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Advection and Groundwater Flow
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==Estimating PCE/TCE Abiotic First-Order Reductive Dechlorination Rate Constants in Clayey Soils Under Anoxic Conditions==
 
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The U.S. Department of Defense (DoD) faces many challenges in restoring aquifers at contaminated sites, often due to back-diffusion of tetrachloroethene (PCE) and trichloroethene (TCE) from low-permeability clay zones. The uptake, storage, and subsequent long-term release of these dissolved contaminants from clays are key processes in understanding the longevity, intensity, and risks associated with many persistent chlorinated ethene groundwater plumes. Although naturally occurring abiotic and biotic dechlorination processes in clays may reduce stored contaminant mass and significantly aid natural attenuation, no standardized field method currently exists to verify or quantify these reactions. It is critical to remediation design efforts to demonstrate and validate a cost-effective in situ approach for assessing these dechlorination processes using first-order rate constants. An approach was developed and applied across eight DoD sites to support Remedial Project Managers (RPMs) and regulators in evaluating natural attenuation potential in clay-rich environments.
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 areas. In 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]]
 
*[[Sorption of Organic Contaminants]]
 
*[[Plume Response Modeling]]
 
  
'''CONTRIBUTOR(S):'''
+
*[[Monitored Natural Attenuation (MNA)]]
*[[Dr. Charles Newell, P.E.]]
+
*[[Monitored Natural Attenuation (MNA) of Chlorinated Solvents]]
*[[Dr. Robert Borden, P.E.]]
+
*[[Monitored Natural Attenuation - Transitioning from Active Remedies]]
 +
*[[Matrix Diffusion]]
 +
*[[REMChlor - MD]]
 +
 
 +
'''Contributors:''' Dani Tran, Dr. Charles Schaefer, Dr. Charles Werth
  
'''Key Resource(s):'''
+
'''Key Resource:'''
*[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.
+
*Schaefer, C.E, Tran, D., Nguyen, D., Latta, D.E., Werth, C.J., 2025. Evaluating Mineral and In Situ Indicators of Abiotic Dechlorination in Clayey Soils<ref name="SchaeferEtAl2025"/>
*[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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==Introduction==
[[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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Cost-effective methods are needed to verify the occurrence of natural dechlorination processes and quantify their dechlorination rates in clays under ambient in situ conditions in order to reliably predict their long-term influence on plume longevity and mass discharge. However, accurately determining these rates is challenging due to slow reaction kinetics, the transient nature of transformation products, and the interplay of biotic and abiotic mechanisms within the clay matrix or at clay-sand interfaces. Tools capable of quantifying these reactions and assessing their role in mitigating plume persistence would be a significant aid for long-term site management.
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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For reductive abiotic dechlorination under anoxic conditions, a 1% hydrochloric acid (HCl) extraction of a sample of native clay coupled with X-ray diffraction (XRD) data can be used as a screening level tool to estimate reductive dechlorination rate constants. These rate constants can be inserted into fate and transport models such as [[REMChlor - MD]]<ref>Falta, R., 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]&nbsp; [[Media: FaltaWang2017.pdf | Open Access Manuscript]]</ref><ref>Kulkarni, P.R., Adamson, D.T., Popovic, J., Newell, C.J., 2022. Modeling a well-charactized perfluorooctane sulfate (PFOS) source and plume using the REMChlor-MD model to account for matrix diffusion. Journal of Contaminant Hydrology, 247, Article 103986. [https://doi.org/10.1016/j.jconhyd.2022.103986 doi: 10.1016/j.jconhyd.2022.103986]&nbsp; [[Media: KulkarniEtAl2022.pdf | Open Access Manuscript]]</ref> to quantify abiotic dechlorination impacts within clay aquitards on chlorinated solvent plumes. Thus, determination of the abiotic reductive dechlorination rate constant for a particular clayey soil can be readily utilized to provide a more accurate assessment of aquifer cleanup timeframes for groundwater plumes that are being sustained by contaminant back-diffusion.
{| class="wikitable" style="float:right; margin-left:10px;text-align:center;"
 
|+ 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"/>
 
|-
 
! 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]]
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==Recommended Approach==
::Where:
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[[File: TranFig1.png | thumb | 500 px | Figure 1: First-order rate constants for abiotic reductive dechlorination of TCE under anaerobic conditions. Circles are data from Schaefer ''et al.'', 2021<ref>Schaefer, C.E., Ho, P., Berns, E., Werth, C., 2021. Abiotic dechlorination in the presence of ferrous minerals. Journal of Contaminant Hydrology, 241, 103839. [https://doi.org/10.1016/j.jconhyd.2021.103839 doi: 10.1016/j.jconhyd.2021.103839]&nbsp; [[Media: SchaeferEtAl2021.pdf | Open Access Manuscript]]</ref>, filled squares from Schaefer ''et al.'', 2018<ref name="SchaeferEtAl2018"/>, and  Schaefer ''et al.'', 2017<ref>Schaefer, C.E., Ho., Gurr, C., Berns, E., Werth, C., 2017. Abiotic dechlorination of chlorinated ethenes in natural clayey soils: impacts of mineralogy and temperature. Journal of Contaminant Hydrology, 206, pp. 10-17. [https://doi.org/10.1016/j.jconhyd.2017.09.007 doi: 10.1016/j.jconhyd.2017.09.007]&nbsp; [[Media: SchaeferEtAl2017.pdf | Open Access Manuscript]]</ref>, and open squares from Schaefer ''et al.'', 2025<ref name="SchaeferEtAl2025"/>. ]]
:::''Q'' = Flow rate (Volume of groundwater flow per time, such as m<sup>3</sup>/yr)
+
[[File: TranFig2.png | thumb | 600 px | Figure 2: Flowchart diagram of field screening procedures]]
:::''A'' = Cross sectional area perpendicular to groundwater flow (length<sup>2</sup>, such as m<sup>2</sup>)
+
The recommended approach builds upon the methodology and findings of a recent study<ref name="SchaeferEtAl2025">Schaefer, C.E., Tran, D., Nguyen, D., Latta, D.E., Werth, C.J., 2025. Evaluating Mineral and In Situ Indicators of Abiotic Dechlorination in Clayey Soils. Groundwater Monitoring and Remediation, 45(2), pp. 31-39. [https://doi.org/10.1111/gwmr.12709 doi: 10.1111/gwmr.12709]</ref>, emphasizing field-based and analytical techniques to quantify abiotic first-order reductive dechlorination rate constants for PCE and TCE in clayey soils under anoxic conditions. Key components of this evaluation are listed below:
:::''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)
+
#<u>Zone Identification:</u> The focus of the investigation should be to delineate clayey zones adjacent to hydraulically conductive zones.
:::''K'' = Hydraulic Conductivity (sometimes called “permeability”) (length per time)
+
#<u>Ferrous Mineral Quantification:</u> Assess ferrous mineral context in clay via 1% HCl extraction at ambient temperature over a 10-minute interval.
:::''ΔH'' = Difference in hydraulic head between two lateral points (length)
+
#<u>Mineralogical Characterization:</u> Conduct XRD analysis with the specific intent of identifying the presence of pyrite and biotite.
:::''ΔL'' = Distance between two lateral points (length)
+
#<u>Reduced Gas Analysis:</u> Measurement of reduced gases such as acetylene, ethene, and ethane concentrations in clay samples. Gas-tight sampling devices (e.g., En Core® soil samplers by En Novative Technologies, Inc.) should be used to ensure sample integrity during collection and transport. 
  
[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).  
+
Clay samples should be collected within a few centimeters of the high-permeability interface, with optional additional sampling further inward. For mineralogical analysis, a defined interval may be collected and subsequently subsampled. To preserve sample integrity, exposure to air should be minimized during collection, transport, and handling. Homogenization should occur within an anaerobic chamber, and if subsamples are required for external analysis, they must be shipped in gas-tight, anaerobic containers.
  
[[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>.]]
+
Estimation of the abiotic reductive first-order rate constant for PCE and TCE is based on the “reactive” ferrous content in the clay. Reactive ferrous content (Fe(II)<sub>r</sub>) is estimated as shown in Equation 1:
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).]]
+
::'''Equation 1:'''&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <big>''Fe(II)<sub><small>r</small></sub> = DA + XRD<sub><small>pyr</small></sub> - XRD<sub><small>biotite</small></sub>''</big>
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):
 
  
[[File:Newell-Article 1-Equation 2r.jpg|400px]]
+
where ''DA'' is the ferrous content from the dilute acid (1% HCl) extraction, ''XRD<sub><small>pyr</small></sub>'' is the pyrite content from XRD analysis, and ''XRD<sub><small>biotite</small></sub>'' is the biotite content from XRD analysis<ref name="SchaeferEtAl2025"/>.
: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.
+
Abiotic dechlorination is unlikely to contribute to mitigating contaminant back-diffusion when reactive ferrous iron (Fe(II)<sub><small>r</small></sub>) concentrations are below 100 mg/kg (Figure 1). For Fe(II)<sub><small>r</small></sub> above 100 mg/kg, the first-order rate constant for PCE and TCE reductive dechlorination can be estimated using the correlation shown in Figure 1<ref name="SchaeferEtAl2018">Schaefer, C.E., Ho, P., Berns, E., Werth, C., 2018. Mechanisms for abiotic dechlorination of trichloroethene by ferrous minerals under oxic and anoxic conditions in natural sediments. Environmental Science and Technology, 52(23), pp.13747-13755. [https://doi.org/10.1021/acs.est.8b04108 doi: 10.1021/acs.est.8b04108]</ref><ref>Borden, R.C., Cha, K.Y., 2021. Evaluating the impact of back diffusion on groundwater cleanup time. Journal of Contaminant Hydrology, 243, Article 103889. [https://doi.org/10.1016/j.jconhyd.2021.103889 doi: 10.1016/j.jconhyd.2021]&nbsp; [[Media: BordenCha2021.pdf | Open Access Manuscript]]</ref>. The rate constant exhibits a strong positive correlation with the logarithm of reactive Fe(II) content (Pearson’s ''r'' = 0.82), with a slope of 4.7 × 10⁻⁸ L g⁻¹ d⁻¹ (log mg kg⁻¹)⁻¹.
  
[[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).]]
+
Figure 2 presents a decision flowchart designed to evaluate the significance and extent of abiotic reductive dechlorination. By applying Equation 1 to the dilute acid extractable Fe(II) plus measured mineral species data from clay samples, the reactive ferrous iron content (Fe(II)<sub><small>r</small></sub>) can be quantified, enabling a streamlined assessment of the extent to which abiotic processes are contributing to the mitigation of contaminant back-diffusion.
  
==Darcy Velocity and Seepage Velocity==
+
If Fe(II)r is ≥ 100 mg/kg, a first-order dechlorination rate constant can be estimated and subsequently used within a contaminant fate and transport model. However, if acetylene is detected in the clay, even with Fe(II)r less than 100 mg/kg, then bench-scale testing using methods similar to those described in a recent study<ref name="SchaeferEtAl2025"/> is recommended, as such results would likely be inconsistent with those shown in Figure 1, suggesting some other mechanism might be involved, or that the system mineralogy might be more complex than anticipated. Even if Fe(II)r ≥ 100 mg/kg, confirmatory bench-scale testing may be conducted for additional verification and to refine estimation of the abiotic dechlorination rate constant.
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==
+
==Summary and Recommendations==
{| class="wikitable" style="float:right; margin-left:10px; text-align:center;"
+
The approach outlined above is intended to serve as a generalized guide for practitioners and site managers to cost-effectively determine the extent to which beneficial abiotic reductive dechlorination reactions are likely occurring in low permeability (e.g., clayey) zones. This approach may be contraindicated if co-contaminants are present. It is currently unclear whether other classes of potentially reactive chemicals, such as trinitrotoluene (TNT) or chlorinated ethanes, could interact competitively with PCE and TCE.  
|+ 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
 
|-
 
| Alluvium, poorly sorted sand and gravel || 0.003 — 0.017
 
|-
 
| Alluvium, sand and gravel || 0.11 — 0.18
 
|-
 
| Siltstone, sandstone, mudstone || 0.01 — 0.05
 
|}
 
  
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).
+
In addition, it remains unclear how other classes of compounds such as per- and polyfluoroalkyl substances (PFAS) may interact or sorb with ferrous minerals and potentially inhibit abiotic dechlorination reactions. Coupling these recommended activities with conventional site investigation tasks would provide an opportunity to perform many of the up-front screening activities with minimal additional project costs. It is important to note that the guidance proposed herein pertains to particularly low permeability media. Sites with complex or varying lithology, where the mineralogy and/or redox conditions may vary, might require evaluation of multiple samples to provide appropriate site-wide information.
  
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"/>
 
<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]]
 
: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]]
 
: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).
 
 
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 removed.  In some cases, matrix diffusion can maintain contaminant concentrations in more permeable zones above target cleanup goals for decades or even centuries after the primary sources have been addressed (Chapman and Parker 2005). Methods for evaluating the impact of matrix diffusion are addressed in a separate article
 
 
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.
 
 
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]
+
*[https://serdp-estcp.mil/projects/details/a7e3f7b5-ed82-4591-adaa-6196ff33dd60 ESTCP Project ER20-5031 – In Situ Verification and Quantification of Naturally Occurring Dechlorination Rates in Clays: Demonstrating Processes that Mitigate Back-Diffusion and Plume Persistence]
*[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 14:37, 28 April 2026

Estimating PCE/TCE Abiotic First-Order Reductive Dechlorination Rate Constants in Clayey Soils Under Anoxic Conditions

The U.S. Department of Defense (DoD) faces many challenges in restoring aquifers at contaminated sites, often due to back-diffusion of tetrachloroethene (PCE) and trichloroethene (TCE) from low-permeability clay zones. The uptake, storage, and subsequent long-term release of these dissolved contaminants from clays are key processes in understanding the longevity, intensity, and risks associated with many persistent chlorinated ethene groundwater plumes. Although naturally occurring abiotic and biotic dechlorination processes in clays may reduce stored contaminant mass and significantly aid natural attenuation, no standardized field method currently exists to verify or quantify these reactions. It is critical to remediation design efforts to demonstrate and validate a cost-effective in situ approach for assessing these dechlorination processes using first-order rate constants. An approach was developed and applied across eight DoD sites to support Remedial Project Managers (RPMs) and regulators in evaluating natural attenuation potential in clay-rich environments.

Related Article(s):

Contributors: Dani Tran, Dr. Charles Schaefer, Dr. Charles Werth

Key Resource:

  • Schaefer, C.E, Tran, D., Nguyen, D., Latta, D.E., Werth, C.J., 2025. Evaluating Mineral and In Situ Indicators of Abiotic Dechlorination in Clayey Soils[1]

Introduction

Cost-effective methods are needed to verify the occurrence of natural dechlorination processes and quantify their dechlorination rates in clays under ambient in situ conditions in order to reliably predict their long-term influence on plume longevity and mass discharge. However, accurately determining these rates is challenging due to slow reaction kinetics, the transient nature of transformation products, and the interplay of biotic and abiotic mechanisms within the clay matrix or at clay-sand interfaces. Tools capable of quantifying these reactions and assessing their role in mitigating plume persistence would be a significant aid for long-term site management.

For reductive abiotic dechlorination under anoxic conditions, a 1% hydrochloric acid (HCl) extraction of a sample of native clay coupled with X-ray diffraction (XRD) data can be used as a screening level tool to estimate reductive dechlorination rate constants. These rate constants can be inserted into fate and transport models such as REMChlor - MD[2][3] to quantify abiotic dechlorination impacts within clay aquitards on chlorinated solvent plumes. Thus, determination of the abiotic reductive dechlorination rate constant for a particular clayey soil can be readily utilized to provide a more accurate assessment of aquifer cleanup timeframes for groundwater plumes that are being sustained by contaminant back-diffusion.

Recommended Approach

Figure 1: First-order rate constants for abiotic reductive dechlorination of TCE under anaerobic conditions. Circles are data from Schaefer et al., 2021[4], filled squares from Schaefer et al., 2018[5], and Schaefer et al., 2017[6], and open squares from Schaefer et al., 2025[1].
Figure 2: Flowchart diagram of field screening procedures

The recommended approach builds upon the methodology and findings of a recent study[1], emphasizing field-based and analytical techniques to quantify abiotic first-order reductive dechlorination rate constants for PCE and TCE in clayey soils under anoxic conditions. Key components of this evaluation are listed below:

  1. Zone Identification: The focus of the investigation should be to delineate clayey zones adjacent to hydraulically conductive zones.
  2. Ferrous Mineral Quantification: Assess ferrous mineral context in clay via 1% HCl extraction at ambient temperature over a 10-minute interval.
  3. Mineralogical Characterization: Conduct XRD analysis with the specific intent of identifying the presence of pyrite and biotite.
  4. Reduced Gas Analysis: Measurement of reduced gases such as acetylene, ethene, and ethane concentrations in clay samples. Gas-tight sampling devices (e.g., En Core® soil samplers by En Novative Technologies, Inc.) should be used to ensure sample integrity during collection and transport.

Clay samples should be collected within a few centimeters of the high-permeability interface, with optional additional sampling further inward. For mineralogical analysis, a defined interval may be collected and subsequently subsampled. To preserve sample integrity, exposure to air should be minimized during collection, transport, and handling. Homogenization should occur within an anaerobic chamber, and if subsamples are required for external analysis, they must be shipped in gas-tight, anaerobic containers.

Estimation of the abiotic reductive first-order rate constant for PCE and TCE is based on the “reactive” ferrous content in the clay. Reactive ferrous content (Fe(II)r) is estimated as shown in Equation 1:

Equation 1:       Fe(II)r = DA + XRDpyr - XRDbiotite

where DA is the ferrous content from the dilute acid (1% HCl) extraction, XRDpyr is the pyrite content from XRD analysis, and XRDbiotite is the biotite content from XRD analysis[1].

Abiotic dechlorination is unlikely to contribute to mitigating contaminant back-diffusion when reactive ferrous iron (Fe(II)r) concentrations are below 100 mg/kg (Figure 1). For Fe(II)r above 100 mg/kg, the first-order rate constant for PCE and TCE reductive dechlorination can be estimated using the correlation shown in Figure 1[5][7]. The rate constant exhibits a strong positive correlation with the logarithm of reactive Fe(II) content (Pearson’s r = 0.82), with a slope of 4.7 × 10⁻⁸ L g⁻¹ d⁻¹ (log mg kg⁻¹)⁻¹.

Figure 2 presents a decision flowchart designed to evaluate the significance and extent of abiotic reductive dechlorination. By applying Equation 1 to the dilute acid extractable Fe(II) plus measured mineral species data from clay samples, the reactive ferrous iron content (Fe(II)r) can be quantified, enabling a streamlined assessment of the extent to which abiotic processes are contributing to the mitigation of contaminant back-diffusion.

If Fe(II)r is ≥ 100 mg/kg, a first-order dechlorination rate constant can be estimated and subsequently used within a contaminant fate and transport model. However, if acetylene is detected in the clay, even with Fe(II)r less than 100 mg/kg, then bench-scale testing using methods similar to those described in a recent study[1] is recommended, as such results would likely be inconsistent with those shown in Figure 1, suggesting some other mechanism might be involved, or that the system mineralogy might be more complex than anticipated. Even if Fe(II)r ≥ 100 mg/kg, confirmatory bench-scale testing may be conducted for additional verification and to refine estimation of the abiotic dechlorination rate constant.

Summary and Recommendations

The approach outlined above is intended to serve as a generalized guide for practitioners and site managers to cost-effectively determine the extent to which beneficial abiotic reductive dechlorination reactions are likely occurring in low permeability (e.g., clayey) zones. This approach may be contraindicated if co-contaminants are present. It is currently unclear whether other classes of potentially reactive chemicals, such as trinitrotoluene (TNT) or chlorinated ethanes, could interact competitively with PCE and TCE.

In addition, it remains unclear how other classes of compounds such as per- and polyfluoroalkyl substances (PFAS) may interact or sorb with ferrous minerals and potentially inhibit abiotic dechlorination reactions. Coupling these recommended activities with conventional site investigation tasks would provide an opportunity to perform many of the up-front screening activities with minimal additional project costs. It is important to note that the guidance proposed herein pertains to particularly low permeability media. Sites with complex or varying lithology, where the mineralogy and/or redox conditions may vary, might require evaluation of multiple samples to provide appropriate site-wide information.


References

  1. ^ 1.0 1.1 1.2 1.3 1.4 Schaefer, C.E., Tran, D., Nguyen, D., Latta, D.E., Werth, C.J., 2025. Evaluating Mineral and In Situ Indicators of Abiotic Dechlorination in Clayey Soils. Groundwater Monitoring and Remediation, 45(2), pp. 31-39. doi: 10.1111/gwmr.12709
  2. ^ Falta, R., 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  Open Access Manuscript
  3. ^ Kulkarni, P.R., Adamson, D.T., Popovic, J., Newell, C.J., 2022. Modeling a well-charactized perfluorooctane sulfate (PFOS) source and plume using the REMChlor-MD model to account for matrix diffusion. Journal of Contaminant Hydrology, 247, Article 103986. doi: 10.1016/j.jconhyd.2022.103986  Open Access Manuscript
  4. ^ Schaefer, C.E., Ho, P., Berns, E., Werth, C., 2021. Abiotic dechlorination in the presence of ferrous minerals. Journal of Contaminant Hydrology, 241, 103839. doi: 10.1016/j.jconhyd.2021.103839  Open Access Manuscript
  5. ^ 5.0 5.1 Schaefer, C.E., Ho, P., Berns, E., Werth, C., 2018. Mechanisms for abiotic dechlorination of trichloroethene by ferrous minerals under oxic and anoxic conditions in natural sediments. Environmental Science and Technology, 52(23), pp.13747-13755. doi: 10.1021/acs.est.8b04108
  6. ^ Schaefer, C.E., Ho., Gurr, C., Berns, E., Werth, C., 2017. Abiotic dechlorination of chlorinated ethenes in natural clayey soils: impacts of mineralogy and temperature. Journal of Contaminant Hydrology, 206, pp. 10-17. doi: 10.1016/j.jconhyd.2017.09.007  Open Access Manuscript
  7. ^ Borden, R.C., Cha, K.Y., 2021. Evaluating the impact of back diffusion on groundwater cleanup time. Journal of Contaminant Hydrology, 243, Article 103889. doi: 10.1016/j.jconhyd.2021  Open Access Manuscript

See Also