Bound-preserving inexact Newton algorithms on parallel computers for wormhole propagation in porous media

Simulating wormhole propagation during reactive dissolution of carbonates is often significantly challenging, because of the high nonlinearity of the governing equations with complex fluid physics. High resolution grids are often required to represent the complex geological heterogeneity, which demands massively parallel computers with a large number of processors. Herein, we present a parallel and scalable simulator on parallel computers for the fully implicit solution of the wormhole propagation model. Our approach is based on a family of mixed finite element methods for the spatial discretization and the implicit Backward Euler scheme for the temporal integration, to handle the combination of complicated flow physics and high resolution grids in their full complexity. Moreover, the active-set reduced-space method, as a class of bound-preserving inexact Newton algorithms, is proposed for the resultant nonlinear system of equations, to guarantee the nonlinear consistency of the fully implicit discretization in a monolithic way and to ensure the boundedness requirement of the solution. Numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed simulator for a set of heterogeneous medium problems. Large-scale results are provided to show the scalability for reservoir simulation with hundreds of millions of unknowns by using several thousand processors.