A New Double Porosity Fractal Model for Well Test Analysis with Transient Interporosity Transference for Petroleum and Geothermal Systems

Abstract

A new double porosity model for Naturally Fractured Reservoirs (NFRs) assuming fractal fracture network behavior and its solution is presented. Primary porosity is idealized as Euclidian matrix blocks (slabs or spheres) and Secondary porosity is defined by any post-depositional geological phenomenon such as fractures and vugs. In order to provide a framework, the generalized radial flow model solution for well test analysis for petroleum and geothermal systems in Laplace and Real space was developed. Development of an appropriate wellbore storage model for fractal reservoirs is also shown. For this model, the dimensionless fractal fracture area parameter was developed. In addition, interporosity skin factor between matrix blocks and fractal fracture network is introduced. Relationship of convergence between interporosity skin under transient transference regime and pseudosteady state transference regime is discussed. An analytical general solution was obtained in Laplace space; besides, analytical solutions in real space that describe the behavior of NFRs at different stages and different cases of flow are also presented. Early, intermediate and late-time approximations are used to obtain reservoir and fractal fracture network parameters. A synthetic example is presented to illustrate the application of this model.