Well Pressure Behavior of a Naturally Fractured Reservoir

Abstract

Abstract The pressure response pattern of a naturally fractured reservoir is considered under the assumption allowing matrix-to-fracture crossflow to result from a diffusion mechanism of fluid transfer through the matrix. The transitional pressure during time-variant crossflow is shown to develop on a semilog plot a linear segment with a slope equal to one-half that of the early- and late-time pressure segments. For a single well, this allows use of a conventional Homer-type analysis. Introduction A naturally fractured formation is generally represented by a tight matrix rock broken up by fractures of secondary origin. The fractures are assumed continuous throughout the formation and to represent the paths of principal permeability. The high diffusivity of a fracture results in a rapid permeability. The high diffusivity of a fracture results in a rapid response along the fracture to any pressure change such as that caused by well production. The rock matrix, having a lower permeability but a relatively higher primary porosity, has a "delayed" response to pressure changes that occur in the surrounding fractures. Such nonconcurrent responses cause pressure depletion of the fracture relative to the matrix, which in turn induces matrix-to-fracture crossflow. This period of transient crossflow takes place immediately after the fracture pressure response and before the matrix and the fracture pressures equilibrate, after which the formation acts as a uniform medium with composite properties. The effect of assumptions made on the nature of matrix and properties. The effect of assumptions made on the nature of matrix and fracture interaction is manifested during this transitional period of matrix-to-fracture fluid transfer. The flux of fluid released by the matrix depends on the matrix size, porosity, permeability, and the matrix/fracture pressure difference. At the matrix/fracture interface, the matrix flux contribution to fracture flow may be assumed proportional to either the pressure difference between matrix and fracture or to the averaged pressure gradient throughout the matrix block. The former assumption, introduced in fractured reservoir description by Barenblatt and Zheltov and Barenblatt et al. and employed by Warren and Root, has an advantage of simplifying the mathematical analysis of the flow problem and a disadvantage of not correctly representing either the mechanism of pressure readjustment between matrix and fracture by time-variant crossflow pressure readjustment between matrix and fracture by time-variant crossflow or the formation pressure response during the transitional time. According to this assumption, the matrix flux is independent of spatial position, which can be true only when pressure is linearly distributed in space-i.e., at a state of pressure equilibrium or at a pseudosteady-state time. This assumption, therefore, is often referred to as a "pseudosteady-state" or "lumped-parameter" flux assumption. It neglects the matrix storage capacitance by allowing an instantaneous pressure drop throughout the matrix as soon as fracture depletion occurs. The pressure response of a medium subject to this assumption has a characteristic S-shape transitional curve with an inflection point. The curve connects the initial pressure segment (the early-time fracture response) to the final pressure segment, representative of the late-time pseudosteady-state flow of an equivalent uniform medium that has fracture permeability and composite (the sum of fracture and matrix) storage. By contrast, the averaged gradient assumption on matrix-to-fracture crossflow, while somewhat complicating a mathematical analysis of the problem, has an advantage of more correctly describing the pressure problem, has an advantage of more correctly describing the pressure equilibration process that occurs during the transitional period. Matrix fluxes arising from fluid expansion forces are subject to Darcy flow and, thus, to diffusivity-type flow constraints. SPEJ p. 769