A two-stage preconditioner for multiphase poromechanics in reservoir simulation

Joshua A. White, Nicola Castelletto, Sergey Klevtsov, Quan M. Bui, Daniel Osei-Kuffuor, and Hamdi A.Tchelepi

Computer Methods in Applied Mechanics and Engineering


Many applications involving porous media–-notably reservoir engineering and geologic applications–-involve tight coupling between multiphase fluid flow, transport, and poromechanical deformation. While numerical models for these processes have become commonplace in research and industry, the poor scalability of existing solution algorithms has limited the size and resolution of models that may be practically solved. In this work, we propose a two-stage Newton–Krylov solution algorithm to address this shortfall. The proposed solver exhibits rapid convergence, good parallel scalability, and is robust in the presence of highly heterogeneous material properties. The key to success of the solver is a block-preconditioning strategy that breaks the fully-coupled system of mass and momentum balance equations into simpler sub-problems that may be readily addressed using targeted algebraic methods. Numerical results are presented to illustrate the performance of the solver on challenging benchmark problems.

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An example multiphase poromechanics problem, in which the displacement, pressure, and saturation fields are solved in a fully coupled manner. The model consists of the SPE10 Model-2 reservoir inserted between a caprock and underburden to provide more realistic mechanical boundary conditions.