Screening and Cleaning Efficiency

The very basic definition of the separation efficiency E is

E _

amout of debris in reject

amount of debris in feed _22_

Traditionally, this equation is employed generally for screens and more or less

exclusively for cleaners. There are some limitations to Eq. (22), however. E turns

unity when all debris is rejected, irrespective of the reject ratio. Likewise, the

operation of merely splitting a feed flow by a plain pipe tee yields a separation

efficiency larger than zero. In total, E disregards the good fiber loss with debris in

the reject stream.

The efficiency of a screen is usually plotted against the reject ratio due to its

overwhelming influence on the efficiency. Nelson has introduced a screen performance

parameter, the screening quotient Q, which can be easily determined by

just two analyses [25]:

Q _ 1 _

cd _ A

cd _ R _23_

where cd,R = mass concentration of debris in oven-dry reject (kg kg–1); and

cd,A = mass concentration of debris in oven-dry accept (kg kg–1).

588 6 Pulp Screening, Cleaning, and Fractionation

The screening quotient becomes zero for the pipe tee, and unity for ideal separation.

When applied to measurements from a given screen, Q was found to vary

only insignificantly over the range of industrially practiced reject ratios. Under

consideration of the mass balance over the screen, the screening efficiency is

obtained by:

E _

Rm

1 _ Q _1 _ Rm _ _24_

where Rm is the mass reject ratio – that is, the oven-dry reject mass divided by the

oven-dry feed mass. Figure 6.23 shows the screening efficiencies calculated for

different values of Q over the mass reject ratio. Since the performance of a given

screen is characterized by a particular Q, the screen’s operating point will, in theory,

move along a curve of constant Q. Typical values of Q for shives are 0.9 and larger.

0%

25%

50%

75%

100%

0.0 0.2 0.4 0.6 0.8 1.0

Efficiency, E

Mass reject ratio, Rm

0.0

0.5

0.7

0.9

Q = 1.0

Fig. 6.23 Screening efficiency as a function of the mass reject

ratio and screening quotient Q.

Using their plug-flow model, Gooding and Kerekes [1] have derived the screening

efficiency by combining Eqs. (5) and (22):

E _ RPc

V _25_

where Rv and Pc are the volumetric reject ratio and passage ratio of the contaminants,

respectively. Figure 6.24 illustrates screening efficiencies calculated for different values

of Pc over the volumetric reject ratio. Again, the performance of a given screen is

characterized by a particular Pc, and the screen’s operating point will move, in theory,

along a curve of constant Pc. Typical values of Pc for shives are 0.1 and smaller.

6.6 Separation Efficiency 589

0%

25%

50%

75%

100%

0.0 0.2 0.4 0.6 0.8 1.0

Efficiency, E

Volumetric reject ratio, Rv

1.0

0.5

0.3

0.1

Pc = 0.0

Fig. 6.24 Screening efficiency as a function of the volumetric reject

ratio and debris passage ratio Pc.

When comparing Fig. 6.23 with Fig. 6.24, the constant- Q curves expose a steeper

inclination at low reject ratios than the constant- Pc curves. This hold true even

after correction between mass reject ratio and volumetric reject ratio. The superiority

of the plug-flow model over the mixed flow model suggests that Eq. (25) is

more appropriate to describe a screen’s performance than Eq. (24) [10].

It must be remembered that all efficiencies calculated from Eqs. (22), (24) and

(25) above are actually contaminant-removal efficiencies. Each of these becomes

100% when the reject ratio is unity – a case which is of no industrial relevance.

Clearly, the economy demands that the amount of good fibers lost with the reject

from a separator is kept at a minimum. Therefore, any contaminant removal efficiency

calculated as per these equations must always be evaluated in conjunction

with the loss of good fibers.

6.6.2

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