The process of digestion of an oil sand lump moving in the heated water flow is considered. A lump is modelled as a heated sphere subjected to shear stresses and ambient temperature and melting when the combined effect of these two factors exceeds some critical value. This critical value is introduced in the form of a critical temperature and it is associated with the minimum adhesive strength of bitumen. This temperature is a model constant that can be determined from an experiment. The complicated heat transfer conditions of a lump are taken into account by averaging the Nusselt number (the second experimental constant of the model). A numerical analysis of the dependence of digestion rates on water and lump temperatures, and on lump sizes is performed to illustrate the applicability of the model. (C) 2002 Published by Elsevier Science Ltd.