A two-dimensional transitory mathematical model developed in a previous paper is expanded and applied to represent the extraction process of oil and its minor compounds (phospholipids, tocopherols and waxes) in a De Smet industrial extractor. Diffusivities and equilibrium parameters are obtained from experimental batch extractions. The mathematical model is solved numerically to predict the concentration of oil and minor compounds in miscella and collets in the different sections of the extractor. The concentration of phospholipids and crystallized waxes in the solid decreases slowly, being sharper at the end of the process. Tocopherols and triacylglycerols are extracted more quickly at 60 degrees C. Numerical simulations of the extraction process reveal that it would be possible to obtain oil with smaller concentrations of phospholipids and waxes, working at 60 degrees C and using fewer stages. Since the last stages do not produce a significant increment of the oil yield at 60 degrees C, the model results show that the extractor is over dimensioned. (C) 2011 Elsevier Ltd. All rights reserved.