Fast binary reactions in a heterogeneous catalytic batch reactor

When heterogeneous chemical reaction is sufficiently fast, transport of reactants becomes limiting. In a well stirred, batch reactor, macroscopic concentration gradients can be eliminated as a factor limiting the rate of reaction, leaving only the mesoscopic mass transfer of reactants to the surface of the catalyst as limiting, if the reaction does not occur inside a porous support. Here, a transformation of the governing equations for the time-dependence of bulk and surface concentrations results in second order ODE in time and a single nonlinear constraint with boundary values at the initial and infinite times for two auxiliary variables termed modified Thiele moduli. This system of two equations—one differential, one algebraic—and two unknowns is an exact consequence of the governing equations (three ODEs and three algebraic constraints). The power of this formulation is demonstrated by analytic solutions for irreversible and nearly irreversible theories. These solutions are corroborated by full nonlinear numerical computations of the boundary value problem, for the case when asymmetric mass transfer coefficients admit the possibility that the mode of operation switches from relative surface depletion of one reactant to depletion of the other in a binary reaction. The modified Thiele modulus formulation reveals the time scale for the switch over, as well as giving a reliable prediction for the time scale for 99% conversion based on the switch time identified from the irreversible theory.