Mass Flux and Mass Discharge - Revision history

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Jhurley: /* Methods for Mass Discharge and Mass Flux Measurement */

2019-05-14T19:26:22Z

‎Methods for Mass Discharge and Mass Flux Measurement

Jhurley: /* Magnitude of Mass Discharge Values */

2019-05-14T19:17:44Z

‎Magnitude of Mass Discharge Values

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Jhurley: /* Methods for Mass Discharge and Mass Flux Measurement */

2019-05-14T19:14:03Z

‎Methods for Mass Discharge and Mass Flux Measurement

Jhurley: /* Mathematics of Mass Flux/Discharge */

2019-05-14T18:36:44Z

‎Mathematics of Mass Flux/Discharge

Jhurley: /* Remedial Considerations */

2019-05-14T18:25:02Z

‎Remedial Considerations

Jhurley: /* Source Zone Models that Link Mass Depletion, Mass Flux/Discharge */

2019-05-14T18:21:42Z

‎Source Zone Models that Link Mass Depletion, Mass Flux/Discharge

Jhurley: /* Mathematics of Mass Flux/Discharge */

2019-05-14T18:07:59Z

‎Mathematics of Mass Flux/Discharge

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 *[[Alternative Endpoints]]
 *[[Monitored Natural Attenuation (MNA)]]
 *[[Natural Source Zone Depletion (NSZD)]]

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 *[[Alternative Endpoints]]
 *[[Plume Response Modeling]]
 *[[Source Zone Modeling]]

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 Use of mass flux and mass discharge measurements for contaminated site management has increased in recent years.  Mass flux is the contaminant mass moving across a unit area of porous media (aquifer), while mass discharge is the total mass crossing a control plane of interest, such as the downgradient edge of the source zone or a property boundary. Use of the mass flux/discharge approach combines three different factors:  1) contaminant concentration in groundwater; 2) groundwater flow rate through the site; and 3) size of the source zone.  Mass flux and discharge can be estimated using data from monitoring well transects, pumping wells, passive flux meters and other methods.  Mass flux and mass discharge can provide site stakeholders a better understanding of the plume behavior, risk, and the relative strength of the source and downgradient plume.
 <div style="float:right;margin:0 0 2em 2em;">__TOC__</div>
 '''Related Article(s):'''

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 Passive flux meters have been used at hundreds of sites for most common volatile organic compound (VOC) contaminants and some nutrients and some metals.  One vendor (Enviroflux) can provide passive flux meter devices for down-well deployment at project sites, with optional full laboratory analysis of the subsequently recovered flux meters.
 ''Well Pumping and Integral Pump Tests''<br />
 A very simple method to measure mass discharge from a plume is to capture the plume with a pumping well.  Mass discharge = pumping flowrate x contaminant concentration in extracted groundwater.   To use this method, one should make sure that the entire plume is captured, and that the pumping is not changing the source zone water flow leading to enhanced dissolution.  The integral pump test (IPT) technique for measuring mass flux or mass discharge is a more sophisticated version of the well pumping approach where contaminant concentration-time series in the effluent of multiple pumping wells aligned perpendicularly to the prevailing direction of groundwater flow are used. Concentration-time series information was initially used to estimate contaminant flux or mass discharge around 2000<ref>Teutsch, G., Ptak, T., Schwarz, R. and Holder, T., 2000. Ein neues integrales Verfahren zur Quantifizierung der Grundwasserimmission, Teil I: Beschreibung der Grundlagen. Grundwasser, 5(4), pp.170-175.</ref><ref>Ptak, T., Schirmer, M. and Teutsch, G., 2000. Development and performance of a new multilevel groundwater sampling system. In Second International Conference on Remediation of Chlorinated and Recalcitrant Compounds. Battelle Press, Columbus, OH, USA (pp. 95-102)</ref>, with applications reported shortly thereafter<ref name="Bockelmann2001">Bockelmann, A., Ptak, T. and Teutsch, G., 2001. An analytical quantification of mass fluxes and natural attenuation rate constants at a former gasworks site. Journal of Contaminant Hydrology, 53(3-4), pp.429-453. [https://doi.org/10.1016/S0169-7722(01)00177-2 doi: 10.1016/S0169-7722(01)00177-2]</ref><ref>Bockelmann, A., Zamfirescu, D., Ptak, T., Grathwohl, P. and Teutsch, G., 2003. Quantification of mass fluxes and natural attenuation rates at an industrial site with a limited monitoring network: a case study. Journal of Contaminant Hydrology, 60(1-2), pp.97-121. [https://doi.org/10.1016/S0169-7722(02)00060-8 doi: 10.1016/S0169-7722(02)00060-8]</ref>. The measured concentration of contaminants is used with independent estimates of the natural gradient Darcy flux. This method is similar to the transect method, but provides an integrated measure of the contaminant flux across the entire well transect and ensures that even very localized high contaminant concentration zones (which might be missed by more discrete methods) are accounted for.

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 In the most detailed form, mass flux, ''J(x,y,z)'', can be calculated using the point scale flux average concentration, ''C(x,y,z)'', the point scale hydraulic conductivity, ''K(x,y,z)'' and the point scale hydraulic gradient, ''dh/dx'', applied in the direction of groundwater flow. Measuring ''K'' and ''dh/dx'' at each location can be a major effort.  As a result, site-wide average values are often applied for ''dh/dx'' and ''K'', while the flux averaged concentration distributions are obtained using multilevel samplers<ref name="Guilbeault2005&quot;">Guilbeault, M.A., Parker, B.L. and Cherry, J.A., 2005. Mass and flux distributions from DNAPL zones in sandy aquifers. Groundwater, 43(1), pp.70-86. [https://doi.org/10.1111/j.1745-6584.2005.tb02287.x doi: 10.1111/j.1745-6584.2005.tb02287.x][//www.enviro.wiki/images/6/6a/Guilbeault_2005_Mass_and_flux_distributions.pdf  report.pdf]</ref>. In this approach, spatial variability is determined for local mass flux that is simply a function of the concentration distribution. Any correlation between the Darcy flux and concentration is not considered.
-The Interstate Technology and Regulatory Council’s (ITRC, 2010) “Use and measurement of mass flux and mass discharge” document<ref name="ITRC2010" /> organized these concepts into five separate methods for obtaining mass flux / mass discharge data.  While several methods are related (for example, passive flux meters are often arrayed in a transect), this list presents five different general strategies to generate mass flux/discharge data:
+The [https://www.itrcweb.org/ Interstate Technology and Regulatory Council’s] (ITRC, 2010) “Use and measurement of mass flux and mass discharge” document<ref name="ITRC2010" /> organized these concepts into five separate methods for obtaining mass flux / mass discharge data.  While several methods are related (for example, passive flux meters are often arrayed in a transect), this list presents five different general strategies to generate mass flux/discharge data:
 #Transect Method

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 |''K''||is the hydraulic conductivity [L/T] and
 |-
-|''dh/dx''||is the rate of change in hydraulic head with distance at the location of interest.
+|''dh/dx''||is the rate of change in [[wikipedia: Hydraulic head | hydraulic head]] with distance at the location of interest.
 |}
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 ''Related Metric: Site Age''<br />
-One measure of the site status related to mass flux/discharge is the '''site age'''<ref name="Jawitz2005">Jawitz, J.W., Fure, A.D., Demmy, G.G., Berglund, S. and Rao, P.S.C., 2005. Groundwater contaminant flux reduction resulting from nonaqueous phase liquid mass reduction. Water Resources Research, 41(10). [https://doi.org/10.1029/2004WR003825 doi: 10.1029/2004WR003825][//www.enviro.wiki/images/1/17/Jawitz_2005_Groundwater_contaminant_flux_reduction.pdf  Report.pdf]</ref>. A simple definition of site age is the fraction of the initial source zone mass that has been removed from the source zone. A site where 90% of the mass has been removed from the source zone would be considered an aged site while those with a small fraction (e.g., 10%) would be considered a young site. Many factors collectively determine how fast a site ages including the solubility limit of the contaminant, the groundwater flow velocity, the size of the source zone in the flow direction, and average non-aqueous phase liquid (NAPL) saturation along the flow path. Sites with a low-solubility dense NAPL (DNAPL), such as tetrachloroethene (PCE) (solubility 150 mg/L), will age more slowly than a comparable site with trichloroethene (TCE) (solubility 1,100 mg/L) (see [[Chlorinated Solvents]]).
+One measure of the site status related to mass flux/discharge is the '''site age'''<ref name="Jawitz2005">Jawitz, J.W., Fure, A.D., Demmy, G.G., Berglund, S. and Rao, P.S.C., 2005. Groundwater contaminant flux reduction resulting from nonaqueous phase liquid mass reduction. Water Resources Research, 41(10). [https://doi.org/10.1029/2004WR003825 doi: 10.1029/2004WR003825][//www.enviro.wiki/images/1/17/Jawitz_2005_Groundwater_contaminant_flux_reduction.pdf  Report.pdf]</ref>. A simple definition of site age is the fraction of the initial source zone mass that has been removed from the source zone. A site where 90% of the mass has been removed from the source zone would be considered an aged site while those with a small fraction (e.g., 10%) would be considered a young site. Many factors collectively determine how fast a site ages including the solubility limit of the contaminant, the groundwater flow velocity, the size of the source zone in the flow direction, and average non-aqueous phase liquid (NAPL) saturation along the flow path. Sites with a low-solubility dense NAPL (DNAPL), such as [[wikipedia: Tetrachloroethylene | tetrachloroethene (PCE)]] (solubility 150 mg/L), will age more slowly than a comparable site with [[wikipedia: Trichloroethylene |trichloroethene (TCE)]] (solubility 1,100 mg/L) (see [[Chlorinated Solvents]]).
 ''Related Metric: Flux Averaged Concentration''<br />

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 ==Remedial Considerations==
-The underlying goal of source zone or DNAPL treatment is to reduce the risks posed by the contamination to humans and the environment. Aqueous contaminant concentrations can be viewed as surrogate measures of risk, and are often the primary metric for regulatory decisions. Under this traditional framework, the goal for NAPL source treatment technologies is to achieve acceptable aqueous concentrations such as drinking water standards by either removing or destroying NAPL mass in the source zone. Unfortunately, current NAPL remedial technologies are unable to completely eliminate NAPL from source areas at all sites, and partial mass removal from NAPL source zones is unlikely to be sufficient to meet drinking water standards at all locations within a site. Other potential benefits may, however, be achieved as a result of source treatment, and one proposed benefit is a reduction in contaminant mass discharge (M/T) from the NAPL source area<ref name="RaoPSC2002" /><ref>Kavanaugh, M.C., Suresh, P. and Rao, C., 2003. The DNAPL remediation challenge: Is there a case for source depletion? National Risk Management Research Laboratory, Office of Research and Development, U.S. Environmental Progtection Agency, Cincinnati, OH, USA. EPA/600/R-03/143. [//www.enviro.wiki/images/7/79/2003-Kavanaugh-The_DNAPL_Remediation_Challenge_Is_there_a_ase_for_source_depletion.pdf  Report.pdf]</ref><ref>Stroo, H.F., Unger, M., Ward, C.H., Kavanaugh, M.C., Vogel, C., Leeson, A., Marqusee, J.A. and Smith, B.P., 2003. Peer reviewed: Remediating chlorinated solvent source zones. Environ. Sci Technol. 37 (11), pp 224A–230A. doi: 10.1021/es032488k [//www.enviro.wiki/images/7/70/2003-Stroo-Remediating_chlorinated_solvent_source_zones.pdf  Report.pdf]</ref><ref>ITRC (Interstate Technology & Regulatory Council). 2003. Assessing the performance of DNAPL source reduction remedies. Dense Nonaqueous Phase Liquids Team, Washington, DC, USA </ref><ref>National Research Council, 2005. Contaminants in the subsurface: Source zone assessment and remediation. National Academies Press.[//www.enviro.wiki/images/6/6d/2005-NRC_Contaminants_in_the_Subsurface_Source_Zone.pdf  Report.pdf]</ref> (see Remediation Performance Assessment).  The magnitude of the benefit realized needs to be quantified by measuring mass flux and discharge before and after remedial efforts are implemented.
+The underlying goal of source zone or DNAPL treatment is to reduce the risks posed by the contamination to humans and the environment. Aqueous contaminant concentrations can be viewed as surrogate measures of risk, and are often the primary metric for regulatory decisions. Under this traditional framework, the goal for NAPL source treatment technologies is to achieve acceptable aqueous concentrations such as drinking water standards by either removing or destroying NAPL mass in the source zone. Unfortunately, current NAPL remedial technologies are unable to completely eliminate NAPL from source areas at all sites, and partial mass removal from NAPL source zones is unlikely to be sufficient to meet drinking water standards at all locations within a site. Other potential benefits may, however, be achieved as a result of source treatment, and one proposed benefit is a reduction in contaminant mass discharge (M/T) from the NAPL source area<ref name="RaoPSC2002" /><ref>Kavanaugh, M.C., Suresh, P. and Rao, C., 2003. The DNAPL remediation challenge: Is there a case for source depletion? National Risk Management Research Laboratory, Office of Research and Development, U.S. Environmental Progtection Agency, Cincinnati, OH, USA. EPA/600/R-03/143. [//www.enviro.wiki/images/7/79/2003-Kavanaugh-The_DNAPL_Remediation_Challenge_Is_there_a_ase_for_source_depletion.pdf  Report.pdf]</ref><ref>Stroo, H.F., Unger, M., Ward, C.H., Kavanaugh, M.C., Vogel, C., Leeson, A., Marqusee, J.A. and Smith, B.P., 2003. Peer reviewed: Remediating chlorinated solvent source zones. Environ. Sci Technol. 37 (11), pp 224A–230A. doi: 10.1021/es032488k [//www.enviro.wiki/images/7/70/2003-Stroo-Remediating_chlorinated_solvent_source_zones.pdf  Report.pdf]</ref><ref>ITRC (Interstate Technology & Regulatory Council). 2003. Assessing the performance of DNAPL source reduction remedies. Dense Nonaqueous Phase Liquids Team, Washington, DC, USA </ref><ref>National Research Council, 2005. Contaminants in the subsurface: Source zone assessment and remediation. National Academies Press.[//www.enviro.wiki/images/6/6d/2005-NRC_Contaminants_in_the_Subsurface_Source_Zone.pdf  Report.pdf]</ref> (see [[Remediation Performance Assessment at Chlorinated Solvent Sites]]).  The magnitude of the benefit realized needs to be quantified by measuring mass flux and discharge before and after remedial efforts are implemented.
 Flux measurements should be conducted using the same protocol before and after remedial treatment, and differences in hydrologic conditions should be considered when interpreting the data. Also critical is the need to provide adequate time between the remedial activity and the post-remedial flux measurement to ensure that conditions are representative of natural groundwater flow and contaminant dissolution from the original source area. Too often there is a rush to measure the effect of the remedial action, and the measurements are only indicative of modifications still significantly influenced by remedial actions such as elevated temperatures or residual flushing agents. A general rule may be to require at least two pore volumes of natural gradient water flow to pass through the source area extending to the monitoring location prior to post-remedial monitoring of mass flux. For many sites this could mean two to five years following remediation. Often site managers may find this length of time unacceptable. Partly for this reason, very few studies have been completed to date with high quality measurements of pre- and post-remediation flux measurements<ref name="Brooks2008" />.

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 Several modeling approaches have been developed to relate mass removal from DNAPL source zones to changes in mass discharge or flux<ref name="Sale2001">Sale, T.C. and McWhorter, D.B., 2001. Steady state mass transfer from single‐component dense nonaqueous phase liquids in uniform flow fields. Water Resources Research, 37(2), pp.393-404. [https://doi.org/10.1029/2000WR900236 doi: 10.1029/2000WR900236][//www.enviro.wiki/images/a/aa/Sale_2001_Steady_state_mass_transfer.pdf  Report.pdf]</ref><ref name="RaoPSC2002">Rao, P.S.C., Jawitz, J.W., Enfield, C.G., Falta Jr, R.W., Annable, M.D. and Wood, A.L., 2001. Technology integration for contaminated site remediation: clean-up goals and performance criteria. Groundwater quality: Natural and enhanced restoration of groundwater pollution, 275, pp.571-578. [//www.enviro.wiki/images/2/2b/2002-Rao_PSC-Technology_integration_for_contaminated_site_remediation.pdf  Report.pdf]</ref><ref name="RaoPSC2003">Rao, P.S.C. and Jawitz, J.W., 2003. Comment on “Steady state mass transfer from single‐component dense nonaqueous phase liquids in uniform flow fields” by TC Sale and DB McWhorter. Water Resources Research, 39(3). [https://doi.org/10.1029/2001WR000599 doi: 10.1029/2001WR000599]</ref><ref>Lemke, L.D., Abriola, L.M. and Lang, J.R., 2004. Influence of hydraulic property correlation on predicted dense nonaqueous phase liquid source zone architecture, mass recovery and contaminant flux. Water Resources Research, 40(12). [https://doi.org/10.1029/2004WR003061 doi:10.1029/2004WR003061][//www.enviro.wiki/images/6/66/Lemke_2004_Influence_of_hydraulic_property.pdf  Report.pdf]</ref><ref name="Parker2004">Parker, J.C. and Park, E., 2004. Modeling field‐scale dense nonaqueous phase liquid dissolution kinetics in heterogeneous aquifers. Water Resources Research, 40(5). [https://doi.org/10.1029/2003wr002807 doi: 10.1029/2003WR002807]</ref><ref>Enfield, C.G., Wood, A.L., Espinoza, F.P., Brooks, M.C., Annable, M. and Rao, P.S.C., 2005. Design of aquifer remediation systems:(1) Describing hydraulic structure and NAPL architecture using tracers. Journal of Contaminant Hydrology, 81(1-4), pp.125-147. [https://doi.org/10.1016/j.jconhyd.2005.08.003 doi: 10.1016/j.jconhyd.2005.08.003]</ref><ref name="Jawitz2005" /><ref>Wood, A.L., Enfield, C.G., Espinoza, F.P., Annable, M., Brooks, M.C., Rao, P.S.C., Sabatini, D. and Knox, R., 2005. Design of aquifer remediation systems:(2) Estimating site-specific performance and benefits of partial source removal. Journal of contaminant hydrology, 81(1-4), pp.148-166. [https://doi.org/10.1016/j.jconhyd.2005.08.004 doi: 10.1016/j.jconhyd.2005.08.004]</ref> (also see [[Source Zone Modeling]]). Common approaches include analytical source strength function models, the power source depletion model, and DNAPL source zone depletion estimation.
 ''Analytical Source Strength Models''<br />
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 ''DNAPL Source Zone Depletion Estimation''<br />
-There is a simplified model for estimating DNAPL source zone mass depletion using an effective Damköhler number (Da) approach that considers the groundwater velocity and the size of the NAPL source zone<ref name="Parker2004" />:
+There is a simplified model for estimating DNAPL source zone mass depletion using an effective [[wikipedia: Damköhler numbers | Damköhler number]] (Da) approach that considers the groundwater velocity and the size of the NAPL source zone<ref name="Parker2004" />:
 ::::[[File:Annable1w2Equation8.PNG | left]]<BR clear="left">

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 ==Mathematics of Mass Flux/Discharge==
-Consider a simplified site involving a contaminant source from which mass is removed under natural gradient groundwater flow, generating a much larger dissolved contaminant plume. We define mass flux, ''J'' [M/L<sup>2</sup>/T] as the product of the Darcy flux (sometimes called Darcy velocity, see [[Advection and Groundwater Flow]]), ''q'' [L/T], and the local concentration of contaminant, ''C'' [M/L<sup>3</sup>], in the aqueous phase:
+Consider a simplified site involving a contaminant source from which mass is removed under natural gradient groundwater flow, generating a much larger dissolved contaminant plume. We define mass flux, ''J'' [M/L<sup>2</sup>/T] as the product of the [[wikipedia: Henry Darcy | Darcy]] flux (sometimes called Darcy velocity, see [[Advection and Groundwater Flow]]), ''q'' [L/T], and the local concentration of contaminant, ''C'' [M/L<sup>3</sup>], in the aqueous phase:
 ::::[[File:Annable1w2Equation1.PNG | left]]<BR clear="left">
-The Darcy flux can be calculated by applying Darcy’s law along the direction of the plume axis at the location of interest:
+The Darcy flux can be calculated by applying [[wikipedia: Darcy’s law | Darcy’s law]] along the direction of the plume axis at the location of interest:
 ::::[[File:Annable1w2Equation2.PNG | left]]<BR clear="left">