Multiscale Finite Volume Method for Discrete Fracture Modeling with Unstructured Grids

Bosma, Sebastian B. M.; Hajibeygi, Hadi; Ţene, M.

doi:10.2118/182654-ms

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…Face normals are assumed to have a length equal to the corresponding face areas A i,k • n i,k , i.e., The one-sided transmissibilities T i,k are related to a single cell and provide a two-point relation between the flux across a cell face and the pressure difference between the cell and face centroids. The proper name for these onesided transmissibilities is half-transmissibilities as they are associated with a half-face [19,54].…”

Section: Two-point Flux Approximation In Corner-point Grid Geometrymentioning

confidence: 99%

Projection-based embedded discrete fracture model (pEDFM) for flow and heat transfer in real-field geological formations with corner-point grid geometries

HosseiniMehr,

Tomala,

Vuik

et al. 2021

Preprint

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In this work, the projection-based embedded discrete fracture model (pEDFM) for corner-point grid (CPG) geometry is developed for simulation of flow and heat transfer in fractured porous media. Unlike classical embedded discrete fracture approaches, this method allows for using any geologically-relevant model with a complex geometry and generic conductivity contrasts between the rock matrix and the fractures (or faults). The mass and energy conservation equations are coupled using the fully-implicit (FIM) scheme, allowing for stable simulation. Independent corner-point grids are imposed on the rock matrix and all fractures. The connectivities between the non-neighboring grid cells are described such that a consistent discrete representation of the embedded fractures occurs within the corner-point grid geometry. Various numerical tests including geologically-relevant and real-field models are conducted to demonstrate the performance of the developed method. It is shown that pEDFM can accurately capture the physical influence of both highly conductive fractures and flow barriers on the flow and heat transfer fields in complex reservoir geometries. This development casts a promising approach for flow simulations of real-field geo-models, increasing the discretization flexibility and enhancing the computational performance for capturing explicit fractures accurately.

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Section: Two-point Flux Approximation In Corner-point Grid Geometrymentioning

confidence: 99%

Projection-based embedded discrete fracture model (pEDFM) for flow and heat transfer in real-field geological formations with corner-point grid geometries

HosseiniMehr,

Tomala,

Vuik

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Face normals are assumed to have a length equal to the corresponding face areas A i,k • n i,k , i.e., The one-sided transmissibilities T i,k are related to a single cell and provide a two-point relation between the flux across a cell face and the pressure difference between the cell and face centroids. The proper name for these one-sided transmissibilities is half-transmissibilities as they are associated with a half face (Karimi-Fard et al, 2004;Bosma et al, 2017).…”

Section: Two-point Flux-approximationmentioning

confidence: 99%

Projection-based Embedded Discrete Fracture Model (pEDFM) on Corner-point Grid Geometry for Subsurface Flow and Geothermal Modeling

et al. 2020

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We develop projection-based embedded discrete fracture model (pEDFM) on corner-point grids (CPG) for fluid flow and heat transfer in subsurface geological formations. The coupling between the flow and heat transfer is fully-implicit, to allow for stable simulations, specially in presence of highly contrasting fractures. We define independent CPG-based mesh for matrix rock and all 3D fractures, which allows for capturing geologically complex geometries. The connectivities between the non-neighbouring cells are described such that a consistent discrete representation of the embedded fractures are developed within the CPG geometry. Numerical rests are developed first to verify the CPG grid implementation compared with the Cartesian structured ones, and then to illustrate the applicability of the pEDFM for field-scale geologically complex reservoirs.Significance and Technical Contributions to the Knowledge Base of the Mathematics of Oil Recovery:• It develops a fully 3D projection-based embedded discrete fracture model (pEDFM).• It extends pEDFM method for corner-point grid geometry.

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“…Locally computed basis functions are employed to interpolate the solution at coarse levels [13], [14], [15]. To honor the heterogeneity of the domain, multiscale finite volume basis functions are used as pressure interpolators [16], [17], [18], [19], [20]. These basis functions are only computed at the beginning of the simulation providing computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Multilevel Multiscale Simulation of Naturally Fractured Reservoirs with Generic Fracture-Matrix Conductivity Contrasts

HosseiniMehr

Kobaisi

Vuik

et al. 2019

Day 2 Wed, September 18, 2019

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An algebraic dynamic multilevel (ADM) method for multiphase flow in heterogeneous fractured porous media using the projection-based embedded discrete fracture model (pEDFM) is presented. The fine-scale discrete system is obtained independently for matrix and each lower-dimensional fracture. On the finescale high resolution computational grids, an independent dynamic multilevel gird (i.e., ADM grid) is imposed. The fully implicit discrete system is mapped completely algebraically to this ADM grid resolution using sequences of restriction and prolongation operators. Multilevel multiscale basis functions are locally computed and employed to honor the heterogeneity contrasts of the fractured domain by interpolating the solution accurately. These basis functions are computed only at the beginning of the simulation to increase the computational efficiency. Once the ADM system is solved for all unknowns (i.e., pressure and saturation), the solution at ADM resolution is prolonged back to fine-scale resolution in order to obtain an approximated fine-scale solution. This dynamic multilevel system employs the fine-scale grid cells only at the sharp gradient of the solution (e.g., at the moving front). With two fractured test-cases (homogeneous and heterogeneous), the performance of ADM is assessed by comparing it to fine-scale results as reference solution. It will be shown that ADM is able to reduce the computational costs and provide efficiency while maintaining the desired accuracy.

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Multiscale Finite Volume Method for Discrete Fracture Modeling with Unstructured Grids

Cited by 4 publications

References 31 publications

Projection-based embedded discrete fracture model (pEDFM) for flow and heat transfer in real-field geological formations with corner-point grid geometries

Projection-based embedded discrete fracture model (pEDFM) for flow and heat transfer in real-field geological formations with corner-point grid geometries

Projection-based Embedded Discrete Fracture Model (pEDFM) on Corner-point Grid Geometry for Subsurface Flow and Geothermal Modeling

Dynamic Multilevel Multiscale Simulation of Naturally Fractured Reservoirs with Generic Fracture-Matrix Conductivity Contrasts

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