Development and application of a dynamic model for hindered-settling column separations

A phenomenological model, termed the “dynamic hindered-settling model”, has been developed to represent the separation in a hindered-settling column. The model is based on the convection–diffusion equation as applied to hindered-settling conditions. The key features of the model development include the derivation of equations for the finite-difference solution scheme for material balance, the integration of the modified form of Concha and Almendra’s hindered-settling equation to calculate settling velocities of particles, the development of a system to account for the continuous input/output of solids, and the addition of time-step functions to account for the underflow control valve action of a hindered-settling column. A Fortran program was written to solve the model. Simulations were carried out to evaluate column performance as a function of design and operating variables and material properties. The results, which are presented as product size distributions or fractional recovery curves, demonstrate that the dynamic hindered-settling model can be used to predict hindered-settling column separations.