The Department of Defense (DoD) has long term liability associated with contaminated groundwater at current and former military installations. The groundwater contaminants at these sites include chlorinated solvents, energetic compounds, and emerging contaminants such as PFAS and 1,4-dioxane. Some of these contaminated sites have proven to be exceedingly difficult to remediate due to the phenomenon of matrix diffusion. Matrix diffusion, also called “back diffusion,” occurs when contaminants diffuse from high permeability zones into adjacent low permeability zones during a “loading period.” During the “release period,” the contamination may be removed from the high permeability zones, but contaminants in the low permeability zones gradually diffuse back into the high permeability zones at significant levels. This process may occur in any heterogeneous setting, but it is particularly important in certain fractured bedrock sites, and in sites with silt or clay lenses and layers. These types of complex site conditions lead to plumes that are long lived, requiring extensive long-term monitoring and high remediation costs.

Existing groundwater plume models can only simulate matrix diffusion processes under ideal circumstances, using computationally intensive fine grids or with crude dual porosity approaches. Groundwater transport models at most sites do not include this important plume process at all, and therefore are likely to be unreliable for making long-term predictions of plume behavior.

The purpose of this effort is to implement the new semi-analytic matrix diffusion method that was recently developed for the REMChlor-MD screening model (ER-201426) in the next generation public domain MODFLOW groundwater flow and transport codes.

Technology Description

The new matrix diffusion method used in REMChlor-MD is a semi-analytical technique based on a method originally used to model transient heat conduction during enhanced oil recovery and geothermal reservoir simulation. With some modifications, this method has been demonstrated to work well for modeling matrix diffusion in both fractured and heterogeneous systems. It has been shown that the semi-analytical method offers a level of simulation accuracy that is comparable to very fine-grid numerical simulations, but at a tiny fraction of the computational and user effort. The current REMChlor-MD screening model assumes a uniform l-D groundwater flow field, so it is limited to relatively simple site conditions.

This project will incorporate the semi-analytical matrix diffusion model into the next generation of open source, public domain, 3-D chemical transport codes for the unstructured grids (MODFLOW-USG and MODFLOW 6). These modified FORTRAN codes will then be incorporated into a widely used commercial groundwater modeling graphical user interface (Aquaveo Groundwater Modeling System [GMS]).


There are 3 products available for the modeling software.  The most useful one for most people is the Aquaveo Groundwater Modeling System (GMS) version 10.7 which can be downloaded here.  This version contains the Matrix Diffusion Transport (MDT) Package developed under this project for both MODFLOW-USG and for MODFLOW 6.  GMS is a commercial product, but a free “community” version is available.  There are also 7 detailed tutorials on the use of the MDT package with MODFLOW-USG and MODFLOW 6 with GMS V10.7.  These can be downloaded here.


The new model capabilities will allow existing flow and chemical transport models of DoD sites to be upgraded to include a full accounting of matrix diffusion effects. Since most DoD site models are already built using MODFLOW from within the GMS platform, this new capability will be readily accessible to the site modelers, and easy to implement in the existing site models. Models based on the older MODFLOW versions can be readily upgraded to MODFLOW-USG or MODFLOW 6 within GMS. Including matrix diffusion in these models will make them more reliable for making important and expensive remediation decisions. (Project Completion - 2023)


Pham, K.T. and R.W. Falta. 2022. Use of Semi-Analytical and Dual-Porosity Models for Simulating Matrix Diffusion in Systems with Parallel Fractures. Advances in Water Resources, 164:104202. doi.org/10.1016/j.advwatres.2022.104202.