Mathematical Models of Flow in Porous Media

  • Adam Szymkiewicz
Part of the GeoPlanet: Earth and Planetary Sciences book series (GEPS)


In this chapter a general model for the two-phase fluid flow in porous media is presented, together with its simplified form, known as the Richards equation, which is applicable (under specific assumptions) to describe water flow in the vadose zone. In each case the governing equations are formulated at the Darcy scale, using the capillary pressure–saturation relationship and an empirical extension of the Darcy equation for the multiphase flow. Initial and boundary conditions for the governing equations are also discussed, together with conditions applicable at material interfaces.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringGdansk University of TechnologyGdanskPoland

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