Computation of Effective Dynamic Properties of Naturally Fractured Reservoirs: Comparison and Validation of Methods

Abstract

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 -IBPOSimplemented 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 ...

Permeability tensor of three‐dimensional fractured porous rock and a comparison to trace map predictions

“…Using analytical means of superposition under the assumption of an impermeable rock matrix, anisotropic permeability tensors were estimated from geometric fracture pattern analysis. Accounting for a permeable rock matrix, Oda [] developed an analytical method based on geometric properties of fracture networks to compute permeability tensors in which the resulting eigenvectors can be taken to be oriented coaxial to the block principal axes, an approach that is still popular in oil reservoir engineering practice [e.g., Elfeel and Geiger , ; Decroux and Gosselin , ]. An analytical model that accounts for individual fracture conductivities is an effective medium approximation developed by Zimmerman and Bodvarsson [], using a conductive element representation of connected joints.…”

A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method

“…Each fracture is modelled individually, as opposed to continuum models with equivalent porosity, and, for geological formations with sparse fracture network that mainly affect the flow path, this approach is recommended [1,19]. DFNs are used in a wide range of applications such as pollutant percolation, gas recovery, aquifers, reservoir analysis, among others [26] [16].…”

Well representation in simulation models of naturally fractured reservoirs considering the impact of DFN upscaling

“…The general 3D grid used to perform the upscaling is not illustrated (modified from Bigi et al, 2015) ..... 40 Warren and Root (1963) (modified from Sabathier et al, 1998) Figure 2.17: dual-continuum grid illustration. Each cell represents a grid block (Lemonnier and Bourbiaux, 2010) Figure 3.2: liquid rate for the heterogeneous model with the no flow method for the thinnest grid (solid orange line) and for the coarse grid (dashed orange line) and for the reference case (black line) (Decroux, 2012) The fractures in blue have no connectivity with other fracture and fractures with other colors are connected to fractures of their color (Tueckmantel et al, 2013)…”

“…However, its uncertainties can cause a significant impact on wells Productivity Index (PI), as the well index is dependent on fracture system properties. Additionally, even if LGR has been an approach used in wells calibration, applying the DFN upscaling in high fidelity models does not necessarily provide the most precise results (Decroux, 2012).…”

“…Despite the variability of DFN permeability upscaling methods, some limitations are reported in the literature. Two main issues are the variability of the permeability results when changing the method, making it difficult to find an adequate upscaling method for a specific case, and the dependency of each method on the grid-scale, changing the outcome according to the grid cell dimension (Ahmed-Elfeel and Geiger, 2012;Decroux, 2012).…”