Multiplicity behavior of adiabatic tubular reactors

Richard Charles Dougherty

doi:10.17918/00000669

Singularity theory is applied to the adiabatic fixed-bed reactor, in which a single reaction occurs, to completely and exactly define its steady state multiplicity features. The impact of backmixing of heat, reaction rate inhibition by adsorption/desorption effects (Langmuir-Hinshelwood kinetic expressions), and interparticle transport resistances on the maximum number of steady states and the number and types of bifurcation diagrams is discussed. Feed rate and feed concentration are considered as slowly changing operating parameters whose variability leads to a changing number of possible steady states. In the absence of interparticle transport resistances, the steady state multiplicity behavior of the tubular reactor is found to be qualitatively similar to that of the CSTR for reaction rates described by power-law or monomolecular Langmuir-Hinshelwood kinetics. Small qualitative deviations between the multiplicity features of the CSTR and tubular reactor exist when the reaction rate is described by bimolecular Langmuir-Hinshelwood kinetics. A uniqueness criterion based on residence time is obtained for the pseudohomogeneous model with power-law kinetics and equal mass and heat Peclet numbers. Uniqueness criteria for both residence time and kinetic parameters are obtained for the more practical case of unequal Peclet numbers. Existing criteria are often based on kinetic parameters and assume equal Peclet numbers. The criteria developed here have particular application for reactions for which isothermal rate data exists but the heat of reaction is not precisely known. Inclusion of interparticle mass and temperature gradients in the model is shown to increase the number of possible solutions by two and substantially increase the numerical complexity of the theory application. Five steady states are possible for the heterogeneous model with intermediate levels of heat dispersion but only three are found for the limiting cases of infinite and zero backmixing. Including in the model published correlations for the transfer coefficients does not increase the number of possible solutions but was found to result in isolated solution branches at low residence times. It is shown, in contrast to the literature, that the qualitative multiplicity behavior of the system is not affected by the choice of boundary conditions for the catalyst temperature. A uniqueness criterion is developed for the general case of finite levels of backmixing by considering the two limiting dispersion cases.

Multiplicity behavior of adiabatic tubular reactors

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Multiplicity behavior of adiabatic tubular reactors

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