Transport in Porous Media

, Volume 84, Issue 1, pp 95–108 | Cite as

Modeling Reservoir Gas Permeability Tests for Cylindrical and Spherical Geometry

  • Mariusz KaczmarekEmail author


Approximate analytical models of non-stationary single and double reservoir gas permeability tests with radial flow through hollow cylindrical or hemispherical samples are developed and compared with numerical solutions of full models. The effects of compressibility and slip of gas are included. The approximate solutions are obtained assuming that the total transient mass flux is spatially homogeneous, i.e., it has constant value in direction of flow (along radius in cylindrical or spherical coordinate system). The evolutions of reservoir pressures and transient spatial distributions of pore pressure are determined and apply both for pumping and suction tests. The solutions of full model were obtained with help of the finite element method and served as references to evaluate the approximate models.


Reservoir tests Permeability Slip Cylindrical Spherical geometry 

Latin Symbols


Cross-section of sample


Klinkenbrg coefficient


Mass flux of gas through the sample


Volume flux from or to reservoir




Permeability without slip effect


Length of cylindrical sample


Molar mass


Atmospheric pressure


Pressure in the reservoir

\({\overline r _{}}\)

Individual gas constant


Universal gas constant




Absolute temperature


Vector of discharge velocity


Volume of reservoir


Radial coordinate

Greek Symbols




Gas dynamic viscosity


Gas density


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Environmental Mechanics and Applied Computer ScienceKazimierz Wielki UniversityBydgoszczPoland

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