Analytical Estimation of Water-Oil Relative Permeabilities through Fractures

Abstract

Modeling multiphase flow through fractures is a key issue for understanding flow mechanism and performance prediction of fractured petroleum reservoirs, geothermal reservoirs, underground aquifers and carbon-dioxide sequestration. One of the most challenging subjects in modeling of fractured petroleum reservoirs is quantifying fluids competition for flow in fracture network (relative permeability curves). Unfortunately, there is no standard technique for experimental measurement of relative permeabilities through fractures and the existing methods are very expensive, time consuming and erroneous. Although, several formulations were presented to calculate fracture relative permeability curves in the form of linear and power functions of flowing fluids saturation, it is still unclear what form of relative permeability curves must be used for proper modeling of flow through fractures and consequently accurate reservoir simulation. Basically, the classic linear relative permeability (X-type) curves are used in almost all of reservoir simulators. In this work, basic fluid flow equations are combined to develop a new simple analytical model for water-oil two phase flow in a single fracture. The model gives rise to simple analytic formulations for fracture relative permeabilities. The model explicitly proves that water-oil relative permeabilities in fracture network are functions of fluids saturation, viscosity ratio, fluids density, inclination of fracture plane from horizon, pressure gradient along fracture and rock matrix wettability, however they were considered to be only functions of saturations in the classic X-type and power (Corey [35] and Honarpour et al. [28, 29]) models. Eventually, validity of the proposed formulations is checked against literature experimental data. The proposed fracture relative permeability functions have several advantages over the existing ones. Firstly, they are explicit functions of the parameters which are known for each of simulation computational cells or easy to measure in laboratory. It is also the first model that takes gravity effects and wettability of fracture walls into consideration and individually developed for water and oil-wet systems. Furthermore, the newly developed formulations are simple, efficient and accurate. Thus, they are recommended for implementation in dual and multiple continuum commercial reservoir simulators.