Isothermal or Concentration Multiplicity

This source of multiplicity is probably the most intrinsic one in catalytic and biocatalytic reactors, for it occurs due to the nonmonotonic dependence of the intrinsic rate of reaction upon the concentration of reactants and products. Although a decade ago, nonmonotonic kinetics of catalytic reactions were considered the exceptional case, today it is clear that nonmonotonic kinetics in catalytic reactions are much more widespread than previously thought. The reader can learn more about various examples from the long list of catalytic reactions exhibiting nonmonotonic kinetics [71-76]. 

However, nonmonotonic kinetics alone will not produce multiplicity. Such kinetics have to be coupled with a diffusion process, either in the form of a mass-transfer resistance between the catalyst pellet surface and the bulk gas, or within the pores of the pellets. If the flow conditions and the catalyst pellets size are such that diffusional resistances between the bulk gas phase and the catalytic active centers are negligible and the 

A word of caution is necessary here. Isothermal multiplicity that is the result of nonmonotonic kinetics occurs only when the nonmonotonic kinetic dependence of the rate of reaction upon species concentration is sharp enough. For flat nonmonotonic behavior, multiplicity can occur only for bulk-phase concentrations which are too high to have much practical relevance. 

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Isothermal or concentration multiplicity and thermal multiplicity may co-exist in cer-... 

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