The Klimpel flotation model
This model is the simplest formulation of the distributed rate constant model. It is based on an observation that was made in the earliest experimental kinetic studies of flotation, namely, that not all particles will be recovered by flotation no matter how much residence time they have in the flotation environment. Each particle type has an ultimate recovery that is less than 100%. The particles that do float are recovered at a rate that is governed by a simple first-order kinetic law. Thus two kinetic parameters are required for each type of particle: the ultimate recovery and the kinetic constant. The model does not usually distinguish between particles on the basis of size and in addition the aeration of the pulp and the behavior of the froth are not specifically considered. The model is not capable of describing the behavior of a bank of flotation cells and each bank is regarded as a single large cell. In general the kinetic parameters do not hold their values as the tailings and concentrates move from rougher to cleaner and from rougher to scavenger and MODSIM allows the user to specify the rate constant and ultimate recovery for each particle type in each stage. Exercise 5-1 shows how to simulate a single flotation cell using the Klimpel model.
All kinetic models for flotation have one requirement in common: they must include a model for water recovery so that the water balance can be established. This is necessary because a significant fraction of the water that is fed to a cell is taken off with the froth. Three methods are commonly used: specify the solid content of the concentrate, specify the solid content of the tails or specify the volumetric flowrate of water into the froth launder. The first two of these methods are demonstrated in this module.
Exercise 5-2 illustrates the advantages that are gained by using a multi-stage rougher-scavenger-cleaner flowsheet configuration. The Klimpel model is not ideally suited to this task but is often used for this purpose so we illustrate how it can be done in this exercise.