Fractionation Index

In most fractionation applications it is important to remove as high a portion of

the one fraction while removing as little a portion as possible from the other fraction.

Therefore, the quality of the fractionation is characterized by the removal

functions of both fractions.

This can be quantified by the introduction of a fiber fractionation index, U. In

case of length-based fractionation, U is defined as the average e (l) for long fibers,

EL, minus the average e (l) for short fibers, ES [9]:

U _ EL _ ES _29_

where EL is basically the long fiber removal and ES is the short fiber loss. Unlike

removal efficiency, the fractionation index is penalized by removal of the fraction

which ought to be accepted, in the above case by the fraction of short fibers. U = 1

applies when the reject stream is composed only of long fibers and the accept

stream is composed only of short fibers – that is, perfect separation. In addition,

U = 0 means that the fiber length distribution remains unchanged – that is, no

separation.

The fractionation index increases as the hole size is reduced below the targeted

marginal fiber length, but deteriorates again as the hole size becomes smaller

than about half the marginal fiber length [9]. At similar reject thickening, the fractionation

index is almost twice as high for holed screen plates as for slotted ones [8].

The plug-flow model delivers a fractionation parameter a which is defined in

terms of the passage ratios of long fibers, PL, and short fibers, PS [10]:

a _ 1 _

PL

PS _30_

6.6 Separation Efficiency 591

Since the passage ratios are independent of the reject ratio, a reflects the performance

of a specific screen and can be used to anticipate the effect of changes in

reject ratio. Applying Eq. (25) to long and short fibers and eliminating Rv yields

EL _ E 1_a

S _31_

Both the fractionation index and fractionation parameter are plotted within the

field of long fiber removal versus short fiber loss in Fig. 6.25. The solid lines calculated

for different values of a represent the curves on which a screen’s operating

point will move. For a given screen, the optimum point for fractionation lies

where the constant-a curve is tangent to a line of constant fractionation index.

Typical values of a are in the range of 0.4 to 0.7 [10].

0%

20%

40%

60%

80%

100%

0% 20% 40% 60% 80% 100%

Long fiber removal, EL

Short fiber loss, ES

0.0

0.4

0.7

Φ = 0.8 0.6 0.4 0.2 0.0

α = 0.9

Fig. 6.25 Screen operating curves (solid lines of constant a)

and fractionation index (dashed lines of constant U) plotted

in a field of long fiber removal versus short fiber loss [10].

6.7

Screening and Cleaning Applications

6.7.1

Дата добавления: 2015-10-21