Performance of Petroleum Reservoirs Containing Vertical Fractures in the Matrix
Authors: Huskey William L. , Crawford Paul B. 
Published: December 2007

Abstract
A study has been made to determine the effects of random vertical fractures existing in a reservoir matrix on the effective matrix properties and producing characteristics of a well. The study indicated that short vertical fractures may distort the isopotentials by 1 percent in the vicinity of the fracture. A correlation was developed which showed the effect of fracture density on the producing capacity of a well. The correlation indicated that fracture shape had little effect on producing capacity, but that total fracture length was closely correlated with the producing capacity. Effective values of reservoir permeability were found to correlate closely with fracture density when measured parallel to the direction of flow.

Introduction
In reviewing the petroleum literature, it is found that in most analytical solutions of hydrocarbon reservoir behavior the assumption is made that the rock is uniform throughout although core analysis and well logging surveys indicate that substantially all reservoirs are heterogeneous and some are fractured. Only in recent years have investigators studied the effects of reservoir heterogeneity. Russell discussed the effect of fractures in reservoirs. The literature indicates that fractures greatly affect the exploitation of many reservoirs. This is described by Elkins and Skov and Littlefield et al. Several types of reservoir heterogeneity have been studied by unsteady-state methods. In 1959, Landrum et al. showed that transient phenomena in hydrocarbon reservoirs could be studied by thermal models. Pickering studied the flow of heat in stratified linear reservoirs consisting of plates of different metals separated by sheets of rubber which were suddenly exposed to a low-temperature source at one end. Cotman studied both laterally and vertically heterogeneous thermal model reservoirs with special reference to cross Low. Another type of reservoir heterogeneity involves the presence of highly permeable, circular lenses around or near the wellbore which was studied by Miesch using a thermal and a steady- state model. Many studies have been made of the effects of induced hydraulic fractures on well performance. Work regarding vertical fractures that exist initially in the reservoir was reported by Givens, et al. Since there appears to be little published work on the importance and influence on reservoir performance of fractures that exist out in the rock matrix, this study was conducted to determine the effects of vertical fractures on pressure distribution, producing capacity and the effective permeability of the reservoir rock. The analogy between the flow of electrical current through a conducting body and the flow of fluid in a porous medium provides a convenient method of studying various aspects of petroleum reservoirs. For electrical radial steady-state flow,
........................................(1)
For steady-state fluid flow,
........................................(2)
With the above analogy, it is only necessary to establish the ratio of the values of the electrical units in terms of the corresponding flow units to make the analogy quantitative. The ratios are shown below.