Naturally Fractured Reservoirs (NFR) are very heterogeneous media containing highly permeable fractures in a poorly permeable rock matrix. Explicit simulations of such reservoirs are complex and computationally time consuming. Alternatively for full-field simulation, dual-medium models are commonly used (dual-porosity, dual-permeability) where fractures are represented as a continuous medium in communication with the rock matrix. Required effective dynamic properties at the coarse continuous scale should produce the same flow simulation results than Discrete Fracture Network (DFN) models with their small-scale properties, using explicit simulation (as reference). Many calculation methods with different accuracy and computational efficiency have been proposed for the estimation of the anisotropic effective permeability tensor of fracture networks. These methods rely on different conceptual models, which are simplified representations of actual complex and partially unknown fracture systems. They are using either a global deterministic DFN, or local representations of DFNs defined by their statistical properties. Analytical methods rely on connectivity assumptions, seldom met in practice. Numerical methods rely on flow simulations, and are supposed to be more accurate but computationally demanding. The development of new simulators using Discrete Fracture and Matrix (DFM) models, where all fractures are represented explicitly as well as the matrix, offers the opportunity to benchmark the accuracy of the different effective permeability calculation methods. Simulations based on effective properties are compared with DFM model simulations, considered as a reference solution.
In a first part, 2D Cartesian fracture networks are simulated explicitly with Eclipse. These reference simulations are compared with simulations based on effective properties. In this paper we consider the following effective permeability calculation techniques: an analytical method (the Oda’s technique); two flow-based numerical methods with different boundary conditions (impermeable boundaries and linearly varying pressure); and a numerical method using a periodic DFN defined locally, that does not depend on boundary conditions (Image Based Periodic Object Simulation – IBPOS -implemented in GoFraK, a plugin of Gocad). In a second part, a simulation was performed on a much more realistic fracture network with CSMP++, simulation software using DFM models. This simulation is compared with simulations using effective properties calculated with the Oda’s method and the two flow-based numerical methods.
The first observation concerns the large variability of results, which stresses the large uncertainty produced by the various methods. When compared to the reference, the most accurate effective permeability calculation methods tested in this paper are the numerical methods, using no-flow boundary condition and the IBPOS technique. These results show the importance of the fracture network connectivity for the calculation of the effective permeability, and highlight the weakness of the Oda’s method, which does not take this parameter into account.
This paper compares the accuracy of the different effective fracture network permeability calculation methods, against reference solutions. It provides information for choosing the most appropriate methods, and an incentive to question the results of upscaling software tools for NFR. It also stresses the importance of uncertainty estimation, and connectivity calibration versus dynamic data.