TY - JOUR
T1 - Adaptive Fully Implicit Simulator with Multilevel Schwarz Methods for Gas Reservoir Flows in Fractured Porous Media
AU - Li , Rui
AU - Yang , Haijian
AU - Yang , Chao
JO - Communications in Computational Physics
VL - 5
SP - 1499
EP - 1528
PY - 2021
DA - 2021/10
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2021-0076
UR - https://global-sci.org/intro/article_detail/cicp/19938.html
KW - Reservoir simulation, fully implicit method, multilevel method, restricted Schwarz preconditioners, parallel computing.
AB - <p style="text-align: justify;">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 with
the Peng-Robinson equation of state (PR-EoS) is used for the mathematical model of
the gas reservoir flow in fractured porous media. We develop and study a parallel and
highly scalable reservoir simulator based on an adaptive fully implicit scheme and
an inexact Newton type method to solve this dual-continuum mathematical model.
In the approach, an explicit-first-step, single-diagonal-coefficient, diagonally implicit
Runge–Kutta (ESDIRK) method with adaptive time stepping is proposed for the fully
implicit discretization, which is second-order and L-stable. And then we focus on the
family of Newton–Krylov methods for the solution of a large sparse nonlinear system
of equations arising at each time step. To accelerate the convergence and improve the
scalability of the solver, a class of multilevel monolithic additive Schwarz methods is
employed for preconditioning. Numerical results on a set of ideal as well as realistic
flow problems are used to demonstrate the efficiency and the robustness of the proposed methods. Experiments on a supercomputer with several thousand processors
are also carried out to show that the proposed reservoir simulator is highly scalable.</p>