Page 284 - Fundamentals of Gas Shale Reservoirs
P. 284
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
permeability as porous media. J Appl Phys 1954;25 (1):48–53.
Aronofsky JS, Wallick CG, Reichertz PP. Method of measuring
characteristics of porous materials. Patent 2867116. 1959.
2
k R 2 1 ( ) K c s , (11.68) Azom P, Javadpour F. Dual‐continuum modeling of shale and tight gas
16 a g 1 reservoirs. SPE Annual Technical Conference and Exhibition;
October 8–10, 2012; San Antonio, TX. doi:10.2118/159584‐MS.
11.10.2 Permeability Estimation with Late‐Time Barrett EP, Joyner LG, Halenda PP. The determination of pore
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
Eng 1999;3 (1):43–77.
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
of Economy Geology. KAM. High‐pressure adsorption of gases on shales: measure-
ments and modeling. Int J Coal Geol 2012;95:34–46.
Chen T, Stagg PW. Semilog analysis of the pulse decay technique
REFERENCES of permeability measurement. SPE J 1984;24:639–642.
Civan F. Effective correlation of apparent gas permeability in tight
Agrawal A, Prabhu SV. Survey on measurement of tangential porous media. Transp Porous Media 2010;82 (2):375–384.
momentum accommodation coefficient. J Vac Sci Technol A DOI: 10.1007/s11242‐009‐9432‐z.
2008;26 (4):634–645. Civan F, Rai C, Sondergeld C. Determining shale permeability to
Akkutlu IY, Fathi E. Multiscale gas transport in shales with local gas by simultaneous analysis of various pressure tests. SPE J
kerogen heterogeneities. SPE J 2012;17(4):1002–1011. 2012;17 (3):717–726.
SPE‐146422‐PA. Coppens M‐O. The effect of fractal surface roughness on diffusion
Amaefule JO, Wolfe K, Walls JD, Ajufo AO, Peterson E. Laboratory and reaction in porous catalysts from fundamentals to practical
determination of effective liquid permeability in low‐quality applications. Catal Today 1999;53 (2):225–243.
reservoir rocks by the pulse decay technique. SPE Coppens M‐O, Dammers AJ. Effects of heterogeneity on diffusion
1986;15149:493–502. in nanopores from inorganic materials to protein crystals and
Arkilic EB, Kenneth SB, Martin AS. Mass flow and tangential ion channels. Fluid Phase Equilib 2006;246 (1–2):308–316.
momentum accommodation in silicon micromachined channels. Crank J. The Mathematics of Diffusion. London: Oxford University
J Fluid Mech 2001;437:29–43. Press; 1979.