TY - JOUR
T1 - Stochastic analysis of transient three-phase flow in heterogeneous porous media
AU - Chen, Mingjie
AU - Keller, Arturo A.
AU - Lu, Zhiming
N1 - Funding Information:
The authors would like to acknowledge the funding from the Chevron-LANL oil shale project and cooperation between Chevron Energy Technology Company and Los Alamos National Laboratory.
PY - 2009
Y1 - 2009
N2 - In this manuscript, we extend the stochastic analysis of transient two-phase flow (Chen et al., Water Resour Res 42:W03425, 2006) to three-phase flow, i.e., water, air, and NAPL. We use the van Genuchten model and the Parker and Lenhard three-phase model to describe the relationships between phase saturation, phase relative permeability, and capillary pressure. The log-transformations of intrinsic permeability Y(x) = ln κ(x), soil pore size distribution parameter β ow(x) = ln α ow (x) between water and NAPL, and β ao(x) = ln α ao(x) between air and NAPL, and van Genuchten fitting parameter n̄(x) = ln [n(x) - 1] are treated as stochastic variables that are normally distributed with a separable exponential covariance model. The Karhunen-Loeve expansion and perturbation method (KLME) is used to solve the resulting equations. We evaluate the stochastic model using two-dimensional examples of three-phase flow with NAPL leakage. We also conduct Monte Carlo (MC) simulations to verify the stochastic model. A comparison of results from MC and KLME indicates the validity of the proposed KLME application in three-phase flow. The computational efficiency of the KLME approach over MC methods is at least an order of magnitude for three-phase flow problems. This verified stochastic model is then used to investigate the sensitivity of fluid saturation variances to the input variances.
AB - In this manuscript, we extend the stochastic analysis of transient two-phase flow (Chen et al., Water Resour Res 42:W03425, 2006) to three-phase flow, i.e., water, air, and NAPL. We use the van Genuchten model and the Parker and Lenhard three-phase model to describe the relationships between phase saturation, phase relative permeability, and capillary pressure. The log-transformations of intrinsic permeability Y(x) = ln κ(x), soil pore size distribution parameter β ow(x) = ln α ow (x) between water and NAPL, and β ao(x) = ln α ao(x) between air and NAPL, and van Genuchten fitting parameter n̄(x) = ln [n(x) - 1] are treated as stochastic variables that are normally distributed with a separable exponential covariance model. The Karhunen-Loeve expansion and perturbation method (KLME) is used to solve the resulting equations. We evaluate the stochastic model using two-dimensional examples of three-phase flow with NAPL leakage. We also conduct Monte Carlo (MC) simulations to verify the stochastic model. A comparison of results from MC and KLME indicates the validity of the proposed KLME application in three-phase flow. The computational efficiency of the KLME approach over MC methods is at least an order of magnitude for three-phase flow problems. This verified stochastic model is then used to investigate the sensitivity of fluid saturation variances to the input variances.
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U2 - 10.1007/s00477-007-0198-y
DO - 10.1007/s00477-007-0198-y
M3 - Article
AN - SCOPUS:56449118599
SN - 1436-3240
VL - 23
SP - 93
EP - 109
JO - Stochastic Environmental Research and Risk Assessment
JF - Stochastic Environmental Research and Risk Assessment
IS - 1
ER -