Dispersion and Diffusion - Revision history

Jhurley: Redirected page to Groundwater Flow and Solute Transport

2020-12-21T22:17:51Z

Redirected page to Groundwater Flow and Solute Transport

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Jhurley: /* Matrix Diffusion */

2020-12-21T18:19:17Z

‎Matrix Diffusion

Jhurley: /* Macrodispersion */

2020-12-21T18:08:45Z

‎Macrodispersion

Jhurley: /* Macrodispersion */

2020-12-21T17:59:29Z

‎Macrodispersion

Jhurley: /* Macrodispersion */

2020-12-21T17:43:22Z

‎Macrodispersion

Jhurley: /* Macrodispersion */

2020-12-21T17:34:12Z

‎Macrodispersion

Jhurley: /* Macrodispersion */

2020-12-21T17:13:20Z

‎Macrodispersion

Jhurley: /* Macrodispersion */

2020-12-21T16:33:04Z

‎Macrodispersion

Admin at 18:38, 24 September 2020

2020-09-24T18:38:39Z

Admin at 18:37, 24 September 2020

2020-09-24T18:37:12Z

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 ===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">Payne, F.C., Quinnan, J.A. and Potter, S.T., 2008. Remediation hydraulics. CRC Press. [https://www.crcpress.com/Remediation-Hydraulics/Payne-Quinnan-Potter/9780849372490 ISBN:978-1-4200-0684-1]</ref><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, overtime, molecular diffusion slowly transports solutes into lower permeability zones (Figure 3). 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 4.
+Recently, an alternate conceptual model for describing large-scale plume spreading in heterogeneous soils has been proposed<ref name="ITRC2011" /><ref name="Payne2008">Payne, F.C., Quinnan, J.A. and Potter, S.T., 2008. Remediation hydraulics. CRC Press. [https://www.crcpress.com/Remediation-Hydraulics/Payne-Quinnan-Potter/9780849372490 ISBN:978-1-4200-0684-1]</ref><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, overtime, molecular diffusion slowly transports solutes into lower permeability zones (Figure 4). 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 4. 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>
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@@ Line 116: / Line 116: @@
 ==Macrodispersion==
-[[File:NewThinkingAboutDispersion.mp4 |thumbnail|right|500px|Figure 3. Matrix diffusion processes and their effects on plume persistence and attenuation.]]
+[[File:ADRFig2.PNG | thumb | right | 350px | Figure 3. Predicted variation in macrodispersivity with distance for varying ''σ<sup>2</sup>Y'' and correlation length = 3 m.]]
 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 2 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.
+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 3 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">Payne, F.C., Quinnan, J.A. and Potter, S.T., 2008. Remediation hydraulics. CRC Press. [https://www.crcpress.com/Remediation-Hydraulics/Payne-Quinnan-Potter/9780849372490 ISBN:978-1-4200-0684-1]</ref><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, overtime, molecular diffusion slowly transports solutes into lower permeability zones (Figure 3). 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 3.
+Recently, an alternate conceptual model for describing large-scale plume spreading in heterogeneous soils has been proposed<ref name="ITRC2011" /><ref name="Payne2008">Payne, F.C., Quinnan, J.A. and Potter, S.T., 2008. Remediation hydraulics. CRC Press. [https://www.crcpress.com/Remediation-Hydraulics/Payne-Quinnan-Potter/9780849372490 ISBN:978-1-4200-0684-1]</ref><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, overtime, molecular diffusion slowly transports solutes into lower permeability zones (Figure 3). 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 4.
 <br clear="left" />

@@ Line 119: / Line 119: @@
 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 2 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) 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.
+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 2 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===

@@ Line 119: / Line 119: @@
 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 2 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 are in the range of 0.5 to 5 m.
+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 2 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) 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===

@@ Line 119: / Line 119: @@
 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 help match the apparent large-scale spreading of the plume<ref name="ITRC2011" />. However, there is limited theoretical support for using large mechanical dispersion coefficients<ref name="Payne2008">Payne, F.C., Quinnan, J.A. and Potter, S.T., 2008. Remediation hydraulics. CRC Press. [https://www.crcpress.com/Remediation-Hydraulics/Payne-Quinnan-Potter/9780849372490 ISBN:978-1-4200-0684-1]</ref><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 transmissive zones, macrodispersion coefficients are often orders of magnitude greater than molecular diffusion coefficients, leading some to conclude that molecular diffusion can be ignored.
+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 2 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 are in the range of 0.5 to 5 m.
-Recently, an alternate conceptual model for describing large-scale plume spreading in heterogeneous soils has been proposed<ref name="Payne2008" /><ref name="ITRC2011" /><ref name="Hadley2014" />. 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, overtime, molecular diffusion slowly transports solutes into lower permeability zones (Figure 3). 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 3.
+===Matrix Diffusion===
 <br clear="left" />

@@ Line 7: / Line 7: @@
 *[[Plume Response Modeling]]
-'''CONTRIBUTOR(S):'''
+'''CONTRIBUTOR(S):''' [[Dr. Charles Newell, P.E.|Dr. Charles Newell]] and [[Dr. Robert Borden, P.E.|Dr. Robert Borden]]
 '''Key Resource(s):'''