Matrix Diffusion describes the gradual transport of dissolved contaminants from higher concentration and higher hydraulic conductivity (K) zones of a heterogeneous aquifer into lower K and lower contaminant concentration zones by molecular diffusion. Initially, the transfer of contaminant mass into the low K zones reduces the concentration in the high K zones and slows the migration of the plume. Once the contaminant source is removed and the high K zone contaminant concentration decreases, the contaminants will then diffuse back out of these low K zones. In some cases, matrix diffusion can maintain contaminant concentrations in more permeable zones at greater than target cleanup goals for decades or even centuries after the primary sources have been addressed. Field and laboratory results have illustrated the importance of this process. Analytical and numerical modeling tools are available for evaluating matrix diffusion.
Matrix Diffusion can have major impacts on solute migration in groundwater and on cleanup time following source removal. As a groundwater plume advances downgradient, dissolved contaminants are transported by molecular diffusion from zones with larger hydraulic conductivity (K) into lower K zones, slowing the rate of contaminant migration in the high K zone. However, once the contaminant source is eliminated, contaminants diffuse out of low K zones, slowing the cleanup rate in the high K zone (Figure 1). This process, termed ‘back diffusion’, can greatly extend cleanup times.
The impacts of back diffusion on aquifer cleanup have been examined in controlled laboratory experiments by several investigators. The video in Figure 2 shows the results of a 122-day tracer test in a laboratory flow cell (sand box). The flow cell contained several clay zones (K = 10-8 cm/s) surrounded by sand (K = 0.02 cm/s). During the loading period, water containing a green fluorescent tracer migrates from left to right with the water flowing through the flow cell, while diffusing into the clay. After 22 days, the fluorescent tracer is eliminated from the feed, and most of the green tracer is quickly flushed from the tank’s sandy zones. However, small amounts of tracer continue to diffuse out of the clay layers for over 100 days. This illustrates how back diffusion of contaminants out of low K zones can maintain low contaminant concentrations long after the contaminant source as been eliminated.
In some cases, matrix diffusion can maintain contaminant concentrations in more permeable zones above target cleanup goals for decades or even centuries after the primary sources have been addressed. At a site impacted by Dense Non-Aqueous Phase Liquids (DNAPL), trichloroethene (TCE) concentrations in downgradient wells declined by roughly an order-of-magnitude (OoM), when the upgradient source area was isolated with sheet piling. However, after this initial decline, TCE concentrations appeared to plateau or decline more slowly, consistent with back diffusion from an underlying aquitard. Numerical simulations indicated that back diffusion would cause TCE concentrations in downgradient wells at the site to remain above target cleanup levels for centuries.
One other implication of matrix diffusion is that plume migration is attenuated by the loss of contaminants into low permeability zones, leading to slower plume migration compared to a case where no matrix diffusion occurs. This phenomena was observed as far back as 1985 when Sudicky et al. observed that “A second consequence of the solute-storage effect offered by transverse diffusion into low-permeability layers is a rate of migration of the frontal portion of a contaminant in the permeable layers that is less than the groundwater velocity.” In cases where there is an attenuating source, matrix diffusion can also reduce the peak concentrations observed in downgradient monitoring wells. The attenuation caused by matrix diffusion may be particularly important for implementing Monitored Natural Attenuation (MNA) for contaminants that do not completely degrade, such as heavy metals and PFAS.
SERPD/ESTCP ResearchThe SERDP/ESTCP programs have funded several projects focusing on how matrix diffusion can impede progress towards reaching site closure, including:
Modeling Matrix Diffusion
Several different modeling approaches have been developed to simulate the diffusive transport of dissolved solutes into and out of lower K zones. The Matrix Diffusion Toolkit is a Microsoft Excel based tool for simulating forward and back diffusion using two different analytical models. Numerical models including MODFLOW/MT3DMS have been shown to be effective in simulating back diffusion process and can accurately predict concentration changes over 3 orders-of-magnitude in heterogeneous sand tank experiments. However, numerical models require a fine vertical discretization with short time steps to accurately simulate back diffusion, greatly increasing computation times. These issues can be addressed by incorporating a local 1-D model domain within a general 3D numerical model.
The REMChlor - MD toolkit is capable of simulating matrix diffusion in groundwater contaminant plumes by using a semi-analytical method for estimating mass transfer between high and low permeability zones that provides computationally accurate predictions, with much shorter run times than traditional fine grid numerical models.
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- ^ 2.0 2.1 Sale, T., Parker, B.L., Newell, C.J. and Devlin, J.F., 2013. Management of Contaminants Stored in Low Permeability Zones – A State of the Science Review. Strategic Environmental Research and Development Program (SERDP) Project ER-1740. Report.pdf Website: ER-1740
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- ^ Chapman, S.W., Parker, B.L., Sale, T.C., Doner, L.A., 2012. Testing high resolution numerical models for analysis of contaminant storage and release from low permeability zones. Journal of Contaminant Hydrology, 136, pp. 106-116. DOI: 10.1016/j.jconhyd.2012.04.006
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