Analytical Solutions for Multiple Matrix in Fractured Reservoirs: Application to Conventional and Unconventional Reservoirs

Abstract

Summary In this paper, we present a new method to model heterogeneity and flow channeling in petroleum reservoirs—especially reservoirs containing interconnected microfractures. The method is applicable to both conventional and unconventional reservoirs where the interconnected microfractures form the major flow path. The flow equations, which could include flow contributions from matrix blocks of various size, permeability, and porosities, are solved by the Laplace-transform analytical solutions and finite-difference numerical solutions. The accuracy of flow from and into nanodarcy matrix blocks is of great interest to those dealing with unconventional reservoirs; thus, matrix flow equations are solved by use of both pseudosteady-state (PSS) and unsteady state (USS) formulations and the results are compared. The matrix blocks can be of different size and properties within the representative elementary volume (REV) in the analytical solutions, and within each control volume (CV) in the numerical solutions. Although the analytical solutions were developed for slightly compressible rock/fluid linear systems, the numerical solutions are general and can be used for nonlinear, multiphase, multicomponent flow problems. The mathematical solutions were used to analyze the longterm and short-term performances of two separate wells in an unconventional reservoir. It is concluded that matrix contribution to flow is very slow in a typical low-permeability unconventional reservoir and much of the enhanced production is from the fluids contained in the microfractures rather than in the matrix. In addition to field applications, the mathematical formulations and solution methods are presented in a transparent fashion to allow easy usage of the techniques for reservoir and engineering applications.