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Special Issue on “NUPUS: Non-linearities and Upscaling in PoroUS Media”

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This special issue of Transport in Porous Media contains contributions from the community of researchers within the NUPUS collaboration. Submissions are authored by the full range of NUPUS members, from senior faculty members to the young researchers whose studies have been shaped by this international training network. Many of the contributions highlight the strong inter-university, inter-disciplinary and international connections which are reviewed in the accompanying foreword (Helmig et al. 2016). The topics of this special issue reflect those of NUPUS itself, and the contributions are grouped in the NUPUS research areas as follows.

Research Area A: Fundamental Methods and Concepts

Bárdossy and Hörning (2015) present a novel methodology for the geostatistical inverse modeling of groundwater flow and transport problems which is based on the concept of random mixing of spatial random fields.

Bode et al. (2015) propose to optimize existing or new monitoring networks in well catchment areas in a multiobjective setting. Their concept brings insight into the costs of reliability, early warning and uncertainty, as well as into the trade-off between covering only severe risks versus the luxury situation of controlling almost tolerable risks as well.

van Duijn et al. (2015) investigate a two-phase porous media flow model, in which dynamic effects are taken into account for the phase pressure difference. Compared to the equilibrium case, their results suggest that operating in a dynamic regime reduces the amount of oil trapped at interfaces, leading to an enhanced oil recovery.

Motivated by observations of saturation overshoot, Hönig et al. (2016) analyze generic classes of smooth travelling wave solutions of a system of two coupled nonlinear parabolic partial differential equations resulting from a flux function of high symmetry. They derive a complete representation of the five-dimensional manifold connecting wave velocities and boundary data.

Jambhekar et al. (2016) extend an REV-scale coupled free-flow porous-medium-flow model concept for salinization to describe reactive transport of ionic species and mixed salt precipitation.

Research Area B: Numerical Methods

Bringedal et al. (2015) present a two-dimensional pore scale model of a periodic porous medium where the ions in the fluid are allowed to precipitate onto the grains, while minerals in the grains are allowed to dissolve into the fluid. They perform a formal homogenization procedure to obtain upscaled equations.

Fetzer et al. (2016) extend a concept for the coupling of free and porous-medium flow to turbulent free-flow conditions and integrate eddy-viscosity and boundary layer models for a rough interface. Results demonstrate the effect of these extensions on the evaporation rate.

Magiera et al. (2015) consider a model problem for coupled surface–subsurface flow that consists of a nonlinear kinematic wave equation for the surface fluid’s height and a Brinkman model for the subsurface dynamics. They establish the existence of weak solutions and apply a finite volume method to solve the coupled problem numerically.

Pettersson (2015) presents a stochastic Galerkin formulation for the transport of carbon dioxide in a tilted aquifer with uncertain heterogeneous properties. Employing the polynomial chaos framework admits low-cost post-processing of the output to obtain statistics of interest.

Skogestad et al. (2015) propose a two-scale nonlinear preconditioning technique for multiphase flow problems in porous media that allows for incorporating physical intuition directly in the preconditioner. The developed preconditioner exhibits good scalability properties for challenging problems regardless of dominant physics.

Research Area C: Modeling Strategies for Selected Applications

Beck et al. (2016) present a conceptual approach to model fault reactivation in porous media. They interpret failure as a dissipation of elastic energy and thus replace the originally linear elastic material law by a visco-elastic law. The dissipation of elastic energy leads to additional displacements which are interpreted as slip on the fault plane.

Ehlers and Häberle (2016) treat transitions between liquid and gaseous phases for a multicomponent porous aggregate in a non-isothermal environment while accounting for the thermodynamics of the fluid-phase transitions. Geometrical and fluid-flow-dependent parameters are included into the phase change process.

Hommel et al. (2015) present a numerical investigation of the effect of various initial biomass distributions and initial amounts of attached biomass on the attachment of bacteria in porous media. This is performed for various injection strategies, changing the injection rate as well as alternating between continuous and pulsed injections.

Kunz et al. (2015) present simulations and experiments of drainage processes in a micro-model and compare them for quasi-static and pure dynamic processes. For both, simulation and experiment, the interfacial area and the pressure at the inflow and outflow are tracked.

In the context of thermally enhanced remediation of soil, Weishaupt et al. (2016) investigate the impacts of preheating the soil on the thermal radius of influence. They consider different preheating scenarios with a full-complexity, 3D, non-isothermal numerical model including phase change and discuss the achievable benefits of preheating.


  1. Bárdossy, A., Hörning, S.: Random mixing: an approach to inverse modeling for groundwater flow and transport problems. Transp. Porous Media 1–19 (2015). doi:10.1007/s11242-015-0608-4

  2. Beck, M., Seitz, G., Class, H.: Volume-based modelling of fault reactivation in porous media using a visco-elastic proxy model. Transp. Porous Media 1–20 (2016). doi:10.1007/s11242-016-0663-5

  3. Bode, F., Nowak, W., Loschko, M.: Optimization for early-warning monitoring networks in well catchments should be multi-objective, risk-prioritized and robust against uncertainty. Transp. Porous Media 1–21 (2015). doi:10.1007/s11242-015-0586-6

  4. Bringedal, C., Berre, I., Pop, I.S., Radu, F.A.: Upscaling of non-isothermal reactive porous media flow with changing porosity. Transp. Porous Media 1–23 (2015). doi:10.1007/s11242-015-0530-9

  5. Ehlers, W., Häberle, K.: Interfacial mass transfer during gas–liquid phase change in deformable porous media with heat transfer. Transp. Porous Media 1–32 (2016). doi:10.1007/s11242-016-0674-2

  6. Fetzer, T., Smits, K.M., Helmig, R.: Effect of turbulence and roughness on coupled porous-medium/free-flow exchange processes. Transp. Porous Media 1–30 (2016). doi:10.1007/s11242-016-0654-6

  7. Helmig, R., Hassanizadeh, S.M., Dahle, H.K.: Foreword. NUPUS—porous media research has got a brand name. Transp. Porous Media 1–3 (2016)

  8. Hommel, J., Lauchnor, E., Gerlach, R., Cunningham, A.B., Ebigbo, A., Helmig, R., Class, H.: Investigating the influence of the initial biomass distribution and injection strategies on biofilm-mediated calcite precipitation in porous media. Transp. Porous Media 1–23 (2015). doi:10.1007/s11242-015-0617-3

  9. Hönig, O., Zegeling, P.A., Doster, F., Hilfer, R.: Non-monotonic travelling wave fronts in a system of fractional flow equations from porous media. Transp. Porous Media 1–32 (2016). doi:10.1007/s11242-015-0618-2

  10. Jambhekar, V.A., Mejri, E., Schröder, N., Helmig, R., Shokri, N.: Kinetic approach to model reactive transport and mixed salt precipitation in a coupled free-flow–porous-media system. Transp. Porous Media 1–29 (2016). doi:10.1007/s11242-016-0665-3

  11. Kunz, P., Zarikos, I.M., Karadimitriou, N.K., Huber, M., Nieken, U., Hassanizadeh, S.M.: Study of multi-phase flow in porous media: comparison of sph simulations with micro-model experiments. Transp. Porous Media 1–20 (2015). doi:10.1007/s11242-015-0599-1

  12. Magiera, J., Rohde, C., Rybak, C.: A hyperbolic–elliptic model problem for coupled surface–subsurface flow. Transp. Porous Media 1–31 (2015). doi:10.1007/s11242-015-0548-z

  13. Pettersson, P.: Stochastic galerkin formulations for Co\(_2\) transport in aquifers: numerical solutions with uncertain material properties. Transp. Porous Media 1–27 (2015). doi:10.1007/s11242-015-0575-9

  14. Skogestad, J.O., Keilegavlen, E., Nordbotten, J.M.: Two-scale preconditioning for two-phase nonlinear flows in porous media. Transp. Porous Media 1–19 (2015). doi:10.1007/s11242-015-0587-5

  15. van Duijn, C.J., Cao, X., Pop, I.S.: Two-phase flow in porous media: dynamic capillarity and heterogeneous media. Transp. Porous Media 1–26 (2015). doi:10.1007/s11242-015-0547-0

  16. Weishaupt, K., Bordenave, A., Atteia, O., Class, H.: Numerical investigation on the benefits of preheating for an increased thermal radius of influence during steam injection in saturated soil. Transp. Porous Media 1–21 (2016). doi:10.1007/s11242-016-0624-z

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First of all, we would like to thank all authors and reviewers for writing and evaluating the excellent contributions to this special issue. We would also like to express our gratitude to Martin Blunt, editor of Transport in Porous Media, for his assistance, encouragement and commitment. Moreover, we appreciate the help from the people at Springer, particularly Petra van Steenbergen for heading the publishing process and Swetha Rajendran for handling many technical matters. Additionally, we would like to thank the national research organizations for funding and supporting NUPUS, namely the German Research Foundation (DFG), the Netherlands Organisation for Scientific Research (NWO) and the Research Council of Norway (RCN). In particular, the funding enabled us to grant open access to all contributions of this special issue. Finally, all the work undertaken within NUPUS would not have been possible without the initiators and leaders of this successful research environment: Rainer Helmig, S. Majid Hassanizadeh and Helge K. Dahle.

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Correspondence to Bernd Flemisch.

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Flemisch, B., Nordbotten, J.M., Nowak, W. et al. Editorial. Transp Porous Med 114, 237–240 (2016). https://doi.org/10.1007/s11242-016-0735-6

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