Journal of Engineering Mathematics

, Volume 84, Issue 1, pp 11–18 | Cite as

On a boundary layer problem related to the gas flow in shales

  • G. I. Barenblatt
  • P. J. M. Monteiro
  • C. H. Rycroft


The development of gas deposits in shales has become a significant energy resource. Despite the already active exploitation of such deposits, a mathematical model for gas flow in shales does not exist. Such a model is crucial for optimizing the technology of gas recovery. In the present article, a boundary layer problem is formulated and investigated with respect to gas recovery from porous low-permeability inclusions in shales, which are the basic source of gas. Milton Van Dyke was a great master in the field of boundary layer problems. Dedicating this work to his memory, we want to express our belief that Van Dyke’s profound ideas and fundamental book Perturbation Methods in Fluid Mechanics (Parabolic Press, 1975) will live on—also in fields very far from the subjects for which they were originally invented.


Porous media Subterranean fluid mechanics 



The authors express their special gratitude to Dmitriy B. Silin, whose work and presentations motivated our study. This publication was based on the work supported in part by Award No. KUS-I1-004021, made by King Abdullah University of Science and Technology. G.I.B. and C.H.R. were partially supported by the Director, Office of Science, Computational and Technology Research, U.S. Department of Energy under Contract No. DE-AC02-05CH11231.


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Copyright information

© US Government 2013

Authors and Affiliations

  • G. I. Barenblatt
    • 1
    • 2
    • 3
  • P. J. M. Monteiro
    • 4
  • C. H. Rycroft
    • 2
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsLawrence Berkeley National LaboratoryBerkeleyUSA
  3. 3.Institute of OceanologyRussian Academy of SciencesMoscowRussia
  4. 4.Department of Civil and Environmental EngineeringUniversity of CaliforniaBerkeleyUSA

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