Computational framework for complex flow and transport in heterogeneous porous media

We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM ® , for flow and transport problems in highly heterogeneous geological media and other porous materials. The framework combines geostatistical pre- and post-processing to...

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Published in:	Engineering with computers Vol. 39; no. 6; pp. 3927 - 3940
Main Authors:	Icardi, Matteo, Pescimoro, Eugenio, Municchi, Federico, Hidalgo, Juan J.
Format:	Journal Article
Language:	English
Published:	London Springer London 01.12.2023 Springer Nature B.V
Subjects:	Boundary conditions Boussinesq approximation CAE) and Design Calculus of Variations and Optimal Control; Optimization Classical Mechanics Computer Science Computer-Aided Engineering (CAD Control Density Fast Fourier transformations Fields (mathematics) Fourier transforms Math. Applications in Chemistry Mathematical and Computational Engineering Mathematical models Original Article Partial differential equations Permeability Physical properties Porous materials Porous media Systems Theory Transport equations Open-source software Natural convection Dual-porosity Porous media flow Variable density Viscous fingerings
ISSN:	0177-0667, 1435-5663
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Abstract	We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM ® , for flow and transport problems in highly heterogeneous geological media and other porous materials. The framework combines geostatistical pre- and post-processing tools with specialised partial differential equations solvers. Random fields, for permeability and other physical properties, are generated by means of continuous or thresholded Gaussian random fields with various covariance/variogram functions. The generation process is based on an explicit spectral Fourier decomposition of the field which, although more computationally intensive than Fast Fourier Transform methods, allows a more flexible choice of statistical parameters and can be used for general geometries and grids. Flow and transport equations are solved for single-phase and variable density problems, with and without the Boussinesq approximation, and for a wide range of density, viscosity, and dispersion models, including dual-continuum (dual permeability or dual porosity) formulations. The mathematical models are here presented in details and the numerical strategies to deal with heterogeneities, equation coupling, and boundary conditions are discussed and benchmarked for the heterogeneous Henry and Horton–Rogers–Lapwood problems, and other test cases. We show that our framework is capable of dealing with large permeability variances, viscous instabilities, and large-scale three-dimensional transport problems.
AbstractList	We present a flexible scalable open-source computational framework, named , based on the finite-volume library OpenFOAM ® , for flow and transport problems in highly heterogeneous geological media and other porous materials. The framework combines geostatistical pre- and post-processing tools with specialised partial differential equations solvers. Random fields, for permeability and other physical properties, are generated by means of continuous or thresholded Gaussian random fields with various covariance/variogram functions. The generation process is based on an explicit spectral Fourier decomposition of the field which, although more computationally intensive than Fast Fourier Transform methods, allows a more flexible choice of statistical parameters and can be used for general geometries and grids. Flow and transport equations are solved for single-phase and variable density problems, with and without the Boussinesq approximation, and for a wide range of density, viscosity, and dispersion models, including dual-continuum (dual permeability or dual porosity) formulations. The mathematical models are here presented in details and the numerical strategies to deal with heterogeneities, equation coupling, and boundary conditions are discussed and benchmarked for the heterogeneous Henry and Horton–Rogers–Lapwood problems, and other test cases. We show that our framework is capable of dealing with large permeability variances, viscous instabilities, and large-scale three-dimensional transport problems. We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM ® , for flow and transport problems in highly heterogeneous geological media and other porous materials. The framework combines geostatistical pre- and post-processing tools with specialised partial differential equations solvers. Random fields, for permeability and other physical properties, are generated by means of continuous or thresholded Gaussian random fields with various covariance/variogram functions. The generation process is based on an explicit spectral Fourier decomposition of the field which, although more computationally intensive than Fast Fourier Transform methods, allows a more flexible choice of statistical parameters and can be used for general geometries and grids. Flow and transport equations are solved for single-phase and variable density problems, with and without the Boussinesq approximation, and for a wide range of density, viscosity, and dispersion models, including dual-continuum (dual permeability or dual porosity) formulations. The mathematical models are here presented in details and the numerical strategies to deal with heterogeneities, equation coupling, and boundary conditions are discussed and benchmarked for the heterogeneous Henry and Horton–Rogers–Lapwood problems, and other test cases. We show that our framework is capable of dealing with large permeability variances, viscous instabilities, and large-scale three-dimensional transport problems. We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM®, for flow and transport problems in highly heterogeneous geological media and other porous materials. The framework combines geostatistical pre- and post-processing tools with specialised partial differential equations solvers. Random fields, for permeability and other physical properties, are generated by means of continuous or thresholded Gaussian random fields with various covariance/variogram functions. The generation process is based on an explicit spectral Fourier decomposition of the field which, although more computationally intensive than Fast Fourier Transform methods, allows a more flexible choice of statistical parameters and can be used for general geometries and grids. Flow and transport equations are solved for single-phase and variable density problems, with and without the Boussinesq approximation, and for a wide range of density, viscosity, and dispersion models, including dual-continuum (dual permeability or dual porosity) formulations. The mathematical models are here presented in details and the numerical strategies to deal with heterogeneities, equation coupling, and boundary conditions are discussed and benchmarked for the heterogeneous Henry and Horton–Rogers–Lapwood problems, and other test cases. We show that our framework is capable of dealing with large permeability variances, viscous instabilities, and large-scale three-dimensional transport problems.
Author	Icardi, Matteo Pescimoro, Eugenio Hidalgo, Juan J. Municchi, Federico
Author_xml	– sequence: 1 givenname: Matteo orcidid: 0000-0003-3924-3117 surname: Icardi fullname: Icardi, Matteo email: matteo.icardi@nottingham.ac.uk organization: School of Mathematical Sciences, University of Nottingham – sequence: 2 givenname: Eugenio surname: Pescimoro fullname: Pescimoro, Eugenio organization: School of Mathematical Sciences, University of Nottingham – sequence: 3 givenname: Federico surname: Municchi fullname: Municchi, Federico organization: Colorado School of Mines – sequence: 4 givenname: Juan J. surname: Hidalgo fullname: Hidalgo, Juan J. organization: Institute of Environmental Assessment and Water Research (IDAEA), Spanish National Research Council (CSIC)
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Cites_doi	10.1016/j.rser.2017.09.084 10.1063/1.478774 10.1016/S0309-1708(96)00064-4 10.1063/1.475259 10.1029/2005rg000178 10.1137/1010093 10.2118/18095-pa 10.1016/j.energy.2007.05.001 10.1017/s030500410002452x 10.1016/0021-8928(60)90107-6 10.1017/s0956792518000189 10.1029/93wr00611 10.1023/A:1014009426274 10.1023/B:MATG.0000037737.11615.df 10.1016/j.cpc.2014.10.005 10.1103/PhysRevResearch.2.013041 10.1063/1.1707601 10.1016/j.cpc.2020.107763 10.1007/s00231-006-0142-6 10.1146/annurev.fl.19.010187.001415 10.1016/j.compfluid.2019.104279 10.1029/2003WR002199 10.1016/j.jconhyd.2017.09.002 10.5281/zenodo.6958098 10.1016/j.crte.2015.10.004 10.1017/s0022112094004386 10.1103/PhysRevE.74.026706 10.1017/jfm.2017.888 10.1016/j.advwatres.2009.04.003 10.1016/j.watres.2017.01.029 10.1016/j.micromeso.2013.02.039 10.1007/s12665-012-1546-x 10.1002/2014wr015811 10.1017/jfm.2013.559 10.1002/2015gl065036 10.1111/j.1745-6584.2008.00489.x 10.1029/91wr00266 10.1017/jfm.2013.511 10.1007/s11242-021-01661-8 10.1017/9781108591416 10.2118/1083-g 10.1016/j.envsoft.2014.01.013 10.1017/jfm.2021.257 10.1007/978-3-662-03550-4_8 10.1016/j.advwatres.2011.03.007
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Copyright_xml	– notice: The Author(s) 2023 – notice: The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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Snippet	We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM ® , for flow and transport... We present a flexible scalable open-source computational framework, named , based on the finite-volume library OpenFOAM ® , for flow and transport problems in... We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM®, for flow and transport...
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SubjectTerms	Boundary conditions Boussinesq approximation CAE) and Design Calculus of Variations and Optimal Control; Optimization Classical Mechanics Computer Science Computer-Aided Engineering (CAD Control Density Fast Fourier transformations Fields (mathematics) Fourier transforms Math. Applications in Chemistry Mathematical and Computational Engineering Mathematical models Original Article Partial differential equations Permeability Physical properties Porous materials Porous media Systems Theory Transport equations
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Title	Computational framework for complex flow and transport in heterogeneous porous media
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