Computation of Efficiency at Low Solids Loadings

In this section we will compute the grade-efficiency curve and overall separation efficiency at low inlet solids (classification only) loadings (co Cql)- The grade-efficiency curve for a given cyclone expresses the functional dependence of separation performance upon particle diameter. As discussed in Chap. 3, it is normally an s-shaped function satisfying the limits  

The grade-efficiency curve r/ is normally defined with the use of just the two parameters the cut size, X50, slope m. A variety of equations have 

When one is designing a new cyclone system, it is customary to perform the calculations indicated above to find 50, choose a slope—based on experience or otherwise - and then use Eq. (6.3.2) to compute points on the cyclone s grade-efficiency curve, r]i as a function of Xi, using the known x o and m. 

The overall collection efficiency is obtained by first dividing the feed into N size fractions, each fraction comprising a known fraction of the total mass of feed solids. Next, each of these mass fractions is multiplied by the efficiency of capture for the average particle size of each fraction. This efficiency of capture is that computed from the grade-efficiency curve. The sum of all N fractions thus computed is the overall collection efficiency. Mathematically, this may be expressed as. 

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