A mathematical model of leaching reactors using the population balance is presented. The model incorporates the material balances for the reactants and products, the population balance which de- scribes the change in particle-size distribution, and the energy balance. The effects of the particle kinetics, the particle-size distribution, and the residence-time distribution are accounted for.

The approach is discussed for the design of multi-stage, continuous reactors, and examples of the application of the model are given for various forms of the leaching reactions.

The method is then used to develop an a priori model for the pressure leaching of sphalerite, and the results are compared with those of the Cominco's plant at Trail, British Colombia, Canada. The model incorporates the leaching reactions, the oxidation of ferrous sulphate, the precipitation of plumbojarosite, and dissolution of oxygen from the gas phase into the solution. The kinetic parameters for each of these reactions have been obtained from independent studies. The model predicts results that compare favourably with data from the plant operation.