Overall Separation Efficiency

The three particle fractions we are concerned with in cyclone operation are the feed, the captured (or collected or miderflow ) and the overflow (or emitted or lost) fractions. Let us represent their masses (or mass flow rates) by the symbols M/, cyclone is  

The overall separation efficiency t) is simply calculated as the mass fi-action of the feed solids captured by the cyclone  

The efficiency is determined by collecting samples and weighing two of the fractions. 

The overall efficiency is usually what counts the most in the context of an industrial process. However, it is not a good measure for characterizing the intrinsic separation performance of a particular cyclone, since, for example, it tells us nothing about the separation capability of the cyclone as a function of particle size. 

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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. 

Figure 38 (Liu et al., 1990b) shows a four-inlet cyclone. Solids tend to be densified around the inlet region as the vertically entering solids-laden streams are suddenly diverted toward tangential flow in a horizontal plane. At inlet velocities exceeding 8.5 m/s, the overall separation efficiency for a typical FCC catalyst was found to be consistently above 99%, as shown in Fig. 39. This design, however, resulted in relatively high pressure drop unless the inlets were appropriately enlarged. The efficiency and pressure drop of this type of multi-inlet cyclones could be approximated by modifying the single-inlet cyclone expressions (Kou, 1987 Shi et al., 1987) ...

Also, acoustic forces cannot be increased arbitrarily without the risk of reducing cell viability, or causing cavitation in the suspension, which may decrease the overall separation efficiency and cause cell destruction. 

Determine the overall separation efficiency for the three experiments nm above, following procedure described in Example 9.2. 

When Equation 10.120 holds, the cut size and the overall separation efficiency, in both cases, should be the same. Equation 10.120 can be used for sizing centrifuges from laboratory tests, or for predicting capacities of existing machines. 

Experience shows that the approximate method (Eq. 3.2.7) comes out surprisingly accurate, even when the cut of the cyclone is far from sharp. This has very practical implications and is often used when one just needs a rough estimate of overall separation efficiency. 

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 ... 

Here, we will determine the overall separation efficiency for saltation conditions, i.e. when Cg > Col- This efficiency includes the efficiency due to saltation in the inlet and the efficiency due to classification in the inner vortex. A portion of the incoming solids that is not collected by the former is collected by the latter, so that the total efficiency becomes (see also Chap. 9) ... 

Inspecting Eq. (3.2.2) shows that the overall separation efficiency, 77, can be calculated from the mass flows of solids at any two of the three sampling points. If also the solids mass flow at the third is determined, one can check on the material balance by way of Eq. (3.2.1). 

Let us answer the last question first. We saw in the early chapters that the distribution that gives us the most direct information about cyclone performance and that allows us to convert between cut size and overall separation efficiency is the mass distribution. If the particle density is independent of particle size, this mass distribution is the same as the volume distribution. This distribution is of overriding importance to our cyclone studies. 

In this section we will compute the grade-efficiency curve and overall separation efficiency at low inlet loadings (co < Col)—the classification-only case. 

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