Grade-efficiency from models

As can be seen from the graph, Bradley s model gives conservative predictions of efficiency, mainly because he applied the approximation in equation 7.20, which was originally fitted to data obtained at radii between 1 and 2 cm, to radii up to rs = 2.223 cm where large discrepancies occur this leads to underestimates of separation efficiency. Bradley s model is still useful because it gives a lower estimate of efficiency, the actual grade efficiency curves are usually found to lie between those predicted by equations 7.9 and 7.21. 

As the best model for grade efficiency calculations we applied model 3 in which the catch and probe 2 sample should be known. This model resembles the procedure proposed by Hermann and Leschonski [3], as a correction of the mass balance is applied in this calculation model as well. It appears from our experience that the size analysis of the probe 2 sample must be carried out very accurately. Enough sample should be collected on the filter in order to perform reliable Coulter Counter analysis. 

Fig. 7.3.3. Grade-efficiency curves from Derksen (2003) at different points in time. The predictions for Stk o of the models of Barth and Mothes and Loffler (Chap. 5) are also indicated...

We note from the experimental data reported above that the model s cut-point diameter, X50, is 0.98 yum. We do not have data at the same Re for model and prototype, so we will make use of the approximations mentioned in the main text. Rein is large enough in both model and prototype to assume that the grade-efficiency is about the same in the two cyclones for the same value of Stk, and that their Eu values are the same. 

We see from the figure that we can expect all catalyst particles greater than about 10 pva to be completely captured in the industrial unit. We also see that the grade-efficiency curve for the prototype has the same s-shape form as that of the model on the logarithmic scale. 

One system we used for this work was comprised of four 30-cm 100-A /x-Styragel columns (from Waters Associates) connected in series with a Rheodyne Model 7105 injector valve and a Varian 4200 syringe pump that maintained a constant flow of either 1 or 2 mL/min. At 1 mL/min the overall resolution efficiency was about 15,000 theoretical plates and the run time was about 50 min. By doubling the flow rate, the run time was cut in half with only a slight loss of column efficiency. The pressure required for a flow rate of 2 mL/min was usually about 1200 psi. Tetrahydrofuran (UV grade from Burdick and Jackson Laboratories) was used as the eluting solvent. The amount of sample solution injected into the system varied from 10 /xL to 500 /xL. 

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