Kinetics of and Transport Phenomena in Gas–Solid Reactors

  • Elio Santacesaria
  • Riccardo Tesser


The fundamental laws of mass, heat, and momentum transport are briefly presented in this chapter and their relationships with chemical kinetics depicted. The approach presented starts with estimation of basic properties like viscosity, thermal conductivity, and mass diffusivity, all of which are of fundamental importance in describing transport phenomena. Transport phenomena originate gradients in temperature, pressure, and concentration that are the driving forces for transformations occurring in a system. Two scales of transformation can be considered, i.e., molecular and macroscopic. Molecular-transport phenomena are normally much slower than macroscopic ones and this can result in a limitation on chemical reaction rates. In this chapter, detailed examples of basic property calculations are reported as are examples of chemical gas–solid reactions limited by diffusional resistance (like ammonia oxidation). Finally, a great part of the chapter is dedicated to the evaluation of catalyst effectiveness factor. Matlab code associated with the examples in this chapter is available online.

Supplementary material

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Supplementary material 1 (DOCX 45 kb)


  1. Aris, R.: On shape factors for irregular particles—I: The steady state problem. Diffusion and reaction. Chem. Eng. Sci. 6(6), 262–268 (1957)Google Scholar
  2. Bird, R.B., Stewart, W.E., Lightfoot., E.N.: Transport Phenomena. John Wiley & Sons (1960)Google Scholar
  3. Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena Italian Edition Casa Editrice Ambrosiana (1970)Google Scholar
  4. Bradshaw, R.D., Bennet, C.O.: Fluid-particle mass transfer in a packed bed. A.I.Ch.E. J. 7(1), 48–52 (1961)Google Scholar
  5. Bridgman, P.W.: The thermal conductivity of liquids. sProc. Natl. Acad. Sci. USA 9(10), 341–345(1923)Google Scholar
  6. Brush, G.: Kinetic Theory, Vol. 1: The Nature of Gases and of Heat. Oxford (1965)Google Scholar
  7. Carberry, J.J.: A boundary-layer model of fluid-particle mass transfer in fixed beds. A.I.Ch.E. J. 6(3),s1960)Google Scholar
  8. Carberry, J.J.: Physico-chemical aspects of mass and heat transfer in heterogeneous catalysis (Chap. 3). In: Anderson, J.R., Boudart, M. (ed.) Catalysis, vol. 8, pp. 131–171. Springer, Berlin (1987)Google Scholar
  9. Carrà, S., Forni, L.: Aspetti Cinetici della Teoria del Reattore Chimico. Tamburini Ed. (1974)Google Scholar
  10. Carrà, S., Ragaini, V., Zanderighi, L.: Operazioni di Trasferimento di Massa. Manfredi Editore, Milano (1969)Google Scholar
  11. Chapman, S.: The kinetic theory of simple and composite monatomic gases: viscosity, thermal conduction, and diffusion. Proc. Roy. Soc. London A 93, 1–20 (1916)Google Scholar
  12. Chapman S., Cowling T.G.: The Mathematical Theory of Non‐Uniform Gases, 3rd edn. Cambridge University Press (1970)Google Scholar
  13. Chilton, T.C., Colburn, A.P.: Mass transfer (absorption) coefficients prediction from data on heat transfer and fluid friction. Ind. Eng. Chem. 26(11), 1183–1187 (1934)Google Scholar
  14. De Acetis, J., Thodos, G.: Mass and heat transfer in flow of gases through spherical packings. Ind. Eng. Chem. 52(12), 1003–1006 (1960)CrossRefGoogle Scholar
  15. Dwydevi, P.N., Upadhay, S.N.: Particle-fluid mass transfer in fixed and fluidized beds. Ind. Eng. Chem. Process Des. Dev. 16, 157 (1977)CrossRefGoogle Scholar
  16. Einstein, A.: Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. J. Physik 17, 549–561 (1905)CrossRefGoogle Scholar
  17. Enskog, D.: Kinetische Theorie der Vorgänge in mässig verdiinten Gases (Almqvist and Wiksells, Uppsala, (1917); translation by S.G. Brush in Kinetic Theory Vol. 3, Pergamon, Oxford (1965)Google Scholar
  18. Fairbanks, D.F., Wilke, C.R.: Diffusion coefficients in multicomponent gas mixtures. Ind. Eng. Chem. 42(3), 471–475 (1950)CrossRefGoogle Scholar
  19. Fogler, H.S.: Elements of Chemical Reaction Engineering. Prentice Hall Int. Editions (1986)Google Scholar
  20. Forni, L.: Fenomeni di Trasporto. Edizioni Cortina Milano (1979)Google Scholar
  21. Froment, G.F.: Fixed bed catalytic reactors—current design status. Ind. Eng. Chem. 59(2), 18–27 (1967)CrossRefGoogle Scholar
  22. Froment, G.F., Bischoff, K.B.: Chemical Reactor Analysis and Design. Wiley, New York (1990)Google Scholar
  23. Frössling, N.: Über die Verdunstung fallender Tropfen. Gerlands Beitr. Geophys. 52, 170–216 (1938)Google Scholar
  24. Gimeno, M.P., Gascon, J., Tellez, C., Herguido, J., Menedez, M.: Selective oxidation of o-xylene to phthalic anhydride over V2O5/TiO2: kinetic study in a fluidized bed reactor. Chem. Eng. Process. 47(9–10), 1844–1852 (2008)Google Scholar
  25. Hirschfelder, J.O., Bird, R.B., Spotz, E.L.: The transport properties of gases and gaseous mixtures. Chem. Revs. 44(1), 205–231 (1949)Google Scholar
  26. Hirschfelder, J.O., Curtiss, C.F., Bird, R.B.: Molecular theory of gases and liquids. Wiley, New York (1954)Google Scholar
  27. Holland, C.D., Anthony, R.G.: Fundamentals of Chemical Reaction Engineering. Prentice-Hall, London (1979)Google Scholar
  28. Horak, J., Pasek, J.: Design of Industrial Chemical Reactors from Laboratory Data. Heyden, London (1978)Google Scholar
  29. Johnson, P.A., Babb, A.L.: Liquid diffusion of non-electrolytes. Chem. Rev. 56, 387–453 (1956)CrossRefGoogle Scholar
  30. Lee, H.H.: Heterogeneous Reactor Design. Butterworth Pu. (1984)Google Scholar
  31. Levenspiel, O.: The Chemical Reactor Omnibook. OSU Book Store, Oregon (1984)Google Scholar
  32. Missen, R.W., Mims, C.A., Saville, B.A.: Introduction to Chemical Reaction Engineering and Kinetics. Wiley. New York (1999)Google Scholar
  33. Ranz, W.E., Marshall Jr., W.R.: Evaporation from drops. Chem. Eng. Prog. 48(3), 141–146 (1952a)Google Scholar
  34. Ranz, W.E., Marshall Jr., W.R.: Evaporation from drops part II. Chem. Eng. Prog. 48(4), 173–180 (1952b)Google Scholar
  35. Rase, H.F.: Chemical Reactor Design for Process Plant, Vol. 2: Case Study N. 109, pp. 115–122j. Wiley, New York (1977)Google Scholar
  36. Riggs, J.B.: Introduction to numerical methods in chemical engineering. Texas Tech Univ. Press (1988)Google Scholar
  37. Rowlinson, J.S., Townley, J.R.: The application of the principle of corresponding states to the transport properties of gases. Trans. Faraday Soc. 49, 20–27 (1953)CrossRefGoogle Scholar
  38. Santacesaria, E.: Kinetics and transpssort phenomena in heterogeneous gas-solid and gas-liquid-solid systems. Catal. Today 34(3–4), 411–420 (1997)CrossRefGoogle Scholar
  39. Satterfield, C.N., Sherwood, T.K.: The Role of Diffusion in Catalysis. Addison Wesley Pu. Co. Inc. (1963)Google Scholar
  40. Satterfield, C.N.: Heterogeneous Catalysis in Practice. Addison-Wesley (1972)Google Scholar
  41. Satterfield, C.N., Cortez, D.H.: mass transfer characteristics of woven-wire screen catalysts. Ind. Eng. Chem. Fundam. 9(4), 613–620 (1970)CrossRefGoogle Scholar
  42. Smith J.M.: Chemical Engineering Kinetics. Mc Graw-Hill Book Co., New York (1981)Google Scholar
  43. Stull, D.R., Westrum, E.F., Sinke, G.C.:The Chemical Thermodynamics of Organic Compounds. Wiley, New York (1969)Google Scholar
  44. Thoenes, D., Kramers, H.: Mass transfer from spheres in various regular packings to a flowing fluid. Chem. Eng. Sci. 8(3–4), 271–283 (1958)Google Scholar
  45. Treybal, R.E.: Mass Transfer Operations. Mc Graw-Hill Co., New York (1955)Google Scholar
  46. Weisz, P.B., Hicks, J.S.: The behavior of porous catalyst particles in view of internal mass and heat diffusion effects. Chem. Eng. Sci. 17, 265-275 (1962)Google Scholar
  47. Weisz, P.B., Prater, C.D.: Interpretation of measurements in experimental catalysis. Adv. Catal. 6, 143–196 (1954)Google Scholar
  48. Wilke, C.R., Chang, P.: Correlation of diffusion coefficients in dilute solutions, AICHE J. 1(2), 264-270 (1955)Google Scholar
  49. Winterbottom, J.M., King, M.: Reactor Design for Chemical Engineers. CRC Press, 1ed (1999)Google Scholar

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Authors and Affiliations

  1. 1.Eurochem Engineering s.r.l.MilanItaly
  2. 2.Dipartimento di Scienze Chimiche, Complesso di Monte Sant’AngeloUniversity of Naples Federico IINaplesItaly

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