Inexact Methods for Sequential Fully Implicit (SFI) Reservoir Simulation

TL;DR

This paper introduces inexact methods for the Sequential Fully Implicit (SFI) reservoir simulation scheme, reducing unnecessary computations and improving efficiency by adaptively controlling solver tolerances during coupled flow and transport problem solving.

Contribution

The paper extends a nonlinear-acceleration framework to multi-component models and develops adaptive inexact methods to mitigate over-solving in SFI, enhancing computational efficiency.

Findings

Adaptive inexact methods reduce computational cost.

Over-solving in standard SFI leads to wasted effort.

New solver maintains convergence while saving resources.

Abstract

The sequential fully implicit (SFI) scheme was introduced (Jenny et al. 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and sequentially solve the pressure and transport sub-problems. In standard SFI, the sub-problems are usually solved with tight tolerances at every outer iteration. This can result in wasted computations that contribute little progress towards the coupled solution. The issue is known as `over-solving'. Our objective is to minimize the cost of inner solvers while maintaining the convergence rate of SFI. We first extended a nonlinear-acceleration (NA) framework (Jiang and Tchelepi 2019) to multi-component compositional models, for ensuring robust outer-loop convergence. We then developed inexact-type methods that alleviate `over-solving'. It is found that there is no need for one sub-problem to strive for perfection, while the coupled (outer) residual remains high due to the other sub-problem. The new SFI solver was tested using several complex cases. The problems involve multi-phase and EoS-based compositional fluid systems. We compared different strategies such as fixed relaxations on absolute and relative tolerances for the inner solvers, as well as an adaptive approach. The results show that the basic SFI method is quite inefficient. Away from a coupled solution, additional accuracy achieved in inner solvers is wasted, contributing to little or no reduction of the overall outer residual. By comparison, the adaptive inexact method provides relative tolerances adequate for the current convergence state of the sub-problems. We show across a wide range of flow conditions that the new solver can effectively resolve the over-solving issue, and thus greatly improve the overall efficiency.