Application of Activity Coefficient Models in VLE Determination for Azeotropic System Using Othmer Type Ebulliometer

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1 Applcaton of Actvty Coeffcent Models n VLE Determnaton for Azeotropc System Usng Othmer Type Ebullometer Manojumar M.S, B. Svapraash 2 Department of Chemcal Engneerng, Annamala Unversty, Annamala Nagar , Inda. Abstract: Vapour lqud equlbrum data are the basc need n the desgn of dstllaton columns. In the present study VLE predcton of four bnary azeotropc systems namely ethanol-water, acetone-water, ethanol-benzene and methanol-water was carred out usng UNIQUAC and UNIFAC models. UNIQUAC parameters of the chosen systems were computed usng Newton Raphson s technque. Computatons of UNIFAC model were done usng ASOG method. VLE predcted from these models was valdated usng expermentatons carred out n Othmer VLE stll and thermodynamc consstency test usng Redlch Kester method. It was observed that both models are able to ft the expermental VLE data for all the systems. The results show that all the four systems are mnmum bolng azeotropes havng postve devaton from dealty. Key words: Azeotrope, Non deal system, Thermodynamc consstency, UNIFAC model UNIQUAC model. I. INTRODUCTION Industral producton of chemcals nvolves purfcaton and recovery of the products, byproducts and unreacted raw materals. Dstllaton s a commonly used method for purfyng lquds and separatng mxtures of lquds nto ther ndvdual components []. It s clearly the domnatng separaton process, accountng for more applcatons than all the others combned (extracton, adsorpton, crystallzaton, membrane-based technologes and so forth). Famlar examples nclude fractonaton of crude ol nto useful products such as gasolne and heatng ol etc., dstllaton of crude fermentaton broths nto alcoholc sprts such as gn, voda and many more [2]. Dstllaton columns consume more than 95 of the total energy used n separatons n chemcal process ndustres worldwde. Hence, desgn of dstllaton columns s a major concern of chemcal engneers. Azeotropc phenomenon s often encountered n dstllaton operatons whch complcates the separaton process by usual fractonaton method. An azeotrope s a mxture of two or more lquds (chemcals) n such a rato that ts composton cannot be changed by smple dstllaton [3].Ths occur because, when an azeotrope s boled, the resultng vapor has the same rato of consttuents as the orgnal mxture. As ther composton s unchanged by dstllaton, azeotropes are also called constant bolng mxtures [4]. The bolng temperature of an azeotrope s ether less than the bolng pont temperatures of any of ts consttuents (a postve azeotrope), or greater than the bolng pont temperatures of any of ts consttuents (a negatve azeotrope). The defnng condton of azeotropc mxtures and physcal phenomena leads to non-dealty [5]. VLE data are essental n the desgn of dstllaton columns for ndustral applcatons. VLE computatons usng theoretcal methods rather than expermentatons are smpler and cheaper. The objectve of the present nvestgaton s to determne the VLE data usng UNIQUAC and UNIFAC models for four azeotropc systems namely ethanol-water, acetone-water, ethanolbenzene and methanol-water. The VLE predcted by these models was valdated usng DOI: /IJRTER GBKO 338

2 Internatonal Journal of Recent Trends n Engneerng & Research (IJRTER) expermentaton wth an Othmer VLE stll. Also thermodynamc consstency test for the UNIQUAC and UNIFAC models was carred out by Redlch-Kester method. II. MATERIALS AND METHODS 2. Chemcals All the chemcals (ethanol, methanol, acetone and benzene) were suppled by the Indan Scentfc Chemcal Industres, Prvate Ltd., Chenna, Inda. The purty of the chemcals was checed by gas chromatography and was found to be mass fractons for methanol and ethanol, and mass fractons for acetone and benzene. Deonsed water was used n the experment. 2.2 Expermentaton Othmer VLE stll was employed to determne vapour lqud equlbrum data. The capacty of the stll s about 00 ml and t s equpped wth reflux condenser. Bnary lqud mxture of nown composton was charged at the top of the VLE stll and dstlled usng electrcal heatng. The dstllate (vapour form) rcher n more volatle compound enters the condenser wth cold water crculaton and s collected at the top. The resdual product (lqud) rcher n less volatle compound can be collected from the bottom. The stll s equpped wth a quartz thermometer to measure the azeotropc dstllaton temperature. After equlbrum was establshed (ndcated by a constant readng n the thermometer), heatng was stopped and the contents of the top and bottom products were allowed to cool and analyzed. The samples were analyzed usng Clarus 680 GC fused wth slca column and paced wth Elte-5MS (5 bphenyl 95 dmethylpolysloxane, 30 m 0.25 mm ID 250μm df). The components were separated usng Helum as carrer gas at a constant flow of ml/mn. The njector temperature was set at 260 C durng the chromatographc run. One μl of extract sample was njected nto the nstrument and the oven temperature was at 60 C(2 mn), followed by 300 C at the rate of 0 C mn and 300 C, where t was held for 6 mn. The mass detector condtons were: transfer lne temperature 240 C, on source temperature 240 C, and onzaton mode electron mpact at 70 electonvolt, a scan tme 0.2 seconds and scan nterval of 0. seconds. The spectra of the components were compared wth the database of spectra of nown components stored n the GC-MS NIST (2008) lbrary. 2.3 VLE Predcton Gbbs lad the foundaton for a systematc study of thermodynamc equlbrum. He proposed the maxmum entropy prncple as the crteron for stable equlbrum for solated systems [6]. Raoult s law s appled for phase equlbrum calculaton to deal soluton. Raoult s law s smple to use when both vapour and lqud phases are deal, whch s gven by the equaton [7]. Sat y P=X P () y s mole fracton n vapour phase; x s mole fracton n lqud phase; P sat s vapour pressure and P s operatng pressure. Raoult s law can be adapted to non-deal solutons by ncorporatng two factors namely fugacty coeffcent (ϕ) and actvty coeffcent (γ) that wll account for the non dealty owng to the nteracton between the molecules of dfferent substances. Modfed Raoult s law that gves the accurate result for non-deal soluton s gven as [8]. Sat φ y P = γ X P All Rghts Reserved 339

3 Internatonal Journal of Recent Trends n Engneerng & Research (IJRTER) 2.4 Actvty coeffcents The predcton of actvty coeffcents for non-deal solutons s accomplshed usng Analytcal soluton of group contrbuton method (AGOS). The functonal groups are structural unts such as CH3, OH and others whch when added form consttuent molecules [0]. In the group contrbuton methods, a soluton of components s treated as a soluton of functonal groups. The actvty coeffcents of the components are then determned by the propertes of the functonal groups rather than by those of the molecules. The group contrbuton methods are necessarly approxmate, because the contrbuton of a gven functonal group may not be dentcal n dfferent molecules []. The assumpton nvolved n the functonal contrbuton methods s that the contrbuton of one functonal group n a molecule s ndependent of that made by the other functonal groups [2] 2.4. Unversal quas-chemcal equaton The UNIversal QUAs Chemcal (UNIQUAC) model was developed by Abrams and Prausntz to express the excess gbbs free energy of a bnary mxture. The UNIQUAC equaton for g E RT contans two parts, a combnatoral part and resdual part [3]. The combnatoral part taes nto account the composton, sze and shape of the consttuton molecules, and contans pure component propertes only. The resdual part taes nto account the ntermolecular forces contanng two adjustable parameters [4]. The UNIQUAC equaton s gven by E g RT lnγ l n γ E E g g = (co mb n ato al) r + (resd u al) (3) RT RT C R = lnγ (combnato ral) +lnγ (Resdual) (4) φ θ C z φ = ln + q ln + l Σ j x j l x 2 x j φ (5) θ τ R j j lnγ = q [- ln (Σ j θ j τ j ) Σ j Σ θ τ (6) j z wh ere l = (r q ) - (r ) (7) 2 The structural parameters r and q are calculated as the sum of the group volume and group area parameters R and Q. r =Σ v R (8) q =Σ v Q (9) Where v s the number of two groups of type n a molecule of component. The UNIQUAC equaton contans only two adjustable parameters τ2 and τ UNIquac Functonal group Actvty Coeffcent (UNIFAC) method UNIFAC s based on UNIQUAC model, has a combnatoral term that depends on the volume and surface area of each molecule and a resdual term that s the result of the energes of nteracton between the molecules [5]. In the UNIFAC model, both combnatoral and resdual terms are obtaned from group contrbuton methods. When usng the UNIFAC model, one frst dentfes the functonal subgroups present n each molecule. Next the actvty coeffcent for each speces s wrtten as All Rghts Reserved 340

4 Internatonal Journal of Recent Trends n Engneerng & Research (IJRTER) ln γ = ln γ (combnato ral) + ln γ (resdual) (0) The combnatoral term s evaluated usng equaton (5). However, the resdual term s also evaluated by a group contrbuton method, so that the mxture s envsoned as a mxture of functonal groups, rather than of molecules.the resdual contrbuton to the logarthm of the actvty coeffcent of group n the mxture, ln Γ s computed from the group contrbuton analog of equaton 6 whch can be wrtten as [7]. φm ψ m lnγ K = Q [ ln(σ m φ m Ψ m ) Σ m ] () Σ n φn Ψ nm φ m = su rface area fracton ofgroupm x m Q = m (2) Σ n x n Q n X m = molefracton ofgroupm n mxture. umnunn mn exp KT (3) a mn = exp (4) T Where umn s measure of the nteracton energy between groups m and n, and the sums are over all groups n the mxture. The resdual part of the actvty coeffcent of speces s computed from v ln γ (resdual)= Σ v [ln Γ lnγ ] (5) Here s the number of groups present n speces, and s the resdual contrbuton to the actvty coeffcent of group n a pure flud of speces molecule. The volume (R) and surface (Q) parameters are anm and ann for each par of functonal groups [8]. Contnung wth the group contrbuton dea, t s next assumed that any par of functonal groups m and n wll nteract n the same manner, that have the same value of amn and anm ndependent of the mxtures n whch these two groups occur. Consequently by a regresson analyss of great quanttes of actvty coeffcent data, the bnary parameters anm and amn for many group-group nteractons can be determned [9]. These parameters can then be used to predct the actvty coeffcent n mxtures for whch no expermental data are avalable. The advantage of ths group contrbuton approach s that wth a relatvely small number of functonal groups [20] the propertes of the mllons up on mllons of dfferent molecules can be obtaned.the parameters used n ths model were taen from lterature. 2.5 Error Analyss The relatve error percentages of the models are calculated usng equaton R Ey = y Experment al- y y C alculated x 00 Experment al (6) 2.6 Consstency of VLE The thermodynamc consstency of measured (vapour + lqud) equlbrum data s valdated usng Redlch-Kester method. Accordng to ths method only pure components are nvolved at the two end state and no mxng effect occurs, [2] at these All Rghts Reserved 34

5 γ ln γ 2 Internatonal Journal of Recent Trends n Engneerng & Research (IJRTER) 0 γ dx = 0 γ 2 ln (7) Calculated from two models s evaluated and plotted aganst x. The area above the x- axs wll be equal to area below t for thermodynamcally consstent data. III. RESULTS AND DISCUSSION The expermental VLE data of the four bnary azeotropes namely Ethanol-water, Acetonewater, Ethanol- benzene and Methanol-water are shown n Tables (-4) respectvely. The expermental values are compared wth lterature and found to be reasonably accurate. The calculated fugacty coeffcents for four azeotropes were found to be closer to unty, hence t s reasonable to assume that vapour phase s deal. The actvty coeffcent () calculated from the expermental values usng Equaton 2 for the four bnary systems s also ncluded n Tables (-4). It s evdent from the values of the actvty coeffcents (greater than unty) from expermental VLE that the lqud phase non-dealty s too hgh. Ths s due to the fact that the molecules of the compounds present n each of the azeotropes are not chemcally smlar. Whle water s onsed and strongly polar, ethanol, methanol and acetone are more organc n character [22]. The expermental Txy dagram of four bnary azeotropc systems shown postve devaton from dealty. For all the four azeotropes the mxture has hgher vapour pressure than Raoult s law, yeldng postve devaton from dealty (mnmum bolng azeotrope). The molecules present n the four azeotropes repel each other but do not attract. Ths results n hgher concentraton of molecules n vapour phase than n the lqud phase wth hgher actvty coeffcent. Eventually mnmum temperature was reached at the azeotropc composton for all the systems representng mnmum bolng homogenous azeotropsm. 3. Modellng VLE computaton wth UNIQUAC model was made usng Newton Raphson technque. Ths was accomplshed usng computer programmng wth Java.6 verson. The model parameters of the systems estmated from the program are presented n Table 5.Analytcal soluton of group contrbuton method (ASOG) was adopted n VLE calculaton usng UNIFAC model. Comparson of the VLE predcted from the two models wth the expermental data s presented n Tables (-4) for ethanol-water, acetone-water, ethanol-benzene and methanolwater respectvely Table. Expermental and Model predcton of VLE Ethanol-water system at Pa Expermental UNIQUAC UNIFAC T/C x y y error y error y y γ All Rghts Reserved 342

6 Internatonal Journal of Recent Trends n Engneerng & Research (IJRTER) Overall error percentage Table 2. Expermental and Model predcton of VLE Acetone-water system at Pa Expermental UNIQUAC UNIFAC T/C x y γ y y error y y error Overall error percentage Table 3. Expermental and Model predcton of VLE Ethanol-benzene system at Pa Expermental UNIQUAC UNIFAC T/C x y y error y error y y γ Overall error percentage All Rghts Reserved 343

7 Internatonal Journal of Recent Trends n Engneerng & Research (IJRTER) Table 4. Expermental and Model predcton of VLE Methanol-water system at Pa Expermental UNIQUAC UNIFAC T/C x y y error y error y y γ Overall error percentage Fg (-4) portrays the comparson of expermental VLE wth the UNIQUAC and UNIFAC models. The overall error percentages of the VLE for ethanol-water system usng UNIQUAC and UNIFAC models are and respectvely. Smlarly for acetone-water system, the calculated overall error percentages from UNIQUAC and UNIFAC models are and In the case of ethanol-benzene system, the error percentage was for UNIQUAC model and 3.84 for UNIFAC model. Percentage errors for methanol-water system usng UNIQUAC and UNIFAC model were found to be and Though both models are able to gve better results n VLE predcton for the systems, UNIFAC model has relatvely lesser error percentage. Fg. Expermental and Correlated xy Dagram of xy dagram Ethanol-water System Fg 2. Expermental and Correlted of Acetone-water All Rghts Reserved 344

8 Internatonal Journal of Recent Trends n Engneerng & Research (IJRTER) Fg 3. Expermental and Correlated xy Dagram of xy Dagram of Ethanol-benzene System Fg 4. Expermental and Correlated Methanol-water System Same trend of results s observed wth the Redlch Kester method of thermodynamcs consstency test Equaton 23. Ths can be seen from fg (5-8) for the four bnary systems. These plots are made usng the actvty coeffcents calculated from UNIQUAC and UNIFAC models (TABLES -4). Area under the curve computed from UNIQUAC and UNIFAC models for all systems s shown n TABLE 6. It can be observed that the computed values are closer to zero for the UNIQUAC model and almost zero for the UNIFAC model. Fg 5. Thermodynamc Consstency of Fg6. Thermodynamc consstency of Acetone- Ethanol-water System water System Fg 7. Thermodynamc Consstency of Ethanol-benzene System Fg 8. Thermodynamc Consstency of Methanolwater All Rghts Reserved 345

9 Internatonal Journal of Recent Trends n Engneerng & Research (IJRTER) Table 5. Estmated UNIQUAC Parameters of four bnary systems UNIQUAC Parameters J/mol K System u2-u22 u2-u Ethanol-water Acetone-water Ethanol-benzene Methanol-water Table 6. VLE Consstency test for four azeotropes System Area UNIQUAC UNIFAC Ethanol-water Acetone-water Ethanol-benzene Methanol-water IV. CONCLUSION In case of VLE predcton of azeotropes, UNIQUAC and UNIFAC models were tested for the systems ethanol-water, acetone-water, ethanol-benzene and methanol-water. The expermental VLE fndngs prove that all the systems are mnmum bolng azeotropes. Major fndng of the present wor s the estmaton of UNIQUAC parameters for the four systems. These parameters can be utlzed for VLE calculaton at any pressure condtons. The error analyss and thermodynamcs consstency test studes reveal that both models gve good representaton of VLE for all the chosen systems. REFERENCES I. W. L. McCabe, J. C. Smth, P. Harrot, Unt Operatons n Chemcal Engneerng 7 th Ed., McGraw Hll Publcaton, II. T. P. Ognsty, Analyze Dstllaton Columns wth Thermodynamcs, Chemcal Engneerng Progress,, 995, III. J. M. Smth, H. C. Van Ness, M. M. Abbott, Textboo of Introducton to Chemcal Engneerng Thermodynamcs, 7 th Ed., McGraw Hll Publcatons, IV. W. Swetoslaws, Azeotropy and Polyazeotropy, Oxford Pergamon Press publcaton, 994. V. R. E. Treybal, Mass Transfer Operaton, 3 rd Ed., McGraw Hll Publcaton, 98. VI. S. T. Ln, S. I. Sandler, A Pror Phase Equlbrum Predcton from a Segment Contrbuton Solvaton Model, Industral Engneerng Chemstry Research, 4, 2002, VII. S. Sogested, Chemcal Process and Energy Process Engneerng, 4 th Ed., CRC Publcaton, VIII. Y. V. C. Rao, Chemcal Engneerng Thermodynamcs, 3 rd Ed., Unverstes Press Inda Lmted, 997. IX. K. S. Ptzer, R. F. Curl, Emprcal Equaton for the Second Vral Coeffcent, Journal of Amercan chemcal socety, , X. G. M. Wlson, C. H. Deal, Actvty Coeffcents and Molecular Structure: Actvty Coeffcents n Changng Envronments - Solutons of Groups, Industral Engneerng Chemstry Fundamentals, 962, XI. XII. XIII. XIV. XV. P. Aless, I. Kc, P. Rasmussen, A. Fredenslund, UNIFAC and Infnte Dluton Actvty Coeffcents, Canadan journal of chemcal Engneerng, 60, 982, A. Fredenslund, R. L. Jones, J. M. Prausntz, Group- Contrbuton Estmaton of Actvty Coeffcents n Nondeal Lqud Mxtures, AIChE JOURNAL 2, 975, T. F. Anderson, J. M. Prausntz, Applcaton of the UNIQUAC Equaton to Calculaton of Multcomponent Phase Equlbra, Industral and Engneerng Chemcal Process Desgn and Development, 7, 978, A. Fredenslund, J. Gmehlng, M. L. Mchelson, P Rasmussen, Computerzed Desgn of Multcomponent Dstllaton Columns usng the UNIFAC Group Contrbuton Method, Industral and Engneerng Chemcal Process Desgn and Development. 6, 977, J. Gmehlng, From UNIFAC to Modfed UNIFAC to PSRK wth the Help of DDB, Flud Phase Equlbra, 07, 995 All Rghts Reserved 339

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