Stochastic analysis of transient three-phase flow in heterogeneous porous media

Mingjie Chen, Arturo A. Keller, Zhiming Lu

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)93-109
Number of pages17
JournalStochastic Environmental Research and Risk Assessment
Volume23
Issue number1
DOIs
Publication statusPublished - 2009

Fingerprint

three phase flow
transient flow
Stochastic models
Porous materials
porous medium
nonaqueous phase liquid
Water
Capillarity
Air
Computational efficiency
Two phase flow
Pore size
Monte Carlo methods
saturation
permeability
Soils
Fluids
capillary pressure
air
two phase flow

ASJC Scopus subject areas

  • Environmental Engineering
  • Environmental Science(all)
  • Environmental Chemistry
  • Water Science and Technology
  • Safety, Risk, Reliability and Quality

Cite this

Stochastic analysis of transient three-phase flow in heterogeneous porous media. / Chen, Mingjie; Keller, Arturo A.; Lu, Zhiming.

In: Stochastic Environmental Research and Risk Assessment, Vol. 23, No. 1, 2009, p. 93-109.

Research output: Contribution to journalArticle

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