In this paper we present an alternative method based upon analytical and numerical solutions for the ordinary differential and partial differential equations which describe the heap leaching problem 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 the use of continuous-discontinuous solutions for the continuity partial differential equations describing balances. All of this, allows to obtain a numerical scheme which is fast and accurate for simulating the heap leaching problem. The model includes the effects of particle scales kinetic factors, heap scales and several operation variables. Finally, numerical experiments are presented.