A Theory for Pressure Transient Analysis in Naturally Fractured Reservoirs

Abstract

Najurieta, Humberto L.,* SPE, Inst. Mexicano del Petroleo A method to calculate the unsteady-state pressure behavior within the fractures of a homogeneously fractured reservoir is presented. The technique allows the analysis of pressure buildup and drawdown tests for layer- like and block-shaped fractured reservoirs. The fractures pressure is shown to depend on four parameters, and a method for its pressure is shown to depend on four parameters, and a method for its determination is proposed. Introduction The importance of the pressure behavior as a source of information on reservoir characteristics is evidenced by the extensive theoretical work developed in this field. Homogeneous reservoirs can be described theoretically for a great number of boundary and production conditions.The basic theory for the analysis of homogeneous isotropic reservoirs is based on the line-source solution to the radial diffusivity equation: (1) The solution is (2) Eq. 2 shows that homogeneous isotropic reservoirs can be described using at least two parameters: the reservoir transmissivity T=k h/mu and the reservoir diffusivity eta=k/phi muc. Several techniques are used widely to estimate these parameters; from them, we can calculated two unknowns (e.g., k and phi provided we know the remaining (h, mu, and c). The provided we know the remaining (h, mu, and c). The definition of the skin effect and the use of the superposition principle and image wells widen the practical applications of Eq. 2. practical applications of Eq. 2. Several authors have dealt with nonhomogeneous and nonisotropic reservoirs. The solutions proposed are complex and generally require computer handling.Among the heterogeneities in a reservoir, there is an important one that is due to the presence of natural matrix fractures. In this case the productive pay is fragmented by a spatial fracture network as a pay is fragmented by a spatial fracture network as a result of the natural geologic factors. Few authors have suggested theories to aid in calculating the characteristics of naturally fractured reservoirs. A detailed theory, developed by Warren and Root, based on the theoretical work by Barenblatt and Zheltov, assumes a network of orthogonal, equally spaced features. Thus, the reservoir is made up of blocks that are able to exchange fluids with the fractures.Barenblatt and Zheltov suggested that the flow from the matrix could be considered as a first approach in a semisteady-state regime. With this assumption Warren and Root developed the differential equations and obtained analytical solutions for well test analysis. When these solutions are plotted in a conventional way (e.g., a Horner plot), plotted in a conventional way (e.g., a Horner plot), they show two parallel straight lines connected by a transition zone of variable slope. The vertical distance between them is related to the relative storage capacity of the fractures and the slopes with the flow capacity of the reservoir. JPT p. 1241