Optimal temperature profiles for parallel-consecutive reactions with deactivating catalyst

A cocurrent tubular reactor with temperature profile control and recycle of moving deactivating catalyst has been investigated. For the temperature-dependent catalyst deactivation, the optimization problem has been formulated in which a maximum of a profit flux is achieved by the best choice of temperature profile and residence time of reactants for the set of catalytic reactions A+B→R and R+B→S with desired product R, the rates of reactions have been described separately for every reagent by the expressions containing (temperature dependent) reaction rate constants, concentrations of reagents, catalyst activity, as well as catalyst concentration in the reacting suspension and a measure of the slip between reagents and solid catalyst particles. The algorithms of maximum principle have been used for optimization. The optimal solutions show that a shape of the optimal temperature profile depends on the mutual relations between activation energies of reactions and catalyst deactivation. It has been proved that the optimal temperature profile is a result of the compromise between the overall production rate of desired reagent R (production rate in the first reaction minus disappearance rate in the second one), necessity of saving of reagents residence time (reactor volume) and necessity of saving catalyst; the most important influence on the optimal temperature profile is associated with necessity of saving the catalyst. When catalyst recycle ratio increases (mean number of catalyst particles residing in reactor increases), optimal temperatures save the catalyst, as the optimal profile is shifted in direction of lower temperatures. The same is observed when catalyst slip increases (catalyst residence time in reactor increases). Despite of variation in the catalyst concentration the optimal profile is practically the same because the decay rate is affected only by instantaneous activity of catalyst. When reactor unit volume price decreases, catalyst residence time increases, whereas optimal temperature profile is shifted to lower temperatures. When economic value of unit activity of outlet catalyst increases (catalyst with a residual activity still has an economic value), catalyst saving should be more and more intense. As far as possible, the optimal profile is shifted in direction of lower temperatures, whereas the optimal residence time is still the same. Then the optimal profile is isothermal at the level of minimum allowable temperature, whereas the catalyst is saved as its residence time in reactor decreases.