Cut size

For smaller particles, the theory indicates that efficiency decreases according to the dotted line of Figure 7. Experimental data (134) (sofld line of Eig. 7) for a cyclone of Eig. 9 dimensions show that equation 15 tends to overstate collection efficiency for moderately coarse particles and understate efficiency for the finer fraction. The concept of particle cut-size, defined as the size of particle collected with 50% mass efficiency, determined by equation 16 has been proposed (134). 

Fig. 17. Overall (integrated) penetration as a function of collector particle cut-size and characteristics and inlet particle parameters for collectors that foUow...

Ideally, the chance of a spherical particle having diameter t passing through an opening would be zero for all particles of relative size djb > 1 and one for all particles of relative size djb < 1. A plot of the probabiUty-of-passing vs size (Fig. 1, curve D) is a step function, and the separation size, so-called cut size, is d/b = 1. A perfect separation is one where all particles of size less than the cut size pass and all particles of size greater than the cut size are retained. 

AH three parameters, the cut size, sharpness index, and apparent bypass, are used to evaluate a size separation device because these are assumed to be independent of the feed size distribution. Other measures, usually termed efficiencies, are also used to evaluate the separation achieved by a size separation device. Because these measures are dependent on the feed size distribution, they are only usefiil when making comparisons for similar feeds. AH measures reduce to either recovery efficiency, classification efficiency, or quantitative efficiency. Recovery efficiency is the ratio of the amount of material less than the cut size in the fine stream to the amount of material less than the cut size in the feed stream. Classification efficiency is defined as a corrected recovery efficiency, ie, the recovery efficiency minus the ratio of the amount of material greater than the cut size in the fine stream to the amount of material greater than the cut size in the feed stream. Quantitative efficiency is the ratio of the sum of the amount of material less than the cut size in the fine stream plus the amount of material greater than the cut size in the coarse stream, to the sum of the amount of material less than the cut size in the feed stream plus the amount of material greater than the cut size in the feed stream. Thus, if the feed stream analyzes 50% less than the cut size and the fine stream analyzes 95% less than the cut size and the fine stream flow rate is one-half the feed stream flow rate, then the recovery efficiency is 95%, the classification efficiency is 90%, and the quantitative efficiency is 95%. 

Data for dry screening on a 20-mm square aperture vibrating screen (8) indicate that the screen is relatively efficient, giving an apparent bypass value of 0.5%, sharpness index of 0.8, and a cut size of 20 mm. On the other hand, results (9) from a plant operating an 8 ft x 20 ft (2.4 m x 6.1 m) double-deck screen with 16 mm woven wire bottom screen deck gave an apparent bypass of 4%, sharpness index of 0.56, and a cut size of 17 mm. Data (10) for smaller... 

Analysis of this type of classifier (15) suggests that the sharpness iadex is between 0.5 and 0.6, consistent with calculated results, because the degree of turbulence can be high ia these devices (16). A DSF Dorr classifier (1.8 m x 7 m), operating at 19 strokes per minute and having a weir depth of 100 cm and a slope of 19.4 cm/m, produced a cut size equal to 240 p.m, a sharpness iadex of 0.5, and an apparent bypass of approximately 26% when the water spht was 26% (15). 

For a properly designed and operated cyclone, the sharpness iadex is constant, typically 0.6. The cut size and apparent bypass are a function of the cyclone geometry, the volumetric feed rate, the material relative density, the feed soflds concentration, and the slurry rheology. The relationship for a standard cyclone geometry, where if is the cylinder diameter ia cm and inlet area = 0.05 vortex finder diameter = 0.35 ... 

Because the cut size decreases with cyclone diameter (d g in fim = 5 in cm) and because the capacity, //s, also decreases with cyclone diameter... 

I/s = 0.022 ), high classification capacity at low cut sizes can only be achieved by feeding many cyclones of the same diameter. The manifolding of... 

Centrifuges. Sohd-bowl centrifuges have been proposed as an alternative classifying device to hydrocyclones for cut sizes below 10 pm. The results appear to be mixed (21). In one apphcation, where the cut size was 6.5 pm and the sharpness index 0.7, there was essentially no apparent bypass. However, in other apphcations operating at higher feed concentrations, the cut size ranged from 5—8 pm, but the sharpness index was between 0.3—0.5 and the apparent bypass between 10—30% or higher (22). Smaller cut sizes have also been reported (23). 

Fig. 15. Population density function for product from crystallizer with classified-fines removal. Cut size Lp = 150 /tm R = 3.7.

Subsequently, Calvert (R-19, p. 228) has combined mathematical modehng with performance tests on a variety of industrial scrubbers and has obtained a refinement of the power-input/cut-size relationship as shown in Fig. 14-130. He considers these relationships sufficiently reliable to use this data as a tool for selection of scrubber type and performance prediction. The power input for this figure is based solely on gas pressure drop across the device. 

The phenomenon is represented by Figs. 17-40 and 17-41 for Geldart-type A and B solids, respectively (see beginning of Sec. 17). The initial efficiency of a particle size cut is found on the chart, and the parametric hue is followed to the proper overall solids loading. The efficiency for that cut size is then read from the graph. 

Three parameters define the performance of a classifier. These are cut size, shaipness of cut, and eapaeity. Cut size, X50, is the size at which 50 percent of the material goes into the coarse product and 50 percent into the fine. (This should not be confused with the cutoff size, a name sometimes given to the top size of the fine product .)... 

Size selectivity is the most thorough method of expressing classifier performance under a given set of operating conditions. Cut size and sharpness can be calcinated from size-selectivity data. Size selectivity is defined by... 

Typical separation efficiency curves of an air classifier versus particle size are given in Fig. 20-14. The amount of top size in the fines may be very low, but there is typically 10 to 30 percent fines in the coarse product that is, the low end of the cui ve tends to flatten out at 10 to 30 percent. In addition, the separation at the cut size is typically a gradu cui ve. Data of this sort, which are needed to evaluate closed-circuit mill performance, are seldom available. See subsection on characteristics of size classifiers for a testing method. 

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