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

Abstract

Abstract In this paper we present a new method to model heterogeneity and flow channeling in petroleum reservoirs—specially reservoirs containing interconnected microfractures. The method is applicable both to 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 nano-Darcy matrix blocks is of great interest to those dealing with unconventional reservoirs; thus, matrix flow equations are solved using both pseudo-steady- state (PSS) and un-steady-state (USS) formulations and the results are compared. The matrix blocks can be of different sizes and properties within the representative elementary volume (REV) in the analytical solutions, and within each control volume (CV) in the numerical solutions. While the analytical solutions were developed for slightly compressible rock-fluid linear systems, the numerical solutions are general and can be used for non- linear multi-phase, multi-component flow problems. The mathematical solutions were used to analyze the long-term performance of a gas well and an oil well in two separate unconventional reservoirs. Finally, the formulations were used to assess enhanced oil recovery potential from a typical nano- Darcy matrix block. 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 than in the matrix. In addition to field applications, the mathematical formulations and solution methods are presented in a transparent fashion to allow easy utilization of the techniques for reservoir and engineering applications.