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## Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide

#### Loubna Nasri [1] , Salima Bensaad [2] , Zouhir Bensetiti [3]

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In this work, we propose to correlate and predict the solubility in supercritical CO2 of disubstituted aromatic isomers of hydroxybenzoic acid and methylbenzoic acid with a new methodology based on the expanded liquid theory, in which the solid–fluid equilibrium is modeled using the local composition model of UNIQUAC in which the interaction parameters are related to the solvent reduced density with an empiric exponential form equations. The experimental solubility of hydroxybenzoic acid isomers, methylbenzoic acid isomers and mixed isomers (m-hydroxybenzoic acid+p-hydroxybenzoic acid) are used for evaluating the correlation and prediction capabilities of this new methodology. The results obtained using the proposed model show good agreement with the experimental data used.
supercritical fluid extraction, aromatic isomers, solubility modelling, UNIQUAC
• m-hydroxybenzoic acid 40 36500 , p-hydroxybenzoic acid 41 30990 ,[15] o-hydroxybenzoic acid 40 19585 ,, , [16] m-methylbenzoic acid 39 15730 p-methylbenzoic acid 48 22720 o-methylbenzoic acid 39 20170 In other hand, Eq. (12) is used to calculate the residual part of the solid solute activity coefficient. Thermodynamic properties of the solid solute listed in Table 1 are used together with Eqs. (7), (8), and (12) to estimate the solubility y 2 using Eq. (6). The interaction parameters and are then regressed according to Eqs. (13a) and (13b) using the solver tool in Excel [10]. The best regression is based on minimizing the error between the regressed and experimental solubility data. The definition of the error is based on the work of Valderama et al. [11] and the objective function that minimizes the sum of average absolute relative deviation (AARD) is 2(exp) 2( ) 1 2(exp) 100
• AARD(%) cal np y y np y    (14) where np is the experimental number of points, and y 2(exp) and y 2(cal) are the solubility of isomer obtained from experimental data and calculated by thermodynamic model, respectively. Table Solvent Physical Properties. Solvent T c (K) P c (bar)  c (mol/cm 3 ) x100 r 1 q 1 Ref. CO 2 302 73.83 1 .063 296 1.261 [9],[18] Correlation Results The interaction parameters and are regressed through the optimization of the adjustable parameters , , and . These fitting parameters are evaluated by minimizing the objective function given in Eq. (14). The analysis of the model results is done through statistical calculations. Tables 3 and 4 provide the quantitative results of the regression for the proposed model. The AARD is listed for each isomer and for each temperature together with the adjustable parameters values and the overall absolute deviations. Results and Discussions Each isomer parameters are obtained by fitting its own and whole solubility data. The overall deviations values obtained are generally low and so indicate a good correlation capability of the model. From Table 3 and Figure 2 we can see clearly that for the hydroxybenzoic acid isomers, the greatest values of AARD are noted at high temperatures especially for T=373K. These can be probably attributed to the melting point depression occurring in some high-pressure-mixtures [19, 20]. Table 3. Regression Results for Hydroxybenzoic Acid Isomers. Comp. np T(K)  12  12  21  21 AARD (%)  m16 318 328 373 overall 24 -0.292 6497.8 -14.5 91 23 1 32 o84 308 313 318 328 373 overall 83 -0.288 35 -2 60 48 04 74 95 37 p16 318 328 373 overall 57 -0.292 6100.3 -14.9 28 35 40 84
• Under the influence of high-pressure carbon dioxide, organic solids may undergo melting point depression [21] which lead to the exhibition of fluid-liquid equilibria and so affect the measured solubility data. Lucien & Foster [15] have mentioned that with their experimental technique for measuring, in all of the systems investigated (pure and mixed) no melting point depression was observed. However, Krukonis & Kurnik [2] have reported measured solubilities of the hydroxybenzoic acid isomers at very high conditions (T=373K and P  207 bar) without indication to the melting point depression phenomenon. Table 4. Regression Results for Methylbenzoic Acid Isomers. Comp. np T(K)  12  12  21  21 AARD (%) m- 18 313 323 333 overall Figure 1. Comparison of the (AARD) for the methylbenzoic acid isomers. In this part, we attempt to predict the solubilities of mixed hydroxybenzoic acid isomers in supercritical carbon dioxide. Experimental solubility data provided by Lucien & AARD 0.1 0.2 0.3 0.4 0.5 AARD T=318 K T=328 K T=373 K 0.E+00 E-06 E-06 E-06 E-06 E-06 E-06 0.E+00 E-06 E-06 E-06 E-06 E-06 y pred y exp ones and confirm predictive ability of the proposed model. Figure 4. Comparison of predicted with experimental solubility of p-hydroxybenzoic acid at T=318K and T=328K. Conclusions In this work, we have proposed the correlation and prediction of the solubility in supercritical CO 2 of disubstituted aromatic isomers of hydroxybenzoic acid and methylbenzoic acid with a new methodology based on the expanded liquid theory, in which the solid–fluid equilibrium is modeled using the local composition model of UNIQUAC. The results obtained using the proposed model show good agreement with the experimental data of isomers used. Moreover predictive capabilities of the proposed model for solid solubility were well demonstrated for mixed isomers-solvent systems. References G. Madras, C. Kulkarni, J. Modak, Modeling the solubilities of fatty acids in supercritical carbon dioxide, Fluid Phase Equilibria, 209, 207-213, 2003.
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Birincil Dil en Regular Original Research Article Yazar: Loubna Nasri Yazar: Salima Bensaad Yazar: Zouhir Bensetiti
 Bibtex @ { ijot77021, journal = {International Journal of Thermodynamics}, issn = {1301-9724}, eissn = {2146-1511}, address = {Yaşar DEMİREL}, year = {2014}, volume = {17}, pages = {81 - 85}, doi = {}, title = {Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide}, key = {cite}, author = {Nasri, Loubna and Bensaad, Salima and Bensetiti, Zouhir} } APA Nasri, L , Bensaad, S , Bensetiti, Z . (2014). Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide. International Journal of Thermodynamics, 17 (2), 81-85. Retrieved from http://dergipark.gov.tr/ijot/issue/5792/77021 MLA Nasri, L , Bensaad, S , Bensetiti, Z . "Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide". International Journal of Thermodynamics 17 (2014): 81-85 Chicago Nasri, L , Bensaad, S , Bensetiti, Z . "Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide". International Journal of Thermodynamics 17 (2014): 81-85 RIS TY - JOUR T1 - Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide AU - Loubna Nasri , Salima Bensaad , Zouhir Bensetiti Y1 - 2014 PY - 2014 N1 - DO - T2 - International Journal of Thermodynamics JF - Journal JO - JOR SP - 81 EP - 85 VL - 17 IS - 2 SN - 1301-9724-2146-1511 M3 - UR - Y2 - 2019 ER - EndNote %0 International Journal of Thermodynamics Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide %A Loubna Nasri , Salima Bensaad , Zouhir Bensetiti %T Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide %D 2014 %J International Journal of Thermodynamics %P 1301-9724-2146-1511 %V 17 %N 2 %R %U ISNAD Nasri, Loubna , Bensaad, Salima , Bensetiti, Zouhir . "Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide". International Journal of Thermodynamics 17 / 2 (Mart 2014): 81-85.