Grade-efficiency

The separation characteristics of a cyclone are best described by the so-called grade-efficiency curve or GEC, which is the separation efficiency for a given feed particle size or (narrow) range of particle sizes. 

If the differential volume or mass density distributions of the charge dust, the captured and overflow (or emitted) fractions are //(x), fc(x) and fe x), respectively, the mass balance for particles with diameter between x —I f2 dx and x+l/2 dx is  

To help make this a little less abstract, let us approximate the particle size differential with a finite, yet small value for dx, and also substitute in some numbers obtained from a hypothetical cyclone performance measm-e-ment Thus, let us assume we determine (through measurements) that 10% of the feed solids (by wt. or vol.) lie within a 5-micron (Ax) band centered about some particular particle size, x. In addition, the measurements show that 80% of the particles within this particular 5-micron band are collected and that they comprise 6% of the collected material. Likewise, 30% of the 

we see that the cyclone brings about the mathematical equivalent of a partition function, i] it partitions the particles in any given size range. Ax, into the underflow and overflow streams. It does this on the basis of the forces acting on the particles within the separation zone of the cyclone. 

Equation (3.2.3) can be integrated term-by-term to give a mass balance for the dust with particle size less than a given size x  

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Fig. 7. Cyclone generalized grade-efficiency curves. The soHd line is for the Lapple cyclone dimension ratios given in Figure 9. The dotted line is theoretical...

Cyclone Efficiency. Most cyclone manufacturers provide grade-efficiency curves to predict overall collection efficiency of a dust stream in a particular cyclone. Many investigators have attempted to develop a generalized grade-efficiency curve for cyclones, eg, see (159). One problem is that a cyclone s efficiency is affected by its geometric design. Equation 15 was proposed to calculate the smallest particle size collectable in a cyclone with 100% efficiency (157). 

This equation is for Eigure 9 cyclone dimension ratios. The term the effective number of spirals the gas makes in the cyclone, was found to be approximately 5 for Lapple s system (134). The soHd line grade-efficiency curve of Eigure 7 is also used with Lapple s cyclone, which is a somewhat taller, less compact cyclone than many commercial designs. 

Practically all cyclone performance data have been related to a present cyclone set of geometric ratios. One model for cyclone grade-efficiency curves has been tested against reported commercial cyclone efficiencies (159). A good fit was obtained. 

The grade efficiency T of most collectors can be expressed as a function of the aerodynamic particle size in the form of an exponential equation. It is simpler to write the equation in terms of the particle penetration Pf (those particles not collected), where the fractional penetration = 1 — T, when T is the fractional efficiency. The typical collection equation is... 

If the same size particle d is located at an initial starting radius less than r given by Eq. (18-110) it is assumed to escape from being captured by the bowl, whereas it would have been captured if it had been at an initial radius greater than / Assuming that the number of particles with size d is uniformly distributed across the annular pool, the recoveiy Rec (known also as grade efficiency) is the differential of the cumulative recovery Z = 1 — Y, with Y given in Eq. (18-92) for particles with size d, as the ratio of the two annular areas ... 

It should be noted, however, that the cut size is an idealization. In practice perfect separation does not occur some smaller particles than expected will be present in the underflow whilst some larger than predicted occur in the overflow leading to a blurring of the separation in a grade efficiency curve (Figure 4.23). 

A typical plot of efficiency versus particle diameter is shown in Fig. 12-8. This is called a grade efficiency curve. Although the efficiency varies with the particle size, a more easily determined characteristic is the cut diameter (d50), the particle size that is collected with 50% efficiency. 

Although this predicts that all particles larger than dm will be trapped and all smaller particles will escept, the actual grade efficiency depends on particle size because of the variation of the inward radial velocity of the gas. 

Leith and Licht (1972) incorporated the effect of turbulent reentrainment of the solids in a solution of Eq. (12-42) to derive the following expression for the grade efficiency ... 

Thus, the grade efficiency of the similar cyclone can be constructed from the grade efficiency of the known (tested) cyclone. 

Grade-efficiency curve, in sedimentation design methods, 22 57... 

In processes where classification or separation of particles is required, the efficiency of separation will be a function of one or more distributed properties of the particles. The function which describes the efficiency with which particles are separated by size (d) is usually termed the grade efficiency, G(d). For particles in a narrow size interval between d and d + Ad, G(d) is defined as the mass ratio of such particles in the underflow to that in the feed. The overall separation efficiency E corresponds to the particle size d for which G(d) equals E. 

The grade efficiency reflects the properties of the particles exploited in the separation. It is influenced by the nature of the fluid/solid system, and by the operating conditions which determine the magnitude of the separating effect, and the period during which particles are subjected to it. Such details should, therefore, accompany any experimental data on G(d). The concept is widely applied to separations using hydrocyclones as discussed in Section 1.5.4. 

A typical grade efficiency curve, shown in Figure 1.10, rises from some minimum value, at small particle size, in a sigmoidal manner to a value of 1, at a size usually defined as dm. ) and G(d) = 1. 

Figure 1.10. Typical grade efficiency curve for a particle separation...

Grade efficiency data are usually derived from experimental trials which provide sufficient information to allow the material balance to be closed for particles of all sizes. Sufficient information for determination of G(d) is provided by a combination of any three of the following four system properties E, Ff(d), Fu(d), F0(d), the remaining property being determined by the material balance. Size distribution data for primary particles, rather than floes or aggregates, are required for the inventory. 

The behaviour of suspended particles in a centrifugal field is considered in detail in Chapter 3. It is, however, convenient to consider here the extension of the preceding treatment of grade efficiency to centrifugal separators. 

In the case of a tubular centrifuge with a free liquid surface at radius r, operating at steady state, the grade efficiency is related to the radius rd which divides the area available for fluid flow (in the axial direction) such that all particles of minimum size d introduced at radii r > rd with the feed, reach the centrifuge wall within the residence time (tR) of the fluid in the equipment. The remainder of the particles (introduced at r < rf) become distributed with increasing non-uniformity in the axial direction across the entire area for flow. rd is a function of the separating power, the residence time and the fluid/particle... 

Figure 1.55. Typical grade efficiency curves for cyclones and a self-induced spray wet collector 53)...

The experimental results reported in this paper demonstrate the ability of a flat-bottom hydrocyclone to separate the coarse fraction of ammonium sulfate crystals from a slurry which contains crystals of a wide size range. It appears that the grade efficiency curve, which predicts the probability of a particle reporting to the underflow of the cyclone as a function of size, can be adjusted by a change in the underflow diameter of the hydrocyclone. These two observations lead to the suggestion to use hydrocyclone separation to reduce the crystal size distribution which is produced in crystallisers, whilst using a variable underflow diameter as an additional input for process control. 

This paper presents the grade-efficiency curves of a 75 n flat bottom cyclone (RWB 1613) provided by the Amberger Kaolin Werke (AKW). It is tested for the ammonium sulfate-water system for both fines removal and product classification. Its results will be compared with the results for fines removal obtained when using an... 

Definitions. The performance of a hydrocyclone is generally characterised by means of a grade efficiency or Tromp-curve which is the fractional mass recovery expressed as a function of particle size. 

From these grade efficiency curves the nominal cut size, that is the size with an efficiency of 50% and the classifier imperfection can be determined. The imperfection is defined by ... 

The shape of this classification function is identical to the shape of the grade efficiency curve for product classification but the ordinate values are changed. 

A typical grade efficiency curve for the product classification step is given in Figure 4. A value of nearly 100 percent is attained at large sizes, whereas normally a value equal to or larger than the so-called dead flux is attained at small sizes. This is caused by the diluted discharge of the coarse fraction. It represents the minimum amount of residual fines in the product after one separation stage. 

In fines removal, both the cut size and the grade efficiency are difficult to assess because of the limited accuracy of the sieve analysis technique and the problems Involved in the determination of the solids concentration in the overflow. For a. 65 m cyclone, whilst using a 20 mm vortexfinder diameter, an apex diameter of 16 mm and a feed flow of 1.6 1/s, solids recovery is over 99 % This recovery corresponds to a cut size between 50 - 100 pm. Typical distributions of size by weight, for the feed flow as well as the overflow are shown in Figure 5 Results are summarised in Table 2. 

Figure A typical grade efficiency curve for the product classification step.

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