An upstream finite element method for solution of transient transport equation in fractured porous media

Noorishad, J.; Mehran, Mohsen

doi:10.1029/wr018i003p00588

Cited by 299 publications

(118 citation statements)

References 16 publications

(20 reference statements)

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“…Further, one must be able to identify the locations and orientations of the discrete fractures for the model to be realistic. Noorishad and Mehran (1982) presented a finite-element method for the transient solution of solute by dispersion and convection in 2D fractured porous media. Baca et al (1984) proposed a 2D finite-element model for single-phase flow with heat and solute transport.…”

Section: Discrete Fracture Modelsmentioning

confidence: 99%

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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Section: Discrete Fracture Modelsmentioning

confidence: 99%

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

et al. 2013

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“…[7] An alternative to dual-porosity/dual-permeability models is the discrete-fracture model [Noorishad and Mehran, 1982;Baca et al, 1984;Granet et al, 1998]. …”

Section: Introductionmentioning

confidence: 99%

Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media

Monteagudo

Firoozabadi

2004

Water Resources Research

195

111

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[1] We provide a numerical procedure for the simulation of two-phase immiscible and incompressible flow in two-and three-dimensional discrete-fractured media. The concept of cross-flow equilibrium is used to reduce the fracture dimension from n to (n-1) in the calculation of flow in the fractures. This concept, which is often referred to as the discrete-fracture model, has a significant effect on the reduction of computational time. The spatial discretization is performed with the control-volume method. This method is locally conservative and allows the use of unstructured grids to represent complex geometries, such as discrete-fracture configurations. The relative permeability is upwinded with a criterion based on the evaluation of the flux direction at the boundaries of the control volumes, which is consistent with the physics of fluid flow. The system of partial differential equations is decoupled and solved using the implicit-pressure, explicitsaturation (IMPES) approach. The algorithm has been successfully tested in two-and three-dimensional numerical simulations of wetting phase fluid injection (such as water) in discrete-fractured media saturated by a nonwetting phase (such as nonaqueous phase liquid or oil) with mild to high nonlinearity in relative permeability and capillary pressure. To the best of our knowledge, results for simulations of two-phase immiscible and incompressible flow in three-dimensional discrete-fractured media, including capillary and gravity effects, are the first to appear in the literature.

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“…where nf denotes the number of intersecting fractures and αk is computed by Equation (14). TPFA scheme requires generating the K-orthogonal grids for flux computation, which is not easy for DFM.…”

Section: Numerical Discretization and Prismatic Meshing Strategiesmentioning

confidence: 99%

“…It is able to account for the effect of large-scale fractures explicitly. Noorishad and Mehran [14], and Baca et al [15] were among the early authors introducing DFM for single-phase flow. Kim and Deo [16], Karimi-Fard and Firoozabadi [17] developed DFMs based on the finite-element method for two-phase flow in fractured reservoirs.…”

Section: Introductionmentioning

confidence: 99%

Discrete Fracture Modeling of 3D Heterogeneous Enhanced Coalbed Methane Recovery with Prismatic Meshing

Zhang

Gong

et al. 2015

Energies

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Abstract:In this study, a 3D multicomponent multiphase simulator with a new fracture characterization technique is developed to simulate the enhanced recovery of coalbed methane. In this new model, the diffusion source from the matrix is calculated using the traditional dual-continuum approach, while in the Darcy flow scale, the Discrete Fracture Model (DFM) is introduced to explicitly represent the flow interaction between cleats and large-scale fractures. For this purpose, a general formulation is proposed to model the multicomponent multiphase flow through the fractured coal media. The S&D model and a revised P&M model are incorporated to represent the geomechanical effects. Then a finite volume based discretization and solution strategies are constructed to solve the general ECBM equations. The prismatic meshing algorism is used to construct the grids for 3D reservoirs with complex fracture geometry. The simulator is validated with a benchmark case in which the results show close agreement with GEM. Finally, simulation of a synthetic heterogeneous 3D coal reservoir modified from a published literature is performed to evaluate the production performance and the effects of injected gas composition, well pattern and gas buoyancy.

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An upstream finite element method for solution of transient transport equation in fractured porous media

Cited by 299 publications

References 16 publications

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

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

Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media

Discrete Fracture Modeling of 3D Heterogeneous Enhanced Coalbed Methane Recovery with Prismatic Meshing

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