Sequential Fully Implicit Formulation for Compositional Simulation using Natural Variables

TL;DR

This paper introduces a new sequential fully implicit (SFI) method for compositional simulation in porous media, improving convergence and robustness by reformulating the coupling between flow and transport problems using natural variables.

Contribution

The paper proposes a novel SFI variant based on a nonlinear overall-volume balance, enhancing convergence and accuracy in compositional simulations compared to traditional methods.

Findings

The new SFI scheme converges to the same solution as the Fully Implicit method.

Controlling splitting errors improves robustness of the simulation.

The method optimizes sub-problem solvers for flow and transport.

Abstract

The Sequential Fully Implicit (SFI) method was proposed to simulate coupled immiscible multiphase fluid flow in porous media. Later, it was extended to the black-oil model, whereby the gas component is allowed to dissolve in the oil phase. Most recently, the SFI approach was extended to fully compositional isothermal displacements. SFI schemes solve the fully coupled system in two steps: (1) Construct and solve the pressure equation (flow problem). (2) Solve the coupled species transport equations for the phase saturations and phase compositions. Experience indicates that complex interphase mass transfer behaviors often lead to large numbers of SFI outer iterations compared with the Fully Implicit (FI) method. Here, we demonstrate that the convergence difficulties are directly related to the treatment of the coupling between the flow and transport problems, and we propose a new SFI variant based on a nonlinear overall-volume balance equation. The first step consists of forming and solving a nonlinear pressure equation, which is a weighted sum of all the component mass conservation equations. The second step of the new SFI scheme entails introducing the overall-mass density as a degree-of-freedom, and solving the full set of component conservation equations cast in the natural-variables form. During the second step, the pressure and the total-velocity fields are fixed. We analyze the `splitting errors' associated with the compositional SFI scheme, and we show how to control these errors in order to converge to the same solution as the Fully Implicit (FI) method. This robust sequential-implicit solution scheme allows for designing numerical methods and linear solvers that are optimized for the sub-problems of flow and transport.