Method of Distributions for Quantification of Geologic Uncertainty in Flow Simulations. Issue 7 (29th June 2020)

• Record Type: Journal Article
• Authors: Yang, Hyung Jun; Boso, Francesca; Tchelepi, Hamdi A.; Tartakovsky, Daniel M.
• Is Part Of: Water resources research. Volume 56:Issue 7(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-06-29
• Subjects: geologic uncertainty -- risk assessment -- probability; Hydrology -- Periodicals; 333.91
• DOI: 10.1029/2020WR027643
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: Probabilistic models of subsurface flow and transport are required for risk assessment and reliable decision making under uncertainty. These applications require accurate estimates of confidence intervals, which generally cannot be ascertained with statistical moments such as mean (unbiased estimate) and variance (a measure of uncertainty) of a quantity of interest (QoI). The method of distributions provides this information by computing either the probability density function or the cumulative distribution function (CDF‐) of the QoI. The standard method can be orders of magnitude faster than Monte Carlo simulations (MCS) but is applicable to stationary, mildly to moderately heterogeneous porous media in which the coefficient of variation of input parameters (e.g., log‐conductivity) is below four. Our CDF‐random domain decomposition (RDD) framework alleviates these limitations by combining the method of distributions and RDD; it also accounts for uncertainty in the geologic makeup of a subsurface environment. For a given realization of the geological map, we derive a deterministic equation for the conditional CDF of hydraulic head of steady single‐phase flow. The solutions of this equation are then averaged over realizations of the geological map‐ to compute the hydraulic head CDF. Our numerical experiments reveal that the CDF‐RDD method remains accurate for two‐dimensional flow in a porous medium composed of two heterogeneous hydrofacies, a setting in which the original CDF method fails. For the same accuracy, the CDF‐RDD method is an order of magnitude faster than MCS. Key Points: Our method combines the random domain decomposition and the method of distributions The method accounts for geologic and parametric uncertainties The method handles high heterogeneity and is orders of magnitude faster than Monte Carlo