Using statistical thermodynamics such as Simplified SAFT equation of state (SSAFTEoS) for estimating phase equilibrium and fluid properties of different materials have been used widely. SSAFT EoS has been developed for associative and non-associative compounds. At high pressure inter molecular forces are very important, on the other hand, in spite of the fact that SSAFT EoS has strength theoretical foundation, it can predict the behavior of high pressure systems. In this research, four solid solubility of benzoic acid, naphthalene, pyrene and Phenanthrene in supercritical carbon dioxide have been studied, SSAFT EoS has been used for modeling. At the end the results have been compared with experimental data. The highest and the absolute average deviation error (AAPD), for carbon dioxide - Phenanthrene and benzoic acid - carbon dioxide systems have been reported 2.22 and 4.43 respectively.Keywords: SSAFT EoS; Supercritical carbon dioxide; Solid compounds; Solubility

Ali, F. Mohebbi

Fatemeh, B. Fijani

Ghanavatiyan, D. Halimeh

Hamidreza, A. Bagheri

Mahdi, E. Yahyanejad

Nooshin, C. Vafa

English

AJOL - African Journals Online

Journal of Fundamental and Applied Sciences is licensed under a Creative Commons Attribution-NonCommercial 4.0International License. Libraries Resource Directory. We are listed under Research Associations category.APPLICATIONS OF SSAFT EOS FOR DETERMINATION OF THE SOLUBILITIESOF SOLID COMPOUNDS IN SUPERCRITICAL CO2A. Bagheri Hamidreza1,2,*, B. Fijani Fatemeh3, C. Vafa Nooshin3, D. Halimeh Ghanavatiyan3,E. Yahyanejad Mahdi4 and F. Mohebbi Ali1,1 Department of Chemical Engineering, Faculty of Engineering, Shahid Bahonar University ofKerman, Kerman, Iran2Young Researchers Society, Shahid Bahonar University of Kerman, Kerman, Iran.3 Department of Chemical Engineering, Yasouj University, Yasouj, Iran4 Department of Chemical Engineering, Payame Noor University of Kerman, Kerman, Iran.Published online: 18 June 2016ABSTRACTUsing statistical thermodynamics such as Simplified SAFT equation of state (SSAFTEoS) forestimating phase equilibrium and fluid properties of different materials have been used widely.SSAFT EoS has been developed for associative and non-associative compounds. At highpressure inter molecular forces are very important, on the other hand, in spite of the fact thatSSAFT EoS has strength theoretical foundation, it can predict the behavior of high pressuresystems. In this research, four solid solubility of benzoic acid, naphthalene, pyrene andPhenanthrene in supercritical carbon dioxide have been studied, SSAFT EoS has been usedfor modeling. At the end the results have been compared with experimental data. The highestand the absolute average deviation error (AAPD), for carbon dioxide - Phenanthrene andbenzoic acid - carbon dioxide systems have been reported 2.22 and 4.43 respectively.Keywords: SSAFT EoS; Supercritical carbon dioxide; Solid compounds; Solubility.Author Correspondence, e-mail: hamidbagheri101@gmail.comdoi: http://dx.doi.org/10.4314/jfas.v8i2s.140Journal of Fundamental and Applied SciencesISSN 1112-9867Available online at http://www.jfas.infoResearch ArticleA. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 8721. INTRODUCTIONToday, a growing desire to develop alternative technologies to reduce the adverse effects onthe environment has emerged. These include measures to reduce energy consumption, reducethe level of toxic waste, the better use of by-products, and improved quality and safety of endproducts. High-pressure technologies create processes that produce new products withspecific characteristics. Supercritical fluids are substances which temperature and pressure areabove the critical temperature and pressure. This was discovered in 1822 by Cagniard andcolleagues during a liquid heating test [1]. The transport properties of supercritical fluids arethe same as gases (i.e. high permeability and low viscosity) and their solubility resemble thoseof liquid solvents. Due to these properties, supercritical fluids are used in a wide range ofpurification, extraction and separation processes [2]. Processes involving supercritical fluidsare sustainable, eco-friendly, cost-effective and provide numerous possibilities to produce newproducts. The major advantage of supercritical fluids is the possibility of the drying ofproducts and their separation with a simple expansion; moreover the recovered gas can bereused without the need for purification. Environmental benefits of using supercritical fluidsin industrial processes are less energy consumption during the process and they canpotentially be used as alternatives for environmentally destructive organic solvents. Thereforesupercritical fluids are called green solvents [3]. Their most important advantages can be seenin the use of supercritical fluids such as carbon dioxide and water. These fluids arenon-carcinogenic, non-toxic, non-inflammable and also thermodynamically stable. Anotheradvantage of supercritical fluids is that the physical properties such as permeability, viscosity,density or dielectric constant can be set easily by changing pressure or operating temperature[4]. By choosing a suitable solvent, operating costs reduced and purity of the productsincreased. Solvent should be Inexpensive and non-toxic and should have a high solubility.Based on the experiences gained in design of a supercritical process, carbon dioxide is usuallythe first choice. Carbon dioxide is inexpensive, widely available, non-toxic, non-flammable;inert chemically suitable for use in food and pharmaceutical processes and has good criticalsituations (31.3 ℃ and 72.9 atm) is [5]. Given the characteristics of supercritical fluids andincreasing use of them, modeling and simulating these types of systems is of particularA. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 873importance. Also, due to high pressure and importance of intermolecular forces at highpressures, finding equation that can predict the behavior of these systems as well, has greatimportance [6]. Among the work done in the field of extraction using supercritical fluids,different modes of equations is used in a number of semi-empirical equations. Due to the highpressure, semi-empirical equations can not predict the solubility of solids as well.The cubic equations of state have been used by many researchers because of their simplicity,but these equations face problems at high pressures. Recently, several equations of state havebeen proposed based on the statistical thermodynamics, since they play a significant role inmodeling and simulation of thermodynamic systems. The so-called Simplified statisticalassociating fluid theory (SSAFT EoS), present a state of the molecule which is close to thereal one [7]. Benzoic acid and carbon dioxide supercritical systems by assuming idealbehavior for supercritical phase have been modeled by Kurnik and colleagues in the early 90swith low accuracy results. They also modeled this system with PR EoS. The results werereported by binary negative interaction parameter. Coimbra and colleagues used SRK EoS forpredicting solubility of solids in supercritical carbon dioxide [8]. Yang and Zhong examinedlittle aromatic solubility in supercritical fluid carbon dioxide by two SSAFT and PR EoS.They mentioned that SSAFT EoS matches with experimental results better than PR EoS [9].Vaferi and colleagues investigated some aromatic solubility in supercritical fluid carbondioxide by SSAFT EoS and neural network [10]. Bagheri and Shariati investigated solubilityof benzoic acid in supercritical carbon dioxide using the PR and PC-SAFT EoS. The results ofPC-SAFT EoS had good adjustment with the experimental data. kij value for the PR andPC-SAFT EoS was reported negative and positive respectively. In this study, the solubility ofdifferent solids in supercritical carbon dioxide has been studied. This was done by SSAFTEoS and the results of modeling have been compared with experimental data. Benzoic aciddue to the hydrogen bonds needs to have associative, so each of the five parameters of SSAFTEoS has been used.2. Thermodynamic modelingSemi-empirical equation was developed in the late 80th century that was considered a lot byA. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 874academic and industrial communities. This equation has been named Statistical associationfluid theory by Chapman and colleagues at Cornell University and was presented on the basisof thermodynamic perturbation of Wertheim. Wertheim derived his theory by expanding theHelmholtz energy in a series of integrals of molecular distribution functions and theassociation potential. On the basis of physical arguments, Wertheim showed that manyintegrals in this series must be zero and, hence, a simplified expression for the Helmholtzenergy can be obtained. The key result of Wertheim's theory is a relationship between theresidual Helmholtz energy due to association and the monomer density. In general, SSAFTEoS is not unchangeable equation that only is written in one form but also a way to evaluatethe effect of the accumulation of different molecules. The parameters of this equation wereobtained to calculate a wide range of fluids including organic matter, light gases, water andpolymers. Many efforts in the past decade were done to improve and develop the EoS forincreasing its accuracy for different systems [1]. In reviewing the statistical thermodynamicsand Grand Canonical sets that all thermodynamic properties can be calculated by use of theHelmholtz energy.The SSAFT EoS is based on the fact that the Helmholtz energy could be introduced as a set ofindividual statements in which not only the effects of short range repulsive forces and longrange gravity forces have been considered but also two chemical bond and intermolecularassociations were added. The general form of the equation will be [7]:res ideal hs disp chain assocA A A A A A ANKT NKT NKT NKT NKT NKT NKT      (1)Where k is Boltzmann's constant and N is the number of molecules. In Eq.(1), first sentence iscontributions of Helmholtz free energy due to the short-range repulsion. At this stagemolecules are considered as hard spheres that repel each other and there is no gravitationalforce between them. The second term of Eq.(1) is contributions of Helmholtz free energy dueto long-range attractive forces. These forces are mostly achieved by quantum effects andmulti-polar energy. The third term of Eq.(1) is share of the Helmholtz free energy throughchemical bonding between atoms and formed links dimmer and the trimmer express or higher.A. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 875Finally, the fourth term of Eq.(1) is contribution of Helmholtz free energy due to mutualeffects of remained electrons of valence layer. In this model it is assumed that a molecule ismade of m pieces of the same size and with diameter  which is called segment. During thefour steps listed energy added to it and a real molecule can be achieved. Fig. 1 shows the trend[7].Fig.1. Procedure to form a molecule in the SSAFT model [7].In general, SSAFT EoS, has five parameters m, , (u / k), ( / k),K  . These parameters areobtained for pure substances and by a series of equations that are similar to mixing rules, areextended to the mixture. Among these five parameters, two parameters ε / k and K was usedonly for material with association and appears in the equation whenever one of the materialshas association property.In this study, the SSAFT parameters have been used for different materials which are obtainedby Huang and Radosz (Table 1). Considering that only benzoic acid has accumulation(hydrogen bonding), the ε/k and k parameters for this material is used.A. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 876Table1. Pure component parameters of SSAFT EoS [7]MComponent--216.0813.5781.417Carbon Dioxide--304.813.7044.671Naphthalene--369.38018.2125.615Pyrene--352.016.5185.327Phenanthrene0.0031495930272.66012.04.608Benzoic acidIn equilibrium of a pure solid (part 1) with a supercritical fluid and, assuming no solubility ofsupercritical fluids in solid phase following term can be recited [1].solid satsat sat 1 11 1 1 1v (P P )ˆy P P exp( )RT  (2)In which is the saturation or sublimation pressure at the system temperature and iscalculated due to Antoine equation. is the molar volume of the solid, R is the universalgas constant, and is the Fugacity coefficient of component 1 in a supercritical phase thatis calculated to help SSAFT EoS (Eq.(3)) [7].resv iiˆln ln ZKT   (3)j k j kres hc disp hc disp hc dispNseg chainiT,v,y j T,v,yj 1k kA A A A A A(Z Z ) ( ) [y ( ( ) )]KT NKT NKT y NKT NKT y NKT NKT          (4)seg chain assocZ 1 Z Z Z    (5)2chain 2.5Z (1 m)(1 )(1 2.5 )    (6)2seg i jij3i j4 2 uZ m[ jD ( ) ( )(1 ) KT      (7)A. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 877iiiAassocAA1 XZ [ 0.5]X  (8)The most important parameter in Eq. (8), is "XA". Before calculating Zassoc, all the non-zerosite-site interactions should be defined. In order to select a proper expression for XA fromTable VII, one has to assign association sites and non-zero sitesite interactions [7].3. RESULTS AND DISCUSSIONPhase equilibrium calculations has been conducted based on the Eq. (2) and using MATLABsoftware and solubility of solids in supercritical fluid was investigated. The results ofmodeling have been compared with existing experimental data. The binary interaction (kij)parameters were obtained using a genetic algorithm. Results are given in the Figs. 2-5. At lowpressures, the solubility of solids in supercritical fluids is low and as the pressure increases,the solubility also increases due to the increase in the enhancement factor and density ofsupercritical CO2. According to Eq. (2) solubility increases as the pressure increase. Reason ofincrease of solubility with pressure increasing can be that as the solvent situated in thesupercritical region because of the changes that is occured in it’s physical properties, thesolvent density increases.However, due to the saturation of the supercritical region, the solubility will not increase byincreasing the pressure continuously. Solubility decreases with decreasing pressure. The causeof this decline can be considered as approaching of carbon dioxide to the transition zone andchanging to liquid phase. This accuracy can be seen in Figs. 2-5. According to the results ofmodeling, SSAFT EoS at high pressures due to strong molecular basis is well able to predictthe experimental data. The Table 2. shows the Absolute Average deviation (AAPD) for thefour systems.(9)A. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 878Fig.2. Solubility of benzoic acid in supercritical CO20.010.0120.0140.0160.018105 135 165 195 225Mole fraction of NaphthalenePressure (bar)Experimental data @ T=308.15 [12]SSAFT EoS, kij= 0.012Fig.3. Solubility of naphthalene in supercritical CO2Fig.4. Solubility of pyrene in supercritical CO2A. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 879Fig.5. Solubility of phenanthrene in supercritical CO2Table 2. Absolute Average deviation estimated amount of supercritical CO2 -solid systemsRef.AAPDPressure range(bar)Temperaturerange (K)Number ofexperimentaldataSystem[11]5.2680-400298.15-333.1516Benzoic acid - CO2[12]4.02105-220300.15-348.1520Naphthalene - CO2[13]2.48100-180298.15-353.1512Pyrene - CO2[14]1.7595-310298.15-343.1510Phenanthrene- CO2-3.38--58-4. CONCLUSIONIn this study, the solubility of solids in supercritical carbon dioxide in the form of four binarysystem was studied. Due to the high operating pressure, system modeling was done with thehelp of SSAFT EoS statistics. The simulation results showed that the SSAFT EoS with strongsubstantial and theory has better compliance with the experimental data. The amounts of1binary interaction parameter (kij) were obtained for all systems. According to the researceswere done by other researchers, Existing potential in extraction of solid materials with use ofsupercritical fluids and also for developing behavior of solid-supercritical systems, modelingof extraction systems by use of supercritical fluids can be investigated which needs the help ofsolvents for increasing the efficiency of the extraction. According to a strong basis ofstatistical equations theory, other equations of SAFT family can be used.A. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 8806. REFERENCES[1] Bagheri, H. and Shariati, A. Prediction of the Solubility of Benzoic Acid in SupercriticalCO2 Using the PC-SAFT EoS. International Journal of Chemical, Materials Science andEngineering, 2014, 8(1), 72-74.[2] Saito, M. History of supercritical fluid chromatography: Instrumental development.Journal of Bioengineering, 2013, 115(6), 590-599.[3] Cha´fer, A. Fornari, T. Stateva, Roumiana P. and Berna, Angel. D-Pinitol Solubility inSupercritical CO2: Experimental Data and Correlation. Journal of Chemical Engineering Data,2006, 51, 612-615.[4] Alwi, R. and Tamura, K. Measurement and Correlation of Derivatized AnthraquinoneSolubility in Supercritical Carbon Dioxide. Journal of Chemical   Engineering Data, 2015,60, 3046−3052.[5] Ravipaty, S. Koebke, Karl and Chesney, David. Polar Mixed-Solid Solute Systems inSupercritical Carbon Dioxide: Entrainer Effect and Its Influence on Solubility andSelectivity. Journal of Chemical Engineering Data, 2008, 53, 415-421.[6] Pai, S. and Bae, Y. Solubility of solids in supercritical fluid using the hard-body Expandedvirial equation of state. Journal of Fluid Phase Equilibria, 2014, 362, 11-18.[7] Huang, S. and Radosz, M. Equation of State for Small, Large, Polydisperse, andAssociating Molecules. Journal of Industrial & Engineering Chemistry Research, 1990,29(11), 2284-2294.[8] Coimbra, R. Silva, M. and Blanco, F. Experimental Determination and Correlation ofArtemisinin’s Solubility in Supercritical Carbon Dioxide. Journal of Chemical EngineeringData, 2006, 51, 1097-1104.[9] Yang, H. and Zhong, C. Modeling of the solubility of aromatic compounds in supercriticalcarbon dioxide–cosolvent systems using SAFT equation of state. Journal of SupercriticalFluids, 2001, 33, 99-106.[10] Vaferi, B. Karimi, M. Azizi, M. and Esmaeili, H. Comparison between the artificialneural network, SAFT and PRSV approach in obtaining the solubility of solid aromaticcompounds in supercritical carbon dioxide. Journal of Supercritical Fluids, 2013, 77, 44-51.A. Bagheri Hamidreza et al. J Fundam Appl Sci. 2016, 8(2S), 871-881 881[11] Yang, S., Zeng, J., Wang G. Modeling of supercritical fluid extraction using dynamicgenetic Algorithm Based optimization. Journal of Supercritical Fluids, 2005, 28(12), 12,48-57.[12] Sako, S., Ohgaki, K., Katayama, T. Solubilities of Naphthalene and Indole insupercritical fluid. Journal of Supercritical Fluids, 1988, 1, 1-6.[13] Anitescu, G., Tavlarides, L. Solubilites of solids in supercritical fluids. I. New quasistaticexperimaental method for polycycilic aromatic hydrocarbons (PAHs) +pure fluids. Journal ofSupercritical Fluids, 1997, 10, 175-189.[14] Sane, A., Taylor, S., Sun, Y., Thies, M. A semicontinous flow apparatus for measuring thesolubility of opaque solids in supercritical solutions. Journal of Supercritical Fluids, 2004, 28,213.How to cite this article:Bagheri Hamidreza A, Fijani Fatemeh B, Vafa Nooshin, Halimeh Ghanavatiyan D,Yahyanejad Mahdi E, Mohebbi Ali F. Applications of ssaft eos for determination of thesolubilities of solid compounds in supercritical CO2. J. Fundam. Appl. Sci., 2016, 8(2S),871-881.

Applications of SSAFT EOS for determination of the solubilities of solid compounds in supercritical CO2.

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Applications of SSAFT EOS for determination of the solubilities of solid compounds in supercritical CO2.

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