An Adaptive Sequential Fully Implicit Domain-Decomposition Solver

Abstract

Summary Modern reservoir simulation must handle complex compositional fluid behavior, orders-of-magnitude variations in rock properties, and large velocity contrasts. We investigate how one can use nonlinear domain-decomposition preconditioning to combine sequential and fully implicit (FI) solution strategies to devise robust and highly efficient nonlinear solvers. A full simulation model can be split into smaller subdomains that each can be solved independently, treating variables in all other subdomains as fixed. In subdomains with weaker coupling between flow and transport, we use a sequential fully implicit (SFI) solution strategy, whereas regions with stronger coupling are solved with an FI method. Convergence to the FI solution is ensured by a global update that efficiently resolves long-range interactions across subdomains. The result is a solution strategy that combines the efficiency of SFI and its ability to use specialized solvers for flow and transport with the robustness and correctness of FI. We demonstrate the efficacy of the proposed method through a range of test cases, including both contrived setups to test nonlinear solver performance and realistic field models with complex geology and fluid physics. For each case, we compare the results with those obtained using standard FI and SFI solvers. This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

Comparison of nonlinear field-split preconditioners for two-phase flow in heterogeneous porous media

“…The multiplicative Schwarz method has been used to split boundary value problems (BVP) into subproblems solver on smaller physical domains [29][30][31][32][33]. It has also been used to split a coupled BVP into subproblems based on the physics [34][35][36], each subproblem being solved on the full domain to update one of the fields (here, pressure and saturation).…”

“…Given k ∈ N * the outer-loop iteration number Given k−1 s ∈ [0, 1[ the tolerance used at outer-loop iteration k − 1 ( 0 = 1) Compute η k using (30), or (31), or (32) Compute the new tolerance…”

“…Two distinct directions have been explored. A class of nonlinear preconditioners leverages domain decomposition methods [29][30][31][32][33] to precondition the nonlinear system in a computationally inexpensive way and speed up convergence. In this work, we focus on nonlinear preconditioners obtained by splitting the system by physical field [34][35][36].…”