An analytical consistent pseudo-component delumping procedure for equations of state with non-zero binary interaction parameters

For mixtures with many components, some or most of the components are grouped into pseudo-components in order to reduce the dimensionality of the problem for phase equilibrium calculations, and therefore the computational effort. However, knowing the detailed fluid phase split may be important for a variety of applications. The detailed phase compositions resulting from a flash calculation performed on a lumped mixture can be predicted using a delumping (inverse lumping) procedure [C.F. Leibovici, E.H. Stenby, K. Knudsen, Fluid Phase Equilibr. 117 (1997) 225–232].If the mixture parameters of an equation of state (EoS) can be expressed as a linear combination of pure component parameters and the phase mole fractions, then the component fugacity coefficients can also be expressed as a linear combination of pure component parameters with coefficients only depending on mixture properties. As a result, the equilibrium coefficients are related only to component properties and EoS coefficients, independently on phase compositions.In this work, we show using a reduction method how to effectively obtain such an expression of the equilibrium constants even for non-zero binary interaction parameters (BIPs) in the EoS, and based on these results, we propose a totally consistent analytical procedure for the estimation of equilibrium constants of detailed mixtures from lumped information, which is an extension of Leibovici's delumping method.For several examples with non-zero BIPs between hydrocarbon components and classical contaminants, phase mole fractions and the vapor mole fraction of the delumped mixture are in excellent agreement with the exact values obtained by flashing the original mixture. The delumping procedure has multiple applications, mainly for reservoir simulation and distillation problems.