An Analytical Solution for Unsteady Liquid Flow in a Reservoir With a Uniformly Fractured Zone Around the Well

Abstract

An analytical model is presented which describes the pressure behaviour of a well completed in a reservoir wherein natural fractures occur over a limited area around the wellbore. The flow in the reservoir is treated as a composite reservoir flow problem, the region adjacent to the wellbore being considered as a fractured medium and the outer region as an homogeneous one. Wellbore storage and skin effects are included in the solution, and the flow in the fractured region is mathematically described by Warren and Root's double porosity theory. Dimensionless log-log plots of pressure vs time show the existence of several well-defined flow regimes, which can be used in the interpretation of pressure transient tests data to estimate the fractured region parameters as well as its radius around the well. This last parameter is of considerable importance for the purposes of reservoir development or infill drilling programs, for it would allow the reservoir engineer to estimate the areal extension of the fractures in the reservoir. Based on the model results for different values of the parameters involved, guidelines are provided for conducting and interpreting a pressure test with the objective of determining the characteristics and areal extent of a natural fracture system. Introduction Due to the large hydrocarbon reserves held by naturally fractured reservoirs, their explotation has become a challenging task for the petroleum industry. Estimation of fracture parameters such as fracture volume, directional trends, storage capacity, etc. are of vital importance for the proper design of explotation strategies. In the past 25 years, a considerable theoretical effort has been made to describe the behaviour of these reservoirs. Based on the work done by Barenblatt, Warren and Root proposed an analytical solution which has been used successfully to describe the transient pressure behaviour of a naturally fractured reservoir. Crawford et al presented field data with no wellbore storage, Sup porting the validity of the Warren and Root model. Mavor compared the Warren and Root's solution with other models and concluded that, from an engineering standpoint, it was the most practical. Also, he extended their work to account for wellbore storage and skin effects. Recently, Da Prat, et al. and Benson and Lai have applied the Warren and Root model to the interpretation of field data with apparent success, indicating the model's practical usefulness. In essence, Warren and Root idealized the fractured reservoir as two distinct systems: matrix and fractures (see Fig. 1). The flow towards a fully penetrating well is assumed to occur only through the fractures. Both the cases of an infinite and a closed reservoir have been treated extensively by the authors mentioned and others. However, to the authors' knowledge, the case of a well completed in a reservoir where natural fractures occur only over a limited area has not been modeled. Such a reservoir situation may be idealized as a composite reservoir model (see Fig. 2) where the inner region adjacent to the well is considered as a radial naturally fractured zone that behaves as proposed by Warren and Root, and an outer radial homogeneous reservoir of either infinite or finite extension. Composite reservoir problems have been the subject of considerable attention in the petroleum literature over the last 25 years. In general, the composite model consists of a well completed in the center of a circular inner region with fluid and rock properties different from those in an outer region. P. 35^

Productivity Evaluation of Vertical Wells Incorporating Fracture Closure and Reservoir Pressure Drop in Fractured Reservoirs

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Rate Decline Analysis for Limited-Entry Well in Abnormally High-Pressured Composite Naturally Fractured Gas Reservoirs

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