An analytical model for pressure behavior in multilayered radially composite reservoir with formation crossflow

Abstract

The present work proposes an analytical model to calculate the pressure response for multilayered radially composite reservoirs considering the presence of formation crossflow along with all layers. The behavior of pressure transient during production tests in radially composite multilayered reservoirs with non-communicating layers has been widely studied, however there is still a lack of studies considering communicating layers, i.e., formation crossflow in such a model. In that sense, the main purpose of this work is to develop a novel analytical solution that can be used to accurately analyze production tests conducted in multilayered radially composite reservoirs considering communicating layers and multiple regions that can have different radii. An infinite reservoir is considered and the properties for each layer, such as permeability, oil viscosity, and porosity may be different. Moreover, the mathematical formulation for this model is presented in the Laplace domain and the Stehfest Algorithm is used to convert the pressure variation into the real-time domain. The results presented in this work show a close agreement when compared to the responses provided by a commercial flow simulator based on finite differences.