In this paper we present an alternative method based on analytical and numerical solutions for solving the differential equations which describe heap leaching of one or more solid reactants from porous pellets. We propose to use analytical solutions for the differential equations which describe rate dissolutions along the pores and the surface of the particles Under suitable regularity conditions. Moreover, we propose to use continuous and discontinuous Solutions for the continuity partial differential equations describing balances. We comment on the efficient numerical solving of the remaining partial differential equations within the proposed numerical scheme. All of this, allows to obtain a numerical algorithm which is fast and accurate for the heap leaching problem. Also. we include particle size distributions oil the proposed numerical methodology. This method applies to the case where the rate-controlling reagent is a component of the lixiviation Solution Only and not of the gas phase. The model includes the effects of particle scales. kinetic factors. heap scales and several operation variables. Finally, numerical experiments are presented. (c) 2008 Elsevier Ltd. All rights reserved.