Wood species Dry density

Qdc

[g cm–3]

Void volume

VV

[cm3 g–1]

Void volume fraction

Fvoid

Aspen, Populus tremula 0.37 2.05 0.76

Spruce, Picea abies 0.43 1.67 0.72

Pine, Pinus silvestris 0.47 1.47 0.69

Beech, Fagus silvatica 0.68 0.82 0.56

Esh, Fraxinus excelsior 0.65 0.88 0.58

Maple, Acer pseudoplatanus 0.59 1.04 0.61

The density (qwc and the volume (Vwc) of wet chips can be calculated according

to equation (28) and (30):

_ wc _

mwc

mdc _

_ dc

DS _28_

_ dc

Vwc _

mwc

Pwc _

mwc _ DS

Pdc _29_

The volume of the wood solids can be calculated by knowing the mass of the wet

wood, the dry solids content and the density of the wood solids:

Vws _

mwc _ DS

_ ws _30_

Thus, the void volume is just the difference between the volumes of the wet wood

and the wood solids:

VV _ VWC _ Vws _31_

Knowing the density of the initially present water, q H 2 O _ i, the volume of this water,

V H 2 O _ i, in the chip can be easily computed:

VH 2 O _ i _

mwc __1 _ DS _

_ H 2 O _ i _32_

The change in the water volume can be estimated by considering the density of

the water at the temperature T, q H 2 O _ T:

VH 2 O _ T _ VH 2 O _ i _

_ H 2 O _ i

_ H 2 O _ T _33_

128 4 Chemical Pulping Processes

During penetration, additional water or aqueous solution is introduced into the

void system of the chips. The volume of the penetrated water, V H 2 O _ P, is then calculated

by:

VH 2 O _ P _

mH 2 O _ P

_ H 2 O _ T _34_

where m H 2 O _ P is the weight of the water penetrated into the chips.

The degree of penetration prior to impregnation, P0, is estimated according to:

P 0 _

VH 2 O _ i

VV _ 100 _35_

After impregnation with e.g., water, the degree of penetration, P, changes to:

P _

VH 2 O _ T VH 2 O _ P _ _ VV _ 100 _36_

Example: A simple example illustrates the way of calculatory the degree of penetration.

What is the degree of penetration and the density prior (300 °K) and after

impregnation (373 °K) of aspen chips with 55% dry solids content (DS) and 0.37 t/

m3 dry density (qdc)?

Impregnation takes place at 373 °K and increases the moisture content, MCw, to

0.65. The densities of water at 300 °K are 0.997 t/m3 and 0.959 t/m3, respectively.

(a) Prior impregnation:

_ wc _

0_37

0_55 _ 0_67 t_m3

mwc _

0_55 _ 1_82 t_t dry solids

One ton of dry chips contains 0.82 ton of water at 55% dry solids content.

The void volume, Vv, is calculated according to equation:

Vv _ Vwc _ Vws _

1_82

0_67 _

1_53 _ 2_06m3_t dry solids

The degree of penetration prior impregnation, P0, at 300 K can be estimated using

the following equations:

1_82 _ _1 _ 0_55_

P 0 _

0_997

2_06 _ 100 _ 39_9_

This simple calculation shows that only 39.9% of the void volume of aspen chips

contains liquid at a DS of 0.55.

4.2 Kraft Pulping Processes 129

(b) After impregnation:

During penetration the moisture content, MCw, increases to 0.65 which equals a

DS of 0.35. The mass of the wet chip, mwc, calculates to:

mwc _

0_35 _ 2_86 t_t dry solids

Assuming an even temperature rise to 373 K, the total volume of the penetrated

water, VH 2 O _ P, is the calculated by:

VH 2 O _ P _

2_86 _ _1 _ 0_35_

0_959 _ 1_938m3_t dry solids

After impregnation, the degree of penetration, P, changes to:

P _

1_938

2_06 _ 100 _ 94_1_

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