Discrete-Fracture and Dual-Permeability Models for Multiphase Flow in Naturally Fractured Reservoirs
Authors: Denney Dennis 
Published: February 2015

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 142295, ’Comparison of Discrete-Fracture and Dual-Permeability Models for Multiphase Flow in Naturally Fractured Reservoirs,’ by Ali Moinfar, SPE, University of Texas at Austin, and Wayne Narr, SPE, Mun-Hong Hui, SPE, Bradley Mallison, SPE, and Seong H. Lee, SPE, Chevron Energy Technology Company, prepared for the 2011 SPE Reservoir Simulation Symposium, The Woodlands, Texas, 21-23 February. The paper has not been peer reviewed.
Two discrete-fracture models (DFMs) based on different numerical techniques have been developed for studying the behavior of naturally fractured reservoirs (NFRs). One model uses unstructured gridding with local refinement near fractures, while in the second model, fractures are embedded in a structured matrix grid. Both models capture the complexity of a typical fractured reservoir better than conventional dual-permeability models.
Introduction
Regarding flow behavior, NFRs can be considered as comprising two media (rock matrix and fractures) with very different properties. Generally, the rock matrix provides primary storage of hydrocarbons while fractures serve as highly conductive flow paths. Fracture apertures are very small compared to matrix dimensions (often 0.1 mm or less in petroleum reservoirs); hence, fractures hold very little fluid, yet the permeability can be very high (e.g., hundreds of darcies). The large contrast between matrix and fracture permeability, coupled with small fracture volumes, makes numerical simulation of fluid flow in NFRs challenging.
A dual-porosity model presumes that flow occurs in fractures, and that the rock matrix acts only as fluid storage. Interconnected fractures provide the flow path to injection and production wells. In this model, matrix and fracture domains are linked through an exchange term that connects each fracture cell to its corresponding matrix cell in a gridblock.
The dual-porosity model is a simplistic representation of a geologically complex reservoir. Consequently, considerable effort has been devoted to make the dual-porosity model more realistic. DFMs were developed to reduce the number of nonphysical abstractions inherent in dual-continuum models. Most DFMs rely on unstructured grids to represent a fracture network explicitly. Compared with dual-porosity models, DFMs can simulate realistic fracture-system geometry; hence, they account explicitly for the effect of individual fractures on fluid flow. DFMs are not overly constrained by grid-defined fracture-geometry constraints; hence, the fracture model is adaptable and updatable. Specification of the exchange between matrix and fracture is more straightforward because it depends directly on fracture geometry. A disadvantage, however, is that DFMs typically lead to discrete systems of equations that have a complex structure and that are difficult to solve numerically. However, advances in numerical-solution methods have helped to minimize this disadvantage.
The accuracy of two recently developed DFMs was studied. Sensitivity of DFMs to background-grid orientation was tested. Comparisons were made of the two new modeling methods with dual-permeability modeling in sparsely fractured reservoirs and in highly and more variably fractured systems.