A consistent set of parametric models for the two‐phase flow of immiscible fluids in the subsurface

TLDR

Accurate estimates of unsaturated hydraulic properties are essential for quantitative multiphase flow modeling, and theoretical and experimental evidence shows the need to match predicted and observed hydraulic conductivities at sub‑saturation, with hysteresis described by the Scott et al. model. The study introduces a consistent set of parametric models for isothermal, hysteretic unsaturated fluid retention and hydraulic conductivity in typical two‑phase systems such as water–air or water–hydrocarbon.

Abstract

Accurate estimates of the unsaturated hydraulic properties are needed for any quantitative description of multiphase flow in porous media. This paper presents a consistent set of parametric models for the isothermal, hysteretic unsaturated fluid phase content (retention) and hydraulic conductivity functions of typical two‐phase systems like water and air, or water and hydrocarbons. The equations are obtained by combining expressions for the hysteretic fluid retention curves with the statistical pore size distribution model of Mualem (1976) which predicts the hydraulic conductivity from more easily measured fluid retention data. Hysteresis is described using the model of Scott et al. (1983). The existence of residual fluid saturations for both the wetting and non wetting fluids is justified. Theoretical and experimental considerations indicate a need to match predicted and observed hydraulic conductivities at fluid phase contents less than full saturation.