Stochastic analysis of three-phase flow in heterogeneous porous media: II. Numerical simulations
The first paper of this two-part series [Abdin and Kaluarachchi, this issue] developed a spectral/perturbation analysis to predict the variability of individual and capillary pressures of three-phase (water, oil, and air) flow in heterogeneous porous media. The work in this manuscript is an extension of that work to validate the applicability of the perturbation analysis and to study the stochastic behavior of three-phase flow. The input stochastic variables were soil grain size distribution index, α, and log k where k is the permeability. In this work a one-dimensional numerical solution was developed to solve the three coupled nonlinear flow equations. The results using three different combinations of input stochastic variables showed good agreement between perturbation and numerical analyses over a wide range of flow conditions. In addition, the results showed a large influence of subsurface heterogeneity on the predicted capillary pressure variability. In general, this variability was highest with the uncorrelated α and log k case followed by deterministic α (stochastic log k) and correlated cases. The results suggest that subsurface heterogeneity is important in predicting three-phase flow in heterogeneous porous media. Finally, the results of this work can be used as a preliminary step for stochastic analysis of three-fluid phase flow.