Plume Response Modeling - Revision history

Jhurley: /* Matrix Diffusion in Plumes */

2019-12-16T19:46:18Z

‎Matrix Diffusion in Plumes

Jhurley: /* Analytical Plume Models */

2019-12-16T19:41:23Z

‎Analytical Plume Models

Jhurley: /* Analytical Plume Models */

2019-12-16T19:31:49Z

‎Analytical Plume Models

Jhurley: /* Matric Diffusion in Plumes */

2019-12-16T19:20:49Z

‎Matric Diffusion in Plumes

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 *Parallel fracture models<ref>Sudicky, E.A. and Frind, E.O., 1982. Contaminant transport in fractured porous media: Analytical solutions for a system of parallel fractures. Water Resources Research, 18(6), 1634-1642. [https://doi.org/10.1029/wr018i006p01634 doi: 10.1029/WR018i006p01634]</ref><ref>West, M.R., Kueper, B.H. and Novakowski, K.S., 2004. Semi-analytical solutions for solute transport in fractured porous media using a strip source of finite width. Advances in Water Resources, 27(11), 1045-1059. [http://dx.doi.org/10.1016/j.advwatres.2004.08.011 doi: 10.1016/j.advwatres.2004.08.011]</ref>
 *Aquifer-aquitard models<ref name= "Sale2008" /><ref name= "Seyedabbasi2012">Seyedabbasi, M.A., Newell, C.J., Adamson, D.T. and Sale, T.C., 2012. Relative contribution of DNAPL dissolution and matrix diffusion to the long-term persistence of chlorinated solvent source zones. Journal of Contaminant Hydrology, 134, 69-81. [https://doi.org/10.1016/j.jconhyd.2012.03.010  doi: 10.1016/j.jconhyd.2012.03.010]</ref>
-The parallel fracture models consider advection, dispersion, retardation, and decay in the fracture, with diffusion, retardation, and decay in the matrix. The two-layer model by Sale et al. (2008)<ref name= "Sale2008" /> considers advection, dispersion, retardation and decay in the aquifer with diffusion, retardation, and decay in an underlying aquitard. Finally, the Sale et al. (2008)<ref name= "Sale2008" /> and Seyedabbasi et al. (2012)<ref name= "Seyedabbasi2012" /> models are included in the [https://www.serdp-estcp.org/Tools-and-Training/Environmental-Restoration/Groundwater-Plume-Treatment/Matrix-Diffusion-Tool-Kit ESTCP Matrix Diffusion Toolkit]<ref>Farhat, S.K., Newell, C.J., Seyedabbasi, M.A., McDade, J.M., Mahler, N.T., Sale, T.C., Dandy, D.S. and Wahlberg, J.J., 2012. Matrix Diffusion Toolkit. ER-201126. Environmental Security Technology Certification Program (ESTCP) by GSI Environmental Inc., Houston, Texas. [https://www.serdp-estcp.org/Tools-and-Training/Environmental-Restoration/Groundwater-Plume-Treatment/Matrix-Diffusion-Tool-Kit ER-201126]</ref>. An enhanced version of the REMChlor model with a matrix diffusion term in the plume (it can already represent matrix diffusion in the source using the gamma source term) called REMChlor-MD is expected to be publically available in 2017.
+The parallel fracture models consider advection, dispersion, retardation, and decay in the fracture, with diffusion, retardation, and decay in the matrix. The two-layer model by Sale et al. (2008)<ref name= "Sale2008" /> considers advection, dispersion, retardation and decay in the aquifer with diffusion, retardation, and decay in an underlying aquitard. Finally, the Sale et al. (2008)<ref name= "Sale2008" /> and Seyedabbasi et al. (2012)<ref name= "Seyedabbasi2012" /> models are included in the [https://www.serdp-estcp.org/Tools-and-Training/Environmental-Restoration/Groundwater-Plume-Treatment/Matrix-Diffusion-Tool-Kit ESTCP Matrix Diffusion Toolkit]<ref>Farhat, S.K., Newell, C.J., Seyedabbasi, M.A., McDade, J.M., Mahler, N.T., Sale, T.C., Dandy, D.S. and Wahlberg, J.J., 2012. Matrix Diffusion Toolkit. ER-201126. Environmental Security Technology Certification Program (ESTCP) by GSI Environmental Inc., Houston, Texas. [https://www.serdp-estcp.org/Tools-and-Training/Environmental-Restoration/Groundwater-Plume-Treatment/Matrix-Diffusion-Tool-Kit ER-201126]</ref>. An enhanced version of the REMChlor model with a matrix diffusion term in the plume (it could already represent matrix diffusion in the source using the gamma source term) called [[REMChlor - MD | REMChlor-MD]] is now available.
 ==Summary==

@@ Line 21: / Line 21: @@
 *[https://www.epa.gov/water-research/remediation-evaluation-model-chlorinated-solvents-remchlor REMChlor]<ref name= "Falta2008" /><ref name= "Falta2007" />
-The REMChlor model employs an analytical [[wikipedia::Mass balance | mass balance]] source function that accounts for partial or complete source remediation at any time. A time-dependent source model is coupled to the plume model (Fig. 1).
+The REMChlor model employs an analytical [[wikipedia:Mass balance | mass balance]] source function that accounts for partial or complete source remediation at any time. A time-dependent source model is coupled to the plume model (Fig. 1).
 [[File:Falta_plume_Fig1.jpg|thumbnail|left|400px|Figure 1. Schematic diagram of the REMChlor analytical plume response model.]]
@@ Line 27: / Line 27: @@
 REMChlor allows for spatially and temporally variable contaminant decay rates in the plume. These decay rates can be user manipulated to simulate plume remediation activities or natural attenuation. Figure 2 shows an example of a plume remediation scheme that could be simulated in REMChlor.
-[[File:Falta_plume_Fig2.jpg|thumbnail|right|400px|Figure 2. Example “time and space” plume remediation scheme for chlorinated solvents in the REMChlor model that enhances reductive dechlorination from 2005 to 2025 between 0 and 400 m and enhances aerobic degradation from 400 to 700 m (from Falta (2008)<ref name= "Falta2008" />).]]
+[[File:Falta_plume_Fig2.jpg|thumbnail|right|400px|Figure 2. Example “time and space” plume remediation scheme for chlorinated solvents in the REMChlor model that enhances reductive dechlorination from 2005 to 2025 between 0 and 400 m and enhances aerobic degradation from 400 to 700 m (from Falta 2008<ref name= "Falta2008" />).]]
-Plume response to remediation depends on characteristics of both the source and the plume behavior. Some plumes may persist long after source remediation, while others may attenuate without any source or plume remediation. The following REMChlor modeling example illustrates one type of plume behavior than can occur with a persistent dense non-aqueous phase liquids (DNAPL) source (from Falta and Kueper (2014)<ref name= "Falta2014">Falta, R.W. and Kueper, B.H., 2014. Modeling plume responses to source treatment. In Chlorinated Solvent Source Zone Remediation, pgs. 145-186. Springer, New York. [https://doi.org/10.1007/978-1-4614-6922-3_6 doi: 10.1007/978-1-4614-6922-3_6]</ref>). In this example, it is assumed that 200 kg of 1,2-DCA was released into a aquifer in 1980. The groundwater pore velocity (the Darcy velocity divided by porosity, sometimes called groundwater seepage velocity) is 60 m/yr, the initial source concentration is 1 mg/L, the retardation factor is 2, and the natural attenuation decay rate in the plume corresponds to a half-life of 2 years. The time-dependent source concentration is assumed to be a linear function of the source mass. The top panel in Figure 3 shows the dissolved 1,2-DCA plume in 2008, 28 years after the initial release.
+Plume response to remediation depends on characteristics of both the source and the plume behavior. Some plumes may persist long after source remediation, while others may attenuate without any source or plume remediation.
 Enhanced plume remediation was simulated between 2010 and 2020 by increasing the 1,2-DCA decay rate over the first 300 m to correspond to a half-life of 0.5 year. This remediation has the effect of greatly shrinking the plume (2020 panel, Fig. 3), but the plume almost completely rebounds after the plume treatment ends (2040 panel, Fig. 3). The plume rebound in this case was due to the fact that the 1,2-DCA source strength remains high due to the low rate of source depletion in this scenario.
@@ Line 35: / Line 37: @@
 Source remediation was modeled by removing 90% of the source mass that remained in 2010 (Fig. 4). The source remediation causes part of the plume to become isolated from the source due to the reduced source strength (2014 panel, Fig. 4). Eventually, the effect of source remediation is felt throughout the plume, and the plume stabilizes at a much smaller size (2024 panel, Fig. 4). The plume in this example does not completely attenuate because it was assumed that the source remediation effort was not perfect, leaving behind 10% of the mass in the source zone.
-[[File:Falta_plume_Fig3.jpg|thumbnail|left|400px|Figure 3. Simulated 1,2-DCA plume following a release in 1980. Plume remediation occurred between 2010 and 2020 (reproduced with permission from &copy;2014 Springer<ref name= "Falta2014" />), and then the plume rebounded because the source was not remediated. Units are ug/L.]]
+[[File:Falta_plume_Fig3.jpg|thumbnail|left|400px|Figure 3. Simulated 1,2-DCA plume following a release in 1980. Plume remediation occurred between 2010 and 2020 (reproduced with permission from &copy;2014 Springer<ref name= "Falta2014" />), and then the plume rebounded because the source was not remediated. Units are μg/L.]]
 [[File:Falta_plume_Fig4.jpg|thumbnail|right|400px|Figure 4. Simulated 1,2-DCA plume following a release in 1980. Source remediation occurred between 2010 and 2020 (reproduced with permission from &copy;2014 Springer<ref name= "Falta2014" />).]]

@@ Line 29: / Line 29: @@
 [[File:Falta_plume_Fig2.jpg|thumbnail|right|400px|Figure 2. Example “time and space” plume remediation scheme for chlorinated solvents in the REMChlor model that enhances reductive dechlorination from 2005 to 2025 between 0 and 400 m and enhances aerobic degradation from 400 to 700 m (from Falta (2008)<ref name= "Falta2008" />).]]
-Plume response to remediation depends on characteristics of both the source and the plume behavior. Some plumes may persist long after source remediation, while others may attenuate without any source or plume remediation. The following REMChlor modeling example, illustrates one type of plume behavior than can occur with a persistent dense non-aqueous phase liquids (DNAPL) source (from Falta and Kueper (2014)<ref name= "Falta2014">Falta, R.W. and Kueper, B.H., 2014. Modeling plume responses to source treatment. In Chlorinated Solvent Source Zone Remediation, pgs. 145-186. Springer, New York. [https://doi.org/10.1007/978-1-4614-6922-3_6 doi: 10.1007/978-1-4614-6922-3_6]</ref>). In this example, it is assumed that 200 kg of 1,2-DCA was released into a aquifer in 1980. The groundwater pore velocity (sometimes called groundwater seepage velocity; the Darcy velocity divided by porosity) is 60 m/yr, the starting source concentration, C0 in equation 1 is 1 mg/L, the retardation factor is 2, and the natural attenuation decay rate in the plume corresponds to a half-life of 2 years. The time-dependent source concentration is assumed to be a linear function of the source mass. The top panel in Figure 3 shows the dissolved 1,2-DCA plume in 2008, 28 years after the initial release.
+Plume response to remediation depends on characteristics of both the source and the plume behavior. Some plumes may persist long after source remediation, while others may attenuate without any source or plume remediation. The following REMChlor modeling example illustrates one type of plume behavior than can occur with a persistent dense non-aqueous phase liquids (DNAPL) source (from Falta and Kueper (2014)<ref name= "Falta2014">Falta, R.W. and Kueper, B.H., 2014. Modeling plume responses to source treatment. In Chlorinated Solvent Source Zone Remediation, pgs. 145-186. Springer, New York. [https://doi.org/10.1007/978-1-4614-6922-3_6 doi: 10.1007/978-1-4614-6922-3_6]</ref>). In this example, it is assumed that 200 kg of 1,2-DCA was released into a aquifer in 1980. The groundwater pore velocity (the Darcy velocity divided by porosity, sometimes called groundwater seepage velocity) is 60 m/yr, the initial source concentration is 1 mg/L, the retardation factor is 2, and the natural attenuation decay rate in the plume corresponds to a half-life of 2 years. The time-dependent source concentration is assumed to be a linear function of the source mass. The top panel in Figure 3 shows the dissolved 1,2-DCA plume in 2008, 28 years after the initial release.
 Enhanced plume remediation was simulated between 2010 and 2020 by increasing the 1,2-DCA decay rate over the first 300 m to correspond to a half-life of 0.5 year. This remediation has the effect of greatly shrinking the plume (2020 panel, Fig. 3), but the plume almost completely rebounds after the plume treatment ends (2040 panel, Fig. 3). The plume rebound in this case was due to the fact that the 1,2-DCA source strength remains high due to the low rate of source depletion in this scenario.
-The source remediation causes part of the plume to become isolated from the source due to the reduced source strength (2014 panel, Fig. 4). Eventually, the effect of source remediation is felt throughout the plume, and the plume stabilizes to a much smaller size (2024 panel, Fig. 4). The plume in this example does not completely go away because it was assumed that the source remediation effort was not perfect, leaving behind 10% of the mass in the source zone.
+Source remediation was modeled by removing 90% of the source mass that remained in 2010 (Fig. 4). The source remediation causes part of the plume to become isolated from the source due to the reduced source strength (2014 panel, Fig. 4). Eventually, the effect of source remediation is felt throughout the plume, and the plume stabilizes at a much smaller size (2024 panel, Fig. 4). The plume in this example does not completely attenuate because it was assumed that the source remediation effort was not perfect, leaving behind 10% of the mass in the source zone.
 [[File:Falta_plume_Fig3.jpg|thumbnail|left|400px|Figure 3. Simulated 1,2-DCA plume following a release in 1980. Plume remediation occurred between 2010 and 2020 (reproduced with permission from &copy;2014 Springer<ref name= "Falta2014" />), and then the plume rebounded because the source was not remediated. Units are ug/L.]]

@@ Line 48: / Line 48: @@
 One new modeling tool is the [https://water.usgs.gov/ogw/mfusg/ MODFLOW-USG] groundwater flow model, where USG stands for “unstructured grids”<ref>Panday, Sorab, Langevin, C.D., Niswonger, R.G., Ibaraki, Motomu, and Hughes, J.D., 2013. MODFLOW-USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation: U.S. Geological Survey Techniques and Methods, book 6, chap. A45, 66 pgs. [http://pubs.usgs.gov/tm/06/a45/ USGS MODFLOW-USG version 1 Website]</ref><ref>USGS, 2016. MODFLOW-USG: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation. [http://water.usgs.gov/ogw/mfusg/ USGS MODFLOW-USG Website]</ref>. Unstructured grids allow for inclusion of various cell geometries and grid-nesting methodologies to provide finer resolution of complex stratigraphy and other hydrologic features. This model is emerging as the standard for modeling groundwater flow, and can be used with the [https://pubs.er.usgs.gov/publication/ofr20161086 MODPATH Version 7]<ref>USGS, 2016. User guide for MODPATH Version 7-A particle-tracking model for MODFLOW. [https://pubs.er.usgs.gov/publication/ofr20161086 USGS MODPATH Website]</ref> to simulate groundwater plumes using particle tracking. A solute transport model, USG-Transport, is currently being beta tested on the Groundwater Vistas platform in 2016.
-==Matric Diffusion in Plumes==
+==Matrix Diffusion in Plumes==
 There is a growing consensus that molecular diffusion of contaminants into and out of low permeability zones can play a significant and even dominant role in plume response. [https://www.serdp-estcp.org/Tools-and-Training/Environmental-Restoration/Groundwater-Plume-Treatment/Matrix-Diffusion-Tool-Kit Matrix diffusion], also called “back diffusion,” occurs when contaminants such as chlorinated solvents 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<ref>Parker, B.L., Gillham, R.W. and Cherry, J.A., 1994. Diffusive disappearance of immiscible‐phase organic liquids in fractured geologic media. Ground Water, 32(5), 805-820. [https://doi.org/10.1111/j.1745-6584.1994.tb00922.x doi: 10.1111/j.1745-6584.1994.tb00922.x ]</ref><ref>Parker, B.L., McWhorter, D.B. and Cherry, J.A., 1997. Diffusive loss of non‐aqueous phase organic solvents from idealized fracture networks in geologic media. Ground Water, 35(6), 1077-1088. [https://doi.org/10.1111/j.1745-6584.1997.tb00180.x  doi: 10.1111/j.1745-6584.1997.tb00180.x]</ref><ref>Ross, B. and Lu, N., 1999. Dynamics of DNAPL penetration into fractured porous media. Ground Water, 37(1), 140-147. [https://doi.org/10.1111/j.1745-6584.1999.tb00967.x doi: 10.1111/j.1745-6584.1999.tb00967.x]</ref><ref>Esposito, S.J. and Thomson, N.R., 1999. Two-phase flow and transport in a single fracture-porous medium system. Journal of Contaminant Hydrology, 37(3), 319-341. [http://dx.doi.org/10.1016/S0169-7722(98)00169-7 doi: 10.1016/S0169-7722(98)00169-7]</ref><ref>Lipson, D.S., Kueper, B.H. and Gefell, M.J., 2005. Matrix Diffusion‐Derived Plume Attenuation in Fractured Bedrock. Ground Water, 43(1), 30-39. [https://doi.org/10.1111/j.1745-6584.2005.tb02283.x doi: 10.1111/j.1745-6584.2005.tb02283.x]</ref><ref>O'Hara, S.K., Parker, B.L., Jorgensen, P.R. and Cherry, J.A., 2000. Trichloroethene DNAPL flow and mass distribution in naturally fractured clay: Evidence of aperture variability. Water Resources Research, 36(1), 135-147. [https://doi.org/10.1029/1999wr900212 doi: 10.1029/1999WR900212]</ref><ref>Reynolds, D.A. and Kueper, B.H., 2001. Multiphase flow and transport in fractured clay/sand sequences. Journal of Contaminant Hydrology, 51(1), 41-62. [http://dx.doi.org/10.1016/S0169-7722(01)00121-8 doi: 10.1016/S0169-7722(01)00121-8]</ref><ref>Reynolds, D.A. and Kueper, B.H., 2002. Numerical examination of the factors controlling DNAPL migration through a single fracture. Ground Water, 40(4), 368-377. [https://doi.org/10.1111/j.1745-6584.2002.tb02515.x doi:10.1111/j.1745-6584.2002.tb02515.x]</ref><ref>Reynolds, D.A. and Kueper, B.H., 2004. Multiphase flow and transport through fractured heterogeneous porous media. Journal of Contaminant Hydrology, 71(1), 89-110. [http://dx.doi.org/10.1016/j.jconhyd.2003.09.008 doi: 10.1016/j.jconhyd.2003.09.008]</ref><ref>Liu, C. and Ball, W.P., 2002. Back diffusion of chlorinated solvent contaminants from a natural aquitard to a remediated aquifer under well‐controlled field conditions: Predictions and measurements. Ground Water, 40(2), 175-184. [https://doi.org/10.1111/j.1745-6584.2002.tb02502.x doi: 10.1111/j.1745-6584.2002.tb02502.x]</ref><ref name= "Parker2004" /><ref name= "Chapman2005">Chapman, S.W. and Parker, B.L., 2005. Plume persistence due to aquitard back diffusion following dense nonaqueous phase liquid source removal or isolation. Water Resources Research, 41(12). [http://dx.doi.org/10.1029/2005wr004224 doi:10.1029/2005WR004224]</ref><ref>Parker, B.L., Chapman, S.W. and Guilbeault, M.A., 2008. Plume persistence caused by back diffusion from thin clay layers in a sand aquifer following TCE source-zone hydraulic isolation. Journal of Contaminant Hydrology, 102(1), 86-104. [http://dx.doi.org/10.1016/j.jconhyd.2008.07.003 doi: 10.1016/j.jconhyd.2008.07.003]</ref><ref name= "Sale2008">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), 72-85. [http://dx.doi.org/10.1016/j.jconhyd.2008.08.002 doi: 10.1016/j.jconhyd.2008.08.002]</ref>. This process may occur in any heterogeneous setting, but it is particularly important in certain fractured bedrock sites, and in sites with extensive clay lenses or layers. These types of complex site conditions tend to lead to plumes that are long lived, requiring extensive long-term monitoring. Matrix diffusion is explained in a 2013 SERDP Report<ref>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. ER-1740. Environmental Security Technology Certification Program (ESTCP) by Colorado State University Fort Collins Department of Civil and Environmental Engineering. [https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-1740 ER-1740]</ref>.
 Both numerical and analytical modeling approaches have been used to simulate matrix diffusion. Examples of the numerical approach can be found in Chapman and Parker (2005)<ref name= "Chapman2005" />, Chapman et al. (2012)<ref name= "Chapman2012">Chapman, S.W., Parker, B.L., Sale, T.C. and 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, 106-116. [http://dx.doi.org/10.1016/j.jconhyd.2012.04.006 doi: 10.1016/j.jconhyd.2012.04.006]</ref>, and Chapman and Parker (2013)<ref>Chapman, SW and. Parker, B.L., 2013. Chapter 5: Type site simulations, in Sale, T., B.L. Parker, C.J. Newell, and J.F. Devlin, Management of contaminants stored in low permeability zones, SERDP Project ER-1740, 348 p. [https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-1740 ER-1740]</ref>. These publications describe high-resolution 2D simulations that capture the plume matrix diffusion process. But a key constraint with using numerical models to simulate matrix diffusion is that very high resolution modeling grids or mesh networks are required. For example, Chapman and Parker (2012)<ref name= "Chapman2012" /> used 9,000 cells in MT3D to simulate matrix diffusion in a small-scale research tank experiment 1.1 meters long and 0.84 meters high. In practice, conventional numerical transport models may need many thin layers just a few centimeters thick to accurately simulate plumes affected by matrix diffusion (e.g., see Rasa et al., (2011)<ref>Rasa, E., Chapman, S.W., Bekins, B.A., Fogg, G.E., Scow, K.M. and Mackay, D.M., 2011. Role of back diffusion and biodegradation reactions in sustaining an MTBE/TBA plume in alluvial media. Journal of Contaminant Hydrology, 126(3), 235-247. [http://dx.doi.org/10.1016/j.jconhyd.2011.08.006 doi: 10.1016/j.jconhyd.2011.08.006]</ref>).
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 *Parallel fracture models<ref>Sudicky, E.A. and Frind, E.O., 1982. Contaminant transport in fractured porous media: Analytical solutions for a system of parallel fractures. Water Resources Research, 18(6), 1634-1642. [https://doi.org/10.1029/wr018i006p01634 doi: 10.1029/WR018i006p01634]</ref><ref>West, M.R., Kueper, B.H. and Novakowski, K.S., 2004. Semi-analytical solutions for solute transport in fractured porous media using a strip source of finite width. Advances in Water Resources, 27(11), 1045-1059. [http://dx.doi.org/10.1016/j.advwatres.2004.08.011 doi: 10.1016/j.advwatres.2004.08.011]</ref>
 *Aquifer-aquitard models<ref name= "Sale2008" /><ref name= "Seyedabbasi2012">Seyedabbasi, M.A., Newell, C.J., Adamson, D.T. and Sale, T.C., 2012. Relative contribution of DNAPL dissolution and matrix diffusion to the long-term persistence of chlorinated solvent source zones. Journal of Contaminant Hydrology, 134, 69-81. [https://doi.org/10.1016/j.jconhyd.2012.03.010  doi: 10.1016/j.jconhyd.2012.03.010]</ref>
 The parallel fracture models consider advection, dispersion, retardation, and decay in the fracture, with diffusion, retardation, and decay in the matrix. The two-layer model by Sale et al. (2008)<ref name= "Sale2008" /> considers advection, dispersion, retardation and decay in the aquifer with diffusion, retardation, and decay in an underlying aquitard. Finally, the Sale et al. (2008)<ref name= "Sale2008" /> and Seyedabbasi et al. (2012)<ref name= "Seyedabbasi2012" /> models are included in the [https://www.serdp-estcp.org/Tools-and-Training/Environmental-Restoration/Groundwater-Plume-Treatment/Matrix-Diffusion-Tool-Kit ESTCP Matrix Diffusion Toolkit]<ref>Farhat, S.K., Newell, C.J., Seyedabbasi, M.A., McDade, J.M., Mahler, N.T., Sale, T.C., Dandy, D.S. and Wahlberg, J.J., 2012. Matrix Diffusion Toolkit. ER-201126. Environmental Security Technology Certification Program (ESTCP) by GSI Environmental Inc., Houston, Texas. [https://www.serdp-estcp.org/Tools-and-Training/Environmental-Restoration/Groundwater-Plume-Treatment/Matrix-Diffusion-Tool-Kit ER-201126]</ref>. An enhanced version of the REMChlor model with a matrix diffusion term in the plume (it can already represent matrix diffusion in the source using the gamma source term) called REMChlor-MD is expected to be publically available in 2017.
 ==Summary==

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