Assessing the validity of a lower-dimensional representation of fractures for numerical and analytical investigations

Heße, Falk; Prykhodko, Vladyslav; Attinger, Sabine

doi:10.1016/j.advwatres.2013.03.003

Cited by 14 publications

(6 citation statements)

References 63 publications

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“…We refer to Berre et al (2018) for a comprehensive review. Although the low-dimensional representation is widely used, these models may be inaccurate (Grillo et al 2012;Heße et al 2013). Some validity criteria can be found in Stichel (2014).…”

Section: Fracturesmentioning

confidence: 99%

Aspects of Solvers for Large-Scale Coupled Problems in Porous Media

et al. 2019

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This work summarizes solution strategies for discrete systems occurring in the simulation of processes in the subsurface. The focus is on scalable solvers for large and coupled systems. The goal of this work is to enable researchers to select suitable algorithms and parameter settings to efficiently solve their problems. The work provides an overview of existing methods, highlighting their features, potential, and also frequent pitfalls. Numerical examples are provided for single phase flow, density driven flow and poroelasticity.Aspects of multiphase flow are discussed briefly; a detailed discussion of reactive transport is beyond the scope of the article. Future trends are discussed. Keywords Multigrid • Scalable solvers • Coupled problems • High performance computing • Porous media U.M. Yang: Portions of this work were performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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Section: Fracturesmentioning

confidence: 99%

Aspects of Solvers for Large-Scale Coupled Problems in Porous Media

et al. 2019

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“…It is noted that a smaller linear system is solved locally, as in (17), for every cluster as compared to the hybrid-grid method because of lower-dimensional fracture cells. Matrix-matrix fluxes and matrix-fracture fluxes in (19) and fracture-fracture fluxes in (33) can be determined separately in parallel and assembled into the coupled linear system (39). We note that for triangular elements the CVD-MPFA scheme is symmetric positive definite (SPD) for quadrature q = 2/3 [30] and thus for the equi-dimensional(2D) case where the fracture is gridded by triangular cells the linear system is SPD.…”

Section: Global Linear Systemmentioning

confidence: 99%

Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model

Ahmed

Edwards

Lamine

et al. 2015

Journal of Computational Physics

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A cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulation is presented for discrete fracture-matrix simulations. The grid is aligned with the fractures and barriers which are then modeled as lower-dimensional interfaces located between the matrix cells in the physical domain. The nD pressure equation is solved in the matrix domain coupled with an (n-1)D pressure equation solved in the fractures. The CVD-MPFA formulation naturally handles fractures with anisotropic permeabilities on unstructured grids. Matrix-fracture fluxes are expressed in terms of matrix and fracture pressures, and must be added to the lower-dimensional flow equation (called the transfer function). An additional transmission condition is used between matrix cells adjacent to low permeable fractures to link the velocity and pressure jump across the fractures. Numerical tests serve to assess the convergence and accuracy of the lower-dimensional fracture model for highly anisotropic fractures having different apertures and permeability tensors. A transport equation for tracer flow is coupled via the Darcy flux for single and intersecting fractures. The lower-dimensional approach for intersecting fractures avoids the more restrictive CFL condition corresponding to the equi-dimensional approximation with explicit time discretization. Lower-dimensional fracture model results are compared with hybrid-grid and equi-dimensional model results. Fractures and barriers are efficiently modeled by lower-dimensional interfaces which yield comparable results to those of the equi-dimensional model. Highly conductive fractures are modeled as lower-dimensional entities without the use of locally refined grids that are required by the equi-dimensional model, while pressure continuity across fractures is built into the model, without depending on the extra degrees of freedom which must be added locally by the hybrid-grid method.The lower-dimensional fracture model also yields improved results when compared to those of the hybrid-grid model for fractures with low-permeability in the normal direction to the fracture. In addition, a transient pressure simulation involving geologically representative complex fracture networks is presented.

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“…Additional assumptions made by this model include: 1) Aquifers exhibit horizontal flow; 2) Capillary pressure is negligible resulting in a sharp fluid interface; 3) CO 2 plume thickness at any given location is assumed to be the maximum plume thickness from all sources in the aquifer; 4) Pressure response from sources and sinks are superimposed in each aquifer; and 5) the injectivity of the formation remains constant. Several of these processes are important [9,11,13,15,17,22,26] and should be included [6,16,23,39] when model accuracy is more important that efficiency (e.g. during final project design).…”

Section: The Estimating Leakage Semi-analytically (Elsa) Algorithmmentioning

confidence: 99%

An iterative global pressure solution for the semi-analytical simulation of geological carbon sequestration

Baù

Cody²,

González‐Nicolás

2015

Comput Geosci

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Successful large-scale implementation of geological CO 2 sequestration (GCS) will require the preliminary assessment of multiple potential injection sites. Risk assessment and optimization tools used in this effort typically require large numbers of simulations. This makes it important to choose the appropriate level of complexity when selecting the type of simulation model. A promising multiphase semi-analytical method proposed by [40] to estimate key system attributes (i.e. pressure distribution, CO 2 plume extent, and fluid migration) has been found to reduce computational run times by three orders of magnitude when compared to other standard numerical techniques. The premise of the work presented herein is that the existing semi-analytically leakage algorithm proposed by [40] may be further improved in computational efficiency by applying a fixed point type iterative global pressure solution to eliminate the need to solve large sets of linear equations at each time step. Results show that significant gains in computational efficiency are obtained with this new methodology. In addition, this modification provides the same enhancement to similar semi-analytical algorithms that simulate singe-phase injection into multi-layer domains.

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Assessing the validity of a lower-dimensional representation of fractures for numerical and analytical investigations

Cited by 14 publications

References 63 publications

Aspects of Solvers for Large-Scale Coupled Problems in Porous Media

Aspects of Solvers for Large-Scale Coupled Problems in Porous Media

Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model

An iterative global pressure solution for the semi-analytical simulation of geological carbon sequestration

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