In the petroleum industry, knowledge of phase behavior is essential to solve many problems, such as the design of the catalytic cracking of heavy oil. The catalyst tends to lose activity as a result of the formation of the solid phase, so the calculation of multiphase behavior of systems containing solid phases will serve to solve the problem. The Soave−Redlich−Kwong equation of state is widely employed to evaluate multiphase behavior, but cubic equations of state are incapable of calculating the properties of solid phases and thus cannot evaluate the multiphase behavior of systems containing solid phases. In this research, a new technique for describing the solid phase has been developed. The multiphase behavior of propane binaries with ployaromatic hydrocarbons was then explored. To evaluate the critical end point, which is difficult to calculate, an algorithm combining the method of Heidemann and Khalil ( AIChE J. 1980, 26, 769−780) to compute the critical point and the tangent-plane criterion was developed previously (Yang et al. Ind. Eng. Chem. Res. 2009, 48, 6877−6881). Setting the initial guesses with the values at the obtained critical end points, the three-phase loci were then computed successfully. The calculation results show that the three-phase loci terminate at a lower critical end point (LCEP), which is wrong according to the experimental data. To correct this mistake, the newly developed technique was employed, and the quadruple points where the three-phase loci really end were evaluated successfully.

In the design of chemical processes, such as catalytic cracking of bitumen and heavy oil, the knowledge of phase behavior at the critical endpoint is essential. Based on the PR equation of state, the algorithm developed by Heidemann and Khalil for calculating critical properties was used to compute critical points. An algorithm for determining the equilibrium phase of the critical point using the tangent plane criterion was developed, and was used to calculate the critical endpoints of different mixtures, including non-polar, polar and associating systems. The critical endpoint, representing the type of the phase behavior, was employed to fit the interaction parameter of mixtures in critical state at high pressure. Lines of critical endpoints for ternary mixtures were also determined with the algorithm.