A continuous-lumped phase-equilibrium model for complex multiphase reactions

Abstract

The accurate prediction of phase equilibrium is vital to the modeling of many complex, multiphase reaction mixtures. Phase-equilibrium calculations for such mixtures often become computationally intensive due to the large number of components in the mixture. Furthermore, such mixtures are frequently described by approximate analyses such as incompletely resolved chromatograms. Before phase-equilibrium calculations can be performed, these analyses must be parameterized, or "lumped." The number of parameters resulting from the lumping process should, in general, be kept as small as possible to minimize the computer time required for the subsequent calculations. A new lumping technique, "continuous lumping," which is especially suited for complex mixtures described by chromatographic data, has been developed. The continuous-lumping method can be considered as an extension of pseudocomponent lumping, which treats the mixture as if it were composed of only a few components, or it can be considered as a generalization of continuous-mixture methods, which treat the mixture as a continuum of components. The continuous-lumping method uses a functional formulation similar to the continuous-mixture method but is based mathematically on the original discrete mixture. This mathematical formalism allows for the evaluation of the errors involved in the lumping process and for the direct incorporation of individual component properties into the continuous-lumping method. In this study, the continuous-lumping method is formally developed from the original discrete equations describing the mixture. The method is then compared to the pseudocomponent method using a simple calculation assuming Raoult's Law. A generalized phase-equilibrium program is then developed using the continuous-lumping method with piecewise-linear basis functions and the Soave modification of the Redlich-Kwong equation-of-state. The resulting program provides a general means for calculating high-pressure phase equilibria for complex mixtures of industrial significance.