PRESSURE TRANSIENT-RESPONSE OF STOCHASTICALLY HETEROGENEOUS FRACTUREDRESERVOIRS

A stochastic model for flow through inhomogeneous fractured reservoirs of double porosity, based on Barenblatt et al.'s continuum approach, is presented. The fractured formation is conceptualized as an intercon nected fracture network surrounding porous blocks, and amenable to the continuum approach. The block permeability is negligible in compariso n to that of the fractures, and therefore the reservoir permeability i s represented by the permeability of the fracture network. The fractur ed reservoir inhomogeneity is attributed to the fracture network, whil e the blocks are considered homogeneous. The mathematical model is rep resented by a coupled system of partial differential random equations, and a general solution for the average and for the correlation moment s of the fracture pressure are obtained by the Neumann expansion (or A domian decomposition). The solution for pressure is represented by an infinite series and an approximate solution for radial flow, is obtain ed by retaining the first two terms of the series. The purpose of this investigation is to get an insight on the pressure behavior in inhomo geneous fractured reservoirs and not to obtain type curves for determi nation of reservoir properties, which owing to the nonuniqueness of th e solution, is impossible. For the present analysis we assumed an idea l reservoir with cylindrical symmetric inhomogeneity around the well. Fractured rock reservoirs being practically inhomogeneous, it is of in terest to compare the pressure behavior of such reservoirs, with Warre n and Roots's solution for (ideal) homogeneous reservoirs, used as a r outine for determining the fractured reservoir characteristic paramete rs lambda and omega, using the results of well tests. The comparison o f the results show that inhomogeneous and homogeneous reservoirs exhib it a similar pressure behavior. While the behavior is identical, the s ame drawdown or a build-up pressure curve may be fitted by different c haracteristic dimensionless parameters lambda and omega, when attribut ed to an inhomogeneous or a homogeneous reservoir. It is concluded tha t the ambiguity in determining the fractured reservoir lambda and omeg a, makes questionable the usefulness of determination of these paramet ers. Computations were also carried out to determine the correlation b etween the fracture pressure at the well and the fracture pressure at different points.