New Pressure Transient Analysis Methods for Naturally Fractured Reservoirs(includes associated papers 12940 and 13014 ) (1983)

Summary This paper presents new methods for analyzing pressure drawdown and buildupdata obtained at wells producing naturally fractured reservoirs. The modelused in this study assumes unsteady-state fluid transfer from the matrixsystem to the fracture system. A new flow regime is identified. The discovery of this flow regimeexplains field behavior that has been considered unusual. The probabilityof obtaining data reflecting this flow regime in a field test is higher than that of obtaining the classical responses given in the literature. The identification of this new flow regime provides methods for preparing acomplete analysis of pressure data obtained from naturally fractured reservoirs. Applications to field data are discussed. Introduction In this work, we investigate the pressure response in a naturally fractured reservoir. Several models of naturally fractured reservoirs have been presented in the literature. Warren and Root and Odeh assume pseudosteady-state flow in the matrix; others assume unsteady-state flow. The model used here is identical to one proposed by de Swaan-O. This model assumes that the matrix is divided by a set of parallel, equally spacedhorizontal fractures(Fig. 1) and also assumes unsteady-state fluidtransfer from the matrix system to the fracture system. We consider constant-rate production followed by a buildup period and present new methods for analyzing drawdown and buildup data. Results presented here assume infinite-reservoir behavior; results on the bounded reservoir case will be presented in a subsequent paper. We identify three flow regimes. The first and third flow regimes correspond, respectively, to the classical early-time and late-time semilogstraight lines reported in the literature. We refer to these two flow regimes as Flow Regimes 1 and 3, respectively. In this work, we establishthe existence of an intermediate-time flow regime, which we refer to as Flow Regime 2. Flow Regime 2 is characterized by the existence of a semilog straight line that has a slope approximately one-half that of the straight lines of Flow Regimes 1 and 3. The discovery of this new semilogstraight line and the analysis procedures that it provides comprise theprincipal contributions of this paper. Mathematical Model Our model is identical to one proposed by de Swaan-O. and also considered by Najurieta. We consider the flow of a slightly compressible fluid of constant viscosity in an isotropic, naturally fractured reservoir ofuniform thickness. The top and outer boundaries are closed, and the drainage radius is infinite. The well is produced at a constant rate andthen shut in to obtain buildup data. Initially, the pressure is uniform throughout the reservoir. We assume all production is via the fracturesystem and that we have one-dimensional, unsteady-state flow in the matrix. The matrix structure consists of "rectangular slabs"; that is, the matrixis divided by a set of parallel horizontal fractures as shown in Fig. 1. We consider an infinitesimally thin skin region and neglect wellbore-storage effects. The properties of both the matrix and fracture systems are assumed constant. Appendix A presents the relevant initial boundary value problem, the analytical solution of this problem in Laplace space, and theintermediate-time and long-time approximations to the analytical solution. JPT P. 2271^