HR: 15:10h
AN: H43H-07    [Abstracts]
TI: Stochastic Analysis Of Water-Oil Phase Flow In Heterogeneous Media By Combining Karhunen-Loeve Expansion And Perturbation Method
AU: * Chen, M
EM: mchen@lanl.gov
AF: UCSB, University of California, Santa Barbara, CA 93106 United States
AU: * Chen, M
EM: mchen@lanl.gov
AF: LANL, Los Alamos National Lab, Los Alamos, NM 87545 United States
AU: Zhang, D
EM: donzhang@ou.edu
AF: OU, University of Oklahoma, Norman, OK 73019 United States
AU: Keller, A
EM: keller@bren.ucsb.edu
AF: UCSB, University of California, Santa Barbara, CA 93106 United States
AU: Lu, Z
EM: zhiming@lanl.gov
AF: LANL, Los Alamos National Lab, Los Alamos, NM 87545 United States
AB: We present a novel approach to modeling stochastic multiphase flow problems, for example NAPL flow, in a heterogeneous subsurface medium with random soil properties, in particular, with randomly heterogeneous intrinsic permeability and soil grain size. A stochastic model for steady state water-oil flow in two-dimensional random field is developed using the Karhunen-Loeve Moment Equation (KLME) approach and is numerically implemented. An exponential model is adopted to define the constitutive relationship between phase relative permeability and capillary pressure. The log-transformed intrinsic permeability Y(x) and soil pore size distribution $\beta$(x) are assumed to be Gaussian random functions with a separable exponential covariance function. The perturbation part of these two log-transformed soil properties is then decomposed into an infinite series based on a set of orthogonal normal random variables . The phase pressure, capillary pressure and phase mobility are decomposed by polynomial expansions and perturbation method. Combining these expansions of Y(x), $\beta$(x) and dependent pressures, the steady state water-oil flow equations and corresponding boundary conditions are reformulated as a series of differential equations up to 2nd order. These differential equations are solved numerically and the solutions are directly used to construct moments of phase pressure and capillary pressure. We demonstrate the validity of the proposed KLME model by favorably comparing 1st and 2nd order approximations to Monte Carlo simulations. The significant computational efficiency of the KLME approach over Monte Carlo simulation is also illustrated.
DE: 1719 Hydrology
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting