An Aquifer Model for Fissured Reservoirs
Authors: Clossman P.J. 
Published: December 2007

Abstract
A model has been developed for describing aquifer influx in a fissured reservoir. This model includes petrophysical properties of good and poor rock, as petrophysical properties of good and poor rock, as well as fissure parameters. For the applications considered thus far, it has been found that flow in the fissures dominates the aquifer performance and that rock properties and spacing between fissures are of lesser importance. For a given aquifer, the fissure permeability and fissure volume fraction appear to be important parameters, as are rock permeability and porosity in cases of a high permeability and porosity in cases of a high percentage of poor rock. percentage of poor rock

Introduction
The use of material balance has been well established in analysis of reservoir performance. For water drive reservoirs, it is usually desirable to have a functional description of aquifer behavior. Such a description is provided by the functions obtained by van Everdingen and Hurst for homogeneous and isotropic reservoirs. This method uses one set of values of permeability, porosity, and compressibility, and usually requires some history matching or curve fitting for determining the best values. Functions analogous to those of van Everdingen and Hurst also would be useful in reservoir performance studies of fissured reservoirs. Any performance studies of fissured reservoirs. Any attempt to formulate a realistic model for such systems, however, will usually confront the problem of insufficient knowledge of aquifer properties. There usually will be a comparatively large number of degrees of freedom corresponding to parameters introduced into the theory. Nevertheless, such a model should provide insight into the relative importance of certain variables. It may also serve as a framework in which more accurate information, if eventually obtained, could be used. Pressure behavior was used to study fissured reservoir properties by Pollard, who characterized the pressure buildup by three exponentials. These exponentials corresponded to a skin near the well, transient behavior in the fracture system, and transient flow of fluid from matrix to fissures. A characteristics feature of fissured reservoir systems and the reservoir fast fluid pressure response of the fissure system compared with response in the porous matrix. A model that treats this aspect porous matrix. A model that treats this aspect appropriately as proposed by Warren and Root, who assumed that flow of fluid from matrix to fissures could be treated as quasi-steady state. The problem of transient pressure distribution within an actual block of the reservoir was thereby circumvented. This model was further studied by Odeh. Kazemi replaced the network of fractures with an equivalent set of horizontal fractures and solved numerically for pressure distribution in fissures and matrix. Because the dimensionless time scale based on fracture properties and well radius was long, Warren and Root and Odeh were able to use the long-time solution for the constant terminal rate case of pressure behavior in an oil reservoir. In the present instance, the inner aquifer radius may be quite large, so that we must consider smaller dimensionless times, and will require a general solution. The actual times of interest, however, will not be so small as to invalidate the model. This model is being considered for use in fissured carbonate reservoirs where two basic rock types, defined in terms of porosity, are sometimes specified. In such cases, the rock permeabilities usually are very much smaller than the fissure permeability, The matrix can be considered as permeability, The matrix can be considered as being made up of good and poor rock. Wide variations in rock type are often encountered in carbonate reservoirs. The designations of good and "poor" are largely arbitrary. A typical example would be: good porosity greater than 12 percent, and poor-porosity 2 to 12 percent, with the remainder poor-porosity 2 to 12 percent, with the remainder of the rock nonproductive. In some cases, however, it may be sufficient to specify only one rock type. In studying the constant terminal pressure case it is desirable to reformulate the fissured reservoir model to include the additional features of change, boundary conditions and two basic rock types.
SPEJ
P. 385