An improved projection-based embedded discrete fracture model (pEDFM) for multiphase flow in fractured reservoirs

Jiang, Jiamin; Younis, Rami M.

doi:10.1016/j.advwatres.2017.09.017

Cited by 121 publications

(56 citation statements)

References 36 publications

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“…Models that apply non-conforming gridding include the embedded discrete fracture matrix model (EDFM) [20], and extended finite element methods (XFEM) [21,22]. These methods avoid the complexities of conforming grid generation discussed below, but must instead incorporate the fracture-matrix interaction in what becomes complex modifications of the numerical method for XFEM [23], or by constructing an upscaled representation, e.g., [24], where the latter approach faces challenges reminiscent of those in continuum-type models. For this reason, our interest herein is DFM methods with conforming grids.…”

Section: Introductionmentioning

confidence: 99%

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

et al. 2020

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Development of models and dedicated numerical methods for dynamics in fractured rocks is an active research field, with research moving towards increasingly advanced process couplings and complex fracture networks. The inclusion of coupled processes in simulation models is challenged by the high aspect ratio of the fractures, the complex geometry of fracture networks, and the crucial impact of processes that completely change characteristics on the fracture-rock interface. This paper provides a general discussion of design principles for introducing fractures in simulators, and defines a framework for integrated modeling, discretization, and computer implementation. The framework is implemented in the open-source simulation software PorePy, which can serve as a flexible prototyping tool for multiphysics problems in fractured rocks. Based on a representation of the fractures and their intersections as lower-dimensional objects, we discuss data structures for mixed-dimensional grids, formulation of multiphysics problems, and discretizations that utilize existing software. We further present a Python implementation of these concepts in the PorePy open-source software tool, which is aimed at coupled simulation of flow and transport in three-dimensional fractured reservoirs as well as deformation of fractures and the reservoir in general. We present validation by benchmarks for flow, poroelasticity, and fracture deformation in porous media. The flexibility of the framework is then illustrated by simulations of non-linearly coupled flow and transport and of injection-driven deformation of fractures. All results can be reproduced by openly available simulation scripts.

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Section: Introductionmentioning

confidence: 99%

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

et al. 2020

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“…Although the treatment of matrix-fracture mass transfer is simple and straightforward, an unphysical flux split may occur when simulating multiphase phase flow, and incorrect modeling results would be obtained as the fracture permeability lies below that of the matrix (Jiang & Younis, 2017). To overcome these limitations, a method was proposed to calculate the fluxes across the two sides of a fracture separately via adding an additional two pairs of matrix-fracture connections (Jiang & Younis, 2017;Tene et al, 2017). Minor shortcomings of this treatment lie in enhancing the complexity of model implementation and increasing the density of the Jacobian matrix, especially for 3-D problems.…”

Section: Two-point Flux Approximation Of 3-d Edfmmentioning

confidence: 99%

Three‐Dimensional Hydrochemical Model for Dissolutional Growth of Fractures in Karst Aquifers

Kang

Feng

et al. 2020

Water Resources Research

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This paper is intended to present a newly developed, comprehensive model to understand hydrochemical behaviors related to dissolutional growth of complex fractures underground. Under a fully implicit solution framework, the finite volume approach is employed to solve the reactive‐convective‐dispersive system. Based on the embedded discrete fracture model, a novel modeling approach is proposed to describe dissolutional fractures with various apertures in three dimensions (3‐D). This model is verified against preexisting numerical models. Then, a 3‐D field case study regarding hypogene speleogenesis in a deep‐seated, artesian setting is carried out, based on field data concerning karst terrain compiled from Western Ukraine. Finally, we perform a case study to elucidate the finger‐like dissolution process related to a synthetic 3‐D fracture network in gypsum and limestone with heterogeneous aperture fields. Simulation results suggest that (a) the combination of the kinetic trigger mechanism and the transverse speleogenesis concept favors the generation of hierarchical caves in homogeneous fractures; (b) the mechanism of reactive infiltration instabilities determines dissolutional propagation in gypsum with rough fractures; and (c) in limestone, nonlinear kinetics matters for both uniform‐ and variable‐aperture fractures.

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“…where Γ is a diagonal matrix filled with ones and zeros to identify whether each regular degree of freedom belongs to Ω + or Ω − , respectively; and is the matrix that propagates the effect of the pressure drop to the regular nodes. By inserting Equation 21into (20), the pressure field inside the element can be rewritten as:…”

Section: Discretisation Of Transverse Flowmentioning

confidence: 99%

“…Having into account that propagates the effect of the pressure to the regular nodes as a rigid body movement, then ∇̃= ∇ = . Thus, by considering Equations (20) and 21:…”

Section: Discretisation Of Transverse Flowmentioning

confidence: 99%

“…[8][9][10][11][12] However, the application of most classic DFM models is limited to matching meshes across the discontinuities, that is, the crack path is enforced along element boundaries. 13 Non-conforming DFM models, for example embedded discrete fracture model (EDFM), have been developed to avoid the need for meshes to match. Lee et al 14 proposed a hierarchical approach to calculate the effective permeability of a fractured domain based on the ratio of the discontinuity length to the finite difference mesh size.…”

Section: Introductionmentioning

confidence: 99%

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Transverse and longitudinal fluid flow modelling in fractured porous media with non‐matching meshes

Damirchi

Carvalho

Bitencourt

et al. 2020

Num Anal Meth Geomechanics

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A new discrete fracture model is introduced to simulate the steady-state fluid flow in discontinuous porous media. The formulation uses a multi-layered approach to capture the effect of both longitudinal and transverse permeability of the discontinuities in the pressure distribution. The formulation allows the independent discretisation of mesh and discontinuities, which do not need to conform. Given that the formulation is developed at the element level, no additional degrees of freedom or special integration procedures are required for coupling the non-conforming meshes. The proposed model is shown to be reliable regardless of the permeability of the discontinuity being higher or lower than the surrounding domain. Four numerical examples of increasing complexity are solved to demonstrate the efficiency and accuracy of the new technique when compared with results available in the literature. Results show that the proposed method can simulate the fluid pressure distribution in fractured porous media. Furthermore, a sensitivity analysis demonstrated the stability regarding the condition number for wide range values of the coupling parameter. K E Y W O R D S coupling finite elements, embedded discontinuity approach, fluid flow, fractured porous media, transverse fluid flow

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An improved projection-based embedded discrete fracture model (pEDFM) for multiphase flow in fractured reservoirs

Cited by 121 publications

References 36 publications

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

Three‐Dimensional Hydrochemical Model for Dissolutional Growth of Fractures in Karst Aquifers

Transverse and longitudinal fluid flow modelling in fractured porous media with non‐matching meshes

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