A coupled geomechanics and reservoir flow model on parallel computers

Land subsidence due to the exploitation of groundwater and hydro- carbon fluids has triggered extensive studies in coupled fluid flow and ge- omechanics simulations. However, numerical modeling of coupled processes imposes great computational challenges. Coupled analysis for large scale full- field applications with millions of unknowns has been, historically, considered extremely complex and unfeasible. The purpose of this dissertation is to in- vestigate accurate and efficient numerical techniques for coupled multiphase flow and geomechanics simulations on parallel computers. We emphasize the iterative coupling approach in extending conven- tional fluid-flow modeling to coupled fluid-flow and geomechanics modeling. To overcome the slow convergence—a major drawback of this method—we propose new preconditioning schemes to achieve a faster convergence rate. Efficient and parallel scalable linear solvers are developed to reduce the com- putational overhead induced by the solution of discrete elasticity equations. Special communications techniques are implemented to optimize parallel effi- ciency. In this dissertation we first derive the mathematical model for multi- phase flowin a deformable porous medium. We then present a new formulation of the iterative coupling scheme and prove the optimality of two physics-based preconditioners that are traditionally used in the petroleum industry. Practi- cal strategies and new preconditioners are proposed to improve the numerical performance of the iteratively coupled approach. In addition, we develop two types of preconditioners for solving the linear elasticity system, namely, multi- level domain decomposition preconditioners using a super-coarsening multigrid algorithm and displacement decomposition preconditioners. Parallel imple- mentation issues are also addressed. Numerical examples are presented to demonstrate the robustness, efficiency and parallel scalability of the proposed linear solution techniques.