The first part of this approach is concerned with the elaboration of a radical polymerization model of styrenne, based on a kinetic diagram that includes chemical and thermal initiation, propagation, termination by recombination and chain transfer to the monomer. Furthermore, volume contraction during polymerization is considered, as well as the gel and glass effects. The mathematical formalism that describes the model in terms of moments is explored in detail. The model was then used to predict the changes in monomer conversion and molecular weight after intermediate addition of initiator and monomer. The results of this operation are dependent on the conditions of the reaction mass, quantity, and moment of substance addition. Therefore, the simulations were performed at different times with respect to the gel effect; before, during and after this phenomenon, and also with respect to different temperatures and initiators. Increasing the initiator concentration before the gel effect leads to an earlier appearance of the phenomenon and to a decrease in molecular weight. The ratio
$$\bar M_w /\bar M_n $$
reveals a polydispersity index smaller for the intermediate addition of initiator. No significant changes take place during or after the gel effect. If along with the initiator, unreacted monomver (used to dissolve the initiator) enters the reactor, a small dip in conversion is observed. The general conclusion of this paper reveals the intermediate addition of initiator as a method to control polymer properties and to prevent the “dead-end” polymerization of styrene.