Verification benchmarks for single-phase flow in three-dimensional fractured porous media

We present version 3 of the open-source simulator for flow and transport processes in porous media DuMux. DuMux is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMux, version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.

DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state Bastian etal. (2008a, 2008b). This discussion is accompanied with a description of various advanced features, such as coupling of domains and cut cells, grid modifications such as adaptation and moving domains, high order discretizations and node level performance, non-smooth multigrid methods, and multiscale methods. A brief discussion on current and future development directions of the framework concludes the paper.

The DUNE framework: Basic concepts and recent developments

Various processes such as heterogeneous reactions or biofilm growth alter a porous medium’s underlying geometric structure. This significantly affects its hydrodynamic parameters, in particular the medium’s effective permeability. An accurate, quantitative description of the permeability is, however, essential for predictive flow and transport modeling. Well-established relations such as the Kozeny–Carman equation or power law approaches including fitting parameters relate the porous medium’s porosity to a scalar permeability coefficient. Opposed to this, upscaling methods directly enable calculating the full, potentially anisotropic, permeability tensor. As input, only the geometric information in terms of a representative elementary volume is needed. To compute the porosity–permeability relations, supplementary cell problems must be solved numerically on this volume and their solutions must be integrated. We apply this approach to provide easy-to-use quantitative porosity–permeability relations that are based on representative single grain, platy, blocky, prismatic soil structures, porous networks, and real geometries obtained from CT-data. As a discretization method, we use discontinuous Galerkin method on structured grids. To make the relations explicit, interpolation of the obtained data is used. We compare the outcome with the well-established relations and investigate the ranges of the validity. From our investigations, we conclude whether Kozeny–Carman-type or power law-type porosity–permeability relations are more reasonable for various prototypic representative elementary volumes. Finally, we investigate the impact of a microporous solid matrix onto the permeability.

Beyond Kozeny–Carman: Predicting the Permeability in Porous Media

Reactive transport modeling is a process-based approach that accounts for advection, diffusion, dispersion and a multitude of biogeochemical reactions. The occurrence of these reactions, by nature, tends to affect the properties of porous media in many ways (Tenthorey and Gerald 2006). If these alteration reactions are significant, then feedback mechanisms could occur that influence the flow of groundwater as well as the migration of solutes and gases through porous media (Le Gallo et al. 1998; Kaszuba et al. 2005; Jin et al. 2013). In addition, changes induced by the reactions on the solid grains can also affect the rates of the reactions themselves (Hao et al. 2012; Harrison et al. 2017). A prime example for reactive transport in evolving porous media is the dissolution of mineral phases. If dissolution reactions are substantial, the porosity, i.e., the void space between grains or apertures of fractures in jointed rocks, will increase. Such an increase in porosity commonly has secondary effects, by altering the connectivity or larger scale pores in the porous medium under consideration (Navarre-Sitchler et al. 2009). Together, these changes in porosity and connectivity can substantially affect flow and transport processes by modifying the key transport parameters such as the medium’s permeability and tortuosity, leading to alteration of the groundwater flow regime and modification of transport pathways. The impact of these changes can affect transport in the water phase as well as in the gas phase. In addition, because mineral dissolution reshapes the surface of the dissolving phases or leads to the complete dissolution of smaller particles, the system’s reactivity can be affected as well, leading to a direct feedback on reaction progress and rates (Noiriel et al. 2009).

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Reactive Transport in Evolving Porous Media

Reactive transport processes in a porous medium will often both cause changes to the pore structure, via precipitation and dissolution of biomass or minerals, and be affected by these changes, via changes to the material’s porosity and permeability. An understanding of the pore structure morphology and the changes to flow parameters during these processes is critical when modeling reactive transport. Commonly applied porosity–permeability relations in simulation models on the REV scale use a power-law relation, often with slight modifications, to describe such features; they are often used for modeling the effects of mineral precipitation and/or dissolution on permeability. To predict the reduction in permeability due to biomass growth, many different and often rather complex relations have been developed and published by a variety of authors. Some authors use exponential or simplified Kozeny–Carman relations. However, many of these relations do not lead to fundamentally different predictions of permeability alteration when compared to a simple power-law relation with a suitable exponent. Exceptions to this general trend are only few of the porosity–permeability relations developed for biomass clogging; these consider a residual permeability even when the pore space is completely filled with biomass. Other exceptions are relations that consider a critical porosity at which the porous medium becomes impermeable; this is often used when modeling the effect of mineral precipitation. This review first defines the scale on which porosity–permeability relations are typically used and aims at explaining why these relations are not unique. It shows the variety of existing approaches and concludes with their essential features.

/pdf/porosity-permeability-relations-for-evolving-pore-space-a-4mdwj9d8yg.pdf

Porosity–Permeability Relations for Evolving Pore Space: A Review with a Focus on (Bio-)geochemically Altered Porous Media

A channel flow coupled with a transversal stream through porous structures is investigated numerically in this study. Velocity profiles are obtained on the pore scale and averaged to the macroscale in order to evaluate the validity of the Beavers–Joseph interface condition. For this purpose, different ratios between the velocity at the inlet of the channel and the velocity at the base of the porous structure are considered. The effects of Reynolds number, velocity ratio, and geometrical arrangement of the porous structure on the Beavers–Joseph constant are then examined. A critical velocity ratio is found where, for lower ratios, the interface momentum transfer is mainly affected by the channel flow and, for higher ratios, the flow in the porous structure governs. The uniformity of the Beavers–Joseph constant at the interface is found to decrease with increasing velocity ratios. The present results have then been compared with simulations from a coupled Navier–Stokes/Darcy–Forchheimer model.

On the Beavers–Joseph Interface Condition for Non-parallel Coupled Channel Flow over a Porous Structure at High Reynolds Numbers

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2020WR027332

Influence of Radiation on Evaporation Rates: A Numerical Analysis

We investigate the influence of near‐surface wind conditions on subsurface gas transport and on soil‐atmosphere gas exchange for gases of different density. Results of a sand tank experiment are supported by a numerical investigation with a fully coupled porous medium‐free flow model, which accounts for wind turbulence. The experiment consists of a two‐dimensional bench‐scale soil tank containing homogeneous sand and an overlying wind tunnel. A point source was installed at the bottom of the tank. Gas concentrations were measured at multiple horizontal and vertical locations. Tested conditions include four wind velocities (0.2/1.0/2.0/2.7 m/s), three different gases (helium: light, nitrogen: neutral, and carbon dioxide: heavy), and two transport cases (1: steady‐state gas supply from the point source; 2: transport under decreasing concentration gradient, subsequent to termination of gas supply). The model was used to assess flow patterns and gas fluxes across the soil surface. Results demonstrate that flow and transport in the vicinity of the surface are strongly coupled to the overlying wind field. An increase in wind velocity accelerates soil‐atmosphere gas exchange. This is due to the effect of the wind profile on soil surface concentrations and due to wind‐induced advection, which causes subsurface horizontal transport. The presence of gases with pronounced density difference to air adds additional complexity to the transport through the wind‐affected soil layers. Wind impact differs between tested gases. Observed transport is multidimensional and shows that heavy as well as light gases cannot be treated as inert tracers, which applies to many gases in environmental studies.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2020WR027600

Edward Coltman

Papers

Porosity–Permeability Relations for Evolving Pore Space: A Review with a Focus on (Bio-)geochemically Altered Porous Media

DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

On the Beavers–Joseph Interface Condition for Non-parallel Coupled Channel Flow over a Porous Structure at High Reynolds Numbers

Influence of Radiation on Evaporation Rates: A Numerical Analysis

Gas Component Transport Across the Soil-Atmosphere Interface for Gases of Different Density: Experiments and Modeling