Multi-Stage Preconditioners for Thermal-Compositional-Reactive Flow in Porous Media

TL;DR

This paper introduces multi-stage preconditioners that enhance the convergence and robustness of thermal-compositional-reactive reservoir simulations, especially in challenging thermal regimes, by integrating AMG into the CPR framework.

Contribution

It develops a novel multi-stage preconditioning approach using Schur-complement and AMG to improve energy equation treatment in thermal reservoir simulations.

Findings

Reduced linear iterations by 40-85% compared to standard CPR.

Improved robustness across various thermal regimes from advection to diffusion.

Demonstrated effectiveness on complex reactive In-Situ Combustion problems.

Abstract

We present a family of multi-stage preconditioners for coupled thermal-compositional-reactive reservoir simulation problems. The most common preconditioner used in industrial practice, the Constrained Pressure Residual (CPR) method, was designed for isothermal models and does not offer a specific strategy for the energy equation. For thermal simulations, inadequate treatment of the temperature unknown can cause severe convergence degradation. When strong thermal diffusion is present, the energy equation exhibits significant elliptic behavior that cannot be accurately corrected by CPR's second stage. In this work, we use Schur-complement decompositions to extract a temperature subsystem and apply an Algebraic MultiGrid (AMG) approximation as an additional preconditioning stage to improve the treatment of the energy equation. We present results for several two-dimensional hot air injection problems using an extra heavy oil, including challenging reactive In-Situ Combustion (ISC) cases. We show improved performance and robustness across different thermal regimes, from advection dominated (high Peclet number) to diffusion dominated (low Peclet number). The number of linear iterations is reduced by 40-85% compared to standard CPR for both homogeneous and heterogeneous media, and the new methods exhibit almost no sensitivity to the thermal regime.