Mimetic Finite Differences for Flow in Fractures from Microseismic Data

Al-Hinai, Omar; Srinivasan, Sanjay; Weeler, Mary F.

doi:10.2118/173319-ms

Cited by 15 publications

(15 citation statements)

References 15 publications

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“…We consider a parametric description of Γ h and indicate with s the arc-length coordinate. We assume to have numbered the fracture edges so that s i is the center ofê i , with s 1 < s 2 …”

Section: Finite Volume Discretization Of the Fracture Problemmentioning

confidence: 99%

Mimetic finite difference approximation of flows in fractured porous media

et al. 2016

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Abstract.We present a possible framework for the numerical simulation of flow in fractured porous media that couples mimetic finite differences for the porous matrix with a finite volume scheme for the flow in the fractures. The resulting method is theoretically analyzed in the case of a single fracture. Moreover, several numerical experiments show the capability of the method to deal also with complicated networks of fractures. Thanks to the implementation of rather general coupling conditions, it encompasses both "conductive fractures", i.e., fractures with high permeability and "sealed fractures", i.e., fractures with low permeability which act as a flow barrier.Mathematics Subject Classification. 65N30, 35Q86, 76S05.

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Section: Finite Volume Discretization Of the Fracture Problemmentioning

confidence: 99%

Mimetic finite difference approximation of flows in fractured porous media

et al. 2016

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“…In recent years the use of MFD has grown considerably, thanks to their flexibility and ability to preserve important properties of the physical and mathematical model. MDF has been employed to simulate flow in networks of fractures, see [12,13], and flows in fractured porous media [3,10], with a primal and mixed formulation, respectively. It has been used also for quasilinear elliptic problems [8], as well as non-linear and control problems [5][6][7].The present work can be considered in continuity with the strategy used in [10], but differs from the previous literature because a dual mixed formulation, discretized with the MFD method, is employed in the bulk medium as well as in the fractures.…”

mentioning

confidence: 99%

Analysis of a mimetic finite difference approximation of flows in fractured porous media

2018

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“…Among the others, in Pichot et al (), the mortar method is used in order to allow for a partial nonconformity of the mesh at fracture intersections. Other strategies involve the use of nonstandard finite element techniques in order to ease the meshing process: the eXtended Finite Element Method (XFEM) has been used in Huang et al (), D'Angelo and Scotti (), Berrone et al (), Formaggia et al (), and Schwenck et al () allowing for meshes that can cross the interfaces; Mimetic Finite Differences (MFD) were used in Huang et al () and Al‐Hinai et al (); the Virtual Element Method (VEM) was applied in Benedetto et al (), allowing for polygonal meshes. A new code for the simulation of flows in fracture networks, also taking into account randomness of input parameters is described in Hyman et al (), Makedonska et al (), and Hyman et al ().…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification in Discrete Fracture Network Models: Stochastic Geometry

Berrone

Canuto

Pieraccini

et al. 2018

Water Resources Research

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We consider the problem of uncertainty quantification analysis of the output of underground flow simulations. We consider in particular fractured media described via the discrete fracture network model; within this framework, we address the relevant case of networks in which the geometry of the fractures is described by stochastic parameters. In this context, due to a possible lack of smoothness in the quantity of interest with respect to the stochastic parameters, well assessed techniques such as stochastic collocation may fail in providing reliable estimates of first‐order moments of the quantity of interest. In this paper, we overcome this issue by applying the Multilevel Monte Carlo method, using as underlying solver an extremely robust method.

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Mimetic Finite Differences for Flow in Fractures from Microseismic Data

Cited by 15 publications

References 15 publications

Mimetic finite difference approximation of flows in fractured porous media

Mimetic finite difference approximation of flows in fractured porous media

Analysis of a mimetic finite difference approximation of flows in fractured porous media

Uncertainty Quantification in Discrete Fracture Network Models: Stochastic Geometry

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