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Transport in Porous Media

, 80:281 | Cite as

Matrix Heterogeneity Effects on Gas Transport and Adsorption in Coalbed and Shale Gas Reservoirs

  • Ebrahim Fathi
  • I. Yücel AkkutluEmail author
Article

Abstract

In coalbeds and shales, gas transport and storage are important for accurate prediction of production rates and for the consideration of subsurface greenhouse gas sequestration. They involve coupled fluid phenomena in porous medium including viscous flow, diffusive transport, and adsorption. Standard approach to describe gas–matrix interactions is deterministic and neglects the effects of local spatial heterogeneities in porosity and material content of the matrix. In this study, adopting weak-noise and mean-field approximations and using a statistical approach in spectral domain, matrix heterogeneity effects are investigated in the presence of non-equilibrium adsorption with random partition coefficient. It is found that the local heterogeneities can generate non-trivial transport and kinetic effects which retard gas release from the matrix and influence the ultimate gas recovery adversely. Macro-transport shows 1/[1 + N Pe /(1 + N Pe )] dependence on the Péclet number, and persists at the diffusive ultra-low permeability limit. Macro-kinetics is directly related to Thiele modulus by the following expression: N Th /(1 + 2N Pe ). It leads to trapping of gas in the adsorbed phase during its release from the matrix, and to an adsorption threshold during the gas uptake by the matrix. Both effects are proportional to the initially available adsorbed gas amount and becomes more pronounced with the increasing variance of the porosity field. Consequently, a new upscaled deterministic gas mass balance is proposed for practical purposes. Numerical results are presented showing free and adsorbed gas distributions and fractional gas sorption curves for unipore coal matrix exhibiting Gaussian porosity distribution. This study is a unique approach for our further understanding of the coalbeds and gas shales, and it is important for the development of sound numerical gas production and sequestration models.

Keywords

Heterogeneity Upscaling Gas adsorption kinetics Macro-transport Macro-kinetics 

List of Symbols

B0

Absolute coal permeability (cm2)

C

Free gas concentration (mol/cc pore)

Cμ

Adsorbed gas concentration (mol/cc solid)

Cμs

Maximum adsorbed gas concentration (mol/cc solid)

D

Molecular diffusion coefficient (cm2/s)

\({\mathcal{D}}\)

Apparent diffusion coefficient (cm2/s)

E

Adsorbate adsorbent interaction energy (J/mol)

g

Average free gas concentration (mol/cc)

K

Partition (distribution) coefficient (fraction)

kf

Gas adsorption rate coefficient (1/s)

kr

Gas desorption rate coefficient (1/s)

kr∞

Gas desorption rate constant at zero energy level (1/s)

R

Universal gas constant (J K−1 mol−1)

r

Pore half width (cm)

t

Time coordinate (s)

T

Temperature (K)

x

Space coordinate (cm)

Greek Symbols

α

Effective drift velocity (m/s)

\({\phi}\)

Porosity (fraction)

\({\phi}\)

Solid-to-bulk volume ratio (fraction)

\({\sigma_{\rm f}^2}\)

Variance of porosity fluctuations

μ

Gas viscosity (kg/cm s)

λ

Porosity correlation length (cm)

References

  1. Alvarado V., Scriven L.E., Davis H.T.: Stochastic-perturbation analysis of a one-dimensional dispersion-reaction equation: effects of spatially-varying reaction rates. Transp Porous Media 32, 139–161 (1998)CrossRefGoogle Scholar
  2. Brusseau M.L., Jessup R.E., Rao P.S.C.: Nonequilibrium sorption of organic chemicals: elucidation of rate limiting processes. Environ. Sci. Technol. 25, 134–142 (1991)CrossRefGoogle Scholar
  3. Do D.D., Wang K.: A new model for the description of adsorption kinetics in heterogeneous activated carbon. Carbon 36(10), 1539–1554 (1998)CrossRefGoogle Scholar
  4. Dubinin M.M.: Chemistry and Physics of Carbon. Marcel Dekker, New York (1966)Google Scholar
  5. Forster D.: Hydrodynamics Fluctuations, Broken Symmetry and Correlation Functions. Benjamin-Cummings, Reading, MA (1977)Google Scholar
  6. Gelhar L.W.: Stochastic Subsurface Hydrology. Prentice Hall, Englewood Cliffs (1993)Google Scholar
  7. Hu B.X., Deng F., Cushman J.H.: Non-local reactive transport with physical and chemical heterogeneity: linear non-equilibrium sorption with random Kd. Water Resour. Res. 31(9), 2239–2252 (1995)CrossRefGoogle Scholar
  8. Jagiello J., Bandosz T.J., Putyera K., Schwarz J.A.: Micropore structure of template-derived carbons studied using adsorption of gases with different molecular diameters. J. Chem. Soc., Faraday Trans. 91, 2929–2933 (1995)CrossRefGoogle Scholar
  9. Jenkins C.D., Boyer C.M. II: Coalbed- and shale-gas reservoirs. J. Petrol. Technol. 60(2), 92–99 (2008)Google Scholar
  10. Karacan O.C.: An effective method for resolving spatial distribution of adsorption kinetics in heterogeneous porous media: applied for carbon dioxide sequestration in coal. Chem Eng. Sci. 58, 4681–4693 (2003)CrossRefGoogle Scholar
  11. King, G.R.: Material balance techniques for coal seam and Devonian Shale. SPE 20730 (1990)Google Scholar
  12. L’Heureux I.: Stochastic reaction-diffusion phenomena in porous media with nonlinear kinetics: effects of quenched porosity fluctuations. Phys. Rev. Lett. 93(18), 180602 (2004)CrossRefGoogle Scholar
  13. Nuttall, B.C.: Analysis of Devonian black shales in Kentucky for potential carbon dioxide sequestration and enhanced natural gas production. Kentucky Geological Survey Report DE-FC26-02NT41442 (2005)Google Scholar
  14. Ruckenstein E., Vaidyanathan A.S., Youngquist G.R.: Sorption by solids with bidisperse pore structures. Chem. Eng. Sci. 26, 1305–1318 (1971)CrossRefGoogle Scholar
  15. Smith D.M., Williams F.L.: Diffusional effects in the recovery of methane from coalbeds. Soc. Petrol. Eng. J. 24, 529–535 (1984)Google Scholar
  16. Weida S.D., Lambert S.W., Boyer II, C.M.: Challenging the traditional coalbed methane exploration and evaluation. SPE 98069 (2005)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Mewbourne College of Earth and EnergyUniversity of OklahomaNormanUSA
  2. 2.School of Petroleum and Geological Engineering, Sarkeys Energy CenterUniversity of OklahomaNormanUSA

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