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Title: Probabilistic Forecast of Single–Phase Flow in Porous Media With Uncertain Properties

Abstract

Uncertainty about geologic makeup and properties of the subsurface renders inadequate a unique quantitative prediction of flow and transport. Instead, multiple alternative scenarios have to be explored within the probabilistic framework, typically by means of Monte Carlo simulations (MCS). These can be computationally expensive, and often prohibitively so, especially when the goal is to compute the tails of a distribution, i.e., probabilities of rare events, which are necessary for risk assessment and decision making under uncertainty. We deploy the method of distributions to derive a deterministic equation for the cumulative distribution function (CDF) of hydraulic head in an aquifer with uncertain (random) hydraulic conductivity. The CDF equation relies on a self-consistent closure approximation, which ensures that the resulting CDF of hydraulic head has the same mean and variance as those computed with either statistical moment equation (the approach used herein) or MCS. We conduct a series of numerical experiments dealing with steady-state two-dimensional flow driven by either a natural hydraulic head gradient or a pumping well. Furthermore, these experiments reveal that the CDF method remains accurate and robust for highly heterogeneous formations with the variance of log conductivity as large as five. For the same accuracy, it is also upmore » to four orders of magnitude faster than MCS in computing hydraulic head with a required degree of confidence (probability).« less

Authors:
 [1]; ORCiD logo [1];  [1]; ORCiD logo [1]
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  1. Stanford Univ., Stanford, CA (United States). Dept. of Energy Resources Engineering
Publication Date:
Research Org.:
Stanford Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER)
OSTI Identifier:
1574863
Alternate Identifier(s):
OSTI ID: 1573410
Report Number(s):
DOE-STANFORD-0019130-4
Journal ID: ISSN 0043-1397
Grant/Contract Number:  
SC0019130
Resource Type:
Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
Journal Volume: 55; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; uncertainty quantification; groundwater flow; random conductivity; method of distributions; risk assessment; rare events

Citation Formats

Jun Yang, Hyung, Boso, Francesca, Tchelepi, Hamdi A., and Tartakovsky, Daniel M. Probabilistic Forecast of Single–Phase Flow in Porous Media With Uncertain Properties. United States: N. p., 2019. Web. doi:10.1029/2019WR026090.
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Jun Yang, Hyung, Boso, Francesca, Tchelepi, Hamdi A., & Tartakovsky, Daniel M. Probabilistic Forecast of Single–Phase Flow in Porous Media With Uncertain Properties. United States. doi:10.1029/2019WR026090.
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Jun Yang, Hyung, Boso, Francesca, Tchelepi, Hamdi A., and Tartakovsky, Daniel M. Fri . "Probabilistic Forecast of Single–Phase Flow in Porous Media With Uncertain Properties". United States. doi:10.1029/2019WR026090. https://www.osti.gov/servlets/purl/1574863.
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@article{osti_1574863,
title = {Probabilistic Forecast of Single–Phase Flow in Porous Media With Uncertain Properties},
author = {Jun Yang, Hyung and Boso, Francesca and Tchelepi, Hamdi A. and Tartakovsky, Daniel M.},
abstractNote = {Uncertainty about geologic makeup and properties of the subsurface renders inadequate a unique quantitative prediction of flow and transport. Instead, multiple alternative scenarios have to be explored within the probabilistic framework, typically by means of Monte Carlo simulations (MCS). These can be computationally expensive, and often prohibitively so, especially when the goal is to compute the tails of a distribution, i.e., probabilities of rare events, which are necessary for risk assessment and decision making under uncertainty. We deploy the method of distributions to derive a deterministic equation for the cumulative distribution function (CDF) of hydraulic head in an aquifer with uncertain (random) hydraulic conductivity. The CDF equation relies on a self-consistent closure approximation, which ensures that the resulting CDF of hydraulic head has the same mean and variance as those computed with either statistical moment equation (the approach used herein) or MCS. We conduct a series of numerical experiments dealing with steady-state two-dimensional flow driven by either a natural hydraulic head gradient or a pumping well. Furthermore, these experiments reveal that the CDF method remains accurate and robust for highly heterogeneous formations with the variance of log conductivity as large as five. For the same accuracy, it is also up to four orders of magnitude faster than MCS in computing hydraulic head with a required degree of confidence (probability).},
doi = {10.1029/2019WR026090},
journal = {Water Resources Research},
number = ,
volume = 55,
place = {United States},
year = {2019},
month = {11}
}
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DOI:  10.1029/2019WR026090
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