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Mat 263 – Principles of Discrete Math Review

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Abstract

Evolution of models and dedicated numerical methods for dynamics in fractured rocks is an active inquiry field, with enquiry moving towards increasingly avant-garde 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 modify characteristics on the fracture-rock interface. This newspaper provides a general discussion of design principles for introducing fractures in simulators, and defines a framework for integrated modeling, discretization, and figurer implementation. The framework is implemented in the open-source simulation software PorePy, which can serve every bit a flexible prototyping tool for multiphysics bug in fractured rocks. Based on a representation of the fractures and their intersections equally lower-dimensional objects, we discuss data structures for mixed-dimensional grids, formulation of multiphysics problems, and discretizations that utilise 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 full general. We nowadays validation by benchmarks for period, poroelasticity, and fracture deformation in porous media. The flexibility of the framework is then illustrated by simulations of not-linearly coupled menstruation and transport and of injection-driven deformation of fractures. All results tin can be reproduced past openly bachelor simulation scripts.

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Acknowledgments

The authors thank ii anonymous reviewers for the comments and suggestions that helped to ameliorate the quality of the paper.

Funding

Open Access funding provided by University of Bergen. This piece of work has been funded in office by Norwegian Research Council grant 250223, 244129/E20, 267908/E20, and 274883, and by a VISTA Scholarship from the Norwegian Academy of Science and Letters.

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Writer notes

  1. Alessio Fumagalli

    Present address: MOX Laboratory, Department of Mathematics, Politecnico di Milano, via Bonardi 9, 20133, Milan, Italy

  2. Michele Starnoni

    Present address: Section of Environment, Country and Infrastructure Engineering, Politecnico di Torino, Turin, Italia

Affiliations

  1. Department of Mathematics, University of Bergen, Lead 7800, 5020, Bergen, Norway

    Eirik Keilegavlen, Runar Berge, Alessio Fumagalli, Michele Starnoni, Ivar Stefansson, Jhabriel Varela & Inga Berre

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Correspondence to Eirik Keilegavlen.

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Keilegavlen, Eastward., Berge, R., Fumagalli, A. et al. PorePy: an open-source software for simulation of multiphysics processes in fractured porous media. Comput Geosci 25, 243–265 (2021). https://doi.org/x.1007/s10596-020-10002-5

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  • DOI : https://doi.org/10.1007/s10596-020-10002-5

Keywords

  • Fractured reservoirs
  • Mixed-dimensional geometry
  • Numerical simulations
  • Multiphysics
  • Discrete fracture matrix models
  • Open-source software
  • Reproducible science

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