A correlated fracture network: Modeling and percolation properties

Masihi, Mohsen; King, Peter R.

doi:10.1029/2006wr005331

Cited by 29 publications

(17 citation statements)

References 40 publications

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“…To change the current configuration of fractures, a fracture j is selected randomly and its length, orientation and/or position are changed slightly. The distribution functions used for selecting updates to the orientation, length and the position are identical to Masihi & King (2007) where R is a random number selected from a uniform distribution in the range of [0–1]. Once again the energy of the new state of the configuration, E i +1 , is calculated using .…”

Section: Methods For Modelling Fracture Distributionsmentioning

confidence: 99%

“…We write the vector displacement field within the fractured rock volume as , noting that the particle at x has moved to . Beginning with the theoretical expressions suggested by Landau & Lifshitz (1982b, chapter IV) that describe elastic deformations in the presence of dislocations, Masihi & King (2007) propose a model in which a fracture is defined as a discontinuity in the displacement vector. Therefore, the displacement vector is assumed to have continuous part (elastic displacement u e ) and a discontinuous part (the inelastic displacement u i ).…”

Section: Elastic Energy Function For Spatially Correlated Fracturesmentioning

confidence: 99%

“…In this paper, we implement and extend a model of the spatial distribution of fractures that directly considers the elastic energy in a fractured material (Masihi & King 2007), a model that has not previously been applied in seismic applications. The modelling is based on the assumption that the elastic free energy associated with the fracture distribution follows the Boltzmann distribution.…”

Section: Introductionmentioning

confidence: 99%

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Generation of spatially correlated fracture models for seismic simulations

Shekhar¹,

Gibson²

2011

Geophysical Journal International

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S U M M A R YThe critical geometrical parameters that quantify the spatial distribution of natural fractures are the orientation, length and position of fractures. Knowledge of their spatial distribution is important as they control the movement of subsurface fluids and also influence seismic waves propagating in the subsurface. However, generating realistic models of all of these geometrical parameters to use in forward seismic modelling or inversion applications can become very difficult, especially when constraints are available only at a few sparse well locations. Hence, this provides strong motivation for applying seismic data to estimate these quantities in field settings, and reliable seismic modelling provides important constraints for interpretation and inversion. The Discrete Fracture Network (DFN) approach has been used frequently to generate models with stochastic distributions of fractures based on sparse well and seismic data. However, most of these studies lack any constraint from physical models of the behaviour of fractured media. In this paper, we implement and extend an alternative modelling technique to generate several realizations of a fracture model beginning with theoretical results for the strain energy of a fractured material and propose ways to better incorporate geological field observations. The method utilizes an elastic energy function that sums the interactions of all pairs of fractures present in the model. The energy for each pair depends on the distance between the two fractures, their orientations, lengths and some material properties. This energy function also serves as an objective function for a simulated annealing (SA) algorithm used to obtain multiple realizations of correlated fracture networks. We improve earlier versions of this technique by incorporating periodic boundary conditions, including criteria to limit the maximum range of pair-wise calculations and suggesting methods to constrain models to match field data. Assuming that the host rock is isotropic and homogeneous, this method produces orthogonal sets of fractures, a pattern that is commonly observed during basin formation or subsidence. This shows how the method can be utilized to provide constraints with a physical basis to facilitate the development of fracture models. We also outline how the fracture model can be converted into an anisotropic seismic velocity model to compute synthetic seismograms for reservoir characterization applications.

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Section: Methods For Modelling Fracture Distributionsmentioning

confidence: 99%

Section: Elastic Energy Function For Spatially Correlated Fracturesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generation of spatially correlated fracture models for seismic simulations

Shekhar¹,

Gibson²

2011

Geophysical Journal International

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“…For random crack networks in a finite domain, the above classical site/bond percolation theory is extended to continuum percolation theory, and the scaling law in Eq. (12) is assumed to still hold but adopt different scaling exponents (Masihi and King 2007;Halperin et al 1985). The main difference between the classical and continuum percolations resides in the definition of probability p, that is, for random crack networks, the probability is substituted by the crack density ρ.…”

Section: Percolation Basismentioning

confidence: 99%

Permeability of Microcracked Solids with Random Crack Networks: Role of Connectivity and Opening Aperture

2015

Transp Porous Med

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This paper investigates the permeability of microcracked porous solids containing 2D random crack networks. The past works on permeability of crack networks are firstly reviewed. The geometry analysis is performed on numerical samples of crack networks with different crack length distributions, crack densities, domain size ratios and clustering degrees. The parameters from continuum percolation theory are used to characterize the geometry of random networks including the percolation threshold, the scaling exponents for percolation probability and correlation length of crack clusters, and the fractal dimension of spanning clusters. The crack density is used as the basic percolation variable, and a new connectivity factor is proposed for the cluster spanning in finite domain. Then the effective permeability of porous matrix containing 2D random crack networks is analyzed on numerical samples via finite element method. A scaling law for effective permeability is established near the percolation threshold taking into account the matrix permeability, crack opening aperture, crack connectivity and tortuosity. The results from geometry analysis and permeability analysis show that: (1) The new connectivity factor is proved pertinent to network percolation, related to both crack density and crack clustering degree; (2) the percolation parameters of uncorrelated crack networks are rather near to the universal values from the continuum percolation theory, but their values change with the clustering degree of crack networks; (3) the numerical results confirm the scaling law proposed for effective permeability, and the permeability is found to scale with the crack opening through a power law.

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“…Heffer and King (2006) introduced a spatial correlation function of fractures as displacement strain vectors using renormalization techniques in representation of stochastic tensor fields for strain modeling. Masihi and King (2007) applied this method to generate fracture networks based on the assumption that the elastic energy in the fractured media follows a Boltzmann distribution. Koike et al (2012) used geostatistical fracture distribution and fracture orientation (strike and dip) in simulation of the fracture system to estimate the hydraulic conductivity.…”

Section: Fracture Simulation Methods For Carbonate Rocksmentioning

confidence: 99%

Naturally fractured hydrocarbon reservoir simulation by elastic fracture modeling

Soleimani

2017

Pet. Sci.

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Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators. General approaches in naturally fractured reservoir simulation involve use of unstructured grids or a structured grid coupled with locally unstructured grids and discrete fracture models. These methods suffer from drawbacks such as lack of flexibility and of ease of updating. In this study, I combined fracture modeling by elastic gridding which improves flexibility, especially in complex reservoirs. The proposed model revises conventional modeling fractures by hard rigid planes that do not change through production. This is a dubious assumption, especially in reservoirs with a high production rate in the beginning. The proposed elastic fracture modeling considers changes in fracture properties, shape and aperture through the simulation. This strategy is only reliable for naturally fractured reservoirs with high fracture permeability and less permeable matrix and parallel fractures with less cross-connections. Comparison of elastic fracture modeling results with conventional modeling showed that these assumptions will cause production pressure to enlarge fracture apertures and change fracture shapes, which consequently results in lower production compared with what was previously assumed. It is concluded that an elastic gridded model could better simulate reservoir performance.

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A correlated fracture network: Modeling and percolation properties

Cited by 29 publications

References 40 publications

Generation of spatially correlated fracture models for seismic simulations

Generation of spatially correlated fracture models for seismic simulations

Permeability of Microcracked Solids with Random Crack Networks: Role of Connectivity and Opening Aperture

Naturally fractured hydrocarbon reservoir simulation by elastic fracture modeling

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