Application of an Unsteady-State Pulp-Partition Model to Dense-Medium Separations

Since there has been a growing interest in using gravity concentration techniques for the processing of fine coal (less than about 0.5 mm in size), it is important that a performance prediction procedure is used which is capable of showing differences in the operating conditions of the separator. The generation of fractional recovery or partition curves is one such procedure. A fractional recovery curve is a plot of the fraction of or probability that a given size feed material of a given density reports to the product against the density. This paper derives a mathematical model, based upon the physics of the separation process, from which fractional recovery values can be obtained. The heart of this derivation is the convection-diffusion equation which takes into account both the settling and the mixing of particles within a free-settling-type separator. The fractional recovery curve can be obtained by fitting these values to an appropriate mathematical function. Although the fractional recovery curves can be described by model parameters such as viscosity, etc., the common industrial practice is to derive certain characteristic parameters directly from the curves. Therefore, if these values are fitted to an appropriate mathematical function, then the derived parameters can be obtained using a parameter estimation technique. Thus, by analyzing the variation of these parameters with operating and design conditions, a valuable technique for studying separator performance is established.