A Semi-Implicit Formulation for Compositional Reservoir Simulation

Abstract

Abstract A new semi-implicit formulation to solve the set of nonlinear difference equations that describe multiphase compositional flow in a reservoir is presented in this paper. Newton's method is applied on the nonlinear difference equations obtained after treating compositions in the flow terms explicitly, one iteration behind. The linearized system of equations generated from this treatment possess a peculiar matrix structure, that allows the reduction of the system, via matrix operations, to three equations in three unknowns per gridblock regardless of the number of components. The level of implicitness of the formulation presented in this paper is intermediate to IMPECS and Fully-Implicit methods and has a higher level of implicitness than a semi-implicit method previously proposed in the literature. It provides an attractive approach to solve problems where the rate of change of pressures, saturations and compositions in the reservoir are important, such that IMPECS method becomes impractical and the Fully-Implicit method becomes too expensive. Applications to the simulation of a well-test in a gas-condensate well and the natural depletion and gas-cycling of a volatile-oil reservoir are presented.