Dilution Factor

Several parameters have been suggested over time to describe the ratio of liquor

flows around a washer. The single most relevant parameter – which has also managed

to find its way into practical application – is the dilution factor.

Imagine a pulp washer as a black box with the flows entering and leaving, as

shown in Fig. 5.17. Depending on the feed consistency N in, a certain amount of

liquor L in enters the washer with the pulp P. At the same time, a certain amount

of liquor L out leaves the washer with the pulp at the outlet consistency N out. Wash

liquor in the amount of WL is used for washing, and the filtrate quantity F is generated.

Washer

Pulp feed

P, Nin, Lin

Pulp discharge

P, Nout, Lout

Filtrate

F

Wash liquor

WL

Fig. 5.17 Streams around a pulp washer.

The dilution factor is defined as the difference of wash liquor flow and liquor

flow leaving with the washed pulp, related to the pulp flow:

DF __

WL _ Lout

P _16_

where DF = dilution factor (t odt–1); WL = flow rate of wash liquor (t h–1); L out = flow

rate of liquor accompanying the discharged pulp (t h–1);and P = flow rate of pulp

(odt h–1).

In practice, the dilution factor is often expressed in volumetric terms (m3 t–1)

rather than as a mass ratio (t t–1). Here, we will continue to use the mass ratio, as

in this way the process engineer’s calculations are simplified. (When we return to

the field, it may sometimes be acceptable simply to substitute the mass ratio by

the volumetric term due to the small error made compared to the variability of

erratic mill data.)

The liquor flow L out can be calculated from the discharge consistency N out and

pulp production capacity P:

Lout _ P

_ Nout _ 1_ _17_

thereby providing another useful formula for the dilution factor:

DF _

WL

P _

Nout _ 1 _18_

So, why is this parameter called the dilution factor? Let us examine the overall

mass balance around the washer:

Lin _ WL _ Lout _ F _ 0 _19_

530 5 Pulp Washing

In another form, this equation reads:

WL _ Lout _ F _ Lin _20_

The left-hand term represents the numerator of Eq. (16). If the quantity of wash

liquor WL is equal to the liquor quantity leaving with the discharged pulp L out, the

filtrate volume F equals the liquor volume in the pulp feed L in. There is no dilution

of the filtrate and the dilution factor is zero.

Any wash liquor charge which increases the amount of filtrate above the

amount of liquor in the pulp feed will dilute the filtrate. In this case, the dilution

factor is positive. Any wash liquor charge which reduces the amount of filtrate

below the amount of liquor in the pulp feed will also reduce the amount of filtrate.

Then, the dilution factor is negative.

When the dilution factor of displacement washing is negative, a portion of the

contaminated liquor stays with the pulp and leaves the washer as carry-over. It is

apparent that a washing stage can reach high efficiency only at positive dilution

factors.

There is a clear correlation of washing efficiency and dilution factor in a way,

that the washing efficiency improves with higher dilution factors. There is, however,

a ceiling for the washing efficiency which is correlated to the physical limits

of liquor penetration through the pulp mat.

Regardless of its undisputable beneficial effect on washing efficiency, it is

important to note that a high positive dilution factor can substantially affect downstream

mill areas. In the case of brownstock washing, an increased dilution factor

means additional evaporation requirements;in the case of washing in the bleach

plant, the increased filtrate flow places a challenge on the hydraulic capacity of the

biological treatment plant or of the alternative filtrate purification system, respectively.

For a particular application, the favorable range of dilution factors is dependent

upon the type and specific design of the washing equipment. As a rule of thumb,

drum and belt washers are typically operated at dilution factors of 1–3 t odt–1,

while wash presses usually perform best at dilution factors of 2–4 t odt–1.

In a multi-stage washing system, it is most important to note that all washers in

the system must be operated at the same dilution factor in order to avoid overflows

or shortage of filtrate between the stages. The dilution factor of a multi-stage

system is therefore set by controlling the flow to the last washing stage.

5.4 Washing Parameters 531

532 5 Pulp Washing

Example: Calculation of wash liquor quantities in a closed, countercurrent,

two-stage washing system

The pulp production capacity, the outlet consistencies of the two washers,

and the desired dilution factor are known:

Pulp production capacity, P = 25 odt h–1

Washer no. 1 discharge consistency, N1,out = 11%

Washer no. 2 discharge consistency, N2,out = 15%

Dilution factor, DF = 2.0 t odt–1

In order to determine the wash liquor quantities, we first calculate the

amounts of liquor leaving the washers with the pulp:

L 1_ out _ P

N 1_ out _ _ 1__ 25

_0_ 11 _ 1__ 202 t h_1

L 2_ out _ P

N 2_ out _ _ 1__ 25

_0_ 15 _ 1__ 142 t h_1

Then, the wash liquor flow rate to the first washer amounts to

WL 1 _ L 1_ out _ DF _ P _ 202 _ 2_ 0 _ 25 _ 252 t h_1

and the wash liquor flow rate to the second washer is

WL 2 _ L 2_ out _ DF _ P _ 142 _ 2_ 0 _ 25 _ 192 t h_1

Note that in a closed countercurrent washing system, the first washer

must be operated with a much higher wash liquor quantity than the second

washer, simply because its discharge consistency is lower.

5.4.3

Дата добавления: 2015-10-21