Prediction of Gas Solubilities

If no experimental data are available gas solubilities can be predicted today with the help of group contribution equations of state, such as Predictive Soave-Redlich-Kwong (PSRK) [43] or VTPR [44]. These models are introduced in Sections 5.9.4 and 5.9.5. 

According to the regular solution theory, the corresponding activity coefficient at infinite dilution can be expressed as 

For supercritical gases no liquid phase and thus no values for vi and Ahvi exist. In Table 5.15 hypothetical values for the molar liquid volume and the solubility parameter for some well-known light gases at = 25 C are listed. As nothing better is available, these values are also applied at other temperatures as well. The Henry constant can finally be calculated using Eq. (5.56), where instead of the vapor pressure the fugacity of the hypothetical liquid is used. 

Estimate the Henry constant of methane (1) in benzene (2) at = 60 C using the method of Prausnitz and Shair. 

For benzene, the solubility parameter can be determined using the following information  

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P. Thorlaksen, J. Abildskov, and G.M. Kontogeorgis, Prediction of gas solubilities in elastomeric polymers for the design of thermopane windows, Fluid Phase Equilib., 211(1) 17—33, August 2003. 

Prediction of gas solubility in binary polymer + solvent mixtures... 

Apostolou, D, A., Kalospiros, N. S and Tassios, D. P., 1995. Prediction of gas solubilities using the LCVM equation of state/excess Gibbs free energy model. Ind. Eng. Chem. Res., 34 948-957. 

Dahl, S., Fredenslund, A., and Rasmussen, R, 1991. The MHV2 model A UNlFAC-based equation of state model for prediction of gas solubility and vapor-liquid equilibria at low and high pressures. Ind. Eng. Chem. Res., 30 1936-1945. 

Shulgin, I. L. and E. Ruckenstein. 2003. Prediction of gas solubility in binary polymer plus solvent mixtures. Polymer. 44, 901. 

Maassen, S., Arlt, W., and Klamt, A. (1995) Prediction of gas solubilities and partition coefficients on the basis of molecular orbital calculations (COSMO) with regard to the influence of solvents. Chem. Ing. Tech., 67 (4), 476-479. 

Kiepe J, Horstmann S, Fischer K, Gmehling J (2004) Experimental determination and prediction of gas solubility data for methane plus water solutions containing different monovalent electrolytes. Ind Eng Chem Res 43 3216-3216 (42 5392, 2004)... 

Kiepe, J., Horstmann, S., Fischer, K., Gmehling, J. (2002). Experimental determination and prediction of gas solubility data for CO2 -I- H2O mixtures containing NaCl or KCl at temperatures between 313 and 393 K and pressures up to 10 MPa. Industrial Engineering Chemistry Research, 41, 4393 398. 

The solubility of a gas is an integral part for the prediction of the permeation properties. Various models for the prediction of the solubility of gases in elastomeric polymers have been evaluated (57). Only a few models have been found to be suitable for predictive calculations. For this reason, a new model has been developed. This model is based on the entropic free volume activity coefficient model in combination with Hildebrand solubility parameters, which is commonly used for the theory of regular solutions. It has been demonstrated that mostly good results are obtained. An exception... 

The solubility of a gas in a mixture of solvents is a problem of interest in many industrial applications. One example is the removal of acidic compounds from industrial and natural gases. The solubility of a gas in a binary mixture containing water has particular importance because it is connected with the solubility of gases in blood, seawater, rainwater, and many other aqueous solutions of biological and environmental significance. Therefore, it is important to be able to predict the gas solubility in a mixture in terms of the solvent composition and the solubilities in the individual constituents of the solvent or in one pure component and a selected composition of the mixed solvent. 

The aim of the present paper is to develop a theoretical approach for the description of the gas solubility in a solvent containing a salt. To achieve this goal, the Kirkwood—Buff formalism for ternary mixtures will be used. Recently, such a formalism has been used to predict the gas solubility in mixed solvents (mixture of two nonelectrol5rtes) in terms of the solubilities in the individual solvents. A similar approach will be employed here. 

In a previous paper [9] we developed an equation which could predict the gas solubility in a mixed solvent from the solubilities in the individual constituents and the properties of their mixture. This equation was applied to mixed solvents composed of small molecules. In the present paper, we will apply it to the solubility of a gas in a polymer + water mixture. 

Eq. (2) does not contain any adjustable parameter and can be used to predict the gas solubility in mixed solvents in terms of the solubilities in the individual solvents (1 and 3) and their molar volumes. Eq. (2) provided a very good agreement [9] with the experimental gas solubilities in binary aqueous solutions of nonelectrolytes a somewhat modified form correlated well the gas solubilities in aqueous salt solutions [17]. The authors also derived the following rigorous expression for the Henry constant in a binary solvent mixture [9] (Appendix A for the details of the derivation) ... 

The present paper is concerned with mixtures composed of a highly nonideal solute and a multicomponent ideal solvent. A model-free methodology, based on the Kirkwood—Buff (KB) theory of solutions, was employed. The quaternary mixture was considered as an example, and the full set of expressions for the derivatives of the chemical potentials with respect to the number of particles, the partial molar volumes, and the isothermal compressibility were derived on the basis of the KB theory of solutions. Further, the expressions for the derivatives of the activity coefficients were applied to quaternary mixtures composed of a solute and an ideal ternary solvent. It was shown that the activity coefBcient of a solute at infinite dilution in an ideal ternary solvent can be predicted in terms of the activity coefBcients of the solute at infinite dilution in subsystems (solute + the individual three solvents, or solute + two binaries among the solvent species). The methodology could be extended to a system formed of a solute + a multicomponent ideal mixed solvent. The obtained equations were used to predict the gas solubilities and the solubilities of crystalline nonelectrolytes in multicomponent ideal mixed solvents. Good agreement between the predicted and experimental solubilities was obtained. 

Li, j. D., Vanderbeken, L, Ye, S. Y., Carrier, H. Xans, P. 1997. Prediction of the solubility and gas-liquid equilibria for gas-water and light hydrocarbon-water systems at high temperatures and pressures with a group contribution equation of state. Fluid Phase Equilibria, 131(1/2), 107-118. 

In closing, we would like to mention some applications of the GEMC/CBMC approach and very much related combination of CBMC and the grand canonical Monte Carlo technique to other complex systems prediction of structure and transfer free energies into dry and water-saturated 1-octanol [72], prediction of the solubility of polymers in supercritical carbon dioxide [73], prediction of the upper critical solution pressure for gas-expanded liquids [74], investigation of the formation of multiple hydrates for a pharmaceutical compound [75], exploration of multicomponent vapor-to-particle nucleation pathways [76], and investigations of the adsorption of articulated molecules in zeolites and metal organic frameworks [77, 78]. 

CO2 is an important substance which is present in many processes in the chemical industry. In the following, a case study on the prediction of the Henry s law constant for CO2 in ethanol and the vapor-hquid equilibrium of the binary mixture CO2 + C2H6 is discussed. The aim is to explore the capabilities of force fields to predict the temperature dependence of gas solubility and to predict azeotropic behavior. 

With respect to our previous work, the model is extended to the case of multicomponent mixtures and a procedure is described for the prediction of gas mixture solubility in glassy polymers based only on pure component equilibrium properties and on the knowledge of the pure polymer density in the glassy state. The reliability of the model is then tested by comparing model predictions with experimental data for the solubility of CO2/C2H4 mixtures in PMMA (4). 

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