Compositional Reservoir Simulator for Fissured Systems -- The Single-Block Model
Authors: Yamamoto Roy H. , Padgett J.B. , Ford Wayne T. , Boubeguira Ahmed 
Published: December 2007

Abstract
A mathematical model is presented for the simulation of pressure, production and saturation behavior of a single block within a fissured system. The matrix block is represented by a tow-dimensional grid system with two-phase (oil and gas) flow through porous media defined by differential and algebraic relations and solved by quasi-implicit methods. The fissure is represented by a single mode opposite the mid-depth of the block and serves to define the boundary conditions around the block. The hydrocarbon system in simulated compositionally in terms of three equivalent components (methane, ethane through hexanes, and heptanes plus). Variable physical properties, drainage and imbibition capillary pressures, pore compressibility, and gravity are included in the formulation. The effects of mass transfer between hydrocarbon phases and of changing composition upon the phases and of changing composition upon the saturation and pressure distribution are considered through the use of known phase behavior concepts and correlations. This method provides a means of evaluating the effects of oil-vapor capillarity, solution gas drive, gravity drainage, fissure-matrix counterflow, effects of phase composition both in the fissures and in the matrix, and the pressure and fissure gas-oil level decline rates upon the pressure-production behavior of a matrix block in a fissured reservoir. The results of the simulation of pressure depletion and pressure maintenance processes obtained for blocks of various sizes reveal significant differences in performance under different environmental conditions in the fissures.

Introduction
Conventional methods used in the analysis of nonfractures reservoirs leave much to be desired in the proper evaluation of displacement mechanisms within naturally fractured reservoirs. In these reservoirs the fissure system provides paths of rapid pressure and fluid communication with the producing wells, and also offers very large surface producing wells, and also offers very large surface areas of the matrix rock for any pressure change to impinge upon. Basic to the evaluation and understanding of the displacement mechanisms in this type of reservoir is the simulation of performance within the matrix blocks for various performance within the matrix blocks for various environmental conditions that could exist in the adjacent fissures. Birks studied matrix block behavior for gas-oil and oil-water systems without solution drive. Aronofsky et al. studied recovery mechanisms in an oil-water system. Freeman and Natanson studied the highly fractured Kirkuk reservoir of Iraq with an abstract mathematical model. Andresen et al, described a mathematical model that judiciously applied well established physical principles to the evaluation and prediction of principles to the evaluation and prediction of performance of the fractured Asmari reservoirs of performance of the fractured Asmari reservoirs of Iran. These investigators and others have shed much light into behavior of fractured formations and fissure flow. It is the purpose of this paper to describe a new method which permits the simulation of block behavior under fissure environments that vary both in time and space for a two-phase (gas-oil) system. It does not, however, simulate flow through the reservoir fissure system. The mathematical model that is presented allows a more detailed evaluation of the physical processes that take place at the boundaries and interior of the blocks and thus affords a better understanding of the displacement efficiencies that result from various modes of reservoir operation.