Drainage

Typical pulp washing operations involve the process steps of initial dewatering,

actual displacement washing, and final thickening. Drainage plays a fundamental

role in all of those process steps. It is driven by a pressure difference across the

pulp mat which is created by applying a fluid pressure or vacuum, or by putting

mechanical pressure on the pulp mat.

The liquor flow through a pulp mat is generally presumed to follow Darcy’s law.

This law describes how, in a laminar flow regime, the flow rate through porous

media is determined by the pressure gradient and permeability:

∂ V

∂ t _ _

K A

l

∂ p

∂ x _1_

where

∂ V /∂ t = volumetric flow rate of the filtrate (in m3 s–1); K = permeability (in m2);

A = filtration area (in m2); l = dynamic viscosity of the filtrate (in Pa.s);and ∂ p /

∂ x = pressure gradient across the fiber web (in Pa m–1).

The permeability K as a qualitative property describes the ease with which a

fluid passes through the porous fiber web. Under the simplifying assumption of

constant parameters, the very basic equation for the drainage velocity v (m s–1)

through a fiber web is [2]:

v _

A

dV

dt _ _

K D pt

l d _2_

where D pt is the total pressure drop across the fiber web and filter medium (Pa),

and d is the thickness of the fiber web (m).

We can see that the drainage velocity increases linearly with the applied differential

pressure D pt. On the other hand, it decreases as the viscosity g goes up and

as the web gets thicker. Remember that the viscosity of a liquor increases with

higher dissolved solids concentration, whereas it decreases with higher temperature.

Hence, drainage works better at lower dissolved solids and at higher temperature.

Numerous approaches have been made theoretically to derive the permeability,

K. An overview over porosity–permeability functions is provided in Ref. [3]. One

of the most frequently used correlations is the Carman–Kozeny relationship [4]:

K _

e3

k _1 _ e_2 S 2

F _3_

where

e = effective porosity of the fiber web (i.e., the volume fraction of the free flow

channels); k = the Kozeny constant;and SF = surface area of the free flow channels

per unit volume (in m2 m–3).

5.2 Pulp Washing Theory 513

It is important to note that, for the purposes of drainage considerations, the

effective porosity must not be mixed up with the total porosity – that is, the web

volume not occupied by fiber solids. This is because the total volume of flow paths

available for liquor to pass through the fiber web is dramatically smaller than the

total filtrate volume within the web. A substantial amount of filtrate is trapped

inside the fiber walls and between the fiber bundles, and is therefore not relevant

to the drainage process. Both the effective porosity and the specific surface area

are difficult to access. They are also fundamentally influenced by surface forces

and hence by the presence of liquor components such as surfactants [5].

0.0

0.2

0.4

0.6

0.8

1.0

100 200 300 400 500

Porosity, å

Fibre concentration, kg/m.

Porosity

Specific surface area

Specific surface area, m./m.

Fig. 5.2 Porosity and specific surface area as a function of the

fiber concentration for a bleached softwood kraft pulp [6].

100 200 300 400 500

Permeability, K x 1012 m. Fiber concentration, kg/m

.

Fig. 5.3 Permeability as a function of the fiber concentration for a bleached softwood kraft pulp [6].

514 5 Pulp Washing

5.2 Pulp Washing Theory

Figure 5.2 illustrates that the porosity and specific surface area of a pulp fiber

web are dramatically reduced as the fiber concentration increases. The effect on

permeability is even more pronounced (Fig. 5.3).

The specific drainage resistance a (m kg–1) is defined by:

a __

d

K

A

W _

K c _4_

where W = mass of oven-dry fibers deposited on the filter medium (kg), and

c = concentration of fibers in the mat (kg m–3).

By combining Eqs. (3) and (4), we can relate the drainage resistance to the structural

properties of the fiber web:

a _

k _1 _ e_2 S 2

F

c e3 _5_

The specific drainage resistance a is the fundamental pulp mat parameter that

characterizes the drainage behavior of a specific pulp. As expected from the permeability

curve, the drainage resistance increases massively with the fiber concentration

(Fig. 5.4).

1E+09

1E+10

1E+11

1E+12

100 200 300 400 500

Specific drainage resistance, m/kg

Fiber concentration, kg/m.

Fig. 5.4 Specific drainage resistance as a function of the fiber

concentration for a bleached softwood kraft pulp (calculated

from permeability data by [6]).

The specific drainage resistance also rises with the beating degree. This has

been explained by the higher levels of fibrillation and fines (short fibers and fiber

fragments) which result in a larger specific surface area, SF,as well as in higher

packing (i.e., reduced porosity e). Similarly, mechanical pulps show higher drai-

5 Pulp Washing

nage resistance than chemical pulps because of the mechanical pulps’ larger fines

fractions, and hardwood pulps have higher drainage resistance values than softwood

pulps due to the presence of shorter fibers. Yet the differences between

hardwood and softwood fade away when the pulps are beaten and the influences

of increasing fibrillation and fines content supersede the effect of different fiber

lengths [7].

The permeability of fiber webs was found to be fairly independent of the specific

surface load W/A over the range applicable to pulp washing [8]. However, the specific

drainage resistance may increase with the specific surface load if a pulp contains

a larger amount of fines, which are washed through the outer layers of the

web and accumulate near the filter medium.

With the specific drainage resistance a, the drainage velocity equation [Eq. (2)]

can be rewritten in the form:

v _ _D pt

la WA

_6_

Further extension to include both the drainage resistance of the fiber web and

the resistance of the filter medium leads to [7]:

v _ _D pt

l a WA

_ _ Rm _ _7_

where Rm is the filtration resistance of the filter medium (m–1). The term a W/A

represents the filtration resistance of the fiber web.

As long as the filter medium is clean, its filtration resistance Rm depends on the

design and structure of the wire. However, in industrial applications, Rm may

increase to a multiple of the clean value if fines are present which tend to plug the

wire.

Another important factor influencing the drainage characteristics is the amount

of entrained air in the pulp fed to the washer. As the sheet forms, air bubbles are

trapped in the fiber network, and these block certain liquor flow paths in the web.

As a consequence, it takes longer for the liquor to pass through the remaining

free flow paths. Experiments with mill pulps have shown that air entrainment can

be responsible for increasing the drainage time by a factor of 3 to 4 [9].

In summary, good drainage is achievable by applying high differential pressure;

limiting the mat thickness;keeping filtrate viscosity low, mainly by operating at

higher temperature;controlling the fines content in the pulp and wash liquor;

controlling the entrained air in the feed stock;and keeping the screen/wire clean.

5.2 Pulp Washing Theory

5.2.3

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