Computation of Gas-liquid Drainage In Fractured Porous Media Recognizing Fracture Liquid Flow
Authors: Dindoruk B. , Firoozabadi A. 
Published: March 2010

Abstract
We propose a simple approach to simulate gas-oil gravity drainage process in fractured porous media by using an appropriate fracture capillary pressure curve and an expression for effective fracture liquid permeability. The effective fracture liquid permeability is approximated by fracture permeability perpendicular to fracture planes. There is no need to provide fracture relative permeabilities in our model Numerical simulation results are in excellent agreement with experimental data.

Introduction
Gravity drainage in fractured porous media is related to:matrix permeability. relative permeability and capillary pressure:matrix block height and fluid density; andfracture two phase gas-oil flow characteristics.
Immiscible gas-oil flow in homogeneous matrix porous media is a resolved issue. Fracture two-phase gas-oil flow is, however, complicated. The fracture permeability from the Poiseuille law (k = 83.3 × 105 (2/)2, k in µm2 / in cm) is for flow parallel to fracture planes, and it may not apply lo flow perpendicular to fracture planes. Fracture relative permeability is also unknown. There is no reason to believe that a straight line relative permeability would apply to gas liquid flow across fractures. Limited measurements by McDonald et al and Pruess et al2reveal that fracture relative permeability may have a shape similar to matrix permeability. These measurement are, however for flow parallel to fracture planes. In a recent study(3). we have investigated liquid flow across a single liquid bridge between two matrix blocks. An expression for the effective liquid permeability perpendicular to the fracture planes was derived. As we will discuss later in this paper, the proposed expression may provide effective fracture liquid permeability for the gas-oil flow across a fracture. It could replace the need for both the Fracture absolute permeability and [he relative permeabilily in the direction perpendicular to fracture plane. In Reference (3), as well as in this study. one witnesses a substantial pressure drop across a liquid bridge (Figure I) in a fracture. Capillary pressure at the inflow end of a liquid bridge could be as much as 3 kPa lower than capillary pressure at the outflow end. In other words capillary pressure at the base of an upper matrix block could be 3 kPa lower than capillary pressure at the top face of the matrix block underneath. The large liquid pressure drop across a fracture provides the driving force for liquid flow from one matrix block to the nei1!hbouring block. Since the effect of gravity force across a fracture with an aperture of say 10 to 100 microns is negligible the flow across; both horizontal and vertical fractures requires the same pressure drop.
In a recent study(4), we have noted that capillary continuity realizes across fractures as thick as 1.000 microns. The same study has also revealed that the Young-Laplace equation of capillarity may underestimate fracture capillary pressure. In another study(5), we demonstrated that a combination of fracture capillary pressure derived from the Young-Laplace equation and various expressions for fracture relative permeability may not fully describe gas-oil gravity drainage in Fractured porous media.