The objective of this project was to develop practical and efficient mathematical methods for simulating the effects of matrix diffusion in groundwater transport and remediation models. These methods apply to various types of heterogeneous settings, including fractured porous media and sites with extensive low permeability layers and lenses. The new mathematical methods were then implemented in the U.S. Environmental Protection Agency groundwater remediation screening model REMChlor to develop a new generation model that considers matrix diffusion in the plume: REMChlor-MD.

Technology Description

The problem of matrix diffusion of chlorinated volatile organic compounds (CVOCs) in groundwater plumes is mathematically analogous to heat conduction in fractured rocks and heterogeneous reservoirs. Elegant numerical and semi-analytical methods for modeling the heat conduction processes that occur during fluid injection or extraction were developed in the 1980s by geothermal reservoir engineers. With some modifications, these methods are directly applicable to the problem of CVOC matrix diffusion. They offer accurate solutions that do not require explicit discretization of the low permeability zones. Instead, the low permeability zones that occur at scales smaller than a normal numerical gridblock are represented with sub-gridblock scale analytical or numerical approximations. In most cases of interest, these approximations are expected to offer a level of simulation accuracy comparable to the fine-grid numerical simulations, but at a tiny fraction of the computational and user effort.

Demonstration Results

REMChlor-MD attempts to assist site managers and site consultants to better understand matrix diffusion and help site stakeholders determine if matrix diffusion processes are significant enough to cause “rebounding” of downgradient plume concentrations above remediation goals after plume remediation or isolation is complete. Having this information readily available before a remedy is implemented, could assist site stakeholders select more appropriate remedies and improve effective risk communication with regulators and the public.

REMChlor-MD is intended to be used as a screening level tool for simulating matrix diffusion effects. REMChlor-MD has the following assumptions and limitations:

  • Assumes the user is familiar with basic groundwater transport and mass balance concepts.
  • Assumes a homogeneous and constant groundwater velocity field with flow in only one direction.
  • The contaminant source mass balance assumes that the contaminant discharge is a power function of the remaining contaminant mass using an exponent Γ (gamma). As a simplistic model of a complicated heterogeneous multiphase transport system, the best value of gamma for a given site will be subject to a range of uncertainty. For this reason, it is probably a good idea to run the model with a range of gamma values.
  • The model assumes that biodegradation reactions in the plume can be described by first order decay reactions. Biogeochemical conditions that control these reactions may not be well represented by first order reactions therefore, there is considerable uncertainty in values of field scale decay rates.
  • First order decay rates are a function of time and distance from the source (x), but they do not depend on the y or z coordinates. This means that a specified reaction zone will extend over the entire model domain in the y and z directions.
  • In the transmissive zone, the model uses a conventional advection-dispersion formulation. However, in the absence of matrix diffusion, this may not accurately represent the physical process at a site. There is a developing conceptual model that suggests that dispersion processes are much weaker than is commonly simulated, and that lower dispersion coefficients should be used in conventional advection dispersion models. By applying this model to a transmissive zone that only occupies part of the overall volume, and by including matrix diffusion, the transport can better fit the newer conceptual model.
  • The matrix diffusion approach applied to the plume is new and has not been tested at a large number of sites. However, this model has been extensively verified with analytical and numerical solutions, and experimental laboratory data.

Implementation Issues

REMChlor-MD will enable site managers and stakeholders to quickly assess the likely impacts of different source and plume remediation schemes (including natural attenuation) with a comprehensive treatment of matrix diffusion effects. This will reduce overall costs of remediating these sites, and it will help ensure that limited resources for site remediation are used most effectively.


Falta, R.W. and W. Wang. 2017. A Semi-Analytical Method for Simulating Matrix Diffusion in Numerical Transport Models, Journal of Contaminant Hydrology, 197:39-49.

Muskus, N., and R.W. Falta. 2018. Semi-Analytical Model for Matrix Diffusion in Heterogeneous and Fractured Systems with Parent-Daughter Reactions. Journal of Contaminant Hydrology, 218:94-109.


Muskus, N. 2017. Evaluation of a Semi-Analytical/Numerical Method for Modeling Matrix Diffusion Effects in Groundwater Chemical Transport, MS Thesis, Clemson University, December 2017.

Wang, W. 2014. Comparison of Analytical, Numerical and Semi-Analytical Methods for Modeling Matrix Diffusion Effects in Aquitards, MS Thesis, Clemson University, December 2014.