(64286) Effective Permeability Estimation for Simulation of Naturally Fractured

SPE 64286 Effective Permeability Estimation for Simulation of Naturally Fractured Reservoirs
T. Nakashima, SPE, Waseda University, K. Sato, SPE, The University of Tokyo, N. Arihara, SPE, Waseda University, and N. Yazawa, SPE, JNOC elements kxy and kyx are strongly affected by both the total length and the angle. Introduction Simulation of naturally fractured reservoirs is conducted commonly by either the continuum or the discrete fracture method. The double porosity or dual permeability method is a typical approach of the continuum model where fractures are assumed to distribute regularly and to be well connected1. The discrete fracture method2 assumes zero matrix permeability, though a fracture system can be modeled more realistically. Naturally fractured reservoirs often comprise irregularly distributed and disconnected fractures which are developed in matrix rock of non-zero permeability. The single-continuum approach, where the fracture system is represented by effective permeability, is more appropriate and flexible to simulate behaviors of naturally fractured reservoirs. Durlofsky3 presented a numerical procedure for computing the effective permeability of a region of periodically distributed heterogeneity. The method first solves the pressure equation over the periodical unit subject to periodic boundary conditions, and then upscales the velocity field to yield the effective permeability. Lough et al.4, 5 proposed a method to estimate the effective permeability of grid blocks used in continuum simulation of naturally fractured reservoirs. The boundary element method was employed to solve the boundary integral equations for the pressure under periodic boundary conditions. They applied the method to a fracture system generated using statistical data of fracture length, orientation, and intensity from an actual reservoir. In calculations of the effective permeability for various sedimentary structures, Pickup et al.6 investigated effectiveness of the periodic boundary condition method, and necessity of the tensor permeability. According to them, the periodic boundary condition method is computationally fast, and robust to always produce a symmetric, positive definite tensor. They also concluded that permeability tensors are required for layers of a high bedding angle, high permeability contrast, and comparable thickness. In this paper, we present an upscaling approach to estimate the effective permeability for naturally fractured reservoirs based on flow calculations for fracture distributions performed by the boundary element method. Fractures are discrete and

Copyright 2000, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE Asia Pacific Oil and Gas Conference and Exhibition held in Brisbane, Australia, 16–18 October 2000. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract Appropriate modeling of naturally fractured reservoirs is one of the most important and challenging issues in reservoir characterization. In simulation, a double porosity or dual permeability model is applied when fractures are well developed to form a fracture network. On the other hand, the single-continuum approach, where the fracture system is represented by effective permeability, is commonly used if fractures are discrete or disconnected. Focusing on the latter case, this paper proposes a semi-analytical technique to evaluate effective permeability for periodically or randomly fractured media including infinitely thin, infinite-conductivity fractures. The complex variable boundary element method is used to compute potential and stream functions in the twodimensional space for discretely distributed fracture system under the periodic boundary conditions. Effective permeability is evaluated first for discrete fracture systems of regular patterns as well as a single inclined fracture to demonstrate the validity of the method. 500 distributions of stochastic fractures are next generated to establish correlation between effective permeability and the fracture statistics, i.e., total length L, mean length m, and standard deviation of fracture length σ. Sensitivity to the parameters shows that the incremental gain of effective permeability is proportional to L, that the larger m, the larger effective permeability, and that non-zero σ increases effective permeability. The effective permeability tensors are also determined for oriented fractures. Analyses by nonparametric regression show that the diagonal elements, kxx and kyy are highly affected by the angle between the oriented fractures and the pressure gradient, while the off-diagonal