Finite volume discretization for poroelastic media with fractures modeled by contact mechanics

Berge, Runar Lie; Berre, Inga; Keilegavlen, Eirik; Nordbotten, Jan Martin; Wohlmuth, Barbara

doi:10.1002/nme.6238

Cited by 60 publications

(75 citation statements)

References 44 publications

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“…As in the previous sections, the relation between the fluid pressures in Ω h and Ω l is governed by a flux law of the type (3.3). The relation between σ l and〚u j 〛is modeled by borrowing techniques from contact mechanics as summarized here (for a full discussion, see [49]). Balance of tractions between the poroelastic stress in Ω h and the contact traction in Ω l is for the two sides expressed as…”

Section: Poroelastic Fracture Deformation By Contact Mechanicsmentioning

confidence: 99%

“…The discretization of the contact mechanics (Eqs. (3.14) and (3.15)) is implemented by a semismooth Newton method to deal with the discontinuities in the solution, for details we refer to [49,63]. The available discretizations on subdomains and interfaces can also be used as building blocks for more complex problems; for instance, the simulations of thermo-poroelasticity with fracture deformation reported in [64] utilized several of the discretization schemes mentioned above.…”

Section: Discretization Classesmentioning

confidence: 99%

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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: Poroelastic Fracture Deformation By Contact Mechanicsmentioning

confidence: 99%

Section: Discretization Classesmentioning

confidence: 99%

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

et al. 2020

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“…In Van Der Kooij et al (2020) , we demonstrated that the statistical variability in fracture aperture for a fixed fracture network can lead to different connectivity between injection and production wells which in turn yields different optimal production rate. In addition, rigorous consideration of the effect of thermoporoelastic deformation of rock on heat production ( Stefansson et al, 2020;Berge et al, 2020 ) can be essential for geothermal applications and has been ongoing development in our group.…”

Section: Discussionmentioning

confidence: 99%

Modeling of multiphase mass and heat transfer in fractured high-enthalpy geothermal systems with advanced discrete fracture methodology

Hoop

Voskov

Bertotti

et al. 2021

Preprint

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Multiphase mass and heat transfer are ubiquitous in the subsurface within manifold applications. The presence of fractures over several scales and complex geometry magnifies the uncertainty of the heat transfer phenomena, which will significantly impact, or even dominate, the dynamic transport process. Capturing the details of fluid and heat transport within the fractured system is beneficial to the subsurface operations. However, accurate modeling methodologies for thermal high-enthalpy multiphase flow within fractured reservoirs are quite limited. In this work, multiphase flow in fractured geothermal reservoirs is numerically investigated. A discrete-fracture model is utilized to describe the fractured system. To characterize the thermal transport process accurately and efficiently, the resolution of discretization is necessarily optimized. A synthetic fracture model is firstly selected to run on different levels of discretization with different initial thermodynamic conditions. A comprehensive analysis is conducted to compare the convergence and computational efficiency of simulations. The numerical scheme is implemented within the Delft Advanced Research Terra Simulator (DARTS), which can provide fast and robust simulation to energy applications in the subsurface. Based on the converged numerical solutions, a thermal Péclet number is defined to characterize the interplay between thermal convection and conduction, which are the two governing mechanisms in geothermal development. Different heat transfer stages are recognized on the Péclet curve in conjunction with production regimes of the synthetic fractured reservoir. A fracture network, sketched and scaled up from a digital map of a realistic outcrop, is then utilized to perform a sensitivity analysis of the key parameters influencing the heat and mass transfer. Thermal propagation and Péclet number are found to be sensitive to flow rate and thermal parameters (e.g., rock heat conductivity and heat capacity). This paper presents a numerical simulation framework for fractured geothermal reservoirs, which provides the necessary procedures for practical investigations regarding geothermal developments with uncertainties.

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“…We note that previous works on similar models circumvent these limitations by linearization processes (complete or partial freezing of the matrix porosity and fracture apertures). Regarding the assumption on the fracture aperture, it could possibly be overcome by introducing contact mechanics in the model [38,10]. This direction will be investigated in a future work.…”

Section: Introductionmentioning

confidence: 99%

Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media

Bonaldi

Brenner

Droniou

et al. 2021

Computers & Mathematics with Applications

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We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical deformation of the matrix assuming that the fractures are open and filled by the fluids, as well as small deformations and a linear elastic constitutive law. The model is discretized using the gradient discretization method [30], which covers a large class of conforming and non conforming schemes. This framework allows for a generic convergence analysis of the coupled model using a combination of discrete functional tools. Here, we describe the model together with its numerical discretization and, using discrete compactness techniques, we prove a convergence result (up to a subsequence) assuming the non-degeneracy of the phase mobilities and that the discrete solutions remain physical in the sense that, roughly speaking, the porosity does not vanish and the fractures remain open. This is, to our knowledge, the first convergence result for this type of model taking into account two-phase flows in fractured porous media and the non-linear poromechanical coupling. Previous related works consider a linear approximation obtained for a single phase flow by freezing the fracture conductivity [41,42]. Numerical tests employing the Two-Point Flux Approximation (TPFA) finite volume scheme for the flows and P2 finite elements for the mechanical deformation are also provided to illustrate the behavior of the solution to the model.

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Finite volume discretization for poroelastic media with fractures modeled by contact mechanics

Cited by 60 publications

References 44 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

Modeling of multiphase mass and heat transfer in fractured high-enthalpy geothermal systems with advanced discrete fracture methodology

Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media

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