The computation of multi-phase equilibrium in compositional reservoir studies

Abstract

A numerical scheme for the calculation of multi-phase equili-brium states in a compositional simulator is suggested. Here, the math-ematical formulation of the compositional simulator is rearranged using a novel concept of mass balance constants. The advantage of this approach is that it decouples the thermodynamic constraints from the flow equations. In this model, the thermodynamic behavior for hydrocarbon phases is predicted using a modified version of the Peng-Robinson equation of state where another empirical constant is introduced to obtain an addi-tional degree of freedom for matching the experimental data. The inter-action parameters are calculated for a number of binary systems in this study and are presented here. The solubility of hydrocarbon and non-hydrocarbon gases in the aqueous phase is calculated using the Cysewski-Prausnitz correlation for Henrrs constant. Here, the water vapour pressure is predicted using the Peng-Robinson equation of state. The prediction is corrected using a temperature dependent water-water inter-action. In addition, a correction is introduced in the calculation of water phase density. In this investigation, the published numerical algorithms are classified in two categories: viz, the minimization of Gibbs free energy and the equal potential approach. These methods are compared on the basis of their operating surfaces. Next, the mathematical basis for the method of successive substitution is analyzed. The analysis has led to the development of accelerated successive substitution and projected successive substitution methods. The performance of Newton and quasi-Newton methods is also examined and the effect of different objective functions and independent variables on the calculation of phase equilibrium are investigated. Aside from this, a new empirical correlation is proposed to initialize three hydrocarbon phase separations and a mathematical development is undertaken for obtaining an initial vector from a previously converged equilibrium state. The numerical scheme developed here is a hybrid scheme of first order and Newton's method. The scheme incorporates a number of other features and is successfully applied for single-, two-, three-and four-phase equilibrium calculations.