The population balance model appears to be the best approach to model particulate systems where multiple heterogeneous reactions occur. This work demonstrates a mathematical formulation that is based on the population balance model, and aims at simulating the non steady-state behaviour of a single-stage CSTR under isothermal operation. The chemical reaction system is a typical example from the field of hydrometallurgy with two parallel reactions, one being leaching, the other precipitation with simultaneous reactant regeneration. The solution of the resulting system of the partial and ordinary differential equations is achieved by combining the moment transformation of the population balance equations with the numerical method of lines, using the Mathematica(R) software. Finally, examples are given for a reactor startup in two cases : a single leaching reaction, and simultaneous leaching and precipitation reactions. In the first case, the difference between simultaneous and sequential feeding in achieving steady-state is also discussed.