Abstract:The calculation of effective flow properties of naturally fractured reservoir (NFR) has been the purpose of research works for many years. Based on a static characterization of the fracture system (orientations and densities), equivalent flow properties provide continuum representations of discrete systems from which multiphase flows can be simulated using dual-permeability and dual-porosity models. Common flow properties include anisotropic permeability tensors attached to the fracture system itself, and bloc… Show more
“…The particularity of this method is that it does not use a global DFN. In addition, the calculation time with this technique is much shorter than with other numerical methods (from 1mn to 15mn for 120,000 cells) (Cottereau et al 2010). Figure 8).…”
“…For instance approximately 1 day of calculation is required for 120,000 cells with Petrel (Cottereau et al 2010;Ahmed-Elfeel and Geiger 2012). For instance approximately 1 day of calculation is required for 120,000 cells with Petrel (Cottereau et al 2010;Ahmed-Elfeel and Geiger 2012).…”
“…A new method for the calculation of the effective permeability named "Image Based Periodic Object Simulation" (IBPOS) has been developed and implemented in GoFraK (Gouth et al 2006;Garcia et al 2007;Cottereau et al 2010). The particularity of this method is that it does not use a global DFN.…”
“…The vertical inter-layer permeability (or transmissibility) is calculated with an analytical formulation (Cottereau et al 2010). In GoFraK fractures are generated inside layers named "mechanical units" and each fracture is assumed to cross vertically at least one layer fully.…”
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 ...
“…The particularity of this method is that it does not use a global DFN. In addition, the calculation time with this technique is much shorter than with other numerical methods (from 1mn to 15mn for 120,000 cells) (Cottereau et al 2010). Figure 8).…”
“…For instance approximately 1 day of calculation is required for 120,000 cells with Petrel (Cottereau et al 2010;Ahmed-Elfeel and Geiger 2012). For instance approximately 1 day of calculation is required for 120,000 cells with Petrel (Cottereau et al 2010;Ahmed-Elfeel and Geiger 2012).…”
“…A new method for the calculation of the effective permeability named "Image Based Periodic Object Simulation" (IBPOS) has been developed and implemented in GoFraK (Gouth et al 2006;Garcia et al 2007;Cottereau et al 2010). The particularity of this method is that it does not use a global DFN.…”
“…The vertical inter-layer permeability (or transmissibility) is calculated with an analytical formulation (Cottereau et al 2010). In GoFraK fractures are generated inside layers named "mechanical units" and each fracture is assumed to cross vertically at least one layer fully.…”
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 ...
“…At the simulator grid-cell scale, it should be determined how fracture properties can be summarized to fully represent the matrix-fracture flow exchange (Bourbiaux et al, 2002;Cottereau et al, 2010). One way of populating reservoir models with fractures is through stochastic modeling of 3D discrete fracture networks (DFNs), using 1D well data to derive fracture geometries, orientations, and spacing (Sabathier et al, 1998).…”
A B S T R A C TModeling naturally fractured reservoirs requires a detailed understanding of the three-dimensional (3D) fracture-network characteristics, whereas generally only one-dimensional (1D) data, often suffering from sampling artifacts, are available as inputs for modeling. Additional fracture properties can be derived from outcrop analogs with the scanline method, but it does not capture their full two-dimensional (2D) characteristics. We propose an improved workflow based on a 2D field-digitizing tool for mapping and analyzing fracture parameters as well as relations to bedding. From fracture data collected along 11 vertical surface outcrops in a quarry in southeast France, we quantify uncertainties in modeling fracture networks. The fracture-frequency distribution fits a Gaussian distribution that we use to evaluate the intrinsic fracture density variability within the quarry at different observation scales along well-analog scanlines. Excluding well length as a parameter, we find that 30 wells should be needed to fully (i.e., steady variance) capture the natural variability in fracture spacing. This illustrates the challenge in trying to predict fracture spacing in the subsurface from limited well data. Furthermore, for models with varying scanline orientations we find that Terzaghi-based spacing corrections fail when the required correction angle is more than 60°. We apply the 1D well Kevin Bisdom holds a M.Sc. degree in petroleum engineering and geosciences from the Delft University of Technology, Netherlands. He is currently a Ph.D. candidate in the section of applied geology at the Delft University of Technology working on geomechanical and fluid flow modeling of fracture networks in folded subsurface structures using outcrop analogs in central Tunisia. is a senior geologist and geophysicist at Total. He is currently head of the naturally fractured reservoir (NFR) study team and scientific adviser for NFR operational and research and development projects. Bertrand holds a Ph.D. in structural geology from the Pierre and Marie Curie University of Paris and has 25 years of experience in the oil and gas industry with Shell and Total. received his master's degree at the University of Pisa (Italy) and the Ph.D. at the ETH-Zurich with a thesis on the tectonosedimentary evolution of the South-Alpine rifted margin. He was then at the VU Amsterdam studying passive margins and foredeep basins. Since 2010, he has been a professor for applied geology at the Delft University of Technology working mainly on fractured reservoirs.
Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length‐aperture scaling), and experiments (Barton‐Bandis conductive shearing). Each method predicts heterogeneous apertures, even along single fractures (i.e., intrafracture variations), but most fractured reservoir models imply constant apertures for single fractures. We compare the relative differences in aperture and permeability predicted by three aperture methods, where permeability is modeled in explicit fracture networks with coupled fracture‐matrix flow. Aperture varies along single fractures, and geomechanical relations are used to identify which fractures are critically stressed. The aperture models are applied to real‐world large‐scale fracture networks. (Sub)linear length scaling predicts the largest average aperture and equivalent permeability. Barton‐Bandis aperture is smaller, predicting on average a sixfold increase compared to matrix permeability. Application of critical stress criteria results in a decrease in the fraction of open fractures. For the applied stress conditions, Coulomb predicts that 50% of the network is critically stressed, compared to 80% for Barton‐Bandis peak shear. The impact of the fracture network on equivalent permeability depends on the matrix hydraulic properties, as in a low‐permeable matrix, intrafracture connectivity, i.e., the opening along a single fracture, controls equivalent permeability, whereas for a more permeable matrix, absolute apertures have a larger impact. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on aperture variations within fractures.
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