Capillary Pressure in Fractured Porous Media (includes associated papers 21892 and 22212 )
Authors: Firoozabadi Abbas , Hauge Jan 
Published: December 2007

Summary.
In a proposed phenomenological model for fracture capillary pressure, the fracture faces are assumed to be covered with cones, each of which contacts the tip of an opposing cone. Cones in contact at the tip represent both roughness and aperture of a fracture surface. The solution to the Young-Laplace equation of capillarity is used to relate fracture capillary pressure (Pc) to saturation. The computed Pc/saturation results show a porous-medium behavior for fracture capillary pressure. Experiments with a stack of small matrix blocks in a centrifuge produced final measured production rates and matrix-block saturations that confirm the validity of the porous-medium model for fracture capillary pressure. In some centrifuge experiments, capillary pressures as high as 40 psi [275 kPa] could be imposed on the fractures of the stack of blocks.

Introduction
Naturally fractured petroleum reservoirs pose a real challenge to reservoir engineers. Description of fractured reservoirs, combined with knowledge of the physics of multiphase flow in fractured porous media and numerical modeling, provides the basis for understanding and forecasting the performance of these reservoirs. Recent advances have been made in modeling and in the description of fractured reservoirs, but knowledge of the physics of the multiphase flow process is still in early development. One can question the value of numerical modeling of fractured reservoirs based on some of the assumptions about the physics of multiphase flow in fractured porous media in the current literature. Two often neglected fundamental aspects of the multiphase flow process are capillary pressure in the fractures and imbibition of the drained liquid from upper to lower blocks and possible changes in fluid distribution caused by this process. Two recent papers discussed the significance of fracture capillary pressure in a gas-gravity-drainage process. Ref. 1 also states that the effect of fracture capillary pressure generally is more pronounced in a gas-gravity-drainage than in a capillary-imbibition process. When the negative side of the water/oil capillary pressure curve (caused by gravity effects) shows significant oil recovery enhancement, however, the fracture capillary pressure could become important. To illustrate this point, let us consider Fig. 1. With assumed water and oil densities of 60 and 40 lbm/ft3 [0.96 and 0.64 g/cm3], respectively, the minimum oil saturation at the base of a 60-ft [18.3-m]-tall matrix block is 15 %, according to Fig. 1. For a stack of six 10-ft[3.05-m] -tall matrix blocks and an assumed zero fracture capillary pressure, the minimum oil saturation at the base of each matrix block is 66 % (Fig. 1). The average oil saturation is the same for all matrix blocks. If nonzero fracture capillary pressure is assumed, however, the minimum oil saturation at the base and the average oil saturation for each matrix block will be different. The minimum oil saturation at the base of each block could be 66, 62, 58, 51, 42, and 15%, with lower saturation values belonging to higher matrix blocks. The capillary continuity for these stacked blocks requires that the fracture capillary pressure exceed 8.5 psi [58.6 kPa]. Ref. 1 provides experimental data for nonzero fracture capillary pressure. Theoretical analysis of the fracture capillary pressure is presented in this paper. Because the parallel-plate model of capillary pressure did not fit the production data in Ref. 1 across a stack of three matrix blocks, a porous-medium-type model of capillary pressure was postulated to represent the fracture capillary pressure. Also, the maximum fracture capillary pressure in the Ref. 1 experiments could not exceed 0.60 psi [4.14 kPa]. The purpose of this paper is (1) to propose a phenomenological model for the fracture capillary pressure based on theoretical considerations and(2) to report on new experimental data where capillary pressures in the fractures as high as 30 to 40 psi [207 to 276 kPa] are realized.