The method of moments was extended to include a more complete description of particle coagulation, namely, the transition and continuum regimes as well as the formation and growth of fractal aggregates. The formalism preserves the numerical efficiency and the physical rigor of the method of moments by inclusion of just two additional moment equations and without prescribing a mathematical form to the particle size distribution function. The extended model was used to simulate soot formation in several 10 bar laminar premixed ethylene-air flames. The results demonstrate that the more complete formulation improves significantly model prediction of experimental data, thereby explaining the appearance of a catastrophic decrease in coagulation rates, which could not be rationalized within the classical theory of Brownian coagulation.