Advertisement

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
Article

Abstract

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.

Keywords

Reservoir tests Permeability Slip Cylindrical Spherical geometry 

Latin Symbols

S

Cross-section of sample

b

Klinkenbrg coefficient

J

Mass flux of gas through the sample

Jres

Volume flux from or to reservoir

k

Permeability

k0

Permeability without slip effect

L

Length of cylindrical sample

M

Molar mass

pa

Atmospheric pressure

pres

Pressure in the reservoir

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

Individual gas constant

R

Universal gas constant

t

Time

T

Absolute temperature

u

Vector of discharge velocity

Vres

Volume of reservoir

r

Radial coordinate

Greek Symbols

ε

Porosity

μ

Gas dynamic viscosity

ρ

Gas density

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Basheer P.A.M.: A brief review of methods for measuring the permeation properties of concrete in situ. Proc. ICE Struct. Build. 99, 74–83 (1993)CrossRefGoogle Scholar
  2. Biloe S., Mauran S.: Gas flow through highly porous graphite matrices. Carbon 41, 525–537 (2003)CrossRefGoogle Scholar
  3. Claisse P.A., Ganjian E., Adham T.A.: Vacuum-air permeability test for in situ assessment of cover concrete. Cem. Concr. Res. 33, 47–53 (2003)CrossRefGoogle Scholar
  4. Dinku A., Reinhardt H.W.: Gas permeability coefficient of cover concrete as a performance control. Mater. Struct. 30, 387–393 (1997)CrossRefGoogle Scholar
  5. Favre E., Simondi B., Vistoli P.P., Adenotand F., Mauviel G.: Experimental measurement of gas permeability through bitumen: results for H2 N2 and O2. Fuel 83, 89–96 (2004)CrossRefGoogle Scholar
  6. Finsterle S., Persoff P.: Determining permeability of tight rock samples using inverse modeling. Water. Res. Res. 33, 1803–1811 (1997)CrossRefGoogle Scholar
  7. Gardner D.R., Jefferson A.D., Lark R.J.: An experimental numerical and analytical investigation of gas flow characteristics in concrete. Cem. Concr. Res. 38, 360–367 (2008)CrossRefGoogle Scholar
  8. Innocentini M.D.M., Pardo A.F., Pandolfelli V.C.: Modified pressure-Decay technique for evaluation the permeability of high dense refractories. J. Am. Ceram. Soc. 83, 220–222 (2000)CrossRefGoogle Scholar
  9. Ivanov A.N., Kozlova S.N., Pechenov A.V.: Measurement. Meas. Tech. 43, 1086–1088 (2000)CrossRefGoogle Scholar
  10. Jannot, Y., Lasseux, D., Delottier, L., Hammon, G.: A simultaneous determination of permeability and klinkenberg coefficient from an unsteady-state pulse-decay experiment. Paper presented at the International Symposium of the Society of Core Analysis, Abu Dhabi, Oct 2008Google Scholar
  11. Kaczmarek M.: Approximate solutions for non-stationary gas permeability tests. Transp. Porous Media 75, 151–165 (2008)Google Scholar
  12. Lafhaj Z., Richard G., Kaczmarek M., Skoczylas F.: Experimental determination of intrinsic permeability of limestone and concrete: comparison between in situ and laboratory results. Build. Environ. 42, 3042–3050 (2007)CrossRefGoogle Scholar
  13. Li K., Horne R.N.: Gas slippage in two-phase flow and the effect of temperature. SPE Int. 68778, 1–9 (2001)Google Scholar
  14. Wu Y.S., Pruess K., Persoff P.: Gas flow in porous media with Klinkenberg effects. Transp. Porous Media 32, 117–137 (1998)CrossRefGoogle Scholar
  15. Wierzbicki M.: Dynamic seepage of nitrogen through coal briquettes. Arch. Min. Sci. 47, 175–188 (2002)Google Scholar
  16. Zeyanaly-Andabily E.M., Rahman S.S.: Measurement of permeability of tight rocks. Meas. Sci. Technol. 6, 1519–1527 (1995)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

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

Personalised recommendations