Copyright 2004, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 2004 SPE/DOE Fourteenth Symposium on Improved Oil Recovery held in Tulsa, Oklahoma, U.S.A., 17–21 April 2004. This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal 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 a proposal of not more than 300 words; illustrations may not be copied. The proposal 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 Until recently 1,2 streamline simulators were limited to single-porosity systems and not suitable for modeling fluid flow and transport in naturally fractured reservoirs. Describing fluid transport in naturally fractured reservoirs entails additional challenge because of the complicated physics arising from matrix-fracture interactions. In this paper the streamline-based simulation is generalized to describe fluid transport in naturally fractured reservoirs through a dual- media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. The transfer functions that describe fluid exchange between the fracture and matrix system can be implemented easily within the framework of the current single-porosity streamline models. In particular, the streamline time of flight concept is utilized to develop a general dual porosity dual permeability system of equations for water injection in naturally fractured reservoirs. We solve the saturations equations using an operator splitting approach that involves ‘convection’ along streamline followed ‘matrix- fracture’ exchange calculations on the grid. Our formulation reduces to the commonly used dual porosity model when the flow in the matrix is considered negligible. 2 We have accounted for the matrix-fracture interactions using two different transfer functions: the conventional transfer function (CTF) and an empirical transfer function (ETF). The ETF allows for analytical solution of the saturation equation for dual porosity systems and is used to validate the numerical implementation. We also compare our results with a commercial finite-difference simulator for waterflooding in five spot and nine-spot patterns. For both dual porosity and dual permeability formulation, the streamline approach shows close agreement in terms of recovery histories and saturation profiles with a marked reduction in numerical dispersion and grid orientation effects. An examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large- scale field applications. INTRODUCTION Streamline-based flow simulation has experienced rapid development and industry acceptance in recent years. The approach has been shown to be highly efficient for modeling fluid flow in large, geologically complex systems where the dominant flow patterns are governed by well positions and heterogeneity. 3-6 Streamline simulation has been applied successfully to a wide range of reservoir engineering problems such as ranking geological models 5,6 , ‘upscaling’ from fine- scale models 7 , well- allocation factors and pore volumes 5 , integration of water-cut and tracer data into reservoir description 8 , and history matching 5,8 . The streamline approach provides sub-grid resolution and minimizes numerical dispersion and grid orientation effects compared to conventional finite-difference methods. Also, it offers efficient use of memory and high computational speed. Until recently 1,2 streamline simulators have been limited to single-porosity system and thus, are not able to explicitly account for the differences in the matrix/fracture transport and more importantly, matrix/fracture exchange mechanisms that can play an importantly role in naturally fractured systems. A common way to circumvent this limitation is to use the dual media approach whereby the matrix and fractures are treated as separate continua throughout the reservoir. 1,2,9,10 The fracture system is typically associated with high permeabilities and low effective porosities whereas the matrix system is assigned low permeabilitites and high porosities. Thus, fluid flow occurs mostly in fracture system and the matrix serves primarily as fluid storage. Additionally, the matrix and the fracture system interact through exchange terms that depend on the differences in fluid pressure between the two systems. Such matrix-fracture exchange is typically modeled using ‘transfer functions’. 9,10 Several authors have studied the matrix-fracture interactions using experimental and theoretical means. Both capillary and gravitational forces can play important role in determining the matrix-fracture exchange rate. Kazemi et al. 9 introduced the first multiphase transfer function. Many authors 10,11,12 have reported successful modeling of fluid flow in fractured systems using this type of transfer functions. In this study, we will refer to such transfer functions as the conventional transfer function (CTF). Sonier et al. 13 and SPE 89443 Streamline Simulation of Water Injection in Naturally Fractured Reservoirs Ahmed H. Al-Huthali*, Saudi Aramco and Akhil Datta-Gupta*, Texas A&M University * SPE member