The influence of local hindered settling on the concentration distribution in slurry transport

For determining the concentration distribution in slurry transport in pipes, often the solution of the 2D advection diffusion equation is used. The solution contains the terminal settling velocity, which is often replaced by the global hindered settling velocity, based on the cross sectional averaged spatial volumetric concentration. The fact that a concentration distribution is determined implies that the local concentration depends on the vertical coordinate in the pipe and is not equal to the cross sectional averaged concentration. With CFD this influence can be determined, however it’s interesting to see if there is also an analytical solution to this. The paper describes this analytical model based on local concentration. The method is iterative and requires about 4-12 iterations to find a stable solution. The hindered settling equation of Richardson and Zaki is modified to find a correct hindered settling velocity for high concentrations. In fact, if the spatial concentration approaches 50% one cannot speak of hindered settling anymore, but its closer to consolidation. The new equation behaves according to Richardson & Zaki for small concentrations and to consolidation for large concentrations. The model is validated with measured concentration profiles from literature, which will be shown.