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Advection and Groundwater Flow
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==Matrix Diffusion==
 
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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 [[wikipedia:Molecular diffusion | 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 potentially even centuries after the primary sources have been addressed<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), Report W12411.  [https://doi.org/10.1029/2005WR004224 DOI: 10.1029/2005WR004224] [[Media:Chapman2005.pdf | Report.pdf]] Free access article from [https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2005WR004224 American Geophysical Union]</ref>. Field and laboratory results have illustrated the importance of this processAnalytical and numerical modeling tools are available for evaluating matrix diffusion.
Groundwater migrates from areas of higher [[wikipedia: Hydraulic head | hydraulic head]] (a measure of pressure and gravitational energy) toward lower hydraulic head, transporting dissolved solutes through the combined processes of [[wikipedia: Advection | advection]] and [[wikipedia: Dispersion | dispersion]]. Advection refers to the bulk movement of solutes carried by flowing groundwater. Dispersion refers to the spreading of the contaminant plume from highly concentrated areas to less concentrated areasIn many groundwater transport models, solute transport is described by the advection-dispersion-reaction equation.
 
 
 
 
<div style="float:right;margin:0 0 2em 2em;">__TOC__</div>
 
<div style="float:right;margin:0 0 2em 2em;">__TOC__</div>
  
 
'''Related Article(s):'''
 
'''Related Article(s):'''
*[[Dispersion and Diffusion]]
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*[[Sorption of Organic Contaminants]]
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*[[Groundwater Flow and Solute Transport]]
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*[[REMChlor - MD]]
 
*[[Plume Response Modeling]]
 
*[[Plume Response Modeling]]
  
'''CONTRIBUTOR(S):'''  
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'''CONTRIBUTOR(S):''' [[Dr. Charles Newell, P.E.|Dr. Charles Newell]] and  [[Dr. Robert Borden, P.E.|Dr. Robert Borden]]
*[[Dr. Charles Newell, P.E.]]
 
*[[Dr. Robert Borden, P.E.]]
 
  
 
'''Key Resource(s):'''
 
'''Key Resource(s):'''
*[http://hydrogeologistswithoutborders.org/wordpress/1979-english/ Groundwater]<ref name="FandC1979">Freeze, A., and Cherry, J., 1979. Groundwater, Prentice-Hall, Englewood Cliffs, New Jersey, 604 pages. Free download from [http://hydrogeologistswithoutborders.org/wordpress/1979-english/ Hydrogeologists Without Borders].</ref>, Freeze and Cherry, 1979.
 
*[https://gw-project.org/books/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow/ Hydrogeologic Properties of Earth Materials and Principals of Groundwater Flow]<ref name="Woessner2020">Woessner, W.W., and Poeter, E.P., 2020. Properties of Earth Materials and Principals of Groundwater Flow, The Groundwater Project, Guelph, Ontario, 207 pages. Free download from [https://gw-project.org/books/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow/ The Groundwater Project].</ref>, Woessner and Poeter, 2020.
 
  
==Groundwater Flow==
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*[https://www.serdp-estcp.org/content/download/23838/240653/file/ER-1740 Management of Contaminants Stored in Low Permeability Zones – A State of the Science Review]<ref name="Sale2013">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. [[Media: Sale2013ER-1740.pdf | Report.pdf]] Website: [https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-1740 ER-1740]</ref>
[[File:Newell-Article 1-Fig1r.JPG|thumbnail|left|400px|Figure 1. Hydraulic gradient (typically described in units of m/m or ft/ft) is the difference in hydraulic head from Point A to Point B (ΔH) divided by the distance between them (ΔL). In unconfined aquifers, the hydraulic gradient can also be described as the slope of the water table (Adapted from course notes developed by Dr. R.J. Mitchell, Western Washington University).]]
 
Groundwater flows from areas of higher [[wikipedia: Hydraulic head | hydraulic head]] toward areas of lower hydraulic head (Figure 1). The rate of change (slope) of the hydraulic head is known as the hydraulic gradient. If groundwater is flowing and contains dissolved contaminants it can transport the contaminants from areas with high hydraulic head toward lower hydraulic head zones, or “downgradient”.
 
  
==Darcy's Law==
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==Introduction==  
{| class="wikitable" style="float:right; margin-left:10px;text-align:center;"
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[[File:NewellMatrixDiffFig1.PNG | thumb |500px| Figure 1.  Diffusion of a dissolved solute (chlorinated solvent) into lower ''K'' zones during loading period, followed by diffusion back out into higher ''K'' zones once the source is removed <ref name="Sale2007">Sale, T.C., Illangasekare, T.H., Zimbron, J., Rodriguez, D., Wilking, B., and Marinelli, F., 2007. AFCEE Source Zone Initiative. Air Force Center for Environmental Excellence, Brooks City-Base, San Antonio, TX. [https://www.enviro.wiki/images/0/08/AFCEE-2007-Sale.pdf Report.pdf]</ref>]]
|+ Table 1.  Representative values of total porosity (''n''), effective porosity (''n<sub>e</sub>''), and hydraulic conductivity (''K'') for different aquifer materials<ref name="D&S1997">Domenico, P.A. and Schwartz, F.W., 1997. Physical and Chemical Hydrogeology, 2nd Ed. John Wiley & Sons, 528 pgs. ISBN 978-0-471-59762-9.  Available from: [https://www.wiley.com/en-us/Physical+and+Chemical+Hydrogeology%2C+2nd+Edition-p-9780471597629 Wiley]</ref><ref>McWhorter, D.B. and Sunada, D.K., 1977. Ground-water hydrology and hydraulics. Water Resources Publications, LLC, Highlands Ranch, Colorado, 304 pgs. ISBN-13: 978-1-887201-61-2 Available from: [https://www.wrpllc.com/books/gwhh.html Water Resources Publications]</ref><ref name="FandC1979"/>
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Matrix Diffusion can have major impacts on solute migration in groundwater and on cleanup time following source removalAs a groundwater plume advances downgradient, dissolved contaminants are transported by [[Wikipedia: Molecular diffusion | 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.
|-
 
! Aquifer Material
 
! Total Porosity<br/><small>(dimensionless)</small>
 
! Effective Porosity<br/><small>(dimensionless)</small>
 
! Hydraulic Conductivity<br/><small>(meters/second)</small>
 
|-
 
| colspan="4" style="text-align: left; background-color:white;"|'''Unconsolidated'''
 
|-
 
| Gravel || 0.25 — 0.44 || 0.13 — 0.44 || 3×10<sup>-4</sup> — 3×10<sup>-2</sup>
 
|-
 
| Coarse Sand || 0.31 — 0.46 || 0.18 — 0.43 || 9×10<sup>-7</sup> — 6×10<sup>-3</sup>
 
|-
 
| Medium Sand || — || 0.16 — 0.46 ||  9×10<sup>-7</sup> — 5×10<sup>-4</sup>
 
|-
 
| Fine Sand || 0.25 — 0.53 || 0.01 — 0.46 ||  2×10<sup>-7</sup> — 2×10<sup>-4</sup>
 
|-
 
| Silt, Loess || 0.35 — 0.50 || 0.01 — 0.39 ||  1×10<sup>-9</sup> — 2×10<sup>-5</sup>
 
|-
 
| Clay || 0.40 — 0.70 || 0.01 — 0.18 ||  1×10<sup>-11</sup> — 4.7×10<sup>-9</sup>
 
|-
 
| colspan="4" style="text-align: left; background-color:white;"|'''Sedimentary and Crystalline Rocks'''
 
|-
 
| Karst and Reef Limestone || 0.05 — 0.50 || — ||  1×10<sup>-6</sup> — 2×10<sup>-2</sup>
 
|-
 
| Limestone, Dolomite || 0.00 — 0.20 || 0.01 — 0.24 ||  1×10<sup>-9</sup> — 6×10<sup>-6</sup>
 
|-
 
| Sandstone || 0.05 — 0.30 || 0.10 — 0.30 ||  3×10<sup>-10</sup> — 6×10<sup>-6</sup>
 
|-
 
| Siltstone || — || 0.21 — 0.41 ||  1×10<sup>-11</sup> — 1.4×10<sup>-8</sup>
 
|-
 
| Basalt || 0.05 — 0.50 || — ||  2×10<sup>-11</sup> — 2×10<sup>-2</sup>
 
|-
 
| Fractured Crystalline Rock || 0.00 — 0.10 || — ||  8×10<sup>-9</sup> — 3×10<sup>-4</sup>
 
|-
 
| Weathered Granite || 0.34 — 0.57 || — || 3.3×10<sup>-6</sup> — 5.2×10<sup>-5</sup>
 
|-
 
| Unfractured Crystalline Rock || 0.00 — 0.05 || — ||  3×10<sup>-14</sup> — 2×10<sup>-10</sup>
 
|}
 
In&nbsp;unconsolidated&nbsp;geologic settings (gravel, sand, silt, and clay) and highly fractured systems, the rate of groundwater movement can be expressed using [[wikipedia: Darcy's law | Darcy’s Law]]. This law is a fundamental mathematical relationship in the groundwater field and can be expressed this way:
 
 
 
[[File:Newell-Article 1-Equation 1rr.jpg|center|500px]]
 
::Where:
 
:::''Q'' = Flow rate (Volume of groundwater flow per time, such as m<sup>3</sup>/yr)
 
:::''A'' = Cross sectional area perpendicular to groundwater flow (length<sup>2</sup>, such as m<sup>2</sup>)
 
:::''V<sub>D</sub>'' = “Darcy Velocity”; describes groundwater flow as the volume of flow through a unit of cross-sectional area (units of length per time, such as ft/yr)
 
:::''K'' = Hydraulic Conductivity (sometimes called “permeability”) (length per time)
 
:::''ΔH'' = Difference in hydraulic head between two lateral points (length)
 
:::''ΔL'' = Distance between two lateral points (length)
 
 
 
[https://en.wikipedia.org/wiki/Hydraulic_conductivity Hydraulic conductivity] (Table 1 and Figure 2) is a measure of how easily groundwater flows through a porous medium, or alternatively, how much energy it takes to force water through a porous medium. For example, fine sand has smaller pores with more frictional resistance to flow, and therefore lower hydraulic conductivity compared to coarse sand, which has larger pores with less resistance to flow (Figure 2).  
 
  
[[File:AdvectionFig2.PNG|400px|thumbnail|left|Figure 2. Hydraulic conductivity of selected rocks<ref>Heath, R.C., 1983. Basic ground-water hydrology, U.S. Geological Survey Water-Supply Paper 2220, 86 pgs. [[Media:Heath-1983-Basic_groundwater_hydrology_water_supply_paper.pdf|Report pdf]]</ref>.]]
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The impacts of back diffusion on aquifer cleanup have been examined in controlled laboratory experiments by several investigators<ref name="Doner2008">Doner, L.A., 2008. Tools to resolve water quality benefits of upgradient contaminant flux reduction. Master’s Thesis, Department of Civil and Environmental Engineering, Colorado State University.</ref><ref name="Yang2015">Yang, M., Annable, M.D. and Jawitz, J.W., 2015. Back Diffusion from Thin Low Permeability Zones. Environmental Science and Technology, 49(1), pp. 415-422.  [https://doi.org/10.1021/es5045634 DOI: 10.1021/es5045634] Free download available from: [https://www.researchgate.net/publication/269189924_Back_Diffusion_from_Thin_Low_Permeability_Zones ResearchGate]</ref><ref name= "Yang2016">Yang, M., Annable, M.D. and Jawitz, J.W., 2016. Solute source depletion control of forward and back diffusion through low-permeability zones. Journal of Contaminant Hydrology, 193, pp. 54-62. [https://doi.org/10.1016/j.jconhyd.2016.09.004 DOI: 10.1016/j.jconhyd.2016.09.004] Free download available from: [https://www.researchgate.net/profile/Minjune_Yang/publication/308004091_Solute_source_depletion_control_of_forward_and_back_diffusion_through_low-permeability_zones/links/5a2ed2c44585155b6179f489/Solute-source-depletion-control-of-forward-and-back-diffusion-through-low-permeability-zones.pdf ResearchGate]</ref><ref name="Tatti2018">Tatti, F., Papini, M.P., Sappa, G., Raboni, M., Arjmand, F., and Viotti, P., 2018. Contaminant back-diffusion from low-permeability layers as affected by groundwater velocity: A laboratory investigation by box model and image analysis. Science of The Total Environment, 622, pp. 164-171. [https://doi.org/10.1016/j.scitotenv.2017.11.347 DOI: 10.1016/j.scitotenv.2017.11.347]</ref>.  The video in Figure 2 shows the results of a 122-day tracer test in a laboratory flow cell (sand tank)<ref name="Doner2008"/>.  The flow cell contained several clay zones (''K'' = 10<sup>-8</sup> cm/s) surrounded by sand (''K'' = 0.02 cm/s).  During the loading period, water containing a green fluorescent tracer migrated from left to right with the water flowing through the flow cell, while also 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.
Darcy’s Law was first described by Henry Darcy (1856)<ref>Brown, G.O., 2002. Henry Darcy and the making of a law. Water Resources Research, 38(7), p. 1106. [https://doi.org/10.1029/2001wr000727 DOI: 10.1029/2001WR000727] [[Media:Darcy2002.pdf | Report.pdf]]</ref> in a report regarding a water supply system he designed for the city of Dijon, France. Based on his experiments, he concluded that the amount of water flowing through a closed tube of sand (dark grey box in Figure 3) depends on (a) the change in the hydraulic head between the inlet and outlet of the tube, and (b) the hydraulic conductivity of the sand in the tube. Groundwater flows rapidly in the case of higher pressure (ΔH) or more permeable materials such as gravel or coarse sand, but flows slowly when the pressure is lower or the material is less permeable, such as fine sand or silt.
 
  
[[File:Newell-Article 1-Fig3..JPG|500px|thumbnail|right|Figure 3. Conceptual explanation of Darcy’s Law based on Darcy’s experiment (Adapted from course notes developed by Dr. R.J. Mitchell, Western Washington University).]]
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[[File: GreenTank.mp4 | thumb |500px| Figure 2. Video of dye tank simulation of matrix diffusion]]
Since Darcy’s time, Darcy’s Law has been adapted to calculate the actual velocity that the groundwater is moving in units such as meters traveled per year. This quantity is called “interstitial velocity” or “seepage velocity” and is calculated by dividing the Darcy Velocity (flow per unit area) by the actual open pore area where groundwater is flowing, the “effective porosity”&nbsp;(Table 1):
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In some cases, matrix diffusion can maintain contaminant concentrations in more permeable zones above target cleanup goals for decades or potentially even centuries after the primary sources have been addressed. At a site impacted by [[Wikipedia: Dense non-aqueous phase liquid | Dense Non-Aqueous Phase Liquids (DNAPL)]], [[Chlorinated Solvents | 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<ref name="Chapman2005"/>.
  
[[File:Newell-Article 1-Equation 2r.jpg|400px]]
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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.<ref name="Sudicky1985"> Sudicky, E.A., Gillham, R.W., and Frind, E.O., 1985. Experimental Investigation of Solute Transport in Stratified Porous Media: 1. The Nonreactive Case. Water Resources Research, 21(7), pp. 1035-1041. [https://doi.org/10.1029/WR021i007p01035 DOI: 10.1029/WR021i007p01035]</ref> 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 [[Metal and Metalloid Contaminants | heavy metals]] and [[Perfluoroalkyl and Polyfluoroalkyl Substances (PFAS)]].
:Where:
 
::''V<sub>S</sub>'' = “interstitial velocity” or “seepage velocity” (units of length per time, such as m/sec)<br />
 
::''V<sub>D</sub>'' = “Darcy Velocity”; describes groundwater flow as the volume of flow per unit area (units of length per time)<br />
 
::''n<sub>e</sub>'' = Effective porosity (unitless)
 
  
Effective porosity is smaller than total porosity. The difference is that total porosity includes some dead-end pores that do not support groundwater. Typically values for total and effective porosity are&nbsp;shown&nbsp;in&nbsp;Table&nbsp;1.
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==SERPD/ESTCP Research==
 
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{|  
[[File:Newell-Article 1-Fig4.JPG|500px|thumbnail|left|Figure 4.  Difference between Darcy Velocity (also called Specific Discharge) and Seepage Velocity (also called Interstitial Velocity).]]
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The SERDP/ESTCP programs have funded several projects focusing on how matrix diffusion can impede progress towards reaching site closure, including:
 
 
==Darcy Velocity and Seepage Velocity==
 
In groundwater calculations, Darcy Velocity and Seepage Velocity are used for different purposes. For any calculation where the actual flow rate in units of volume per time (such as liters per day or gallons per minute) is involved, then the original Darcy Equation should be used (calculate V<sub>D</sub>; Equation 1) without using effective porosity. When calculating solute travel time, then the seepage velocity calculation (V<sub>S</sub>; Equation 2) must be used and an estimate of effective porosity is required. Figure 4 illustrates the differences between Darcy Velocity and Seepage Velocity.
 
 
 
==Mobile Porosity==
 
{| class="wikitable" style="float:right; margin-left:10px; text-align:center;"
 
|+ Table 2.  Mobile porosity estimates from 15 tracer tests<ref name="Payne2008">Payne, F.C., Quinnan, J.A. and Potter, S.T., 2008. Remediation Hydraulics. CRC Press. ISBN 9780849372490  Available from: [https://www.routledge.com/Remediation-Hydraulics/Payne-Quinnan-Potter/p/book/9780849372490 CRC Press]</ref>
 
|-
 
! Aquifer Material
 
! Mobile Porosity<br/><small>(volume fraction)</small>
 
|-
 
| Poorly sorted sand and gravel || 0.085
 
|-
 
| Poorly sorted sand and gravel || 0.04 — 0.07
 
|-
 
| Poorly sorted sand and gravel || 0.09
 
|-
 
| Fractured sandstone || 0.001 — 0.007
 
|-
 
| Alluvial formation || 0.102
 
|-
 
| Glacial outwash || 0.145
 
|-
 
| Weathered mudstone regolith || 0.07 — 0.10
 
|-
 
| Alluvial formation || 0.07
 
|-
 
| Alluvial formation || 0.07
 
|-
 
| Silty sand || 0.05
 
|-
 
| Fractured sandstone || 0.0008 — 0.001
 
 
|-
 
|-
| Alluvium, sand and gravel || 0.017
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|
 +
*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-1740 SERDP Management of Contaminants Stored in Low Permeability Zones, A State-of-the-Science Review] <ref name="Sale2013"/>
 
|-
 
|-
| Alluvium, poorly sorted sand and gravel || 0.003 — 0.017
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|  
 +
*[https://www.serdp-estcp.org/Tools-and-Training/Environmental-Restoration/Groundwater-Plume-Treatment/Matrix-Diffusion-Tool-Kit ESTCP Matrix Diffusion Toolkit]<ref name="Farhat2012">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. Environmental Security Technology Certification Program (ESTCP) Project ER-201126.  [[Media:Farhat2012ER-201126UsersManual.pdf | User’s Manual.pdf]]  Website: [https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-201126 ER-201126]</ref>
 
|-
 
|-
| Alluvium, sand and gravel || 0.11 — 0.18
+
|  
 +
*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-200530 ESTCP Decision Guide]<ref>Sale, T. and Newell, C., 2011. A Guide for Selecting Remedies for Subsurface Releases of Chlorinated Solvents. Environmental Security Technology Certification Program (ESTCP) Project ER-200530. [[Media: Sale2011ER-200530.pdf | Report.pdf]]  Website: [https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-200530 ER-200530]</ref>
 
|-
 
|-
| Siltstone, sandstone, mudstone || 0.01 — 0.05
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|
 +
*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-201426 ESTCP REMChlor-MD: the USEPA’s REMChlor model with a new matrix diffusion term for the plume]<ref name="Farhat2018">Farhat, S. K., Newell, C. J., Falta, R. W., and Lynch, K., 2018. A Practical Approach for Modeling Matrix Diffusion Effects in REMChlor. Environmental Security Technology Certification Program (ESTCP) Project ER-201426.  [https://enviro.wiki/images/0/0b/2018-Falta-REMChlor_Modeling_Matrix_Diffusion_Effects.pdf  User’s Manual.pdf]  Website: [https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-201426 ER-201426]</ref>
 
|}
 
|}
 +
[[File:ADRFig3.png | thumb| left |400px| Figure 3.  Comparison of tracer breakthrough (upper graph) and cleanup curves (lower graph) from advection-dispersion based (gray lines) and advection-diffusion based (black lines) solute transport<ref name="ITRC2011">Interstate Technology and Regulatory Council (ITRC), 2011. Integrated DNAPL Site Strategy (IDSS-1),  Integrated DNAPL Site Strategy Team, ITRC, Washington, DC. [https://www.enviro.wiki/images/d/d9/ITRC-2011-Integrated_DNAPL.pdf Report.pdf]  Free download from: [https://itrcweb.org/GuidanceDocuments/IntegratedDNAPLStrategy_IDSSDoc/IDSS-1.pdf ITRC]</ref>.]]
  
Payne&nbsp;et&nbsp;al.&nbsp;(2009)&nbsp;reported the results from multiple short-term tracer tests conducted to aid the design of amendment injection systems<ref name="Payne2008"/>. In these tests, the dissolved solutes were observed to migrate more rapidly through the aquifer than could be explained with typically reported values of n<sub>e</sub>. They concluded that the heterogeneity of unconsolidated formations results in a relatively small area of an aquifer cross section carrying most of the water, and therefore solutes migrate more rapidly than expected. Based on these results, they recommend that a quantity called “mobile porosity” should be used in place of ''n<sub>e</sub>'' in equation 2 for calculating solute transport velocities. Based on 15 different tracer tests, typical values of mobile porosity range from 0.02 to 0.10 (Table 2).   
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==Transport Modeling==
 
+
Several different modeling approaches have been developed to simulate the diffusive transport of dissolved solutes into and out of lower ''K'' zones<ref>Falta, R.W., and Wang, W., 2017. A semi-analytical method for simulating matrix diffusion in numerical transport models. Journal of Contaminant Hydrology, 197, pp. 39-49.  [https://doi.org/10.1016/j.jconhyd.2016.12.007 DOI: 10.1016/j.jconhyd.2016.12.007]</ref><ref>Muskus, N. and Falta, R.W., 2018. Semi-analytical method for matrix diffusion in heterogeneous and fractured systems with parent-daughter reactions. Journal of Contaminant Hydrology, 218, pp. 94-109.  [https://doi.org/10.1016/j.jconhyd.2018.10.002 DOI: 10.1016/j.jconhyd.2018.10.002]</ref>The [https://www.serdp-estcp.org/Tools-and-Training/Environmental-Restoration/Groundwater-Plume-Treatment/Matrix-Diffusion-Tool-Kit 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://en.wikipedia.org/wiki/MODFLOW MODFLOW]/[https://xmswiki.com/wiki/GMS:MT3DMS 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://xmswiki.com/wiki/GMS:MT3DMS MT3DMS website]</ref> have been shown to be effective in simulating back diffusion processes 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>.
A data mining analysis of 43 sites in California by Kulkarni et al. (2020) showed that on average 90% of the groundwater flow occurred in about 30% of cross sectional area perpendicular to groundwater flow. These data provided “moderate (but not confirmatory) support for the&nbsp;mobile&nbsp;porosity&nbsp;concept.”<ref name="Kulkarni2020">Kulkarni, P.R., Godwin, W.R., Long, J.A., Newell, R.C., Newell, C.J., 2020. How much heterogeneity? Flow versus area from a big data perspective. Remediation 30(2), pp. 15-23. [https://doi.org/10.1002/rem.21639 DOI: 10.1002/rem.21639]  [[Media:Kulkarni2020.pdf | Report.pdf]]</ref>
 
<br clear="right"/>
 
 
 
==Advection-Dispersion-Reaction Equation for Solute Transport==
 
The transport of dissolved solutes in groundwater is often modeled using the Advection-Dispersion-Reaction (ADR) equation. [[wikipedia:Advection|Advection]] refers to the bulk movement of solutes carried by flowing groundwater. [[wikipedia:Dispersion|Dispersion]] refers to the spreading of the contaminant plume from highly concentrated areas to less concentrated areas. Dispersion coefficients are calculated as the sum of [[wikipedia:Molecular diffusion | molecular diffusion]] mechanical dispersion, and macrodispersion. Reaction refers to changes in mass of the solute within the system resulting from biotic and abiotic processes.
 
 
 
'''Related Article(s):'''
 
*[[Advection and Groundwater Flow]]
 
*[[Dispersion and Diffusion]]
 
*[[Sorption of Organic Contaminants]]
 
*[[Plume Response Modeling]]
 
 
 
'''CONTRIBUTOR(S):'''
 
*[[Dr. Charles Newell, P.E.]]
 
*[[Dr. Robert Borden, P.E.]]
 
 
 
'''Key Resource(s):'''
 
 
 
==The ADR Equation==
 
In many groundwater transport models, solute transport is described by the advection-dispersion-reaction equation. As shown below (Equation 3), the ADR equation describes the change in dissolved solute concentration (''C'') over time (''t'') where groundwater flow is oriented along the ''x'' direction.
 
  
[[File:AdvectionEq3r.PNG|center|650px]]
+
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<ref name="Farhat2018"/>.
:Where:
 
::''R''  is the linear, equilibrium retardation factor (see [[Sorption of Organic Contaminants]]), 
 
::''D<sub>x</sub>, D<sub>y</sub>, and D<sub>z</sub>''  are hydrodynamic dispersion coefficients in the ''x, y'' and ''z'' directions (L<sup>2</sup>/T),
 
::''v''  is the advective transport or seepage velocity in the ''x'' direction (L/T), and
 
::''λ''  is an effective first order decay rate due to combined biotic and abiotic processes (1/T).
 
[[File:AdvectionFig5.png | thumb | right | 300px | Figure 5. Curves of concentration versus distance (a) and concentration versus time (b) generated by solving the ADR equation for a continuous source of a non-reactive tracer with ''R'' = 1, λ = 0, ''v'' = 5 m/yr, and ''D<sub>x</sub>'' = 10 m<sup>2</sup>/yr.]]
 
The term on the left side of the equation is the rate of mass change per unit volume.  On the right side are terms representing the solute flux due to dispersion in the ''x, y'', and ''z'' directions, the advective flux in the ''x'' direction, and the first order decay due to biotic and abiotic processes. Dispersion coefficients (''D<sub>x,y,z</sub>'') are commonly estimated using the following relationships:
 
  
[[File:AdvectionEq4.PNG|center|350px]]
+
==Impacts on Breakthrough Curves==
:Where:
 
::''D<sub>m</sub>''  is the molecular diffusion coefficient (L<sup>2</sup>/T), and
 
::''&alpha;<sub>L</sub>, &alpha;<sub>T</sub>'', and ''&alpha;<sub>V</sub>''  are the longitudinal, transverse and vertical dispersivities (L).
 
Figures 5a and 5b were generated using a numerical solution of the ADR equation for a non-reactive tracer (''R'' = 1; λ = 0) with ''v'' = 5 m/yr and ''D<sub>x</sub>'' = 10 m<sup>2</sup>/yr. 
 
Figure 5a shows the predicted change in concentration of the tracer, chloride, versus distance downgradient from the continuous contaminant source at different times (0, 1, 2, and 4 years).  Figure 5b shows the change in concentration versus time (commonly referred to as the breakthrough curve or BTC) at different downgradient distances (10, 20, 30 and 40 m).  At 2 years, the mid-point of the concentration versus distance curve (Figure 5a) is located 10 m downgradient (x = 5 m/yr * 2 yr).  At 20 m downgradient, the mid-point of the concentration versus time curves (Figure 5b) occurs at 4 years (t = 20 m / 5 m/yr).
 
  
The dispersion coefficient in the ADR equation accounts for the combined effects of molecular diffusion and mechanical dispersion which cause the spreading of the contaminant plume from highly concentrated areas to less concentrated areas. [[wikipedia:Molecular diffusion | Molecular diffusion]] is the result of the thermal motion of individual molecules which causes a flux of dissolved solutes from areas of higher concentration to areas of lower concentration.  Mechanical dispersion (hydrodynamic dispersion) results from groundwater moving at rates that vary from the average linear velocity. Because the invading solute-containing water does not travel at the same velocity everywhere, mixing occurs along flow paths. Typical values of the mechanical dispersivity measured in laboratory column tests are on the order of 0.01 to 1 cm (Anderson and Cherry, 1979).
+
The impacts of matrix diffusion on the initial breakthrough of the solute plume and on later cleanup are illustrated in Figure 3<ref name="ITRC2011"/>. Using a traditional advection-dispersion model, the breakthrough curve for a pulse tracer injection appears as a bell-shaped ([[wikipedia:Gaussian function |Gaussian]]) curve (gray line on the right side of the upper graph) where the peak arrival time corresponds to the average groundwater velocity. Using an advection-diffusion approach, the breakthrough curve for a pulse injection is asymmetric (solid black line) with the peak tracer concentration arriving earlier than would be expected based on the average groundwater velocity, but with a long extended tail to the flushout curve.
  
Matrix Diffusion is the process where dissolved contaminants are transported into low K zones by molecular diffusion, and then can diffuse back out of these low K zones once the contaminant source is removedIn 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 (Chapman and Parker 2005). Methods for evaluating the impact of matrix diffusion are addressed in a separate article
+
The lower graph shows the predicted cleanup concentration profiles following complete elimination of a source area.  The advection-dispersion model (gray line) predicts a clean-water front arriving at a time corresponding to the average groundwater velocityThe advection-diffusion model (black line) predicts that concentrations will start to decline more rapidly than expected (based on the average groundwater velocity) as clean water rapidly migrates through the highest-permeability strata. However, low but significant contaminant concentrations linger much longer (tailing) due to diffusive contaminant mass exchange between zones of high and low permeability. A similar response to source remediation is seen in models such as the sand tank experiment shown in Figure 2, and also in field observations of plume contaminant concentrations in heterogeneous aquifers.
  
Spatial variations in hydraulic conductivity can increase the apparent spreading of solute plumes observed in groundwater monitoring wells. This spreading of the solute caused by large-scale heterogeneities in the aquifer and associated spatial variations in advective transport velocity is referred to as macrodispersion. In some groundwater modeling projects, large values of dispersivity are used as an adjustment factor to help match the apparent large-scale spreading of the plume (ITRC, 2015). Theoretical studies (Gelhar et al. 1979; Gelhar and Axness,1983; Dagan 1988) suggest that macrodispersivity will increase with distance near the source, and then increase more slowly further downgradient, eventually reaching an asymptotic value.  Figure 10 shows values of macrodispersivity calculated using the theory of Dagan (1986) with an autocorrelation length of 3 m and several different values of the variance of Y (σ2Y) where Y= Log K. The calculated macrodispersivity increases more rapidly and reaches higher asymptotic values for more heterogeneous aquifers with greater variations in K (larger σ2Y).  The maximum predicted dispersivity values are in the range of 0.5 to 5 m.
+
<br clear="left" />
 
 
The ADR equation can be solved to find the spatial and temporal distribution of solutes using a variety of analytical and numerical approaches.  The design tools [https://www.epa.gov/water-research/bioscreen-natural-attenuation-decision-support-system BIOSCREEN]<ref name="Newell1996">Newell, C.J., McLeod, R.K. and Gonzales, J.R., 1996. BIOSCREEN: Natural Attenuation Decision Support System - User's Manual, Version 1.3. US Environmental Protection Agency, EPA/600/R-96/087. [https://www.enviro.wiki/index.php?title=File:Newell-1996-Bioscreen_Natural_Attenuation_Decision_Support_System.pdf Report.pdf]  [https://www.epa.gov/water-research/bioscreen-natural-attenuation-decision-support-system BIOSCREEN website]</ref>, [https://www.epa.gov/water-research/biochlor-natural-attenuation-decision-support-system BIOCHLOR]<ref name="Aziz2000">Aziz, C.E., Newell, C.J., Gonzales, J.R., Haas, P.E., Clement, T.P. and Sun, Y., 2000. BIOCHLOR Natural Attenuation Decision Support System. User’s Manual - Version 1.0. US Environmental Protection Agency, EPA/600/R-00/008.  [https://www.enviro.wiki/index.php?title=File:Aziz-2000-BIOCHLOR-Natural_Attenuation_Dec_Support.pdf Report.pdf]  [https://www.epa.gov/water-research/biochlor-natural-attenuation-decision-support-system BIOCHLOR website]</ref>, and [https://www.epa.gov/water-research/remediation-evaluation-model-chlorinated-solvents-remchlor REMChlor]<ref name="Falta2007">Falta, R.W., Stacy, M.B., Ahsanuzzaman, A.N.M., Wang, M. and Earle, R.C., 2007. REMChlor Remediation Evaluation Model for Chlorinated Solvents - User’s Manual, Version 1.0. US Environmental Protection Agency. Center for Subsurface Modeling Support, Ada, OK.  [[Media:REMChlorUserManual.pdf | Report.pdf]]  [https://www.epa.gov/water-research/remediation-evaluation-model-chlorinated-solvents-remchlor REMChlor website]</ref> employ an analytical solution of the ADR equation.  [https://www.usgs.gov/software/mt3d-usgs-groundwater-solute-transport-simulator-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. [[Media:Mt3dmanual.pdf | Report.pdf]]  [https://www.usgs.gov/software/mt3d-usgs-groundwater-solute-transport-simulator-modflow MT3DMS website]</ref> uses a numerical method to solve the ADR equation using the head distribution generated by the groundwater flow model MODFLOW<ref name="McDonald1988">McDonald, M.G. and Harbaugh, A.W., 1988. A Modular Three-dimensional Finite-difference Ground-water Flow Model, Techniques of Water-Resources Investigations, Book 6, Modeling Techniques. U.S. Geological Survey, 586 pages. [https://doi.org/10.3133/twri06A1  DOI: 10.3133/twri06A1]  [[Media: McDonald1988.pdf | Report.pdf]]  Free MODFLOW download from: [https://www.usgs.gov/mission-areas/water-resources/science/modflow-and-related-programs?qt-science_center_objects=0#qt-science_center_objects USGS]</ref>.
 
  
 
==References==
 
==References==
  
<references/>
+
<references />
  
 
==See Also==
 
==See Also==
*[http://iwmi.dhigroup.com/solute_transport/advection.html International Water Management Institute Animations]
+
 
*[http://www2.nau.edu/~doetqp-p/courses/env303a/lec32/lec32.htm NAU Lecture Notes on Advective Transport]
+
*[http://www.gsi-net.com/en/publications/useful-groundwater-resources/colorado-state-matrix-diffusion-video.html Matrix Diffusion Movie]
*[https://www.youtube.com/watch?v=00btLB6u6DY MIT Open CourseWare Solute Transport: Advection with Dispersion Video]
+
*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-1737 Impact of Clay-DNAPL Interactions on Transport and Storage of Chlorinated Solvents in Low Permeability Zones]
*[https://www.youtube.com/watch?v=AtJyKiA1vcY Physical Groundwater Model Video]
+
*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-200320 Prediction of Groundwater Quality Improvement Down-Gradient of ''In Situ'' Permeable Treatment Barriers and Fully Remediated Source Zones]
*[https://www.coursera.org/learn/natural-attenuation-of-groundwater-contaminants/lecture/UzS8q/groundwater-flow-review Online Lecture Course - Groundwater Flow]
+
*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Persistent-Contamination/ER-201032 Determining Source Attenuation History to Support Closure by Natural Attenuation]
 +
*[https://www.coursera.org/learn/natural-attenuation-of-groundwater-contaminants/lecture/2R7yh/matrix-diffusion-principles Coursera Matrix Diffusion Online Lecture]

Latest revision as of 14:37, 28 December 2020

Matrix Diffusion

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 potentially even centuries after the primary sources have been addressed[1]. Field and laboratory results have illustrated the importance of this process. Analytical and numerical modeling tools are available for evaluating matrix diffusion.

Related Article(s):

CONTRIBUTOR(S): Dr. Charles Newell and Dr. Robert Borden

Key Resource(s):

Introduction

Figure 1. Diffusion of a dissolved solute (chlorinated solvent) into lower K zones during loading period, followed by diffusion back out into higher K zones once the source is removed [3]

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[4][5][6][7]. The video in Figure 2 shows the results of a 122-day tracer test in a laboratory flow cell (sand tank)[4]. 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 migrated from left to right with the water flowing through the flow cell, while also 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.

Figure 2. Video of dye tank simulation of matrix diffusion

In some cases, matrix diffusion can maintain contaminant concentrations in more permeable zones above target cleanup goals for decades or potentially 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[1].

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.”[8] 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 Perfluoroalkyl and Polyfluoroalkyl Substances (PFAS).

SERPD/ESTCP Research

The SERDP/ESTCP programs have funded several projects focusing on how matrix diffusion can impede progress towards reaching site closure, including:
Figure 3. Comparison of tracer breakthrough (upper graph) and cleanup curves (lower graph) from advection-dispersion based (gray lines) and advection-diffusion based (black lines) solute transport[12].

Transport Modeling

Several different modeling approaches have been developed to simulate the diffusive transport of dissolved solutes into and out of lower K zones[13][14]. The Matrix Diffusion Toolkit[9] is a Microsoft Excel based tool for simulating forward and back diffusion using two different analytical models[15][16]. Numerical models including MODFLOW/MT3DMS[17] have been shown to be effective in simulating back diffusion processes and can accurately predict concentration changes over 3 orders-of-magnitude in heterogeneous sand tank experiments[18]. However, numerical models require a fine vertical discretization with short time steps to accurately simulate back diffusion, greatly increasing computation times[19]. These issues can be addressed by incorporating a local 1-D model domain within a general 3D numerical model[20].

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[11].

Impacts on Breakthrough Curves

The impacts of matrix diffusion on the initial breakthrough of the solute plume and on later cleanup are illustrated in Figure 3[12]. Using a traditional advection-dispersion model, the breakthrough curve for a pulse tracer injection appears as a bell-shaped (Gaussian) curve (gray line on the right side of the upper graph) where the peak arrival time corresponds to the average groundwater velocity. Using an advection-diffusion approach, the breakthrough curve for a pulse injection is asymmetric (solid black line) with the peak tracer concentration arriving earlier than would be expected based on the average groundwater velocity, but with a long extended tail to the flushout curve.

The lower graph shows the predicted cleanup concentration profiles following complete elimination of a source area. The advection-dispersion model (gray line) predicts a clean-water front arriving at a time corresponding to the average groundwater velocity. The advection-diffusion model (black line) predicts that concentrations will start to decline more rapidly than expected (based on the average groundwater velocity) as clean water rapidly migrates through the highest-permeability strata. However, low but significant contaminant concentrations linger much longer (tailing) due to diffusive contaminant mass exchange between zones of high and low permeability. A similar response to source remediation is seen in models such as the sand tank experiment shown in Figure 2, and also in field observations of plume contaminant concentrations in heterogeneous aquifers.


References

  1. ^ 1.0 1.1 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), Report W12411. DOI: 10.1029/2005WR004224 Report.pdf Free access article from American Geophysical Union
  2. ^ 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
  3. ^ Sale, T.C., Illangasekare, T.H., Zimbron, J., Rodriguez, D., Wilking, B., and Marinelli, F., 2007. AFCEE Source Zone Initiative. Air Force Center for Environmental Excellence, Brooks City-Base, San Antonio, TX. Report.pdf
  4. ^ 4.0 4.1 Doner, L.A., 2008. Tools to resolve water quality benefits of upgradient contaminant flux reduction. Master’s Thesis, Department of Civil and Environmental Engineering, Colorado State University.
  5. ^ Yang, M., Annable, M.D. and Jawitz, J.W., 2015. Back Diffusion from Thin Low Permeability Zones. Environmental Science and Technology, 49(1), pp. 415-422. DOI: 10.1021/es5045634 Free download available from: ResearchGate
  6. ^ Yang, M., Annable, M.D. and Jawitz, J.W., 2016. Solute source depletion control of forward and back diffusion through low-permeability zones. Journal of Contaminant Hydrology, 193, pp. 54-62. DOI: 10.1016/j.jconhyd.2016.09.004 Free download available from: ResearchGate
  7. ^ Tatti, F., Papini, M.P., Sappa, G., Raboni, M., Arjmand, F., and Viotti, P., 2018. Contaminant back-diffusion from low-permeability layers as affected by groundwater velocity: A laboratory investigation by box model and image analysis. Science of The Total Environment, 622, pp. 164-171. DOI: 10.1016/j.scitotenv.2017.11.347
  8. ^ Sudicky, E.A., Gillham, R.W., and Frind, E.O., 1985. Experimental Investigation of Solute Transport in Stratified Porous Media: 1. The Nonreactive Case. Water Resources Research, 21(7), pp. 1035-1041. DOI: 10.1029/WR021i007p01035
  9. ^ 9.0 9.1 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. Environmental Security Technology Certification Program (ESTCP) Project ER-201126. User’s Manual.pdf Website: ER-201126
  10. ^ Sale, T. and Newell, C., 2011. A Guide for Selecting Remedies for Subsurface Releases of Chlorinated Solvents. Environmental Security Technology Certification Program (ESTCP) Project ER-200530. Report.pdf Website: ER-200530
  11. ^ 11.0 11.1 Farhat, S. K., Newell, C. J., Falta, R. W., and Lynch, K., 2018. A Practical Approach for Modeling Matrix Diffusion Effects in REMChlor. Environmental Security Technology Certification Program (ESTCP) Project ER-201426. User’s Manual.pdf Website: ER-201426
  12. ^ 12.0 12.1 Interstate Technology and Regulatory Council (ITRC), 2011. Integrated DNAPL Site Strategy (IDSS-1), Integrated DNAPL Site Strategy Team, ITRC, Washington, DC. Report.pdf Free download from: ITRC
  13. ^ Falta, R.W., and Wang, W., 2017. A semi-analytical method for simulating matrix diffusion in numerical transport models. Journal of Contaminant Hydrology, 197, pp. 39-49. DOI: 10.1016/j.jconhyd.2016.12.007
  14. ^ Muskus, N. and Falta, R.W., 2018. Semi-analytical method for matrix diffusion in heterogeneous and fractured systems with parent-daughter reactions. Journal of Contaminant Hydrology, 218, pp. 94-109. DOI: 10.1016/j.jconhyd.2018.10.002
  15. ^ 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. DOI: 10.1111/j.1745-6584.1994.tb00922.x
  16. ^ 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. DOI: 10.1016/j.jconhyd.2008.08.002
  17. ^ 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. User’s Guide.pdf MT3DMS website
  18. ^ 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
  19. ^ 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. DOI: 10.1111/gwmr.12373
  20. ^ 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. DOI: 10.1002/rem.21440

See Also