Iterative methods for solving the pressure problem at multiphase filtration

TL;DR

This paper explores iterative numerical methods for solving the pressure equation in multiphase fluid flow models relevant to oil and gas recovery, emphasizing properties at the discrete level and parallel computation techniques.

Contribution

It analyzes the properties of the pressure problem and discusses iterative algorithms suitable for parallel computing environments.

Findings

The pressure problem has a non-selfadjoint elliptic operator.

Iterative methods can effectively approximate solutions.

Parallel algorithms improve computational efficiency.

Abstract

Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the algebraic expression for the sum of saturations. Primary computational algorithms are implemented for such problems using the pressure equation. In this paper, we highlight the basic properties of the pressure problem and discuss the necessity of their fulfillment at the discrete level. The resulting elliptic problem for the pressure equation is characterized by a non-selfadjoint operator. Possibilities of approximate solving the elliptic problem are considered using the iterative methods. Special attention is given to the numerical algorithms for calculating the pressure on parallel computers.