Title

Stochastic analysis of three-phase flow in heterogeneous porous media: I. Spectral/perturbation analysis

Document Type

Article

Journal/Book Title/Conference

Water Resources Research

Volume

33

Issue

7

Publication Date

7-1-1997

First Page

1549

Last Page

1558

DOI

10.1029/96WR00041

Abstract

Stochastic analysis of steady state three-phase (water, oil, and air) flow in heterogeneous porous media was performed using the perturbation theory and spectral representation technique. The governing equations describing flow of water, oil, and air are coupled and nonlinear. The key stochastic input variables are intrinsic permeability, k, and the soil grain size distribution index, α. Three different stochastic combinations of these two input parameters were considered in the analysis. The spectral/perturbation approach was used to develop closed-form expressions to describe stochastic variability of key output processes, such as capillary and individual phase pressures. The second paper of this two-part series [Abdin and Kaluarachchi, this issue] will discuss the applicability and the validity of the spectral/perturbation technique to study the stochastic behavior of three-phase flow using numerical simulations.

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