy change upon mxng and s the lowest possble Gbbs energy that the mxture may attan subject to the condtons of constant pressure, temperature and overall composton. At constant temperature and pressure, the mathematcal nterpretaton of Fgure 3-5 requres that G and ts frst and second dervatves must be contnuous functons of and that the second dervatve must everywhere be postve. Hence for a bnary system: 2 d G dx 2 > 0 (3-2) The stablty requrement n terms of the Gbbs excess energy for a bnary system s: d 2 E ( G RT ) dx 2 > (3-22) x x 2 Applcaton of the phase equlbrum crteron from Equaton (3-0) to two lquds phases, noted as α and β, results n: 6

98 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES fˆ = ˆ (3-23) α β f Introducng the actvty coeffcent and consderng each pure component as a lqud at the temperature of the system yelds: x γ f = x γ f (3-24) α α α β β β where refers to the component. Equaton (3-24) s the fundamental relaton for LLE and shows that unlke VLE, the role of the actvty coeffcents n LLE are the only thermodynamc contrbuton to an LLE calculaton Bnary LLE Data Regresson For a lqud phase actvty coeffcent model to be used n LLE regresson, t must frstly satsfy the stablty crteron. The actvty coeffcent model of Wlson (964) s one model that fals to meet the stablty crteron and therefore s not able to predct LLE (Smth et al., 200). However the TK- Wlson equaton s able to predct LLE. Unlke the regresson of VLE data, the actvty coeffcent model n LLE data regresson s used to represent both lqud phases. It should also be noted that the drect method, n whch an EoS s used, can also be used to regress LLE data. Ths method however s only applcable for the modelng of hgh pressure LLE data where the effect of pressure on phase equlbra cannot be gnored (Walas, 985 and Raal and Mühlbauer, 998). The LLE data measured n ths study was done at a moderate pressure (350 kpa) and thus the drect method would not have been approprate for ths study. Therefore no further dscusson wll be made on ths method but the reader s referred to Peng et al. (2002) and Ohta et al. (2004) for a detaled dscusson. Raal and Mühlbauer (998) note that at least two data ponts for each phase at dfferent temperatures are needed to obtan the temperature dependent parameters of the lqud phase actvty model used. Some of the smplest lqud phase actvty coeffcent models used to represent LLE ncludes the three-suffx Margules and the Van Laar (90) models. These models were not consdered for ths study as they cannot accurately represent LLE data though they are sometmes favoured due to ther comparatve algebrac smplcty. The lqud phase actvty coeffcent models dscussed n Secton 3.2. were also consdered for the bnary LLE regresson n ths study. 62

99 should and CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Accordng to Raal and Mühlbauer (998), actvty coeffcent models wth more than two parameters cannot be used to model solublty data (bnary LLE) unless all subsequent parameters are fxed at some tral value/s. Ths s necessary snce havng more than 2 parameters as unknown means that there would be more unknown parameters than known equatons to solve. Therefore n the case of the NRTL model for bnary LLE data, the non-randomness parameter (α) s fxed to allow calculaton of the other two parameters (τ of α τ). Prausntz et al. (999) suggest that the value be obtaned from expermental results of the same class of components as those under study. Due to the algebrac complexty of the TK-Wlson, NRTL and modfed UNIQUAC equatons, the parameters cannot be determned n a smple manner as compared to the three-suffx Margules or Van Laar (90) models. Therefore graphs have been publshed to assst n the computaton for the parameters of these models. Walas (985) however suggests an algorthm for such calculatons as well whch was subsequently used n ths study. 3.5 Vapour-Lqud-Lqud Equlbrum (VLLE) When the solublty curve that represents LLE ntersects the VLE bubble pont curve, a phenomenon known as vapour-lqud-lqud equlbrum (VLLE) s obtaned. Ths secton wll focus on a bref descrpton of bnary VLLE and the regresson of such data snce only bnary VLLE data were consdered n ths study. From the Gbbs phase rule, only one degree of freedom exsts for a bnary VLLE system (Smth et al., 200). Therefore, f the system pressure s specfed for a bnary system then the temperature and the compostons for all three phases are fxed. Hence for an sobarc bnary VLLE system, the state of three phases n equlbrum wll necessary occur at one temperature (T * ) when represented on a T-x-y phase dagram, as shown n Fgure 3-6. Ponts C and D n Fgure 3-6 represent the two lqud phases n equlbrum wth the vapour phase that s represented by pont E. For ths bnary VLLE system, f more of ether component s added to the system whose overall composton les between ponts C and D together wth the three phase equlbrum pressure beng mantaned, then the Gbbs phase rule necesstates that the temperature and the compostons of the three phases wll reman unchanged. However the law of mass conservaton must be satsfed to account for the change n the overall composton of the system. Ths s acheved by the adjustment of the relatve amounts of the phases. For temperatures that are above T * and dependng on the overall composton, the system may be a sngle lqud phase (represented by α or β), a vapour phase (represented as V) or a mxture of the two phases (represented as α-v or β-v). On the other hand, for 63

100 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES temperature below T *, the system s represented by a mxture of two lqud phases (LLE) or a sngle lqud phase (ether α or β) dependng on the overall composton of the system. Fgure 3-6: A common T-x-y dagram at constant pressure for a bnary system exhbtng VLLE (Smth et al., 200). In smlar manner, VLLE can also be measured at a constant temperature as shown by a P-x-y phase dagram n Fgure 3-7. In ths case the pressure (where all three phases exst n equlbrum) s dentfed as P *. As mentoned earler, pressure has a weak nfluence on the solublty of lquds except at very hgh pressure near the crtcal pont. Hence n Fgure 3-7 for moderate pressures above P *, the LLE phase boundares are nearly vertcal. 64

101 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES Fgure 3-7: A common P-x-y dagram at constant temperature for a bnary system exhbtng VLLE (Smth et al., 200). The regresson of VLLE data s carred n a smlar manner as outlned for VLE. Usng the crteron for phase equlbrum (Equaton 3-0) for the pont where the two lqud phases (α and β) are n equlbrum wth ts vapour (V) yelds: f ˆ α ˆ = fˆ (3-25) = f β v Elmnaton of the vapour and lqud fugactes n favour of the fugacty and actvty coeffcents for a bnary system results n: α α sat β β sat y P = x γ P = x γ P Φ (3-26) α α sat β β sat y2 2P = x2 γ 2 P2 = x2 γ 2 P2 Φ (3-27) 65

102 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES From Equatons (3-26) and (3-27), a total of fve varables ( x, x,, T and P) need to be solved. From the Gbbs phase rule, when one of the varables s specfed (usually ether P or T), the other four varables can be solved. α β 3.5. VLLE Data Regresson Snce VLLE s concerned wth two lqud phases, any lqud phase actvty coeffcent model used n the regresson of VLLE data must necessarly pass the stablty crteron. The regresson technque used for VLLE data depends on whether the data are for an sothermal or sobarc system. Walas (985) provdes good gudelnes for solvng each case usng one of two methods:. Solve drectly the system of equatons representng materal balances and equlbra between phases. 2. Fnd the mnmum Gbbs energy of the overall mxture. In ths case the varables are the amounts and compostons of all the phases and the mnmum s constraned subject to the mole fractons summng to unty n each phase. Regresson usng an EoS was not consdered as ths method s only mportant for hgh pressure LLE regresson. The regresson procedure made use of the vral EoS wth the second vral coeffcent correlaton of Tsonopoulos (974) to account for the vapour phase non-dealtes. The TK-Wlson, NRTL and modfed UNIQUAC lqud phase actvty coeffcent models were used to descrbe the two lqud phase non-dealtes. 3.6 Thermodynamc Consstency Tests Wth regards to bnary VLE data, a system s sad to be over specfed when the temperature, pressure, vapour and lqud compostons are all measured. Ths over specfcaton however enables thermodynamc consstency of the VLE data. Usually the vapour compostons ( values) contan the greatest error and therefore thermodynamc consstency tests often focus on the vapour compostons to determne thermodynamc consstency of the VLE data. Thermodynamc consstency tests are based on the Gbbs-Duhem equaton that was ntroduced n Secton 3.2 as Equaton (3-86). If VLE data conform to the Gbbs-Duhem equaton, then the data are sad to be thermodynamcally consstent. Ths subject matter has receved much attenton n the 66

103 and vs CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES lterature and thus many adaptatons of the of the Gbbs-Duhem equaton have been ntroduced. One of the earlest used thermodynamc consstency tests s the slope test. Ths test compares slopes of curves drawn to ft γ γ graphs. Ths test was rather tedous and also led to uncertanty (Van Ness, 995). Thus another test known as the area test was ntroduced as an mprovement over the slope test (Herngton, 947 and Redlch and Kster, 948). Accordng to Walas (985), the area test s necessary but nsuffcent as ndvdual data ponts that are nconsstent could actually compensate/cancel each other. For example, the pressure s cancelled off and therefore one of the most accurately measured system propertes s lost. Hence, the test could actually pass data sets that were nconsstent and also fal data sets that actually were consstent. For ths reason the area test was not consdered for ths study but rather two well-known thermodynamc consstency tests were used: the pont test of Van Ness et al. (973) and the drect test of Van Ness (995). One should note that thermodynamc consstency testng cannot be used for VLE data measured wth the statc synthetc method snce the vapour compostons are not measured. Also, LLE data cannot be tested for thermodynamc consstency as well (Raal and Mühlbauer, 998). Ths s due to two reasons: frstly, ndvdual actvty coeffcents cannot be determned drectly snce the expermental LLE data furnsh only a rato of actvty coeffcents. Secondly, the LLE data do not extend over a contnuous composton range, whch s a requrement for thermodynamc consstency testng. VLLE data however can be tested for thermodynamc consstency wth the pont test but only for the homogenous (VLE) regon. The drect test on the other hand can be appled to the entre composton range The Pont Test The pont test was ntroduced by Van Ness et al. (973) as an mprovement to the area test. Generally the vapour compostons ntroduce the most error to VLE data measurement and are therefore used to test for thermodynamc consstency. The pont test smply compares the measured vapour compostons ( ) to the calculated values ( ) where the calculated values are determned from data regresson usng the combned or the drect method. The comparson of the expermental and the calculated values generate resduals, Δy, whch gves an ndcaton of the consstency of the VLE data. Hence the pont test s model dependent. Danner and Gess (990) provde a quanttatve 67

104 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES crteron for the consstency of VLE data by proposng that the absolute average devaton (AAD) should be less than 0.0 for the data to be thermodynamcally consstent. AAD = n n = y y (3-28) where n refers to the number of expermental data ponts, Δy s the dfference between the expermental and the calculated value and y s the average dfference between the expermental and the calculated value. The AAD s not the only crteron used n the pont test. The test also requres that a plot of Δy vs should scatter about zero to ndcate thermodynamc consstency The Drect Test The drect test was developed by Van Ness (995) as a drect test of thermodynamc consstency for each pont of a VLE data set wth respect the Gbbs-Duhem equaton tself. The test makes use of the followng defntons: * V E dp ε P = (3-29) RT dx * H E dt ε T = 2 (3-30) RT dx * where ε P s zero for sobarc data and ε * T s zero for sothermal data and consequently only one ε term s requred for the dervaton of the drect test. Usng Equatons (3-8) and (3-86) for one mole of lqud phase and wth g = / RT results n: dg dx = ln γ γ + 2 * ε (3-3) d ln γ d lnγ 2 * x + x2 ε = 0 (3-32) dx dx 68

105 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES where ε * depends on the nature of the VLE data (ether sobarc or sothermal). Usng Equaton (3-85) for a bnary system: g = x + γ (3-33) lnγ x2 ln 2 If the expermental value of g s replaced wth and dfferentatng Equaton (3-33) wth respect to : dg dx exp = x d lnγ dx exp + lnγ exp + x 2 d lnγ dx exp 2 lnγ exp 2 (3-34) whch may alternatvely be wrtten as: dg dx exp γ = ln γ exp exp 2 + ε + x d lnγ dx exp + x 2 d lnγ dx exp 2 * ε (3-35) Subtractng Equaton (3-55) from Equaton (-3) and wrtng t n the terms of resduals (δg = g ), yelds: ( δg) d dx γ = δ ln γ 2 x d lnγ dx exp + x 2 d lnγ dx exp 2 * ε (3-36) 2 Now f an sothermal or sobarc data set s reduced wth ( δ g) the term d(δg) / s effectvely zero. Hence: as the objectve functon, then γ d lnγ d lnγ δ ln = γ 2 exp exp 2 * x + x2 ε (3-37) dx dx From the Gbbs-Duhem equaton, the rght hand sde of Equaton (3-37) s requred to be zero for thermodynamcally consstent data and the resdual on the left hand sde provdes a drect measure of devatons from the Gbbs-Duhem equaton. The extent to whch values of ths resdual fal to scatter about zero provdes a measure of the departure from thermodynamc consstency, whch Van Ness (995) expressed n the form of a consstency ndex. Table 3-2 shows ths consstency ndex as 69

106 CHAPTER 3 THERMODYNAMIC FUNDAMENTALS AND PRINCIPLES a quanttatve crteron, where an ndex of one sgnfes excellent data and an ndex of ten very poor data. Table 3-2: Consstency ndex for the drect test of Van Ness (995) wth the root mean square values (RMSD). Index RMSD δln(γ/γ) > > > > > > > > > >

107 CHAPTER 4 FRENCH SUMMARY Ce chaptre fournt les nformatons détallées sur l'apparel récemment développé. La cellule d'équlbre est construte autour d'un cylndre en saphr, acheté auprès de Rayotek Scentfc Inc., ce cylndre a un volume nterne d'envron 7.4. Le saphr a été chos en rason de ses proprétés optques, et de résstance à la fos mécanque et chmque. L'acer noxydable (type 36) est employé comme matérau prncpal pour construre les dverses pèces de l'équpement à cause de sa résstance mécanque et chmque, de son usnage facle et de ses caractérstques favorables de soudage. La verson moble de l échantllonneur électromagnétque : «Rapd On Lne Samplng Injector» ROLSI est utlsée pour échantllonner à dvers nveaux dans la cellule d équlbre chacune des phases en équlbre, une nouvelle technque d'échantllonnage est également développée pour lmter la perturbaton de presson dans la cellule d'équlbre quand un échantllonneur ROLSI moble est employé. La technque se sert d'un dogt métallque dans un arrangement qu mantent un volume constant dans la cellule d'équlbre pendant le prélèvement. L'homogénésaton du contenu de la cellule d'équlbre est réalsée au moyen d'un agtateur magnétque revêtu de téflon qu est actvé par un amant extéreurement entrané par un moteur. Un ban d'hule permet la régulaton thermque de la cellule d'équlbre pour les mesures à hautes températures entreprses dans cette étude. La cellule d'équlbre est mantenue dans une poston fxe alors qu un élévateur mécanque sert à mmerger la cellule d'équlbre dans son envronnement thermque. La température de la cellule d'équlbre est mesurée à l ade de deux sondes REB modèles Pt00 de classe A avec bulbe en céramque. L une des sondes est placée en haut et l'autre au fond de la cellule d'équlbre. Les deux sondes ont une précson de 0.05 K dans le domane 298 à 355 K et une précson de 0.07 K dans le domane 355+ à 465 K. La presson dans la cellule d'équlbre est mesurée à l ade du capteur de presson absolue 0 bar, modèle P-0 de WIKA pour des pressons sous-atmosphérques et à l ade du capteur de presson absolue 0 6 bar, modèle P-0 de WIKA des 0-6 pour les pressons supéreures. Le capteur «basse presson» a une précson de 0.02 kpa pour une gamme de 5 à 99 kpa, tands que l autre a une précson de 0.9 kpa pour une gamme de 97 à 33 kpa. Les acqustons numérques sont obtenues avec le boter d acquston 34970A de Aglent. La composton chmque de chaque phase à l'équlbre est détermnée en utlsant un chromatographe phase gazeuse modèle 204 de Shmadzu possédant un détecteur à conductvté thermque, étalonné. Des cartouches chauffantes et du fl nchrome sont employés pour le chauffage électrque pour évter tout pont frod sur les lgnes de transferts des échantllons. Avant toute mesure, chaque produt chmque est dégazé suvant la méthode de dstllaton sous vde de 7

108 CHAPTER 4 FRENCH SUMMARY Van Ness et Abbott (978) moyennant l emplo d'une colonne de fractonnement de type «Vgreux». 72

109 CHAPTER 4 EQUIPMENT DESCRIPTION 4 CHAPTER FOUR EQUIPMENT DESCRIPTION In order to successfully desgn an expermental apparatus, one has to carefully consder the objectve of the desgn together wth the factors that constran the desgn. Accordng to Snnott (2005), these constrants can ether be fxed, nvarable or due to physcal laws. It could also be restrcted by government regulatons and standards whlst other constrants are less strct to allow the desgner flexblty to acheve the best desgn. Usually the desgn of an expermental apparatus s not entrely novel but bulds on exstng desgns wth mnor changes. The Thermodynamcs Research Unt wthn the Unversty of KwaZulu-Natal has over the past 25 years successfully developed many phase equlbrum equpment desgns coverng both statc and dynamc equpment. However, all of these equpments requre rather large amounts of chemcals (on average 20 ) n order to carry out phase equlbrum measurements. Chemcal companes/ndustres often fnd t expensve to physcally synthesze large volumes of hgh purty chemcals. In lght of ths, phase equlbrum measurements on these equpment would prove rather costly as large quanttes of chemcals would be requred to complete phase equlbrum measurements. Therefore, the man objectve of ths study was to successfully desgn, develop and commsson a new statc analytcal apparatus capable of carryng out both vapour pressure and phase equlbra of multple lqud and vapour phases for small volumes of chemcals (less than 20 ). As mentoned prevously, Lauger and Rchon (986) state that there s no equpment capable of measurement for all operatng condtons and physcal propertes of chemcals. The equpment for ths study would allow for an operatng temperature range from 253 to 473 K and an operatng pressure range from absolute vacuum to 6000 kpa. Ths chapter focuses on the followng expermental features: 73

110 CHAPTER 4 EQUIPMENT DESCRIPTION Descrpton of the equlbrum cell and ts housng Samplng technque and assembly Method of agtaton wthn the equlbrum cell Isothermal envronment for the equlbrum cell Temperature and pressure measurement Composton analyss Data loggng Degassng apparatus Compresson devce for cell loadng Safety features Overvew 4. Descrpton of the Equlbrum Cell and ts Housng The equlbrum cell, whch s the heart of the expermental equpment used n ths study, was constructed around a sapphre cylnder. The optcal propertes of sapphre make t sutable to vew phase separaton wthn the cell whch s mportant pror to samplng. Apart from ts optcal propertes useful wthn ts transmsson range, sapphre s by far the strongest, toughest and chemcally resstant materal avalable. It can also be used at far hgher temperatures and pressures than most optcal materals. Sapphre also has a hgh thermal conductvty despte ts extreme electrcal non-conductvty (General Ruby and Sapphre Company). The sapphre cell was constructed by and purchased from Rayotek Scentfc Inc., wth the followng dmensons: mm (±0.05 mm) outer dameter, 7.80 mm (±0.0 mm) nternal dameter and mm heght. Ths results n an approxmate nternal volume of 7.4 for the equlbrum cell. The equlbrum cell was enclosed wthn two 36 stanless steel (36 SS) flanges of 5 mm thckness and 0 mm dameter each, by three evenly dstrbuted 36 SS spacer rods of 0 mm dameter. The propertes of 36 SS make t desrable to use n many ndustral applcatons. One of the remarkable propertes of ths materal s ts mechancal strength (such as hgh tensle and yeld strength) and the ablty to retan these propertes for long perods of tme under extreme hgh or low temperatures (Snnott, 2005). Apart from ts mechancal strength propertes, 36 SS s also more attractvely known for ts corroson resstance and s thus wdely used for many laboratory applcatons. Stanless steel s known to succumb to pttng and crevce corroson n warm chlorde envronments, however, the addton of 2% molybdenum to 304 SS to produce 36 SS offers a 74

111 CHAPTER 4 EQUIPMENT DESCRIPTION sgnfcant ncrease n resstance to pttng (Fontana and Greene, 967). Furthermore, no such chlorde envronments were used n ths study. The 36 SS materal also has very good weldng and machnng propertes makng t sutable to use n the constructon of varous equpment parts. Economcally, 36 SS s consdered a medum cost materal when compared to carbon steel (low cost) and ttanum (hgh cost). Hence consderng all these key factors, 36 SS was thus chosen as the prncpal materal of constructon for ths study. (a) (b) Photograph 4-: (a) The sapphre equlbrum cell and (b) the cell housed wthn two 36 stanless steel flanges. In order to prevent leaks wthn the equlbrum cell, two O-rngs are used at each end of the cell to provde a seal for the equlbrum cell. At each end of the cell, one of the O-rngs (9 mm nternal dameter) s stuated n a groove to provde a seal from the bottom/top whlst the other O-rng (35 mm nternal dameter) s stuated n a groove on the near bottom/top sde of the cell to provde an extra seal aganst leaks (see Photograph 4-2). The materal of the O-rngs depends on the nature of the chemcals used to carry out phase equlbrum measurements. For systems explctly contanng alcohols, ketones, esters and ethers, Ethylene Propylene Dene Monomer (EPDM) O-rngs were used whlst perfluoroelastomer O-rngs were used for systems contanng (n addton to the above mentoned groups) alkanes, alkenes and ntrles as t has good compatblty wth a wder range of chemcal functonal groups. 75

112 CHAPTER 4 EQUIPMENT DESCRIPTION Photograph 4-2: The O-rngs n the upper 36 stanless steel flange that seal the equlbrum cell. The upper 36 SS flange of the equlbrum cell contans the followng on ts sde: ) 6 mm dameter hole machned n such a manner that t narrows to a 3 mm dameter upon entry nto the equlbrum cell. Ths s used for the feed lne wth a / 8 nch OD SS ppe fttng. ) 6 mm dameter hole also machned n such a manner that t narrows to a 3 mm dameter upon entry nto the equlbrum cell. Ths s used for the pressure measurement lne wth a / 8 nch OD SS ppe fttng. ) v) 6 mm dameter hole wth a depth of 30 mm to accommodate a heater cartrdge. 2 6 mm dameter holes wth a depth of 30 mm each to accommodate two temperature probes (explaned further n Secton 4.5). The top of the upper 36 SS flange contans a 6 mm dameter hole wth M6 threads and 2 mm ptch to cater for the samplng devce used (explaned n more detal n Secton 4.2). The lower 36 SS flange of the equlbrum cell contans the followng: ) 6 mm dameter hole machned n such a manner that t narrows to a 3 mm dameter upon entry nto the equlbrum cell. Ths s used for the dran lne wth a / 8 nch OD SS ppe fttng. ) 6 mm dameter hole wth a depth of 30 mm to accommodate a temperature probe. To mnmze dead volume, the feed and dran valves are located as close as possble to the equlbrum cell and the connectng lne from the equlbrum cell to the pressure transmtters are kept to a mnmum. The WIKA model P-0 pressure transmtters for ths study contan neglgble dead volume. Thus the total dead volume s estmated at

113 CHAPTER 4 EQUIPMENT DESCRIPTION 4.2 Samplng Technque and Assembly For ths study, the accurate composton analyss of equlbrum phases s acheved usng an electromagnetc verson Rapd-On-Lne-Sampler-Injector ( ) (Gulbot et al., 2000). A schematc dagram of the was shown earler as Fgure 2-0 n Chapter 2. To promote versatlty for the measurement of multple lqud and vapour phases n equlbrum, a sngle s utlzed. Ths means that the must be moble wthn the equlbrum cell to sample all phases. Snce the nteror volume of the equlbrum cell s small (approxmately 7.4 ), t s antcpated that the movement of the wthn the equlbrum cell causes an apprecable change n volume and hence a change of pressure durng samplng. To counter ths shortcomng, a novel technque s desgned for samplng. In order to keep the volume wthn the equlbrum cell constant durng samplng, the volume dsplaced by the capllary of the must be compensated for by a smlar mechansm. To acheve ths, a 36 SS dowel wth smlar dmensons to that of the capllary of the s operated from the bottom of the cell. The dea centered on creatng an arrangement such that when the capllary of the moved wthn the equlbrum cell durng samplng, the 36 SS dowel would smultaneously move n the same drecton thereby keepng the volume wthn the equlbrum cell constant. The s mounted on a 36 SS flange of 5 mm thckness and 0 mm dameter wth a 45 mm dameter cutaway n the center for the base of the. The capllary of the enters nto the equlbrum cell va a 6 mm dameter hole wth M6 threads and 2 mm ptch from the upper flange of the equlbrum cell. To provde a seal at the entry pont of the capllary of the nto the equlbrum cell, Techtron HVP polyphenylene sulfde (Techtron HVP PPS) s used as a sealant. Techtron HVP PPS offers extreme wear resstance as well as resstance to a wde varety of organc and norganc chemcals. Furthermore, Techtron HVP PPS has a maxmum allowable operatng temperature of 493 K and preserves excellent dmensonal stablty despte temperature varaton and chemcal attack (Professonal Plastcs). Extra sealng s provded by usng a perfluoroelastomer O-rng on top of the Teflon sealant wth a stanless steel washer that s tghtly sealed wth a nut. Three spacer 36 SS rods of 0 mm dameter and 55 mm length each were used to attach the flange on whch the base was mounted to another 0 mm dameter and 5 mm thck 36 SS flange (upper flange of the ) to mantan a fxed heght for the. The s made movable by use of a 70 mm length shaft wth M6 threads and 2 mm ptch, attached from the upper flange of the to a 36 SS turn-dal. Two 36 SS gude rods of 2 mm dameter and 250 mm length are used to connect the upper flange of the equlbrum cell to the base 77

114 CHAPTER 4 EQUIPMENT DESCRIPTION flange (0 mm dameter and 28 mm thckness) of the turn-dal. The shaft contans a slot where a pn s ftted to act as a gude mechansm to prevent msalgnment of the arrangement. The operaton of the turn-dal wth ths set of connectons moves the upper flange of the. Ths causes the lower flange of the to smultaneously move (due to the spacer rods between the flanges), thereby movng the capllary of the wthn the equlbrum cell (see Fgure 4-). The challenge remaned to smultaneously move the 36 SS dowel wth the capllary of the. Ths s acheved by usng two 36 SS gude rods of 2 mm dameter and 200 mm length to attach the flange on whch the s mounted to another 36 SS flange (0 mm dameter and 5 mm thckness) where the 36 SS dowel s mounted (drectly below the equlbrum cell). Hence, when the capllary of the moves wthn the equlbrum cell, the 36 SS dowel moves n the same drecton thereby mantanng a constant volume wthn the equlbrum cell. The 36 SS dowel enters the equlbrum cell va a 6 mm dameter hole wth M6 threads and 2 mm ptch from the bottom flange of the equlbrum cell. The method of sealng s the same to that of the capllary (explaned above). 4.3 Method of Agtaton wthn the Equlbrum Cell Agtaton wthn the equlbrum cell promotes the establshment of thermodynamc equlbrum n a shorter tme. The most common method of agtaton used by researchers (as dscussed n Chapter 2) makes use of a magnetc strrer drven by a magnet va a motor. Usually the magnetc strrer s placed wthn the equlbrum cell and s agtated from the bottom of the cell. Ths same concept s employed n ths study. However, snce the space below the equlbrum cell s already utlzed for the metallc dowel arrangement for the samplng mechansm, an alternate postonng for the magnet and motor must be found. Ths s acheved by mountng a bracket for the motor on the bottom 36 SS flange of the equlbrum cell to support the motor. The motor s postoned such that t s always above the lqud level of the bath when the cell s mmersed nto the lqud bath. The magnet for strrng s postoned at the sde of the equlbrum cell and lnked to the motor by a pulley mechansm usng a stanless steel chan to prevent slppage. The motor, drven by a DC power supply, allows the magnetc strrer wthn the equlbrum cell to rotate near the bottom of the equlbrum cell. A schematc of the assembly set-up s shown n Fgure

115 CHAPTER 4 EQUIPMENT DESCRIPTION Fgure 4-: Schematc of the equlbrum cell assembly. A: turn-dal; B: ; C: motor for strrer; D: equlbrum cell; E: strrer assembly; F: magnetc strrer; G: metallc dowel. 79

116 CHAPTER 4 EQUIPMENT DESCRIPTION When compared to conventonal strrng at the bottom of the equlbrum cell, the proposed arrangement of strrng provdes effcent strrng and dd not seem to have an adverse effect on the thermodynamc equlbrum tme. From expermental observatons, an average of 40 mnutes s requred for the system to reach thermodynamc equlbrum. A system s sad to be at thermodynamc equlbrum when the system temperature and pressure are constant wthn expermental uncertantes for at least 5 mnutes and the vapour and lqud samples wthdrawn wth the for at least 5 samples are constant wthn expermental uncertantes. 4.4 Isothermal Envronment for the Equlbrum Cell Gas (e.g. ar and ntrogen) and lqud (e.g. water and ol) baths are the two most common thermal envronments used by researchers (as dscussed n Chapter 2). Lqud baths are favoured as t avods the long tmes requred for thermal stablty when compared to gas baths. The bath used n ths study s custom-made wth the followng dmensons: 545 mm length, 340 mm wdth and 280 mm depth for the exteror cover and 485 mm length, 300 mm wdth and 260 mm depth for the nteror lnng. The exteror cover s made from 0.8 mm galvanzed steel and the nteror lnng made from 304 type stanless steel. Fberfrax s used as the nsulaton materal between the nteror lnng and the exteror cover of the bath snce t offers hgh temperature stablty and low thermal conductvty (Slumpys). The bath s custom-made specfcally for the depth n order to cater for the complete submerson of the equlbrum cell nto the lqud of the bath. Snce the expermental work carred out n ths study was to be done at hgh temperatures, slcone ol s chosen as the heatng medum for the thermal envronment. Slcon ol (SI-044) s a waterclear slcone flud wth a wde vscosty range. Ths would thus enable observaton durng experments. Other mportant features of slcone ol nclude: lttle change n physcal propertes over a wde temperature range, the flud can be used from 233 to 553 K, t has a low surface tenson so the flud wets clean surfaces and t also has low toxcty (Power Chemcal Corporaton). In order to mmerse the equlbrum cell nto the ol, the equlbrum cell assembly s held at a fxed poston on an ron framework and a mechancal jack s used to lft the ol bath. The ron framework s also used as a gude for the ol bath n order to prevent t from fallng over. Removng the cell from the ol bath s accomplshed by smply usng the mechancal jack to lower the ol bath. Photograph 4-3 shows the ron framework and the two postons of the ol bath. 80

117 CHAPTER 4 EQUIPMENT DESCRIPTION (a) (b) Photograph 4-3: The ron framework for the ol bath and fxed poston of the equlbrum cell wth the mechancal jack used to (a) lower the ol bath and (b) to rase the ol bath. In order to mnmze heat leaks and conductve paths, the equlbrum cell s mmersed wthn the ol bath such that at least 40 mm of lqud s above the upper 36 SS flange of the equlbrum cell. Snce the top of the ol bath could not be covered wth a ld, odd peces of galvanzed steel were wrapped n fberfrax and alumnum fol and carefully placed on top of the ol bath to form a coverld for the ol bath to help mnmze heat losses to the envronment. However for hgher temperatures, these provsons alone dd not prove to be suffcent. Ths was evdent from the temperature of the upper 36 SS flange of the equlbrum cell beng approxmately 0.7 K lower than the temperature of the lower 36 SS flange of the equlbrum cell for a temperature settng of 373 K. To overcome ths, a 6 mm dameter and 30 mm hole s drlled nto the upper 36 SS flange of the equlbrum cell to accommodate, a 3 mm dameter and 90 mm length wth a 90 o bend 70 mm from the tp, heater cartrdge wth 00 W power ratng. The heater cartrdge s powered by an ACDC kva voltage regulator model TDGC2. Another 6 mm dameter and 30 mm hole s drlled nto the upper 36 SS flange of the equlbrum cell to accommodate a WIKA model REB Pt00 wth class A ceramc bulb type sensor temperature probe, of / 8 nch dameter and 40 mm length. The temperature readng of ths probe s controlled by a Shnko ACS 3A dgtal ndcatng controller. The temperature probe s calbrated usng the WIKA CTB 900 temperature calbraton unt. The precson of the temperature probe s wthn 0.04 K error for a temperature range of 303 to 465 K. The calbraton graph s presented n Appendx C as Fgures C-9 and C-0. Ths arrangement compensates for heat losses to the envronment and conductve paths (parts of the cell assembly that protrude out of the ol bath). 8

118 CHAPTER 4 EQUIPMENT DESCRIPTION 4.5 Temperature and Pressure Measurement 4.5. Temperature Measurement The bath temperature s controlled usng a Polyscence model 732 programmable temperature controller capable of mantanng temperature stablty to wthn 0.02 K. Statstcally, ths mples a standard devaton of 0.0 K. The temperature measurement of the equlbrum cell s taken va the temperature measurement of the two 36 SS flanges that encased the equlbrum cell. A hole of 6 mm dameter and 30 mm depth s drlled nto each of the 36 SS flanges to accommodate for the temperature measurement. Two WIKA model REB Pt00 wth class A ceramc bulb type sensor temperature probes, one of / 8 nch dameter and 270 mm length wth a 90 o bend 70 mm from the tp, s used for the lower 36 SS flange and the other of / 8 nch dameter and 90 mm length wth a 90 o bend 70 mm from the tp, s used for the upper 36 SS flange. The temperature probes are connected to a 34970A Aglent data acquston unt through whch the temperatures are read and logged va a computer. All the temperature probes are calbrated usng the WIKA CTB 900 temperature calbraton unt. The overall (calbraton and repeatablty) precson of the temperature probes for the upper and lower 36 SS flanges of the equlbrum cell are wthn 0.05 K error for a temperature range of 298 to 355 K and 0.07 K error for a temperature range of 354 to 465 K. The calbraton graphs are presented n Appendx C as Fgures C- to C Pressure Measurement To obtan the pressure readngs, two pressure transmtters are used for greater precson as opposed to one. For sub-atmospherc pressure readngs, a 0 00 kpa absolute WIKA model P-0 pressure transmtter s used, whlst for moderate pressure readngs, a kpa absolute WIKA model P- 0 pressure transmtter s used. The pressure transmtters are connected to the equlbrum cell by a sngle entry pont va the upper 36 SS flange usng / 8 nch OD stanless steel ppng and connected to each other by usng a stanless steel T-pece. Two ¼ nch stanless steel ball valves are used to manpulate whether one or both of the pressure transmtters would read the pressure wthn the equlbrum cell. To prevent damage to the low pressure transmtter, the stanless steel ball valve that leads to the low pressure transmtter s closed when the pressure wthn the equlbrum cell s hgher than atmospherc pressure. To avod temperature dsturbances on the pressure readngs, both the low and hgh pressure transmtters are kept at a constant temperature of 33 K. Ths s acheved by encasng each pressure 82

119 CHAPTER 4 EQUIPMENT DESCRIPTION transmtter wthn separate alumnum blocks that are each heated wth two 6 mm dameter and 36 mm length 00 W heater cartrdges, powered by an ACDC kva voltage regulator model TDGC2. The temperature n each alumnum block s measured wth a 3 mm dameter and 20 mm length class A, 3-wre Pt 00 smplex 36 SS temperature probe and controlled by a Shnko ACS 3A dgtal ndcatng controller. The temperature probes are calbrated usng the WIKA CTB 900 temperature calbraton unt. The low pressure transmtter s calbrated usng the WIKA CPH 6000 pressure calbraton unt wth a WIKA CCP 30 hand test pump and a 0 bar absolute WIKA CPT 6000 standard pressure transmtter. The moderate pressure transmtter s nternally calbrated by measurng the vapour pressure of ethanol and comparng t to lterature (Red et al., 988). The ethanol lterature vapour pressure of Red et al. (988) also serves as verfcaton for the low pressure transmtter calbraton. The pressure transmtters are also connected to the same 34970A Aglent data acquston unt as the temperature probes for the equlbrum cell through whch the pressures are read and logged va a computer. The precson for the temperature probes of the low and moderate pressure transmtter alumnum blocks are wthn 0.02 K error and 0.0 K error respectvely for a temperature range of 298 to 37 K. The overall (calbraton and repeatablty) precson for the low pressure transmtter was wthn 0.02 kpa error for a pressure range of 5 to 99 kpa and that for the hgh pressure transmtter was wthn 0.9 kpa error for a pressure range of 97 to 33 kpa. The calbraton graphs are presented n Appendx C from Fgures C-25 to C Composton Analyss The equlbrum phase samples n ths study are analyzed by gas chromatography usng a Shmadzu 204 gas chromatograph (GC) whch s ftted wth a thermal conductvty detector (TCD). A 0.32 mm ID, 30 m length and 0.25 μm flm thckness crosslnked 5 % PH ME slcone Hewlett Packard 5 (HP5) capllary column s used for the analyss wth helum as the carrer gas. A TCD s used to detect the presence of water as an mpurty. The GC Solutons software package s used to convert the output sgnal from the GC to a peak area sgnal and perform ntegraton. The calbraton of the TCD s then used to determne the phase composton of the samples. 83

120 CHAPTER 4 EQUIPMENT DESCRIPTION A sngle s used to sample vapour and lqud equlbrum phases. The contans a dfferental screw that s used to adjust the path of the stem, closng the end of the capllary. Ths path controls the pressure drop at the capllary ext and hence the amount of sample wthdrawn n a gven openng tme, montored by a Crouzet TOP 948 electronc tmer. A 6 mm dameter and 42 mm length heater cartrdge of 200 W power ratng s used to heat the expanson chamber of the. Ths s done to completely vapourse the lqud samples rapdly for good chromatographc analyss. The heater cartrdge n the expanson chamber of the s heated by use of an ACDC kva voltage regulator model TDGC2. The temperature wthn the expanson chamber s measured wth a.5 mm by 2 mm class A, 3-wre Pt 00 surface element and controlled by a Shnko ACS 3A dgtal ndcatng controller. The surface element s calbrated usng the WIKA CTB 900 temperature calbraton unt. The precson of the surface element s wthn 0.04 K error for a temperature range of 330 to 465 K. The calbraton graph s presented n Appendx C as Fgures C-5 and C-6. The s connected to the GC va a 6-port GC samplng valve and / 6 nch OD stanless steel lnes. Ths 6-port valve s the same type used by Ramjugernath (2000) as dscussed n Chapter 2. The 6- port GC samplng valve s manufactured by Shmadzu to wthstand hgh temperatures and pressures. The 6-port GC samplng valve enables the wthdrawn sample to be swept by the carrer gas and taken to the GC for analyss. Ths allows the calbraton procedure of the GC to be carred out separately thus preventng all the / 6 nch OD stanless steel lnes from becomng contamnated. The 6-port GC samplng valve s also necessary to carry out samplng for sub-atmospherc measurements. Ths s necessary snce for sub-atmospherc pressures wthn the equlbrum cell, samples cannot be wthdrawn wth the unless the pressure n the sample crcut s lower (close to absolute vacuum) than the pressure n the equlbrum cell. Thus to enable the vacuum n the sample crcut, the 6-port GC samplng valve s used n connecton wth the vacuum pump. However durng tral runs of ths set-up, the GC dsplayed a peak wth an unusually large talng effect when the 6-port GC samplng valve was swtched. Ths was most probably due to nsuffcent sealng n the for sub-atmospherc operaton. Ths could not be corrected tmeously for the study and hence no sub-atmospherc vapour-lqud equlbrum measurements were carred out. Fgure 4-2 shows the two postons of the GC samplng valve. Poston A s known as the flushng mode, where the / 6 nch stanless steel lnes and the GC samplng valve are flushed from any contamnants by vacuum usng a two-stage Edwards RV3 vacuum pump. The vacuum created n poston A also would have enabled samplng durng low pressure measurements. It s also used when GC calbratons are carred out. Poston B s known as the samplng mode, where the sample 84

121 CHAPTER 4 EQUIPMENT DESCRIPTION that s wthdrawn from the equlbrum cell by the s swept by the carrer gas to the GC. The expermental procedures are explaned n detal n Chapter 5. (a) (b) Fgure 4-2: Postons of the GC samplng valve durng operaton for (a) flushng and (b) samplng. Partal condensaton of the samples wthn these lnes results n an ncorrect determnaton of the sample composton. Hence n order to prevent ths, nchrome wre n an nsulaton sleeve s carefully wrapped around these lnes to avod any cold ponts. The nchrome wre s powered by an ACDC kva voltage regulator model TDGC2. The temperature of the stanless steel lnes are measured wth a 3 mm dameter and 20 mm length class A, 3-wre Pt 00 smplex 36 SS temperature probe and controlled by a Shnko ACS 3A dgtal ndcatng controller. The temperature probes are calbrated usng the WIKA CTB 900 temperature calbraton unt and the temperature of the lne s controlled by a Shnko ACS 3A dgtal ndcatng controller. To ensure that there s no partal condensaton wthn the GC samplng valve, the valve s mounted onto an alumnum block that s heated usng two 6 mm dameter and 36 mm length 00 W heater cartrdges, powered by an ACDC kva voltage regulator model TDGC2. The temperature of the alumnum block s measured wth a 3 mm dameter and 20 mm length class A, 3-wre Pt 00 smplex 36 SS temperature probe and controlled by a Shnko ACS 3A dgtal ndcatng controller. 85

122 CHAPTER 4 EQUIPMENT DESCRIPTION 4.7 Data Loggng The temperature of the upper and lower 36 SS flanges of the equlbrum cell and the readngs from the pressure transmtters are all logged usng the 34970A Aglent data acquston unt. The software allows the user to log the data contnuously for a specfed tme nterval between each data pont, e.g. the data can be logged every 2 seconds for 00 data ponts. Once the data has been logged and stored, t can be easly exported to a Mcrosoft Excel spreadsheet. The GC Solutons software s used to convert the output sgnal from the GC to a peak area sgnal and perform ntegraton. The calbraton of the GC TCD s then used to determne the phase composton of the samples. The user-nterface of the 34970A Aglent data acquston unt and GC Solutons software are shown n Appendx D. 4.8 Degassng Apparatus The vacuum dstllaton method of Van Ness and Abbott (978) s employed n ths study. The method made use of bolng the lqud to be degassed n a MRC heatng mantle under vacuum followed by dstllaton wth a Vgreux fractonatng column. The dstllate s then passed through a total condenser where the dstllate s returned to the bolng flask, whle the hghly volatle components (or dssolved gases) are drawn through a fne capllary after escapng the total condenser. The pressure of the degassng apparatus s montored wth a stanless steel vacuum pressure gauge nserted n the vacuum tubng that leads to the apparatus. The total condenser used n ths study makes use of a spral col and jacket and s shown schematcally n Fgure 4-3 (a). The acton of bolng s not usually a bubblng process but rather one that occurs by surface evaporaton (Van Ness and Abbott, 978). The Vgreux fractonatng column asssts n separatng the dssolved gases from the lqud by usng a condensaton-vapoursaton cycle. Accordng to Van Ness and Abbott (978), when a flask contanng a certan thoroughly degassed lqud s rapdly nverted, a sharp metallc clck s heard that presumably results from a sudden collapse of trapped vapour under the lqud head. However, Van Ness and Abbott (978) also menton that a postve result from a clck test s evdently suffcent but not necessary evdence of thorough degassng. Fgure 4-7 (b) shows the schematc of the degassng apparatus used n ths study. 86

123 CHAPTER 4 EQUIPMENT DESCRIPTION The bolng flask, Vgreux fractonatng column, total condenser and the fttng for the fne capllary are all constructed of glassware, made by a glassblower Mr. P. Seglng, based n Durban, South Afrca. Ethanol s used as the coolng medum through the condenser, where a Polyscence KR80A chller s used to cool the temperature of the ethanol n a lqud bath. The temperature of the ethanol s mantaned as low as 253 K by usng a Polyscence model PN7306A2E temperature controller. The temperature controller also conssts of a lqud pump and s thus used to crculate the ethanol through the total condenser. (a) (b) Fgure 4-3: Schematc of the (a) total condenser and (b) the degassng unt assembly. A: fne capllary tube to vacuum; B: fttng for ar vent; C: total condenser; D: Vgreux fractonatng column; E: bolng flask. 4.9 Compresson Devce for Cell Loadng 87

124 CHAPTER 4 EQUIPMENT DESCRIPTION The equlbrum cell can be ntally charged by makng use of vacuum and the effect of gravty. However durng bnary phase equlbrum measurements, each progressve data pont s obtaned by the addton of the degassed lquds for one of the components. The drvng force for the method of addton s pressure. Hence, a compresson devce s needed to carefully add more of the degassed lqud nto the cell. The compresson devce used n ths study s constructed from 36 SS. The man body of the compresson devce has an OD of 40 mm, ID of 25 mm and length of 35 mm. The pston used to compress the lqud s also made of 36 SS wth a dameter of 25 mm and length of 33 mm. Therefore when the pston s fully depressed, the nternal volume of the compresson devce s approxmately 50. The pston s attached to a shaft of 260 mm length wth M6 threads and 2 mm ptch. To ndcate the poston of the pston wthn the compresson devce, a stanless steel rod of 3 mm dameter and 00 mm length s welded onto the pston. Two 36 SS spacer rods of 0 mm dameter and 00 mm length are used to connect the man body of the compresson devce to a turndal. The shaft passes through the turn-dal and contans a slot where a pn s ftted to act as a gude mechansm to prevent msalgnment of the arrangement. Each end of the man body of the compresson devce contans a cover-ld that s attached to the man body of the compresson devce by 6 hgh tensle, 8 mm steel caphead screws. Each cover-ld contans an O-rng to provde an excellent seal. The pston also contans grooves for an O-rng at each end to provde a tght seal. The materal of the O-rng s dependent on the nature of chemcal used. For alcohols, ketones, esters and ethers, EPDM O-rngs are used whlst perfluoroelastomer O- rngs are used for alkanes, alkenes and ntrles as t has good compatblty wth a wder range of chemcal functonal groups. A / 8 nch stanless steel needle valve s attached to one of the coverlds va an 8 mm dameter hole to control the entry and ext flow of the degassed lqud. The coverld and pston are shown n Photograph 4-4. Fgure 4-4 shows a schematc of the compresson devce. To ensure that the pressure wthn the compresson devce s hgher than the pressure wthn the equlbrum cell, a stanless steel gauge pressure (- to 25 bar) s nserted nto the feed lne of the equlbrum cell. The compresson devce s connected to the equlbrum cell va a three-way stanless steel valve, wth the feed lne beng the common lne. The thrd connecton of the threeway valve leads to the vacuum pump. The procedure for chargng the equlbrum cell wth the compresson devce s explaned n detal n Chapter 5. 88

125 CHAPTER 4 EQUIPMENT DESCRIPTION (a) Photograph 4-4: The compresson devce (a) cover-ld and (b) pston assembly. (b) Fgure 4-4: Schematc of the compresson devce. A: stanless steel needle valve; B: cell body of the compresson devce; C: pston; D: level ndcator for pston; E: turn-dal; F: shaft. 4.0 Safety Features The process of carryng out expermental work n a laboratory envronment necesstates the practce of safety precautons. Most safety precautons are consdered n the desgn of an expermental apparatus. For ths study, the followng safety precautons were consdered: 89

126 CHAPTER 4 EQUIPMENT DESCRIPTION The desgn calculatons were done consderng a +00 % over desgn safety factor. Examples of ths nclude: wall thckness of the equlbrum cell, wall thckness of the auxlary apparatus, etc. A safety relef valve s nstalled on the lne before the pressure transmtters to prevent damage. Furthermore, the pressure transmtters had a 50 % over-pressure safety feature. A safety relef valve s also nstalled n the transfer lne where the carrer gas flows from the GC to the GC samplng valve, to prevent a sudden ncrease of pressure nto the GC. The relef valve s strategcally placed n ths poston to avod any dead volume that would result when the sample s taken from the and sent to the GC. Any dead volume would necessarly lead to an ncorrect determnaton of the composton as they can accumulate contamnates. The equlbrum cell and the degassng apparatus both made use of a sngle Edwards RV3 vacuum pump. To prevent vapours from corrodng the vacuum pump, a cold trap s used before the vacuum tubng entered the vacuum pump. The cold trap made use of lqud ntrogen to condense and trap the vapours before enterng the vacuum pump. The lne that contaned the exhaust vapours of the vacuum pump are sent to the fume hood. The exhaust fans wthn the laboratory are swtched on at all tmes. A Perspex sheld s placed n front of the degassng apparatus as a safety precauton n the event of an exploson. Ths ensures that the shards of glassware would not cause njury. The materal safety data sheets for the chemcal used are made vsble near the equpment. Snce hgh temperature systems are nvestgated n ths study, thermal gloves are worn to open the feed lne to the equlbrum cell. All the Shnko ACS 3A dgtal ndcatng controllers are mounted wthn closed boxes such that only the dsplay faces of the controllers could be vewed. Ths s done to prevent any lqud (for example from an accdental spll) from enterng the controllers and causng damage. Standard safety precautons of a laboratory must be adhered to at all tmes wthn the laboratory. These nclude: use of a safety glasses and lab coat, use of correct latex gloves when handlng chemcals and closed shoes. 90

127 CHAPTER 4 EQUIPMENT DESCRIPTION 4. Overvew The desgn of the statc analytcal apparatus nvolved careful consderatons and calculatons were the man focus was to ensure relable phase equlbra measurements for small volumes of chemcals. Ths resulted n the development of a novel samplng technque that made use of 36 SS compensaton rod. Ths rod was used to mantan a constant nteror volume of the equlbrum cell when the moble was used durng samplng. Auxlary equpments were also desgned to complement the phase equlbra measurements. Ths ncluded the desgn of a degassng apparatus and compresson devce. Photograph 4-5 shows the expermental set-up n the laboratory. Photograph 4-5: Expermental set-up n the laboratory. A: ol bath; B: bath temperature controller; C: equlbrum cell assembly; D: pressure transmtters; E: 6-port gas chromatograph samplng valve; F: gas chromatograph; G: Shnko dgtal temperature controllers; H: data acquston unt. 9

128 CHAPTER 5 FRENCH SUMMARY Ce chaptre se concentre sur les procédures opératonnelles expérmentales relatves à l'apparel qu vent d être développé. L'apparellage de dégazage est tout d abord examné pour vérfer l absence de futes, pus l est nettoyé complètement à l'acétone et ms sous une presson d envron 5 kpa. De l'éthanol à 253 K est employé au nveau du condensateur pour rédure au maxmum les pertes de produt chmque par évaporaton. Un dégazage n-stu est préféré lors de l utlsaton de produts chmques coûteux. Un dspostf de compresson a été conçu pour réalser le transfert du produt chmque dans la cellule d'équlbre en vue des mesures d'équlbres «lqude-vapeur» (ELV). Le dspostf de compresson est nettoyé avec de l'éthanol et chargé sous vde par le produt chmque à étuder. Les sondes de la température sont étalonnées au moyen de l'unté d étalonnage de température : WIKA CTB 900. Le capteur basse presson est étalonné grâce à l'unté d étalonnage de presson : WIKA CPH 6000 assocée à une presse hydraulque manuelle : CCP 30 de WIKA et au transmetteur de presson standard absolu : 0-00 kpa WIKA CPT Le capteur de presson dt «moyenne presson» a été étalonné par référence à la presson de vapeur de l'éthanol en utlsant les valeurs des tensons de vapeur dsponbles dans Red et al. (988). Le détecteur du chromatographe en phase gazeuse est étalonné en utlsant la méthode du rapport des surfaces, comme décrt par Raal et Muhlbauer (998), et ce, pour tous les systèmes en équlbre "lqudevapeur" mesurés dans cette étude. La méthode de rapport des surfaces évte le problème de la nécessté d'être capable d'njecter des volumes constants et ben défns d'un composant pur. Par contre, c'est la méthode la méthode drecte d'njecton des composants purs qu a été employée pour l'étalonnage du détecteur du chromatographe en phase gazeuse dans le cas des systèmes nonmscbles étudés. Avant d entreprendre les mesures d'équlbres de phase, l'apparel est complètement testé à la recherche d éventuelles futes et nettoyé à l'éthanol. La cellule d'équlbre, garante sans fute et propre est alors chargée avec le premer composant. Des mesures de presson de vapeur peuvent alors être fates, après mmerson de la cellule d'équlbre dans son envronnement thermque, et ce, à chacune des températures désrées. Pour les mesures à hautes températures, un son tout partculer est prs pour compenser les pertes de chaleur par conducton et convecton dans l'envronnement drect en se servant de l'solaton et du chauffage électrque. Les mesures d ELV sont réalsées de proche en proche par de pettes addtons du deuxème composant va le dspostf de compresson. L'équlbre thermo-dynamque est consdéré comme établ quand les valeurs de la température et de la presson sont constantes dans les lmtes de l'erreur expérmentale durant 30 mnutes. Le chauffage électrque de la lgne de transfert entre la cellule et le chromatographe est actvé pour évter tout rsque de condensaton 92

129 CHAPTER 5 FRENCH SUMMARY partelle. Au mons 5 échantllons de chaque phase sont alors prélevés avec le ROLSI moble et envoyés au chromatographe en phase gazeuse pour analyse afn de tester la répétablté des résultats compostonnels et estmer leur dsperson. Des mesures d'équlbre (ELL) «lqude-lqude» de bnares sont réalsées après pressursaton à 350 kpa par de l'azote. Le procédé pour des mesures d ELL est semblable aux mesures d ELV. Pour des mesures des systèmes bnares en équlbre «lqude-lqude-vapeur» (ELLV), la régon à 3 phases est premèrement détermnée comme pour les mesures ELL de bnares pus les régons à deux phases. 93

130 CHAPTER 5 EXPERIMENTAL PROCEDURE 5 CHAPTER FIVE EXPERIMENTAL PROCEDURE In order to successfully carry out expermental measurements, t s mportant that the apparatus used be properly operated and calbrated. Ths s to ensure that varables such as temperature, pressure and composton are accurately measured. Ths chapter thus focuses on the followng sectons: Preparaton and operaton of the degassng apparatus Preparaton and operaton of the compresson devce Preparaton of the phase equlbra apparatus Calbraton procedure for the temperature probes, pressure transmtters and the gas chromatograph (GC) detector Operatng procedure of the phase equlbra apparatus for n-stu degassng, vapour pressure, vapour-lqud equlbrum (VLE), lqud-lqud equlbrum (LLE) and vapourlqud-lqud equlbrum (VLLE) measurements. Ths chapter frst hghlghts the preparaton and operaton of the degassng apparatus and compresson devce as these equpment are used pror to undertakng phase equlbra measurements. Emphass s also placed on the methods of GC detector calbraton and phase samplng. The chapter also shows the feasblty of the apparatus by notng the small volume of chemcal utlzed n each procedure. A schematc of the entre apparatus s presented n Appendx E. 94

131 CHAPTER 5 EXPERIMENTAL PROCEDURE 5. Degassng Apparatus 5.. Preparaton The vacuum tubng from the degassng apparatus to the Edwards RV3 vacuum pump was frstly checked for any leaks. Ths nvolved drawng a vacuum wthn the degassng unt and solatng the degassng unt overnght. If a sgnfcant ncrease n pressure was observed, other than that of room temperature effects, hgh vacuum grease was appled to ground glass jonts suspected of leaks. Polytetrafluoroethylene (PTFE) tape was used on the stanless steel ppe jonts that were suspected of leakng Cleanng of the Degassng Apparatus Cleanng the degassng apparatus was mportant to remove traces of other chemcals wthn the apparatus. Before cleanng the degassng apparatus, the Polyscence KR80A chller was swtched on to cool the ethanol n the lqud bath used for the total condenser. The bath temperature controller was set at 253 K. The ethanol was crculated through the total condenser usng the bultn lqud pump of the temperature controller. When the temperature of the ethanol was mantaned at the set-pont (after approxmately three hours), cleanng of the degassng apparatus could then begn. Acetone was used as the cleanng solvent for the degassng apparatus. Approxmately 50 of acetone was ntroduced nto the bolng flask and the valve of the bolng flask was gently closed. Thereafter the bolng flask was postoned on the heatng mantle and carefully nserted nto the recever end of the Vgreux fractonatng column asssted wth a mechancal jack. Hgh vacuum grease was used to seal the ground glass jont of the bolng flask and the Vgreux fractonatng column. The valves of the degassng apparatus and vacuum pump ar-vent lnes were then closed. Snce a common vacuum pump was used for the entre apparatus, all valves for the vacuum tubes leadng to equpment other than the degassng apparatus, were closed. The valve for the vacuum tube that led to the degassng apparatus was opened. The glassware for the cold-trap was then cleaned wth acetone. A 2 lter nsulated flask, that was used as a vessel for the cold-trap flud (lqud ntrogen), was then flled wth lqud ntrogen and the glassware for the cold-trap carefully nserted nto the nsulated flask. 95

132 CHAPTER 5 EXPERIMENTAL PROCEDURE The vacuum pump was then swtched on and the pressure wthn the degassng unt was montored from the vacuum pressure gauge. When the pressure wthn the degassng apparatus stablzed wthn 5 kpa, the valve of the bolng flask was partally opened. The heat nput from the heatng mantle was not necessary as the evaporaton of the acetone at such low pressure occurred wthout any heat nput. When the evaporaton of the acetone wthn the degassng apparatus became vgorous, the valve of the vacuum tube that led to the degassng apparatus was partally closed to prevent excess vapours from escapng and enterng the vacuum pump. Snce the cleanng process occurs at very low pressure, the temperature wthn the degassng apparatus becomes qute low, resultng n the formaton of condensate on the outer glassware. Therefore, absorbent paper was placed around the bolng flask to absorb the condensate that formed on the outer glassware. A tme of approxmately 0 mnutes was allowed for the process of cleanng. Thereafter, the valve on the vacuum tube that led to the degassng apparatus was closed. The valve of the ar-vent lne for the vacuum pump was then partally opened before swtchng the vacuum pump off so that the ol wthn the vacuum pump would not be sucked nto the vacuum tubng. The valve of the ar-vent lne for the degassng apparatus was then slowly opened to release the vacuum wthn the degassng apparatus. A few mnutes were then allowed for the acetone to drp back nto the bolng flask. The bolng flask was then dsconnected from the Vgreux fractonatng column by frstly lowerng the poston of the heatng mantle wth the mechancal jack. The acetone n the bolng flask was then dscarded nto a waste bottle and the remanng acetone wthn the degassng apparatus was allowed to dry wth ar. The cleanng procedure was then repeated at least once to ensure the degassng apparatus was thoroughly cleaned Operatng Procedure of the Degassng Apparatus The steps followed n the cleanng procedure of the degassng apparatus were also used for the operatonal procedure. The preparaton of the coolant used for the condenser and the cold-trap are as outlned n Secton Approxmately 50 of the lqud to be degassed was placed nto a clean bolng flask and connected to the Vgreux fractonatng column wth the valve of the bolng flask closed. Hgh vacuum grease was used to seal the ground glass jont of the bolng flask and the Vgreux fractonatng column. The valves of the degassng apparatus and vacuum pump ar-vent lnes were then closed and the valve for the vacuum tube that led to the degassng apparatus was opened. The vacuum pump was then swtched on and the pressure wthn the degassng unt was montored from the vacuum gauge pressure. When the pressure wthn the degassng apparatus 96

133 CHAPTER 5 EXPERIMENTAL PROCEDURE stablzed wthn 5 kpa, the valve of the bolng flask was not opened as n the cleanng procedure but remaned closed for approxmately 5 mnutes to ensure that the degassng apparatus was free of any acetone resdue followng the cleanng procedure. Ths allowed any acetone resdue to be vapoursed from the degassng apparatus. Once ths was done, the valve of the bolng flask was then partally opened. In order to mnmze loss of the degassed chemcal due to evaporaton, the valve of the bolng flask and that of the vacuum tube that led to the degassng apparatus were partally opened nstead of beng fully opened. Furthermore a total condenser was used wth the temperature of the coolng flud kept at 253 K. The estmated chemcal loss due to evaporaton was approxmately (approxmately 6 % of total volume), whch s an acceptable loss. Expensve chemcals were degassed n-stu (outlned n Secton ). The heat nput from the heatng mantle was dependent on the nature of the chemcal degassed. For chemcals such as methanol, ethanol, hexane, 2-methoxy-2-methylpropane, ethyl acetate, butan-2- one and acetontrle used n ths study, no heat nput from the heatng mantle was necessary as the evaporaton of the chemcals occurred wthout any heat nput. The formaton of condensate on the outer glassware was also notced for the degassng of all above mentoned chemcals. However, for hgher bolng chemcals such as heptane that was used n ths study, the heatng mantle was kept at a constant temperature of 303 K. Each chemcal was allowed to degas for approxmately 4 hours. Once ths tme had elapsed, the valve of the bolng flask was then closed. Thereafter, the valve for the vacuum tube that led to the degassng apparatus was closed. The valve on the ar-vent lne for the vacuum pump was then partally opened before swtchng the vacuum pump off. The valve on the ar-vent lne to the degassng apparatus was then slowly opened to release the vacuum wthn the degassng apparatus. The bolng flask was then dsconnected from the Vgreux fractonatng column by frstly lowerng the poston of the heatng mantle wth the mechancal jack. The clck test of Van Ness and Abbott (978) was then done to check f suffcent degassng was acheved. Ths nvolved rapdly nvertng the bolng flask to hear a for a metallc clck sound that presumably results from a sudden collapse of trapped vapour under the lqud head. Accordng to Van Ness and Abbott (978), the metallc clck sound for some chemcals can only be heard when the temperature of the degassed lqud s suffcently low. However for all the chemcals used n ths study, the clck test of Van Ness and Abbott (978) was postve when tested mmedately after degassng. 97

134 CHAPTER 5 EXPERIMENTAL PROCEDURE 5.2 Compresson Devce 5.2. Preparaton and Cleanng The compresson devce was frstly checked for any leaks. Hgh pressure ntrogen from a cylnder was charged nto the compresson devce to a pressure of 3000 kpa. The devce was then left overnght to montor any decrease n the pressure readng. If a sgnfcant decrease n pressure was observed, other than that of room temperature effects, a soapy soluton was appled to jonts suspected of leakng. A leak at a jont was confrmed by the presence of bubbles. When leaks were detected at the connecton pont of the cover-ld wth the cell body, the cover-ld was opened and the O-rngs were examned and replaced f they were found to be damaged. When a leak was detected at the connecton pont of the needle valve to the cover-ld, the needle valve was removed and the threaded hole n the cover-ld was cleaned. The needle valve was then replaced and sealed usng a hgh strength thread-locker. The connecton lnes to the compresson devce were also examned usng hgh pressure and a soapy soluton. Where a leak was detected on these connecton ponts, PTFE tape was used on the ferrule of these connectons. Ethanol was used as the cleanng solvent for the compresson devce. The cover-ld at each end of the compresson devce was frstly removed. Ethanol was then flushed nto the cell body and needle valve of the compresson devce. The pston was also cleaned wth ethanol. Whlst dsassembled, the O-rngs of the cover-lds and the pston were also examned and replaced f they were found to be damaged. Compressed ar was then used to dry the compresson devce. The compresson devce was then reassembled and the pressure leak test as explaned above was carred out. Vacuum was then used for approxmately 30 mnutes to flash off any resdue ethanol from the compresson devce pror to use Chargng the Compresson Devce The compresson devce was charged wth the degassed lqud by makng use of gravty and vacuum. Fgure 5- shows the schematc of the set-up for chargng the compresson devce. The compresson devce s held n an uprght poston (as shown n Fgure 5-) by usng a laboratory stand and clamps. The compresson devce and the bolng flask were connected to a sngle stanless steel three-way valve by usng a / 8 nch stanless steel ppng. A specal fttng was made to connect the bolng flask to the / 8 nch stanless steel ppe. The stanless steel ppng that connected the compresson devce to the three-way valve was used as the common lne. The bolng flask, whch 98

135 CHAPTER 5 EXPERIMENTAL PROCEDURE contaned the degassed lqud, was nverted and then connected to the three-way valve. The bolng flask was held n an uprght poston by usng clamps and a laboratory stand. Before chargng the compresson devce wth the degassed lqud, all the connecton lnes were thoroughly cleaned wth ethanol and checked for leaks. To remove any ethanol resdue that was left behnd from cleanng, the compresson devce (n a fully depressed poston) together wth the connectng lne was opened to the vacuum pump va the three-way valve for approxmately 30 mnutes to evaporate the resdue ethanol. Ths procedure was also done for the connectng lne of the bolng flask and the three-way valve. The compresson devce, connectng lnes and valves were also heated wth a heatng gun durng the vacuum procedure to assst the dryng process. No actual analyss was done to ensure that all the resdue ethanol was removed as t was assumed that 30 mnutes wth vacuum and heat was suffcent to remove any resdual ethanol. The compresson devce was ensured to be n the fully depressed poston. Usng the arrangement as shown n Fgure 5- and wth the vacuum pump swtched on, the three-way valve was swtched to the vacuum lne untl the pressure wthn the compresson devce was as close as possble to absolute vacuum. When ths was acheved, the needle valve of the compresson devce was closed. The three-way valve was then swtched from the vacuum lne poston to the poston that leads to the bolng flask for a few seconds and then back to the vacuum lne poston. Ths was done several tmes to remove the ar that was present n the lne that connected the bolng flask to the compresson devce. Once t was assumed that no ar was present n ths connectng lne, the threeway valve was fnally postoned to the lne that leads to the bolng flask. The valve of the bolng flask was then carefully opened to allow the degassed lqud to flow nto the compresson devce. The needle valve of the compresson devce was then fully opened to receve the degassed lqud nto the compresson devce. Snce the pressure wthn the bolng flask and the compresson devce are as close as possble to absolute vacuum, the degassed lqud moves from the bolng flask to the compresson devce due to the effect of gravty and s rather slow. To speed up ths process, the bolng flask was gently heated wth a temperature gun to cause a pressure dfferental. Once the compresson devce was almost full wth approxmately 45 of degassed lqud, the valve of the bolng flask and the needle valve were closed. To ensure that no ar was present n the compresson devce, the three-way valve was swtched to the vacuum lne poston and the needle valve partally opened for a few seconds to dspel any ar that could have entered the compresson devce. 99

136 CHAPTER 5 EXPERIMENTAL PROCEDURE Fgure 5-: Schematc of the set-up for chargng the compresson devce. A: bolng flask wth degassed lqud; B: tube that leads to vacuum pump; C: three-way valve; D: needle valve; E: cell body of compresson devce. 5.3 Phase Equlbrum Apparatus 5.3. Preparaton Leak Detecton To detect for any leaks, the equlbrum cell was charged wth hgh pressure ntrogen at 500 kpa, then solated and left overnght to montor any decrease n the pressure readng. If a sgnfcant decrease n pressure was observed, other than that of room temperature effects, a soapy soluton was appled to jonts suspected of leakng. A leak at a jont was confrmed by the presence of bubbles. 00

137 CHAPTER 5 EXPERIMENTAL PROCEDURE All the connectng lnes to and from the equlbrum cell were also checked for leaks usng hgh pressure and a soapy soluton. If a leak was detected between the upper or lower 36 SS flange of the equlbrum cell, the assembly was dsmantled to examne the O-rngs wthn the equlbrum cell and were replaced f they were damaged. If leaks were detected on the connecton nut stuated on top of the upper 36 SS flange of the equlbrum cell or the connecton nut for the metallc dowel stuated below the lower 36 SS flange of the equlbrum cell, the O-rng was examned and replaced f damaged. If leaks were detected on the connecton ponts on the / 8 nch stanless steel lnes to and from the equlbrum cell, PTFE tape was used on the ferrule of these connectons. Leaks were also checked on the / 6 nch stanless steel samplng lnes that connected the to the 6- port gas chromatograph (GC) valve and the GC. Ths was acheved by swtchng the 6-port GC valve to the samplng poston and usng the GC carrer gas. The connectons n these lnes were then tested for leaks wth a soapy soluton. Any leaks found on these connectons were also prevented usng PTFE tape on the ferrule of these connectons Cleanng the Equlbrum Cell The equlbrum cell was always cleaned pror to undertakng any expermental measurements. Ethanol was used as the cleanng solvent. Intally, the / 8 nch stanless steel lnes that connected the equlbrum cell to the pressure transmtters were heated and mantaned at 373 K. It was also ensured the stanless steel ball valves connected on these lnes were opened to both the low and hgh pressure transmtters. The three-way valve of the feed lne to the equlbrum cell was swtched to the vacuum poston, where the common lne of ths three-way valve was the lne that led to the equlbrum cell. Ths caused the pressure wthn the equlbrum cell to decrease as close as possble to absolute vacuum (0.05 kpa). Once ths was acheved, the needle valve of the feed lne was then closed and the three-way valve was then swtched to the charge poston. Approxmately 5 of ethanol was then charged nto the equlbrum cell by usng a syrnge wth a fttng attached to the three-way valve and slowly openng the needle valve of the feed lne. When the equlbrum cell was charged, the needle valve of the feed lne was then closed. The temperature controller of the ol bath was then set to 323 K and the equlbrum cell was mmersed nto the ol bath by rasng the ol bath wth the mechancal jack. The magnetc strrer was then actvated. The equlbrum cell was left n ths condton for approxmately 30 mnutes for cleanng. Thereafter, the bath temperature controller was swtched off, the magnetc strrer was deactvated 0

138 CHAPTER 5 EXPERIMENTAL PROCEDURE and the ol bath was lowered wth the mechancal jack. The equlbrum cell was then left to cool for approxmately one hour. Once the equlbrum cell had cooled, the ethanol was draned from the equlbrum cell usng compressed ar to create a pressure dfferental. Ths was acheved by ensurng the three-way valve was swtched to the charge poston and connected to the compressed ar lne. Before the compressed ar was charged nto the equlbrum cell, t was ensured that the stanless steel valve for the low pressure transmtter was closed. The compressed ar was then charged nto the equlbrum cell by slowly openng the needle valve on the feed lne. The pressure wthn the equlbrum cell was montored wth the moderate pressure transmtter and a value of approxmately 3 bars was mantaned n the equlbrum cell. The needle valve for the dran lne on the equlbrum cell was then slowly opened and the ethanol was receved nto a beaker and dscarded nto a waste bottle. The compressed ar lne was then dsconnected from the apparatus and the entre cleanng procedure was repeated at least once to ensure that the equlbrum cell was thoroughly cleaned. Once the cleanng process was completed, the equlbrum cell was left open to the atmosphere va the needle valves on the feed and dran lnes to dry the resdue ethanol wthn the equlbrum cell. Occasonally, compressed ar was used to speed up the dryng process. To ensure trace amounts of the ethanol were removed, the equlbrum cell was evacuated wth the ad of the vacuum pump for approxmately 30 mnutes. Samples were taken from the equlbrum cell to the GC for analyss to ensure that there was no resdual ethanol present. The samplng lnes were also cleaned by heatng these lnes and mantanng the temperature at 473 K. When the temperature of these lnes was reached, the carrer gas (helum) was used to flush these lnes. The lnes were then evacuated for approxmately 30 mnutes wth the ad of the vacuum pump. The flushng and evacuaton procedure was repeated at least once to ensure the sample lnes dd not contan any trace amount of mpurtes. As a measure to check that the sample lnes dd not contan any trace mpurtes, the sample lnes were flushed wth the carrer gas and a sample was sent to the GC for analyss. If a peak was found to appear on the GC software, the entre cleanng process for the samplng lnes was repeated untl no such peaks for the trace mpurtes were found to appear on the GC chromatograph Calbraton Temperature Probe Calbraton 02

139 CHAPTER 5 EXPERIMENTAL PROCEDURE All the temperature probes used for ths study were calbrated usng the WIKA CTB 900 temperature calbraton unt. The calbraton unt makes use of slcone ol (SI 40) as the flud medum wthn the bath. The standard temperature probe for the WIKA CTB 900 temperature calbraton unt was calbrated by WIKA wth an accuracy of 0.02 K. The results of the calbraton are all presented n Appendx C, Fgures C- to C Pressure Transmtter Calbraton The 0 00 kpa absolute WIKA model P-0 pressure transmtter was used for readng subatmospherc pressure. Ths low pressure transmtter was calbrated usng the WIKA CPH 6000 pressure calbraton unt wth a WIKA CCP 30 hand test pump and 0 00 kpa absolute WIKA CPT 6000 standard pressure transmtter. The WIKA CPT 6000 standard pressure transmtter was calbrated by WIKA wth an accuracy of 0.02 kpa. The kpa absolute WIKA model P-0 pressure transmtter was used for readng moderate to hgh pressure. Ths hgh pressure transmtter was nternally calbrated usng the ethanol lterature vapour pressure of Red et al. (988). Ths was done to avod any tme lapse as the WIKA CPH 6000 hgh pressure calbraton unt wth a WIKA PCS 250 hand pump and kpa absolute WIKA CPT 6000 standard pressure transmtter was sent to the manufacturer for repars. When the unt was receved after repars, t stll dsplayed severe fluctuatons and thus could not be used wth confdence. Ths calbraton was only carred out after the temperature calbraton was done as the calbrated temperature readngs were needed to determne the lterature vapour pressure of Red et al. (988), whch was used as a standard. The certfed purty of ethanol as stated by the suppler s reported n Table 6- of Chapter 6 together wth GC tests and refractve ndex verfcatons. The ethanol was ntally degassed followng the procedure as outlned Secton 5..3 above and charged nto the equlbrum cell followng the procedure outlned n Secton Before chargng the equlbrum cell wth the degassed lqud from the bolng flask, the equlbrum cell and all the connecton lnes were thoroughly cleaned wth ethanol and checked for leaks. To remove any ethanol resdue that was left behnd from cleanng, the equlbrum cell and lnes were evacuated wth the ad of the vacuum pump va the three-way valve for approxmately 20 mnutes. Once the equlbrum cell was charged, the ol bath was then rased to mmerse the equlbrum cell nto the ol. Wth the degassed ethanol n the equlbrum cell, the temperature controller of the ol 03

140 CHAPTER 5 EXPERIMENTAL PROCEDURE bath was set to a desred value and tme was allowed for equlbrum to be reached wthn the equlbrum cell. Equlbrum wthn the equlbrum cell was deemed establshed when the temperature of the 36 SS flanges of the equlbrum cell and the pressure wthn the equlbrum cell remaned constant wthn expermental uncertanty. The 34970A Aglent data acquston unt was used to log the temperature and pressure readngs for 200 data ponts wth 2 s nterval between each data pont. Ths was done for dfferent temperature settngs on the ol bath temperature controller that ranged from 350 to 436 K. The ethanol lterature vapour pressure of Red et al. (988) was used as the standard pressure for the calbraton and also served as verfcaton for the low pressure transmtter calbraton. The results of the pressure calbraton are all presented n Appendx C, Fgures C-25 to C Gas Chromatograph Calbraton The equlbrum phase samples n ths study were analyzed by gas chromatography usng a Shmadzu 204 GC whch was ftted wth a thermal conductvty detector (TCD). A 0.32 mm ID, 30 m length and 0.25 μm flm thckness crosslnked 5 % PH ME slcone Hewlett Packard 5 (HP5) capllary column was used for the analyss wth helum as the carrer gas. The GC Solutons software package was used to convert the output sgnal from the GC to a peak area sgnal and perform ntegraton. The composton of the samples were then determned from the GC detector calbraton. The area rato method outlned by Raal and Mühlbauer (998) was used to perform the GC detector calbraton n ths study. The method made use of analyzng standards that were prepared gravmetrcally to cover the entre composton range. In general, the peak area obtaned from the ntegraton of the peak s proportonal to the number of moles that passes the detector of the GC: n = A F (5-) * where, s the number of moles of component, A s the peak area of component and s the proportonalty constant of component that s more commonly known as the response factor. The peak area s dependent on the volume of the sample njected nto the GC and ths volume njected s often not reproducble. Hence the response factor obtaned for the GC calbraton can have * 04

141 CHAPTER 5 EXPERIMENTAL PROCEDURE sgnfcant devatons, especally for small volumes of samples njected. Therefore, Raal and Mühlbauer (998) suggested the use of area ratos. In the case of a bnary system: n n 2 F A x * = * F = 2 A (5-2) 2 x2 where, subscrpts and 2 refer to the components and x s the mole fracton. To obtan the response factor rato ( / ) for the dlute regon of component, the area rato ( * / * ) was plotted aganst the mole fracton rato ( / ) for a composton range of 0 to of the mole fracton rato, where the response factor rato was equal to the slope of the plot. In smlar manner, the response factor rato ( / ) was obtaned for the dlute regon of component 2. The plots were also extrapolated through the orgn, snce no peak area should necessarly be observed wthout a sample beng njected. Accordng to Equaton (5-2), the response factor rato should necessarly be constant for a lnear plot of area rato aganst the mole fracton rato. If the lnearty exsts over the entre composton range, then / should equal to the nverse of / and vce versa. Ths was used as a check for the lnearty of the GC detector calbraton. The area rato method outlned by Raal and Mühlbauer (998) was used for the GC calbratons of all the phase equlbra measurements that were undertaken n ths study, except for systems that exhbted mmscblty. Lqud-lqud equlbrum (LLE) and vapour-lqud-lqud equlbrum (VLLE) (whch exhbt mmscblty) expermental measurements were undertaken for the hexane + acetontrle and methanol + heptane systems. For these systems, the drect GC detector calbraton method was used, where Equaton (5-) was used for each component nstead of Equaton (5-2). Before the GC detector calbratons were undertaken, the carrer gas lnes were examned for any leaks. The carrer gas pressure, njector temperature, oven temperature and the TCD temperature were then actvated. For each system studed n ths work, tral njectons were carred out on the GC to optmze the parameters for good peak areas and separaton (retenton tme) of the components. The njectons for the GC detector calbratons were made wth the Shmadzu 204 AOC-20 autosampler that used a good qualty 0 μl Dynatech SGE lqud syrnge. Care was taken to check for blockages, tghtness of the pston plunger and needle seal of the lqud syrnge. For each njecton, the syrnge was rnsed 5 tmes wth acetone (solvent) before a sample was taken and also rnsed 3 05

142 CHAPTER 5 EXPERIMENTAL PROCEDURE tmes wth the sample. Ths was to ensure that the mpurtes n the needle of the syrnge were removed. The syrnge was also flushed 4 tmes wth the sample to remove the entranment of ar bubbles n the syrnge. After the sample was njected nto the GC, the syrnge was rnsed a further 5 tmes wth acetone. The septum for the GC njector was replaced after every 00 njectons to avod errors that would result from leaks. The samples for the GC detector calbraton were prepared n 4 ml vals such that the vals were nearly full wth only a very small vapour space. Ths was done to ensure that the mxture n the sample val dd not evaporate and thus lead to an ncorrect composton. Furthermore, the sample vals were kept n cy water to prevent evaporaton before beng analyzed by the GC. By tral, t was found that 6 μl of the sample was suffcent to perform GC detector calbratons as ths was wthn the range of the volume sampled from the equlbrum cell by the. For each calbraton pont, at least 5 samples were njected untl the average absolute devaton for the peak area rato (or peak area for the drect calbraton) was wthn % error. The optmzed parameters for the GC, together wth the calbraton results are presented n Appendx C, Fgures C-25 to C-45. The response factor rato (or the response factor for drect calbraton) was determned usng lnear regresson. The accuracy of the mole fractons for each system studed s also presented n Appendx C, Table C Operatng Procedures for Phase Equlbrum Measurements In-Stu Degassng The method of n-stu degassng was only used for expensve chemcals to mnmze loss of the chemcal. Pror to n-stu degassng, the equlbrum cell and / 8 nch stanless steel feed lne were cleaned as outlned n Secton The / 8 nch stanless steel lnes that connected the equlbrum cell to the pressure transmtters were heated and mantaned at 373 K. It was also ensured the stanless steel ball valves connected on these lnes were opened to both the low and hgh pressure transmtters. The three-way valve on the feed lne to the equlbrum cell was swtched to the vacuum poston, where the common lne of ths three-way valve was the lne that led to the equlbrum cell. Ths caused the pressure wthn the equlbrum cell to decrease as close as possble to absolute vacuum. Once ths was acheved, the needle valve on the feed lne was then closed and the three-way valve was then swtched to the charge poston. Approxmately 8 of the chemcal to be degassed was then charged nto the equlbrum cell by usng a syrnge wth a fttng attached to the three-way valve and slowly openng the needle valve on the feed lne. When the equlbrum cell was charged, the needle valve on the feed lne was then closed. The temperature 06

143 CHAPTER 5 EXPERIMENTAL PROCEDURE controller of the ol bath was then set to 303 K and the equlbrum cell was mmersed nto the ol bath. The magnetc strrer was then actvated. The three-way valve was then swtched to the vacuum poston. Once the temperature wthn the ol bath had stablzed, the needle valve on the feed lne was then opened for approxmately 20 s to vacuum and then closed. After 3 mnutes the needle valve on the feed lne was agan opened to vacuum for approxmately 20 s and then closed. Ths process was repeated for approxmately hour. The clck test of Van Ness and Abbott (978) could not be performed for n-stu degassng to check f suffcent degassng was acheved. Alternatvely, the measurement of vapour pressure for the chemcal and comparson to lterature was performed as a check for thorough degassng. When a large devaton was observed between the vapour pressure of the degassed chemcal and that of lterature, the temperature of the ol bath was ncreased to 33 K and the degassng procedure repeated for a further 30 mnutes. At ths pont the devaton was wthn expermental error Vapour Pressure Measurement To undertake expermental vapour pressure measurement, the chemcal was ntally degassed followng the procedure as outlned n Secton Fgure 5-2 shows the schematc of the set-up for chargng the equlbrum cell wth the degassed lqud from the bolng flask. The bolng flask was nverted and connected to the stanless steel three-way valve by usng / 8 nch stanless steel ppng. A specal fttng was made to connect the bolng flask to the / 8 nch stanless steel ppe. The stanless steel ppng that connected the equlbrum cell to the three-way valve was used as the common lne. The bolng flask, whch contaned the degassed lqud, was nverted and then connected to the three-way valve. Before chargng the equlbrum cell wth the degassed lqud from the bolng flask, the equlbrum cell and all the connecton lnes were thoroughly cleaned wth ethanol and checked for leaks. To remove any ethanol resdue that was left behnd from cleanng, the equlbrum cell lnes were evacuated wth the ad of the vacuum pump va the three-way valve for approxmately 20 mnutes. Usng the arrangement as shown n Fgure 5-2 and wth the vacuum pump swtched on, the threeway valve was swtched to the vacuum poston untl the pressure wthn the equlbrum cell was as close as possble to absolute vacuum. When ths was acheved, the needle valve on the feed lne to the equlbrum cell was closed. The three-way valve was then alternated from the vacuum poston 07

144 CHAPTER 5 EXPERIMENTAL PROCEDURE to the poston that leads to the bolng flask for a few seconds and then back to the vacuum poston. Ths was done several tmes to remove the ar that was present n the lne that connected the bolng flask to the three-way valve. Once t was assumed that no ar was present n ths connectng lne (read from the pressure gauge), the three-way valve was fnally postoned to the lne that leads to the bolng flask. Fgure 5-2: Schematc of the set-up for chargng the equlbrum cell wth degassed lqud from the bolng flask. A: bolng flask wth degassed lqud; B: pressure gauge; C: three-way valve; D: lne that leads to the vacuum pump; E: common lne of three-way valve that leads to the equlbrum cell. The valve of the bolng flask was then carefully opened to allow the degassed lqud to flow to the equlbrum cell. The needle valve for the feed lne on the equlbrum cell was then fully opened to receve the degassed lqud nto the equlbrum cell. Snce the pressure wthn the bolng flask and the equlbrum cell are as close as possble to absolute vacuum, the degassed lqud moves from the bolng flask to the equlbrum cell due to the effect of gravty and s rather slow. To speed up ths process, the bolng flask was gently heated wth a temperature gun to cause a pressure dfferental. 08

145 CHAPTER 5 EXPERIMENTAL PROCEDURE The ol bath was then rased to mmerse the equlbrum cell nto the ol. Wth the degassed chemcal n the equlbrum cell, the temperature controller of the ol bath was set to a desred value and the system was left to allow for equlbrum to be reached wthn the equlbrum cell. Equlbrum wthn the equlbrum cell was deemed establshed when the temperature of the 36 SS flanges of the equlbrum cell and the pressure wthn the equlbrum cell dsplayed a mnmum change wth tme. The crteron used here was a constant temperature and pressure readng wthn 0.02 K and 0. kpa respectvely for 30 mnutes. The 34970A Aglent data acquston unt was used to log the temperature and pressure readngs for 200 data ponts wth 2 s nterval between each data pont. Ths was done for dfferent temperature settngs on the ol bath temperature controller Bnary Vapour-Lqud Equlbrum (VLE) Measurement Before bnary vapour-lqud equlbrum (VLE) measurements were undertaken, the equlbrum cell and samplng lnes were cleaned as outlned n Secton The two components were also thoroughly degassed wth the degassng apparatus as outlned n Secton 5. or n-stu degassng as outlned n Secton One of the components was then used to charge the compresson devce as outlned n Secton whst the other component was used to charge the equlbrum cell as outlned n Secton above wth only approxmately 4. In the case where an expensve chemcal was used, n-stu degassng was used for ths chemcal and thus the equlbrum cell was already charged wth ths component. Once the equlbrum cell was charged wth approxmately 4 of one component, the needle valve on the feed lne was closed and the compresson devce (charged wth the second component) was then ftted to the three-way valve of the equlbrum apparatus feed lne usng / 8 nch stanless steel ppng as shown n Fgure 5-3. The stanless steel ppng was ntally cleaned wth ethanol to remove any contamnants and the resdue ethanol was removed va evaporaton wth the ad of vacuum and heat. The three-way valve was then swtched to the vacuum poston to remove any ar present n the feed lne. Thereafter, the three-way valve was swtched to the charge poston for a few seconds before returnng to the vacuum poston. Ths process was repeated untl all the ar was removed from the stanless steel lne that connected the compresson devce to the three-way valve on the feed lne. Once ths was acheved, the thee-way valve was then swtched to the charge poston and the 09

146 CHAPTER 5 EXPERIMENTAL PROCEDURE pressure gauge was used to check that the vacuum pressure n the lne was as close as possble to absolute vacuum. If leaks were observed, all the fttngs were then checked to elmnate the leaks. Fgure 5-3: Schematc of the set-up for chargng the second component nto the equlbrum cell. A: pressure gauge; B: three-way valve; C: lne that leads to vacuum pump; D: common lne of three-way valve that leads to equlbrum cell; E: needle valve of compresson devce; F: cell body of compresson devce. The turn-dal on the compresson devce was operated to compress the second lqud component wthn the compresson devce untl the frst nstance of resstance was felt. The needle valve on the compresson devce was then slowly opened to fll the stanless steel lnes leadng to the needle valve on the feed lne of the equlbrum cell wth the second component lqud. The turn-dal on the compresson devce was then operated agan to compress the lqud such that ts pressure was at least.5 tmes hgher than that of the equlbrum cell, where the pressure gauge was used to check the pressure wthn the stanless steel lnes. The needle valve on the feed lne was then partally 0

147 CHAPTER 5 EXPERIMENTAL PROCEDURE opened to allow a small amount of the second component lqud nto the equlbrum cell before beng closed. The capllary was then postoned n the vapour phase of the equlbrum cell n preparaton for samplng usng the turn-dal on the equlbrum apparatus. The magnetc strrer was then actvated. The ol bath was then rased to mmerse the equlbrum cell nto the ol. The temperature controller of the ol bath was set to the sotherm value and the system was left to equlbrate wthn the equlbrum cell. The heater cartrdge n the upper 36 SS flange of the equlbrum cell was also actvated to account for heat losses to the envronment and conductve paths. The 34970A Aglent data acquston unt was then used to log the temperature and pressure readngs. Equlbrum wthn the equlbrum cell was deemed establshed when the temperature of the 36 SS flanges of the equlbrum cell and the pressure wthn the equlbrum cell dsplayed mnmum change wth tme. As wth the vapour pressure measurements, the crteron used here was a constant temperature and pressure readng wthn 0.02 K and 0. kpa respectvely for 30 mnutes. Whle equlbrum was beng establshed, the expanson chamber, samplng lnes and the alumnum block for the 6-port GC samplng valve were heated and mantaned at a temperature that was 5 K hgher than the normal bolng temperature of the less volatle component for the bnary system. The 6-port GC samplng valve was also swtched to the flushng mode. Snce all the systems measured n ths study were for moderate to hgh pressures, t was not necessary to swtch the 6-port GC valve from ths poston durng samplng as the pressure wthn the equlbrum cell was always hgher than the pressure of the carrer gas n the samplng lne. Once equlbrum was establshed, the 34970A Aglent data acquston unt was reset to start loggng the temperature and pressure readngs and the vapour and lqud phases were then ready to be sampled. The magnetc strrer was also deactvated at ths pont. By tral t was found that the temperature for the upper 36 SS flange of the equlbrum cell was necessarly needed to be kept at 0.5 K hgher than the sotherm value of the system beng measured. Ths was to prevent condensaton of the vapour at the tp of the capllary that would lead to an ncorrect value for the vapour composton. The vapour phase was sampled frst as ths phase requred less cleanng tme when compared to the lqud phase. The capllary of the was cleaned by settng a specfc openng tme on the Crouzet TOP 948 electronc tmer. Ths openng tme was found by tral such that the peak areas obtaned where wthn the GC detector calbraton range. The Crouzet TOP 948 electronc tmer was also used to set the tme between each successve sample. Ths tme was set to the retenton tme of the frst peak. In ths way, samples were taken automatcally accordng to the specfed tmes set on the Crouzet TOP

148 CHAPTER 5 EXPERIMENTAL PROCEDURE 948 electronc tmer. The frst 3 samples taken were used to clean the capllary of the. Thereafter, at least 5 samples were taken untl the absolute average devaton of the composton was wthn % error. The turn-dal on the phase equlbrum apparatus was then operated to move the capllary of the to the lqud phase for samplng. Markngs that were made on the 36 SS rods of the phase equlbrum apparatus were used as a gudelne to know the poston of the capllary; else the ol bath was lowered to vew the equlbrum cell pror to postonng the capllary of the. Durng ths process, the pressure wthn the equlbrum cell was montored to check that the pressure was not changng apprecably. Once the capllary of the was postoned n the lqud phase, the temperature for the upper 36 SS flange of the equlbrum cell was returned to the sotherm value of the system and samples were taken usng the Crouzet TOP 948 electronc tmer. As n the vapour phase, the openng tme for the capllary of the was found by tral such that the peak areas obtaned where wthn the GC detector calbraton range. The frst 3 samples taken were used to clean the capllary of the. Thereafter, at least 5 samples were taken untl the absolute average devaton of the composton was wthn % error. The loggng of temperature and pressure readngs were then stopped and recorded. The turn-dal on the phase equlbrum apparatus was then operated to return the capllary of the to the vapour phase wthn the equlbrum cell. The ol bath was then lowered to vew the lqud level n the equlbrum cell. If the lqud level was less than ¾ of the total cell heght, then the compresson devce was used as before to add more of the second component nto the equlbrum cell and the entre procedure repeated untl the heght of the lqud wthn the equlbrum cell was ¾ that of the cell heght. Ths pont was generally reached when the phase equlbrum dagram was half complete. The ol bath was then lowered to dran some of the lqud from the cell va the dran valve of the equlbrum cell such that the level of lqud wthn the cell was approxmately / 5 that of the heght of the equlbrum cell. Ths was possble snce for all systems measured n ths study, the pressure wthn the equlbrum cell was always at a hgher value than the atmospherc pressure. The process of dranng the equlbrum cell was done as quck as possble as the temperature (and thus the pressure) wthn the equlbrum cell was constantly decreasng snce the equlbrum cell was out of the ol bath. Ths method saved tme for cleanng the equlbrum cell and the amount of chemcal used (especally that of the expensve chemcal that was ntally charged nto the equlbrum cell). Once ths was done, the ol bath was then rased to mmerse the equlbrum cell wthn the ol and the procedure contnued untl the phase equlbrum dagram was completed. 2

149 CHAPTER 5 EXPERIMENTAL PROCEDURE Once the phase equlbrum measurements for the entre composton range was completed, the heat suppled to the expanson chamber, samplng lnes and the alumnum block for the 6-port GC samplng valve were deactvated. The temperature controller for the ol bath was swtched off and the equlbrum cell was allowed to cool down before beng cleaned. Overall t was found that only 50 of each component was requred to carry out GC detector calbratons, degassng, vapour pressure and phase equlbra measurements for a sngle sotherm. Where more than one sotherm was measured, only an addtonal 25 of each component was further requred per sotherm Bnary Lqud-Lqud Equlbrum (LLE) Measurement The equlbrum cell and samplng lnes were ntally cleaned as outlned n Secton pror to undertakng lqud-lqud equlbrum (LLE). The two components were also thoroughly degassed wth the degassng apparatus as outlned n Secton 5. or n-stu degassng as outlned n Secton One of the components was then used to charge the compresson devce as outlned n Secton whst the other component was used to charge the equlbrum cell as outlned n Secton above wth only approxmately 6. In the case where an expensve chemcal was used, n-stu degassng was used for ths chemcal and thus the equlbrum cell was already charged wth ths component. The second component was charged nto wth the compresson devce as already outlned n Secton above, however approxmately 6 was charged nto the cell nstead of a small amount as mentoned n Secton The needle valves of the feed lne and the compresson devce were then closed. The stanless steel lne connecton on the compresson devce at the three-way valve on the feed lne was then carefully removed and the three-way valve was also swtched to the vacuum poston to remove the excess second component lqud from the feed lne. At ths pont, the pressure wthn the equlbrum cell was also montored and the needle valve on the feed lne was opened for a few seconds to the vacuum to ensure that no ar was present n the equlbrum cell. Thereafter, the needle valve on the feed lne was closed and the three-way valve was postoned to the charge poston. Hgh pressure ntrogen gas was then connected to the charge poston of the three-way valve usng / 8 nch stanless steel ppng. Wth the valve of the hgh pressure ntrogen gas closed, the three-way valve was then alternated between the vacuum and charge poston 3

150 CHAPTER 5 EXPERIMENTAL PROCEDURE several tmes to remove all ar present n the stanless steel lnes before beng left n the charge postoned. The hgh pressure ntrogen valve was then slowly opened untl the pressure n the stanless steel lne was approxmately 500 kpa. The needle valve was then partally opened to allow the hgh pressure ntrogen nto the equlbrum cell untl the pressure n the equlbrum cell was approxmately 350 kpa, where care was taken to ensure that the stanless steel ball valve for the low pressure transmtter was closed. The hgh pressure ntrogen was used to pressurze the equlbrum cell to enable samplng. The equlbrum composton analyss was n no way compromsed snce ntrogen, an nert gas, has a very low solublty n lquds used n ths study for low to moderately hgh pressures. Furthermore, lquds are generally ncompressble and the phase equlbrum compostons for LLE systems do not sgnfcantly change when the pressure s ncreased from subatmospherc pressure to a moderately hgh pressure. The magnetc strrer was actvated and the ol bath was then rased to mmerse the equlbrum cell nto the ol. The temperature controller of the ol bath was set to the sotherm value and the system was left to equlbrate wthn the equlbrum cell. The heater cartrdge n the upper 36 SS flange of the equlbrum cell was also actvated to account for heat losses to the envronment and conductve paths. The 34970A Aglent data acquston unt was then used to log the temperature and pressure readngs. Equlbrum wthn the equlbrum cell was deemed establshed when the temperature of the 36 SS flanges of the equlbrum cell and the pressure wthn the equlbrum cell dd not change wth tme. If the pressure wthn the equlbrum cell was below 350 kpa, addtonal ntrogen was added to the equlbrum cell to mantan a pressure of 350 kpa pror to samplng. The ol bath was also lowered to vew the equlbrum cell n order to verfy that the poston of the capllary for the was ndeed n the upper lqud phase. The mxture was then allowed a few more mnutes to reach equlbrum once agan. The procedure for samplng was followed as outlned n Secton wth the lower lqud phase beng sampled frst. The loggng of temperature and pressure readngs were then stopped and recorded. The turn-dal on the phase equlbrum apparatus was then operated to return the capllary of the to the upper lqud phase wthn the equlbrum cell. The temperature controller was then set to the next sotherm value and tme was allowed for equlbrum to be establshed. When equlbrum was reached, the procedure for samplng was repeated as before whereby t was ensured that the pressure n the equlbrum cell was mantaned at 350 kpa. The entre procedure was repeated for as many sotherms as were requred. Once the phase equlbrum dagram was completed the heat suppled to the expanson chamber, samplng lnes and the alumnum block for 4

151 CHAPTER 5 EXPERIMENTAL PROCEDURE the 6-port GC samplng valve were deactvated. The temperature controller for the ol bath was swtched off and the equlbrum cell was allowed to cool down before beng cleaned. Overall t was found that only 30 of each component was requred to carry out GC detector calbratons, degassng, vapour pressure and phase equlbra measurements Bnary Vapour-Lqud-Lqud Equlbrum (VLLE) Measurement The equlbrum cell and samplng lnes were cleaned as outlned n Secton The two components were also thoroughly degassed wth the degassng apparatus as outlned n Secton 5. or n-stu degassng as outlned n Secton The expermental phase dagram was completed n the same manner as the bnary VLE measurements wth the excepton of the expermental pont of vapour-lqud-lqud equlbrum (VLLE) whch was determned frst. The procedure for obtanng the VLLE pont followed the same procedure to charge the equlbrum cell as descrbed for LLE measurements n Secton except that no hgh pressure ntrogen was charged nto the equlbrum cell. Once, the equlbrum cell was charged wth both lqud components, the capllary was then postoned n the vapour phase of the equlbrum cell n preparaton for samplng usng the turn-dal on the equlbrum apparatus. The magnetc strrer was then actvated. The procedure for establshng equlbrum and samplng were then followed as outlned n Secton However n ths case, three samples were analysed startng wth the vapour phase. Once the pont of VLLE was determned, the turn-dal on the phase equlbrum apparatus was then operated to return the capllary of the to the vapour phase wthn the equlbrum cell. The temperature controller for the ol bath was swtched off and the equlbrum cell was allowed to cool down before beng cleaned. Thereafter each homogeneous regon of the VLLE system was then determned expermentally followng the procedure for VLE measurements as outlned n Secton Once the phase equlbrum dagram was complete, the heat suppled to the expanson chamber, samplng lnes and the alumnum block for the 6-port GC samplng valve were deactvated. The temperature controller for the ol bath was swtched off and the equlbrum cell was allowed to cool before beng cleaned. Overall t was found that only 60 of each component was requred to carry out GC detector calbratons, degassng, vapour pressure and phase equlbra measurements for a sngle sotherm. 5

152 CHAPTER 5 EXPERIMENTAL PROCEDURE 6

153 CHAPTER 6 FRENCH SUMMARY Avant d'entreprendre des mesures nouvelles d'équlbres de phase, l'apparel qu vent d être développé devat être préalablement testé pour vérfer qu l est capable de permettre de reprodure des données précédemment mesurées et auss pour examner les performances de la technque d'échantllonnage orgnale. Indépendamment de cec, l'apparel a également été testé pour montrer sa polyvalence dans la mesure des pressons de vapeur, des équlbres «lqude vapeur» (ELV), des équlbres «lqude-lqude» (ELL) et des équlbres «lqude-lqude-vapeur» (ELLV). Avant utlsaton, chacun des produts chmques a été contrôlé en vue de la vérfcaton de sa pureté. Pour cela ans nous avons réalsé des mesures d'ndce de réfracton avec le réfractomètre modèle RX 7000α de Atago et des analyses par chromatographe en phase gazeuse. Ces contrôles de pureté ont perms de montrer qu'aucune mpureté n est présente en quantté sgnfcatve dans les produts chmques utlsés pour cette étude. Les systèmes tests étaent : l équlbre «lqude vapeur» (ELV) du mélange 2 methoxy-2-méthylpropane + acétate d éthyle à K et deséqulbres«lqude-lqude» (ELL) concernant les mélanges méthanol + heptane et hexane + acétontrle, tous les deux mesurés à 350 kpa sous presson d azote. Ces systèmes tests (excepté hexane + acétontrle) ont serv à établr que l'apparel est ben capable de permettre de mesurer des données fables d'équlbres de phase. Les valeurs publées par Bernabe et al. (988) ontété utlsées pour comparason sur ce systéme bnare en équlbre «lqude-lqude». Cependant ces données obtenues par la méthode du pont de broullard ne sont pas très précses et sujettes á des observatons vsuelles. De nouvelles données expérmentales d'équlbre de phase ont été obtenues pour les systèmes suvants : a) ELV pour le système méthanol + butan-2-one à , et K b) ELV pour le système éthanol + butan-2-one à , et 43.2 K c) ELV pour le système éthanol + 2 méthoxy-2-méthylbutane à et 43.9 K d) ELV pour le système éthanol + 2 méthylpent-2-ène à K e) ELLV pour le système hexane + acétontrle à K Le système (a) présente un azéotrope à et K aux envrons de = et respectvement, mas pas à K. Le système (b) présente un azéotrope à , et 43.2 K respectvement aux envrons de = 0.75, 0.84 et 0.9. Le système (c) présente lu auss un azéotrope, cet azéotrope a pour compostons : = et à et 43.9 K respectvement. Le système (d) est azéotropque avec la composton = La presson d'équlbre trphasque du système (e) a été détermnée expérmentalement à88.0 kpa avec les 7

154 CHAPTER 6 FRENCH SUMMARY compostons suvantes = 0.32, = pour les deux phases lqudes et = pour la phase vapeur. 8

155 CHAPTER 6 EXPERIMENTAL RESULTS 6 CHAPTER SIX EXPERIMENTAL RESULTS The phase equlbrum apparatus was desgned, commssoned and tested by measurng vapour pressure data and three phase equlbrum test systems. These measurements were done to ensure that the apparatus was n correct workng order and to test the novel desgn developed for phase samplng. The test systems ncluded one vapour-lqud equlbrum (VLE) system of 2-methoxy-2- methylpropane + ethyl acetate at K and two lqud-lqud equlbrum (LLE) systems of methanol + heptane and hexane + acetontrle both measured wth the ad of hgh pressure ntrogen at 350 kpa. A vapour-lqud-lqud equlbrum (VLLE) test system of water + butan--ol at K was also expected to be measured but t was later realzed that the polymer used on the stem of the was not sutable for water. A specal stem was needed n order to sample any system that contaned water. Ths specal stem was to be ordered from France and the tmeframe for recevng t meant that ths study would not have been completed tmeously. New expermental phase equlbrum data were also measured for the followng systems: VLE for methanol + butan-2-one at , and K VLE for ethanol + butan-2-one at , and 43.2 K VLE for ethanol + 2-methoxy-2-methylbutane at and 43.9 K VLE for ethanol + 2-methylpent-2-ene at K VLLE for hexane + acetontrle at K Ths chapter presents the chemcal purty analyss for all the reagents used n ths study, together wth the results of the vapour pressure measurements, VLE, LLE and VLLE phase equlbrum measurements. 9

156 CHAPTER 6 EXPERIMENTAL RESULTS 6. Chemcal Purty Acetontrle, butan-2-one, ethanol and methanol were purchased from Merck, whle 2-methoxy-2- methylbutane, 2-methoxy-2-methylpropane, 2-methylpent-2-ene, ethyl acetate, heptane and hexane were purchased from Captal Laboratory Supplers cc. Table 6-: Chemcal purtes and refractve ndces for all reagents used n ths study. Refractve Index GC Analyss Mn. Purty Expermental a Lterature %) (Mass %) f (Peak Area 2-methoxy-2-methylbutane methoxy-2-methylpropane methylpent-2-ene acetontrle butan-2-one ethanol ethyl acetate heptane hexane methanol a at K, b Weast et al. (984), c Am and Cpran (980), d Schmtt and Boord (932), e Mcbee and Chrstman (955), f Stated by suppler All the reagents used n ths study were subjected to a purty check usng gas chromatographc analyss wth a thermal conductvty detector (TCD) as t s able to pck up non-hydrocarbon mpurtes as well. It was revealed that no sgnfcant mpurtes were found for all reagents. Hence, all reagents were used wthout further purfcaton. Each chemcal was also subjected to refractve ndex measurement and compared to lterature. The refractve ndex measurements were made wth the Atago refractometer model RX 7000α. The analyses from gas chromatography and refractve ndex measurements are reported n Table Expermental Uncertantes The expermental uncertantes assocated wth the two temperature probes used to measure the equlbrum temperature and the low and moderate pressure transmtters are reported n Table 6-2. The expermental uncertanty from the gas chromatograph (GC) TCD calbraton for the mole fracton composton of each vapour-lqud equlbrum (VLE) system studed s reported n Table 20

157 CHAPTER 6 EXPERIMENTAL RESULTS 6-3, where calbratons were carred out for dlute regons of each bnary par. All the uncertanty calculatons followed the gudelnes outlned by the Natonal Insttute of Scence and Technology (Taylor et al., 2007). The accuracy of the temperature controller of the ol bath was prevously reported as 0.02, thus mplyng an uncertanty of 0.0. The uncertanty due to the mole number ( n) of each chemcal speces was mol, determned from the OHAUS mass balance used. The standard devaton from the GC TCD calbraton can be consdered as the uncertanty for the mole fracton, gven by the followng equaton: 2 2 dx dx = n2 dn dn 2 2 ( n ) + ( ) 2 x (6-) Table 6-2: Expermental uncertantes for temperature and pressure measurements. Descrpton Calbraton Uncertanty Repeatablty Uncertanty Global Uncertanty equlbrum cell upper 36 SS flange low range: 0.02 K hgh range: 0.05 K low range: 0.05 K hgh range: 0.05 K low range: 0.05 K hgh range: 0.07 K equlbrum cell lower 36 SS flange low range: 0.02 K hgh range: 0.05 K low range: 0.04 K hgh range: 0.04 K low range: 0.05 K hgh range: 0.07 K low pressure transmtter kpa 0.02 kpa 0.02 kpa moderate pressure transmtter 0.6 kpa 0.7 kpa 0.9 kpa Table 6-3: Expermental uncertantes for mole fracton compostons of VLE systems. System Calbraton Uncertanty for Repeatablty Uncertanty for Global Uncertanty for 2-methoxy-2- methylpropane () + ethyl acetate (2) dlute regon (): dlute regon (2): dlute regon (): dlute regon (2): dlute regon (): dlute regon (2): methanol () + butan-2- one (2) dlute regon (): dlute regon (2): dlute regon (): dlute regon (2): dlute regon (): dlute regon (2):

158 CHAPTER 6 EXPERIMENTAL RESULTS Table 6-3: Expermental uncertantes for mole fracton compostons of VLE systems System one (2) ethanol () + 2- ethanol () + butan-2- methoxy-2- methylbutane (2) 2-methylpent-2-ene () + ethanol (2) Calbraton Uncertanty for dlute regon (): dlute regon (2): dlute regon (): dlute regon (2): dlute regon (): dlute regon (2): (contnued). Repeatablty Uncertanty for dlute regon (): dlute regon (2): 0.00 dlute regon (): dlute regon (2): 0.00 dlute regon (): dlute regon (2): Global Uncertanty for dlute regon (): dlute regon (2): dlute regon (): dlute regon (2): dlute regon (): dlute regon (2): The GC TCD calbratons for the lqud-lqud equlbrum (LLE) systems were acheved usng the drect njecton method as opposed to the area rato method of Raal and Mühlbauer (998) as dscussed n Chapter 5. All the calbraton equatons are reported n Appendx C. 6.3 Vapour Pressure Data Vapour pressure data were measured for all the reagents used n ths study. The data measured were compared to the Wagner equaton usng the lterature data of Red et al. (988) and the extended Antone equaton from the property data bank n Aspen Plus (2004). The expermental data were also compared to values obtaned usng the Redlch-Kwong and the Peng-Robnson equatons of state. The comparson to lterature data served as a check for thorough degassng of the chemcals. All the expermental vapour pressure data were subjected to least squares regresson to obtan parameters for the Wagner and Antone emprcal equatons and also the Redlch-Kwong and Peng- Robnson equatons of state. The results of the regresson are dscussed further n Chapter 7. The expermental vapour pressure data are reported n Table 6-4 and presented graphcally n Fgures 6- to

159 CHAPTER 6 EXPERIMENTAL RESULTS 2-methoxy-2- methylbutane Table 6-4: Expermental vapour pressure data. 2-methoxy-2- methylpropane 2-methylpent-2-ene T / K P / kpa T / K P / kpa T / K P / kpa acetontrle butan-2-one ethyl acetate T / K P / kpa T / K P / kpa T / K P / kpa heptane hexane methanol T / K P / kpa T / K P / kpa T / K P / kpa

160 CHAPTER 6 EXPERIMENTAL RESULTS Table 6-4: Expermental vapour pressure data (contnued). ethanol T / K P / kpa T / K P / kpa T / K P / kpa ln (Pressure / kpa) methoxy-2-methylbutane 2-methoxy-2-methylpropane 2-methoxy-2-methylbutane: Aspen Plus (2004) 2-methoxy-2-methylpropane: Aspen Plus (2004) ( / Temperature) / K - Fgure 6-: Vapour pressure plots for the ethers used n ths study, 2-methoxy-2-methylbutane and 2-methoxy-2-methylpropane, compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature. 24

161 CHAPTER 6 EXPERIMENTAL RESULTS 8 7 ethanol methanol ln (Pressure / kpa) ethanol: Aspen Plus (2004) methanol: Aspen Plus (2004) ( / Temperature) / K - Fgure 6-2: Vapour pressure plots for the alcohols used n ths study, ethanol and methanol, compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature. 7 ln (Pressure / kpa) butan-2-one ethyl acetate butan-2-one: Aspen Plus (2004) ethyl acetate: Aspen Plus (2004) ( / Temperature) / K - Fgure 6-3: Vapour pressure plots for the ketone (butan-2-one) and ester (ethyl acetate) used n ths study compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature. 25

162 CHAPTER 6 EXPERIMENTAL RESULTS ln (Pressure / kpa) heptane hexane heptane: Aspen Plus (2004) hexane: Aspen Plus (2004) Temperature / K Fgure 6-4: Vapour pressure plots for the alkanes used n ths study, heptane and hexane, compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature. ln (Pressure / kpa) methylpent-2-ene acetontrle 2-methylpent-2-ene: Aspen Plus (2004) acetontrle: Aspen Plus (2004) Temperature / K Fgure 6-5: Vapour pressure plots for the alkene (2-methylpent-2-ene) and ntrle (acetontrle) used n ths study compared to lterature. Error bars show % error for pressure and 0.5 % error for temperature. 26

163 CHAPTER 6 EXPERIMENTAL RESULTS 6.4 Phase Equlbra of Test Systems The Shmadzu 204 gas chromatograph (GC) was used for the composton analyss of samples for all the test systems undertaken n ths study. The GC calbraton results and optmzed parameters for the GC operaton are presented n Appendx C3. The mole fracton values for each phase sampled were wthn % error for the average absolute devaton of at least 5 samples taken Vapour-Lqud Equlbrum (VLE) Result Methoxy-2-Methylpropane () + Ethyl Acetate (2) The lterature data of Lee et al. (997) for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K was used as a test system to demonstrate the capablty of the newly developed phase equlbra apparatus to measure vapour-lqud equlbrum (VLE) data. Ths lterature data set was chosen as the pressure lmts were wthn range for the pressure transmtter used n ths study. Furthermore, ths lterature data set was measured usng a relable technque and accordng to Lee et al. (997), the data was found to be thermodynamcally consstent. The expermental data measured n ths study s reported n Table 6-5 and graphcally presented as x-y and P-x-y plots n Fgures 6-6 and 6-7 respectvely. Table 6-5: Expermental vapour-lqud equlbrum data for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K. P / kpa

164 CHAPTER 6 EXPERIMENTAL RESULTS ths work Lee et al. (997) x y Fgure 6-6: The x-y plot for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K, error bars show 2% error for and. 380 Pressure / kpa P - x: ths work P - y: ths work P - x: Lee et al. (997) P - y: Lee et al. (997) x, y Fgure 6-7: The P-x- y plot for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K, error bars show % error for pressure and 2% error for and. 28

165 CHAPTER 6 EXPERIMENTAL RESULTS Lqud-Lqud Equlbrum (LLE) Results Hexane () + Acetontrle (2) Two lqud-lqud equlbrum (LLE) systems were measured and compared to lterature to show the capablty of the newly developed phase equlbra apparatus to measure LLE data. The frst test system of hexane () + acetontrle (2) was measured and compared to the lterature data of Bernabe et al. (988) and Sug and Katayama (978). The expermental data measured at 350 kpa n ths study are reported n Table 6-6 and graphcally presented as a T-- plot n Fgure 6-8. Table 6-6: Expermental lqud-lqud equlbrum data for the hexane () + acetontrle (2) system at 350 kpa. Phase I Phase II T / K Temperature / K T - x': ths work at 350 kpa T - x": ths work at 350 kpa T - x': Sug and Katayama (978) at 0.3 kpa T - x": Sug and Katayama (978) at 0.3 kpa T - x: Bernabe et al. (988) at 0.3 kpa x I, x II Fgure 6-8: The T-- plot for the hexane () + acetontrle (2) system at 350 kpa, error bars show 0.3% error for temperature and 2% error for and. 29

166 CHAPTER 6 EXPERIMENTAL RESULTS The data of Sug and Katayama (978) was n agreement wth the expermental data of ths work whereas the data of Bernabe et al. (988) showed dsagreement (dscussed further n Secton 7.5.) Methanol () + Heptane (2) The second LLE test system of methanol () + heptane (2) was measured to confrm the technque of LLE measurement, snce the frst LLE test system of hexane () + acetontrle (2) dd not compare well to the lterature data of Bernabe et al. (988) (dscussed further n Secton 7.5.2). Ths second LLE test system was compared to the lterature data of Hgashuch et al. (987), Katayama and Ichkawa (995) and Matsuda et al. (2002). The expermental data measured at 350 kpa n ths study are reported n Table 6-7 and graphcally presented as a T-- plot n Fgure 6-9. Incdentally, Bernabe et al. (988) also measured data for ths system whch was shown to be n dsagreement wth other researchers (see Fgure 6-9). Temperature / K T - x': ths work at 350 kpa 300 T - x": ths work at 350 kpa T - x': Hgashuch et al. (987) at 0.3 kpa 290 T - x": Hgashuch et al. (987) at 0.3 kpa 280 T - x: Bernabe (988) at 0.3 kpa 270 T - x': Katayama and Ichkawa (995) at 0.3 kpa T - x": Katayama and Ichkawa (995) at 0.3 kpa 260 T - x: Matsuda et al. (2002) at 00 kpa x ', x " Fgure 6-9: The T-- plot for the methanol () + heptane (2) system at 350 kpa, error bars show 0.3% error for temperature and 2% error for and. 30

167 CHAPTER 6 EXPERIMENTAL RESULTS Table 6-7: Expermental lqud-lqud equlbrum data for the methanol () + heptane (2) system at 350 kpa. Phase I Phase II T / K The expermental data of the test systems showed that the newly developed apparatus was capable of performng vapour pressure and phase equlbra measurements. The test systems also showed versatlty of the apparatus to measure vapour-lqud equlbrum (VLE) and lqud-lqud equlbrum (LLE) data. 6.5 Phase Equlbra of New Systems For all the systems, the GC TCD calbraton results and optmzed parameters for the GC operaton are presented n Appendx C3. The mole fracton values for each phase sampled were wthn % error for the average absolute devaton of at least 5 samples taken. All the new systems expermentally measured n ths work have prevously not been reported n the open lterature Vapour-Lqud Equlbrum (VLE) Methanol () + Butan-2-one (2) Data for ths system were measured at three temperatures: , and K. They are reported n Table 6-8 and graphcally presented as x-y plots n Fgure 6-0 and P-x-y plots n Fgure 6-. Ths system exhbted an azeotrope for the and K sotherms at approxmately = and 0.98 respectvely. The expermental data does not however seem to ndcate an azeotrope at K. The presence of an azeotrope mples that a system s non-deal and that conventonal dstllaton cannot separate the components nto hgh purty chemcals. Hence alternate forms of dstllaton should be consdered such as pressure-swng dstllaton or homogeneous or heterogeneous azeotropc dstllaton. 3

168 CHAPTER 6 EXPERIMENTAL RESULTS Table 6-8: Expermental vapour-lqud equlbrum data for the methanol () + butan-2-one (2) system K K K P / kpa P / kpa P / kpa ths work ( K) ths work (398.4 K) ths work (43.20 K) y x Fgure 6-0: The x-y plot for the methanol () + butan-2-one (2) system, error bars show 2% error for and. 32

169 CHAPTER 6 EXPERIMENTAL RESULTS Pressure / kpa P - x: ths work ( K) P - y: ths work ( K) P - x: ths work (398.4 K) P - y: ths work (398.4 K) P - x: ths work (43.20 K) P - y: ths work (43.20 K) x, y Fgure 6-: The P-x-y plot for the methanol () + butan-2-one (2) system, error bars show % error for pressure and 2% error for and Ethanol () + Butan-2-one (2) Data for ths system were measured at three temperatures: , and 43.2 K. They are reported n Table 6-9 and graphcally presented as x-y plots n Fgure 6-2 and P-x-y plots n Fgure 6-3. Ths system exhbted an azeotrope for the , and 43.2 K sotherms at approxmately = 0.75, 0.84 and 0.9 respectvely. Hence as mentoned prevously, alternate forms of dstllaton need to be consdered to separate these components nto hgh purty chemcals. 33

170 CHAPTER 6 EXPERIMENTAL RESULTS Table 6-9: Expermental vapour-lqud equlbrum data for the ethanol () + butan-2-one (2) system K K 43.2 K P / kpa P / kpa P / kpa ths work ( K) ths work ( K) ths work (43.2 K) y x Fgure 6-2: The x-y plot for the ethanol () + butan-2-one (2) system, error bars show 2% error for and. 34

171 CHAPTER 6 EXPERIMENTAL RESULTS Pressure / kpa P - x: ths work ( K) P - y: ths work ( K) P - x: ths work ( K) P - y: ths work ( K) P - x: ths work (43.2 K) P - y: ths work (43.2 K) x, y Fgure 6-3: The P-x-y plot for the ethanol () + butan-2-one (2) system, error bars show % error for pressure and 2% error for and Ethanol () + 2-Methoxy-2-Methylbutane (2) Data for ths system were measured at two temperatures: and 43.9 K. They are reported n Table 6-0 and graphcally presented as x-y plots n Fgure 6-4 and P-x-y plots n Fgure 6-5. Ths system exhbted an azeotrope for both the and 43.9 K sotherms at approxmately = 0.77 and 0.78 respectvely. Agan, alternate forms of conventonal dstllaton should be consdered for the separaton of these chemcals. 35

172 CHAPTER 6 EXPERIMENTAL RESULTS Table 6-0: Expermental vapour-lqud equlbrum data for the ethanol () + 2-methoxy-2- methylbutane (2) system K 43.9 K P / kpa P / kpa ths work ( K) ths work (43.9 K) y x Fgure 6-4: The x-y plot for the ethanol () + 2-methoxy-2-methylbutane (2) system, error bars show 2% error for and. 36

173 CHAPTER 6 EXPERIMENTAL RESULTS P - x: ths work ( K) P - y: ths work ( K) P - x: ths work (43.9 K) P - y: ths work (43.9 K) Pressure / kpa x, y Fgure 6-5: The P-x-y plot for the ethanol () + 2-methoxy-2-methylbutane (2) system, error bars show % error for pressure and 2% error for and Methylpent-2-ene () + Ethanol (2) Data for ths system was measured at an sotherm of K. The data are reported n Table 6- and graphcally presented as an x-y plot and P-x-y plot n Fgures 6-6 and 6-7 respectvely. Ths system also exhbted an azeotrope at approxmately = Once more, alternate forms of conventonal dstllaton should be consdered for separaton of these chemcals. 37

174 CHAPTER 6 EXPERIMENTAL RESULTS Table 6-: Expermental vapour-lqud equlbrum data for 2-methylpent-2-ene () + ethanol (2) at K. P / kpa ths work y x Fgure 6-6: The x-y plot for the 2-methylpent-2-ene () + ethanol (2) system at K, error bars show 2% error for and. 38

175 CHAPTER 6 EXPERIMENTAL RESULTS Pressure / kpa P - x: Expermental P - y: Expermental x Fgure 6-7: The P-x-y plot for the 2-methylpent-2-ene () + ethanol (2) system at K, error bars show % error for pressure and 2% error for and Vapour-Lqud-Lqud Equlbrum (VLLE) Hexane () + Acetontrle (2) The expermental measurement of ths system was done to demonstrate that the newly developed apparatus was capable of measurng vapour-lqud-lqud equlbrum (VLLE). Data for ths system was measured at K. The data are reported n Table 6-2 and graphcally presented as a --y plot and P---y plot n Fgures 6-27 and 6-28 respectvely. 39

176 CHAPTER 6 EXPERIMENTAL RESULTS Table 6-2: Expermental vapour-lqud-lqud equlbrum data for hexane () + acetontrle (2) at K. P / kpa * 0.32 * * * * Pont of VLLE y ths work mmscblty gap x I, x II Fgure 6-8: The --y plot for the hexane () + acetontrle (2) system at K, error bars show 2% error for, and. 40

177 CHAPTER 6 EXPERIMENTAL RESULTS mmscblty gap Pressure / kpa P - x': ths work P - x": ths work P - y: ths work x II, x II, y Fgure 6-9: The P---y plot for the hexane () + acetontrle (2) system at K, error bars show % error for pressure and 2% error for, and. 4

178 CHAPTER 7 FRENCH SUMMARY Toutes les données de tensons de vapeur et d'équlbres de phase mesurées avec l'apparellage récemment développé ont été soumses à une procédure d'analyse de données et dscutées. Toutes les données de presson de vapeur se sont révélées thermodynamquement cohérentes. Elles ont toutes été régressées en utlsant les équatons emprques étendues d'antone et de Wagner ans que les équatons d état PR et SRK. Des méthodes combnées et drectes de régresson de données ont été employées pour obtenr les paramètres des modèles assocés aux systèmes en équlbres «lqude-vapeur». Pour les méthodes combnées, la non-déalté de la phase vapeur a été prse en compte par l'équaton du vrel avec un deuxème coeffcent du vrel provenant de la corrélaton de Tsonopoulos (974). Le non- déalté de la phase lqude pour les méthodes combnées a été représentée au moyen des modèles de solutons lqudes fasant appel au coeffcent d'actvté de phase (à savor TK-Wlson, NRTL et modfed UNIQUAC). Quant à la méthode drecte, les nondéaltés en phases vapeur et lqude ont été prses en compte par des équatons d état cubque (à savor celles de Peng et Robnson et de Soave, Redlch et Kwong avec la foncton alpha (α), dépendante de la température, celle de Mathas et Copeman (983)). Les mêmes modèles de solutons lqudes avec coeffcent d'actvté utlsés dans les méthodes combnées ont été également employés pour régresser des données des systèmes mesurés, en équlbre «lqude-lqude». Pour montrer la polyvalence de l'apparellage de mesure d'équlbres, des équlbres «lqude-lqudevapeur» ont été mesurés et les résultats analysés suvant la méthode combnée de régresson de données. De façon générale, l'analyse a ndqué que toutes les données expérmentales mesurées ont été modélsées de manère satsfasante à l excepton de celles d équlbres «lqude-lqudevapeur». Les tests de cohérence thermo-dynamque (pont and drect tests) concernant les données ELV comme élément de l'analyse des données ont été utlsés. Ils ont perms de constater que la majeure parte des données état thermodynamquement cohérente à l excepton de peu d entres elles. 42

179 CHAPTER 7 DATA ANALYSIS AND DISCUSSION 7 CHAPTER SEVEN DATA ANALYSIS AND DISCUSSION Ths chapter focuses on the data analyss and dscusson thereof for all the expermental results that were presented n Chapter 6 and begns wth referencng the pure component propertes for all the chemcals used n ths study. Ths chapter also ncludes the analyss of vapour pressure data usng both emprcal equatons and equatons of state, determnaton of expermental actvty coeffcents, vapour-lqud equlbrum (VLE) data reducton wth the combned and drect methods, lqudlqud equlbrum (LLE) data reducton for the test systems measured and vapour-lqud-lqud equlbrum (VLLE) data reducton wth the combned method. A dscusson on thermodynamc consstency testng s also ncluded. 7. Pure Component Propertes These propertes descrbe the nature of the chemcal and thus play an mportant role when analyzng thermodynamc data. Thermodynamc models rely on pure component propertes to determne the model parameters, whch are then used for predctons. Hence, the use of accurate pure component propertes s essental for the correct theoretcal treatment of phase equlbrum data. The pure component propertes of all the chemcals used n ths study were taken from the Dortmund Data Bank (200). These propertes nclude: crtcal temperature, crtcal pressure, crtcal volume and the acentrc factor. The second vral coeffcents were evaluated usng the correlaton of Tsonopoulos (974) as dscussed n Secton 3... Ths correlaton requres the use of two pure component parameters: one to account for the polar effects and another to account for the hydrogen bondng effect. These parameters were taken from the publcaton of Tsonopoulos (974) for all of the chemcals used n ths study, except for ethyl acetate, 2-methoxy-2-methylbutane and 2-methoxy-2-methylpropane 43

180 CHAPTER 7 DATA ANALYSIS AND DISCUSSION whch were not avalable. Tsonopoulos (974) however found a correlaton for the polar effect pure component parameter of ethers that requred the use of dpole moments. The dpole moments for 2- methoxy-2-methylbutane and 2-methoxy-2-methylpropane were taken from the Dortmund Data Bank (200) and used wth the correlaton of Tsonopoulos (974) to determne the polar effect pure component parameter. Tsonopoulos (974) also mentoned that these two pure component parameters were determned from the regresson of expermental second vral coeffcents. Thus the polar effect pure component parameter for ethyl acetate was found from the least squares regresson of expermental second vral coeffcents usng the data presented n Dymond and Smth (980). The lqud molar volumes of all the chemcals used n ths study were determned from the correlaton of Rackett (970) as dscussed n Secton 3., Equaton (3-25). The pure component propertes for all the chemcals used n ths study are presented n Appendx B. 7.2 Expermental Vapour Pressure Data Expermental vapour pressure data were measured usng the newly developed apparatus (see Chapter 4) for all chemcals used n ths study. Apart from verfyng the operaton of the apparatus, the measurement of expermental vapour pressure also served as a check for thorough degassng of the chemcals. Numerous emprcal correlatons are avalable to correlate vapour pressure of chemcals; however the Antone and Wagner equatons are the two most commonly used (Smth et al., 200). These correlatons contan pure component parameters that are vald for a specfed temperature range. For ths study, a modfed Antone equaton known as the extended Antone equaton and the Wagner equaton were used to correlate vapour pressure for the combned method of VLE data reducton. An equaton of state (EoS) can also be used to correlate vapour pressure of chemcals. The pure component parameter used n an EoS s dependent on the temperature dependent functon (α) utlzed. These pure component parameters, from an emprcal correlaton or EoS, are found by the regresson of expermental vapour pressure measurements. For ths study, the Soave-Redlch- Kwong (SRK) and Peng-Robnson (PR) equatons of state wth the temperature dependent functon (α) of Mathas and Copeman (983) were used as thermodynamc models for the drect method of VLE data reducton. In order to mprove the accuracy of vapour pressure correlatons n VLE data reducton, the pure component parameters from the emprcal correlatons and the temperature dependent functon (α) of Mathas and Copeman (983) n the SRK or PR EoS were regressed. 44

181 CHAPTER 7 DATA ANALYSIS AND DISCUSSION 7.2. Comparson of Expermental and Lterature Vapour Pressure Expermental vapour pressures were measured for all chemcals used n ths study and compared to lterature values obtaned from the extended Antone equaton n Aspen Plus (2004), except for butan-one and methanol. The lterature values for butan-2-one and methanol were taken from Red et al. (988). Aspen Plus s a smulaton software that contans a property data bank and s wdely used n unverstes, research nsttutes and even n ndustres. The expermental vapour pressure data were compared to lterature and presented graphcally n Chapter 6 (Fgures 6- to 6-5). The comparson of the expermental and lterature vapour pressures are presented as devaton plots for all chemcals used n ths study n Fgures 7- to methoxy-2-methylbutane, ths work 2-methoxy-2-methylpropane, ths work (P exp - P lt ) / P exp Temperature / K Fgure 7-: Vapour pressure devaton plots for the comparson of expermental data wth Aspen Plus (2004) for 2-methoxy-2-methylbutane and expermental data wth Red et al. (988) for 2-methoxy-2-methylpropane. 45

182 CHAPTER 7 DATA ANALYSIS AND DISCUSSION.5 ethanol, ths work methanol, ths work (P exp - P lt ) / P exp Temperature / K Fgure 7-2: Vapour pressure devaton plots for the comparson of expermental data wth Red et al. (988) for ethanol and expermental data wth Aspen Plus (2004) for methanol. 2.5 butan-2-one, ths work ethyl acetate, ths work (P exp - P lt ) / P exp Temperature / K Fgure 7-3: Vapour pressure devaton plots for the comparson of expermental data wth Red et al. (988) for butan-2-one and expermental data wth Aspen Plus (2004) for ethyl acetate. 46

183 CHAPTER 7 DATA ANALYSIS AND DISCUSSION heptane, ths work hexane, ths work (P exp - P lt ) / P exp Temperature / K Fgure 7-4: Vapour pressure devaton plots for the comparson of expermental data wth Red et al. (988) for heptane and hexane. 2-methylpent-2-ene, ths work 0.5 acetontrle, ths work (P exp - P lt ) / P exp Temperature / K Fgure 7-5: Vapour pressure devaton plots for the comparson of expermental data wth Aspen Plus (2004) for 2-methylpent-2-ene and expermental data wth Red et al. (988) for acetontrle. 47

184 CHAPTER 7 DATA ANALYSIS AND DISCUSSION The expermental and lterature values were also compared by determnng the average absolute devatons (AAD): AAD = n n = P (7-) where n s the number of expermental ponts and P s the dfference between the expermental and lterature vapour pressure. The AAD values are reported n Table 7-. The devaton plots n Fgures 7- to 7-5 and the AAD values n Table 7- show that the expermental vapour pressure data compares well wth lterature values for all chemcals except for, ethanol, hexane and methanol. The lterature values for butan-2-one and methanol were taken from an alternate source (Red et al., 988) for comparson purpose only as large devatons were observed for these chemcals wth the lterature values from Aspen Plus (2004). In fact lterature values for methanol from Red et al. (988), Aspen Plus (2004) and the Dortmund Data Bank (200) all showed sgnfcant devatons when compared wth each other especally for temperatures greater than 363 K. The scatter observed n the devaton plots was expected snce the correlaton coeffcents n lterature sources have most lkely been obtaned from the regresson of expermental measurements. Table 7-: Average absolute devatons (AAD) for the vapour pressures. AAD Temperature Range Chemcal / kpa Mn / K Max / K 2-methoxy-2-methylbutane methoxy-2-methylpropane methylpent-2-ene acetontrle butan-2-one ethanol ethyl acetate heptane hexane methanol

185 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Regresson usng Emprcal Correlatons The extended Antone equaton used n ths study s of the form: B' E' ln P = A' + + C'ln( T ) + D' T (7-2) T The parameter E' was kept as a constant nteger and therefore only the other four parameters were determned from the regresson of the expermental data. The Wagner equaton s known as: ln P P c = 6 [ ].5 3 ( x' ) A" x' + B" ( x' ) + C" ( x' ) + D" ( x' ) (7-3) where: T x' = (7-4) T c For both the extended Antone and Wagner equatons, the pressure s gven n kpa and the temperature n Kelvn. The regresson algorthm was based on the Nelder-Mead smplex method (Lagaras et al., 998). Intal estmates of the parameters for the method of regresson were taken from Aspen Plus (2004) for the extended Antone equaton and Red et al. (988) for the Wagner equaton. The objectve functon used was the least squares devaton of the pressure: n = [( ) ( ) ] 2 F = P P (7-5) exp cal where n s the number of expermental ponts. The pure component parameters from the regresson usng the extended Antone and Wagner equatons are presented n Tables 7-2 and 7-3 respectvely. The root mean squared devaton was used as a measure to compare the regresson results of the extended Antone and Wagner equatons: 49

186 CHAPTER 7 DATA ANALYSIS AND DISCUSSION RMSD = n = [( P ) ( P ) ] 2 exp cal (7-6) n The RMSD values for both equatons ndcate a good ft of the expermental vapour pressure data. The comparson of the RMSD values ndcates that the extended Antone equaton provdes a better ft for 2-methoxy-2-methylbutane, 2-methylpent-2-ene, ethyl acetate and methanol whlst the Wagner equaton provdes a better ft for 2-methoxy-2-methylpropane, acetontrle, butan-2-one, ethanol, heptane and hexane. Therefore, each component n the bnary VLE data reducton wth the combned method made use of the equaton that corresponded to the lower RMSD. Overall, the result was not surprsng snce both equatons cater for a greater degree of complexty wth each havng 4 adjustable parameters Regresson usng Equatons of State The SRK and PR equatons of state are the two most wdely used cubc equatons of state for ndustral applcatons as they requre lttle nput nformaton to produce reasonable phase equlbrum predctons. They also generate reasonably good vapor pressure predctons for nonpolar components. Snce polar components were used n ths study, the temperature dependent functon (α) of Mathas and Copeman (983) was used wth the SRK and PR equatons of state. The temperature dependent functon (α) of Mathas and Copeman (983) has the advantage of ntroducng a greater degree of complexty by usng adjustable parameters to mprove vapour pressure predctons and cater for polar components. Furthermore, the temperature dependent functon (α) of Mathas and Copeman (983) can be used n any cubc EoS; however the adjustable parameters would dffer for each cubc EoS. The accuracy of VLE calculatons s greatly nfluenced by the accurate predcton of vapour pressure (Twu et al., 99). Hence the expermental vapour pressure data were also regressed to determne the parameters of the temperature dependent functon (α) of Mathas and Copeman (983) n order mprove vapour pressure predctons. The regresson was carred out usng the THERMOPACK verson.0 software program developed by A. Baba Ahmed and C. Coquelet. Equaton (7-4) was also used as the objectve functon. The pure component parameters from the regresson usng the temperature dependent functon (α) of Mathas and Copeman (983) n the 50

187 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-2: Regressed pure component parameters for the extended Antone equaton. RMSD Temperature Range Chemcal A' B' C' D' E' / kpa Mn / K Max / K 2-methoxy-2-methylbutane E methoxy-2-methylpropane E methylpent-2-ene E acetontrle E butan-2-one E ethanol E ethyl acetate E heptane E hexane E methanol E Table 7-3: Regressed pure component parameters for the Wagner equaton. RMSD Temperature Range Chemcal A'' B'' C'' D'' / kpa Mn / K Max / K 2-methoxy-2-methylbutane methoxy-2-methylpropane methylpent-2-ene acetontrle butan-2-one ethanol ethyl acetate heptane hexane methanol

188 CHAPTER 7 DATA ANALYSIS AND DISCUSSION SRK and PR equatons of state are reported n Tables 7-4 and 7-5 respectvely (see Equaton (3-6)). The root mean squared devaton, Equaton (7-5), was used a measure to compare the regresson results from the two equatons of state. The results from the regresson ndcated a reasonably good ft for the vapour pressure of all chemcals except for 2-methoxy-2-methylpropane wth the PR EoS. The hgh RMSD for ethanol and methanol are due to a wder temperature range. Furthermore, methanol has a steeper gradent for the vapour pressure curve. Overall, the emprcal correlatons provde a better ft for the vapour pressure. The best ft of the emprcal correlatons for each component s shown graphcally n Fgures 7-6 to 7-0. ln (Pressure / kpa) methoxy-2-methylbutane, ths work 2-methoxy-2-methylpropane, ths work Extended Antone Regressed Wagner Regressed ( / Temperature) / K - Fgure 7-6: Vapour pressure plots for the ethers used n ths study, 2-methoxy-2- methylbutane and 2-methoxy-2-methylpropane, wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature. 52

189 κ κ / κ κ / CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-4: Regressed pure component parameters for the α functon of Mathas and Copeman (983) wth the SRK EoS. κ RMSD Temperature Range Chemcal kpa Mn / K Max / K 2-methoxy-2-methylbutane methoxy-2-methylpropane methylpent-2-ene acetontrle butan-2-one ethanol ethyl acetate heptane hexane methanol Table 7-5: Regressed pure component parameters for the α functon of Mathas and Copeman (983) wth the PR EoS. κ RMSD Temperature Range Chemcal kpa Mn / K Max / K 2-methoxy-2-methylbutane methoxy-2-methylpropane methylpent-2-ene acetontrle butan-2-one ethanol ethyl acetate heptane hexane methanol

190 CHAPTER 7 DATA ANALYSIS AND DISCUSSION ln (Pressure / kpa) ethanol, ths work methanol, ths work Extended Antonne Regressed Wagner Regressed ( / Temperature) / K - Fgure 7-7: Vapour pressure plots for the alcohols used n ths study, ethanol and methanol, wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature. ln (Pressure / kpa) butan-2-one, ths work ethyl acetate, ths work Extended Antone Regressed Wagner Regressed ( / Temperature) / K - Fgure 7-8: Vapour pressure plots for the ketone (butan-2-one) and ester (ethyl acetate) used n ths study wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature. 54

191 CHAPTER 7 DATA ANALYSIS AND DISCUSSION ln (Pressure / kpa) heptane, ths work hexane, ths work Wagner Regressed (/Temperature) / K - Fgure 7-9: Vapour pressure plots for the alkanes used n ths study, heptane and hexane, wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature. 7 ln (Pressure / kpa) methylpent-2-ene, ths work acetontrle, ths work Extended Antone Regressed Wagner Regressed Temperature / K Fgure 7-0: Vapour pressure plots for the alkene (2-methylpent-2-ene) and ntrle (acetontrle) used n ths study wth the best ft of the emprcal correlatons. Error bars show % error for pressure and 0.5 % error for temperature. 55

192 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Thermodynamc Consstency Testng for Vapour Pressure Data The expermental vapour pressure data were also checked for qualtatve thermodynamc consstency usng the recommendaton of researchers n the Desgn Insttute for Physcal Property Data (DIPPR) Complaton Project (Daubert et al., 990). Ths bascally nvolved representng the data n the form of a ln P versus ( / T) plot to vsually check for the occurrence of decomposton or polymerzaton wth an ncrease n temperature. If the plot shows a lnear trend, then the data are consdered thermodynamcally consstent as no decomposton or polymerzaton would have occurred. However care should be exercsed to ensure that a wde temperature range s consdered to reach a compellng concluson. The expermental vapour pressure data presented n Chapter 6 (Fgures 6- to 6-5) showed a lnear trend for all chemcals used n ths study and therefore passed the qualtatve thermodynamc consstency test wthn ts temperature range. 7.3 Expermental Actvty Coeffcents VLE/VLLE Systems The determnaton of the expermental actvty coeffcents was possble due to an over specfcaton of the system where the temperature, pressure and both lqud and vapour compostons were measured. However, n order to determne the expermental actvty coeffcents, the vapour phase correcton factor (Ф ) was frst evaluated wth Equaton (3-24). Ths was acheved by employng the Tsonopoulos (974) correlaton for the second vral coeffcents, Equaton (3-30), as outlned n Secton 3.., usng the expermental pressure and vapour composton values. Ths correlaton was chosen as t caters for both polar and non-polar components and provdes very good predctons for the second vral coeffcents. Furthermore, less nput nformaton was requred than compared to other correlatons such as Hayden and O Connell (975). Once the vapour phase correcton factor was evaluated, Equaton (3-23) was then used to determne the expermental actvty coeffcent values. The actvty coeffcent determned n ths manner s termed expermental as only expermental data was used n ts evaluaton and no thermodynamc model was used to determne the values. The expermental actvty coeffcents were also requred to carry out thermodynamc consstency testng. The expermental actvty coeffcents for the VLE/VLLE systems studed n ths work are reported n Tables 7-6 to 7-. The comparson of expermental and calculated actvty coeffcents are presented n Secton 7-4 and the thermodynamc consstency test s presented n Secton

193 γ γ CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-6: Expermental lqud-phase actvty coeffcents for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K Table 7-7: Expermental lqud-phase actvty coeffcents for the methanol () + butan-2-one (2) system K K K γ γ γ γ γ γ

194 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-8: Expermental lqud-phase actvty coeffcents for the ethanol () + butan-2-one (2) system K K 43.2 K γ γ γ γ γ γ Table 7-9: Expermental lqud-phase actvty coeffcents for the ethanol () + 2-methoxy-2- methylbutane (2) system K 43.9 K γ γ γ γ

195 γ γ γ γ CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-0: Expermental lqud-phase actvty coeffcents for the 2-methylpent-2-ene () + ethanol (2) system at K Table 7-: Expermental lqud-phase actvty coeffcents for the hexane () + acetontrle (2) system at K * 3.07 *.09 * *.47 * 2.6 * * Pont of VLLE 59

196 CHAPTER 7 DATA ANALYSIS AND DISCUSSION 7.4 Expermental VLE Data Reducton The reducton of the expermental VLE data was accomplshed usng the combned method and the drect method whch were dscussed n detal n Secton In the combned method, the vapour phase correcton factor was determned usng the vral equaton of state where the correlaton of Tsonopoulos (974) was used to evaluate the second vral coeffcents. The correlaton of Tsonopoulos (974) was able to cater for non-polar, polar and hydrogen bondng components and combnatons thereof. The lqud phase correcton factor was determned from three localcomposton based lqud phase actvty coeffcent models vz. the TK-Wlson, NRTL and modfed UNIQUAC thermodynamc models. The saturated pressures used n the combned method of VLE data reducton made use of the extended Antone and Wagner equatons, where the equaton wth a better ft of the expermental vapour pressure data were used for each component. In the drect method, the two most ndustrally used equatons of state were consdered vz. the SRK and PR equatons of state. To mprove predctons wth these equatons of state, the temperature dependent functon (α) of Mathas and Copeman (983) was used to replace the orgnally proposed temperature dependent functon n each EoS. Ths allowed the EoS to become more flexble and cater for both polar and non-polar components, where the regressed adjustable parameters for the temperature dependent functon (α) of Mathas and Copeman (983) were utlzed. The drect method also requred the use of a mxng rule to account for the nteracton of the components n order to accurately model the expermental VLE data. For ths purpose, the Wong and Sandler (992) mxng rule, as dscussed n Secton 3..3, was used. The mxng rule also requred the use of an actvty coeffcent model; hence the NRTL actvty coeffcent model was used for ths purpose. The combnatons used for the combned and drect methods are summarzed n Tables 7-2 and 7-3 respectvely. Table 7-2: The regresson combnatons used for the combned method. Second Vral Actvty Coeffcent Coeffcent Correlaton Model Abbrevaton Tsonopoulos (974) TK-Wlson TS-TKWILSON Tsonopoulos (974) NRTL TS-NRTL Tsonopoulos (974) modfed UNIQUAC TS-UNIQUAC 60

197 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-3: The regresson combnatons used for the drect method. Actvty Coeffcent Equaton of α Model for State Correlaton Mxng Rule Mxng Rule Abbrevaton Mathas and Wong and Soave (972) Copeman (983) Sandler (992) NRTL SRK-MC-WS-NRTL Peng and Mathas and Wong and Robnson (976) Copeman (983) Sandler (992) NRTL PR-MC-WS-NRTL The regresson algorthm for the expermental VLE data reducton for the combned method made use of the Nelder-Mead smplex method (Lagaras et al., 998). The regresson wth the drect method was acheved usng the THERMOPACK verson.0 developed by A Baba Ahmed and C. Coquelet. The objectve functon used for both methods was: F n P = = exp, P P exp, cal, 2 (7-6) Van Ness and Abbott (982) found that usng such an objectve functon as shown n Equaton (7-6) provdes a ft that was at least as good as any other and was the most smplest and drect objectve functon. The regresson for the combned method was wrtten n MATLAB as a varety of bult-n optmzaton functons were avalable for use. The fmnsearch functon, whch fnds the mnmum of an unconstraned mult-varable functon, was chosen n ths study Methoxy-2-Methylpropane () + Ethyl Acetate (2) Once the novel apparatus was constructed, test systems were selected to verfy that the apparatus was capable of measurng phase equlbrum data and to check the accuracy of the expermental procedure. Wth regards to VLE, the system of 2-methoxy-2-methylpropane + ethyl acetate at K was selected as a test system. Ths system was chosen snce lterature data was avalable wthn the pressure range of the apparatus and the data were also proven to be thermodynamcally consstent (Lee et al., 997). 6

198 CHAPTER 7 DATA ANALYSIS AND DISCUSSION The GC TCD calbraton for ths system s presented n Fgures C-25 and C-26 and reported n Table C-5 of Appendx C. The calbratons showed a lnear response for both dlute regons of ths system. The nverse of the response factor rato of the 2-methoxy-2-methylpropane dlute regon dd not dffer sgnfcantly from the response factor rato of the ethyl acetate dlute regon. Ths confrmed a lnear relatonshp for the entre composton range. An average response factor rato was however not used but care was taken to ensure that the correct calbraton graph was employed, dependng whether the samples were taken n the dlute 2-methoxy-2-methylpropane regon or dlute ethyl acetate regon. The nfluence of takng an average response factor rato would slghtly affect the accuracy especally for very dlute regons. Fgures 6- and 6-2 show that the expermental data measured compared well wth lterature data of Lee et al. (997). However, there were slght devatons n the vapour composton values. Intally when the vapour composton was sampled, there were sgnfcant devatons between the expermental data and the lterature data of Lee et al. (997). It was found that these devatons were attrbuted to a thermal gradent that exsted on the upper 36 SS flange of the equlbrum cell due to conductve and convectve paths of heat transfer. Hence the capllary of the was at a slghtly lower temperature than compared to the equlbrum temperature. Ths mpled that there was slght condensaton of the vapour on the tp of the capllary thus leadng to an ncorrect determnaton of the vapour phase composton. By tral and error, t was found that when the temperature of the upper 36 SS flange of the equlbrum cell was kept at 0. K hgher than the equlbrum temperature, the condensaton of vapour at the tp of the capllary was prevented. Ths test system was also subjected to thermodynamc modelng wth the combned and drect methods of VLE data regresson. The combned method used the second vral coeffcent correlaton of Tsonopoulos (974) to represent the vapour phase non-dealty and the lqud phase non-dealtes were represented wth NRTL, modfed UNIQUAC and TK-Wlson actvty coeffcent models. Regresson of the expermental data showed that the NRTL model (wth the α parameter ncluded n the regresson) provded the best ft to the expermental data, where the best ft was judged from the lowest root mean square devaton (RMSD) of the pressure and vapour compostons. The parameters from the regresson of the expermental data wth the combned method are reported n Table 7-4. As can be seen from the RMSD values for pressure and vapour composton n Table 7-4, the NRTL model offers only a slghtly better ft than compared to the other thermodynamc models. 62

199 CHAPTER 7 DATA ANALYSIS AND DISCUSSION The regressed value of the non-randomness parameter (α) s rather large, mplyng that the local dstrbuton s hghly non-random around the centre molecule. Generally, a hgh value of α s typcal of systems that exhbt hydrogen bondng. Although 2-methoxy-2-methylpropane and ethyl acetate do not exhbt hydrogen bonds, they are both polar compounds. Nevertheless, Walas (985) emphaszes that the parameter α s strctly an emprcal factor and does not clearly relate to any mechansm. Indeed ths can be seen when α s fxed at a value of 0.3, the regresson results show that the NRTL model offers no dstnct advantage over the TK-Wlson or modfed UNIQUAC models n the representaton of ths expermental data (see Table 7-3). The TK-Wlson, NRTL (wth α fxed at 0.3 durng regresson) and the modfed UNIQUAC models all show large values for the bnary nteracton parameters. However the NRTL model wth α ncluded as a regresson parameter showed smaller values for the bnary nteracton parameters, ndcatve of the emprcal nature of the α parameter. The large value of α = 3.54 could also ndcate a very organzed soluton n terms of molecular structure. The x-y and P-x-y plots for the combned method are presented n Fgures 7- and 7-2 respectvely. The expermental actvty coeffcents and those calculated by the NRTL model (wth α = 3.54) are presented n Fgure 7-3, whch shows that there s consderable devaton. Ths could possbly be due to errors n the measurement of the vapour compostons (dscussed further n thermodynamc consstency testng). The estmated uncertanty on the actvty coeffcent s 3 %. Table 7-4: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K. RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α = 3.54) TS-UNIQUAC : = - and = - ; NRTL: = - and = - ; mod UNIQUAC: = - and = -. 63

200 CHAPTER 7 DATA ANALYSIS AND DISCUSSION ths work TS-NRTL y x Fgure 7-: Ft of the TS-NRTL model combnaton to the x-y plot of the methoxy-2- methylpropane () + ethyl acetate (2) system at K for the combned method. Pressure / kpa P - x: ths work P - y: ths work P - x: TS-NRTL P - y: TS-NRTL x, y Fgure 7-2: Ft of the TS-NRTL model combnaton to the P-x-y plot of the methoxy-2- methylpropane () + ethyl acetate (2) system at K for the combned method. 64

201 CHAPTER 7 DATA ANALYSIS AND DISCUSSION 0.35 ln(γ ), ln(γ 2 ) ln(γ): ths work ln(γ2): ths work ln(γ): TS-NRTL ln(γ2): TS-NRTL x Fgure 7-3: Comparson of the expermental actvty coeffcents and those calculated from the TS-NRTL model combnaton for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K for the combned method. The drect method made use of the PR and the SRK equatons. For each equaton of state (EoS), the α-functon of Mathas and Copeman (983) and the mxng rule of Wong and Sandler (992) wth the NRTL model were used to regress the expermental data. The regresson showed that the PR EoS provdes a slghtly better ft to the expermental data. The parameters from the regresson of the expermental data wth the drect method are reported n Table 7-5. As can be seen from the RMSD values for pressure and vapour composton n Table 7-5, the PR EoS offers only a slghtly better ft than compared to the SRK EoS. The x-y and P-x-y plots for the combned method are presented n Fgures 7-4 and 7-5 respectvely. Table 7-5: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method of the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K. - - RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa SRK-MC-WS-NRTL PR-MC-WS-NRTL

202 CHAPTER 7 DATA ANALYSIS AND DISCUSSION ths work PR-MC-WS-NRTL y Fgure 7-4: Ft of the PR-MC-WS-NRTL model combnaton to the x-y plot of the 2- methoxy-2-methylpropane () + ethyl acetate (2) system at K for the drect method. x Pressure / kpa P - x: ths work P - y: ths work P - x: PR-MC-WS-NRTL P - y: PR-MC-WS-NRTL x, y Fgure 7-5: Ft of the PR-MC-WS-NRTL model combnaton to the P-x-y plot of the 2- methoxy-2-methylpropane () + ethyl acetate (2) system at K for the drect method. 66

203 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Overall by comparson, the regresson results from the drect method show slghtly hgher values for the pressure RMSD but slghtly lower values for the vapour composton RMSD. Thus the thermodynamc models from both methods show good representaton of the expermental data Methanol () + Butan-2-one (2) Ths system was one of the systems prmarly measured for a South Afrcan petrochemcal company, where thermodynamc nteractons of lght alcohols and carbonyls for a number of dstllaton systems are not well descrbed. Ths system has also been studed by other researchers such as Brtton et al. (947), Hll and Van Wnkle (952), Prvott et al. (966), Eduljee and Twar (976), Knapp and Doherty (992) and Lee et al. (995) to name a few. However, VLE data n the open lterature for ths system was not expermentally measured at , and K. Hence, VLE data measured for ths system at these temperatures consttute new expermental data. The GC TCD calbraton for ths system s presented n Fgures C-28 and C-29 and reported n Table C-5 of Appendx C. The calbratons showed a lnear response for both dlute regons of ths system. The nverse of the response factor rato of the methanol dlute regon does not dffer sgnfcantly from the response factor rato of the butan-2-one dlute regon. Ths confrmed a lnear relatonshp for the entre composton range. An average response factor rato was however not used but care was taken to ensure that the correct calbraton graph was employed, dependng whether the samples were taken n the dlute methanol regon or dlute butan-2-one regon. The parameters from the regresson of the expermental data wth the combned method are reported n Table 7-6. Based on the RMSD values, t can be seen that the TK-Wlson model provdes a slghtly better ft for the system at and K but the NRTL model (wth α beng regressed) provded a better ft for the system at K. The NRTL model (wth α beng regressed) seemed to represent the expermental data well for ths system at all the sotherms measured, however the TK-Wlson model offered a slghtly better ft at and K. The modfed UNIQUAC model on the other hand, was also able to show a good ft of the expermental data at and K but dsplayed a large devaton from the expermental data at K. The x-y plots for , and K are shown n Fgure 7-6. The P-x-y plots for , and K are shown n Fgure 7-7. The expermental actvty coeffcents and those calculated by the respectve best ft models for the system at , and K are presented n Fgure 7-8, where t can be seen that temperature has no sgnfcant effect on the 67

204 CHAPTER 7 DATA ANALYSIS AND DISCUSSION actvty coeffcent. Ths could be due the excess enthalpy beng ndependent of temperature wthn the range measured. The estmated uncertanty on the actvty coeffcent s 3 %. Table 7-6: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the methanol () + butan-2-one (2) system. Model J.mol - J.mol - P / kpa P / kpa RMSD AAD RMSD AAD K TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α =.45) TS-UNIQUAC K TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α = 0.077) TS-UNIQUAC K TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α =.89) TS-UNIQUAC : = - and = - ; NRTL: = - and = - ; mod UNIQUAC: = - and = -. The system exhbts an azeotrope for the and K sotherms at approxmately = and 0.98 respectvely. The expermental data does not however seem to ndcate an azeotrope at K. Hence, as the temperature ncreases, the composton of the azeotrope changes such that t becomes rcher n the more volatle component. The presence of an azeotrope for ths system s not surprsng as expermental measurements at lower temperatures and pressure have been prevously carred out by researchers such as Brtton et al. (947), Hll and Van Wnkle (952) and Knapp and Doherty (992) to name a few, who have found that ths system exhbts a homogeneous azeotrope. The presence of an azeotrope mples that a system s non-deal and that conventonal dstllaton cannot separate the components nto hgh purty chemcals. Knapp and Doherty (992) 68

205 CHAPTER 7 DATA ANALYSIS AND DISCUSSION explored the use of pressure-swng dstllaton for separatng such a homogeneous azeotropc mxture. The best ft models for the respectve sotherms of ths system were also able to show a good representaton of the expermental actvty coeffcents. The expermental actvty coeffcents were used to carry out the drect test for thermodynamc consstency (dscussed later). Wth regards to the drect method, both the SRK and PR EoS provde a good ft of the expermental data of ths system. The PR EoS however provdes a margnally better ft at and K whlst the SRK EoS provded a slghtly better ft at K. The parameters from the regresson of the expermental data wth the drect method are reported n Table 7-7. The x-y plots for , and K are shown n Fgure 7-9 and the P-x-y plots for , and K are shown n Fgures y x ths work ( K) ths work (398.4 K) ths work (43.20 K) TS-TKWILSON ( K) TS-NRTL (398.4 K) TS-TKWILSON (43.20 K) Fgure 7-6: Best ft model combnaton for the x-y plot of the methanol () + butan-2-one (2) system wth the combned method. 69

206 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Pressure / kpa P - x: ths work ( K) P - y: ths work ( K) P - x: ths work (398.4 K) P - y: ths work (398.4 K) P - x: ths work (43.20 K) P - y: ths work (43.20 K) P - x: best ft model P - y: best ft model Fgure 7-7: Best ft model combnaton ( K: TS-TKWILSON; K: TS-NRTL; K: TS-TKWILSON) to the P-x-y plot of the methanol () + butan-2-one (2) system wth the combned method. x ln(γ ), ln(γ 2 ) ln(γ): ths work ( K) ln(γ2): ths work ( K) ln(γ): ths work (398.4 K) ln(γ2): ths work (398.4 K) ln(γ): ths work (43.20 K) ln(γ2): ths work (43.20 K) ln(γ): TS-TKWILSON ( K) ln(γ2): TS-TKWILSON ( K) ln(γ): TS-NRTL (398.4 K) ln(γ2): TS-NRTL (398.4 K) ln(γ): TS-TKWILSON (43.20 K) ln(γ2): TS-TKWILSON (43.20 K) Fgure 7-8: Comparson of the expermental actvty coeffcents and those calculated from the best ft model combnaton for the methanol () + butan-2-one (2) system wth the combned method. x 70

207 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-7: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method appled to the methanol () + butan-2-one (2) system. - - RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa K SRK-MC-WS-NRTL PR-MC-WS-NRTL K SRK-MC-WS-NRTL PR-MC-WS-NRTL K SRK-MC-WS-NRTL PR-MC-WS-NRTL y x ths work ( K) ths work (398.4 K) ths work (43.20 K) PR-MC-WS-NRTL ( K) SRK-MC-WS-NRTL (398.4 K) PR-MC-WS-NRTL (43.20 K) Fgure 7-9: Best ft model combnaton for the x-y plot of the methanol () + butan-2-one (2) system wth the drect method. 7

208 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Pressure / kpa P - x: ths work ( K) P - y: ths work ( K) P - x: ths work (398.4 K) P - y: ths work (398.4 K) P - x: ths work (43.20 K) P - y: ths work (43.20 K) P - x: best ft model P - y: best ft model x Fgure 7-20: Best ft model combnaton ( K: PR-MC-WS-NRTL; K: SRK-MC- WS-NRTL; K: PR-MC-WS-NRTL) to the P-x-y plot of the methanol () + butan-2-one (2) system wth the drect method Ethanol () + Butan-2-one (2) Ths system was a contnuaton of the work carred out for a South Afrcan petrochemcal company for another lght alcohol vz. ethanol. Expermental data for ths bnary system at low temperatures and sub-atmospherc pressures were avalable n the open lterature but there were no data for moderate to hgh pressure ranges (Hellwg and Van Wnkle, 953; Ohta et al., 98; Arce et al., 996; Wen and Tu, 2007 and Martínez et al., 2008). Hence the expermental work carred or ths system at , and 43.2 K were not prevously reported n the open lterature and thus consttuent as new expermental data. The GC TCD calbraton for ths system s presented n Fgures C-3 and C-32 and reported n Table C-5 of Appendx C. Smlar to the prevously dscussed system, the calbratons showed a lnear response for both dlute regons of ths system. The nverse of the response factor rato of the ethanol dlute regon dd not dffer sgnfcantly from the response factor rato of the butan-2-one dlute regon. Ths confrmed a lnear relatonshp for the entre composton range. As before, an average response factor rato was however not used but care was taken to ensure that the correct 72

209 CHAPTER 7 DATA ANALYSIS AND DISCUSSION calbraton graph was employed, dependng whether the samples were taken n the dlute ethanol regon or dlute butan-2-one regon. Table 7-8: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the ethanol () + butan-2-one (2) system. RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa K TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α = 0.044) TS-UNIQUAC K TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α = 0.028) TS-UNIQUAC K TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α = 2.06) TS-UNIQUAC : = - and = - ; NRTL: = - and = - ; mod UNIQUAC: = - and = -. The parameters from the regresson of the expermental data wth the combned method are reported n Table 7-8. Based on the RMSD values, t can be seen that the modfed UNIQUAC model provdes the best ft for the system at and K but the NRTL model (wth α beng regressed) provded the best ft for the system at 43.2 K. Nevertheless all the lqud phase actvty coeffcent models provded a reasonable ft to the expermental data for all the sotherms measured. The x-y plots are shown n Fgure 7-2. The P-x-y plots are shown n Fgure The expermental actvty coeffcents and those calculated by the respectve best ft models for the system are presented n Fgure Smlar to the prevous system, t can be seen that temperature has no sgnfcant effect on the actvty coeffcent. Ths could be due the excess enthalpy beng 73

210 CHAPTER 7 DATA ANALYSIS AND DISCUSSION ndependent of temperature wthn the range measured. The estmated uncertanty on the actvty coeffcent s 3 %. The system exhbts an azeotrope for the , and 43.2 K sotherms at approxmately = 0.75, 0.84 and 0.9 respectvely, whch ndcates that as the temperature ncreases, the composton of the azeotrope changes such that t becomes rcher n the more volatle component. The presence of an azeotrope for ths system was also observed at atmospherc pressure by researchers such as Wen and Tu (2007) and Martínez et al. (2008). As mentoned prevously, the presence of an azeotrope mples that a system s non-deal and that conventonal dstllaton cannot separate the components nto hgh purty chemcals. Accordng to Martínez et al. (2008), an azeotrope for ths system was found to be rather senstve to pressure and thus the use of pressureswng dstllaton would prove to be a useful technque to overcome ths azeotropc mxture. The best ft models for the respectve sotherms of ths system were also able to show a good representaton of the expermental actvty coeffcents. However, the modfed UNIQUAC model shows sgnfcant devaton n the butan-2-one dlute regon for the system at and K (see Fgure 7-7). The expermental actvty coeffcents were used to carry out the drect test for thermodynamc consstency (dscussed later) y x ths work ( K) ths work ( K) ths work (43.2 K) TS-UNIQUAC ( K) TS-UNIQUAC ( K) TS-NRTL (43.2 K) Fgure 7-2: Best ft model combnaton for the x-y plot of the ethanol () + butan-2-one (2) system wth the combned method. 74

211 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Pressure / kpa P - x: ths work ( K) P - y: ths work ( K) P - x: ths work ( K) P - y: ths work ( K) P - x: ths work (43.2 K) P - y: ths work (43.2 K) P - x: best ft model P - y: best ft model x, y Fgure 7-22: Best ft model combnaton ( K: TS-UNIQUAC; K: TS-UNIQUAC; K: TS-NRTL) to the P-x-y plot of the ethanol () + butan-2-one (2) system wth the combned method. ln(γ ), ln(γ 2 ) ln(γ): ths work ( K) ln(γ2): ths work ( K) ln(γ): ths work ( K) ln(γ2): ths work ( K) ln(γ): ths work (43.2 K) ln(γ2): ths work (43.2 K) ln(γ): TS-UNIQUAC ( K) ln(γ2): TS-UNIQUAC ( K) ln(γ): TS-UNIQUAC ( K) ln(γ2): TS-UNIQUAC ( K) ln(γ): TS-NRTL (43.2 K) ln(γ2): TS-NRTL (43.2 K) x Fgure 7-23: Comparson of the expermental actvty coeffcents and those calculated from the best ft model combnaton for the ethanol () + butan-2-one (2) system wth the combned method. 75

212 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-9: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method of the ethanol () + butan-2-one (2) system. - - RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa K SRK-MC-WS-NRTL PR-MC-WS-NRTL K SRK-MC-WS-NRTL PR-MC-WS-NRTL K SRK-MC-WS-NRTL PR-MC-WS-NRTL y Fgure 7-24: Best ft model combnaton for the x-y plot of the ethanol () + butan-2-one (2) system wth the drect method. x ths work ( K) ths work ( K) ths work (43.2 K) SRK-MC-WS-NRTL ( K) SRK-MC-WS-NRTL ( K) SRK-MC-WS-NRTL (43.2 K) Wth regards to the drect method, both the SRK and PR EoS provded a good ft of the expermental data of ths system. The SRK EoS however provded a margnally better ft for ths system at K, whereas at and 43 K there s no sgnfcant advantage of one EoS to the other. The parameters from the regresson of the expermental data wth the drect method are 76

213 CHAPTER 7 DATA ANALYSIS AND DISCUSSION reported n Table 7-9. The x-y and P-x-y plots for , and 43.2 K are shown respectvely n Fgures 7-24 and Pressure / kpa P - x: ths work (43.2 K) P - y: ths work (43.2 K) P - x: ths work ( K) P - y: ths work ( K) P - x: ths work ( K) P - y: ths work ( K) P - x: best ft model P - y: best ft model x Fgure 7-25: Best ft model combnaton (383.26, and 43.2 K: SRK-MC-WS-NRTL) to the P-x-y plot of the ethanol () + butan-2-one (2) system wth the drect method Ethanol () + 2-Methoxy-2-Methylbutane (2) Ths system was also measured as a contnuaton of the work carred out for a South Afrcan petrochemcal company. Over the years 2-methoxy-2-methylbutane has been consdered as a fuel oxygenate to ncrease octane enhancement and oxygen content n gasolne n formng lead-free gasolne (Ignatus et al., 995). VLE data at 0.32 kpa and physcal propertes for the ternary mxture of water + ethanol + 2-methoxy-2-methylbutane have been studed by Arce et al. (997 and 998). Expermental data for the bnary system of ethanol + 2-methoxy-2-methylbutane at 0.32 kpa were avalable n the open lterature but there were no data for moderate to hgh pressure ranges (Arce et al., 996). Hence the expermental work carred or ths system at and 43.9 K were not prevously reported n the open lterature and thus consttuent as new expermental data. It should be noted that 2-methoxy-2-methylbutane s a costly chemcal. A quotaton obtaned from Captal Lab Supplers cc on 22 Aprl 200 showed a cost of R5 50 for 500 ml of 2-methoxy-2- methylbutane wth purty greater than 97%. As explaned n Chapter 5, only approxmately 75 of 77

214 CHAPTER 7 DATA ANALYSIS AND DISCUSSION each component was needed to carry out GC calbratons, degassng, vapour pressure and VLE measurements for two sotherms. The GC TCD calbraton for ths system s presented n Fgures C-34 and C-35 and reported n Table C-5 of Appendx C. Smlar to the prevously dscussed systems, the calbratons showed a lnear response for both dlute regons of ths system. The nverse of the response factor rato of the ethanol dlute regon dd not dffer sgnfcantly from the response factor rato of the 2-methoxy-2- methylbutane dlute regon. Ths confrmed a lnear relatonshp for the entre composton range. As before, an average response factor rato was however not used but care was taken to ensure that the correct calbraton graph was employed, dependng whether the samples were taken n the dlute ethanol regon or dlute 2-methoxy-2-methylbutane regon. Table 7-20: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the ethanol () + 2-methoxy-2- methylbutane (2) system. RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa K TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α = 0.083) TS-UNIQUAC K TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α = 0.55) TS-UNIQUAC : = - and = - ; NRTL: = - and = - ; mod UNIQUAC: = - and = -. The parameters from the regresson of the expermental data wth the combned method are reported n Table Based on the RMSD values, t can be seen that the NRTL model (wth α beng regressed) provdes the best ft for the system at both and 43.9 K. Nevertheless all the lqud phase actvty coeffcent models provde a reasonable ft to the expermental data for both the sotherms measured. The x-y and P-x-y plots for and 43.9 K are shown respectvely n Fgures 7-26 and The expermental actvty coeffcents and those calculated by the respectve 78

215 CHAPTER 7 DATA ANALYSIS AND DISCUSSION best ft models for the system at and 43.9 K are presented n Fgure Once more ths system lke the prevous two shows that temperature has no sgnfcant effect on the actvty coeffcent. Ths could be due the excess enthalpy beng ndependent of temperature wthn the range measured. The estmated uncertanty on the actvty coeffcent s 3 %. The system exhbts an azeotrope for both the and 43.9 K sotherms at approxmately = 0.77 and 0.78 respectvely. From the expermental data, one can observe that the azeotropc composton s hardly affected by the 5 K change n temperature between the two sotherms. The presence of an azeotrope for ths system was also observed at 0.32 kpa by Arce et al. (996). As mentoned prevously, an azeotrope mples that a system s non-deal and that conventonal dstllaton cannot separate the components nto hgh purty chemcals. Unlke the prevous dscussed system of ethanol () + butan-2-one (2), pressure-swng dstllaton cannot be consdered for ths system of ethanol () + 2-methoxy-2-methylbutane (2) snce the expermental data suggests that the azeotropc composton hardly changes wth a 5 K change of temperature. Therefore, alternatve forms of dstllaton should be consdered vz. homogeneous or heterogeneous azeotropc dstllaton. Such dstllaton technques are dscussed by Seader and Henley (998). y x ths work ( K) ths work (43.9 K) TS-NRTL ( K) TS-NRTL (43.9 K) Fgure 7-26: Best ft model combnaton for the x-y plot of the ethanol () + 2-methoxy-2- methylbutane (2) system wth the combned method. 79

216 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Pressure / kpa P - x: ths work (43.9 K) P - y: ths work (43.9 K) P - x: ths work ( K) P - y: ths work ( K) P - x: best ft model P - y: best ft model x, y Fgure 7-27: Best ft model combnaton ( and 43.9 K: TS-NRTL) to the P-x-y plot of the ethanol () + 2-methoxy-2-methylbutane (2) system wth the combned method. ln(γ ), ln(γ 2 ) ln(γ): ths work ( K) ln(γ2): ths work ( K) ln(γ): ths work (43.9 K) ln(γ2): ths work (43.9 K) ln(γ): TS-NRTL ( K) ln(γ2): TS-NRTL ( K) ln(γ): TS-NRTL (43.9 K) ln(γ2): TS-NRTL (43.9 K) x Fgure 7-28: Comparson of the expermental actvty coeffcents and those calculated from the best ft model combnaton for the ethanol () + 2-methoxy-2-methylbutane (2) system wth the combned method. 80

217 CHAPTER 7 DATA ANALYSIS AND DISCUSSION The best ft models for both sotherms of ths system were also able to show a good representaton of the expermental actvty coeffcents. The expermental actvty coeffcents were used to carry out the drect test for thermodynamc consstency (dscussed later). Table 7-2: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method of the ethanol () + 2-methoxy-2-methylbutane (2) system. - - RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa K SRK-MC-WS-NRTL PR-MC-WS-NRTL K SRK-MC-WS-NRTL PR-MC-WS-NRTL y ths work ( K) ths work (43.9 K) PR-MC-WS-NRTL ( K) SRK-MC-WS-NRTL (43.9 K) Fgure 7-29: Best ft model combnaton for the x-y plot of the ethanol () + 2-methoxy-2- methylbutane (2) system wth the drect method. x 8

218 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Pressure / kpa P - x: ths work (43.9 K) P - y: ths work (43.9 K) P - x: ths work ( K) P - y: ths work ( K) P - x: best ft model P - y: best ft model x, y Fgure 7-30: Best ft model combnaton ( K: PR-MC-WS-NRTL and 43.2 K: SRK- MC-WS-NRTL) to the P-x-y plot of the ethanol () + 2-methoxy-2-methylbutane (2) system wth the drect method. Wth regards to the drect method, both the SRK and PR EoS provde a good ft of the expermental data of ths system. There s no advantage of one EoS compared to the other at K but for the sotherm at 43.9 K, the SRK EoS provdes a margnally better ft to the expermental data. The parameters from the regresson of the expermental data wth the drect method are reported n Table 7-2. The x-y plots for and 43.9 K are shown n Fgure 7-29 and the P-x-y plots for and 43.9 K are shown n Fgure Methylpent-2-ene + Ethanol (2) Ths system was also measured as a contnuaton of the work carred out for a South Afrcan petrochemcal company. The component 2-methylpent-2-ene s best known for ts use as a fuel addtve (Hodges and Ketley, 2003). Due to 2-methylpent-2-ene beng an expensve chemcal, there s very lttle or no reported thermodynamc data for the bnary system of 2-methylpent-2-ene () + ethanol (2) n the open lterature. A quotaton obtaned from Captal Lab Supplers cc on 22 Aprl 200 showed a cost of R2 605 for 50 ml of 2-methylpent-2-ene wth a mnmum purty of 98%. Hence, the expermental VLE data measured for ths system n ths study consttutes as new expermental data. 82

219 CHAPTER 7 DATA ANALYSIS AND DISCUSSION The GC TCD calbraton for ths system s presented n Fgures C-37 and C-38 and reported n Table C-5 of Appendx C. Unlke the prevously dscussed systems, the calbratons here showed a non-lnear response for both dlute regons of ths system. A second order polynomal equaton was found to adequately descrbe both dlute regons well. However the calbraton curve for the ethanol dlute regon showed a more dstnctve shape when compared to the calbraton curve for the 2- methylpent-2-ene dlute regon. Hence, care was taken to ensure that the correct calbraton graph was employed, dependng on whether the samples were taken n the dlute ethanol regon or dlute 2-methylpent-2-ene regon. The parameters from the regresson of the expermental data wth the combned method are reported n Table Based on the RMSD values, t can be seen that the NRTL model (wth α beng regressed) provdes the best ft. The TK-Wlson and modfed UNIQUAC models both show sgnfcantly larger devatons for pressure. However, the vapour composton devatons are somewhat large but smlar for all the lqud phase actvty models. Hence the expermental vapour compostons must therefore contan some error. The x-y and P-x-y plots for ths system are shown n Fgures 7-3 and 7-32 respectvely. The expermental actvty coeffcents and those calculated by the best ft model are presented n Fgure The estmated uncertanty on the actvty coeffcent s 3 %. Table 7-22: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the 2-methylpent-2-ene () + ethanol (2) system at K. RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α = -0.55) TS-UNIQUAC : = - and = - ; NRTL: = - and = - ; mod UNIQUAC: = - and = -. 83

220 CHAPTER 7 DATA ANALYSIS AND DISCUSSION ths work TS-NRTL y x Fgure 7-3: Ft of the TS-NRTL model combnaton to the x-y plot of the 2-methylpent-2-ene () + ethanol (2) system at K for the combned method Pressure / kpa P - x: ths work P - y: ths work P - x: TS-NRTL P - y: TS-NRTL Fgure 7-32: Ft of the TS-NRTL model combnaton to the P-x-y plot of the 2-methylpent-2- ene () + ethanol (2) system at K for the combned method. x 84

221 CHAPTER 7 DATA ANALYSIS AND DISCUSSION ln(γ ), ln(γ 2 ) ln(γ): ths work ln(γ2): ths work ln(γ): TS-NRTL ln(γ2): TS-NRTL Fgure 7-33: Comparson of the expermental actvty coeffcents and those calculated from the TS-NRTL model combnaton for the 2-methylpent-2-ene () + ethanol (2) system at K for the combned method. x Pressure / kpa ethanol 2-methylpent-2-ene Bancroft pont Temperature / K Fgure 7-34: Comparson of the vapour pressures of ethanol and 2-methylpent-2-ene showng the Bancroft pont. 85

222 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Ths system also exhbts an azeotrope at approxmately = The vapour pressure data for these two components show that they have very close bolng ponts. When the vapour pressures of two separate pure components are the same, the temperature and pressure at whch ths occurs s known as the Bancroft pont (Rowlnson, 969). The regressed expermental vapour pressure data for these two components studed n ths work s shown n Fgure 7-34, where the Bancroft pont occurs at approxmately 389 K and 380 kpa. Accordng to Ellott and Ranwater (2000), the exstence of a Bancroft pont can ndcate a sgnfcant composton dependence of an azeotropc system. Due to tme constrants and chemcal avalablty, only one sotherm was measured for ths system. Hence the effect of temperature on the azeotropc composton could not be studed for ths system. Ellott and Ranwater (2000) also menton that the lkelhood of an azeotrope dmnshes as condtons dverge from the Bancroft pont and as a consequence the composton of the azeotrope shfts, ncreasng the mole fracton of the component whose vapour pressure ncreases more rapdly wth temperature (n ths case ethanol). As dscussed prevously, alternate forms to conventonal dstllaton (such as pressure-swng and homogeneous or heterogeneous azeotropc dstllaton) must be consdered to separate these two components nto hgh purty chemcals. The best ft model for ths system was also able to show good representaton of the expermental actvty coeffcents whch were used to carry out the drect test for thermodynamc consstency (dscussed later). Wth regards to the drect method, the PR EoS provded a better ft than the SRK EoS to the expermental data of ths system. Smlar to the combned method, the models for the drect method also showed consderable devaton for the vapour compostons. The parameters from the regresson of the expermental data wth the drect method are reported n Table The x-y and P-x-y plots are shown n Fgures 7-35 and Table 7-23: Model parameters, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the drect method of the 2-methylpent-2-ene () + ethanol (2) system at K. - - RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa SRK-MC-WS-NRTL PR-MC-WS-NRTL

223 CHAPTER 7 DATA ANALYSIS AND DISCUSSION ths work PR-MC-WS-NRTL y Fgure 7-35: Ft of the PR-MC-WS-NRTL model combnaton to the x-y plot of the 2- methylpent-2-ene () + ethanol (2) system at K for the drect method. x Pressure / kpa P - x: ths work P - y: ths work P - x: PR-MC-WS-NRTL P - y: PR-MC-WS-NRTL x, y Fgure 7-36: Ft of the PR-MC-WS-NRTL model combnaton to the P-x-y plot of the 2- methylpent-2-ene () + ethanol (2) system at K for the drect method. 87

224 CHAPTER 7 DATA ANALYSIS AND DISCUSSION 7.5 Expermental LLE Data Reducton The expermental LLE data measured n ths study was to confrm the versatlty of the newly developed apparatus. Hence bnary systems of LLE data were measured for two systems used as tests: hexane + acetontrle and methanol + heptane. Bnary systems of LLE data are also known as mutual solublty data. Raal and Mühlbauer (998) mentoned that there s no means for fndng the actvty coeffcents from mutual solublty data but only the rato of the actvty coeffcents. Hence, mutual solublty data can only be used to obtan the parameters of a lqud phase actvty coeffcent model as a functon of temperature (usually two parameters per temperature for asymmetrc models). The actvty coeffcent models that were used for VLE data reducton were also used for the LLE data reducton as these models were also capable of representng LLE data. Therefore the expermental mutual solublty data were regressed wth the TK-Wlson, NRTL and modfed UNIQUAC actvty coeffcent models. Wth regards to the NRTL model, the nonrandomness parameter (α) was fxed to a value of 0.3. For both the LLE systems measured n ths study, the GC TCD calbraton was carred out usng the drect calbraton method as opposed to the area rato method. Ths was done snce a sutable solvent for the heterogeneous mxtures could not be found such that the retenton tme of the solvent peak was dfferent from the bnary components. Varous avalable GC columns were also nvestgated but to no aval Hexane () + Acetontrle (2) Ths test system was selected snce both bnary LLE and VLLE data could be measured. In fndng such a system, one had to ensure that the pressure values of the VLLE data were above atmospherc pressure to enable the to sample the respectve equlbrum phases. Wth regards to the bnary LLE data, hgh pressure ntrogen was used to mantan a pressure of 350 kpa n the equlbrum cell to enable samplng wth the, as was outlned n Chapter 5. The expermental data of Bernabe et al. (988) and Sug and Katayama (978) were avalable for comparson and are shown n Secton of Chapter 6. The data measured n ths study showed consderable devaton to that of Bernabe et al. (988). It should be noted that the data measured by Bernabe et al. (988) made use of the cloud pont method whch was rather subjectve snce the equlbrum pont was judged from vsual observatons. On the other hand, the data of Sug and Katayama (978) was n agreement wth the data measured n ths study for the hexane rch phase. 88

225 CHAPTER 7 DATA ANALYSIS AND DISCUSSION The GC TCD calbraton results are presented n Fgures C-40 and C-4 for hexane and acetontrle respectvely and reported n Table C-6 of Appendx C. The model parameters for the LLE data reducton are reported n Table 7-24 and the temperature dependence of the parameters are presented n Fgures 7-37 to The ftted equatons for the model parameters wthn the temperature range are reported n Table Table 7-24: Model parameters from mutual solublty data for the hexane () + acetontrle (2) system. Actvty Coeffcent Models TK-Wlson NRTL mod. UNIQUAC Temperature (K) J.mol - J.mol - J.mol - J.mol - J.mol - J.mol a 2 - a 22, a 2 - a / J.mol a 2 - a 22 a 2 - a Ft for a 2 - a 22 Ft for a 2 - a Temperature / K Fgure 7-37: Temperature dependence of the TK-Wlson model parameters for the hexane () + acetontrle (2) system. 89

226 CHAPTER 7 DATA ANALYSIS AND DISCUSSION 6000 g 2 - g 22, g 2 - g / J.mol g 2 - g 22 g 2 - g Ft for g 2 - g 22 Ft for g 2 - g Temperature / K Fgure 7-38: Temperature dependence of the NRTL model parameters for the hexane () + acetontrle (2) system g 2 - g 22, g 2 - g / J.mol u 2 - u 22 u 2 - u Ft for u 2 - u 22 Ft for u 2 - u Temperature / K Fgure 7-39: Temperature dependence of the modfed UNIQUAC model parameters for the hexane () + acetontrle (2) system. 90

227 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-25: Ftted equatons for the actvty coeffcent models used n the LLE data reducton Actvty Coeffcent Model TK-Wlson NRTL Mod. UNIQUAC for the hexane () + acetontrle (2) system. Ftted Equatons 2 a 2 a22 =.4565T T a 2 a = 5.328T T g 2 g 22 =.035T T g 2 g = T T u 2 u22 =.6997T T u 2 u = T T Temperature Range / K 348 to to to 34 The actvty coeffcent model parameters from the LLE data reducton was satsfactorly ftted wth a second order polynomal equaton for the temperature range studed. It was clear from Fgures 7-3 to 7-33 that the trend of the ftted equatons showed consderable devatons to the reduced LLE data. It should be noted however that each mutual solublty data pont was reduced ndvdually. Hence such devatons can be explaned snce there are multple solutons that can be obtaned from each data reducton. However t should be noted that uncertantes n the measurement of the data could also have contrbuted to the devatons. Therefore care should be exercsed when usng the ftted equatons for predctons outsde the temperature range Methanol () + Heptane (2) As the expermentally measured LLE data for the hexane + acetontrle system dd not agree to the lterature data of Bernabe et al. (988), a second LLE test system was chosen to consoldate and verfy the versatlty of the newly developed apparatus to measure LLE data. Hence only a few data ponts were measured for the methanol + heptane system to accomplsh ths purpose. The results presented n Secton of Chapter 6 showed that the expermental data measured was n agreement wth the lterature data of Hgashuch et al. (987), Katayama and Ichkawa (995) and Matsuda et al. (2002). The comparson of data confrmed that the newly developed apparatus was capable of measurng LLE data. The GC TCD calbraton results are presented n Fgures C-43 and C-44 for methanol and heptane respectvely and reported n Table C-6 of Appendx C. The model parameters for the LLE data reducton are reported n Table 7-26 and the temperature dependence of the parameters are 9

228 CHAPTER 7 DATA ANALYSIS AND DISCUSSION presented n Fgures 7-40 to The ftted equatons for the model parameters wthn the temperature range are reported n Table Table 7-26: Model parameters from mutual solublty data for the methanol () + heptane (2) system. Actvty Coeffcent Models TK-Wlson NRTL mod. UNIQUAC Temperature (K) J.mol - J.mol - J.mol - J.mol - J.mol - J.mol a 2 - a 22, a 2 - a / J.mol a a 22 a a Ft for a a 22 Ft for a 2 - a Temperature / K Fgure 7-40: Temperature dependence of the TK-Wlson model parameters for the methanol () + heptane (2) system. 92

229 CHAPTER 7 DATA ANALYSIS AND DISCUSSION g 2 - g 22, g 2 - g / J.mol g 2 - g 22 g 2 - g Ft for g 2 - g 22 Ft for g 2 - g Temperature / K Fgure 7-4: Temperature dependence of the NRTL model parameters for the methanol () + heptane (2) system u 2 - u 22, u 2 - u / J.mol u 2 - u 22 u 2 - u Ft for u 2 - u 22 Ft for u 2 - u Temperature / K Fgure 7-42: Temperature dependence of the modfed UNIQUAC parameters for the methanol () + heptane (2) system. 93

230 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-27: Ftted equatons for the actvty coeffcent models used n the LLE data reducton Actvty Coeffcent Model TK-Wlson NRTL Mod. UNIQUAC a for the methanol () + heptane (2) system. Ftted Equatons a22 = 7.748T T a 2 a = 0.577T 390.9T g 2 g 22 = 0.54T 326.3T g 2 g =.095T 730.4T u 2 u22 = 0.32T 86.35T u 2 u = 0.58T 384.6T Temperature Range / K 308 to to to 38 Snce only three data ponts were measured for ths system, no conclusve comment on the ftted equatons can be made as a second order polynomal equaton requres a mnmum of three data ponts for fttng. 7.6 Expermental VLLE Data Reducton As mentoned prevously n Chapter 3, systems that exhbt VLLE behavour are hghly non-deal. Expermental VLLE data was also measured as part of ths study to show versatlty of the newly developed apparatus. The measurement of the VLLE pont also showed the success of usng a sngle moble to sample all three phases. The combned method for data reducton was used for the VLLE system measured n ths study Hexane () + Acetontrle (2) As mentoned prevously, ths system was chosen snce VLLE data could be measured at pressures hgher than atmospherc to accommodate the use of the. Although there are numerous aqueous systems that exhbt LLE or VLLE behavour, water was avoded as a component for ths study. Ths was done to avod damage to the polymer used n the. Although modfcatons for the polymer were avalable, ths was not ncluded as part of ths study due to tme constrants. Hence, a sutable non-aqueous VLLE test system wthn the pressure transmtter range could not be found n lterature for data comparson. However, snce the system of hexane + acetontrle met all the condtons for use n the newly developed apparatus, t was therefore chosen as a system to test the 94

231 CHAPTER 7 DATA ANALYSIS AND DISCUSSION versatlty of the apparatus. Ths also means that the VLLE data for the hexane + acetontrle at K consttutes as a new expermental VLLE data set. The GC TCD calbraton results were already mentoned and dscussed prevously n Secton The parameters from the regresson of the expermental data wth the combned method are reported n Table Based on the RMSD values, t can be seen that the NRTL model (wth α beng regressed) and the TK-Wlson models provded the best ft wth the latter havng only a margnally better RMSD for the pressures. The UNIQUAC model showed a sgnfcantly larger value for the pressure RMSD. However, the vapour composton devatons are sgnfcantly large but smlar for all the lqud phase actvty models. Hence the expermental vapour compostons must therefore contan some error or t could mean that the second vral coeffcent of Tsonopoulos (974) could not represent the vapour phase accurately. The x-y and P-x-y plots for ths system are shown n Fgures 7-43 and 7-44 respectvely. Table 7-28: Model parameters ( and ) a, root mean square devatons (RMSD) and absolute average devaton (AAD) values for the combned method of the hexane () + acetontrle (2) system at K. RMSD AAD RMSD AAD Model J.mol - J.mol - P / kpa P / kpa TS-TKWILSON TS-NRTL (α = 0.3) TS-NRTL (α = 0.44) TS-UNIQUAC : = - and = - ; NRTL: = - and = - ; mod UNIQUAC: = - and = -. 95

232 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Pont of VLLE y ths work TS-TKWILSON x Fgure 7-43: Ft of the TS-TKWILSON model combnaton to the x-y plot of the hexane () + acetontrle (2) system at K for the combned method Pont of VLLE Pressure / kpa P - x: ths work P - y: ths work 00 P - x: TS-TKWILSON P - y: TS-TKWILSON x, y Fgure 7-44: Ft of the TS-TKWILSON model combnaton to the P-x-y plot of the hexane () + acetontrle (2) system at K for the combned method. 96

233 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Pont of VLLE Pressure / kpa x, y Fgure 7-45: Comparson of the P-x-y predcton plot usng the parameters regressed from LLE and VLLE data wth the TK-Wlson model for the hexane () + acetontrle (2) system at K. P - x: ths work P - y: ths work P - x: TS-TKWILSON (VLLE Regresson) P - y: TS-TKWILSON (VLLE Regresson) P - x: TK-Wlson (LLE Regresson) P - x: TK-Wlson (LLE Regresson) LLE Regresson VLLE Regresson G / J.mol x I x II x Fgure 7-46: Comparson of the molar Gbbs energy of mxng usng the parameters regressed from LLE and VLLE data wth the TK-Wlson model for the hexane () + acetontrle (2) system at K. 97

234 CHAPTER 7 DATA ANALYSIS AND DISCUSSION All the models used for the VLLE data regresson faled to correctly predct the VLLE pont. Interestngly though, when the model parameters from the LLE regresson at K were used to predct the VLLE phase envelope, the results revealed some degree of devaton as shown n Fgure The devaton was more pronounced for the P-x regon and the pont of VLLE but the P-y regon remaned farly the same. The G plotted aganst also verfed that the VLLE regresson faled to predct the regon where the two lqud phases splt as shown n Fgure On the other hand, usng the parameters from the regresson of the bnary LLE data, one cannot clearly dentfy the regons of phase splttng n Fgure 7-46, although the crteron for LLE was satsfed n the regresson algorthm. To determne whether the model predcton or the expermentally measured vapour composton for ths system s correct, an experment usng a transparent varable-volume cell can be carred out. Ths would nvolve preparng a gaseous mxture of hexane ( ) + acetontrle ( ), say = 0.5, n a varable-volume cell that s kept constant at K (n a transparent lqud bath for example). Once ths s acheved, the pressure of the cell would then be gradually ncreased (by use of a pston for example) untl the formaton of a dewpont s observed. The pressure at whch ths occurs s then noted and compared to Fgure For an overall composton of = 0.5, the expermentally measured VLLE data n Fgure 7-44 suggests the dewpont occurs at approxmately 44 kpa. On the other hand for the same overall composton, the model n Fgure 7-44 suggests the dewpont occurs at approxmately 64 kpa. Hence by comparson of the pressure obtaned from the varable-volume cell experment and that of Fgure 7-44, one can deduce whether the vapour composton gven by the model s correct. 7.7 Thermodynamc Consstency Testng for VLE Systems As mentoned n Secton 3.6 of Chapter 3, an over specfcaton of VLE data allows for thermodynamc consstency testng to be carred out. The pont test of Van Ness et al. (973) and the drect test of Van Ness (995) were used n ths study to test the thermodynamc consstency of the expermental VLE data measured as part of ths study. Ths secton wll thus focus on the results obtaned from each test appled to the expermental VLE data and a dscusson thereof. 98

235 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Methoxy-2-Methylpropane () + Ethyl Acetate (2) The values of the average absolute devaton (AAD) for the pressure and vapour composton values for all models are reported n Tables 7-3 and 7-4 for the combned and drect methods respectvely. Wth regards to the pont test, the NRTL model shows AAD values of 0.4 kpa and for the pressure and vapour mole fracton respectvely, whlst the PR EoS shows AAD values of 0.40 kpa and for the pressure and vapour mole fracton respectvely. Snce the vapour mole fracton AAD values for both the NRTL model and PR EoS are less than 0.0, one can assume that the pont test has been partly satsfed. The P and plots are presented n Fgures 7-47 and 7-48 respectvely. The P plot shows random scatterng around the x-axs for both the NRTL model and the PR EoS (a postve ndcaton for the pont test). However, the plot showed no scatterng around the x-axs for the NRTL model but a negatve bas whlst the PR EoS shows very poor scatterng where only two devaton ponts are postve and the rest are negatve. Ths s ndcatve that the pont test s subjectve to the model employed. Hence, accordng to the pont test, one cannot successfully conclude that the data are thermodynamcally consstent as only one of the two condtons has been adequately satsfed. The drect test requres the RMSD value for ln (γ/γ) of the combned method. The results for combned method are reported n Table Accordng to Table 3-, all the models ndcate excellent results for thermodynamc consstency as seen by the ndex values for the drect test. However for the NRTL model, Fgure 7-49 shows no random scatterng about the x-axs for the ln (γ/γ) plot, whch s also a requrement of the drect test. Hence, smlar to the pont test, one cannot successfully conclude that the data are thermodynamcally consstent accordng to the drect test. It may well be true that the data are ndeed thermodynamcally consstent but the models employed render them thermodynamcally nconsstent. 99

236 CHAPTER 7 DATA ANALYSIS AND DISCUSSION.5 TS-NRTL PR-MC-WS-NRTL 0.5 ΔP / kpa x Fgure 7-47: P plot for the TS-NRTL and PR-MC-WS-NRTL model combnatons for the 2- methoxy-2-methylpropane () + ethyl acetate (2) system at K. Table 7-29: Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system at K. RMSD Model ln(γ/γ) Index * TK-Wlson NRTL (α = 0.3) NRTL (α = 3.54) mod UNIQUAC * Ranges from to 0, where sgnfes excellent consstency and 0 poor consstency 200

237 CHAPTER 7 DATA ANALYSIS AND DISCUSSION TS-NRTL PR-MC-WS-NRTL Δy x Fgure 7-48: plot for the TS-NRTL and PR-MC-WS-NRTL model combnatons for the 2- methoxy-2-methylpropane () + ethyl acetate (2) system at K Δln (γ /γ 2 ) x Fgure 7-49: ln (γ/γ) plot for the TS-NRTL model combnaton for the 2-methoxy-2- methylpropane () + ethyl acetate (2) system at K. 20

238 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Methanol () + Butan-2-one (2) The values of the average absolute devaton (AAD) for the pressure and vapour composton values for the combned method and drect method models were presented n Tables 7-5 and 7-6 respectvely. The vapour phase mole fracton AAD crteron of the pont test s satsfed for both the combned and drect methods and each sotherm measured. The P and plots for each sotherm wth the drect method are presented n Fgures 7-50 and 7-5 respectvely. The P plots for each sotherm show random scatterng about the x-axs. However, more mportantly the plots for each sotherm does not scatter randomly about the x-axs but dsplayed a postve bas. Hence as mentoned for the prevously dscussed system, t cannot be satsfactorly concluded that the data are thermodynamcally consstent accordng to the pont test appled to the drect method as only one of the two condtons were satsfed. The P and plots for each sotherm wth the combned method are presented n Fgures 7-52 and 7-53 respectvely. For ths method the P and plots for each sotherm dsplay random scatterng about the x-axs. Hence, snce all the condtons for the pont test appled to the combned method are satsfed, t can be concluded that the data are thermodynamcally consstent. Agan, ths llustrates that the pont test s subjected to the model employed n the regresson technque K K K 2 P / kpa x Fgure 7-50: P plot for the best ft drect method model combnatons of the methanol () + butan-2-one (2) system at , and K. 202

239 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Wth regards to Table 3- for the drect test of thermodynamc consstency, all the sotherms show excellent results as reported n Table 7-30, where an ndex value of 2 s observed for all sotherms, ndcatve of thermodynamc consstent data. The ln (γ/γ) plot n Fgure 7-54 on the other hand, shows random scatterng about the x-axs for the and K sotherms. The data for the K sotherm however dsplay a postve bas. Hence, accordng to the drect test, t can be concluded that the data for the and K sotherms are thermodynamcally consstent, whereas the drect test for the K sotherm data s nconclusve K K K y x Fgure 7-5: plot for the best ft drect method model combnatons of the methanol () + butan-2-one (2) system at , and K. 203

240 CHAPTER 7 DATA ANALYSIS AND DISCUSSION K K K P / kpa x Fgure 7-52: P plot for the best ft combned method model combnatons of the methanol () + butan-2-one (2) system at , and K K K K y x Fgure 7-53: plot for the best ft combned method model combnatons of the methanol () + butan-2-one (2) system at , and K. 204

241 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Table 7-30: Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the methanol () + butan-2-one (2) system at , and K. RMSD Model ln(γ/γ) Index * K TK-Wlson NRTL (α = 0.3) NRTL (α =.45) mod UNIQUAC K TK-Wlson NRTL (α = 0.3) NRTL (α = 0.077) mod UNIQUAC K TK-Wlson NRTL (α = 0.3) NRTL (α =.89) mod UNIQUAC * Ranges from to 0, where sgnfes excellent consstency and 0 poor consstency K K K 0.02 ln(γ /γ 2 ) x Fgure 7-54: ln (γ/γ) plot for the combned method best ft model combnatons of the methanol () + butan-2-one (2) system at , and K. 205

242 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Ethanol () + Butan-2-one (2) The values of the average absolute devaton (AAD) for the pressure and vapour composton values for the combned method and drect method models are presented n Tables 7-7 and 7-8 respectvely. Smlar to the methanol + butan-2-one system, the vapour phase mole fracton AAD crteron of the pont test s satsfed for both the combned and drect methods and each sotherm measured. The P and plots for each sotherm wth the drect method are presented n Fgures 7-55 and 7-56 respectvely. The P plot for each sotherm shows random scatterng about the x- axs. The plots for each sotherm do not scatter randomly about the x-axs but dsplay a postve bas. Hence as mentoned for the prevously dscussed system, t cannot be satsfactorly concluded that the data are thermodynamcally consstent accordng to the pont test appled to the drect method as only one of the two condtons s satsfed. P / kpa K K 43.2 K x Fgure 7-55: P plot for the best ft drect method model combnatons of the ethanol () + butan-2-one (2) system at , and 43.2 K. 206

243 CHAPTER 7 DATA ANALYSIS AND DISCUSSION K K 43.2 K y Fgure 7-56: plot for the best ft drect method model combnatons of the ethanol () + butan-2-one (2) system at , and 43.2 K. x K K 43.2 K 0.5 P / kpa x Fgure 7-57: P plot for the best ft combned method model combnatons of the ethanol () + butan-2-one (2) system at , and 43.2 K. 207

244 CHAPTER 7 DATA ANALYSIS AND DISCUSSION K K 43.2 K y x Fgure 7-58: plot for the best ft combned method model combnatons of the ethanol () + butan-2-one (2) system at , and 43.2 K. The P and plots for each sotherm wth the combned method are presented n Fgures 7-57 and 7-58 respectvely. For ths method the P and plots for each sotherm dsplay random scatterng about the x-axs. Thus all the condtons for the pont test appled to the combned method are satsfed. It can be concluded that the data are thermodynamcally consstent. Accordng to Table 3- for the drect test of thermodynamc consstency, all the sotherms show excellent results as reported n Table 7-3, where ndex values of and 2 are observed for the sotherms, ndcatve of thermodynamc consstent data. The ln (γ/γ) plot n Fgure 7-59 moreover shows random scatterng about the x-axs for all the sotherms. Therefore, accordng to the drect test, t can be concluded that the data for all the sotherms are thermodynamcally consstent. Table 7-3: Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the ethanol () + butan-2-one (2) system at , and 43.2 K. 208

245 CHAPTER 7 DATA ANALYSIS AND DISCUSSION RMSD Model ln(γ/γ) Index K TK-Wlson NRTL (α = 0.3) NRTL (α = 0.044) mod UNIQUAC K TK-Wlson NRTL (α = 0.3) NRTL (α = 0.028) mod UNIQUAC K TK-Wlson NRTL (α = 0.3) NRTL (α = 2.06) mod UNIQUAC * Ranges from to 0, where sgnfes excellent consstency and 0 poor consstency ln(γ /γ 2 ) K K 43.2 K Fgure 7-59: ln (γ/γ) plot for the combned method best ft model combnatons of the ethanol () + butan-2-one (2) system at , and 43.2 K Ethanol () + 2-Methoxy-2-Methylbutane (2) x 209

246 CHAPTER 7 DATA ANALYSIS AND DISCUSSION The values of the average absolute devaton (AAD) for the pressure and vapour composton values for the combned method and drect method models are presented n Tables 7-9 and 7-20 respectvely. The vapour phase mole fracton AAD crteron of the pont test s satsfed for both the combned and drect methods and both sotherms measured. The P and plots for each sotherm wth the drect method are presented n Fgures 7-60 and 7-6 respectvely. The P plot for each sotherm shows random scatterng about the x-axs. The plot at K shows random scatterng about the x-axs whereas at 43.9 K the plot dsplays a postve bas. Hence accordng to the pont test appled to the drect method, only the data at K can be consdered thermodynamcally consstent but the data at 43.9 K cannot be strctly consdered thermodynamcally consstent as only one of the two condtons s satsfed. The P and plots for both sotherms wth the combned method are presented n Fgures 7-62 and 7-63 respectvely. For ths method the P and plots for each sotherm dsplay random scatterng about the x-axs. Hence, snce all the condtons for the pont test appled to the combned method are satsfed, t can be concluded that the data are thermodynamcally consstent K 43.9 K 0.5 P / kpa x Fgure 7-60: P plot for the best ft drect method model combnatons of the ethanol () + 2- methoxy-2-methylbutane (2) system at and 43.9 K. 20

247 CHAPTER 7 DATA ANALYSIS AND DISCUSSION K 43.9 K y x Fgure 7-6: plot for the best ft drect method model combnatons of the ethanol () + 2- methoxy-2-methylbutane (2) system at and 43.9 K K 43.9 K P / kpa x Fgure 7-62: P plot for the best ft combned method model combnatons of the ethanol () + 2-methoxy-2-methylbutane (2) system at and 43.9 K. 2

248 CHAPTER 7 DATA ANALYSIS AND DISCUSSION K 43.9 K y x Fgure 7-63: plot for the best ft combned method model combnatons of the ethanol () + 2-methoxy-2-methylbutane (2) system at and 43.9 K. Table 7-32: Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the ethanol () + 2-methoxy-2-methylbutane (2) system at and 43.9 K. RMSD Model ln(γ/γ) Index K TK-Wlson NRTL (α = 0.3) NRTL (α = 0.083) mod UNIQUAC K TK-Wlson NRTL (α = 0.3) NRTL (α = 0.56) mod UNIQUAC * Ranges from to 0, where sgnfes excellent consstency and 0 poor consstency 22

249 CHAPTER 7 DATA ANALYSIS AND DISCUSSION K 43.9 K ln(γ /γ 2 ) x Fgure 7-64: ln (γ/γ) plot for the combned method best ft model combnatons of the ethanol () + 2-methoxy-2-methylbutane (2) system at and 43.9 K. Accordng to Table 3- for the drect test of thermodynamc consstency, both sotherms show excellent results as reported n Table 7-32, where an ndex value of 2 s observed for both sotherms, ndcatve of thermodynamc consstent data. Furthermore, the ln (γ/γ) plot n Fgure 7-64 shows random scatterng about the x-axs for both sotherms. Therefore, accordng to the drect test, t can be concluded that the data for both sotherms are thermodynamcally consstent Methylpent-2-ene () + Ethanol (2) System The values of the average absolute devaton (AAD) for the pressure and vapour composton values for the combned method and drect method models are presented n Tables 7-2 and 7-22 respectvely. The vapour phase mole fracton AAD crteron (< 0.0) of the pont test s strctly not satsfed for the combned method as the AAD value s slghtly hgher (0.0). Wth regards to the drect method, the vapour phase mole fracton AAD value (0.009) s slghtly lower than the crteron and therefore partly satsfes the pont test. The P and plots wth the drect and combned methods and are presented n Fgures 7-65 and 7-66 respectvely. The P plots show random scatterng about the x-axs. The plots also show some degree of random scatterng about the x- axs but dsplay a slghtly postve bas. The data can therefore be cautously consdered as thermodynamcally consstent usng the pont test. 23

250 CHAPTER 7 DATA ANALYSIS AND DISCUSSION.5 TS-NRTL PR-MC-WS-NRTL 0.5 P / kpa x Fgure 7-65: P plot for the TS-NRTL and PR-MC-WS-NRTL model combnatons for the 2- methylpent-2-ene () + ethanol (2) system at K TS-NRTL PR-MC-WS-NRTL 0.0 y x Fgure 7-66: plot for the TS-NRTL and PR-MC-WS-NRTL model combnatons for the 2- methylpent-2-ene () + ethanol (2) system at K. 24

251 CHAPTER 7 DATA ANALYSIS AND DISCUSSION Accordng to Table 3- for the drect test of thermodynamc consstency, the data shows very good thermodynamc consstency as reported n Table 7-33, where an ndex value of 3 s observed. On the other hand the ln (γ/γ) plot n Fgure 7-67 shows very lttle degree of random scatterng about the x-axs wth a slghtly postve bas. Therefore, accordng to the drect test, t could not be strctly concluded that the data are thermodynamcally consstent. Table 7-33: Results obtaned for the drect test when usng a lqud phase actvty coeffcent model for the 2-methylpent-2-ene () + ethanol (2) system at K. RMSD Model ln(γ/γ) Index TK-Wlson NRTL (α = 0.3) NRTL (α = -0.55) mod UNIQUAC * Ranges from to 0, where sgnfes excellent consstency and 0 poor consstency ln(γ /γ 2 ) x Fgure 7-67: ln (γ/γ) plot for the TS-NRTL model combnaton for the 2-methylpent-2-ene () + ethanol (2) system at K. 25

252 CHAPTER 7 DATA ANALYSIS AND DISCUSSION 7.8 Concludng Remarks All the vapour pressure and phase equlbrum data measured wth the newly developed phase equlbrum apparatus were subjected to data analyss and dscussed. All the vapour pressure data were regressed usng the extended Antone and Wagner emprcal equatons as well as the PR and SRK EoS. The combned and drect methods of data regresson were used to obtan model parameters for VLE systems. For the combned method, the vapour phase non-dealty was accounted for by the vral EoS wth the second vral coeffcent correlaton of Tsonopoulos (974). The lqud phase non-dealty of the combned methods was accounted for by use of lqud phase actvty coeffcent models (vz. TK-Wlson, NRTL and modfed UNIQUAC). Wth regards to the drect method, both the vapour and lqud phase non-dealtes were accounted for by the use of a cubc EoS (vz. the PR and SRK EoS wth the temperature dependent functon (α) of Mathas and Copeman (983)). The same lqud phase actvty coeffcent models used n the combned method were also used to regress data for the LLE systems measured. To show versatlty of the equlbrum apparatus, VLLE data were also measured and analysed usng the combned method of data regresson. Overall, the analyss revealed that all expermental data measured were satsfactorly modeled wth an excepton to the VLLE data. Thermodynamc consstency testng of the VLE data was also checked as part of the data analyss where the pont and drect tests were employed. It was found that most of the data were thermodynamcally consstent wth a few beng nconclusve. 26

253 CHAPTER 8 FRENCH SUMMARY L étude décrte dans ce chaptre a conssté en la concepton, la constructon et la mse en route d'un nouvel apparel permettant, sur de petts volumes, des mesures fables d'équlbres de phases, pluseurs phases lqudes et une phase vapeur. La parte centrale de la cellule d'équlbre a été réalsée en saphr par Rayotek Scentfc Inc. Le volume nterne de cette cellule d équlbre a un volume d envron 7.4. La température de fonctonnement de l'apparel s étend de 253 et 473 K, tands que la presson de fonctonnement s étend du vde à 600 kpa. Une méthode expérmentale pour la mesure des équlbres de phase adaptée à l utlsaton de cet apparel a été développée avec succès. Les prélèvements des phases à l équlbre ont été réalsés avec succès au moyen du «Rapd On Lne samplng Injector» (ROLSI ). En préalable aux mesures d équlbres, chaque produt chmque a été dégazé au moyen de la méthode de dstllaton sous vde de Van Ness et Abbott (978). L'apparellage de dégazage a été construt avec de la verrere et des nstruments dsponbles à l'école du géne chmque, unversté KwaZulu Natal, Durban, Afrque du Sud. Les données expérmentales de presson de vapeur obtenues ont été régressées en utlsant des modèles mathématques, à savor l'équaton d'antone et de Wagner et ont été également régressées avec des équatons d'état à savor l'équaton d état (EdE) dte de Peng et Robnson et de Soave, Redlch et Kwong. Un test de cohérence thermodynamque quanttatf a été effectué pour examner les données expérmentales de presson de vapeur, qu sute à cet essa ont toutes été déclarées comme thermodynamquement cohérentes. Deux méthodes dfférentes ont été employées pour la régresson des données expérmentales de d équlbres «lqude-vapeur» (ELV) : les méthodes combnées et drectes. La méthode combnée utlse le deuxème coeffcent de la corrélaton du vrel de Tsonopoulos (974) pour la non-déalté en phase vapeur et les modèles : TK-Wlson, NRTL et Modfed UNIQUAC pour la non-déalté phase lqude. La méthode drecte fat appel aux équatons d état (EdE) de Peng et Robnson et de Soave, Redlch et Kwong avec une foncton alpha, (α), dépendante de la température, celle de Mathas et Copeman (983). Dans l'ensemble, nous avons été amené à constater que tous les modèles : méthodes drecte et combnée permettaent de décrre de manère satsfasante les équlbres de phase. Cependant le modèle de NRTL, dans la méthode combnée, s'est avéré melleur au nveau de la qualté de l'ajustement de la plupart des données obtenues, tands que pour la méthode drecte c est l équaton d état (EdE) de Peng et Robnson (PR) qu s est révélée supéreure. 27

254 CHAPTER 8 FRENCH SUMMARY De manère générale, la comparason des deux méthodes (drecte et combnée) a perms de conclure que tous les systèmes sont meux décrts par la méthode combnée. De manère synthétque on peut dre que l'apparel a été conçu, construt et ms en oeuvre avec succès à l'école du géne chmque de l unversté KwaZulu Natal, Durban, Afrque du Sud. 28

255 CHAPTER 8 CONCLUSION 8 CHAPTER EIGHT CONCLUSION Ths study was concerned wth the desgn, constructon and commssonng of a new apparatus that enabled relable equlbra measurements for multple lqud and vapour phases for small volumes. The need for such a small volume apparatus was to enable relable phase equlbrum measurements for new chemcals that are extremely costly to synthesze. The equlbrum cell was constructed of sapphre by Rayotek Scentfc Inc. wth a volume of approxmately 7.4. The operatng temperature of the apparatus ranged from 253 to 473 K and the operatng pressure ranged from absolute vacuum to 600 kpa. A successful expermental method for the measurement of phase equlbra was also developed. The novel technque for the samplng of the equlbrum phases was successfully accomplshed usng a Rapd-OnLne-Sampler-Injector ( ) that was capable of wthdrawng as lttle as μl of sample from each phase. Overall the apparatus was successfully desgned, constructed and commssoned at the School of Chemcal Engneerng, Unversty of KwaZulu Natal, Durban, South Afrca. Pror to carryng out measurements, each chemcal was thoroughly degassed successfully usng the vacuum dstllaton method of Van Ness and Abbott (978). The degassng apparatus was constructed of glassware and set-up n the School of Chemcal Engneerng, Unversty of KwaZulu Natal, Durban, South Afrca. Vapour pressure and phase equlbrum data were measured for the followng systems: a) VLE for 2-methoxy-2-methylpropane + ethyl acetate at K b) LLE for methanol + heptane at 350 kpa c) LLE for hexane + acetontrle at 350 kpa d) VLLE for hexane + acetontrle at K e) VLE for methanol + butan-2-one at , and K 29

256 CHAPTER 8 CONCLUSION f) VLE for ethanol + butan-2-one at , and 43.2 K g) VLE for ethanol + 2-methoxy-2-methylbutane at and 43.9 K h) VLE for ethanol + 2-methylpent-2-ene at K The frst three systems mentoned above (a c) were used as test systems to verfy that the newly developed apparatus was capable of vapour pressure and phase equlbrum measurements. Ths also demonstrated the successful versatlty of the apparatus n measurng VLE, LLE and VLLE data. The novel technque for samplng was also found to be hghly successful. The expermental vapour pressure data obtaned were regressed usng mathematcal models, vz. the extended Antone and Wagner equaton and were also regressed wth equatons of state vz. the PR and SRK EoS. A quanttatve thermodynamc consstency test was also carred out to test the expermental vapour pressure data where t was found that all the data were thermodynamcally consstent. Two dfferent methods were used for the regresson of expermental VLE data: the combned and drect methods. The combned method made use of the second vral coeffcent correlaton of Tsonopoulos (974) for the vapour phase non-dealty and the TK-Wlson, NRTL and modfed UNIQUAC models for the lqud phase non-dealty. The drect method used the PR and SRK EoS wth the temperature dependent functon (α) of Mathas and Copeman (983). On the whole, t was found that all the models of both the drect and combned method were able to descrbe the phase equlbrum measurements suffcently well. However the NRTL model n the combned method was found to provde the best ft to most of the systems whlst the PR EoS n the drect method seemed to provde the best ft to most the systems as well. Overall, a comparson of the two methods suggested that the all systems were better descrbed by the combned method. Systems (e) to (h) above consttuted as new expermental data and each were found to contan an azeotrope. For systems (e) and (f), pressure swng dstllaton was recommended to overcome the azeotrope whlst for systems (g) and (h) homogeneous or heterogeneous azeotropc dstllaton should be consdered. Expermental LLE data were carred out wth the ad of hgh pressure ntrogen to enable samplng wth the. The expermental LLE data measured were regressed wth the TK-Wlson, NRTL and modfed UNIQUAC lqud phase actvty coeffcent models. The regresson revealed that a second 220

257 CHAPTER 8 CONCLUSION degree polynomal was suffcent to ft all the model parameters wth a least squares devaton reasonably well. A VLLE system (d) was also expermentally measured to demonstrate versatlty of the apparatus. Ths data was regressed usng the combned method wth the same models as used for VLE. It was found that the expermental vapour compostons measured showed consderable devatons to that of the models. Ths was attrbuted to error n vapour composton measurements or that the models could not adequately descrbe the expermental data. Thermodynamc consstency testng was also performed on all VLE data measured usng the pont and drect tests. Systems (e), (f) and (g) were found to show excellent thermodynamc consstency. However, systems (a) and (h) were found not to be strctly thermodynamcally consstent as only one of the two condtons were met for both the pont and drect tests. Overall, the study was found to be hghly successful. There are however some recommendatons to modfy the apparatus to enable low or very hgh pressure phase equlbrum measurements as well. These are further dscussed n Chapter 9. 22

258 CHAPTER 9 FRENCH SUMMARY Ce chaptre présente les recommandatons qu pourraent et devraent être mses en applcaton afn d amélorer la polyvalence et la mse en œuvre de l'apparel conçu et développé au cours de ce traval de thèse. Des modfcatons au ROLSI sont envsagées pour rendre effcace le prélèvement à basse presson et pour permettre l échantllonnage des systèmes aqueux à haute température. Des modèles thermo-dynamques plus complexes sont attendus pour régresser les données d'équlbres de phase de composés très polares. 222

259 CHAPTER 9 RECOMMENDATIONS 9 CHAPTER NINE RECOMMENDATIONS To further mprove versatlty and operaton of the newly developed apparatus, the followng recommendatons should be consdered: ) The 6-port GC valve and were successfully lnked to the GC to enable samplng at low pressures. However, t was found that when the 6-port GC valve was swtched to send the sample to the GC, a rather larger peak wth a long talng effect was observed. Ths could have been due to the change n pressure experenced when the 6-port GC valve was swtched. Ths should be further nvestgated by perhaps usng a flame onzaton detector nstead of a thermal conductvty detector. 2) Hgh pressure phase equlbrum systems could also be measured by smply replacng the pressure transmtter wth a sutable one. Care however should be taken to thoroughly check the apparatus for pressure leaks. 3) The apparatus should be carefully mantaned wth regular checks done on the condton of the O-rngs used and replaced when necessary or not compatble wth the chemcals used. The apparatus must also be constantly checked for pressure leaks pror to operaton. 4) Aqueous VLLE systems should be studed wth the specalzed polymer to consoldate that the newly developed apparatus s capable of undertakng expermental VLLE measurements. 5) The movement control of the could be acheved wth a stepper motor nstead of manual operaton. 223

260 CHAPTER 9 RECOMMENDATIONS 6) More complex models can be used n regresson to account for non-dealtes, especally for VLLE systems. The use of a cubc equaton of state to represent the vapour phase nondealty n the combned method should be nvestgated. 224

261 REFERENCES REFERENCES Abbott, M. M., (979), Cubc Equatons of State: An Interpretve Revew, Advances n Chemstry Seres, Vol. 82, pp Abbott, M. M., (986), Low-Pressure Phase Equlbra: Measurement of VLE, Flud Phase Equlbra, Vol. 29, pp Abrams, D. S. and Prausntz, J. M., (975), Statstcal Thermodynamcs of Lqud Mxtures: A New Expresson for the Excess Gbbs Energy of Partly or Completely Mscble Systems, Amercan Insttute of Chemcal Engneers Journal, Vol. 2(), pp Am, K. and Cpran, M., (980), Vapor Pressures, Refractve Index at 20.0, and Vapor-Lqud Equlbrum at kpa n the Methyl Tert-Butyl Ether - Methanol System, Journal of Chemcal and Engneerng Data, Vol. 25(2), pp Am, K., (978), Measurement of Vapor-Lqud Equlbrum n Systems wth Components of Very Dfferent Volatlty by the Total Pressure Statc Method, Flud Phase Equlbra, Vol. 2(2), pp Azawa, T., Kanakubo, M., Ikushma, Y., Satoh, N., Ara, K. and Smth Jr, R. L., (2004), Totsu - Wndow Optcal Cell for Absorpton and Emsson Studes of Hgh Pressure Lquds and Supercrtcal Fluds, Journal of Supercrtcal Fluds, Vol. 29, pp Anderko, A., (990), Equaton-of-State Methods for the Modellng of Phase Equlbra, Flud Phase Equlbra, Vol. 6(-2), pp Andersen, W. C., Severs, R. E., Lagalante, A. F. and Bruno, T. J., (200), Solubltes of Cerum(IV), Terbum(III), and Iron(III) β-dketonates n Supercrtcal Carbon Doxde, Journal of Chemcal and Engneerng Data, Vol. 46(5), pp Anderson, T. F. and Prausntz, J. M., (978), Applcaton of the UNIQUAC Equaton to Calculaton of Multcomponent Phase Equlbra. : Vapor-Lqud Equlbra; 2: Lqud-Lqud Equlbra, Industral and Engneerng Chemstry. Process Desgn and Development, Vol. 7(4), pp

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277 REFERENCES of Mxng", Journal of the Amercan Chemcal Socety, Vol. 86(2), pp Wong, D. S. H. and Sandler, S. I., (992), A Theoretcally Correct Mxng Rule for Cubc Equatons of State, Amercan Insttute of Chemcal Engneers Journal, Vol. 38(5), pp Wu, X., Du, X. and Zheng, D., (200), Measurement of Vapor-Lqud Equlbrum for the DME + Dsopropyl Ether Bnary System and Correlaton for the DME + + Dsopropyl Ether Ternary System, Internatonal Journal of Thermophyscs, Vol. 3(2), pp Zabaloy, M. S., Gros, H. P., Bottn, S. B. and Brgnole, E. A., (994), Isohermal Vapor-Lqud Equlbrum Data for the Bnares Isobutane-Ethanol, Isobutane--Propanol, and Propane-Ethanol, Journal of Chemcal and Engneerng Data, Vol. 39(2), pp Zmmermann, A. and Keller, J. U., (989), Vapor-Lqud Equlbrum n the System Water-Ammona- Lthum Bromde, Flud Phase Equlbra, Vol. 53, pp

278 APPENDIX A CRITERION FOR PHASE EQUILIBRIUM Appendx A Crteron For Phase Equlbrum For any closed system, the temperature and pressure are related to the Gbbs energy usng prmary thermodynamc propertes and the defnton of the Gbbs energy: d ( ng) ( nv ) dp ( ns )dt = (A-) Applcaton of Equaton (A-) to a sngle-phase flud, n whch there s no chemcal reacton, mples that the composton of such a system s constant. Ths leads to the followng deductons: ( ng) P T, n = nv (A-2) ( ng) T P, n = ns (A-3) where n s the number of moles of all chemcal speces n the system. The subscrpts sgnfy propertes that are held constant. Wth regards to an open system, the surroundngs can nterchange matter wth the system. However, the Gbbs energy s stll a functon of temperature and pressure but also becomes a functon of the number of moles of a specfc chemcal speces n the system ( ). Hence: ( P, T ) ng = g, (A-4) n The total dfferental of Equaton (A-4) yelds: ( ng) = ( nv ) dp ( ns ) dt + d µ dn (A-5) 242

279 s APPENDIX A CRITERION FOR PHASE EQUILIBRIUM and ( ng) µ = (A-6) n P, T, n j where μ known as the chemcal potental of speces n the mxture. Now when two phases (say α and β) are n equlbrum n an overall closed system, each phase can be consdered an open system that s free to transfer mass wth each other. If one assumes the equlbrum temperature and pressure to be unform throughout the closed system, Equaton (A-5) can be used to express each phase: d d α α α ( ng) = ( nv ) dp ( ns ) dt + β β β ( ng) = ( nv ) dp ( ns ) dt + α α µ dn (A-7) β β µ dn (A-8) The sum of Equatons (A-7) and (A-8) gves the change n the total Gbbs energy for ths system. The total system property can be expressed by the followng relaton: ( nm ) α ( nm ) β nm = + (A-9) where M represents any extensve thermodynamc property. Applcaton of Equaton (A-9) shows: d α α ( ng) = ( nv ) dp ( ns ) dt + dn + β β µ µ dn (A-0) Snce the system s a closed system, Equaton (A-) s applcable. A comparson of Equaton (A-) and (A-0) at equlbrum reveals that: α α β β + µ dn = µ dn 0 (A-) 243

280 and represent are = APPENDIX A CRITERION FOR PHASE EQUILIBRIUM The terms α β changes and result from the mass transfer between the two phases. For a non-reactve system, the law of mass conservaton requres that α becomes: - β. Hence Equaton (A-) ( α µ β ) dn α = 0 µ (A-2) Snce the changes α ndependent and arbtrary, the only way that Equaton (A-2) can n general be zero s when each term n parentheses s separately equated to zero: α β µ µ = (A-3) Equaton (A-3) can be generalzed to nclude more than two phases by successvely consderng pars of phases. In the case of a closed system consstng N chemcal speces and π phases at the same temperature and pressure, the general result s: α β π µ µ = = µ =... (A-4) where =, 2,, N. Hence the crteron for phase equlbrum of a system consstng of multple phases at the same temperature and pressure s acheved when the chemcal potental of each speces s the same n all phases (Smth et al, 200). 244

281 APPENDIX B PURE COMPONENT PROPERTIES Appendx B Pure Component Propertes The crtcal propertes and the UNIQUAC pure component constants for all the chemcals used n ths study were taken the Dortmund Data Bank (2009). Table B-: Physcal propertes of chemcals used n ths study. Chemcal / K / kpa /.mol - ω 2-methoxy-2-methylbutane methoxy-2-methylpropane methylpent-2-ene acetontrle butan-2-one ethanol ethyl acetate heptane hexane methanol Table B-2: Pure component constants for the modfed UNIQUAC model. Chemcal r q q' 2-methoxy-2-methylbutane methoxy-2-methylpropane methylpent-2-ene acetontrle butan-2-one ethanol ethyl acetate heptane hexane methanol

282 APPENDIX C CALIBRATIONS C. Temperature Calbratons Appendx C Table C-: Calbraton results for temperature probes/sensors used n ths study. Probe/Sensor Descrpton Equlbrum cell upper 36 SS flange Equlbrum cell lower 36 SS flange T Calbraton Equaton actual = dsplay 0.994T T actual T T T = dsplay actual = dsplay 0.994T actual = dsplay T Temperature control upper 36 T actual = Tdsplay SS flange Low pressure transmtter T actual = Tdsplay alumnum block Moderate pressure transmtter T actual = Tdsplay.593 alumnum block Temperature sensor n expanson T actual =.000T dsplay chamber Sensor n the lnes between the and the 6-port GC valve T T Sensor n the lnes between the 6-port GC valve and the GC Sensor n the lnes between the pressure transmtters and the equlbrum cell Sensor n the alumnum block for the GC valve T T T actual = dsplay 0.998T actual = dsplay actual = dsplay T 3.75 actual = dsplay T Temperature Range 298 to 355 K 354 to 465 K 298 to 355 K 354 to 465 K 303 to 465 K 298 to 37 K 298 to 37 K 330 to 465 K 324 to 465 K 330 to 465 K 298 to 465 K 330 to 465 K Calbraton Uncertanty T / K

283 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-: Temperature calbraton plot for the probe of the upper 36 SS flange of the equlbrum cell (low temperature range) T / K Reference Temperature / K Fgure C-2: Temperature devaton plot for the probe of the upper 36 SS flange of the equlbrum cell (low temperature range). 247

284 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-3: Temperature calbraton plot for the probe of the upper 36 SS flange of the equlbrum cell (hgh temperature range). T / K Reference Temperature / K Fgure C-4: Temperature devaton plot for the probe of the upper 36 SS flange of the equlbrum cell (hgh temperature range). 248

285 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-5: Temperature calbraton plot for the probe of the lower 36 SS flange of the equlbrum cell (low temperature range). T / K Reference Temperature / K Fgure C-6: Temperature devaton plot for the probe of the lower 36 SS flange of the equlbrum cell (low temperature range). 249

286 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-7: Temperature calbraton plot for the probe of the lower 36 SS flange of the equlbrum cell (hgh temperature range). T / K Reference Temperature / K Fgure C-8: Temperature devaton plot for the probe of the lower 36 SS flange of the equlbrum cell (hgh temperature range). 250

287 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-9: Temperature calbraton plot for the probe of the upper 36 SS flange of the equlbrum cell used to control the heater cartrdge T / K Reference Temperature / K Fgure C-0: Temperature devaton plot for the probe of the upper 36 SS flange of the equlbrum cell used to control the heater cartrdge. 25

288 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-: Temperature calbraton plot for the sensor on the low pressure transmtter alumnum block T / K Reference Temperature / K Fgure C-2: Temperature devaton plot for the sensor on the low pressure transmtter alumnum block. 252

289 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-3: Temperature calbraton plot for the sensor on the hgh pressure transmtter alumnum block T / K Reference Temperature / K Fgure C-4: Temperature devaton plot for the sensor on the hgh pressure transmtter alumnum block. 253

290 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-5: Temperature calbraton plot for the sensor n the expanson chamber. T / K Reference Temperature / K Fgure C-6: Temperature devaton plot for the sensor n the expanson chamber.. 254

291 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-7: Temperature calbraton plot for the sensor n the lnes between the and the 6- port GC valve. T / K Reference Temperature / K Fgure C-8: Temperature devaton plot for the sensor n the lnes between the and the 6- port GC valve. 255

292 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-9: Temperature calbraton plot for the sensor n the lnes between the 6-port GC valve and the GC T / K Reference Temperature / K Fgure C-20: Temperature devaton plot for the sensor n the lnes between the 6-port GC valve and the GC. 256

293 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-2: Temperature calbraton plot for the sensor n the lnes between the pressure transmtters and the equlbrum cell. T / K Reference Temperature / K Fgure C-22: Temperature devaton plot for the sensor n the lnes between the pressure transmtters and the equlbrum cell. 257

294 APPENDIX C CALIBRATIONS Probe Temperature / K Reference Temperature / K Fgure C-23: Temperature calbraton plot for the sensor n the alumnum block for the GC valve T / K Reference Temperature / K Fgure C-24: Temperature devaton plot for the sensor n the alumnum block for the GC valve. 258

295 APPENDIX C CALIBRATIONS C.2 Pressure Calbratons Transmtter Descrpton Low pressure transmtter Moderate pressure transmtter Table C-2: Calbraton results for pressure transmtters used n ths study. P P actual actual Calbraton Equaton = dsplay.0002p = dsplay P Pressure Range 5 to 99 kpa 97 to 33 kpa Calbraton Uncertanty P / kpa Transmtter Pressure / kpa Reference Pressure / kpa Fgure C-25: Pressure calbraton plot for the low pressure transmtter. 259

296 APPENDIX C CALIBRATIONS P / kpa Reference Pressure / kpa Fgure C-26: Pressure devaton plot for the low pressure transmtter Transmtter Pressure / kpa Reference Pressure / kpa Fgure C-27: Pressure calbraton plot for the moderate pressure transmtter. 260

297 APPENDIX C CALIBRATIONS P / kpa Reference Pressure / kpa Fgure C-28: Pressure devaton plot for the moderate pressure transmtter. C.3 Gas Chromatograph Operatng Condtons Table C3: Specfcatons of the gas chromatograph capllary columns used n ths study. Name JW Scentfc HP-5 Phase loadng GS-Q: polarty wth phases between Porapak Q and Porapak N Crosslnked 5% PH ME Slcone Seral number J-43 Maxmum temperature / K Length / m Internal dameter / mm Flm thckness / μm The GC operatng condtons are presented n Table C4 for the followng systems: a) 2-methoxy-2-methylpropane () + ethyl acetate (2) b) methanol () + butan-2-one (2) c) ethanol () + butan-2-one (2) 26

298 APPENDIX C CALIBRATIONS d) ethanol () + 2-methoxy-2-methylbutane (2) e) 2-methylpent-2-ene () + ethanol (2) f) hexane () + acetontrle (2) g) methanol () + heptane (2) Table C4: Gas chromatograph (GC) operatng condtons for the systems studed n ths work. System a b c d e f g GC column JW Scentfc HP-5 HP-5 HP-5 HP-5 HP-5 HP-5 Carrer gas Helum Helum Helum Helum Helum Helum Helum Column pressure / kpa Column flow / ml.mn lnear lnear lnear lnear lnear lnear lnear Flow control mode velocty velocty velocty velocty velocty velocty velocty Splt rato Injector temperature / K Column temperature / K Detector temperature / K

299 APPENDIX C CALIBRATIONS C.4 Gas Chromatograph Calbratons C.4. VLE Systems For each calbraton pont, at least fve samples were used for repeatablty wth a maxmum error of %, where the error was found from the followng equaton: Average Re peatblty Error = 00% (C-) Standard Devaton The absolute average devaton (AAD) for mole fracton composton n gas GC TCD detector calbraton was found from: where: AAD k ( x ) = = k (C-2) ( x ) ( x ) calbraton standard (C-3) x = Table C-5: Gas chromatograph calbraton results for all VLE systems used n ths study. System 2-methoxy-2-methylpropane () + ethyl acetate (2) Calbraton Equaton 2-methoxy-2-methylpropane dlute regon: A x =.026 A x 2 ethyl acetate dlute regon: A 2 x = A x 2 AAD for 2-methoxy-2-methylpropane dlute regon: ethyl acetate dlute regon: methanol () + butan-2-one (2) methanol dlute regon: A x = A x 2 butan-2-one dlute regon: A 2 x = A x 2 methanol dlute regon: butan-2-one dlute regon:

300 APPENDIX C CALIBRATIONS Table C-5: Gas chromatograph calbraton results for all VLE systems used n ths study System ethanol () + butan-2-one (2) (contnued). Calbraton Equaton ethanol dlute regon: A x = A x 2 butan-2-one dlute regon: A 2 x = A x 2 AAD for ethanol dlute regon: butan-2-one dlute regon: ethanol () + 2-methoxy-2- methylbutane (2) 2-methylpent-2-ene () + ethanol (2) ethanol dlute regon: A x = A x 2 2-methoxy-2-methylbutane dlute regon: A 2 x = A x 2-methylpent-2-ene dlute regon: A A 2 A A 2 x = x x x ethanol dlute regon: x = x x x 2 ethanol dlute regon: methoxy-2-methylbutane dlute regon: methylpent-2-ene dlute regon: ethanol dlute regon:

301 APPENDIX C CALIBRATIONS.4.2 A /A x /x 2 Fgure C-29: GC calbraton graph for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system (2-methoxy-2-methylpropane dlute regon) A 2 / A x 2 / x Fgure C-30: GC calbraton graph for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system (ethyl acetate dlute regon). 265

302 APPENDIX C CALIBRATIONS x Mole Fracton of Standard, x Fgure C-3: Composton devaton plot for the 2-methoxy-2-methylpropane () + ethyl acetate (2) system A /A x /x 2 Fgure C-32: GC calbraton graph for the methanol () + butan-2-one (2) system (methanol dlute regon). 266

303 APPENDIX C CALIBRATIONS A 2 /A x 2 /x Fgure C-33: GC calbraton graph for the methanol () + butan-2-one (2) system (butan-2-one dlute regon) x Mole Fracton of Standard, x Fgure C-34: Composton devaton plot for the methanol () + butan-2-one (2) system. 267

304 APPENDIX C CALIBRATIONS A /A x /x 2 Fgure C-35: GC calbraton graph for the ethanol () + butan-2-one (2) system (ethanol dlute regon) A 2 /A x 2 /x Fgure C-36: GC calbraton graph for the ethanol () + butan-2-one (2) system (butan-2-one dlute regon). 268

305 APPENDIX C CALIBRATIONS x Mole Fracton of Standard, x Fgure C-37: Composton devaton plot for the ethanol () + butan-2-one (2) system A /A x /x 2 Fgure C-38: GC calbraton graph for the ethanol () + 2-methoxy-2-methylbutane (2) system (ethanol dlute regon). 269

306 APPENDIX C CALIBRATIONS A 2 /A Fgure C-39: GC calbraton graph for the ethanol () + 2-methoxy-2-methylbutane (2) system x 2 /x (2-methoxy-2-methylbutane dlute regon) x Mole Fracton of Standard, x Fgure C-40: Composton devaton plot for the ethanol () + 2-methoxy-2-methylbutane (2) system. 270

307 APPENDIX C CALIBRATIONS A /A x /x 2 Fgure C-4: GC calbraton graph for the 2-methylpent-2-ene () + ethanol (2) system (2- methylpent-2-ene dlute regon) A 2 /A x 2 /x Fgure C-42: GC calbraton graph for the 2-methylpent-2-ene () + ethanol (2) system (ethanol dlute regon). 27

308 APPENDIX C CALIBRATIONS x Mole Fracton of Standard, x Fgure C-43: Composton devaton plot for the 2-methylpent-2-ene () + ethanol (2) system. C.4.2 LLE and VLLE Systems Table C-6: Gas chromatograph calbraton results for all LLE and VLLE systems used n ths study. System hexane () + acetontrle (2) Calbraton Equaton hexane: 8 2 n = A A acetontrle: 9 2 n2 = A A 2 AAD for n hexane: acetontrle: methanol () + heptane (2) methanol: 8 2 n = A A heptane: 20 2 n2 = A A 2 methanol: heptane:

309 APPENDIX C CALIBRATIONS 3.00E E E-05 n / kmol.50e-05.00e E E Fgure C-44: GC calbraton graph for the hexane () + acetontrle (2) system (hexane calbraton, A second order polynomal ft). 7.00E E E-05 n 2 / kmol 4.00E E E-05.00E E Fgure C-45: GC calbraton graph for the hexane () + acetontrle (2) system (acetontrle calbraton, second order polynomal ft). A 2 273

310 APPENDIX C CALIBRATIONS 5.00E E E-07 Hexane Acetontrle n 2.00E-07.00E E E E E E E n Fgure C-46: Composton devaton plot for the hexane () + acetontrle (2) system..40e-04.20e-04.00e-04 n / kmol 8.00E E E E E Fgure C-47: GC calbraton graph for the methanol () + heptane (2) system (methanol calbraton, second order polynomal ft). A 274

311 APPENDIX C CALIBRATIONS 3.50E E E-05 n 2 / kmol 2.00E-05.50E-05.00E E E Fgure C-48: GC calbraton graph for the methanol () + heptane (2) system (heptane calbraton, A 2 second order polynomal ft). 2.00E-06.50E-06 Methanol Heptane.00E-06 n 5.00E E E E E E-06 n Fgure C-49: Composton devaton plot for the methanol () + heptane (2) system. 275

312 APPENDIX D DATA LOGGING Appendx D Fgure D-: User-nterface of the software for the 34970A Aglent data acquston unt. Fgure D-2: User-nterface of the software for the 34970A Aglent data acquston unt, showng the scan control optons. 276

313 APPENDIX D DATA LOGGING Fgure D-3: User-nterface of the GC Solutons software used for the equlbrum phase composton analyss. Fgure D-4: User-nterface for the ntegraton of the peak areas. 277