A New Model to Calculate Three-Phase Relative Permeabilities: Application and Validation for a Sandstone

Abstract

Three-phase flow in a porous medium is usually described by the Stone model (1970). This model is based on two-phase data and relies on empirical correlations. It is valid only under strong water wettability and recognized as being a poor predictor. The goal of the present study is to develop a mathematical model for three-phase flow avoiding any empirical correlations. In this paper, only strong water-wet and spreading conditions are considered. However the model could be relatively easily extended to oil-wet or even mixed-wet conditions. The model is based on a physically relevant description of phase distribution and flow mechanisms at the pore scale. The porous medium is described as a set of fractal pores, whose linear fractal dimension and size distributions are derived from a mercury intrusion capillary pressure curve. The fluids are allowed to flow together in the same fractal pore, gas in the center, water near the walls and oil in an intermediate phase. The relative permeabilities are evaluated by calculating the flow of each fluid applying Poiseuille's law. The model results are compared to relative permeabilities obtained by history matching of gas injection experiments. The same experiments are also simulated using Stone's model and laboratory measured two-phase data.