An integral fluidodynamic model for hollow fibre (HF) has been developed and analysed. The model explains the pressure and flow profiles in three operation modes: open- and full-shell mode with forced circulation in the shell in cocurrent or countercurrent (OSFC); closed- and full-shell mode with forced recirculation in the shell in cocurrent or countercurrent (CSFR) and open- and empty-shell mode (OES). A methodology has been proposed to determine the parameters of the system and to verify the different operational systems proposed. Simple expressions have been developed to evaluate the pressures and the flows in the lumen fibres and in the shell, the transmembrane pressure, and the permeate flow for each operation mode assayed. The behaviour of the HT depends on the geometry of the module, on the operation mode chosen, and on the flows circulating through the lumen fibres and through the shell. The experimental results found with a commercial HT verified the model developed. The use of these expressions led us to choose the HF, the operation mode and the adequate flows that optimise the objective desired. (C) 2009 Elsevier B.V. All rights reserved.