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Groundwater migrates from areas of higher [[wikipedia: Hydraulic head | hydraulic head]] 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 areas. In many groundwater transport models, solute transport is described by the advection-dispersion-reaction equation in which dispersion coefficients can be calculated as the sum of molecular diffusion, mechanical dispersion, and macrodispersion.
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==Thermal In Situ Sustainable Remediation to Enhance Biotic and Abiotic Reactions and Accelerate Remediation Timeframes==
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Thermal In Situ Sustainable Remediation (TISR<sup>®</sup>; US Pat. Nos. 10,384,246 and 10,688,545) is a cost-effective and adaptable low temperature thermal remediation technology that accelerates contaminant treatment. It achieves this by enhancing biotic and abiotic contaminant degradation rates through a modest increase in subsurface temperature. TISR<sup>®</sup> is suitable for a wide range of hydrogeologic settings. It also offers reduced operational costs, a lower carbon footprint, and possibly shorter remedial timeframes than more conventional methods.
 
<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):'''
  
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*[[Dispersion and Diffusion]]
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*[[Thermal Remediation]]
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*[[Sorption of Organic Contaminants]]
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*[[Thermal Remediation - Electrical Resistance Heating | Electrical Resistance Heating]]
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*[[Plume Response Modeling]]
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*[[Thermal Conduction Heating (TCH)]]
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*[[Matrix Diffusion]]
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*[[Thermal Remediation - Combined Remedies | Combined Remedies]]
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'''CONTRIBUTOR(S):''' [[Dr. Charles Newell, P.E.|Dr. Charles Newell]] and  [[Dr. Robert Borden, P.E.|Dr. Robert Borden]]
 
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'''Key Resource(s):'''
 
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*[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.
 
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*[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.
 
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==Groundwater Flow==
 
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[[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).]]
 
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Groundwater flows from areas of higher [[wikipedia: Hydraulic head | hydraulic head]] (a measure of pressure and gravitational energy) 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 by advection from areas with high hydraulic head toward lower hydraulic head zones, or “downgradient”.
 
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===Darcy's Law===
 
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{| class="wikitable" style="float:right; margin-left:10px;text-align:center;"
 
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|+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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|-
 
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!Aquifer Material
 
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!Total Porosity<br /><small>(dimensionless)</small>
 
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!Effective Porosity<br /><small>(dimensionless)</small>
 
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!Hydraulic Conductivity<br /><small>(meters/second)</small>
 
−
|-
 
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| colspan="4" style="text-align: left; background-color:white;" |'''Unconsolidated'''
 
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|-
 
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|Gravel||0.25 - 0.44||0.13 - 0.44||3×10<sup>-4</sup> - 3×10<sup>-2</sup>
 
−
|-
 
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|Coarse Sand||0.31 - 0.46||0.18 - 0.43||9×10<sup>-7</sup> - 6×10<sup>-3</sup>
 
−
|-
 
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|Medium Sand||—||0.16 - 0.46||9×10<sup>-7</sup> - 5×10<sup>-4</sup>
 
−
|-
 
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|Fine Sand||0.25 - 0.53||0.01 - 0.46||2×10<sup>-7</sup> - 2×10<sup>-4</sup>
 
−
|-
 
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|Silt, Loess||0.35 - 0.50||0.01 - 0.39||1×10<sup>-9</sup> - 2×10<sup>-5</sup>
 
−
|-
 
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|Clay||0.40 - 0.70||0.01 - 0.18||1×10<sup>-11</sup> - 4.7×10<sup>-9</sup>
 
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|-
 
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| colspan="4" style="text-align: left; background-color:white;" |'''Sedimentary and Crystalline Rocks'''
 
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|-
 
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|Karst and Reef Limestone||0.05 - 0.50||—||1×10<sup>-6</sup> - 2×10<sup>-2</sup>
 
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|-
 
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|Limestone, Dolomite||0.00 - 0.20||0.01 - 0.24||1×10<sup>-9</sup> - 6×10<sup>-6</sup>
 
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|-
 
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|Sandstone||0.05 - 0.30||0.10 - 0.30||3×10<sup>-10</sup> - 6×10<sup>-6</sup>
 
−
|-
 
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|Siltstone||—||0.21 - 0.41||1×10<sup>-11</sup> - 1.4×10<sup>-8</sup>
 
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|-
 
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|Basalt||0.05 - 0.50||—||2×10<sup>-11</sup> - 2×10<sup>-2</sup>
 
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|-
 
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|Fractured Crystalline Rock||0.00 - 0.10||—||8×10<sup>-9</sup> - 3×10<sup>-4</sup>
 
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|-
 
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|Weathered Granite||0.34 - 0.57||—||3.3×10<sup>-6</sup> - 5.2×10<sup>-5</sup>
 
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|-
 
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|Unfractured Crystalline Rock||0.00 - 0.05||—||3×10<sup>-14</sup> - 2×10<sup>-10</sup>
 
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|}
 
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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:
 
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[[File:Newell-Article 1-Equation 1rr.jpg|center|500px]]
 
  
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::Where:
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'''Contributors:''' Jonah Munholland, Julia Vidonish, and Craig Divine
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:::''Q'' = Flow rate (Volume of groundwater flow per time, such as m<sup>3</sup>/yr)
 
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:::''A'' = Cross sectional area perpendicular to groundwater flow (length<sup>2</sup>, such as m<sup>2</sup>)
 
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:::''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)
 
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:::''K'' = Hydraulic Conductivity (sometimes called “permeability”) (length per time)
 
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:::''ΔH'' = Difference in hydraulic head between two lateral points (length)
 
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:::''ΔL'' = Distance between two lateral points (length)
 
  
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[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).  
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'''Key Resources:'''
 +
*Thermal In Situ Sustainable Remediation to Enhance Biotic and Abiotic Reactions and Accelerate Remediation Timeframes, Final Report. ESTCP Project ER20-5028<ref>Divine, C., Munholland, J., Zardouzian, E., Justicia-Leon, S., Aspinall, J.V., Randhawa, D., Falta, R., Freedman, D., Becker, M., 2025. Thermal In Situ Sustainable Remediation to Enhance Biotic and Abiotic Reactions and Accelerate Remediation Timeframes, Final Report. Environmental Security Technology Certification Program (ESTCP), Project ER20-5028. [https://serdp-estcp.mil/projects/details/bab4bc87-b4bc-42df-ad0e-11ea0adf27dc/er20-5028-project-overview Project Website]&nbsp; [[Media: ER20-5028 FR DevineEtAl2025.pdf | Final Report.pdf]]</ref>.
  
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[[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. [//www.enviro.wiki/images/c/c4/Heath-1983-Basic_groundwater_hydrology_water_supply_paper.pdf Report pdf]</ref>.]]
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*Advances in Low-Temperature Thermal Remediation. Munholland ''et al.'', 2024<ref name="MunhollandEtAl2024">Munholland, J, Rosso, D., Randhawa, D., Devine, C., Pennington, A., 2024. Advances in Low-Temperature Thermal Remediation. In: García-Rincón, J., Gatsios, E., Lenhard, R.J., Atekwana, E.A., Naidu, R. (eds), Advances in the Characterisation and Remediation of Sites Contaminated with Petroleum Hydrocarbons, Chapter 18 pp. 623-653. Environmental Contamination Remediation and Management series, Springer Nature. [https://doi.org/10.1007/978-3-031-34447-3_18 doi: 10.1007/978-3-031-34447-3_18]&nbsp; [[Media: MunhollandEtAl2024.pdf | Open Access Chapter]]</ref>.  
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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] [//www.enviro.wiki/images/4/40/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 (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 difference is lower or the material is less permeable, such as fine sand or silt.
 
  
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[[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).]]
+
*A Design Tool for Solar Thermal Remediation Using Borehole Heat Exchangers. Ornelles, Falta, and Divine, 2023<ref name="Ornelles">Ornelles, A.D., Falta, R.W., Divine, C.E., 2023. A Design Tool for Solar Thermal Remediation Using Borehole Heat Exchangers. Ground Water, 61(2), pp. 245-254. [https://doi.org/10.1111/gwat.13265 doi: 10.1111/gwat.13265]&nbsp; [https://ngwa.onlinelibrary.wiley.com/doi/epdf/10.1111/gwat.13265 Free download from NGWA]</ref>.
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Since&nbsp;Darcy’s&nbsp;time,&nbsp;Darcy’s Law has been extended to develop a useful variation of Darcy's formula that calculates 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):
 
  
−
[[File:Newell-Article 1-Equation 2r.jpg|400px]]
+
*Low-Temperature Thermal Remediation: Gaining Traction as a Green Remedial Alternative. Horst, ''et al.'', 2018<ref name="HorstEtAl2018">Horst, J., Flanders, C., Klemmer, M., Randhawa, D.S., Rosso, D., 2018. Low-Temperature Thermal Remediation: Gaining Traction as a Green Remedial Alternative. Groundwater Monitoring and Remediation, 38(3), pp. 18-27. [https://doi.org/10.1111/gwmr.12295 doi: 10.1111/gwmr.12295]</ref>.
  
−
:Where:
+
==Introduction==
−
::''V<sub>S</sub>'' = “interstitial velocity” or “seepage velocity” (units of length per time, such as m/sec)<br />
+
[[File: MunhollandFig1.png | thumb | 500 px | Figure 1: Components and layout of a TISR<sup>®</sup> system]]
−
::''V<sub>D</sub>'' = “Darcy Velocity”; describes groundwater flow as the volume of flow per unit area per time (also units of length per time)<br />
+
TISR<sup>®</sup> utilizes [[Wikipedia: Downhole heat exchanger | borehole heat exchangers (BHEs)]] to heat target treatment areas in the subsurface. This is achieved through a combination of solar collectors, which harness solar radiation as heat, and the utilization of other heat sources such as waste heat or hybrid heating with heat pumps. That heat is then transferred to the subsurface via a closed loop circulation system connected to the BHEs (Figure 1). By incorporating these additional heat sources, TISR<sup>®</sup> ensures a more robust and constant heat supply, enabling customization of the system to address specific site challenges and facilitate efficient heat transfer.
−
::''n<sub>e</sub>'' = Effective porosity - fraction of cross section available for groundwater flow (unitless)
 
  
−
Effective porosity is smaller than total porosity. The difference is that total porosity includes some dead-end pores that do not support groundwater. Typical values for total and effective porosity are&nbsp;shown&nbsp;in&nbsp;Table&nbsp;1.
+
The heating of the subsurface through TISR<sup>®</sup> accelerates various processes such as biodegradation, abiotic reactions, and contaminant desorption and dissolution. The technology is also suitable for diverse hydrogeologic environments, including sites with low permeability zones, due to the relatively uniform thermal conductivity of geologic materials, which is unaffected by grain size<ref name="MunhollandEtAl2024"/>. This versatility allows TISR<sup>®</sup> to integrate with conventional remediation technologies, enhancing their performance.
  
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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).]]
+
One of the key advantages of TISR<sup>®</sup> is its ability to accelerate treatment processes while minimizing energy consumption. By harnessing renewable and sustainable energy sources such as solar radiation and effectively utilizing waste heat or hybrid heating with heat pumps, TISR<sup>®</sup> delivers an efficient, cost-effective remediation solution. Compatibility with multiple conventional remediation technologies makes it an effective option for addressing a variety of contamination challenges.
  
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===Darcy Velocity and Seepage Velocity===
+
==Scientific Principles==
−
In&nbsp;groundwater&nbsp;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, the original Darcy Equation should be used (calculate ''V<sub>D</sub>'', Equation 1) without using effective porosity. When calculating solute travel time however, 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&nbsp;Seepage&nbsp;Velocity.
+
[[File: MunhollandFig2.png | thumb | 500 px | Figure 2: Effect of temperature on hydrolysis rates for VOCs]]
 +
During the TISR<sup>®</sup> heating process, thermal conduction and advection play a crucial role in boosting physical, biological, and chemical processes within the treatment zones, leading to enhanced attenuation, degradation, and removal of contaminants from the subsurface<ref>Dettmer, K., 2002. A Discussion of the Effects of Thermal Remediation Treatments on Microbial Degradation Processes. U.S. Environmental Protection Agency, Office of Solid Waste and Emergency Response, Technology Innovation Office, Washington, DC. [[Media: dettmer2002.pdf | free report]]&nbsp; [https://www.clu-in.org/download/techdrct/dettmer.pdf free download from clu-in.org]</ref><ref name="HorstEtAl2018"/>. TISR<sup>®</sup> systems are typically designed to enhance the biological activity and performance of other active technologies, such as [[Wikipedia: Air sparging | air sparge]]/[[Soil Vapor Extraction (SVE) | soil vapor extraction]] (AS/SVE) or [[Chemical Oxidation (In Situ - ISCO) | chemical oxidation]], by increasing the subsurface temperature by approximately 10°C to 20°C. The target groundwater temperature is often set to reach up to about 35°C, which is the optimal temperature for promoting the activity of mesophilic microbial communities responsible for biodegradation of certain contaminants. In cases where the objective is to maximize abiotic hydrolysis mechanisms, such as for some chlorinated alkanes, TISR<sup>®</sup> systems can be designed to reach a final groundwater temperature of up to 60°C.
  
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===Mobile Porosity===
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The effectiveness of TISR<sup>®</sup> in enhancing treatment performance has been demonstrated through several mechanisms, which are discussed below:
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{| class="wikitable" style="float:right; margin-left:10px; text-align:center;"
 
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|+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>
 
−
|-
 
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!Aquifer Material
 
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!Mobile Porosity<br /><small>(volume fraction)</small>
 
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|-
 
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|Poorly sorted sand and gravel||0.085
 
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|-
 
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|Poorly sorted sand and gravel||0.04 - 0.07
 
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|-
 
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|Poorly sorted sand and gravel||0.09
 
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|-
 
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|Fractured sandstone||0.001 - 0.007
 
−
|-
 
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|Alluvial formation||0.102
 
−
|-
 
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|Glacial outwash||0.145
 
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|-
 
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|Weathered mudstone regolith||0.07 - 0.10
 
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|-
 
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|Alluvial formation||0.07
 
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|-
 
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|Alluvial formation||0.07
 
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|-
 
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|Silty sand||0.05
 
−
|-
 
−
|Fractured sandstone||0.0008 - 0.001
 
−
|-
 
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|Alluvium, sand and gravel||0.017
 
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|-
 
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|Alluvium, poorly sorted sand and gravel||0.003 - 0.017
 
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|-
 
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|Alluvium, sand and gravel||0.11 - 0.18
 
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|-
 
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|Siltstone, sandstone, mudstone||0.01 - 0.05
 
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|}
 
  
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Payne&nbsp;et&nbsp;al.&nbsp;(2008)&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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*Primary dechlorinating bacteria, such as [[Wikipedia: Dehalococcoides | Dehalococcoides]] and [[Wikipedia: Dehalogenimonas | Dehalogenimonas]], are known to be [[Wikipedia: Mesophile | mesophilic]]. Therefore, increasing the temperature can significantly enhance microbial activity and biodegradation by multiple orders of magnitude<ref>Macbeth, T., Truex, M., Powell, T., Michalsen, M., 2012. Combining Low-Energy Electrical Resistance Heating with Biotic and Abiotic Reactions for Treatment of Chlorinated Solvent DNAPL Source Areas. [https://serdp-estcp.mil/ Environmental Security Technology Certification Program (ESTCP)] [https://serdp-estcp.mil/projects/details/877a3b41-6bed-4f4a-b43a-87fbcd9b7f0b/er-200719-project-overview Project ER-200719 webpage]&nbsp; [[Media: Macbeth2012_ER-200719-FR.pdf | free download]]&nbsp; [https://www.youtube.com/watch?v=-EbwKbs8scE Project Summary Presentation]</ref>.
  
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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] [//www.enviro.wiki/images/9/9b/Kulkarni2020.pdf Report.pdf]</ref>
+
*Reduced iron minerals, particularly iron sulfides, can participate in the abiotic degradation of chlorinated ethenes and other contaminants. The rates of these reactions generally depend on temperature, following the [[Wikipedia: Arrhenius equation | Arrhenius equation]].
  
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==Advection-Dispersion-Reaction Equation==
+
*[[Wikipedia: Hydrolysis | Hydrolysis]] rates for certain compounds exhibit high temperature dependence. For example, a 10°C increase can lead to a 50% reduction in the half-life of [[Wikipedia: 1,1,1-Trichloroethane | 1,1,1-trichloroethane (1,1,1-TCA)]]<ref>Suthersan, S., Horst, J., Klemmer, M., Malone, D., 2012. Temperature-Activated Auto-Decomposition Reactions: An Under-Utilized In Situ Remediation Solution. Groundwater Monitoring and Remediation, 32(3), pp. 34-40. [https://doi.org/10.1111/j.1745-6592.2012.01407.x doi: 10.1111/j.1745-6592.2012.01407.x]</ref>. Figure 2 presents the calculated temperature-dependent hydrolysis rates for 13 common [[Wikipedia: Volatile organic compound | volatile organic compounds (VOCs)]] at a pH of 7.
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The transport of dissolved solutes in groundwater is often modeled using the Advection-Dispersion-Reaction (ADR) 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.
 
  
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{|
+
*[[Wikipedia: Henry's law | Henry's Law]] constant, [[Wikipedia: Vapor pressure | vapor pressure]], solubility, and viscosity values are also temperature dependent. For instance, the Henry's Law constant values for many VOCs, including [[Wikipedia: Tetrachloroethylene | tetrachloroethene (PCE)]], have been observed to double between 8 and 24°C<ref>Chen, F., Freedman, D.L., Falta, R.W., Murdoch, L.C., 2012. Henry's law constants of chlorinated solvents at elevated temperatures. Chemosphere, 86(2), pp.156-165. [https://doi.org/10.1016/j.chemosphere.2011.10.004 doi: 10.1016/j.chemosphere.2011.10.004]</ref>.
−
| || [[File:AdvectionEq3r.PNG|center|635px]]
 
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|-
 
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| Where: ||
 
−
|-
 
−
|
 
−
:''D<sub>x</sub>, D<sub>y</sub>, and D<sub>z</sub>''&nbsp;&nbsp;
 
−
| are hydrodynamic dispersion coefficients in the ''x, y'' and ''z'' directions (L<sup>2</sup>/T),  
 
−
|-
 
−
|
 
−
:''v''
 
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| 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).
 
−
|-
 
−
|
 
−
:''R''
 
−
| is the linear, equilibrium retardation factor (see [[Sorption of Organic Contaminants]]), 
 
−
|}
 
  
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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 (Equation 4):
+
*Rates of other processes that often limit the pace of remediation, such as dissolution, desorption, and [[Matrix Diffusion | back diffusion]], are positively correlated with temperature. This results in an enhanced bioavailability of contaminant mass that may otherwise be inaccessible.
  
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{|
+
These various mechanisms collectively contribute to the improved performance of other active treatments when temperature is moderately increased by utilization of TISR®.
−
| || [[File:AdvectionEq4.PNG|center|360px]]
 
−
|-
 
−
| 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>''&nbsp;&nbsp;
 
−
| are the longitudinal, transverse and vertical dispersivities (L), respectively.  
 
−
|}
 
  
−
===ADR Applications===
+
==Implementation and Practical Considerations==
−
[[File:AdvectionFig5.png | thumb | right | 350px | 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.]]
+
[[File: MunhollandFig3.png | thumb | 500 px | Figure 3: Transformation of 1,1-DCE and VC following installation of a TISR<sup>®</sup> system]]
−
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> (see also [[REMChlor - MD]]) 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>.
+
TISR<sup>®</sup> has proven successful in reducing contaminant concentrations across diverse hydrogeologic settings, including those with low and complex hydraulic conductivity conditions. Figure 3 shows a sharp initial decrease in [[Wikipedia: 1,1-Dichloroethylene | 1,1-dichloroethene (1,1-DCE)]] concentrations due to enhanced biodegradation, and then a temporary small increase followed by subsequent decreases in 1,1-DCE concentrations to below detection limits, possibly the result of temperature-enhanced desorption or dissolution of 1,1-DCE from the aquifer. There is also a temporary increase and then decrease in the concentrations of [[Wikipedia: Vinyl chloride | vinyl chloride (VC)]] (a biodegradation product) to very low levels.  
  
−
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 TISR<sup>®</sup> system construction utilizes off-the-shelf modular components, promoting cost-efficiency, reusability, and a reduced carbon footprint. Waste heat can supplement or replace the solar setup, and remote monitoring through dashboard apps reduces operation and maintenance costs. TISR® projects typically achieve an average capital cost payback within 1 to 3 years due to accelerated rates of remediation.
  
−
===Modeling Dispersion===
+
When implementing TISR<sup>®</sup>, [[Wikipedia: Solar irradiance | solar insolation]] and groundwater velocity must be considered for optimal equipment sizing and cycling. Depending on remedial goals and site history and conditions, the TISR<sup>®</sup> system and target temperatures may be designed to enhance specific remedial mechanisms (e.g. hydrolysis over bioremediation). Recently Ornelles ''et al.''<ref name="Ornelles"/> developed an easy to use Excel-based model that can be used to optimize TISR<sup>®</sup> design and predict subsurface temperature changes over time. Frequent monitoring of the temperature and microbial community composition relative to targets is useful for evaluating treatment effectiveness and optimizing system performance. The system and target temperatures can be customized to enhance specific remedial mechanisms based on site conditions and goals.  
−
Mechanical&nbsp;dispersion (hydrodynamic dispersion) results from groundwater moving at rates both greater and less than the average linear velocity. This is due to: 1) fluids moving faster through the center of the pores than along the edges, 2) fluids traveling shorter pathways and/or splitting or branching to the sides, and 3) fluids traveling faster through larger pores than through smaller pores<ref>Fetter, C.W., 1994. Applied Hydrogeology: Macmillan College Publishing Company. New York New York. ISBN-13:978-0130882394</ref>. Because the invading solute-containing water does not travel at the same velocity everywhere, mixing occurs along flow paths. This mixing is called mechanical dispersion and results in distribution of the solute at the advancing edge of flow. The mixing that occurs in the direction of flow is called longitudinal dispersion. Spreading normal to the direction of flow from splitting and branching out to the sides is called transverse dispersion (Figure 6). Typical values of the mechanical dispersivity measured in laboratory column tests are on the order of 0.01 to 1 cm<ref name="Anderson1979">Anderson, M.P. and Cherry, J.A., 1979. Using models to simulate the movement of contaminants through groundwater flow systems. Critical Reviews in Environmental Science and Technology, 9(2), pp.97-156.  [https://doi.org/10.1080/10643387909381669 DOI: 10.1080/10643387909381669]</ref>.
 
−
[[File:Fig2 dispanddiff.JPG|thumbnail|left|400px|Figure 6. Conceptual depiction of mechanical dispersion (adapted from ITRC (2011)<ref name="ITRC2011">ITRC Integrated DNAPL Site Strategy Team, 2011. Integrated DNAPL Site Strategy. Technical/Regulatory Guidance Document, 209 pgs. [//www.enviro.wiki/images/d/d9/ITRC-2011-Integrated_DNAPL.pdf Report pdf]</ref>).]]
 
  
−
The dispersion coefficient in the ADR equation accounts for the combined effects of mechanical dispersion and molecular diffusion, both of which cause spreading of the contaminant plume from highly concentrated areas toward 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.
+
==Summary==
−
 
+
TISR<sup>®</sup> is a cost-effective and adaptable technology that can be customized to address specific site challenges. It can be used as a standalone solution or be integrated with existing remediation strategies to enhance their effectiveness. TISR<sup>®</sup> is particularly effective in challenging hydrogeological conditions and can be optimized to suit specific treatment mechanisms. By shortening the active remediation timeframe, TISR<sup>®</sup> reduces lifecycle costs and minimizes the carbon footprint associated with the remediation process.
−
===Modeling Diffusion===
+
<br clear="right"/>
−
[[File:Fig1 dispanddiff.JPG|thumbnail|right|400px|Figure 7. Conceptual depiction of diffusion of a dissolved chemical recently placed in a container at Time 1 (left panel) and then distributed throughout the container (right panel) at Time 2.]]
 
−
[[wikipedia: Molecular diffusion | Molecular&nbsp;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 (Figure 7). The diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the concentration gradient and is a function of the temperature and molecular weight. In locations where advective flux is low (clayey aquitards and sedimentary rock), diffusion is often the dominant transport mechanism.
 
−
 
 
−
The&nbsp;diffusive&nbsp;flux&nbsp;''J'' (M/L<sup>2</sup>/T) in groundwater is calculated using [[wikipedia:Fick's laws of diffusion | Fick’s Law]]:
 
−
 
 
−
{|
 
−
|
 
−
|<big>'''''J&nbsp;=&nbsp;-D<sub>e</sub>&nbsp;dC/dx'''''</big>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(Equation&nbsp;5)
 
−
|-
 
−
|Where:||
 
−
|-
 
−
|
 
−
:''D<sub>e</sub>''
 
−
|is the effective diffusion coefficient and
 
−
|-
 
−
|
 
−
:''dC/dx''&nbsp;&nbsp;&nbsp;&nbsp;
 
−
|is the concentration gradient.
 
−
|}
 
−
The effective diffusion coefficient for transport through the porous media, ''D<sub>e</sub>, is estimated as:''
 
−
{|
 
−
|
 
−
|<big>'''''D<sub>e</sub>&nbsp;=&nbsp;D<sub>m</sub>&nbsp;n<sub>e</sub>&nbsp;&delta;/&Tau;'''''</big>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(Equation&nbsp;6)
 
−
|-
 
−
|Where:||
 
−
|-
 
−
|
 
−
:''D<sub>m</sub>''&nbsp;&nbsp;&nbsp;&nbsp;
 
−
|is the [[wikipedia:Mass diffusivity | diffusion coefficient]] of the solute in water,
 
−
|-
 
−
|
 
−
:''n<sub>e</sub>''
 
−
|is the effective porosity (dimensionless),
 
−
|-
 
−
|
 
−
:''&delta;''
 
−
|is the constrictivity (dimensionless) which reflects the restricted motion of particles in narrow pores<ref name="Grathwohl1998">Grathwohl, P., 1998. Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics. Kluwer Academic Publishers, Boston. DOI: 10.1007/978-1-4615-5683-1 Available from: [https://link.springer.com/book/10.1007/978-1-4615-5683-1 Springer.com]</ref>, and
 
−
|-
 
−
|
 
−
:''&Tau;''
 
−
|is the [[wikipedia:Tortuosity | tortuosity]] (dimensionless) which reflects the longer diffusion path in porous media around sediment particles<ref name="Carey2016">Carey, G.R., McBean, E.A. and Feenstra, S., 2016. Estimating Tortuosity Coefficients Based on Hydraulic Conductivity. Groundwater, 54(4), pp.476-487.  [https://doi.org/10.1111/gwat.12406 DOI:10.1111/gwat.12406] Available from: [https://ngwa.onlinelibrary.wiley.com/doi/abs/10.1111/gwat.12406 NGWA]</ref>.
 
−
|}
 
−
''D<sub>m</sub>'' is a function of the temperature, fluid viscosity and molecular weight.  Values of ''D<sub>m</sub>'' for common groundwater solutes are shown in Table 3.
 
−
 
 
−
{| class="wikitable" style="float:left; margin-right:20px; text-align:center;"
 
−
|+Table 3. Diffusion Coefficients (''D<sub>m</sub>'') for Common Groundwater Solutes.
 
−
|-
 
−
!Aqueous Diffusion Coefficient
 
−
!Temperature<br /><small>(&deg;C)</small>
 
−
!''D<sub>m</sub>''<br /><small>(cm<sup>2</sup>/s)</small>
 
−
!Reference
 
−
|-
 
−
|Acetone||25||&nbsp;&nbsp;1.16x10<sup>-5</sup>&nbsp;&nbsp;||Cussler 1997 <ref name="Cussler1997">Cussler, E.L., 1997. Diffusion: Mass Transfer in Fluid Systems, Cambridge University Press, New York, 580 pages.  ISBN: 9780521450782</ref>
 
−
|-
 
−
|Benzene||20||1.02x10<sup>-5</sup>||Bonoli and Witherspoon 1968 <ref name="Bonoli1968">Bonoli, L. and Witherspoon, P.A., 1968. Diffusion of Aromatic and Cycloparaffin Hydrocarbons in Water from 2 to 60 deg. The Journal of Physical Chemistry, 72(7), pp.2532-2534.  [https://doi.org/10.1021/j100853a045 DOI: 10.1021/j100853a045]</ref>
 
−
|-
 
−
|Carbon dioxide||25||1.92x10<sup>-5</sup>||Cussler 1997 <ref name="Cussler1997"/>
 
−
|-
 
−
|Carbon tetrachloride||25||9.55x10<sup>-6</sup>||Yaws 1995 <ref name="Yaws1995">Yaws, C.L., 1995. Handbook of Transport Property Data: Viscosity, Thermal Conductivity and Diffusion Coefficients of Liquids and Gases, Gulf Publishing Company, Houston, TX.  ISBN: 0884153924</ref>
 
−
|-
 
−
|Chloroform||25||1.08x10<sup>-5</sup>||Yaws 1995 <ref name="Yaws1995"/>
 
−
|-
 
−
|Dichloroethene||25||1.12x10<sup>-5</sup>||Yaws 1995 <ref name="Yaws1995"/>
 
−
|-
 
−
|1,4-Dioxane||25||1.02x10<sup>-5</sup>||Yaws 1995 <ref name="Yaws1995"/>
 
−
|-
 
−
|Ethane||25||1.52x10<sup>-5</sup>||Witherspoon and Saraf 1965 <ref name="Witherspoon1965">Witherspoon, P.A. and Saraf, D.N., 1965. Diffusion of Methane, Ethane, Propane, and n-Butane in Water from 25 to 43&deg;. The Journal of Physical Chemistry, 69(11), pp. 3752-3755.  [https://doi.org/10.1021/j100895a017 DOI: 10.1021/j100895a017]</ref>
 
−
|-
 
−
|Ethylbenzene||20||8.10x10<sup>-6</sup>||Bonoli and Witherspoon 1968 <ref name="Bonoli1968"/>
 
−
|-
 
−
|Ethene||25||1.87x10<sup>-5</sup>||Cussler 1997 <ref name="Cussler1997"/>
 
−
|-
 
−
|Helium||25||6.28x10<sup>-5</sup>||Cussler 1997 <ref name="Cussler1997"/>
 
−
|-
 
−
|Hydrogen||25||4.50x10<sup>-5</sup>||Cussler 1997 <ref name="Cussler1997"/>
 
−
|-
 
−
|Methane||25||1.88x10<sup>-5</sup>||Witherspoon and Saraf 1965 <ref name="Witherspoon1965"/>
 
−
|-
 
−
|Nitrogen||25||1.88x10<sup>-5</sup>||Cussler 1997 <ref name="Cussler1997"/>
 
−
|-
 
−
|Oxygen||25||2.10x10<sup>-5</sup>||Cussler 1997 <ref name="Cussler1997"/>
 
−
|-
 
−
|Perfluorooctanoic acid (PFOA)||20||4.80x10<sup>-6</sup>||Schaefer et al. 2019 <ref name="Schaefer2019">Schaefer, C.E., Drennan, D.M., Tran, D.N., Garcia, R., Christie, E., Higgins, C.P. and Field, J.A., 2019. Measurement of Aqueous Diffusivities for Perfluoroalkyl Acids. Journal of Environmental Engineering, 145(11).  [https://doi.org/10.1061/(ASCE)EE.1943-7870.0001585 DOI: 10.1061/(ASCE)EE.1943-7870.0001585]</ref>
 
−
|-
 
−
|Perfluorooctane sulfonic acid (PFOS)||20||5.40x10<sup>-6</sup>||Schaefer et al. 2019 <ref name="Schaefer2019"/>
 
−
|-
 
−
|Tetrachloroethene||25||8.99x10<sup>-6</sup>||Yaws 1995 <ref name="Yaws1995"/>
 
−
|-
 
−
|Toluene||20||8.50x10<sup>-6</sup>||Bonoli and Witherspoon 1968 <ref name="Bonoli1968"/>
 
−
|-
 
−
|Trichloroethene||25||8.16x10<sup>-6</sup>||Rossi et al. 2015 <ref name="Rossi2015">Rossi, F., Cucciniello, R., Intiso, A., Proto, A., Motta, O. and Marchettini, N., 2015. Determination of the Trichloroethylene Diffusion Coefficient in Water. American Institute of Chemical Engineers Journal, 61(10), pp.3511-3515.  [https://doi.org/10.1002/aic.14861 DOI: 10.1002/aic.14861]</ref>
 
−
|-
 
−
|Vinyl chloride||25||1.34x10<sup>-5</sup>||Yaws 1995 <ref name="Yaws1995"/>
 
−
|}
 
−
</br>
 
−
===Macrodispersion===
 
−
[[File:ADRFig2.PNG | thumb | right | 350px | Figure 8. Predicted variation in macrodispersivity with distance for varying ''σ<sup>2</sup>Y'' and correlation length = 3 m.]]
 
−
[[File:NewThinkingAboutDispersion.mp4 |thumbnail|right|500px|Figure 9. Matrix diffusion processes and their effects on plume persistence and attenuation.]]
 
−
Spatial variations in hydraulic conductivity can increase the apparent spreading of solute plumes observed in groundwater monitoring wells. For example, in an aquifer composed of alternating layers of lower hydraulic conductivity (''K'') silty sand and higher ''K'' sandy gravel layers, the dissolved solute rapidly migrates downgradient through the sandy gravel layers resulting in relatively high concentration fingers surrounded by relatively uncontaminated material. Over time, contaminants in lower ''K'' layers eventually breakthrough at the monitoring well, causing a more gradual further increase in measured concentrations.  This rapid breakthrough followed by gradual increases in solute concentrations gives the appearance of a plume with a very large dispersion coefficient. This spreading of the solute caused by large-scale heterogeneities in the aquifer and the associated spatial variations in advective transport velocity is referred to as macrodispersion.
 
−
 
 
−
In some groundwater modeling projects, large values of the dispersion coefficient are used as an adjustment factor to better represent the observed large-scale spreading of plumes<ref name="ITRC2011"/>. Theoretical studies suggest that macrodispersivity will increase with distance near the source, and then increase more slowly farther downgradient, eventually approaching an asymptotic value<ref name="Gelhar1979">Gelhar, L.W., Gutjahr, A.L. and Naff, R.L., 1979. Stochastic analysis of macrodispersion in a stratified aquifer. Water Resources Research, 15(6), pp.1387-1397.  [https://doi.org/10.1029/WR015i006p01387 DOI:10.1029/WR015i006p01387]</ref><ref name="Gelhar1983">Gelhar, L.W. and Axness, C.L., 1983. Three‐dimensional stochastic analysis of macrodispersion in aquifers. Water Resources Research, 19(1), pp.161-180.  [https://doi.org/10.1029/WR019i001p00161 DOI:10.1029/WR019i001p00161]</ref><ref name="Dagan1988">Dagan, G., 1988. Time‐dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers. Water Resources Research, 24(9), pp.1491-1500.  [https://doi.org/10.1029/WR024i009p01491 DOI:10.1029/WR024i009p01491]</ref>.  Figure 8 shows values of macrodispersivity calculated using the theory of Dagan<ref name="Dagan1988"/> with an autocorrelation length of 3 m and several different values of the variance of ''Y'' (σ<small><sup>2</sup><sub>''Y''</sub></small>) where ''Y'' = Log ''K''. The calculated macrodispersivity increases more rapidly and approaches higher asymptotic values for more heterogeneous aquifers with greater variations in ''K'' (larger σ<small><sup>2</sup><sub>''Y''</sub></small>).  The maximum predicted dispersivity values were in the range of 0.5 to 5 m.  Zech, et al. (2015)<ref>Zech, A., Attinger, S., Cvetkovic, V., Dagan, G., Dietrich, P., Fiori, A., Rubin, Y. and Teutsch, G., 2015. Is unique scaling of aquifer macrodispersivity supported by field data? Water Resources Research, 51(9), pp.7662-7679.  [https://doi.org/10.1002/2015WR017220 DOI: 10.1002/2015WR017220]&nbsp;&nbsp; Free access article from [https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1002/2015WR017220 American Geophysical Union]</ref> presented moderate and high reliability measurements of longitudinal macrodispersivity versus distance. Typical values of the longitudinal macrodispersivity varied from 0.1 to 10 m, with much lower values for transverse and vertical dispersivities.
 
−
 
 
−
===Matrix Diffusion===
 
−
Recently, an alternate conceptual model for describing large-scale plume spreading in heterogeneous soils has been proposed<ref name="ITRC2011" /><ref name="Payne2008"/><ref name="Hadley2014">Hadley, P.W. and Newell, C., 2014. The new potential for understanding groundwater contaminant transport. Groundwater, 52(2), pp.174-186. [http://dx.doi.org/10.1111/gwat.12135 doi:10.1111/gwat.12135]</ref>. In this approach, solute transport in the transmissive zones is reasonably well described by the advection-dispersion equation using relatively small dispersion coefficients representing mechanical dispersion. However, over time, molecular diffusion slowly transports solutes into lower permeability zones. As the transmissive zones are remediated, these solutes slowly diffuse back out, causing a long extended tail to the flushout curve. This process, referred to as [[Matrix Diffusion |matrix diffusion]], is controlled by [[wikipedia: Molecular diffusion | molecular diffusion]] and the presence of geologic heterogeneity with sharp contrasts between transmissive and low permeability media<ref>Sale, T.C., Illangasekare, T., Zimbron, J., Rodriguez, D., Wilkins, B. and Marinelli, F., 2007. AFCEE source zone initiative. Report Prepared for the Air Force Center for Environmental Excellence by Colorado State University and Colorado School of Mines. [//www.enviro.wiki/images/0/08/AFCEE-2007-Sale.pdf Report pdf]</ref> as discussed in the [//www.enviro.wiki/images/8/8a/NewThinkingAboutDispersion.mp4 video] shown in Figure 9. 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<ref>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): W12411.  [https://doi.org/10.1029/2005WR004224 DOI: 10.1029/2005WR004224] &nbsp;&nbsp; Free access article from [https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2005WR004224 American Geophysical Union]</ref>.  
 
−
<br clear="left" />
 
  
 
==References==
 
==References==
−
 
 
<references />
 
<references />
  
 
==See Also==
 
==See Also==
−
 
+
[https://vimeo.com/1019489395 TISR<sup>®</sup> Explanation Video]
−
*[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]
 
−
*[https://www.youtube.com/watch?v=00btLB6u6DY MIT Open CourseWare Solute Transport: Advection with Dispersion Video]
 
−
*[https://www.youtube.com/watch?v=AtJyKiA1vcY Physical Groundwater Model Video]
 
−
*[https://www.coursera.org/learn/natural-attenuation-of-groundwater-contaminants/lecture/UzS8q/groundwater-flow-review Online Lecture Course - Groundwater Flow]
 

Latest revision as of 19:44, 13 October 2026

Thermal In Situ Sustainable Remediation to Enhance Biotic and Abiotic Reactions and Accelerate Remediation Timeframes

Thermal In Situ Sustainable Remediation (TISR®; US Pat. Nos. 10,384,246 and 10,688,545) is a cost-effective and adaptable low temperature thermal remediation technology that accelerates contaminant treatment. It achieves this by enhancing biotic and abiotic contaminant degradation rates through a modest increase in subsurface temperature. TISR® is suitable for a wide range of hydrogeologic settings. It also offers reduced operational costs, a lower carbon footprint, and possibly shorter remedial timeframes than more conventional methods.

Related Article(s):

Contributors: Jonah Munholland, Julia Vidonish, and Craig Divine

Key Resources:

  • Thermal In Situ Sustainable Remediation to Enhance Biotic and Abiotic Reactions and Accelerate Remediation Timeframes, Final Report. ESTCP Project ER20-5028[1].
  • Advances in Low-Temperature Thermal Remediation. Munholland et al., 2024[2].
  • A Design Tool for Solar Thermal Remediation Using Borehole Heat Exchangers. Ornelles, Falta, and Divine, 2023[3].
  • Low-Temperature Thermal Remediation: Gaining Traction as a Green Remedial Alternative. Horst, et al., 2018[4].

Introduction

File:MunhollandFig1.png
Figure 1: Components and layout of a TISR® system

TISR® utilizes borehole heat exchangers (BHEs) to heat target treatment areas in the subsurface. This is achieved through a combination of solar collectors, which harness solar radiation as heat, and the utilization of other heat sources such as waste heat or hybrid heating with heat pumps. That heat is then transferred to the subsurface via a closed loop circulation system connected to the BHEs (Figure 1). By incorporating these additional heat sources, TISR® ensures a more robust and constant heat supply, enabling customization of the system to address specific site challenges and facilitate efficient heat transfer.

The heating of the subsurface through TISR® accelerates various processes such as biodegradation, abiotic reactions, and contaminant desorption and dissolution. The technology is also suitable for diverse hydrogeologic environments, including sites with low permeability zones, due to the relatively uniform thermal conductivity of geologic materials, which is unaffected by grain size[2]. This versatility allows TISR® to integrate with conventional remediation technologies, enhancing their performance.

One of the key advantages of TISR® is its ability to accelerate treatment processes while minimizing energy consumption. By harnessing renewable and sustainable energy sources such as solar radiation and effectively utilizing waste heat or hybrid heating with heat pumps, TISR® delivers an efficient, cost-effective remediation solution. Compatibility with multiple conventional remediation technologies makes it an effective option for addressing a variety of contamination challenges.

Scientific Principles

File:MunhollandFig2.png
Figure 2: Effect of temperature on hydrolysis rates for VOCs

During the TISR® heating process, thermal conduction and advection play a crucial role in boosting physical, biological, and chemical processes within the treatment zones, leading to enhanced attenuation, degradation, and removal of contaminants from the subsurface[5][4]. TISR® systems are typically designed to enhance the biological activity and performance of other active technologies, such as air sparge/ soil vapor extraction (AS/SVE) or chemical oxidation, by increasing the subsurface temperature by approximately 10°C to 20°C. The target groundwater temperature is often set to reach up to about 35°C, which is the optimal temperature for promoting the activity of mesophilic microbial communities responsible for biodegradation of certain contaminants. In cases where the objective is to maximize abiotic hydrolysis mechanisms, such as for some chlorinated alkanes, TISR® systems can be designed to reach a final groundwater temperature of up to 60°C.

The effectiveness of TISR® in enhancing treatment performance has been demonstrated through several mechanisms, which are discussed below:

  • Primary dechlorinating bacteria, such as Dehalococcoides and Dehalogenimonas, are known to be mesophilic. Therefore, increasing the temperature can significantly enhance microbial activity and biodegradation by multiple orders of magnitude[6].
  • Reduced iron minerals, particularly iron sulfides, can participate in the abiotic degradation of chlorinated ethenes and other contaminants. The rates of these reactions generally depend on temperature, following the Arrhenius equation.
  • Rates of other processes that often limit the pace of remediation, such as dissolution, desorption, and back diffusion, are positively correlated with temperature. This results in an enhanced bioavailability of contaminant mass that may otherwise be inaccessible.

These various mechanisms collectively contribute to the improved performance of other active treatments when temperature is moderately increased by utilization of TISR®.

Implementation and Practical Considerations

File:MunhollandFig3.png
Figure 3: Transformation of 1,1-DCE and VC following installation of a TISR® system

TISR® has proven successful in reducing contaminant concentrations across diverse hydrogeologic settings, including those with low and complex hydraulic conductivity conditions. Figure 3 shows a sharp initial decrease in 1,1-dichloroethene (1,1-DCE) concentrations due to enhanced biodegradation, and then a temporary small increase followed by subsequent decreases in 1,1-DCE concentrations to below detection limits, possibly the result of temperature-enhanced desorption or dissolution of 1,1-DCE from the aquifer. There is also a temporary increase and then decrease in the concentrations of vinyl chloride (VC) (a biodegradation product) to very low levels.

The TISR® system construction utilizes off-the-shelf modular components, promoting cost-efficiency, reusability, and a reduced carbon footprint. Waste heat can supplement or replace the solar setup, and remote monitoring through dashboard apps reduces operation and maintenance costs. TISR® projects typically achieve an average capital cost payback within 1 to 3 years due to accelerated rates of remediation.

When implementing TISR®, solar insolation and groundwater velocity must be considered for optimal equipment sizing and cycling. Depending on remedial goals and site history and conditions, the TISR® system and target temperatures may be designed to enhance specific remedial mechanisms (e.g. hydrolysis over bioremediation). Recently Ornelles et al.[3] developed an easy to use Excel-based model that can be used to optimize TISR® design and predict subsurface temperature changes over time. Frequent monitoring of the temperature and microbial community composition relative to targets is useful for evaluating treatment effectiveness and optimizing system performance. The system and target temperatures can be customized to enhance specific remedial mechanisms based on site conditions and goals.

Summary

TISR® is a cost-effective and adaptable technology that can be customized to address specific site challenges. It can be used as a standalone solution or be integrated with existing remediation strategies to enhance their effectiveness. TISR® is particularly effective in challenging hydrogeological conditions and can be optimized to suit specific treatment mechanisms. By shortening the active remediation timeframe, TISR® reduces lifecycle costs and minimizes the carbon footprint associated with the remediation process.

References

  1. ^ Divine, C., Munholland, J., Zardouzian, E., Justicia-Leon, S., Aspinall, J.V., Randhawa, D., Falta, R., Freedman, D., Becker, M., 2025. Thermal In Situ Sustainable Remediation to Enhance Biotic and Abiotic Reactions and Accelerate Remediation Timeframes, Final Report. Environmental Security Technology Certification Program (ESTCP), Project ER20-5028. Project Website  Final Report.pdf
  2. ^ 2.0 2.1 Munholland, J, Rosso, D., Randhawa, D., Devine, C., Pennington, A., 2024. Advances in Low-Temperature Thermal Remediation. In: García-Rincón, J., Gatsios, E., Lenhard, R.J., Atekwana, E.A., Naidu, R. (eds), Advances in the Characterisation and Remediation of Sites Contaminated with Petroleum Hydrocarbons, Chapter 18 pp. 623-653. Environmental Contamination Remediation and Management series, Springer Nature. doi: 10.1007/978-3-031-34447-3_18  Open Access Chapter
  3. ^ 3.0 3.1 Ornelles, A.D., Falta, R.W., Divine, C.E., 2023. A Design Tool for Solar Thermal Remediation Using Borehole Heat Exchangers. Ground Water, 61(2), pp. 245-254. doi: 10.1111/gwat.13265  Free download from NGWA
  4. ^ 4.0 4.1 Horst, J., Flanders, C., Klemmer, M., Randhawa, D.S., Rosso, D., 2018. Low-Temperature Thermal Remediation: Gaining Traction as a Green Remedial Alternative. Groundwater Monitoring and Remediation, 38(3), pp. 18-27. doi: 10.1111/gwmr.12295
  5. ^ Dettmer, K., 2002. A Discussion of the Effects of Thermal Remediation Treatments on Microbial Degradation Processes. U.S. Environmental Protection Agency, Office of Solid Waste and Emergency Response, Technology Innovation Office, Washington, DC. free report  free download from clu-in.org
  6. ^ Macbeth, T., Truex, M., Powell, T., Michalsen, M., 2012. Combining Low-Energy Electrical Resistance Heating with Biotic and Abiotic Reactions for Treatment of Chlorinated Solvent DNAPL Source Areas. Environmental Security Technology Certification Program (ESTCP) Project ER-200719 webpage  free download  Project Summary Presentation
  7. ^ Suthersan, S., Horst, J., Klemmer, M., Malone, D., 2012. Temperature-Activated Auto-Decomposition Reactions: An Under-Utilized In Situ Remediation Solution. Groundwater Monitoring and Remediation, 32(3), pp. 34-40. doi: 10.1111/j.1745-6592.2012.01407.x
  8. ^ Chen, F., Freedman, D.L., Falta, R.W., Murdoch, L.C., 2012. Henry's law constants of chlorinated solvents at elevated temperatures. Chemosphere, 86(2), pp.156-165. doi: 10.1016/j.chemosphere.2011.10.004

See Also

TISR® Explanation Video

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