A minimum-type nonlinear complementarity simulator with constrained pressure residual (CPR) methods for wormhole propagation in carbonate acidization

Abstract

Due to the high computational complexity of wormhole propagation in carbonate acidization, nonphysical oscillations of the numerical solutions often appear, which seriously ruins the physical accuracy or even breaks down the whole process of reservoir flows at large-scale simulation. In this paper, we introduce and study a family of recently developed nonlinear complementarity formulations for handling the nonphysical oscillations. Typically, this bound-preserving process is modeled by the corresponding nonlinear partial differential equations (PDEs) along with the inequality restrictions as a non-smooth system of equations under the application of a minimum-type complementary function. Because of the non-smoothness of the nonlinear complementarity system, the nonlinear algebraic system after the fully implicit discretization is solved by using a semismooth Newton method combined with a generalized Jacobian matrix. To accelerate the convergence and enhance the robustness of the corresponding linear iterations, we employ an improved class of constrained pressure residual (CPR) preconditioners with different combinations of physics-based and domain decomposition methods. Experiments on two- and three-dimensional wormhole propagation problems are presented to demonstrate the applicability of the aforementioned algorithms. Large-scale reservoir simulation with more than one billion degrees of freedom is provided to show the algorithmic scalability by using tens of thousands of processors.