Page 284 - Fundamentals of Gas Shale Reservoirs
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264   GAS TRANSPORT PROCESSES IN SHALE

              The slope of the straight line  s  is related to the   Aronofsky JS. Effect of gas slip on unsteady flow of gas through
                                           1
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                                               2
                       k     R 2    1 (  ) K  c s ,   (11.68)    Azom P, Javadpour F. Dual‐continuum modeling of shale and tight gas
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            Cumulative Desorbed Gas Data                           volume and area distribution in porous media. I. Computations
                                                                   of nitrogen isotherms. J Am Chem Soc 1951;73 (1):373–380.
            Equation 11.64 is approximated for the late time as  Beskok A, Karniadakis GE. A model for flows in channels, pipes,
                                                                   and ducts at micro and nano scales. Microscale Thermophys
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                                      4   K  2
                        ln (1 F  )  ln       1  t,    (11.69)    Binnig G, Rohrer H, Gerber C,  Weibel E. Surface studies by
                              D       2    R 2
                                      1     a                      scanning tunneling microscopy. Phys Rev Lett 1982;49:57–61.
                                                                 Binnig G, Quate CF, Gerber C. Atomic force microscope. Phys Rev
            where ξ  is the first root of Bessel function, J (ξ) = 0, equal to   Lett 1986;56:930–933.
                  1
                                               0
            2.404834. The  cumulatively  desorbed  gas  fraction  for  the   Blanchard  V,  Lasseux  D, Bertin  H,  Pichery  T, Chauveteau  G,
            late time is described as follows:                     Tabary R, Zaitoun A. Gas/water flow in porous media in the
                                                                   presence of adsorbed polymer: experimental study on non‐
                            ln(1 F  )  f  st,         (11.70)      Darcy effects. SPE Reserv Eval Eng J 2007;10 (4):423–431.
                                  D    0  1
                                                                 Borwein JM, Lewis  AS.  Convex  Analysis and Nonlinear
                                                                   Optimization, Theory and Examples. Canadian Mathematical
            and the permeability can be determined with the late‐time   Society Books in Mathematics. New York: Springer; 2000.
            data as follows:                                     Bourbie T, Walls J. Pulse decay permeability: analytical solution
                                                                   and experimental test. SPE J 1982;22:719–721.
                            R [   1 (  ) K ]  cs                 Brace WF, Walsh JB, Frangos WT. Permeability of granite under
                             2
                         k              a    g  1     (11.71)
                                     2                             high pressure. J Geophys Res 1968;736:2225–2236.
                                     1
                                                                 Brown GP, Dinardo  A, Cheng GK, Sherwood  TK.  The flow
                                                                   of  gases in pipes at low pressures. J  Appl Phys 1946;17:
            ACKNOWLEDGMENTS                                        802–813.
                                                                 Bruce GH, Peaceman DW, Hachford HH. Calculation of unsteady‐
            AFM and SEM images are courtesy of the NanoGeosciences   state gas flow through porous media.  Trans  AIME 1952;
            Lab at the Bureau of Economic Geology, The University of   221G:1–16.
            Texas at  Austin.  Ayaz Mehmani wrote the section about   Carslaw HS, Jaeger JC.  Conduction of Heat in Solids. London:
              network modeling in shale system. Chris Parker edited the   Oxford University Press; 1947. p 198–207.
            manuscript. Publication authorized by the Director Bureau   Chareonsuppanimit P, Mohammad SA, Robinson RL Jr, Gasem
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