Modeling solubility of biological compounds in supercritical fluids

High Pressure Chemical Engineering Ph. Rudolf von Rohr and Ch. Trepp (Editors) 9 1996 Elsevier Science B.V. All rights reserved.

265

Modeling Solubility of Biological Compounds in Supercritical Fluids E. Neau', S. Gamier a, P. Alessib, A. Cortesi b, I. Kikicb Laboratoire de Chimie Physique, Universit6 de Luminy, Aix-Marseille II, France bDept, of Chemical Engineering, Enviromental and Raw Materials, DICAMP, Univ. of Trieste, P.le Europa, 1, 34127 Trieste, Italy

1. ABSTRACT Solubility data of biological compounds taken from literature are considered in this work. Different thermodynamic models based on cubic equations of state and UNIFAC are used in the correlation of experimental data. Interaction parameters are obtained by group contribution approach in order to establish correlations suitable for the prediction of the solid solubility. 2. INTRODUCTION Since to measure solid solubility data is time consuming and the cost of the operation is quite high the existing data should be considered in the framework of optimizing the experimental effort and reducing the overall expenses by applying a suitable thermodynamic model. In this work solubility data of biological compounds taken from literature were considered. Different thermodynamic models based on cubic equations of state (EOS) are used in the correlation of experimental data. The interaction parameters are described on the basis of group contribution (G.C.) approach in order to establish correlations suitable for the prediction of the solubility of compounds of similar molecular structure. 3. SOLUBILITY OF SOLIDS IN SUPERCRITICAL FLUID The solubility of a solid solute (component 2), in a supercritical fluid is calculated, if the solid phase is a pure component, by: ~exp

~

P-

(1)

where at temperature T, psub is the sublimation pressure, v~ is the solid molar volume and ) is the fugacity coefficient in the supercritical phase at pressure P. The fugacity coefficient ~ ~ is calculated by using a thermodynamic model. In this work the SRK (Soave) and Peng Robinson (PR) Equations of State were considered.

266 The EOS energy parameters were determined by using classical mixing rules or UNIFAC method. In any cases, the critical parameters Tc and Pc, and acentric factor m are unknown and should be estimated by G.C. methods. Different approaches are available in literature and have been applied for the calculation of the solubility. 4. INFLUENCE OF CRITICAL PROPERTIES Four G.C. approaches for the evaluation of To, Pc and m have been used for characterizing steroids and non steroidal drugs. In particular, the Ambrose approach [1] was used by calculating the normal boiling point Tb with Constantinou and Gani approach (method 1) and with the Lydersen method modified by Joback [ 1] (method 2); the method 3 is the Lydersen approach modified by Joback; the method 4 is the Constantinou and Gani approach [2, 3]. The results obtained with the different methods using the PR EOS [4] and fitting the parameter k~2 of the classical Van der Waals mixing rules are reported in Table 1. For these calculations the sublimation pressure P ~ and solid volume v'2 were taken from the literature. By comparing the different deviations dY% on the solubility of the solid in the supercritical phase, some remarks can be made: steroidal compound solubilities are generally better correlated by method 1, while method 4 seems more suitable for the other compounds. This can be explained by considering the values of the critical pressures for steroidal compounds. The Constantinou and Gani approach (method 4) is underestimating Pc (for example, for cholesterol: PJbar = 11.9 with method 4, and 17.7 with method 1) with close values of To. This behaviour can be due to the particular structure of steroids which mainly contain naphthenic carbons for which few experimental data of Pc are avalaible in the literature. On the contrary, for the other molecules having many different functional groups (esters, aromatics, heterocycles ...) the more detailed Constantinou and Gain method leads to more realistic critical pressures (for example, for nitrendipine, with similar To, method 4 gives 12.2 bars while method 1 gives 45.1 bars). Methods 2 and 3 give intermediate results. Also the Somayajulu method [ 12] was applied and led to deviations comparable to method 2 and 3. In further calculations we focused on steroidal compounds and only method 1 was used for the estimation of the pure solid properties. 5. THERMODYNAMIC MODEL 5.1. Influence of the equation of state The original Peng Robinson EOS (Table 1) is compared in Table 2 with: - the PR EOS with the volume correction ofPeneloux (PIL~r) [13]; - the Soave-Redlich-Kwong EOS (SRK) [ 14]; - and the PR EOS with a modification of the volume function in the attractive part (PRmod) where the assumption of the one fluid model is not more valid [15]. For all the calculations the parameter k~2 of the classical van der Waals mixing rules was fired. It can be seen from Table 2 that the volume correction does not give a significant improvement; slightly worst results are obtaned with SRK EOS while the PRmod shows a clear improvement at lower temperatures (as in the case of Cholesterol, Progesterone..).

267 Table 1 Choice of critical properties for the calulation of solubility (y) of solids in CO2 using the PR equation (1 - Ambrose with Tb Constantinou Gani: 2 - Ambrose with Tb Lydersen modified by Joback: 3 - Lydersen modified by Joback: 4 - Constantinou and Gani). Compounds

T/K

1

2

3

4

D~/~

D~,4

D~,4

D),%

Authors

Cholesterol

308.15 318.15 328.15

32.48 66.18 66.54

70.17 69.11 59.47

86.10 69.21 63.37

86.10 69.21 63.27

Wong and Johnston (1986), [5]

Cholesterol

328.15 333.15

18.40 33.00

38.19 41.81

83.56 82.81

59.43 58.81

Kosal and al. (1992), [6]

Cholesterol

313.15 323.15 333.15

20.38 18.08 23.28

73.49 73.98 66.70

96.87 90.08 86.27

85.59 87.37 73.73

Yun and al. (1991), [7]

Progesterone

308.15 313.15 318.15 328.15 313.15 333.15 308.15 313.15 318.15 328.15

17.75 18.67 17.03 35.01

84.58 73.96 71.64 80.46 41.40 44.13 68.36 66.88 77.61 45.10

53.80 51.04 43.90 67.09 11.93 13.44 56.92 61.22 70.51 40.34

Kosal and al. (1992), [6]

27.46 19.43 14.26 21.78 32.11 21.72

58.82 52.56 44.63 66.72 12.06 13.79 43.79 49.45 57.49 32.33

Stigmasterol

308.15 323.15 333.15

45.07 50.84 70.31

85.07 80.42 81.25

87.74 84.95 83.80

87.23 80.38 85.81

Wong and Johnston (1986), [5]

Ketoprofene

312.50 331.50

17.18 26.58

21.33 33.63

20.90 28.02

15.13 20.92

Mosca (1995), [9]

Piroxicam

312.50 331.50 313.15 333.15 333.15 350.15 373.15

29.33 25.15 28.11 48.24 53.42 57.37 65.85

13.74 12.04 20.84 39.03 44.07 46.10 51.75

25.34 20.17 10.27 16.73 29.73 40.60 21.18

15.57 14.90 9.52 24.61 12.08 23.24 21.23

Mosca (1995), [9] Schuchardt (1995), [10]

333.15 353.15 373.15

55.01 52.04 61.87

47.39 44.48 47.20

24.73 19.60 24.21

16.24 19.75 20.40

Progesterone Testosterone

Nimesulide Nitrendipine

Nifedipine

Valli (1995), [8] Kosal and al. (1992), [6]

Knez and al. (1995), [11] Knez and al. (1995), [11]

268 Table 2 Fitting of k~2using different EOS (PR with volume correction (PR~r), SRK, PR with modified volume function (PRmod)) and pure prediction using UNIFAC model with scaling factor Compounds Cholesterol

T/K 308.15 318.15 328.15 global

PRr 27.02 64.42 64.21 51.88

RKS 38.93 68.70 69.92 59.18

PRmoa 22.45 71.36 75.76 56.52

UNIFAC 64.26 59.72 65.35 63.11

Authors Wong and Johnston (1986), [5]

Cholesterol

328.15 333.15 global

17.66 31.33 21.76

20.63 35.62 25.12

25.36 35.06 28.13

53.83 66.49 57.64

Kosal and al. (1992), [6]

Cholesterol

313.15 323.15 333.15 global

20.52 16.12 22.26 19.48

21.34 19.44 24.57 21.62

4.28 4.43 11.06 6.33

17.03 18.77 22.97 19.39

Yun and al. (1991), [7]

Progesterone 308.15 313.15 318.15 328.15 global

18.01 16.18 16.13 34.66 21.24

18.61 21.48 18.28 36.84 23.80

9.32 7.17 16.29 27.76 15.14

28.93 23.53 26.86 35.19 28.63

Kosal and al. (1992), [6]

Progesterone 313.15 333.15 global

28.69 19.28 24.41

25.91 22.82 24.51

35.38 40.45 37.68

93.33 88.69 91.22

Valli (1995), [8]

Testosterone

308.15 313.15 318.15 328.15 global

15.22 20.27 30.92 19.89 21.61

13.75 23.64 34.25 24.85 24.13

14.80 17.46 23.52 38.95 23.84

72.54 64.71 64.93 66.66 67.27

Kosal and al. (1992), [6]

Stigmasterol

308.15 323.15 333.15 81obal

40.28 48.59 66.43 51.16

49.46 54.65 74.97 59.16

36.12 46.17 75.63 51.77

>100 >100 >100 >100

Wong and Johnston (1986), [5]

5.2. Influence of mixing rules The UNIFAC model was introduced in the attractive parameters of the EOS using a scaling factor L~2 according to Garduza [ 16] and Gamier [17]; this approach is similar to the method proposed by Wong and Sandier [18]. The calculations performed with the original UNIFAC parameters [ 19, 20, 21] do not give satisfactory results. This probably is due to the use of the reported interaction parameters am between CO2 and the functional groups present in paraffins instead of those characteristic of cyclic paraftins which are present in the steroidal structure. Fitting the solubility data new parameters am and am, setting bmnand Cmnequal to zero, were obtained; these parameters with a single scaling factor L~2 were used for the pure prediction of

269 solubility data presented in Table 2. The deviations are sometimes in the same order as with classical mixing rules fitting one k~2 parameter and, as it was expected, in other cases the prediction is very poor.

5.3. Influence of sublimation pressure As it was pointed out by Chen et al [22] the calculation of solubility data requires a proper estimation of sublimation pressures The data were correlated using the PR EOS with classical mixing rules and the UNIFAC model with previously determined am parameters. Table 3 Influence of sublimation pressure (ps,b) on the calculation of the solubility (for PR and UNIFAC models, k12 and L12 were fitted respectively together with the parameters of the sublimation pressure). Compounds

T/K

Cholesterol

308.15 318.15 328.15 global 328.15 333.15 global 313.15 323.15 333.15 global 308.15 313.15 318.15 328.15 global 313.15 333.15 global 308.15 313.15 318.15 328.15 global 308.15 323.15 333.15 global

Cholesterol

Cholesterol

Progesterone

Progesterone

Testosterone

Stigmasterol

PR P~' 1.10.10 "1~ 9.27.10 "l~ 6.81.10 .o9 7.37.10 .o8 1.44.10 .o7 6.01.10 -l~ 2.12.10 .o9 6.98.10 .o9 6.71.10 11 1.35.10 "1~ 2.67.10 1~ 1.02.10 .o9 6.70.10 .o9 5.36.10 .o8 1.60.10 l~ 3.41.10 l~ 7.12.10 l~ 2.89.10 "1~ 2.18.10 12 2.90.10 l l 1.43.10 "1~

UNIFAC dY% 16.47 46.35 33.49 32.10 13.09 33.42 19.19 5.38 7.33 5.93 6.23 7.91 6.22 14.73 20.84 12.43 10.45 13.79 11.97 14.02 15.53 24.02 22.04 18.99 15.71 13.43 21.15 16.71

PS~ 1.18.10 "1~ 1.09.10 .o9 8.75.10 .o9 4.33.10 .o8 1.56.10 .o7 5.31.10 -l~ 2.09.10 .o9 7.56.10 .o9 7.45.10 11 1.51.10 "1~ 2.98.10 1~ 1.10.10 .o9 6.66.10 .o9 5.32.10 .o8 1.97.10 "1~ 4.19.10 l~ 8.68.10 "l~ 3.49.10 .o9 1.94.10 "12 3.00.10 11 1.63.10 "l~

dY% 16.86 46.34 32.77 31.99 13.23 33.36 19.27 5.25 7.50 7.05 6.57 7.81 6.01 14.59 22.00 12.60 10.36 14.31 12.16 13.95 15.87 25.07 21.49 19.18 15.62 13.76 20.46 16.56

Authors Wong and Johnston (1986),[5]

Kosal and al. (1992),[6] Yun and al. (1991), [7]

Kosal and al. (1992), [6]

Valli (1995),[8] Kosal and al. (1992),[6]

Wong and Johnston (1986),[5]

270 In each cases two parameters for correlating the sublimation pressure were fitted together with the k12 (classical mixing roles) or L12 (UNIFAC scaling factor) parameter. Results of the calculations are reported in Table 3. In both cases there is a clear improvement of the estimation of the solubility when using a proper evaluation of the sublimation pressure. Similar conclusions were drawn by Chen et al [22], but using a higher number of parameters. Furthermore, the order of magnitude of the p~b obtained in both cases is realistic. It must be underlined that the values of the solubility y2 and the sublimation pressure are close even if the two approaches are different. 6. CONCLUSIONS The importance of a suitable G.C. method for evaluating the pure solid properties was evidenced. The limitations of the different G.C. methods are due to the limited experimental data available in the literature for heavy multifunctional compounds. The PR EOS with classical mixing roles gives the same results than the most complex UNIFAC approach. The importance of the sublimation pressure for correlating solubility data was underlined. ACKNOWLEDGEMENT

The authors acknowledge financial support from MURST and CNR. REFERENCES o

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

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