Catalyst Dilution as a Means to Establish an Optimum Temperature Profile G. Narsimhan Department of Chemical Engineering, Indian lnstitufe of Science. Bangalore. lndia
An analytical procedure has been developed for predicting a catalyst dilution profile which establishes an optimum temperature profile along a nonisothermal, nonadiabatic plug flow reactor wherein a reversible exothermic reaction takes place. The treatment has been extended to the consideration of a sequence of ideal fluidized bed reactors. A performance criterion, which is the ratio of overall conversion to a catalyst dilution factor in a reactor of fixed volume, has been suggested for evaluating the relative performances of several schemes of reactor operation. A numerical example has been worked out to illustrate the design procedures.
For highly exothermic gas-solid catalytic reactions catalyst dilution has been suggested as a logical and expedient method to control the severity of axial temperature profile in a packed bed reactor (Calderbank, 1969). This strategy is also often used to effect isothermal kinetic measurements and a stochastic model for describing quantitatively the influence of catalyst dilution on conversion has been proposed by van Den Bleek (van Den Bleek et al., 1969). An alternative method for achieving such a reactor operation under controlled temperature limits by adopting a special reactor configuration is possible for laboratory investigations, but translation of such a strategy into industrial practice is extremely difficult. In the past, the general features of an optimal design problem, based on principles of dynamic programming, have been considered (Aris, 1965) but the analysis has not been specific for the optimization problem of tubular reactors cooled from the wall and subject to temperature bounds. In this investigation an attempt is made for the prediction of an axial catalyst dilution profile which forces a nonisothermal, nonadiabatic reactor to operate on an optimum temperature progression when a reversible exothermic reaction takes place in the reactor. The analysis has been extended to the consideration of a sequence of well-mixed fluidized bed reactors.
Analysis When an exothermic reversible reaction is carried out in a plug flow reactor and under steady-state conditions, it is possible to predict a unique reactor-temperature profile under the influence of which the reaction rate is maximized a t any cross section along the reactor. The optimum temperature which maximizes the reaction rate a t a given conversion is obtained by setting the partial derivative of the reaction rate with respect to temperature to zero. Intuitively it is obvious that a t the reactor inlet where the reverse reaction is absent, the highest possible temperature would be desirable and as the conversion builds up along the length of the reactor, the reactor temperature would be progressively decreased in order to counteract the adverse effect of temperature on equilibrium constant (or conversion). For a first-order exothermic reversible reaction proceeding according to the stoichiometry
A=R
(AH,
