Groundwater Contaminant Transport: Prediction Under Uncertainty, With Application to the MADE Transport Experiment
Transport of solutes in porous media at the laboratory scale is governed by an Advection Dispersion Equation (ADE). The advection is by the fluid velocity U and dispersion by DdL = UαdL, where the longitudinal dispersivity αdL is of the order of the pore size. Numerous data revealed that the longitu...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2019-06-01
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| Series: | Frontiers in Environmental Science |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fenvs.2019.00079/full |
| _version_ | 1818144072202715136 |
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| author | Aldo Fiori Antonio Zarlenga Alberto Bellin Vladimir Cvetkovic Gedeon Dagan |
| author_facet | Aldo Fiori Antonio Zarlenga Alberto Bellin Vladimir Cvetkovic Gedeon Dagan |
| author_sort | Aldo Fiori |
| collection | DOAJ |
| description | Transport of solutes in porous media at the laboratory scale is governed by an Advection Dispersion Equation (ADE). The advection is by the fluid velocity U and dispersion by DdL = UαdL, where the longitudinal dispersivity αdL is of the order of the pore size. Numerous data revealed that the longitudinal spreading of plumes at field scale is characterized by macrodispersivity αL, larger than αdL by orders of magnitude. This effect is attributed to heterogeneity of aquifers manifesting in the spatial variability of the logconductivity Y. Modeling Y as a stationary random field and for mean uniform flow (natural gradient), αL could be determined in an analytical form by a first order approximation in σY2 (variance of Y) of the flow and transport equations. Recently, models and numerical simulations for solving transport in highly heterogeneous aquifers (σY2>1), primarily in terms of the mass arrival (the breakthrough curve BTC), were advanced. In all cases ergodicity, which allows to exchange the unknown BTC with the ensemble mean, was assumed to prevail for large plumes, compared to the logconductivity integral scale. Besides, the various statistical parameters characterizing the logconductivity structure as well as the mean flow were assumed to be known deterministically. The present paper investigates the uncertainty of the non-ergodic BTC due to the finiteness of the plume size as well as due to the uncertainty of the various parameters on which the BTC depends. By the use of a simplified transport model we developed in the past (which led to accurate results for ergodic plumes), we were able to get simple results for the variance of the BTC. It depends in an analytical manner on the flow parameters as well as on the dimension of the initial plume relative to the integral scale of logconductivity covariance. The results were applied to the analysis of the uncertainty of the plume spatial distribution of the MADE transport experiment. This was achieved by using the latest, recent, analysis of the MADE aquifer conductivity data. |
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| institution | Directory Open Access Journal |
| issn | 2296-665X |
| language | English |
| last_indexed | 2024-12-11T11:41:45Z |
| publishDate | 2019-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Environmental Science |
| spelling | doaj.art-0b71fd0f14df45a189814d7e954da92d2022-12-22T01:08:36ZengFrontiers Media S.A.Frontiers in Environmental Science2296-665X2019-06-01710.3389/fenvs.2019.00079442673Groundwater Contaminant Transport: Prediction Under Uncertainty, With Application to the MADE Transport ExperimentAldo Fiori0Antonio Zarlenga1Alberto Bellin2Vladimir Cvetkovic3Gedeon Dagan4Department of Engineering, Roma Tre University, Rome, ItalyDepartment of Engineering, Roma Tre University, Rome, ItalyDepartment of Civil, Environmental and Mechanical Engineering, University of Trento, Trento, ItalyDepartment of Water Resources Engineering, Royal Institute of Technology, Stockholm, SwedenSchool of Mechanical Engineering, Tel Aviv University, Ramat Aviv, IsraelTransport of solutes in porous media at the laboratory scale is governed by an Advection Dispersion Equation (ADE). The advection is by the fluid velocity U and dispersion by DdL = UαdL, where the longitudinal dispersivity αdL is of the order of the pore size. Numerous data revealed that the longitudinal spreading of plumes at field scale is characterized by macrodispersivity αL, larger than αdL by orders of magnitude. This effect is attributed to heterogeneity of aquifers manifesting in the spatial variability of the logconductivity Y. Modeling Y as a stationary random field and for mean uniform flow (natural gradient), αL could be determined in an analytical form by a first order approximation in σY2 (variance of Y) of the flow and transport equations. Recently, models and numerical simulations for solving transport in highly heterogeneous aquifers (σY2>1), primarily in terms of the mass arrival (the breakthrough curve BTC), were advanced. In all cases ergodicity, which allows to exchange the unknown BTC with the ensemble mean, was assumed to prevail for large plumes, compared to the logconductivity integral scale. Besides, the various statistical parameters characterizing the logconductivity structure as well as the mean flow were assumed to be known deterministically. The present paper investigates the uncertainty of the non-ergodic BTC due to the finiteness of the plume size as well as due to the uncertainty of the various parameters on which the BTC depends. By the use of a simplified transport model we developed in the past (which led to accurate results for ergodic plumes), we were able to get simple results for the variance of the BTC. It depends in an analytical manner on the flow parameters as well as on the dimension of the initial plume relative to the integral scale of logconductivity covariance. The results were applied to the analysis of the uncertainty of the plume spatial distribution of the MADE transport experiment. This was achieved by using the latest, recent, analysis of the MADE aquifer conductivity data.https://www.frontiersin.org/article/10.3389/fenvs.2019.00079/fullsolute transportheterogeneous porous formationsbreakthrough curve (BTC)uncertaintyMADE experimentstochastic subsurface hydrology |
| spellingShingle | Aldo Fiori Antonio Zarlenga Alberto Bellin Vladimir Cvetkovic Gedeon Dagan Groundwater Contaminant Transport: Prediction Under Uncertainty, With Application to the MADE Transport Experiment Frontiers in Environmental Science solute transport heterogeneous porous formations breakthrough curve (BTC) uncertainty MADE experiment stochastic subsurface hydrology |
| title | Groundwater Contaminant Transport: Prediction Under Uncertainty, With Application to the MADE Transport Experiment |
| title_full | Groundwater Contaminant Transport: Prediction Under Uncertainty, With Application to the MADE Transport Experiment |
| title_fullStr | Groundwater Contaminant Transport: Prediction Under Uncertainty, With Application to the MADE Transport Experiment |
| title_full_unstemmed | Groundwater Contaminant Transport: Prediction Under Uncertainty, With Application to the MADE Transport Experiment |
| title_short | Groundwater Contaminant Transport: Prediction Under Uncertainty, With Application to the MADE Transport Experiment |
| title_sort | groundwater contaminant transport prediction under uncertainty with application to the made transport experiment |
| topic | solute transport heterogeneous porous formations breakthrough curve (BTC) uncertainty MADE experiment stochastic subsurface hydrology |
| url | https://www.frontiersin.org/article/10.3389/fenvs.2019.00079/full |
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