Adaptive Fully Implicit Simulator with Multilevel Schwarz Methods for Gas Reservoir Flows in Fractured Porous Media (Communications in Computational Physics, 2021)
Large-scale reservoir modeling and simulation of gas reservoir flows in fractured porous media is currently an important topic of interest in petroleum engineering. In this paper, the dual-porosity dual-permeability (DPDP) model coupled withthe Peng-Robinson equation of state (PR-EoS) is used for the mathematical model ofthe gas reservoir flow in fractured porous media. We develop and study a parallel andhighly scalable reservoir simulator based on an adaptive fully implicit scheme andan inexact Newton type method to solve this dual-continuum mathematical model.In the approach, an explicit-first-step, single-diagonal-coefficient, diagonally implicitRunge–Kutta (ESDIRK) method with adaptive time stepping is proposed for the fullyimplicit discretization, which is second-order and L-stable. And then we focus on thefamily of Newton–Krylov methods for the solution of a large sparse nonlinear systemof equations arising at each time step. To accelerate the convergence and improve thescalability of the solver, a class of multilevel monolithic additive Schwarz methods isemployed for preconditioning. Numerical results on a set of ideal as well as realisticflow problems are used to demonstrate the efficiency and the robustness of the proposed methods. Experiments on a supercomputer with several thousand processorsare also carried out to show that the proposed reservoir simulator is highly scalable.
Keywords: Reservoir simulation; fully implicit method; multilevel method; restricted Schwarz preconditioners; parallel computing.