G.M.N. Costa, V.J. Pereira, R.L. Matos, G.L. Santana, A. São Pedro, E.C.M. Cabral-Albuquerque, S.A.B. Vieira de Melo *

Transcription

1 PREDICTION OF SOLID-LIQUID-VAPOR EQUILIBRIUM FOR SUPERCRITICAL PROCESSING OF PHARMACEUTICALS USING A CUBIC EQUATION OF STATE AND GROUP CONTRIBUTION METHODS G.M.N. Costa, V.J. Perera, R.L. Matos, G.L. Santana, A. São Pedro, E.C.M. Cabral-Albuquerque, S.A.B. Vera de Melo * Programa de Engenhara Industral, Escola Poltécnca, Unversdade Federal da Baha Rua Prof. Arstdes Novs, 2, Federação, , Salvador-BA, Brazl * sabvm@ufba.br Tel Fax Abstract In ths work s examned whether t s possble to predct sold-lqud-vapor phase equlbrum of ternary systems used n the SAS processng by the Peng-Robnson equaton of state coupled wth the LCVM mxng rules and the UNIFAC method for excess Gbbs free energy calculaton. The enthalpy of fuson and the meltng pont temperature are estmated by group contrbuton methods. The results show a good agreement between expermental and calculated data and the man concluson s that the PR-LCVM can be used n a totally predctve way. As a consequence, ths EOS can be used to montor the behavor of the antsolvent molar fracton as a functon of the ternary mxture sold-lqud-vapor phase equlbrum. Keywords: Pharmaceutcals, supercrtcal solvents, cubc equaton of state, group contrbuton INTRODUCTION Recently, there s an nterest n producng nanomaterals utlzng alternatve technology. There are several technques for scalng-nanopartcles, however, the nanopartcles produced by supercrtcal technology are more unform n terms of morphology and sze dstrbuton. Another advantage of the producton of nanopartcles usng supercrtcal flud s the elmnaton of mult-stage, snce they may be produced n a sngle step, wthout toxc organc solvent [1]. Nowadays, the utlzaton of supercrtcal flud based technology s consdered as a promsng substtute to the tradtonal methods for pharmaceutcal processng, snce t s an effcent and envronmental-frendly technque. The utlzaton of supercrtcal fluds n the pharmaceutcal feld has been under ntense nvestgaton snce the 1980s [2, ] Supercrtcal antsolvent mcronzaton (SAS) has been wdely studed to produce nanopartcles of pharmaceutcals, bopolymers, explosves, and so on [4]. The morphology of the precptated nanopartcles obtaned by SAS process depends on the operatng pont that s often at pressures much hgher than the mxture crtcal pont of the ternary system solventsolute-supercrtcal antsolvent. Usually t s assumed that the ternary phase dagram formed

2 by ths ternary system behaves lke the bnary system solvent-antsolvent. However, the lterature shows that ths hypothess s not confrmed for all cases [5]. To obtan a successful SAS producton of nanopartcles t s crucal to well understand the ternary phase dagram formed by the system solvent-solute-supercrtcal antsolvent [6]. Understandng of ternary phase equlbra behavor also represents a crucal step for assessng the feasblty to produce sold lpd nanopartcles (SLN) and selectng the correct operatng condtons for PGSS [7]. The nterpretaton of the lpd phase behavor under a compressed gas and after expanson process prevents the overheatng of termolable drugs as well as allows producng partcles on sold form [8, 9]. Consderng that on SLN manufacturng by PGSS a compressed gas s dssolved n molten pure lpd or a mxture of lpds, from a thermodynamc pont of vew, the system can be sutably descrbed by a sold lqud vapor (SLV) phase equlbrum [8]. However, takng nto account the hghly asymmetry among flud, lpds and drug molecules, the thermodynamc modelng of these systems s a challengng task. The man goal of ths work s to nvestgate the possblty to predct sold-lqud-vapor phase equlbrum of ternary systems used n supercrtcal flud partcle processng by the Peng- Robnson equaton of state coupled wth the LCVM mxng rules and the UNIFAC method for excess Gbbs free energy calculaton. MODELING The man thermodynamc problem n SAS process s to fnd for a gven sold solute the approprate combnatons of the organc solvent and the supercrtcal antsolvent. It s not easy to predct a pror whether a certan solvent s mscble wth the supercrtcal antsolvent. To assure a successful precptaton process, t s essental to know the solublty of the sold solute as a functon of the solvent and the antsolvent compostons. In ths way the change of the solvent composton can be fnely tuned to acheve supersaturaton. Consderng that the solvent and the antsolvent do not dssolve n the sold phase, there s only pure crystallne solute n ths phase. As a consequence, the sold-lqud-vapor phase equlbra for the ternary system solute-solvent-supercrtcal antsolvent can be descrbed by the followng equatons: x. ˆ φ = y. ˆ φ (1) L V x. ˆ φ = y. ˆ φ (2) L V x. ˆ φ = y. ˆ φ () L V f = x. ˆ φ. P (4) s L x = 1 x x (5) 1 2 y = 1 y y (6) 1 2

3 where ˆ α s φ s the fugacty coeffcent of the component n the phase α, f s the fugacty of the pure solute, x and y are molar fracton of component n the lqud and vapor phases, respectvely. Subscrpts L, V and S denotes for lqud, vapor and sold phases. Component 1, 2 and are the antsolvent, the solvent and the solute, respectvely. Equatons (5) and (6) may be ncorporated nto Eqs. () and (4) to yeld the followng system of non-lnear equatons. F = x. ˆ φ y. ˆ φ = 0 (7) L V F = x. ˆ φ y. ˆ φ = 0 (8) L V ( ) ˆL φ ( ) F = 1 x x. 1 y y. ˆ φ = 0 (9) V ( ) F = f 1 x x. ˆ φ. P = 0 (10) s L Fxng temperature and pressure, Eqs. (7) to (10) represent a set of four non-lnear equatons wth four unknowns: the molar composton of the flud phases. The followng constrants should also be consdered before solvng ths system of non-lnear equatons: x + (11) 1 x2 1 y + (12) 1 y2 1 x y (1) 1 1 x y (14) 2 2 Solvng ths system of non-lnear equatons usng the tradtonal methods s a hard task. Therefore, an alternatve s to treat ths system as an optmzaton problem whose objectve functon to be mnmzed s the quadratc sum of the F functons gven by Eqs. (7) to (10) subject to the constrants (11) to (14): mn J 4 2 = F (15) = 1 It s mportant to say that constrants (1) and (14) are coupled,.e., they should occur smultaneously but not ndvdually. These constrants should be transformed n the followng nequaltes x y (16) 1 1 1

4 x y (17) where are the penalty values to the soluton. Ths optmzaton problem can be solved by the sequental quadratc programmng (SQP) or the genetc algorthm (GA) methods. SQP s an teratve method for nonlnear optmzaton used on problems for whch the objectve functon s contnuously dfferentable and the constrants are also contnuously dfferentable, subject to lnearzaton of the constrants [10]. GA s an evolutonary algorthm-based method used to optmze a set of equatons by a program s ablty to perform a gven computatonal task [11,12]. In ths work the GA method was adopted. The proposed optmzaton problem s nherently dffcult to be solved due to the exstence of several local mnmum for the objectve functon. Therefore, further smplfcatons should be consdered. It s reasonable to assume that the solute concentraton n the vapor phase s neglgble because the solute vapor pressure s qute low at the system temperature. So, the vapor phase s consdered as a bnary mxture of solvent and supercrtcal antsolvent and the only phase that contans the three components smultaneously s the lqud phase. The fugacty of the pure solute s obtaned by L S ( v ) fus fus. S L H T P v f ( T, P) = f ( T, P).exp 1 fus + R. T T R. T (18) fus fus where H s the fuson enthalpy and T s the meltng pont temperature of the pure S L solute, v and v are the molar volumes of the pure solute n the sold phase and n the lqud phase at temperature and pressure of sold-lqud equlbrum, respectvely. Usually, the S L dfference between v and v s relatvely small and therefore the thrd term of Eq. (18) can be neglected. For the descrpton of lqud and vapor phases, the Peng-Robnson equaton of state [1] has been selected wth mxng rules from LCVM method coupled wth UNIFAC model [14] to calculate the fugacty coeffcent of the three components n the mxture. RT a P = v b v v b b v b ( + ) + ( ) (19) Pure component parameters for Peng-Robnson equaton of state are obtaned by the followng expressons RTc b = 0. (20) Pc

5 α a = b RT (21) 2 2 R Tc a = f ( Tr ) (22) Pc ( ) = 1+ ( 1 ) [ ] f Tr m Tr 2 Tr = T Tc (24) (2) m = (25) w w The fugacty coeffcent of solute n the lqud phase s calculated usng the Peng-Robnson EOS wth two types of mxng rules: the classcal ones, wth two adjustable parameters, and those from LCVM method coupled wth UNIFAC actvty coeffcent model, wth only one adjustable parameter, as follows. Classcal mxng rules a = x x jaj (26) j ( ) a = a a 1 k (27) j j j b = x x j b j (28) j b j b + bj = ( 1 ηj ) (29) 2 LCVM mxng rules ( v b) α ( + ) ( ) v 1 2 b ln RT 2 2 v 1 2 b b Pv P ln ˆ φ = 1 ln (0) b RT b = x b (1) λ λ λ α = + E 1 G 1 + b x ln + xα (2) A A RT A b V M M

6 nα α = γ n = + + A T P n n V A ln + M A ln + 1 M b b,, j λ 1 λ 1 λ b b α () A V and A M are constants related to Vdal and Mchelsen mxng rules, respectvely. For the Peng-Robnson equaton of state, A V = e A M = γ s the actvty coeffcent calculated by the UNIFAC group contrbuton model and λ s the LCVM parameter that weght Vdal and Mchelsen mxng rules contrbuton. In ths work, λ s used n two ways: wthout estmaton (consderng ts orgnal value fxed at 0.6) and ftted to expermental data. RESULTS An sothermal flash calculaton was performed for the ternary mxtures CO 2 -toluenephenanthrene and CO 2 -toluene-naphthalene. Expermental equlbrum data was taken from the lterature [15]. Equlbrum constants were calculated usng PR EOS wth classcal mxng rules (2 adjustable parameters), PR-LCVM for λ=0.6 and PR-LCVM wth λ ftted to expermental data. Parameter estmaton was done usng a genetc algorthm (GA). The performance of the models were compared based on the lqud molar fracton mean absolute devaton ( x%) gven by 100 x% =. x x NEP = NEP exp cal (4) 1 Table 1 shows the values of the nteracton parameters of the Peng-Robnson equaton of state wth the classcal mxng rules (PR-CMR) estmated for the bnary systems whch contans the same components of the ternary systems CO 2 -toluene-phenanthrene and CO 2 -toluenenaphthalene at 25 o C. Table 1: Parameters of the PR-CMR EOS estmated for the bnary systems at 25 o C. Bnary systems k j η j CO 2 -Toluene CO 2 -Phenanthrene CO 2 -Naphthalene Toluene-Phenanthrene Toluene- Naphthalene Table 2 shows the results obtaned for the system CO 2 -toluene-phenanthrene. In ths case PR- CMR EOS presents the best performance. Also t can be seen that there s no sgnfcant dfference between PR-LCVM wth or wthout fttng parameter λ to expermental data. Therefore, PR-LCVM can be used n a totally predctve way by fxng λ equal to 0.6 as orgnally suggested.

7 Table 2: Lqud molar fracton mean absolute devatons ( x%) for the system CO 2 -toluenephenanthrene at 25 o C. x(%) EOS CO 2 Toluene Phenanthrene PR-CMR PR-LCVM (λ=0.6) PR-LCVM (λ=0.55) Table shows the results obtaned for the system CO 2 -toluene- naphthalene. In ths case PR- LCVM EOS wth λ fxed equal to 0.6 gves the best performance. The dfference between PR-LCVM wth or wthout fttng parameter λ to expermental data s consderable and should not be neglected. Ths result confrms the good predctve power of PR-LCVM. Table : Lqud molar fracton mean absolute devatons ( x%) for the system CO 2 -toluenenaphthalene at 25 o C. x(%) EOS CO 2 Toluene Naphthalene PR-CMR PR-LCVM (λ=0.6) PR-LCVM (λ=0.50) Fgures 1 to show the pressure versus lqud molar fracton curves for the system CO 2 - toluene-phenanthrene at 25 o C wth a good agreement between expermental and calculated data for all models. Fgure 1: CO 2 molar fracton n the lqud phase calculated by a three-phase flash algorthm for CO 2 -toluene-phenanthrene system at 25 o C usng the PR-EOS and PR-LCVM. Expermental data were taken from [15].

8 Fgure 2: Toluene molar fracton n the lqud phase calculated by a three-phase flash algorthm for CO 2 -toluene-phenanthrene system at 25 o C usng the PR-EOS and PR-LCVM. Expermental data were taken from [15]. Fgure : Phenanthrene molar fracton n the lqud phase calculated by a three-phase flash algorthm for CO 2 -toluene-phenanthrene system at 25 o C usng the PR-EOS and PR-LCVM. Expermental data were taken from [15].

9 Fgures 4 and 5 show the pressure versus lqud molar fracton curves for the system CO 2 - toluene-naphthalene at 25 o C. There s a good agreement between expermental and calculated data for the EOS nvestgated. Fgure 4: CO 2 molar fracton n the lqud phase calculated by a three-phase flash algorthm for CO 2 -toluene-naphthalene system at 25 o C usng the PR-EOS and PR-LCVM. Expermental data were taken from [15]. Fgure 5: Toluene molar fracton n the lqud phase calculated by a three-phase flash algorthm for CO 2 -toluene-naphthalene system at 25 o C usng the PR-EOS and PR-LCVM. Expermental data were taken from [15].

10 CONCLUSION In ths work the possblty to predct sold-lqud-vapor phase equlbrum of ternary systems used n supercrtcal flud partcle processng by the Peng-Robnson equaton of state coupled wth the LCVM mxng rules and the UNIFAC method for excess Gbbs free energy s nvestgated. The results are very promssory because show that the PR-LCVM EOS can be used n a totally predctve way wth a good agreement between expermental and calculated data. Therefore, t s possble to montor the behavor of the antsolvent molar fracton as a functon of sold-lqud-vapor phase equlbrum of the ternary mxture. Further research s n progress to apply the PR-LCVM EOS to montor the supercrtcal processng of pharmaceutcals wthout the need of ternary sold-lqud-vapor phase equlbrum expermental data. ACKNOWLEDGMENT The authors wsh to thank CNPq (Brazlan Natonal Scence Foundaton) for the fnancal support (grant numbers / and /2010-9). REFERENCES [1] REVERCHON, E., ADAMI, R., CAPUTO, G., DE MARCO, I., J. Supercrt. Fluds, Vol. 47, 2008, p.70. [2] YORK, P., KOMPELLA, V.B. AND SHEKUNOV, B.Y. (Eds.), Supercrtcal flud technology for drug product development. Marcel Dekker, 2004, New York. [] PASQUALI, I. AND BETTINI, R., Int. J. of Pharmaceutcs, Vol. 64, 2008, [4] REVERCHON, E., DE MARCO, I., J. Supercrt. Fluds, Vol. 1, 2004, p.207. [5] VEZZÙ, K., BERTUCCO, A., LUCIEN, F.P., AIChE J., Vol. 54, n. 9, 2008, p [6] VIEIRA DE MELO, R.L.F., NASCIMENTO, I.S.B., COSTA, G.M.N., CABRAL- ALBUQUERQUE. E.C.M., TAVARES-CARDOSO, M.A., VIEIRA DE MELO, S.A.B., Proc. 9 th Conf. Supercrt. Fluds and Ther Applcatons, September 5-8, 2010, Sorrento, Italy. [7] CALDERONE, M., RODIER, E., LETOURNEAU, J., FAGES, J., J. Supercrt. Fluds, Vol. 42, n. 2, 2007, p [8] SAMPAIO DE SOUSA, A.R., CALDERONE, M., RODIER, E., FAGES, J., DUARTE, C.M., J. Supercrt. Fluds, Vol. 9, n. 1, 2006, p. 1. [9] LI, J., RODRIGUES, M., PAIVA, A., MATOS, H.A., GOMES DE AZEVEDO, E., Flud Phase Equlbra, Vol. 241, n. 1-2, 2006, p.196. [10] NOCEDAL, J., WRIGHT, S.J., Numercal Optmzaton, 2006, Sprnger. [11] BANZHAF, W., NORDIN, P., KELLER, R.E., AND FRANCONE, F.D., Genetc Programmng: An Introducton: On the Automatc Evoluton of Computer Programs and Its Applcatons, 1998, Kaufmann. [12] CHARBONNEAU, P., AND KNAPP, B., A User's gude to PIKAIA 1.0, NCAR Techncal Note 418+IA,1995. [1] PENG, D.Y., ROBINSON, D.B., Ind. Eng. Chem. Fundam., Vol. 15, 1976, p. 59. [14] BOUKOUVALAS, C., SPILIOTS, N., COUTSIKOS, N., TASSIOS, D., Flud Phase Equlbra, Vol. 92, 1994, p. 75. [15] DIXON, D.J., JOHNSTON, K.P., AIChE J., Vol. 7, 1991, 1440.