Reduced-Order Modeling of Reactive Solute Transport for Advection-Dominated Problems with Nonlinear Kinetic Reactions

Groundwater is a vital natural resource, and our ability to protect and manage this resource efficiently and effectively relies heavily on our ability to perform reliable and accurate computer modeling and simulation of subsurface systems. This frequently raises research questions involving parameter estimation and uncertainty quantification, which are often prohibitively expensive to answer using standard high-dimensional computational models. We have previously demonstrated the ability to replace the high-dimensional models used to solve linear, uncoupled, diffusion-dominated multi-species reactive transport systems with low-dimension approximations using reduced order modeling (ROM) based on proper orthogonal decomposition (POD). In this work, we seek to apply ROM to more general reactive transport systems, where the reaction terms may be nonlinear, mathematical models may be coupled, and the transport may be advection-dominated. We discuss the use of operator splitting, which is prevalent in the reactive transport field, to simplify the computation of complex systems of reactions in the transport model. We also discuss the use of some stabilization methods which have been developed in the computational science community to treat advection-dominated transport problems. We present a method by which we are able to incorporate stabilization and operator splitting together in the finite element setting. We go on to develop methods for implementing both operator splitting and stabilization in the ROM setting, as well as for incorporating both of them together within the ROM framework. We present numerical results which establish the ability of this new approach to produce accurate approximations with a significant reduction in computational cost, and we demonstrate the application of this method to a more realistic reactive transport problem involving bioremediation.