Improved models to predict gas–water relative permeability in fractures and porous media

Abstract

Fractures and pores are major flow channels of fluid in low permeability and unconventional reservoirs. So, it is very important to accurately predict multiphase flow in fractures and porous media.In this paper, the empirical, semi-empirical, and theoretical relative permeability models in fractures and porous media are investigated. Among these models, four models have been usually suggested to represent two-phase flow behavior: X-model, Corey or Brooks–Corey model, viscous-coupling model and Chima's model. However, these models have not considered some factors that affect relative permeability significantly. For example, X-model doesn't reflect nonlinear characteristic, Corey or Brooks–Corey model neglects gas–liquid interaction, and viscous-coupling model and Chima's model don't consider irreducible phase.According to Chima's method, when the surface geometry of fracture is assumed to be two ideal parallel planes and that of fracture or pore is assumed to be a pipe, new analytical relative permeability models of fractures and porous media considering irreducible water have been proposed respectively, based on cubic law for flow in rectangular fractures, Poiseuille law for flow in pores; and the momentum balance and Newton's law of viscosity both in fractures and pores. Furthermore, we also improved these relative permeability models by considering the influence of tortuosity based on Brooks–Corey model. The results show that the relative permeability models are nonlinear functions of mobile water, viscosity, irreducible water and the fracture or pore-size distribution index. The gas and water relative permeabilities are different in fractures and pores, and the gas phase relative permeability is more sensitive to the surface geometry of flow channels. And compared with model of fractures, the gas phase relative permeability deviates by more than 50% while the water phase relative permeability deviates by less than 20% in pores. What's more, the deviation will become smaller with the increase of irreducible water saturation.The proposed model with irreducible water saturation of fractures is validated with experimental data from literature and good agreements between experimental data and those evaluated by the proposed model. And the model of porous media is validated by Brooks–Corey model and there is consistency in the forecasting result of two models when there is no irreducible water. The relative permeability models proposed in this work will be useful to professionals involved in modeling well performance, and gas production forecasting in low permeability and unconventional reservoirs.