Efficient solution techniques for two-phase flow in heterogeneous porous media using exact Jacobians
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ORIGINAL PAPER
Efficient solution techniques for two-phase flow in heterogeneous porous media using exact Jacobians 1 ¨ Henrik Busing
Received: 3 August 2019 / Accepted: 6 August 2020 © The Author(s) 2020
Abstract Two efficient and scalable numerical solution methods will be compared using exact Jacobians to solve the fully coupled Newton systems arising during fully implicit discretization of the equations for two-phase flow in porous media. These methods use algebraic multigrid (AMG) to solve the linear systems in every Newton step. The algebraic multigrid methods rely on (i) a Schur Complement Reduction (SCR-AMG) and (ii) a Constrained Pressure Residual method (CPR-AMG) to decouple elliptic and hyperbolic contributions. Both methods employ automatic differentiation (AD) to calculate exact Jacobians and are compared with finite difference (FD) approximations of the Jacobian. The superiority of AD is shown by several numerical test cases from the field of CO2 geo-sequestration comprising two- and three-dimensional examples. A weak scaling test on JUQUEEN, a BlueGene/Q supercomputer, demonstrates the efficiency and scalability of both methods. To achieve maximum comparability and reproducibility, the Portable Extensible Toolkit for Scientific Computation (PETSc) is used as framework for the comparison of all solvers. Keywords Algebraic multigrid (AMG) · Schur complement reduction (SCR-AMG) · Constrained pressure residual (CPR-AMG) · Multiphase flow in porous media · Automatic differentiation (AD) · CO2 geo-sequestration Mathematics Subject Classification (2010) 65F08 · 65M55 · 76T10
1 Introduction Applications for two-phase flow in porous media are found in numerous scientific fields, e.g., geothermal energy, the remediation of groundwater contamination by non-aqueous phase liquids (NAPLs), hydrogen emission due to barrel corrosion during nuclear waste management, enhanced oil recovery where oil is produced by the injection of water, and production of oil and gas fields as well as geological storage of CO2 . In geothermal energy, high-enthalpy reservoirs may contain water as liquid and vapor. Successful production The research leading to these results has received funding from the European Union’s Horizon2020 Research and Innovation Program under grant agreement No. 640573 (Project DESCRAMBLE) and No. 676629 (Project EoCoE) Henrik B¨using
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Institute for Applied Geophysics and Geothermal Energy, E.ON Energy Research Center, RWTH Aachen University, 52074 Aachen, Germany
requires an assessment of the behavior of the phases over time. Remediation of NAPLs during groundwater contamination may involve the injection of hot steam. This reduces the viscosity of the NAPLs and supports their easier transport out of the reservoir. Here, groundwater, injected steam, and the NAPL are the existing phases. During nuclear waste storage, brines may corrode the storage containers, finally resulting in the emission of H2 . Enhanced oil recovery makes use of water or CO2 injection to increase the oi
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