Using the multiple cell balance method to solve the problem of two-dimensional groundwater flow and contaminant transport with nonequilibrium sorption

The problem of large-scale contamination of groundwater by relatively low levels of organic contaminants is most frequently addressed by extracting and treating the impacted groundwater. This pump-and-treat strategy is often unsuccessful because of difficulties encountered in recovering the contaminants from relatively immobile zones within the porous medium. These zones can exist at the particle scale, as intraparticle or intra-aggregate porosity, and at the larger scales, as low-permeability layers or lenses interspersed in substantially more permeable layers. This work focuses on achieving an efficient numerical solution to a system of groundwater flow and contaminant transport equations that sufficiently captures the dynamics of slow desorption in a two-dimensional porous medium. The conceptual model and governing equations are presented. A numerical method for solving the governing equations, the upstream-weighted, multiple cell balance (UMCB) method, is proposed. The UMCB algorithm has been employed previously for the case of solute transport with equilibrium sorption, and is extended here to the nonequilibrium case. The approach employs a finite-element basis function and a finite-difference local mass balance, and is designed to reduce computational and storage requirements, while minimizing the mass balance error. The computational grid is formed by division of the flow domain into triangular elements. An invented node at the center of each element divides the element into three subtriangular regions. By linking the center of each triangular element and the mid-point of each elemental side, a multiangular region, referred to as an exclusive subdomain, is defined. The discretized system of governing equations is derived from the integral form that describes the mass balance in the exclusive subdomain of each node. The paper details the application of the numerical method, and demonstrates that the method is reasonably accurate and computationally efficient for a two-dimensional domain subject to nonequilibrium sorption.