Tuning the Interaction Parameter for the Soave-Redlich-Kwong Equation of State Using the Critical End Points

In the petroleum industry, to solve problems such as the design of the catalytic cracking of heavy oil, correct knowledge of the phase behavior is essential. As a benchmark where the number of degrees of freedom for binary mixtures is zero, the critical end points can represent the type of phase behavior of the binary mixtures according to van Konynenburg and Scott's classification scheme (van Konynenburg, P. H.; Scott, R. L. Philos. Trans. R. Soc. London A 1980, 298, 495-540). Calculating the phase behavior of binary mixtures using interaction parameters evaluated by other methods can cause wrong determinations of the type of phase behavior. The critical end points were employed to fit the interaction parameters for binary mixtures in the critical state at high pressure. The molar Gibbs energy of mixing was evaluated to locate the ranges of values for the interaction parameters where exploration for the critical end point would not fail. The phase behavior at the critical end point is rather complex. Based on the Soave-Redlich-Kwong equation of state, the method developed by Heidemann and Khalil for calculating critical properties (Heidemann, R. A.; Khalil, A. M. AlChE J. 1980, 26, 769-780) was used to compute the critical points. A technique for determining the equilibrium phase of the critical point and thus determining the critical end point, which was difficult to evaluate, using the tangent plane criterion was developed. The developed algorithm was found to be rather stable and to converge rather quickly. The critical end points of different nonpolar, polar, and associating binary mixtures were calculated employing this algorithm. According to the calculation results and the experimental data for the critical end points, the interaction parameters were fitted successfully.