Continuous kinetic lumping of catalytic cracking processes

Processes, in which a multicomponent mixture of chemically similar compounds undergoes cracking reactions governed by nonlinear kinetics, are analyzed. Cracking reactions in general imply cleavage of chemical bonds between monomeric units. The article focuses on the case of the "uniform" kinetics. To obtain an analytical solution of the kinetic equations describing this process, we present an approach based on a continuous description of the mixture. The resulting nonlinear integro-differential equation has been linearized by a warped time scale, and a formal solution has been obtained via a regular perturbation method. The perturbation parameter is twice the inverse of the initial average number of monomeric units in excess of the minimum number that can be cracked by the reactions considered