Beyond Kozeny–Carman: Predicting the Permeability in Porous Media

  • Raphael SchulzEmail author
  • Nadja Ray
  • Simon Zech
  • Andreas Rupp
  • Peter Knabner


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.


Permeability Kozeny Carman Power law Upscaling 



This research was kindly supported by the DFG RU 2179 “MAD Soil-Microaggregates: Formation and turnover of the structural building blocks of soils.” We acknowledge the group of Stephan Peth, University of Kassel, Germany, who provided the real 3D scan data.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Raphael Schulz
    • 1
    Email author
  • Nadja Ray
    • 1
  • Simon Zech
    • 1
  • Andreas Rupp
    • 1
  • Peter Knabner
    • 1
  1. 1.Department of MathematicsFriedrich–Alexander University of Erlangen–NürnbergErlangenGermany

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