Critical point calculations for semi-continuous mixtures

A typical problem in the oil and gas industry is the calculation of high pressure phase equilibria in systems containing a very large number of similar components. Treating the composition of these mixtures as a continuous distribution, instead of trying to characterize each individual component, has proven to be an elegant and efficient approach to solve this type of problem. In this paper, we rigorously formulate the critical point conditions for continuous and semi-continuous mixtures, but as is often the case with such formulations, the complexity of the expressions prevents an analytical solution of the equilibrium problem, and discretization is required in order to use realistic thermodynamic models. Once in discrete form, the critical point equations were solved using a modified form of the Hicks and Young algorithm and the thermodynamic stability of the solutions was guaranteed by the calculation of higher terms in the Helmholtz free energy expansion and by global phase stability analyses. The resulting procedure was employed to perform an investigation of the influence of the distribution parameters on the types of critical phase diagrams that can be obtained from the Peng-Robinson equation of state.