| − | Several different modeling approaches have been developed to emulate the diffusive transport of dissolved solutes into and out of lower ''K'' zones. The Matrix Diffusion Toolkit<ref name="Farhat2012"/> is a Microsoft Excel based tool for simulating forward and back diffusion using two different analytical models<ref name="Parker1994">Parker, B.L., Gillham, R.W., and Cherry, J.A., 1994. Diffusive Disappearance of Immiscible Phase Organic Liquids in Fractured Geologic Media. Groundwater, 32(5), pp. 805-820. [https://doi.org/10.1111/j.1745-6584.1994.tb00922.x DOI: 10.1111/j.1745-6584.1994.tb00922.x]</ref><ref>Sale, T.C., Zimbron, J.A., and Dandy, D.S., 2008. Effects of reduced contaminant loading on downgradient water quality in an idealized two-layer granular porous media. Journal of Contaminant Hydrology, 102(1), pp. 72-85. [https://doi.org/10.1016/j.jconhyd.2008.08.002 DOI: 10.1016/j.jconhyd.2008.08.002]</ref>. Numerical models including [https://www.usgs.gov/software/mt3d-usgs-groundwater-solute-transport-simulator-modflow MODFLOW/MT3DMS]<ref name="Zheng1999">Zheng, C. and Wang, P.P., 1999. MT3DMS: A Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems; Documentation and User’s Guide. Contract Report SERDP-99-1 U.S. Army Engineer Research and Development Center, Vicksburg, MS. [https://www.enviro.wiki/images/3/32/Mt3dmanual.pdf User’s Guide.pdf] [https://www.usgs.gov/software/mt3d-usgs-groundwater-solute-transport-simulator-modflow MT3DMS website]</ref> 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<ref>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. [https://doi.org/10.1016/j.jconhyd.2012.04.006 DOI: 10.1016/j.jconhyd.2012.04.006]</ref>. However, numerical models require a fine vertical discretization with short time steps to accurately simulate back diffusion, greatly increasing computation times<ref>Farhat, S.K., Adamson, D.T., Gavaskar, A.R., Lee, S.A., Falta, R.W. and Newell, C.J., 2020. Vertical Discretization Impact in Numerical Modeling of Matrix Diffusion in Contaminated Groundwater. Groundwater Monitoring and Remediation, 40(2), pp. 52-64. [https://doi.org/10.1111/gwmr.12373 DOI: 10.1111/gwmr.12373]</ref>. These issues can be addressed by incorporating a local 1-D model domain within a general 3D numerical model<ref>Carey, G.R., Chapman, S.W., Parker, B.L. and McGregor, R., 2015. Application of an Adapted Version of MT3DMS for Modeling Back‐Diffusion Remediation Timeframes. Remediation, 25(4), pp. 55-79. [https://doi.org/10.1002/rem.21440 DOI: 10.1002/rem.21440]</ref>.
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