Steady State Immiscible Oil And Water Flow In a Smooth-walled Fracture
Authors: Pan X. , Wong R.C. , Maini B.B. 
Published: March 2010

Abstract
Steady state immiscible oil/water flow experiments were conducted in horizontal smooth-walled fractures. The effects of fracture aperture, injection rate and injection method on the immiscible flow characteristics were investigated. The experimental data were analysed using a porous medium approach and an equivalent homogeneous single-phase method. The pressure gradients predicted by the latter are in good agreement with those measured in the experiments. Contrary to the well-known Romm's relative permeability versus saturation correlation, the experimental data indicated that the sum of the relative permeabilitiesis less than one over a range of saturation, which is attributed to the effect of phase interference on the immiscible flow. The effect of phase interference is more significant in the case of well mixed oil/water flow than otherwise. The results also indicate that the fracture aperture does not have a significant influence on the relative permeabilities of oil and water flow in smooth-walled fractures.

Introduction
Investigation of fluid flow in porous and fractured media is of practical importance in areas such as the recovery of oil and gas, the isolation and remediation of nuclear and toxic wastes in geological formation, and the exploitation of geothermal energy. In these applications, fluid flow in fractured media is often dominated by the highly permeable pathways provided by rock fractures, either natural or induced. Understanding the mechanics, which govern the multiphase flow in fractures, will certainly help to improve the energy recovery efficiency and optimize the waste isolation and remediation process.
It is well known that the flow of multiphase fluids in a porous medium is generally governed by the saturation of the pore space occupied by the percolating fluids. Pores occupied by one phase are not available for the flow of the other, which implies that each phase interferes with the flow of the other. At steady state, only the portion that forms a continuous path contributes to the fluid production, whereas the discontinuous portion is considered to be immobile. The phase interference is attributed to the capillary forces developed at the contact zones of the fluid phases in the pore channels. The smaller the size of the pores, the more significant will be the effect of capillary forces. To quantify the interference between different fluids, relative permeability functions are introduced and defined as:
Equation 1 (available in full paper)
where ki is the effective permeability to phase i, k is the absolute permeability of the medium, and kri is the relative permeability to phase i. Numerous experimental studies have shown that the relative permeabilities of multiphase flow in porous media are strong functions of phase saturation and phase saturation is governed by capillary forces. It is postulated that phase interference also exists in multiphase flow in fractures. However, the mechanisms governing the phase interference in a fracture is not well understood.
The physics of fluid flow in a fracture is different from that in a homogeneous porous medium. Unlike the three-dimensional nature of flow in a porous medium, fluid flow in a fracture occurs in a two-dimensional variable aperture plane.