MODELING THE HIGH-PRESSURE BEHAVIOR OF BINARY MIXTURES OF CARBON DIOXIDE+ALKANOLS USING AN EXCESS FREE ENERGY MIXING RULE

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1 Brazlan Journal of Chemcal Engneerng ISSN Prnted n Brazl Vol. 21, No. 04, pp , October - December 04 MODELING THE HIGH-PRESSURE BEHAVIOR OF BINARY MIXTURES OF CARBON DIOXIDE+ALKANOLS USING AN EXCESS FREE ENERGY MIXING RULE M. Caster 1, L.A. Galca-Luna 2 and S.I. Sandler 3* 1 Escola de Químca, Unversdade Federal do Ro de Janero, Cx P , , Ro de Janero - RJ, Brazl. E-mal: caster@eq.ufrj.br 2 Insttuto Poltécnco Naconal, Lab. de Termodnámca para Graduados ESIQIE, Edf Z, Secc 6, 1 er Pso, Mexco Cty 07738, DF, Mexco. 3 Center for Molecular and Engneerng Thermodynamcs, Department of Chemcal Engneerng, Unversty of Delaware Newark - DE, , USA Emal: sandler@che.udel.edu (Receved: September 5, 03 ; Accepted: June 7, 04) Abstract - The behavor of bnary mxtures of carbon doxde+alkanol (1-butanol, 2-butanol, 1-pentanol, or 2-pentanol) at hgh pressures was modeled usng the Stryjek-Vera verson of the Peng-Robnson equaton of state. Two mxng rules were compared for ths purpose: the classcal one-flud and the mxng rules. In the case of the latter mxng rule, the NRTL model for the excess Gbbs free energy was used. We observed that both mxng rules can reproduce the qualtatve aspects of the crtcal dagrams of these bnary mxtures. A comparson of the results shows that there s no clear superorty of one mxng rule over the other n terms of the ablty to predct the crtcal behavor of these mxtures. Keywords: hgh pressure, carbon doxde, alkanols, crtcal ponts. INTRODUCTION The use of carbon doxde as extractng solvent has many advantages, such as beng nontoxc, nonflammable and havng a relatvely mld crtcal temperature and pressure. A possble use of supercrtcal carbon doxde s for the separaton of water + alkanol mxtures. To determne proper processng condtons for such separatons, t s necessary to calculate phase equlbrum at hgh pressures for these systems, whch requres the measurement and correlaton of the behavor of bnary mxtures of these components. Of specal nterest s the behavor of bnary mxtures of carbon doxde and alkanols. Jennngs et al. (1993) measured phase equlbra of carbon doxde separately wth ethanol, 1-butanol, and 1-pentanol. Lee and Lee (1998) measured the phase equlbra of the carbon doxde + 2-pentanol mxture. More recently, Galca- Luna and coworkers obtaned phase equlbrum and crtcal pont data for bnary mxtures of carbon doxde and dfferent alkanols. Slva-Olver and Galca-Luna (01) studed bnary mxtures of carbon doxde separately wth 1-butanol and 2- *To whom correspondence should be addressed

2 6 M. Caster, L.A. Galca-Luna, and S.I. Sandler butanol, Slva-Olver et al. (02) wth 1-pentanol and 2-pentanol, and Elzalde-Sols et al. (03) wth 1-hexanol and 1-heptanol. In ths paper, we focus on the modelng of bnary mxtures of carbon doxde and an alkanol (1-butanol, 2-butanol, 1-pentanol, or 2-pentanol) usng the data of Slva-Olver and Galca-Luna (01) and Slva- Olver et al. (02). The Stryjek-Vera (1986) verson of the Peng-Robnson (1976) equaton of state (PRSV EOS) was used. We compare the results of two mxng rules: the classcal one-flud and the (1992) mxng rules. THERMODYNAMIC MODEL AND CRITICAL POINT CALCULATIONS The PRSV EOS P RT a = v b v + 2bv b 2 2 (1) was used to model the behavor of the systems, wth the a and b parameters gven by a and c 2 2 c R T = α PR, (2) P RTc b = (3) P wth c ( ) α = 1+κ 1 T PR, R where the reduced temperature s T R c 2 (4) = T T (5) κ = ω ω ω (7) and κ 1 s a characterstc parameter of each component. For our calculatons, we used separately the oneflud mxng rules and the Wong- Sandler (1992) mxng rules. The one-flud van der Waals mxng rules are nc nc j jj( j ) (8) a = xx a a 1 k = 1 j1 = n c b= xb (9) = 1 The mxng rules are RTQwsDws a = = RTDwsb 1 D ws ws (10) Qws b = (11) 1 D where D ws E n c a xa = + crt (12) RTb nc nc = 1 ws j = 1 j1 = a Q = xx b (13) RT Parameter c s characterstc of each equaton of state, equal to for the PRSV EOS. In Eq. E (12), a represents the molar excess Helmholtz free energy at nfnte pressure, whch was calculated usng the NRTL (Renon and Prausntz, 1968) excess free energy model. The followng combnng rule for the term j In the PRSV EOS, κ s gven by ( 1 T )( 0.7 T ) κ =κ +κ + (6) 0 1 R R where a b RT j j was employed: ( ) a b + bj a a 1 k b = RT 2 RT jj j (14) Brazlan Journal of Chemcal Engneerng

3 Modelng the Hgh-Pressure Behavor 661 Addtonal detals about the mxng rule can be found n the orgnal reference (Wong and Sandler, 1992). Its use for calculaton of the crtcal pont of mxtures s dscussed n the work of Caster and Sandler (1997a,b). The procedure uses a modfed verson of the Hcks and Young (1977) algorthm to determne possble multple crtcal ponts for each composton and refnes the solutons wth the Hedemann and Khall (19) procedure. The crtcal ponts reported here passed the local and global stablty tests for the possble appearance of addtonal flud phases; the unlkely possblty of formng sold phases was not tested n our mplementaton. PARAMETER FITTING AND CRITICAL POINT CALCULATIONS Parameters of the pure components used n the PRSV EOS were taken from Stryjek and Vera (1986), wth the excepton of those for 2-pentanol, whose propertes were not avalable n that reference. For ths component, the values used for the crtcal propertes and acentrc factor ( Tc = 5.4 K, Pc = 38.7 bar, ω= ) are those adopted by Lee and Lee (1998). The value of the κ parameter n the PRSV EOS was ftted usng the procedure developed by Orbey and Sandler (1998) usng vapor pressure data compled by Boublík et al. (1973). A κ value of was determned n ths way. 1 1 Bnary nteracton parameters were ftted from the VLE data. These parameters were estmated usng modfed versons of the parameter fttng program orgnally developed by Orbey and Sandler (1998) to take nto account the possblty of smultaneously usng data sets at dfferent temperatures. The followng objectve functon was used: n p c e j j (15) j1 = f = P P where c P j and e P j respectvely denote the calculated and measured values of the pressure at expermental pont j. Ponts that caused a numercal problem n the parameter fttng procedure, such as lack of convergence, were removed from the data sets used for parameter fttng. These were usually the data ponts at the hghest pressures, where obtanng convergence s dffcult. No crtcal pont data on the mxture were used n the parameter fttng procedures, nor were data ponts for three-phase equlbra. However, we dd observe that for the mxng rule, several dfferent parameter sets produced very smlar VLE results for some systems. In such cases the parameter set chosen for the crtcal pont calculatons was the one that produced the best representaton of the crtcal data based on a vsual analyss. A smlar problem dd not arse when fttng the sngle parameter n the van der Waals one-flud mxng rule. The values of the ftted parameters are shown n Tables 1 and 2. Table 1: Parameters for the Systems Studed: PRSV EOS usng the mxng rule Component 1 Component 2 k 12 Carbon doxde 1-butanol Carbon doxde 2-butanol Carbon doxde 1-pentanol Carbon doxde 2-pentanol Table 2: Parameters for the Systems Studed: PRSV EOS + NRTL, usng the mxng rule. The non randomness parameter (α )of the NRTL model was set equal to 0.3 n all cases. g Component 1 Component 2 21 (K) R g 21 (K) k R 12 Carbon doxde 1-butanol Carbon doxde 2-butanol Carbon doxde 1-pentanol Carbon doxde 2-pentanol Brazlan Journal of Chemcal Engneerng Vol. 21, No. 04, pp , October - December 04

4 662 M. Caster, L.A. Galca-Luna, and S.I. Sandler The results for the four bnary mxtures are shown n Fgures 1 to 4. The PRSV EOS usng ether the one-flud mxng rule or the mxng rule correctly predcted the qualtatve aspects of the crtcal loc of the four mxtures. For the systems carbon doxde + 1- butanol (Fg. 1) and carbon doxde + 2-butanol (Fg. 2), the two mxng rules produced very smlar results, even though the mxng rule contans two addtonal parameters. In the case of the carbon doxde + 1-pentanol mxture (Fg. 3), the temperature-mole fracton (Tx) projecton (Fg. 3b) and the pressure-mole fracton (P-x) projecton (Fg. 3c) are margnally better represented by the mxng rule, whereas the pressure-temperature (P-T) projecton (Fg. 3a) s slghtly better represented by the one-flud mxng rule. For the carbon doxde + 2-pentanol (Fg. 4) mxture, the T-x projecton (Fg. 4b) s slghtly better represented by the mxng rule, whle the P-x and T-P projectons (Fg. 4a and c) are somewhat better represented by the Wong- Sandler mxng rule CO 2 1-butanol Temperature (Kelvn) Fgure 1: Crtcal curve of the system carbon doxde+1-butanol: pressure-temperature projecton (PRSV EOS wth the one-flud and the mxng rules). 1 1 CO 2 2-butanol Temperature (Kelvn) Fgure 2: Crtcal curve of the system carbon doxde+2-butanol: pressure-temperature projecton (PRSV EOS wth the one-flud and the mxng rules). Brazlan Journal of Chemcal Engneerng

5 Modelng the Hgh-Pressure Behavor (A) (B) CO 2 1-pentanol Temperature (Kelvn) (a) Temperature (Kelvn) Mole fracton of carbon doxde (b) (C) Mole fracton of carbon doxde (c) Fgure 3: Crtcal curve of the system carbon doxde+1-pentanol: pressure-temperature (a), temperature-mole fracton (b), and pressure-mole fracton (c) projectons (PRSV EOS wth the one-flud and the mxng rules). Brazlan Journal of Chemcal Engneerng Vol. 21, No. 04, pp , October - December 04

6 664 M. Caster, L.A. Galca-Luna, and S.I. Sandler 0 1 (A) (B) 1 CO 2 2-pentanol Temperature (Kelvn) (a) Temperature (Kelvn) Mole fracton of carbon doxde (b) 0 1 (C) Mole fracton of carbon doxde (c) Fgure 4: Crtcal curve of the system carbon doxde+2-pentanol: pressure-temperature (a), temperature-mole fracton (b), and pressure-mole fracton (c) projectons (PRSV EOS wth the one-flud and the mxng rules). Brazlan Journal of Chemcal Engneerng

7 Modelng the Hgh-Pressure Behavor 665 CONCLUSIONS Four bnary mxtures contanng carbon doxde and an alkanol (1-butanol, 2-butanol, 1-pentanol, or 2-pentanol), whose hgh-pressure phase equlbrum data had recently been measured, were modeled usng the Stryjek-Vera verson of the Peng-Robnson equaton of state. For predcton of the crtcal ponts of these mxtures, two mxng rules were tested: the classcal one-flud and the mxng rules. Both mxng rules can reproduce the qualtatve aspects of the crtcal dagrams of these bnary mxtures at about the same level of accuracy. Consequently, for these mxtures the smpler van der Waals one-flud mxng rule s preferred. α PR auxlary term n the Peng-Robnson equaton of state ω acentrc factor κ parameter of the PRSV equaton κ κ parameters of PRSV equaton 0, 1 Subscrpts c,j R Superscrpts crtcal property refer respectvely to components and j reduced property property at nfnte pressure ACKNOWLEDGMENTS M.C. acknowledges the fnancal support of CNPq/Brazl, PRONEX (Grant 124/96), and FAPERJ. c e E EOS calculated expermental excess property equaton of state NOMECLATURE REFERENCES a molar Helmholtz free energy or EOS attractve parameter b EOS covolume parameter c characterstc parameter of the equaton of state ( for PRSV EOS) D ws auxlary parameter of the Wong- Sandler mxng rule f objectve functon for parameter estmaton g j nteracton parameter n the NRTL (orgnal or modfed) model bnary nteracton parameter k j n c n p number of components number of expermental data ponts P pressure Q ws auxlary parameter of the Wong- Sandler mxng rule R unversal gas constant T temperature v molar volume x mole fracton of component Greek Letters α NRTL nonrandomness parameter Boublík, T., Fred, V., and Hála, E., The Vapour Pressures of Pure Substances, Elsever, Amsterdam (1973). Caster, M. and Sandler, S.I, Crtcal Ponts wth the Mxng Rule. Part I: Calculatons wth the Equaton of State, Chem. Engng Sc. 52, 3393 (1997a). Caster, M. and Sandler, S.I., Crtcal Ponts wth the Mxng Rule. Part II: Calculatons wth a Modfed Peng-Robnson Equaton of State, Chem. Engng Sc. 52, 3579 (1997b). Elzalde-Sols, O., Galca-Luna, L.A., Sandler, S.I., and Sampayo-Hernandez, J.G., Vapor-Lqud Equlbra and Crtcal Ponts of the CO Hexanol and CO 2 +1-Heptanol Systems, Flud Phase Equlbra, 210 (2), 215 (03). Hedemann, R.A. and Khall, A.M., The Calculaton of Crtcal Ponts, AIChE J. 26, 769 (19). Hcks, C.P. and Young, C.L., Theoretcal Predctons of Phase Behavour at Hgh Temperatures and Pressures for Non-Polar Mxtures: 1. Computer Soluton Technques and Stablty Tests, J. Chem. Soc., Faraday II, 73, 597 (1977). Jennngs, D.W., Gude, M.T., and Teja A.S., Hgh- Pressure Vapor-Lqud-Equlbra n Carbon- Doxde and 1-Alkanol Mxtures, ACS Symposum Seres, 514, 10 (1993). Brazlan Journal of Chemcal Engneerng Vol. 21, No. 04, pp , October - December 04

8 666 M. Caster, L.A. Galca-Luna, and S.I. Sandler Lee, H.-S. and Lee, H., Hgh-pressure Phase Equlbra for the Carbon Doxde-2-Pentanol and Carbon Doxde-Water-2-Pentanol Systems, Flud Phase Equlbra, , 695 (1998). Orbey, H. and Sandler, S.I., Modelng Vapor-Lqud Equlbra: Cubc Equatons of State and Ther Mxng Rules, Cambrdge Unv. Press, Cambrdge (1998). Peng, D.Y. and Robnson, D.B., A New Twoconstant Equaton of State, Ind. Eng. Chem. Fundamentals 15, 59 (1976). Renon, H. and Prausntz, J.M., Local Compostons n Thermodynamc Excess Functons for Lqud Mxtures, AIChE J., 14, 135 (1968). Slva-Olver, G. and Galca-Luna, L.A., Vapor- Lqud Equlbra Near Crtcal Pont and Crtcal Ponts for the CO 2 +1-Butanol and CO 2 +2-Butanol Systems at Temperatures from 324 to 432 K, Flud Phase Equlbra, 182 (1-2), 145 (01). Slva-Olver, G., Galca-Luna, L.A., and Sandler, S.I., Vapor-Lqud Equlbra and Crtcal Ponts for the Carbon Doxde+1-Pentanol and Carbon Doxde+2-Pentanol Systems at Temperatures from 332 to 432 K, Flud Phase Equlbra, 0 (1), 161 (02). Stryjek, R. and Vera, J.H., PRSV: An Improved Peng-Robnson Equaton of State for Pure Compounds and Mxtures, Can. J. Chem. Engng. 64, 323 (1986). Wong, D.S.H. and Sandler, S.I., A Theoretcally Correct Mxng Rule for Cubc Equatons of State, AIChE J., 38, 671 (1992). Brazlan Journal of Chemcal Engneerng