A global method for coupling transport with chemistry in heterogeneous porous media

Abstract

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.

PhreeqcRM: A reaction module for transport simulators based on the geochemical model PHREEQC

“…Although, smaller time steps for this simulation are feasible, a better approach is to implement an automatic time-stepping algorithm [63], which would allow for variable time steps that achieve a specified accuracy. The height and location of the peak are similar to the results of Mayer and MacQuarrie [63] and Amir and Kern [65]. All other concentration results, which are resolved at a coarser scale, are consistent between PHAST and the other simulators.…”

Reactive Transport in Porous Media

“…Recently, more global approaches have been used with good success, based on variants of Newton's method. Several papers implementing global methods are [1,8,15,18,19]. The paper [9] explains why the so called fixed-point method should more properly be viewed as a Block Gauss-Seidel method.…”

“…We do not report results for this method, noting that most of the modules developed for the fixed-point method can be reused for Newton's method, but in addition modules for the derivatives are needed. The Newton-Krylov method has been used in the same context by Hammond et al [15], and with the formulation described here, but with only a 1D geometry by Amir and Kern [1]. It is this work that is currently being extended to the setup described in this paper.…”

Numerical simulation of two-phase multicomponent flow with reactive transport in porous media: application to geological sequestration of CO2

“…In the direct substitution approaches, the equation of chemistry are directly substituted in the equations of transport. This can be done explicitly as in [14] or implicitly as in [19,23] or [4]. The problem can also be reformulated as a differential algebraic system (DAE) as in [11].…”