For obvious industrial and theoretical reasons the problem of accounting for the effect of impurities in the population balance modelling of solution crystallization processes is a very important issue, and yet it has never been reported until today. Meanwhile, several kinetic models are proposed in the literature that relate the effect of impurities on the crystal growth and could be used for PBE modelling. The goal of the present paper is to address this issue and to present a new method, based on characteristics, which is shown to efficiently solve the difficulties raised by the specificity of the mathematical formulation of the Population Balance Equation (PBE) in the presence of impurities. Indeed, as far as hindering effects of the impurities on the crystal growth are concerned, it turns out that the "age" of the particles (i.e. the time they spent in the presence of impurities) might plays a key-role in the overall dynamic crystallization process. Accounting for such a new internal variable required a specific PBE resolution algorithm to be developed and evaluated.