The classic breakage problem is a population-balance problem using first-order kinetics and product distribution rules over a multidimensional continuum, mathematically expressed as linear integrodifferential equations for the multiindexed frequency distribution functions of entities. To model the catalytic cracking of petroleum fractions, population-balance equations are solved through Galerkin formalism. It focuses on a simplified version of such equations, which was solved analytically through the method of characteristics, Kinetic and stoichiometric parameters were statistically estimated for both models from a set of pseudoexperimental data generated using available traditional lumped models. For this purpose, an arbitrary structural description for a continuous representation of the species also had to be developed.