Iterative coupling reservoir simulation on high performance computers

Abstract

In this paper, the iterative coupling approach is proposed for applications to solving multiphase flow equation systems in reservoir simulation, as it provides a more flexible time-stepping strategy than existing approaches. The iterative method decouples the whole equation systems into pressure and saturation/concentration equations, and then solves them in sequence, implicitly and semi-implicitly. At each time step, a series of iterations are computed, which involve solving linearized equations using specifi c tolerances that are iteration dependent. Following convergence of subproblems, material balance is checked. Convergence of time steps is based on material balance errors. Key components of the iterative method include phase scaling for deriving a pressure equation and use of several advanced numerical techniques. The iterative model is implemented for parallel computing platforms and shows high parallel effi ciency and scalability.

A new treatment of capillarity to improve the stability of IMPES two-phase flow formulation

“…Different from the classical Newton-like FI methods, this approach splits the whole equation system into a pressure and a saturation equation that are solved in the sequence as IMPES. An iterative scheme based on the sequential method is developed in [42,45,46], in which a pressure is solved implicitly and followed by an implicit saturation equation in each iteration. Iterative coupling is also popular in the simulation of single-phase and two-phase flow and reactive transport [3,22,25,50,[59][60][61]67].…”

Evaluating linear and nonlinear solvers for density driven flow

“…As a last alternative, we study a strategy also referred to as iterative coupling in the context of different equations [4][5][6]8]. Starting from (12), we state it as a non-linear Gauss-Seidel type iteration [29] here:…”

“…These provide a natural way to couple different modules and can be considered as variants of operator splitting technique. This class has widely been applied, e.g., to multiphase flow [4,5], or geomechanics [6][7][8][9]. Based on a Picard iteration a similar (partially explicit) strategy is pursued in [10,11].…”

Numerical Treatment of Two-phase Flow in Porous Media Including Specific Interfacial Area

“…Because the decoupling between the pressure equation and the saturation equation, the IMPES method is conditionally stable. Iterative IMPES splits the equation system into a pressure and a saturation equation that are solved sequentially as IMPES [14,15,13].…”