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Cite Details

H.-J. Yang, H. A. Tchelepi and D. M. Tartakovsky, "Method of distributions for two-phase flow in heterogeneous porous media", Water Resour. Res., vol. 58, no. 12, doi:10.1029/2022WR032607, pp. e2022WR032607, 2022


Multiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi-phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid-flow response is typically done within a probabilistic framework. This task is computationally demanding due to, e.g., the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision-making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two-phase fluid flow problems; however, FROST relies on MCS to compute the travel-time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF-FROST approach yields the CDF of the saturation field without resorting to sampling-based strategies. Our numerical experiments demonstrate the high accuracy of CDF-FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

BibTeX Entry

author = {H.-J. Yang and H. A. Tchelepi and D. M. Tartakovsky},
title = {Method of distributions for two-phase flow in heterogeneous porous media},
year = {2022},
urlpdf = {},
journal = {Water Resour. Res.},
volume = {58},
number = {12},
doi = {10.1029/2022WR032607},
pages = {e2022WR032607}