Influence of Block Size on the Transition Curve for a Drawdown Test in a Naturally Fractured Reservoir

Abstract

Abstract Block size is considered one of the main parameters of a fractured rock reservoir. In one-phase flow, it controls the transition from the early stages of production to asymptotic behavior, and in two-phase wetting-nonwetting displacement it controls the rate of production by imbibition. In nonwetting-wetting displacement it controls the pressure difference between the extremities of the block, which, provided that the threshold pressure is exceeded, permits displacement of the nonwetting fluid from the blocks into the fractures. Warren and Root relate the size of the block to the transient pressure variation from the first to the second straight line of the drawdown/buildup test. The numerical solutions presented in this paper for reservoirs with ordered fractures and blocks show that the drawdown pressures are not sensitive enough to the variation in sizes of the block. This means that a drawdown/buildup test cannot yield a solution unique for the size of the block. In most practical cases of the one-phase flow, transition to homogeneous behavior is reached in a relatively short time and not noticed, except in a narrow region around the well. Therefore, in terms of reservoir performance, only the homogeneous behavior is of practical interest and the size of the block is not a relevant parameter of the one-phase flow. It is believed that in two-phase flow the displacing fluid circumvents the blocks in groups rather than singly. If so, the individual size of the block is not a relevant parameter, even in two-phase flow. Introduction Because of their complicated structure, the details of the fractured reservoir will always remain inaccessible. Therefore, simulators of the discrete structure of the fractured rock reservoirs are limited to theoretical investigations. Only numerical or analytical solutions to equations formulated through the continuum approach with average properties can be considered as "type" solutions for the determination of reservoir properties by drawdown or buildup tests. The equations of single-phase flow through "double-porosity" fractured reservoirs were formulated by Barenblatt et al. In them, the actual composite medium of fractures and blocks is replaced by two overlapping continua: the continuum of the blocks and the continuum of the fractures. A pair of average properties are defined over the common bulk volume at each mathematical point. The transfer of fluid from blocks into fractures is represented in the equation of mass conservation (written separately for each continuum) by a semisteady-state source/sink function. Analytical solutions to radial flow were presented by Warren and Root, Barenblatt, Odeh, Kazemi, Seth, and Thomas, de Swaan, and Najurieta. Da Prat et al. presented a solution to Barenblatt's equations for a well producing at constant pressure. A numerically-solved model proposed by Kazemi in an attempt to verify Warren and Root's analytical solution based on Barenblatt et al.'s assumptions, assumed discrete blocks and fractures in a stratified disposition. With the need of the semisteady source function obviated, a smoother transition curve was obtained between the two straight lines of the early stages of production and the homogeneous behavior. The main parameters of a fractured rock reservoir are block size and the permeabilities and porosities of the fractures and blocks. A large class of fractured reservoirs, those commonly encountered, are characterized by negligible block permeability compared with that of the fracture network and negligible fracture porosity compared with that of the blocks. The overall permeability and the porosity of the formation may be approximated by those of the fractures and blocks, respectively. Owing to differences in permeability during production, fluid is removed faster from the fractures than the blocks. As a consequence, a fluid pressure difference is generated between fractures and blocks and fluid is displaced from the blocks into the fractures. This behavior is indicated by three typical stages in the drawdown graph. The first stage is characterized by rapid removal of fluid from the fractures with insignificant response of the blocks to the pressure decrease, and the reservoir behaves like a homogeneous formation with the fractures as the dominant element. In the p, log t graph this is represented by a straight line with slope and intercept (at delta p = 0) corresponding to the permeability and porosity (or more accurately the permeability-thickness and porosity-compressibility products) of the fracture network. The second intermediate stage is characterized by the onset of fluid displacement from the blocks into the fractures, represented by a curve of the variable slope. In the third stage, the displacement proceeds under a semisteady state regime. SPEJ P. 498^