### 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 language | English |
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Pages (from-to) | 93-109 |

Number of pages | 17 |

Journal | Stochastic Environmental Research and Risk Assessment |

Volume | 23 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 |

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### ASJC Scopus subject areas

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

### Cite this

*Stochastic Environmental Research and Risk Assessment*,

*23*(1), 93-109. https://doi.org/10.1007/s00477-007-0198-y