Analytical solution of the apparent-permeability gas-transport equation in porous media

Regular Article


The current paper is concerned with the power-series solution of the apparent permeability (Klinkenberg) model of gas transport in porous media. The one-dimensional radial partial differential equation has been transformed into an ordinary differential equation using a universal transform. The transformed equation has been solved using the infinite power-series technique. Results are obtained for various values of the given physical parameters and represented in graphs. We have presented results for both Dirichlet and Neumann boundary conditions at the well to express, respectively, the pressure and the flow rate at the well.


  1. 1.
    L.J. Klinkenberg, The permeability of porous media to liquids and gases. Drilling and Production Practice (American Petroleum Institute, 1941) conference paperGoogle Scholar
  2. 2.
    R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport phenomena (Wiley, 2007)Google Scholar
  3. 3.
    F. Javadpour, J. Can. Petrol. Technol. 48, 16 (2009)CrossRefGoogle Scholar
  4. 4.
    J.E. Warren, P.J. Root, Soc. Petrol. Eng. 3, 245 (1963)CrossRefGoogle Scholar
  5. 5.
    G. Moridis, T. Blasingame, C. Freeman, Analysis of mechanisms of flow in fractured tight-gas and shale-gas reservoirs, in Latin American and Caribbean Petroleum Engineering Conference 1-3 December (2010) SPE-139250-MSGoogle Scholar
  6. 6.
    E. Ozkan, R. Raghavan, O. Apaydin, Modeling of fluid transfer from shale matrix to fracture network, in Annual Technical Conference and Exhibition, Lima, Peru, 1-3 December (2010) SPE-134830-MSGoogle Scholar
  7. 7.
    T. Ertekin, G.R. King, F.C. Schwerer, Dynamic Gas Slippage: A Unique Dual-Mechanism Approach to the Flow of Gas in Tight Formations (SPE, 1986) DOI:10.2118/12045-PA
  8. 8.
    A. Bustin, R. Bustin, X. Cui, Importance of fabric on the production of gas shales, in Unconventional Reservoirs Conference in Colorado, USA, 10-12 February (SPE, 2008) SPE-114167-MSGoogle Scholar
  9. 9.
    Wu Yu-Shu, P. Fakcharoenphol, A Unified Mathematical Model for Unconventional Reservoir Simulation, in EUROPEC/EAGE Annual Conference and Exhibition in Vienna, Austria, 23-26 May (SPE, 2011) SPE-142884-MSGoogle Scholar
  10. 10.
    H. Kazemi, Soc. Petrol. Eng. J. 9, 451 (1969)CrossRefGoogle Scholar
  11. 11.
    C. Guo, M. Wei, H. Chen, X. He, B. Bai, Improved numerical simulation for shale gas reservoirs, in Offshore Technology Conference (2014)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Collage of EngineeringEffat UniversityJeddahSaudi Arabia
  2. 2.Mathematics Department, Faculty of ScienceAswan UniversityAswanEgypt

Personalised recommendations