MODELING OF ASSOCIATION EFFECTS IN MIXTURES OF CARBOXYLIC ACIDS WITH ASSOCIATING AND NON-ASSOCIATING COMPONENTS

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1 Latn Amercan Appled Research 33: (003) MODELING OF ASSOCIATION EFFECTS IN MIXTURES OF CARBOXYLIC ACIDS WITH ASSOCIATING AND NON-ASSOCIATING COMPONENTS O. FERREIRA, T. FORNARI, E. A. BRIGNOLE and S. B. BOTTINI Planta Ploto de Ingenería Químca (UNS-CONICET) CC 717, 8000 Bahía Blanca, Argentna. Abstract-- The group contrbuton wth aton equaton of state GCA-EOS has been appled to calculate thermodynamc propertes of pure compounds and mxtures of carboxylc acds wth paraffns, alcohols, water and gases, at low and hgh pressures. Two atng groups, OH and COOH, were defned. Self- and cross-aton n these mxtures were quantfed through two parallel COOH/COOH and OH/OH atons. The valdty of ths approach s supported by an excellent representaton of pure compound propertes (vapor pressures and compressblty factors) and phase equlbra n mxtures of (atng + nert) and (atng + atng) components at low and hgh pressures. Keywords-- Assocaton, Group Contrbuton, Carboxylc acds. I. INTRODUCTION Assocaton and solvaton effects, when present, play a maor role n the propertes of pure compounds and mxtures. They are partcularly mportant n carboxylc acds, where aton s present even at low vapor denstes. In the present work the group contrbuton wth aton equaton of state GCA-EOS (Gros et al., 1996) s appled to calculate phase equlbrum propertes n mxtures of carboxylc acds, alcohols, water and gases, at low and hgh pressures. The aton term n the GCA-EOS model s based on Werthem s theory for fluds wth hghly drected attractve forces as appled n the SAFT equaton (Chapman et al, 1990), and follows a group contrbuton approach. Gros et al. (1996) have used a sngle hydroxyl (OH) atng group to represent aton effects n alcohols, water and ther mxtures. In ths work the applcaton of the GCA-EOS s extended to mxtures contanng carboxylc acds, by defnng a new COOH atng group. To allow a straghtforward extenson of the model to multcomponent mxtures contanng OH and COOH atng groups, a new approach s proposed to solve the cross aton problem. II. SELF- AND CROSS-ASSOCIATION IN MIXTURES WITH CARBOXYLIC ACIDS Carboxylc acds present a hgh degree of non-dealty even at low pressures, whch can be ascrbed to the formaton of olgomers n both, lqud and vapor phases. Generally only the formaton of dmers s consdered, and t s possble to fnd n the lterature (Gmehlng et al, 198a) the values of the vapor phase dmerzaton constants for a number of carboxylc acds. In order to model aton by the GCA-EOS model, t s necessary to determne the number of atng groups, the number of actve stes n each group and the values of the correspondng aton strengths. The aton strength s a functon of two parameters: the volume (κ) and the energy (ε/k) of aton. In ths work a new atng group (COOH) was defned as havng one atng ste that self-ates by double hydrogen bondng (Fg. 1). C OH O O HO OH Fg.1. Schematc representaton of self and cross aton n carboxylc acds. Followng the procedure adopted by Gros et al. (1996) for the hydroxyl (OH) group, the COOH aton parameters were determned by reproducng the fracton of non-bonded molecules predcted by the SAFT equaton for lnear acds from propanoc to decanoc at saturated lqud condtons (Wolbach and Sandler, 1997). The values obtaned for the energy and volume of aton were ε/k COOH = 6500Κ and κ COOH = cm 3 /gmol, respectvely. As expected, the COOH energy of aton s much larger than that of the OH group (ε/k OH = 700Κ), whch s n accordance wth the hgher degree of aton of carboxylc acds. The extenson of aton theores to mxtures contanng more than one atng compound requres the estmaton of cross-aton parameters and n some cases the numercal soluton of a set of nonlnear equatons. Kraska (1998) presents a revson of the varous rgorous and approxmate solutons for cross-aton models. Usually the problem s solved by settng some combnaton rule to evaluate the cross- C 307

2 Latn Amercan Appled Research 33: (003) aton strength from the correspondng selfatons (n general geometrc and/or arthmetc rules are appled) (Suresh et al., 199, Voutsas et al., 1999). The large dfference between the energes of aton of the COOH and OH groups precludes the use of ths approach to evaluate cross-aton effects n mxtures of carboxylc acds wth water and/or alcohols. At room temperature, for example, the COOH self-aton strength s ten thousand tmes that of the OH group. A mean value between such dssmlar quanttes would be physcally meanngless, and the cross-aton strength calculated ths way wll tend to over-predct the degree of cross-aton n a soluton where the acd molecules are predomnantly self-ated. In ths work a dfferent emprcal approach s proposed to evaluate cross-aton n these mxtures. From the pont of vew of aton, each carboxylc acd molecule s consdered to have two atng groups: one COOH group whch self-ates through a double hydrogen bondng, and a certan fracton of OH group that has a remnant aton capacty and can self-ate wth another OH group (see Fg. 1). In ths way, the cross aton problem s replaced by the self-aton between the OH group from the alcohol or water, and the fracton of OH group present n the carboxylc acd molecule. Followng ths methodology, the aton of carboxylc acds and mxtures of carboxylc acds wth water and/or alcohols s represented by two self-atons n parallel: COOH/COOH and OH/OH. The value of each selfaton strength s calculated from the respectve COOH and OH aton parameters (ε/k COOH = 6500Κ, κ COOH = cm 3 /gmol, ε/k OH = 700Κ and κ OH = cm 3 /gmol). The fracton of atng OH group provded by the carboxylc acd molecules was emprcally determned by fttng vapor-lqud equlbrum (VLE) data on bnary mxtures of acds wth water and alcohols. A fracton of OH group equal to 0.5 gave the best correlaton of these data. The methodology proposed here has the addtonal advantage of solvng the aton problem by two explct mathematcal expressons for the fracton of non-bonded COOH and OH atng groups. Ths makes straght forward the applcaton of the GCA-EOS model to multcomponent mxtures of carboxylc acds, water, alcohols and nert components. III. ATTRACTIVE-ENERGY PARAMETERS There are three contrbutons to the resdual Helmholtz energy n the GCA-EOS model: free volume, attractve and atve contrbutons. The group-contrbuton attractve term has fve pure-group parameters (T, q, g, g and g ) and four bnary nteracton parameters (the symmetrcal k and k and the asymmetrcal nonrandomness parameters α and α.). The COOH functonal group was not avalable n the GCA-EOS parameter table. In ths work the attractveenergy parameters for ths group and ts nteractons wth the paraffnc (CH 3 and CH ), alcohol (CHOH, CH OH, CH 3 OH), water (H O), trglycerde (TG) and CO functonal groups were determned. Tables 1 an show, respectvely, the correspondng pure-group and bnary nteracton parameters. The expermental nformaton used to ft these parameters nclude: vapor pressures (P vap ) of pure carboxylc acds; bnary lowpressure vapor-lqud equlbra (LPVLE) for mxtures of carboxylc acds wth alkanes, alcohols and water; hgh-pressure vapor-lqud equlbra (HPVLE) for bnary mxtures of carboxylc acds wth carbon doxde; and nfnte dluton actvty coeffcents (γ ) of alkanes n mxtures of tracetn wth palmtc acd. Table 1. Pure-group parameters Group T (K) q g g g Expermental nformaton COOH P vap (1) and LPVLE acds-alkanes () Source of data: (1) Daubert and Danner (1989); () Gmehlng et al. (198a) I J k Table. Bnary nteracton parameters k α α Expermental nformaton COOH CH LPVLE acds-alkanes () CH LPVLE acds-alkanes () CO HPVLE acds-co (3) CHOH LPVLE acds-alcohols (4, 5) CH OH LPVLE acds-alcohols (4, 5) CH 3 OH LPVLE acds-alcohols (4, 5) H O LPVLE acds-water (6, 7) TG γ (8) Source of data: () Gmehlng et al. (198a); (3) Bharath et al. (1993); (4) Gmehlng and Onken (1977a); (5) Gmehlng et al. (198); (6) Gmehlng and Onken (1977); (7) Gmehlng et al. (1998); (8) Bermudez et al. (001) 308

3 O. FERREIRA, T. FORNARI, E. A. BRIGNOLE, S. B. BOTTINI IV. RESULTS AND DISCUSSION The correlaton of carboxylc acd vapor pressures gave an average relatve error of 3% wthn a reduced temperature range between 0.55 and 0.90 (see Table 3). Table 4, on the other hand, compares expermental vapor compressblty factors (Z) at saturaton (Myamoto et al., 1999) wth GCA-EOS predctons. The low values of Z reflect the strong aton of carboxylc acds n the vapor phase, even at low pressures. It s nterestng to notce that the GCA-EOS s able to follow the slght ncrease of Z wth temperature showed by the expermental data. Table 3: Pure-component vapor pressures. Components T(K) Error % Acetc acd Propanoc acd Butanoc acd Pentanoc acd Hexanoc acd Heptanoc acd Octanoc acd Nonanoc acd Decanoc acd Error = [( P Pcalc )/ P ] / NP exp exp ; NP: number of data ponts. Table 4. Vapor phase compressblty factors Component T(K) Z exp Z calc Z / Z exp (%) Acetc acd Propanoc acd Butanoc acd Pentanoc acd Fgures to 8 represent vapor-lqud equlbra (VLE) results for some bnary mxtures of carboxylc acds wth alkanes, carbon doxde, alcohols and water. Excellent correlaton (Fg. ) and predcton (Fg. 3) of low- and hgh-pressure VLE were acheved for mxtures of alkanes wth low and hgh molecular weght carboxylc acds. The same s true for mxtures wth CO, as t can be nferred from the results shown n Fg. 4 (predcton) and Fg. 5 (correlaton). Fgs. 6 and 7 present some results from the correlaton of vaporlqud equlbra of cross atng mxtures. Fnally, Fg. 8 shows GCA-EOS predctons of hghpressure VLE for the ternary system CO + olec acd + trolen. Even though the CO solvent power predcted by the model s lower than the data measured by Bharath et al. (199), the selectvty s correct;.e. the equaton shows the hgher affnty of CO for the fatty acd. V. CONCLUSIONS In ths work, aton effects n carboxylc acds were represented by a group contrbuton approach. Crossaton effects n mxtures of carboxylc acds wth alcohols and water, were taken nto account by solvng two parallel self-aton problems. Wth ths approach and usng a sngle set of parameters, good representaton was obtaned for pure component propertes and phase equlbra n mxtures of carboxylc acds wth nert compounds, alcohols and water at low and hgh pressures. The group contrbuton nature of the GCA-EOS allows t to be appled to mxtures for whch expermental nformaton s scarce or not avalable. In ths respect, the GCA-EOS s a useful tool to explore 309

4 Latn Amercan Appled Research 33: (003) process condtons for the extracton and fractonaton of fatty acds and other fatty ol dervatves wth supercrtcal fluds T=33.15K T=353.15K Fg.. VLE of heptane (1) + propanoc acd (): Exp. (Gmehlng et al., 198a, pg. 15); GCA-EOS Fg. 5. VLE of CO (1)+ palmtc acd(): Exp. (Bharath et al., 1993); GCA-EOS T=313.15K T(K) P=1atm Fg. 3. VLE of ethane (1) + olec acd(): Exp.(Peter et al., 1991); GCA-EOS Fg. 6. VLE of 1-propanol (1)+ propanoc acd (): Exp. (Gmehlng et al., 198, pg.486); GCA-EOS T=313.15K T=333.15K T=373.15K Fg. 4. VLE of CO (1)+ butanoc acd (): Exp (Byun et al., 000), GCA-EOS T=373.15K T=353.15K Fg. 7. VLE of H O (1)+ propanoc acd(): Exp. (Gmhelng and Onken, 1977a, pgs. and 4); GCA-EOS. T=313K P=50bar T=313K P=50bar CO CO ác.oleco Olec acd OOO Trolen Fg. 8. VLE of the system CO + olec acd + trolen: O Expermental (Bharath et al, 199); GCA- EOS REFERENCES Bermudez, A., O. Ferrera and G. Foco, Infnte dluton actvty coeffcents of solvents n fatty ol dervatves, Proc. of Enpromer, Santa Fe, Argentna, , (001). Bharath, R., H. Inomata, T. Adschr and K. Ara, Phase equlbrum study for the separaton and 310

5 O. FERREIRA, T. FORNARI, E. A. BRIGNOLE, S. B. BOTTINI fractonaton of fatty ol components usng supercrtcal carbon doxde, Flud Phase Equlbra, 81, , (199). Bharath, R., S. Yamane, H. Inomata H, T. Adschr and K. Ara, Phase equlbra of supercrtcal CO- fatty ol component bnary systems, Flud Phase Equlbra, 83, , (1993). Bottn, S.B., T. Fornar and E.A. Brgnole, Phase equlbrum modelng of trglycerdes wth near crtcal solvents, Flud Phase Equlbra, , (1999). Byun, Hun-soo, Nam-seok Jeon and M.A. Mchugh, Phase behavor and modelng of supercrtcal carbon doxde - acd mxtures, Proc. 5th Int. Symposum on Supercrtcal Fluds (CD-ROM), Atlanta, Georga, USA, (000). Chapman, W., K. Gubbns, J. Jackson and M. Radosz, New reference equaton of state for atng lquds, Ind. Eng. Chem. Res, 9, , (1990). Daubert, T.E. and R.P. Danner, Physcal and Thermodynamc Propertes of Pure Chemcals: Data Complaton, Hemsphere Publshng Corporaton, (1989). Gmehlng, J. and U. Onken, Vapor Lqud Equlbrum Data Collecton. Aqueous-organc systems, Dechema Chemstry Data Seres I 1, Frankfurt, Germany, (1977). Gmehlng, J. and U. Onken, Vapor Lqud Equlbrum Data Collecton. Organc hydroxyl compounds: alcohols, Dechema Chemstry Data Seres I a, Frankfurt, Germany, (1977a). Gmehlng, J., U. Onken and W. Arlt, Vapor Lqud Equlbrum Data Collecton. Organc hydroxyl compounds: alcohols (suplement 1), Dechema Chemstry Data Seres I c, Frankfurt, Germany, (198). Gmehlng, J., U. Onken and P. Grenzheuser, Vapor Lqud Equlbrum Data Collecton. Carboxylc acds, anhydrdes, esters, Dechema Chemstry Data Seres I 5, Frankfurt, Germany, (198a). Gmehlng, J., U. Onken and W. Arlt, Vapor Lqud Equlbrum Data Collecton. Aqueous-organc systems (Suplement 1), Dechema Chemstry Data Seres I 1a, Frankfurt, Germany, (1998). Gros, H., S.B. Bottn and E.A. Brgnole, A group contrbuton equaton of state for atng mxtures, Flud Phase Equlbra, 116, (1996). Gros, H.P, S.B. Bottn and E.A. Brgnole, Hgh pressure phase equlbrum modelng of mxtures contanng atng compounds and gases, Flud Phase Equlbra, 139, (1997). Kraska, T., Analytc and fast numercal solutons and approxmatons for cross aton models wthn statstcal aton flud theory, Ind. Eng. Chem. Res., 37, , (1998). Mansoor, G.A. and T.W. Leland, Statstcal thermodynamcs of mxtures, J. Chem. Soc. Faraday Trans. II, 68, 30, (197). Myamoto, S., S. Nakamura, F. Iwa and Y. Ara, Measurement of vapor phase compressblty factors of monocarboxylc acds usng a flow type apparatus, J.Chem.Eng.Data, 44, 48-51, (1999). Peter, S. and H. Jakob, The rheologcal behavor of coexstng phases n systems contanng fatty acds and dense gases, The Journal of Supercrtcal Fluds, 4, , (1991). Renon, H and J.M. Prausntz, Local compostons n thermodynamc excess functons for lqud mxtures, AIChE J., 14, (1968). Skold-Jørgensen, S., Gas solublty calculatons II. Applcaton of a new group-contrbuton equaton of state, Flud Phase Equlbra, 16, (1984). Skold-Jørgensen, S., Group contrbuton equaton of state (GC-EOS): A predctve method for phase equlbrum computatons over wde ranges of temperature and pressures up to 30 Mpa, Ind. Eng. Chem. Res., 7, (1988). Suresh, S. and J. Ellot, Multphase equlbrum analyss va a generalzed equaton of state for atng mxtures, Ind. Eng. Chem. Res., 31, , (199). Voutsas, E.C., I.V. Yakoums and D.P. Tassos, Predcton of phase equlbra n water/alcohol/alkane systems, Flud Phase Equlbra, , , (1999). Werthem, M.S., Fluds wth hghly drectonal attractve forces. I. Statstcal thermodynamcs, J. Stat. Phys., 35, 19, (1984a). Werthem, M.S., Fluds wth hghly drectonal attractve forces. II. Thermodynamc perturbaton theory and ntegral equatons, J. Stat. Phys., 35, 35, (1984b). Werthem, M.S., Fluds wth hghly drectonal attractve forces. III. Multple attracton stes, J. Stat. Phys., 4, 459, (1986a). Werthem, M.S., Fluds wth hghly drectonal attractve forces. IV. Equlbrum polymerzaton, J. Stat. Phys., 4, 477, (1986a). Wolbach, J.P. and S.I. Sandler, Usng molecular orbtal calculatons to descrbe phase behavor of hydrogen-bondng fluds, Ind. Eng. Chem. Res., 36, , (1997). APPENDIX There are three contrbutons to the resdual Helmholtz functon (A res ) n the GCA-EoS model: free volume (A fv ), attractve (A att ) and atve (A ). res fv att A = A + A + A (A1) The free volume contrbuton s represented by the extended Carnahan-Starlng equaton for mxtures of hard spheres developed by Mansoor and Leland (197): 311

6 Latn Amercan Appled Research 33: (003) fv ( λ λ λ )( Y -1) + ( λ ) ( A / RT ) = λ3 LKKKKK ( Y + Y ln Y ) + n ln Y wth: 1 πλ 1-3 = 6V Y and λ = NC n d k 3 k (A) n beng the number of moles of component, NC the number of components n the mxture, n the total number of moles, V the total volume and d the hardsphere dameter per mol of speces. The followng generalzed expresson gves the temperature dependence of the hard-sphere dameter: d = d {1 0.1 exp[ T /(3T )]} (A3) c where d c and T c are, respectvely, the crtcal hardsphere dameter and crtcal temperature of component. The value of d c can be determned from the crtcal propertes: c 1/ 3 ( RTc / Pc d = ) (A4) or t can be calculated by fttng data on the vapor pressure of speces (Skold-Jørgensen, 1984). For hgh molecular weght compounds (for whch T c and P c are unknown and vapor pressure data s unavalable) the d c value can be determned by fttng expermental data on nfnte dluton actvty coeffcents of alkanes n compound (Bottn et al., 1999). The attractve contrbuton to the Helmholtz energy accounts for dspersve forces between functonal groups, through a densty-dependent, local-composton expresson based on the NRTL model (Renon and Prausntz, 1968): att ( A / RT ) NG K K K k wth: q ~ = θ = (θ NC n NG ν q = k g k q ~ k c z NC NG - n ν q τ NC ( q q ~ ) nν exp( q ~ RTV ) / RTV)/ NG θ l l τ l (A5) (A6) / (A7) τ (A8) = α / g = g g (A9) z beng the coordnaton number (set equal to 10), the number of groups of type n molecule, q the number of surface segments assgned to group, q ~ the total number of surface segments, θ k the surface fracton of group k, g the attractve energy between segments of groups and, and α the non-randomness parameter. The attractve energy g s calculated from the ν energy between lke-group segments trough the followng combnaton rule: 1/ g = k ( g g ) (A10) where the bnary nteracton parameter k s symmetrcal (k = k ). Both, the attractve energy between lke segments and the bnary nteracton parameter are temperature dependent: g ' " ( + g ( T T 1) + g ln( T T ) 1 = g (A11) ' k = k {1 + k ln[t /( T + T )]} (A1) where T s an arbtrary but fxed reference temperature for group ;, and are pure-group energy g k g ' ' k parameters and and are bnary group nteracton parameters. The aton contrbuton to the Helmholtz functon s calculated wth a group contrbuton expresson (Gros et al., 1996) based on Wherthem s theory (1984a,b, 1986a,b) of atng fluds: NGA M ) A ) X = 1 n ln X + M (A13) RT = 1 k= 1 where NGA represents the number of atng groups, n the number of moles of atng group, M the number of atng stes assgned to group and X (k,) the mole fracton of group not bonded at ste k. The number of moles of atng group s: n NC, m m=1 ν m, m g " = ν n (A14) where represents the number of tmes atng group s present n molecule m and nm s the total number of moles of speces m; the summaton ncludes all NC components n the mxture. The mole fracton of group not bonded at ste k s determned from the followng expresson: 1 NGA M (, ) (,,, ) = 1 = 1 l k l X l ) X = 1 + ρ (A15) The value of X (k,) depends on the molar densty of atng group ( ρ = n V ) and the / aton strength (k,,l,) between ste k of group and ste l of group :, l, ), l, ), l, ) [ exp( ε / kt ) 1] = κ (A16) where the aton parameters are the energy (ε) and volume (κ) of aton. In mxtures contanng alcohols and/or water, aton effects can be computed by the same hydrogen-bondng hydroxyl group characterzed by an energy ε/k = 700 K and a volume κ = cm 3 /mol (Gros et al., 1997). Receved: September 16, 001. Accepted for publcaton: February 18, 00. Recommended by Guest Edtors: J. Cerdá, S. Díaz and A. Bandon. 31