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Stochastic analysis of three‐phase flow in heterogeneous porous media: 1. Spectral/perturbation approach
Author(s) -
Abdin Alaa E.,
Kaluarachchi Jagath J.
Publication year - 1997
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/96wr00041
Subject(s) - perturbation (astronomy) , porous medium , nonlinear system , stochastic process , two phase flow , mathematics , permeability (electromagnetism) , statistical physics , mechanics , flow (mathematics) , porosity , physics , statistics , geotechnical engineering , geology , geometry , quantum mechanics , membrane , biology , genetics
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.