Modeling of Matrix-Fracture Interaction for Conventional Fractured Gas Reservoirs

Abstract

A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a dual-porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition (Ranjbar and Hassanzadeh, 2011). However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this chapter is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the 1 This chapter is an exact copy of: Ranjbar, E. Hassanzadeh, H. Chen, Z. (2011). Effect of Fracture Pressure Depletion Regimes on the Dual-Porosity Shape Factor for Flow of Compressible Fluids in Fractured Porous Media, Advances in Water Resources, Vol. 34 (12), Page: 1681-1693. 2 The focus of our previous study (Ranjbar, E. Hassanzadeh, H. (2011), Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media, Advances in Water Resources, 34(5), page 627-639) was to find the shape factor for the single-phase flow of compressible fluids (gases) in fractured porous media for the case of constant fracture pressure. In this study (Ranjbar and Hassanzadeh, 2011), a theoretical analysis of the constant fracture pressure shape factor for the flow of a compressible fluid in fractured porous media was presented. The presented semi-analytical solution for constant fracture pressure was validated with fine-grid numerical simulations. In this chapter we further develop our previous study to consider the effect of pressure variation in the fracture on the matrix-fracture shape factor. 3 It is worth noting that the fracture pressure in this thesis is different than the hydraulic fracture pressure and it implies the fluid pressure inside the fracture or the boundary condition imposed on the matrix block. 4 In this thesis the fracture depletion regime implies the pressure variations in the fracture which acts as a boundary condition for the matrix block. Chapter 2. Effect of fracture pressure depletion regimes on the dual-porosity ... 11 literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media. Chapter 2. Effect of fracture pressure depletion regimes on the dual-porosity ... 12 2.