Efficient Monte Carlo With Graph-Based Subsurface Flow and Transport Models
Abstract
Simulating flow and transport in fractured porous media frequently involves solving numerical discretizations of partial differential equations with a large number of degrees of freedom using discrete fracture network (DFN) models. Uncertainty in the properties of the fracture network that controls flow and transport requires a large number of DFN simulations to statistically describe quantities of interest. However, the computational cost of solving more than a few realizations of a large DFN can be intractable. As a means of circumventing this problem, we utilize both a high-fidelity DFN model and a graphbased model of flow and transport in combination with a multifidelity Monte Carlo (MC) method to reduce the number of high-fidelity simulations that are needed to obtain an accurate estimate of the quantity of interest. We demonstrate the approach by estimating quantiles of the breakthrough time for a conservative tracer in an ensemble of fractured porous media. Our results demonstrate that a multifidelity MC estimate, whose computational cost is equal to the cost of 10 DFN simulations, can be as accurate as a standard MC estimate that utilizes 1,000 DFN simulations. Thus the combination of our graphbased model with multifidelity MC estimates effectively reduces the computational cost of themore »
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1492540
- Alternate Identifier(s):
- OSTI ID: 1438943
- Report Number(s):
- LA-UR-18-29485
Journal ID: ISSN 0043-1397
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Water Resources Research
- Additional Journal Information:
- Journal Volume: 54; Journal Issue: 5; Journal ID: ISSN 0043-1397
- Publisher:
- American Geophysical Union (AGU)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; Earth Sciences; Mathematics
Citation Formats
O'Malley, D., Karra, S., Hyman, J. D., Viswanathan, H. S., and Srinivasan, G. Efficient Monte Carlo With Graph-Based Subsurface Flow and Transport Models. United States: N. p., 2018.
Web. doi:10.1029/2017WR022073.
O'Malley, D., Karra, S., Hyman, J. D., Viswanathan, H. S., & Srinivasan, G. Efficient Monte Carlo With Graph-Based Subsurface Flow and Transport Models. United States. https://doi.org/10.1029/2017WR022073
O'Malley, D., Karra, S., Hyman, J. D., Viswanathan, H. S., and Srinivasan, G. Fri .
"Efficient Monte Carlo With Graph-Based Subsurface Flow and Transport Models". United States. https://doi.org/10.1029/2017WR022073. https://www.osti.gov/servlets/purl/1492540.
@article{osti_1492540,
title = {Efficient Monte Carlo With Graph-Based Subsurface Flow and Transport Models},
author = {O'Malley, D. and Karra, S. and Hyman, J. D. and Viswanathan, H. S. and Srinivasan, G.},
abstractNote = {Simulating flow and transport in fractured porous media frequently involves solving numerical discretizations of partial differential equations with a large number of degrees of freedom using discrete fracture network (DFN) models. Uncertainty in the properties of the fracture network that controls flow and transport requires a large number of DFN simulations to statistically describe quantities of interest. However, the computational cost of solving more than a few realizations of a large DFN can be intractable. As a means of circumventing this problem, we utilize both a high-fidelity DFN model and a graphbased model of flow and transport in combination with a multifidelity Monte Carlo (MC) method to reduce the number of high-fidelity simulations that are needed to obtain an accurate estimate of the quantity of interest. We demonstrate the approach by estimating quantiles of the breakthrough time for a conservative tracer in an ensemble of fractured porous media. Our results demonstrate that a multifidelity MC estimate, whose computational cost is equal to the cost of 10 DFN simulations, can be as accurate as a standard MC estimate that utilizes 1,000 DFN simulations. Thus the combination of our graphbased model with multifidelity MC estimates effectively reduces the computational cost of the problem by a factor of approximately 100.},
doi = {10.1029/2017WR022073},
journal = {Water Resources Research},
number = 5,
volume = 54,
place = {United States},
year = {2018},
month = {4}
}
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