Conditional simulations of water–oil flow in heterogeneous porous media

Abstract

This study is an extension of the stochastic analysis of transient two-phase flow in randomly heterogeneous porous media (Chen et al. in Water Resour Res 42:W03425, 2006), by incorporating direct measurements of the random soil properties. The log-transformed intrinsic permeability, soil pore size distribution parameter, and van Genuchten fitting parameter are treated as stochastic variables that are normally distributed with a separable exponential covariance model. These three random variables conditioned on given measurements are decomposed via Karhunen-Loève decomposition. Combined with the conditional eigenvalues and eigenfunctions of random variables, we conduct a series of numerical simulations using stochastic transient water-oil flow model (Chen et al. in Water Resour Res 42:W03425, 2006) based on the KLME approach to investigate how the number and location of measurement points, different random soil properties, as well as the correlation length of the random soil properties, affect the stochastic behavior of water and oil flow in heterogeneous porous media.

Conditional Multilevel Monte Carlo Simulation of Groundwater Flow in the Culebra Dolomite at the Waste Isolation Pilot Plant (WIPP) Site

“…In Zang and Lu (2004) and Chen et al (2008), the KL expansion of the covariance function in (10) was used to generate conditional log hydraulic conductivity field. However, the corresponding conditional covariance function is not spatially stationary.…”

Macroscopic visual displacement of a polymer solution for enhanced oil recovery: Hele-Shaw cell experiments and computational simulation

“…The results of the oil displacement processes can be analyzed and matched with the computational simulations of porous media with multiphase flow for validating the transport phenomena in the oil-water-porous-medium systems [21][22][23]. In 2006, Behbahani et al published results of simulations of two-dimensional water systems embedded in a heterogeneous porous medium displacing oil, comparing the simulation with experimental results [24].…”