An Asymptotic Solution for Washcoat Pore Diffusion in Catalytic Monoliths: Reformulation and Extension to Small Concentrations

  • Edward J. BissettEmail author


A recent publication (Bissett in Emission Control Sci. Technol. 1(1), 3–16, 2015) proposed an alternative to the so-called 1 + 1D modeling of aftertreatment reactors with nontrivial washcoat pore diffusion. Rather than numerically solve the 1D reaction-diffusion problem within the washcoat(s), asymptotic results based on small diffusion resistance give the concentration profiles within the washcoat analytically, and these are integrated within the overall solution for transient reactor performance. The description of the asymptotic solution in the former publication is suitable for the formal derivation and demonstration that all special properties of this solution follow from small diffusion resistance alone, but experience has shown that alternative descriptions and further extensions to accommodate small washcoat concentrations are desirable and perhaps necessary for practical application. In this paper and in a less formal style, we provide the new alternatives and analysis necessary for small concentrations.


Washcoat Diffusion Modeling Asymptotic Monolith Catalytic 


\( {D}_{inv}^{(l)} \)

Diagonal matrix of dimensionless pore diffusion resistances for washcoat layer l = 1, 2

j( l)

Dimensionless species mass fluxes at front of washcoat layer l = 1, 2


Diagonal matrix of dimensionless mass transfer coefficients

R( l)

Dimensionless species mass rates for washcoat layer l = 1, 2


Dimensionless position through the washcoat

xm, i

Locations of boundaries of zero concentration regions within washcoat


Scaled mass fractions in the washcoat


Scaled mass fractions of channel gas


Compliance with Ethical Standards

Conflict of Interest

The author declares that there is no competing interest.


  1. 1.
    Oh, S.H., Cavendish, J.C.: Transients of monolithic catalytic converters: response to step changes in feedstream temperature as related to controlling automobile emissions. Ind. Eng. Chem. Prod. Res. Dev. 21(1), 29–37 (1982)CrossRefGoogle Scholar
  2. 2.
    Bissett, E.J.: An asymptotic solution for washcoat pore diffusion in catalytic monoliths. Emission Control Sci. Technol. 1(1), 3–16 (2015)CrossRefGoogle Scholar
  3. 3.
    Joshi, S., Harold, M., Balakotaiah, V.: Overall mass transfer coefficients and controlling regimes in catalytic monoliths. Chem. Eng. Sci. 65(5), 1729–1747 (2010)CrossRefGoogle Scholar
  4. 4.
    Aris, R.: The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Vol. I. Oxford University Press, London (1975)Google Scholar
  5. 5.
    Gundlapally, S.R., Dudgeon, R., Wahiduzzaman, S.: Efficient solution of washcoat diffusion-reaction problem for real-time simulations. Emission Control Sci. Technol. 4(2), 90–102 (2018)CrossRefGoogle Scholar
  6. 6.
    Gundlapally, S., Dudgeon, R., Wahiduzzaman S: "An asymptotic solution approach for real time simulation of aftertreatment reactors in HiL Environments," 19 September 2018. [Online]. Available: [Accessed 6 November 2018]

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Gamma TechnologiesWestmontUSA

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