Scientific and technical journal

«Proceedings of Gubkin University»

ISSN 2073-9028


UDC: 622
DOI: 10.33285/2073-9028-2021-1(302)-19-28



1 Gubkin Russian State University of Oil and Gas (National Research University), Moscow, Russian Federation

Keywords: porosity, permeability, tortuosity, Forchheimer's equation, Klinkenberg effect


To describe the fluid flow in a porous medium it is proposed to use the semi-analytical universal equation previously proposed by the authors. The equation allows replacing the explicit description of the reservoir structure with the obtained relationships of permeability, porosity, tortuosity and various correction factors. The paper provides an assessment of the model based on experimental data obtained for clastic samples with a permeability range of 0,000017- 1132 mD.


1. Ahlers C.F., Finsterle S., Wu Y.S., Bodvarsson G.S. Determination of pneumatic permeability of a multi-layered system by inversion of pneumatic pressure data. Proc. of the 1995 AGU Fall Meeting. San Francisco, California. - 1995.
2. Fuente M., Muñoz E., Sicilia I., Goggins J., Hung L.C., Frutos B., Foley M. Investigation of gas flow through soils and granular fill materials for the optimisation of radon soil depressurisation system. J. Environ. Radioact. - 2019. - Vol. 198. - Р. 200-209. 10.1016/ j.jenvrad.2018.12.024 DOI: 10.1016/j.jenvrad.2018.12.024
3. Ghane E., Fausey N.R., Brown L.C. Non-Darcy flow of water through woodchip media. J. Hydrol. - 2014. - Vol. 519. - Р. 3400-3409. DOI: 10.1016/j.jhydrol.2014.09.065
4. Freeman D.L., Bush D.C. Low-permeability laboratory measurements by nonsteady-state and conventional methods. Soc. Petrol. Eng. J. - 1983. - Vol. 23. - P. 928-936. DOI: 10.2118/10075-PA
5. Rodwell W.R., Nash P.J. Mechanisms and Modeling of Gas Migration From Deep Radioactive Waste Repositories. London: United Kingdom Nirex Ltd. - 1992. - 86 p.
6. Tanikawa W., Shimamoto T. Comparison of Klinkenberg-corrected gas permeability and water permeability in sedimentary rocks. Int. J. Rock. Mech. and Min Sci. - 2009. - Vol. 46. - P. 229-238. DOI: 10.1016/j.ijrmms.2008.03.004
7. Heid J.G., McMahon J.J, Nielson R.F. Study of the permeability of rocks to homogeneous fluids. Am. Pet. Inst. Drill. Prod. Pract. - 1950. - Vol. 230.
8. Jones S.C. A rapid accurate unsteady-state Klinkenberg permeameter. Soc. Petrol. Eng. J. - 1972. - Vol. 12. - P. 383-397. DOI: 10.2118/3535-PA
9. Jones F.O., Owens W.W. A laboratory study of low-permeability gas sands. J. Pet. Tecnol. - 1980. - Vol. 32. - P. 1631-1640. DOI: 10.2118/7551-PA
10. Faulkner D.R, Rutter E.H. Comparisons of water and argon permeability in natural clay-bearing fault gouge under high pressure at 20 °C. J. Geophys. Res. - 2000. - P. 16415-16426. DOI: 10.1029/2000JB900134
11. Klinkenberg L.J. The permeability of porous media to liquids and gases. Drilling and Production Practice, American Petroleum Inst. - 1941. - P. 200-213.
12. Forchheimer P. Wasserberwegung durch Boden. Z Vereines deutscher Ing. - 1901. - Vol. 45 (50). - P. 1782-1788.
13. Ergun S. Fluid flow through packed columns. Chem. Eng. Prog. - 1952. - Vol. 48 (2). - P. 89-94.
14. Cooper J.W., Wang X., Mohanty K.K. Non-Darcy flow studies in anisotropic porous media. Soc. Petrol. Eng. J. - 1999. - Vol. 4 (4). - P. 334-341. DOI: 10.2118/57755-PA
15. Choi C.S., Song J.J. Estimation of the Non-Darcy coefficient using supercritical CO2 and various sandstones. JCR Solid Earth. - 2019. - Vol. 124. - P. 442-455. 10.1029/ 2018JB016292 DOI: 10.1029/2018JB016292
16. Skjetne E. High-velocity flow in porous media; analytical, numerical and experimental studies. Doctoral Thesis at Department of Petroleum Engineering and Applied Geophysics, Faculty of Applied Earth Sciences and Metallurgy, Norwegian University of Science and Technology. - 1995.
17. Zolotukhin A.B., Gayubov A.T. Machine learning in reservoir permeability prediction and modeling of fluid flow in porous media. IOP Conf. Ser.: Mater. Sci. Eng. - 2019. - Vol. 700. 012023. DOI: 10.1088/1757-899X/700/1/012023
18. Zolotukhin A.B., Gayubov A.T. Semi-analytical Approach to Modeling Forchheimer Flow in Porous Media at Meso- and Macroscales. Transp Porous Med. - 2021. - Vol. 136. - P. 715-741. DOI: 10.1007/s11242-020-01528-4
19. Zolotukhin A.B., Ursin J.R. Introduction to petroleum reservoir engineering. Norwegian Academic Press, Høyskoleforlaget. - 2000.
20. Tessem R. High Velocity Coefficient's Dependence on Rock Properties: A Laboratory Study. Thesis Pet. Inst., NTH. Trondheim. - 1980.
21. Torsæter O., Tessem R., Berge B. High velocity coefficient's dependence on rock properties. SINTEF report, NTH. Trondheim. - 1981.
22. Wu Y.S., Pruess K., Persoff P. Gas flow in porous media with Klinkenberg effects. Transp. Porous Media. - 1998. - Vol. 32. - P. 117-137.
23. Amao A.M. Mathematical model for darcy forchheimer flow with applications to well performance analysis. MSc Thesis, Department of Petroleum Engineering, Texas Tech University, Lubbock, TX, USA. - 2007.