A natural variable fully implicit compositional reservoir simulation

Abstract

The fluid flow in porous media, such as oil reservoirs, is described by complex systems of partial differential equations. Several algorithms to solve these equations have been and continue to be proposed in the literature, each having different impact on convergence rate and computational cost for different scenarios. Numerical formulations differ in their nature due to the level of implicitness degree selected, primary variables and primary equations, and solution algorithm. Fully Implicit algorithms are remarkably important due to their stability, which allows the selection of large time-steps, even for complex reservoirs. In this work, a natural variable formulation, in terms of pressure, phase mole fractions, and saturations is presented for the compositional reservoir simulation based on equation of state using Cartesian grids. In this algorithm, the flow equations are decoupled from the constraint equations (equilibrium relationships) through a Gaussian elimination, significantly reducing the number of variables to be solved in the linear system arising from the discretization of the partial differential equations. The model implemented considers an arbitrary number of components; up to four-phase flow; no mass transfer between the hydrocarbon phases and the aqueous phase; permeability heterogeneity and anisotropy; advection and dispersion. The natural variable formulation is validated with an IMPEC formulation. The results are compared in terms of production data, saturation fronts, and computational cost. It is observed that this new formulation is extremely robust, has low computational cost and requires a low number of iterations per time-step.