Chemical Engineering Science, Vol. 42, No. 4, pp. 737-744, 1987. Printed in Great Britain. 0X%‘-2509/87 $3.00 f 0.00 Pergamon Journals Ltd. SOLIDS FLOW VELOCITY PROFILES IN MASS FLOW HOPPERS H.G. POLDERMAN, J. BOOM, E. DE HILSTER and A.M. SCOTT Koninklijke/Shell-Laboratorium, Amsterdam (Shell Research B.V.) Badhuisweg 3, 1031 CM Amsterdam, The Netherlands Abstract - A mathematical model is presented for the solids velocity distribution in mass flow hoppers; it is based on classical plasticity theory. The analytical solutions are in good agreement with the results of experiments performed with sand and organic prills in model hoppers of 0.11 and 0.60 m diameter. INTRODUCTION A technically important aspect of the flow of bulk solids in storage bunkers or moving bed reactors is the flow pattern, which is directly related to the solids residence time distribution. The abundant literature on this subject has recently been discussed in great detail in the review article by Tiiziin et al. [l]. Their conclusion is that quantitative pre- diction methods hardly exist and that 'the whole topic of velocity prediction in granu- lar materials is wide open for further in- vestigation'. In the following we present a simple mathematical model for the velocity distri- bution in the flow of free-flowing granular solids from mass flow hoppers, which seems to have escaped the attention of previous investigators in the field. The equations for a radial velocity field were solved by assuming coaxiality of stress and strain and by adopting the same simplifications about the stress field that were used in various differential slice models for bunker wall stresses. Further we discuss the verification of the theory by means of residence time dis- tribution measurements and flow visualisa- tion studies on two different scales. Finally the applicability of the model is illustrated by calculations of solids flow residence time distributions for various hopper geometries. THEORY A granular solid behaves essentially as a plastic material. The flow of a plastic material in a converging channel has been examined theoretically by Hill [2] and Shield [3], in connection with the drawing of sheets and wires in the steel industry. This theory of metal plasticity can be gene- ralized to obtain a simple description of Fig. 1. Geometry definition sketch 737