The problem of gravity-driven thickening of a dispersion in a long, vertical tube of diameter larger than the dimensions of the dispersed phase particles has been treated. Inflow of the suspension takes place through the porous tube wall and suspension is pumped away both at the upper and lower ends. A theoretical analysis of the problem is given. A material balance over a differential element spanning the cross-section leads to a model equation that has been solved analytically and numerically. The behaviour of the model as a function of various parameters, such as the axial dispersed phase concentration profile and the ratio of flows through the upper and lower pumps, is discussed. Comparison with the experimental results obtained in an industrial system shows good agreement.