A new mathematical model of processes in a "Rotocell" extractor was developed. The model considers: a two-dimensional approach of counter-current crossed flows (CCC) with oil diffusion for miscela; mass transfer between the bulk, pore and solid phases; the effect of the existing processes in the drainage and loading sections; oil losses; and variation in the miscela viscosity and density. The model leads to a system of coupled partial and ordinary differential equations, whereupon is transformed in the neural network. The solution is compared with experimental data and with the method of ideal stages. The numerical simulations reveal the extraction field properties in the transient regimes. (C) 2004 Elsevier B.V. All rights reserved.