A population balance based transient reactor model is applied to a particulate process employed in the hydrometallurgical industry. The process is the pressure oxidation of pyritic concentrates, pertinent to the treatment of refractory gold materials. The chemical reaction system involves first an oxygen gas to aqueous mass transfer step, followed by a chemical reaction on the surface of mineral particles. The chemical reactor stimulated is a multi-stage continuous autoclave with variable compartment size. The model accounts for recycling oxidized solids, as well as for venting the gas phase. A complex system of partial and non-linear ordinary differential equations is rendered dimensionless and solved by a method developed previously using the Mathematica(R) software. The transient response of the reactor to different modes of reactor start-up, as well as the response to a step change of a key variable, are examined. The validity of the steady-state solution is assessed by comparing it to previous modelling attempts.