Empirical Models

At present, empirical models are the most commonly used technique for hydrocyclone selection and performance prediction. Empirical hydrocyclone models use the partition curve as a basis for describing size separation. Suitable equations are developed from experimental results to relate the parameters of the corrected partition curve to physical variables. In general, empirical hydrocyclone models consist of four relationships that describe the cut size, the sharpness of separation, the water balance around the hydrocyclone and the throughput-pressure drop relationship.

An empirical hydrocyclone model was described in 1976 that is still commonly used to predict separation performance. This model was the first to document an empirical form for the sharpness of separation and therefore allow direct simulation of expected performance without any testwork. This model form is often used as a basis for the development of models that include further variables, such as, for example, angle of inclination, or for an operating range in which the model has not been tested.

The Rosin-Rammler function describes the reduced partition curve:

where m indicates the sharpness of separation and xi is:

di dsi

In SI units, and using the symbols in Table 1, the Plitt equation for the cut size is:

50.5 DO D0 6 D121 exp[6.3^] Do.71 h0 38Q0A5(ps — pl)°-5

where ps, pi and pp are the densities of the solid, liquid and pulp, respectively.

To describe the water balance, Plitt develops a relationship for the volumetric flow split between the overflow and underflow streams, S, rather than the bypass:

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