A numerical post-processing strategy to reconstruct the size of soot primary particles is presented in this work in the context of the chemical sectional models. The proposed technique is based on solving the transport equation of the primary particle number density for each considered aggregate size. The chemical source terms are derived from the corresponding chemical reactions. The validity of the proposed approach is tested on target flames of the International Sooting Flame (ISF) Workshop. In particular, first, a laminar premixed ethylene flame is considered. Profiles of soot volume fraction and mean primary particle size are compared between simulation and measurements and a satisfactory agreement is observed, validating the proposed post-processing strategy. Second, a laminar coflow ethylene flame is put under the scope. Numerical results are compared to experimental data once again in terms of soot volume fraction and primary particle size. The sensitivity to model parameters, such as accounting for surface rounding and the choice of the smallest aggregating particle size, is explored. Once validated, the effect of dilution on the mean primary particle diameter in laminar diffusion flames is examined. The general trends observed experimentally are recovered. The correlation between temperature, precursor concentrations, soot volume fraction and primary particle diameter is explored. Finally, formation rates and residence time along the particle trajectories are investigated to explain the effect of dilution on the spatial localization of the biggest particles along the flame. The relation between the soot volume fraction and the mean primary particle diameter is examined.