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Abstract
Naturally fractured reservoirs are found throughout the world and contain significant amounts of oil reserves. The so-called dual porosity model is one of the most widely used conceptual models for simulating such reservoirs. In the dual porosity model, two types of porosity are in a rock volume: fracture and matrix where matrix blocks are surrounded by fractures and the system is visualized as a set of stacked cubes, representing matrix blocks separated by fractures. There is no communication between matrix blocks in this model, and the fracture network is continuous. Matrix blocks do communicate with the fractures that surround them. A transfer function characterizes fluid flow between matrix blocks and fractures. The performance of dual porosity simulators is determined by the accuracy of the transfer function employed.

A new parallel simulator for naturally fractured reservoirs, capable of modeling fluid flow in both rock matrix and fractures, has been developed. The simulator is a parallel, 3D, fully implicit with equation-of-state compositional model that uses a generalized dual porosity model, the multiple-interacting-continua (MINC). The matrix blocks are discretized into subgrids in both horizontal and vertical directions to offer a more accurate transient flow description in matrix blocks. Some notable features of this simulator are modeling of improved oil recovery (IOR) processes including both gas and water injection with the ability of two-dimensional matrix subgridding for naturally fractured reservoirs. To the best of our knowledge, such features are not available in commercial reservoir simulators. For coupling of the fracture and matrix continua, numerical methods are used to treat the transient flow of fluid between matrix and fractures.

In this study, we investigated the effect of vertical and horizontal matrix subgridding on oil recovery, oil production, and water cut using the above mentioned simulator. The effects of matrix permeability and capillary pressure on the number of vertical and horizontal matrix subgrids were also investigated. The results showed that in some circumstances, there is more than 15% error in oil recovery for simulations with insufficient matrix subgrids.

Introduction
Naturally fractured reservoirs consist of a network of interconnected fractures surrounding porous matrix blocks. Most of the porosity of naturally fractured reservoirs is contained in the matrix blocks. The fractures normally have little pore volume but are orders-of-magnitude more permeable than the matrix blocks. Recovery of oil from naturally fractured reservoirs is envisioned to take place in two steps: expulsion of oil from the matrix blocks followed by flow through the highly permeable fracture network to the well. Water and/or gas injection are processes used to recover oil from naturally fractured reservoirs. Several mechanisms such as capillary imbibition, gravity drainage, and miscible displacement operate during water/gas injection that force oil from matrix blocks into the fractures. Numerical simulation of water/gas injection into naturally fractured reservoirs requires a description of the geometry and properties of the reservoir and a formulation of fluid flow that can adequately model the above recovery mechanisms. Most models developed for simulating fractured reservoir performance use the dual porosity continuum approach. This approach assumes that a sufficient amount of randomly oriented and interconnected open fractures exist in the reservoir to define statistically meaningful, spatially averaged rock and fluid properties. The fracture system is considered to behave as a type of porous medium that communicates with the other type of porous medium (the matrix) at the same spatial point in the reservoir. Because of the dual medium nature of this approach, these models are commonly called “dual porosity models.”