A general analysis of multicomponent mass transfer with simultaneous reversible chemical reactions in multiphase systems

A general analysis is presented for describing the dynamics of multicomponent mass transport with simultaneous reversible or irreversible first-order chemical reactions in particulate systems consisting of large numbers of drops, bubbles or solid particles with residence time and particle size distributions. The method of approach and the general fundamental formulations are demonstrated by using matrix notation and appropriate transformations. The resulting partial differential equations for multicomponent, multiphase systems are first decoupled and then transformed into ordinary differential equations by employing an integral operator whose kernel takes into account the residence time distributions. Interaction among neighbor particles are taken into account by appropriate boundary conditions corresponding to an ensemble of spherical cell models. The total average transfer rates from the entire particle population are evaluated in terms of reaction rate constants, diffusivities, partition coefficients, average residence times, dispersed-phase holdup fraction and particle size distribution. The results of this general analysis are useful in predicting the yields and effluent concentrations of reacting dispersed systems as a function of the physical and operating variables. The practical application of the general solution presented is illustrated for the two-phase continuous stirred tank reactor and for the case of a three-component dispersed system undergoing pseudosteady-state diffusion in both phases with simultaneous reversible reaction in the continuous phase. One interesting general conclusion from this analysis is that the error involved in assuming a uniform particle size in lieu of a distribution of sizes is small when calculating total average transfer rates. It is found also that a reversal of the transfer may take place under certain conditions which depend on the average residence time and the relative raes of the backward to the forward reactions.