E. S. Romm in 1966 (Romm 1966) proposed an equation to calculate the relative permeability curves in fractured systems based on experimental results. His research concluded that relative permeability is a linear function of saturation (krw = Sw, krnw=Snw). Currently most fractured reservoir simulators use E. S. Romm's equation to estimate relative permeability curves in fractures. Later in 1994, D. A. Pieters and R. M. Graves (Pieters & Graves 1994) demonstrated experimentally that relative permeability curves are not a linear function of saturation. In this work, we use the concepts of shell momentum balance (Bird, Stewart & Lightfoot 2002), the equation of change for isothermal systems, Newton's law of viscosity and Darcy's law in order to derive an analytical equation to calculate relative permeability curves in fractured systems for two phase flow. These proposed equations assume gravitational segregation between the two phases (Rossen & Kumar 1992), Newtonian fluids, incompressible fluids, Laminar flow, steady-state and constant temperature. These proposed equations in this paper could be applied to calculate relative permeability curves in two-phase flow systems in fractures. Further, the two-phase relative permeability curves can be used to predict the behavior of naturally fractured reservoirs. This work also includes a comparison of the calculated data between E. S. Romm's equation, Pieters and Graves's Laboratory data and the equations proposed in this paper. As a result of this research we demonstrated analytically that relative permeability curves in two-phase flow in fractures are not a linear function of saturation. Also we confirmed the non linearity of the fracture's relative permeability curves using a reservoir and fluid data with the proposed equation.
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