Reduced grade efficiency

If 20% of the the total volume of the feed reports to the underflow the reduced grade efficiency is  

Particle diameter, pm Mass in range Mass flow in range Grade effidouy  

Other conditions are inlet and overflow concentrations, 20.3 and 7.6 kg m , and rates 2.02xl0 and 1.81x10 m s respectively. Therefore, mass flow rate inlet and overflow was 4. lOx 10 and 1.38x10 kg s req ectively, and flow q Ht was 0.104. 

---

For separators which operate with Rf > 0, the grade efficiency curve does not start at G = 0% (Figure 11JB). This is because the separator operation always gives a minimum efficiency almost equal to the flow ratio Rf. The reduced grade efficiency G may be obtained in the same way as the reduced total efficiency E ... 

A chart showing the reduced grade efficiency versus cell size starts in the origin, and the cell size corresponding to 50% reduced grade efficiency is known as the reduced cut size dso (Figure 11.6). 

Reduced grade efficiency curve and reduced cut size (c/50). 

If, in order to practically assess the performance of solid-fluid separators, a reduced grade efficiency curve is used, the particle size which gives 50% efficiency in such a curve is called the reduced cut size and is represented by x o-The maximum attainable efficiency related to particle size would be that minimum particle size with 100% probability of being reported to the underflow. Graphically, by extrapolating the end part of the curve to the horizontal axis, such size will be obtained. It has been proved that in practice, the maximum of the efficiency is around 98%, and the minimum size corresponding to this efficiency is represented by Xgg and known as the approximate limit of separation. 

Table 10.2 presents the particle size distributions for the overflow and underflow through the hydrocyclone. Therefore, Equation 10.28 would be the appropriate to derive the grade efficiency. Since the separation was carried out in a hydrocyclone, and this type of device normally presents a dead flux effect previously described. Equation 10.29 should be used to derive the reduced grade efficiency. Carrying out the proper computations using the tabulated data and the equations mentioned. Table 10.3 is obtained. 

Following a procedure like the one described in Example 9.2, derive the reduced grade efficiency curve for the separation process. 

Figure 3.9 Plots of G(x) from Table 3.2, columns 3-6 and the reduced grade efficiency G (x) from equation 3.34...

This section describes a new and simple experimental method for obtaining the reduced cut size and the rest of the reduced grade efficiency curve of an operating separator. The method relies on feeding a known and fiiUy characterized slurry to the separator under test, and on measuring only two solids concentrations (in the feed and in the overflow), one static pressure differential (or some other flow rate-dependent variable) and the slurry temperature. These measurements are best done and logged by a personal computer, and, for hydrocyclones, have to be repeated at two different pressure settings. 

This forces the curve to pass through the origin as indicated by the second curve, G (x) in Figure 3.15. The reduced grade efficiency curve can, for some separators, be approximated by an analytical expression such as the one used in this method—see equation 3.51 in the following section. 

The reduced grade efficiency curves of separators can often be fitted by a cumulative log-normal function in the following form ... 

In the above equation, the response of the separator to the operating conditions, in terms of the cut size x g and the standard geometric deviation of the reduced grade efficiency CTs, can be found experimentally by using a feed of a known particle size distribution (described by Xg and a-g in equation 3.53 above), and by monitoring the two concentrations c and Cq. 

Grade efficiency (efficiency of separation for particle size x) Reduced grade efficiency defined as G x) = [G(x) — Rf]/(1 — R ) Vortex finder length Constant... 

On the basis of the available experimental evidence it can be concluded that for a given cyclone design and low feed solids concentrations (say below 1% by volume) the shape of the reduced grade-efficiency curve is reasonably constant. At higher solids concentrations, it becomes dependent on the feed material and experimental measurement may be necessary. Alternatively, with smaller diameter cyclones, the log-normal law with a measured geometric standard deviation may also be used. Knowledge of the cut size is of course necessary in any of these cases to obtain the fiiU curve. 

Geometric standard deviation of the reduced grade efficiency curve of the cyclone Performance criteria Total coarse recovery by mass, r Total reduced mass recovery, r Actual cut size, xso Reduced cut size,... 

The last point needs explaining a little further. There are two reasons for deriving the sharpness index from the reduced grade efficiency curve rather than from the actual one. Firstly, the sharpness of cut is always to some degree affected by Rf and this way the effect is removed. Secondly, as can be seen later, the sharpness index for the actual grade efficiency curve sometimes cannot have a value because the whole of the curve may be greater than 25% and X25 cannot be determined. 

Figure 16.4 The reduced grade efficiency cun/es of single-stage, two-stage and three-stage series on overflow, plotted against dimensionless particle size...

The last conclusion is qualitatively the same as that for the overflow series in that they both sharpen the cut. Even quantitatively, when using a symmetrical sharpness index derived from the reduced grade efficiency curves, one obtains very much the same results for the underflow series as contained in... 

Figure 16.16 Reduced grade efficiency of underflow series with recycles compared with that of a simple underflow series (both plotted against dimensionless particle size)...

Separator specified by the flow ratio and a log-normal reduced grade efficiency... 

The solid-liquid separation in hydrocyclones is never complete, because there is always liquid discharging with the solids through the underflow. The term separation efficiency used for the hydrocyclone is usually defined for measuring the capability of the hydrocyclone of separating the solids from the feed into the underflow. There are a number of different terms for the separation efficiency used in the literature. They include total efficiency, reduced total efficiency, grade efficiency, reduced grade efficiency, and cut size. 

---