Simulation of Fractured Gas Reservoir - An Overview
Authors: Vossoughi S. , Asghari K. 
Published: December 2007

Abstract
Fractured gas reservoirs are conventionally described by a dual porosity type model. In this model, the flow from the matrix to fracture is assumed to be in a semi-steady state. It has been demonstrated that such models do not predict the matrix-fracture flow accurately. This is particularly true when the matrix permeability is very low. This necessitates taking the full transient flow behavior within the matrix continuum. It may be noted that the transient time in a very low permeability rock for a gas reservoir may range from a few days to several months. The time is further increased for a two-phase flow.
To represent flow through a fractured porous medium more accurately, a Multiple Interacting Continua (MINC) model, which fully accounts for the unsteady-state flow within the matrix blocks at all times, has been proposed. In MINC formulation, the matrix blocks associated with a fracture are subdivided into a set of one dimensional discrete elements. It has been shown that MINC formulation is practical and realistic. However, to achieve reasonable accuracy the matrix blocks must be fier subdivided into more elements. This renders the method computationally burdensome, and often limits its utility to only small problems.
Recently, an improved solution method of the MINC procedure has been proposed which results in an order of magnitude reduction in the computation time and a similar reduction in the memory requirement. The method is based on decomposition of the overall matrix of coefficients (i.e. matrix of coefficients of the matrix equation generated for the blocks and the fracture network) such that 1-D matrix problems are generated and solved sequentially. The decoupled matrix of the fracture network is solved using the conventional iterative or direct method. This technique has been successfully employed in the simulation of fractured geothermal reservoirs.
A review of the fractured gas reservoir simulation will be presented and the recent advancement, taking advantage of parallel computational techniques, will be discussed.

Introduction
Numerical solution of partial differential equations, governing flow of mass and heat in fractured porous media, is of considerable interest in gas and oil production, geohydrology, and geothermal energy, to mention a few. The earliest study of the fractured reservoir was performed by Elkins in 1953. He performed fractured reservoir performance analysis for the Spraberry Field in West Texas. Later in 1959, Pollard proposed a pressure analysis technique specifically for the fractured reservoirs to determine fracture volume from pressure buildup data. It was then extended by Pirson and Pirson to estimate the matrix volume as well.
The first classical approach in formulating the fractured reservoirs appears in 1963 by Warren and Root. Their approach was based on dual porosity concept originally proposed by Barenblatt et al. In this approach the reservoir is considered to be consisted of two continua of different rock properties namely the matrix continuum with high porosity but very low conductivity, and the fracture continuum with very low porosity and high conductivity. In this approach the flow from the reservoir matrix to the fracture is assumed to be a semi-steady state process. The physical concept of dual porosity model has been the basis for many analytical and numerical models presented in the literature.
Analysis of the Original Warren and Root Model Warren and Root assumed that there are two types of porosity present in a fractured reservoir:primary porosity which is intergranular and controlled by deposition and lithification such as rock matrix porosity, andsecondary porosity that is controlled by fracturing which is not highly interconnected.
They idealized the actual heterogeneous porous media as a systematic array of identical, rectangular parallelopipeds as shown in Figure 1.
The flux of fluid released by matrix depends on the matrix size, porosity, permeability, and the matrix/fracture pressure difference.