Transport in Porous Media

, Volume 84, Issue 1, pp 229–240 | Cite as

An Efficient Modeling Approach to Simulate Heat Transfer Rate between Fracture and Matrix Regions for Oil Shale Retorting

  • Fan ZhangEmail author
  • Jack C. Parker


The conversion of hydrocarbons in oil shale into liquid fuels has gained interest due to decreasing conventional oil reserves. Thermal conversion involves heating fractured rock and recovering gas and liquid phase products. The efficiency of this process is markedly dependent on heat transfer limitations between fracture porosity and rock matrix. Computer models are useful tools for process optimization. Explicit modeling of heat transfer processes within rock fragments would require great computational effort, making inverse modeling and forward process optimization very difficult if not impracticable. In this article, we evaluate the feasibility of using first-order heat transfer formulations to approximate these processes by comparing first-order model results with a rigorous explicit formulation and by comparison with laboratory retorting experiments published in the literature. Comparison of the two modeling approaches indicates that the first-order heat transfer approximation can be used without significant loss of accuracy if the block size and/or heating rate are not too large, as quantified by a proposed dimensionless heating rate. However, computational effort can be decreased by an order of magnitude compared with explicitly simulating diffusive heat transfer.


Oil shale retorting Modeling Heat transfer Computation efficiency 

List of symbols


Heating rate


Rock fragment diameter


Rate of heat generated (+) or absorbed (−) by reactions


Heat transfer rate from the matrix to fractures (+) or visa versa (−)


Radial distance from the center of the rock fragment


Rate of temperature increase in fractures


Radius of rock fragments


Rate of rock surface temperature increase


Dimensionless heating rate


Specific heat of the rock matrix, T m is the rock matrix temperature




Fracture-rock interface temperature at the corresponding location


Initial rock temperature

\({\overline{T_{\rm m}}}\)

Average rock matrix temperature


Linearized heat transfer coefficient


Thermal conductivity of the rock matrix


Rock matrix density defined as the solid phase mass per total fracture-matrix volume


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  1. Arbogast T., Douglas J., Hornung U.: Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal. 21, 823–836 (1990)CrossRefGoogle Scholar
  2. Bird B.R., Stewart W.E., Lightfoot E.N.: Transport Phenomena. Wiley, New York (2002)Google Scholar
  3. Braun, R.L.: Mathematical modeling of modified in situ and aboveground oil shakle retorting. Lawrence Livermore National Laboratory 46 (1981)Google Scholar
  4. Braun, R.L., Diaz, J.C., Lewis, A. E.: Results of mathematical modeling of modified in situ oil shale retorting. SPE/AIME, SPE 11000 (1982)Google Scholar
  5. Campbell J.H., Gallegos G., Gregg M.: Gas evolution during oil shale pyrolysis. 2. Kinetic and stoichiometric analysis. Fuel 59, 727–732 (1980)CrossRefGoogle Scholar
  6. Carter S.D., Citiroglu M., Gallacher J., Snape C.E., Mitchell S., Lafferty C.J.: Secondary coking and cracking of shale oil vapours from pyrolysis or hydropyrolysis of a Kentucky Cleveland oil shale in a two-stage reactor. Fuel 73(9), 1455–1458 (1994)CrossRefGoogle Scholar
  7. Chen Z., You J.: The Behavior of Naturally Fractured Reservoirs Including Fluid Flow in Matrix Blocks. Transp. Porous Media 2, 145–163 (1987)CrossRefGoogle Scholar
  8. Douglas J., Arbogast T.: Dual porosity models for flow in naturally fractured reservoirs. In: Cushman, J.H. (eds) Dynamics of Fluids in Hierarchical Porous Media, pp. 177–221. Academic Press, San Diego (1990)Google Scholar
  9. Dung N.V., Duffy G.J., Charlton B.G.: Comparison between model predictions and performance of process development units for oil shale processing. Fuel 699, 1158–1163 (1990)CrossRefGoogle Scholar
  10. Dyni J.R.: Geology and resources of some world oil-shale deposits. Oil Shale 20(3), 193–252 (2003)Google Scholar
  11. Font R., Williams P.T.: Pyrolysis of biomass with constant heating rate: Influence of the operating conditions. Thermochim. Acta 250(1), 109–123 (1995)CrossRefGoogle Scholar
  12. Forgac, J.M., Hoekstra, G.B.: In situ retorting of oil shale with pulsed combustion. U.S. Patent. 4436344 (1984)Google Scholar
  13. George J.H., Harris H.G.: Mathematical modeling of in situ oil shale retorting. SIAM Numer. Anal. J. 14, 137 (1977)CrossRefGoogle Scholar
  14. Granoff B., Nuttall H.E. Jr: Pyrolysis kinetics for oil-shale particles. Fuel 56(3), 234–240 (1977)CrossRefGoogle Scholar
  15. Gregg M.L., Campbell J.H., Taylor J.R.: Laboratory and modelling investigation of a Colorado oil-shale block heated to 900°C. Fuel 60, 179 (1981)CrossRefGoogle Scholar
  16. Khraisha Y.H.: Kinetics of isothermal pyrolysis of Jordan oil shales. Energy Convers. Manag. 39(3–4), 157–165 (1998)CrossRefGoogle Scholar
  17. Levenspiel O.: Chemical Reaction Engineering. Wiley, New York (1999)Google Scholar
  18. Li S., Qian J.: Study of the pyrolysis of Maoming oil shale lumps. Fuel 70(12), 1371–1375 (1991)CrossRefGoogle Scholar
  19. Lin J.-P., Chang C.-Y., Wu C.-H.: Pyrolytic treatment of rubber waste: pyrolysis kinetics of styrenebutadiene rubber. J. Chem. Technol. Biotechnol. 66(1), 7–14 (1996)CrossRefGoogle Scholar
  20. Nazzal J.M.: Influence of heating rate on the pyrolysis of Jordan oil shale. J. Anal. Appl. Pyrol. 62, 225–238 (2002)CrossRefGoogle Scholar
  21. Nazzal J.M.: The influence of grain size on the products yield and shale oil composition from the Pyrolysis of Sultani oil shale. Energy Convers. Manag. 49, 3278–3286 (2008)CrossRefGoogle Scholar
  22. Parker J.C., Valocchi A.J.: Constraints on the validity of equilibrium and first-order kinetic transport models in structured soils. Water Resour. Res. 22, 399–407 (1986)CrossRefGoogle Scholar
  23. Shih S.-M.: Lumped-parameter model for the retorting of a large block of oil shale with an internal temperature gradient. Fuel 62, 746–748 (1983)CrossRefGoogle Scholar
  24. Shih S.-M., Sohn H.Y.: A mathematical model for the retorting of a large block of oil shale: effect of the internal temperature gradient. Fuel 57, 622–630 (1978)CrossRefGoogle Scholar
  25. Sohn H.Y., Szekely J.: A structural model for gas-solid reaction with a moving boundary-III, A general dimensionless representation of the irreversible reaction between a porous solid and a reactant gas. J. Chem. Eng. Sci. 27, 763–778 (1972)CrossRefGoogle Scholar
  26. Widiyastuti W., Wang W.-N., Lenggoro I.W., Iskandar F., Okuyama K.: Simulation and experimental study of spray pyrolysis of polydispersed droplets. J. Mater. Res. 22(7), 1888–1898 (2007)CrossRefGoogle Scholar
  27. Yeh, G.T., Sun, J.T., Jardine, P.M., Burger, W.D., Fang, Y.L., Li, M.H., Siegel, M.D.: HYDROGEOCHEM 5.0: A three-dimensional model of coupled fluid flow, thermal transport, and hydrogeochemical transport under variably saturated conditions—Version 5.0, Oak Ridge National Laboratory, Oak Ridge TN 37831 (2004)Google Scholar
  28. Yeh L.-M.: Homogenization of two-phase flow in fractured media. Math. Model. Methods Appl. Sci. 16, 1627–1651 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Tibetan Plateau ResearchChinese Academy of SciencesBeijingChina
  2. 2.Institute for a Secure and Sustainable Environment, Department of Civil and Environmental EngineeringUniversity of TennesseeKnoxvilleUSA

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