combining geostatistics and physically-based simulations
TRANSCRIPT
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Mathieu Le Coz (IRSN) / Léa Pannecoucke (Mines ParisTech) / Xavier Freulon (Mines ParisTech) / Charlotte Cazala (IRSN) / Chantal de Fouquet (Mines ParisTech)
Combining geostatistics and physically-based simulations to characterize contaminated soils
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Context
How to characterize contamination in soils or groundwater when dealing witha polluted site needing remediation and with a small amount of availableobservations?
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Context
How to characterize contamination in soils or groundwater when dealing witha polluted site needing remediation and with a small amount of availableobservations?
Geostatistical estimation (kriging)
+ Observations honored
- Physical information not taken into account
- Performances limited if few data available
Direct flow-and-transport simulations
+ Physically-based model
- Uncertainties in modeling parameters
- Observations not honored
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Outline
Development of a method using physical information given by physically-basedsimulations into a geostatistical framework
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Outline
Development of a method using physical information given by physically-basedsimulations into a geostatistical framework:
1. The Kriging with numerical variograms (KNV) method
2. A synthetic reference test case
3. Comparison of KNV to classical krigings
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Kriging with Numerical Variograms (KNV)
Development of a method using physical information given by physically-basedsimulations into a geostatistical framework:
1. The Kriging with numerical variograms (KNV) method
2. A synthetic reference test case
3. Comparison of KNV to classical krigings
![Page 7: Combining geostatistics and physically-based simulations](https://reader034.vdocuments.us/reader034/viewer/2022051406/627d208ffe4fd1121c51301b/html5/thumbnails/7.jpg)
Kriging with Numerical Variograms (KNV)Numerous observations
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Kriging with Numerical Variograms (KNV)Numerous observations
Variogram fitting
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Kriging with Numerical Variograms (KNV)Numerous observations
Variogram fitting
Kriging
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Kriging with Numerical Variograms (KNV)Numerous observations Small amount of observations
Variogram fitting
Kriging
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Kriging with Numerical Variograms (KNV)Numerous observations Small amount of observations
Variogram fitting
Kriging
Variogram fitting
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Kriging with Numerical Variograms (KNV)Numerous observations Small amount of observations
Variogram fitting
Kriging
Variogram fitting
Kriging?
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Kriging with Numerical Variograms (KNV)Small amount of observations
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Kriging with Numerical Variograms (KNV)Small amount of observationsFlow-and-transport simulations
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Kriging with Numerical Variograms (KNV)Small amount of observationsFlow-and-transport simulations
Numerical variograms
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Kriging with Numerical Variograms (KNV)Small amount of observations
Kriging
Flow-and-transport simulations
Numerical variograms
![Page 17: Combining geostatistics and physically-based simulations](https://reader034.vdocuments.us/reader034/viewer/2022051406/627d208ffe4fd1121c51301b/html5/thumbnails/17.jpg)
Synthetic reference test case
Development of a method using physical information given by physically-basedsimulations into a geostatistical framework:
1. The Kriging with numerical variograms (KNV) method
2. A synthetic reference test case
3. Comparison of KNV to classical krigings
![Page 18: Combining geostatistics and physically-based simulations](https://reader034.vdocuments.us/reader034/viewer/2022051406/627d208ffe4fd1121c51301b/html5/thumbnails/18.jpg)
Synthetic reference test case
Model settings (2D vertical section)
- Sandy loam facies with heterogeneous textural properties (i.e., sand, silt, clay contents);
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Synthetic reference test case
Model settings (2D vertical section)
- Sandy loam facies with heterogeneous textural properties (i.e., sand, silt, clay contents);- Fixed upstream-downstream head: unsaturated zone ~7 m deep;- Contamination due to a point source of tritium: 4 years simulation with the code MELODIE.
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Synthetic reference test case
Model settings (2D vertical section)
- Sandy loam facies with heterogeneous textural properties (i.e., sand, silt, clay contents);- Fixed upstream-downstream head: unsaturated zone ~7 m deep;- Contamination due to a point source of tritium: 4 years simulation with the code MELODIE.
Zone of interest
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Synthetic reference test case
Model settings (2D vertical section)
- Sandy loam facies with heterogeneous textural properties (i.e., sand, silt, clay contents);- Fixed upstream-downstream head: unsaturated zone ~7 m deep;- Contamination due to a point source of tritium: 4 years simulation with the code MELODIE.
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Synthetic reference test case
Sampling scenario
- 4 boreholes with activity;
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Synthetic reference test case
Sampling scenario
- 4 boreholes with activity;- 8 boreholes with soil texture.
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Synthetic reference test case
Observations of texture
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Synthetic reference test case
Observations of texture
Conditional simulations of texture
RGeostats
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Synthetic reference test case
Observations of texture
Conditional simulations of texture
Conditional simulations of hydraulic parameters
RGeostats
Rosetta PTF
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Synthetic reference test case
Observations of texture
Conditional simulations of texture
Conditional simulations of hydraulic parameters
Simulations of tritium plume
RGeostats
Rosetta PTF
MELODIE
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Synthetic reference test caseSmall amount of observations
Kriging
Flow-and-transport simulations
Numerical variograms
![Page 29: Combining geostatistics and physically-based simulations](https://reader034.vdocuments.us/reader034/viewer/2022051406/627d208ffe4fd1121c51301b/html5/thumbnails/29.jpg)
KNV vs. classical krigings
Development of a method using physical information given by physically-basedsimulations into a geostatistical framework:
1. The Kriging with numerical variograms (KNV) method
2. A synthetic reference test case
3. Comparison of KNV to classical krigings
![Page 30: Combining geostatistics and physically-based simulations](https://reader034.vdocuments.us/reader034/viewer/2022051406/627d208ffe4fd1121c51301b/html5/thumbnails/30.jpg)
KNV vs. classical krigings
Ordinary kriging (OK), which is widely used but known to perform poorly whenthe number of data is too small or when the phenomenon under study is complex;
Kriging with external drift (KED), which enables the incorporation of auxiliaryvariables to take non-stationarity into account.
![Page 31: Combining geostatistics and physically-based simulations](https://reader034.vdocuments.us/reader034/viewer/2022051406/627d208ffe4fd1121c51301b/html5/thumbnails/31.jpg)
KNV vs. classical krigings
Ordinary kriging (OK), which is widely used but known to perform poorly whenthe number of data is too small or when the phenomenon under study is complex;
Kriging with external drift (KED), which enables the incorporation of auxiliaryvariables to take non-stationarity into account.
Auxiliary variable: empirical mean of set of simulations
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KNV vs. classical krigings
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KNV vs. classical krigings
![Page 34: Combining geostatistics and physically-based simulations](https://reader034.vdocuments.us/reader034/viewer/2022051406/627d208ffe4fd1121c51301b/html5/thumbnails/34.jpg)
KNV vs. classical krigings
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Conclusion
The characterization of the tritium plume within the unsaturated zone is notaccurate, due to the uncertainties related to hydraulic parameters, even if theinitial boundary conditions of the flow-and-transport model are fixed.
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Conclusion
The characterization of the tritium plume within the unsaturated zone is notaccurate, due to the uncertainties related to hydraulic parameters, even if theinitial boundary conditions of the flow-and-transport model are fixed.
KNV improves the estimates of the tritium plume in the unsaturated zonecompared to OK and KED: estimation errors and standard deviation errors arereduced.
![Page 37: Combining geostatistics and physically-based simulations](https://reader034.vdocuments.us/reader034/viewer/2022051406/627d208ffe4fd1121c51301b/html5/thumbnails/37.jpg)
Conclusion
The characterization of the tritium plume within the unsaturated zone is notaccurate, due to the uncertainties related to hydraulic parameters, even if theinitial boundary conditions of the flow-and-transport model are fixed.
KNV improves the estimates of tritium plume in the unsaturated zonecompared to OK and KED: estimation errors and standard deviation errors arereduced.
KNV is even more interesting when the number of observations of pollutant isreduced. It also works when the boreholes are located around the zone of highvalues of activities.
![Page 38: Combining geostatistics and physically-based simulations](https://reader034.vdocuments.us/reader034/viewer/2022051406/627d208ffe4fd1121c51301b/html5/thumbnails/38.jpg)
Conclusion
The characterization of the tritium plume within the unsaturated zone is notaccurate, due to the uncertainties related to hydraulic parameters, even if theinitial boundary conditions of the flow-and-transport model are fixed.
KNV improves the estimates of tritium plume in the unsaturated zonecompared to OK and KED: estimation errors and standard deviation errors arereduced.
KNV is even more interesting when the number of observations of pollutant isreduced. It also works when the boreholes are located around the zone of highvalues of activities.
Ongoing work: implementation on a real 3D study-case…
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Thank you for your attention
This study is a part of Kri-Terres project, supported by the French National Radioactive Waste Management Agency (ANDRA) underthe French “Investments for the Future” Program.