A Fractal Gas-Water Relative Permeability Model in Geothermal Reservoirs

Abstract

Reliable gas-water relative permeability models are of significance for accurate numerical simulation for both petroleum and geothermal reservoirs. In this study, a modified Hagen-Poiseuille equation for gas/water flow was proposed based on the shell momentum balance method (Bird, 2002) with the water and gas distributed within pores. A gas-water relative permeability model is proposed based on fractal scaling theory. The Young-Laplace equations were employed in the proposed model to capture the mechanical equilibrium of gas and water at different temperatures. The new model has been validated by comparison to various experiments in the literature for steam-water relative permeability in geothermal rock samples. The results show that an increased fractal dimension for pore size distribution increases gas relative permeability but decreases the water relative permeability for a given saturation. However, the tortuosity fractal dimension only shows a significant effect on the water phase relative permeability. In addition, increasing temperature leads to lower surface tension which will then increase the steam relative permeability.