Fiber Passage and Reject Thickening

The essential part of the screening operation occurs in the annular gap between

the rotor and the screen basket.

Both a mixed-flow model and a plug-flow model have been used to describe the

flow pattern in a pressure screen [1,6]. Here, we will focus on the plug-flow model

because it is more flexible and seems to describe the actual flow regime in a pressure

screen more accurately.

The plug-flow model assumes ideal radial mixing between the rotor and the

screen basket without backmixing in axial direction. Let us define a parameter

called passage ratio, P:

P _

cs

cz _2_

where cs is the solids concentration in the stream through a screen aperture (kg m–3)

and cz is the solids concentration of the stream just upstream of the aperture at a

position z [1].

The passage ratio is a characteristic parameter of the screening system, which is

influenced by many variables including screen plate and rotor design, screen operating

conditions and pulp grade. P is best determined individually for a given

screening application based on field measurements. A passage ratio of zero

means that all the solids are retained on the screen and will be rejected. At P = 1,

the concentrations in the accept and reject are equal to the feed concentration and

there is no separation.

z = 0

z = L

z

dQz, P · cz

Rotor

Screen basket

Qz, cz

Qz- dQz, cz - dcz

Annular volume element

Fig. 6.5 Flows and concentrations around an annular differential volume element.

Considering Fig. 6.5, the mass balance for pulp over the annular differential element

between the screen plate and the rotor gives:

Qz cz _ dQz P cz _ _ Qz _ dQz _ _ cz _ dcz _ _ 0 _3_

6.2 Screening Theory

where Qz stands for the total flow rate (m3 h–1) entering the element in axial direction

and dQz for the flow rate leaving in radial direction, respectively.

Equation (3) can be rewritten to give:

dcz

cz _ _ P _ 1_

dQz

Qz _4_

In a first approach, it is assumed that the fiber passage ratio P is independent

of the flow rate and consistency. Then, Eq. (4) can be integrated using the overall

screen boundary conditions as per Fig. 6.1; that is, cz = cF and Qz = QF for z = 0, and

cz = cR and Qz = QR for z = L. L is the length of the screening zone.

cR

cF _

QR

QF _ __ P _1_

_5_

Note that the concentrations may relate to the totality of pulp as well as to a

fraction only, for example, to shives. Then, different passage ratios will apply for

total pulp and shives. When the concentrations in Eq. (5) refer to total pulp concentrations,

the quotient cR / cF is defined as the reject thickening factor, T. QR / QF is

termed the volumetric reject ratio, Rv. With these definitions we obtain a relationship

between the thickening factor, total fiber passage ratio and volumetric reject

ratio:

T _ R _ P _1_ v _6_

The mixed-flow model of pressure screening assumes a completely mixed volume

inside the screen. In the mixed-flow model, the feed entering at the pulp concentration

cF is immediately mixed into the volume inside the screen which is at

the reject concentration cR. All accept passes through the screen apertures at the

accept concentration cA. The overall mass balance, pulp mass balance and passage

ratio of this system are:

QF _ QA _ QR _ 0 _7_

QF cF _ QA cA _ QR cR _ 0 _8_

P _

cA

cR _9_

Equations (7) to (9) can be combined and rewritten using the definitions of the

thickening factor and volumetric reject ratio to give the expression for the thickening

factor in the mixed-flow model:

T _

P _1 _ Rv __ Rv _10_

6 Pulp Screening, Cleaning, and Fractionation

While the mixed-flow model seems worth considering for screens with open

rotors, it has proven to be second to the plug-flow model at lower reject rates for

virtually any screen configuration. Figure 6.6 shows, graphically, the comparison

of the reject thickening behavior predicted by the mixed-flow and plug-flowmodels.

0.5

1.0

1.5

2.0

2.5

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

Reject thickening factor, T

Volumetric reject ratio, Rv

Plug-flow model

Mixed-flow model

Fig. 6.6 Reject thickening in a pressure screen predicted by the mixed-flow

and plug-flow models at a constant fiber passage ratio of P = 0.7.

By examining the fit between experimental data and the curves calculated from

the plug-flow model in Fig. 6.7, it can be seen that the plug-flow model describes

the thickening behavior of an industrial screen quite well. Note that reject thickening

increases dramatically at reject ratios smaller than 10%, and that a lower passage

ratio generally leads to higher thickening.

Earlier, it was assumed that the fiber passage ratio is constant along the screening

zone, which implies that the single fibers do not interact with each other. This

holds true only for very low consistencies and, to a certain degree, for fiber suspensions

under high shear forces in a turbulent environment. Figure 6.8 shows

that the fiber passage ratio in a commercial pressure screen is fairly constant over

the first two-thirds of the screen length, but then can fall significantly at the reject

end of the screen [4].

6.2 Screening Theory

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0% 10% 20% 30% 40% 50%

Reject thickening factor, T

Volumetric reject ratio, Rv

1.8 mm holes

0.4 mm slots

Fig. 6.7 Example of reject thickening as a function of the volumetric reject ratio.

Comparison of experimental data [6] with calculation results from the plug-flow

model; P = 0.72 for 0.4-mm slots, P = 0.55 for 1.8-mm holes.

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Fiber passage ratio, P

Normalised length of screening zone, z/L

Bump rotor

Step rotor

Fig. 6.8 Example of fiber passage ratio as a function of the screen length

and rotor geometry;smooth hole screen, eucalyptus pulp, Rv = 10% [4].

Figure 6.9 illustrates a typical consistency profile over the length of a pressure

screen. While the consistency of the accept remains fairly constant, the consistency

of the pulp flow passing along the screen increases disproportionately

towards the end of the screening zone. The profile explains why screens tend to

blind from the reject end.

6 Pulp Screening, Cleaning, and Fractionation

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.2 0.4 0.6 0.8 1.0

ed consistency, cz/cF

ed length of screening zone, z/L

Feed

Rejects

Accepts

Normaliz

Normaliz

Fig. 6.9 Example of consistencies as a function of the screen length;

smooth hole screen, bump rotor, eucalyptus pulp, Rv = 10% [4].

6.2.4

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