Hierarchical modeling of flow in naturally fractured formations with multiple length scales

Lee, S. H.; Lough, M.F.; Jensen, Clair

doi:10.1029/2000wr900340

Cited by 424 publications

(222 citation statements)

References 29 publications

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“…[50] Figure 5 depicts a two-dimensional (304.8 Â 304.8 m 2 ) fractured system representing a portion of a model introduced by Lee et al [2001]. It contains 70 fractures and the fine-grid DFM includes 12,280 cells.…”

Section: Two-dimensional Casementioning

confidence: 99%

Generation of coarse‐scale continuum flow models from detailed fracture characterizations

Karimi-Fard

Gong

Durlofsky

2006

Water Resources Research

133

101

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[1] A procedure for developing coarse-scale continuum models from detailed fracture descriptions is developed and applied. The coarse models are in the form of a generalized dual-porosity representation, in which matrix rock and fractures exchange fluid locally while large-scale flow occurs through the fracture network. The methodology developed here introduces local subgrids to resolve dynamics within the matrix and provides appropriate coarse-scale parameters describing fracture-fracture, matrix-fracture, and matrix-matrix flow. The geometry of the local subgrids, as well as the required parameters for the coarse-scale model, are determined from local flow solutions using the underlying discrete fracture model. The method is applied to two-and three-dimensional singlephase and two-phase flow problems, and the accuracy of the coarse models is assessed relative to fully resolved discrete fracture simulations. For the cases considered, it is shown that the technique is capable of generating highly accurate coarse models with many fewer unknowns than the detailed characterizations, and speedups of about a factor of 100 are achieved.

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Section: Two-dimensional Casementioning

confidence: 99%

Generation of coarse‐scale continuum flow models from detailed fracture characterizations

Karimi-Fard

Gong

Durlofsky

2006

Water Resources Research

133

101

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“…Generation of such grid for an arbitrary fracture network can be a substantial challenge. Lee et al (2000Lee et al ( , 2001) and Li and Lee to model fractures in a traditional finite-difference simulator is also discussed by Hearn et al (1997) and Philip (2003).…”

Section: Discrete Fracture Modelsmentioning

confidence: 99%

“…Moreover, this approach can be easily incorporated in existing finite difference reservoir simulators. Li and Lee (2008) extended the approach described by Lee et al (2000Lee et al ( , 2001, who modeled large-scale fractures explicitly as a two-dimensional plane crossing multiple cells and presented a systematic way to calculate transport parameters between fractures and the discretized homogenized matrix medium. Lee et al (2000Lee et al ( , 2001 formulated the fluid transport between a matrix cell and a segment of a fracture embedded in that cell as…”

Section: Overview Of Edfmmentioning

confidence: 99%

“…Therefore, challenges associated with unstructured gridding are bypassed entirely. For simplicity of geometric design, Lee et al (2000Lee et al ( , 2001 and Li and Lee (2008) implemented the mentioned approach only for vertical fractures. However, field characterization studies have shown that the occurrence of obliquely dipping fractures is quite common in NFRs (Walsh and Watterson, 1988;Angerer et al, 2002;Grechka and Tsuankin, 2004).…”

Section: List Ofmentioning

confidence: 99%

“…To take advantage of both dual continuum and discrete fracture models, Lee et al (2000Lee et al ( , 2001 and Li and Lee (2008) presented an approach for simulating fluid flow in NFRs called the embedded discrete fracture model (EDFM). The model borrows the dual-medium concept from dual continuum models and also incorporates the effect of each fracture explicitly.…”

Section: List Ofmentioning

confidence: 99%

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Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

et al. 2013

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Summary Many naturally fractured reservoirs around the world have depleted significantly, and improved-oil-recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs (NFRs) is still challenging because of permeability anisotropies and contrasts. Nonphysical abstractions inherent in conventional dual-porosity and dual-permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies for discrete fracture modeling may suffer from large simulation run times, and the industry has not used such approaches widely, even though they give more-accurate representations of fractured reservoirs than dual-continuum models. We developed an embedded discrete fracture model (DFM) for an in-house compositional reservoir simulator that borrows the dual-medium concept from conventional dual-continuum models and also incorporates the effect of each fracture explicitly. The model is compatible with existing finite-difference reservoir simulators. In contrast to dual-continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity of a typical NFR. The accuracy of the embedded DFM is confirmed by comparing the results with the fine-grid, explicit-fracture simulations for a case study including orthogonal fractures and a case with a nonaligned fracture. We also perform a grid-sensitivity study to show the convergence of the method as the grid is refined. Our simulations indicate that to achieve accurate results, the embedded discrete fracture model may only require moderate mesh refinement around the fractures and hence offers a computationally efficient approach. Furthermore, examples of waterflooding, gas injection, and primary depletion are presented to demonstrate the performance and applicability of the developed method for simulating fluid flow in NFRs.

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Physics-based preconditioners for flow in fractured porous media

2014

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Discrete fracture models are an attractive alternative to upscaled models for flow in fractured media, as they provide a more accurate representation of the flow characteristics. A major challenge in discrete fracture simulation is to overcome the large computational cost associated with resolving the individual fractures in large-scale simulations. In this work, two characteristics of the fractured porous media are utilized to construct efficient preconditioners for the discretized flow equations. First, the preconditioners are tailored to the fracture geometry and presumed flow properties so that the dominant features are well represented there. This assures good scalability of the preconditioners in terms of problem size and permeability contrast. For fracture dominated problems, numerical examples show that such geometric preconditioners are comparable or preferable when compared to state-of-the-art algebraic multigrid preconditioners. The robustness of the physics-based preconditioner for less favorable fracture conditions is further demonstrated by a systematic degradation of the fracture hierarchy. Second, the preconditioners are physics preserving in the sense that conservative fluxes can be computed even for an inexact pressure solutions. This facilitates a scheme where accuracy in the linear solver can be traded for efficiency by terminating the iterative solvers based on error estimates, and without sacrificing basic physical modeling principles. With the combination of these two properties a novel preconditioner is obtained which bridges the gap between multiscale approximations and iterative linear solvers.

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Hierarchical modeling of flow in naturally fractured formations with multiple length scales

Cited by 424 publications

References 29 publications

Generation of coarse‐scale continuum flow models from detailed fracture characterizations

Generation of coarse‐scale continuum flow models from detailed fracture characterizations

Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

Physics-based preconditioners for flow in fractured porous media

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