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Title: Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach

Abstract

In this paper, we present a method combining multilevel Monte Carlo (MLMC) and a graph-based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are performed using a discrete fracture network (DFN), and instead of using various grid resolutions for levels in the MLMC, which is standard practice in MLMC, we identify a hierarchy of subnetworks in the DFN based on the shortest topological paths through the network using a graph-based method. While the mean of these ensembles is of critical importance, the variance is also essential in fractured media where uncertainty is an overarching theme, and understanding variability across an ensemble is a requirement for safety assessments. The method provides good estimates of the mean and variance at two orders of magnitude lower computational cost than MC.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]
  1. Politecnico di Torino, Turin (Italy); INdAM Research Group GNCS, Rome (Italy)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. INdAM Research Group GNCS, Rome (Italy); Politecnico di Torino, Turin (Italy)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program; MIUR
OSTI Identifier:
1638630
Alternate Identifier(s):
OSTI ID: 1633493
Report Number(s):
LA-UR-19-29755
Journal ID: ISSN 0043-1397;1944-7973
Grant/Contract Number:  
89233218CNA000001; 20180621ECR; 20170103DR; E11G18000350001
Resource Type:
Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
Journal Volume: 56; Journal Issue: 6; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; Discrete fracture networks; multilevel Monte Carlo; graph theory; first passage time; uncertainty quantification

Citation Formats

Berrone, S., Hyman, J. D., and Pieraccini, S. Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach. United States: N. p., 2020. Web. https://doi.org/10.1029/2019wr026493.
Berrone, S., Hyman, J. D., & Pieraccini, S. Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach. United States. https://doi.org/10.1029/2019wr026493
Berrone, S., Hyman, J. D., and Pieraccini, S. Wed . "Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach". United States. https://doi.org/10.1029/2019wr026493. https://www.osti.gov/servlets/purl/1638630.
@article{osti_1638630,
title = {Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach},
author = {Berrone, S. and Hyman, J. D. and Pieraccini, S.},
abstractNote = {In this paper, we present a method combining multilevel Monte Carlo (MLMC) and a graph-based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are performed using a discrete fracture network (DFN), and instead of using various grid resolutions for levels in the MLMC, which is standard practice in MLMC, we identify a hierarchy of subnetworks in the DFN based on the shortest topological paths through the network using a graph-based method. While the mean of these ensembles is of critical importance, the variance is also essential in fractured media where uncertainty is an overarching theme, and understanding variability across an ensemble is a requirement for safety assessments. The method provides good estimates of the mean and variance at two orders of magnitude lower computational cost than MC.},
doi = {10.1029/2019wr026493},
journal = {Water Resources Research},
number = 6,
volume = 56,
place = {United States},
year = {2020},
month = {5}
}

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