Optimal Temperature Policy for a Reversible Reaction

This Demonstration shows the temperature trajectory that maximizes the reaction rate of a reversible reaction.
For the reaction
, the rate is
with and ,
where and are the pre-exponential Arrhenius constants for the forward and reverse reactions, and are the energies of activation, is the universal gas constant, is the absolute temperature, , , , and are the initial concentration of the reactants, and is the conversion of species . The temperature function that gives the maximum reaction rate satisfies the condition at each point in time; this function has an analytical solution for this reaction [1]
, and
the initial concentrations of and are taken equal to 0.5, and 1.0.
One complication can occur: for low conversions, may have a value sufficiently small enough to make ; then the equation for gives a value (or negative); in practice the temperature is limited by the reactor materials or the catalyst's physical properties. The optimum temperature profile and the concentration of the reactants as a function of time are shown for user-set values of reaction time, maximum allowable temperature, and parameters and .


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[1] G. F. Froment, K. B. Bischoff, and J. de Wilde, Chemical Reactor Analysis and Design, 3rd ed., Hoboken, NJ: Wiley, 2011.
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