In part II of this study, we present the application of the unsteady state solutions to fluid flow in naturally and or vertically fractured reservoirs whose internal boundaries are assumed to be elliptically shaped. Type curves generated using solutions to unsteady-state elliptical flow equations are used to analyze several published field pressure data for parameters such as permeability, skin factor, wellbore storage and fracture length.

The field data analysis results show close agreement with results obtained using other reservoir flow geometries such as radial or linear.


Many naturally fractured reservoirs are often routinely analyzed by methods based upon ideal linear or radial flow models which also among other assumptions consider the reservoir to be isotropic and homogeneous. Naturally fractured reservoirs are typical heterogeneous and anisotropic systems and include many of the important producing fields in the world such as siltstone units of Alberta Canada and the Asmari reservoirs of Iran. It is widely accepted that fluid flow through heterogeneous reservoir with anisotropic permeability or fractured reservoir is often strictly neither radial or linear. Indeed, flow is elliptical during the transitional flow period.

Many theoretical models of naturally fractured systems tend to be generally only applicable to reservoirs with characteristics similar to that assumed in the theoretical development. This is become fractured reservoirs present difficulty of analysis due to the variety of possible fracture systems and correspondingly, the several possible pressure responses from the systems. Pollard developed a method to analyze a fractured limestone in Venezuela. T his method has also been used to analyze pressure data from the fractured coal and siltstone units of Alberta, Canada and the Asmari reservoirs of Iran. In studies by Warren and Root and Kazemi, they pointed out that this method can give false indication of damage, incorrect fracture volume and that if the method is applied to non-fractured reservoirs it may erroneously indicate that the reservoir is fractured. Furthermore, Earlougher has recommended that this method not be used.

Warren and Roots developed a method based on an idealized fracture system where the matrix was assumed to be composed of equal sized blocks and the space between the blocks represented the fractures. Kazemi, later confirmed the results of this model. The pressure response of this model is manifested by the occurrence of two straight lines of equal slope on a Horner plot. Quite often the first line is obscured by wellbore storage; further, the test may not last long enough in many cases to develop the second line. Sometimes it is easy to misinterpret the pressure response in these situations for another type of heterogeneity. Odeh concluded in a study of reservoirs with "homogeneous fracturing" that it was not possible to distinguish between fractured and homogeneous reservoirs.

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