Model Structure

The impregnation model is limited to the following assumptions:

_ Chemical impregnation follows Fick’s second law of diffusion.

_ The model considers axial and radial diffusion. Both axial and

radial diffusion coefficients are independent of radial and axial

position in the cylindrical samples. However, radial and tangential

diffusion are not distinguished and are treated equally.

_ The solute concentration (NaOH) in the impregnation solution

remains constant.

_ The temperature is uniform throughout the sample.

_ No chemical reactions occur between the matrix and the diffusing

chemicals at the temperature of impregnation.

_ The diffusion coefficient of NaOH into wood is considered to be

independent of pH (valid for concentrations > 1 mol L–1).

_ Despite swelling, the sample geometry remains invariant with time.

In the present model, D is assumed to be dependent only on pressure, temperature

and the pore structure of the chip sample.

The pressure influence on diffusion can be expressed by extending the Arrhenius-

type equation [Eq. (49)]:

D _ D 0 _ __ T _

_ Pm _ Exp _ _

EA

RT _ _ _66_

where:

_ D = diffusion coefficient, cm2·s–1

_ D0 = diffusivity constant, cm2 s–1·K–0.5

_ p = dimensionless pressure term (i.e., the ratio of absolute pressure

to atmospheric pressure)

_ m= pressure power constant

Considering all of the assumptions made above, the diffusion process can be

described by Fick’s second law of diffusion [35]. Its differential form in cylindrical

coordinates is given by Eq. (67):

∂ C

∂ t _

r _

∂

∂ r

r _ Dr

∂ C

∂ r _ _

∂

∂ z

Dz

∂ C

∂ z _ _ ___ k _ Cn _67_

where C is the concentration of the diffusing species at the position (r, z), k is the

reaction constant between chemical and matrix, n is reaction order, r is radial

direction and z is axial direction.

152 4 Chemical Pulping Processes

If it is assumed that no chemical reaction (of relevance) takes place, the term

k · Cn can be eliminated from Eq. (67).

Radial and axial diffusion are investigated separately. Thus, the radial directional

impregnation is isolated from the axial one by sealing the outer surface in

the radial and axial directions. The surfaces were sealed with an appropriate sealing

material, thereby creating impermeable barriers. The open faces represent

then either the axial or the radial surfaces (Fig. 4.14).

Sealed surfaces

radial

axial

A B

Fig. 4.14 Sketch of the wood sample prepared for unidirectional

impregnation according to Kazi and Chornet [57].

(A) For radial impregnation, the axial surfaces are impermeable;

(B) for axial impregnation, the radial surfaces are

impermeable.

Equation (67) is divided into two separate equations: one for radial concentration

and one for axial concentration only. Thus, it is assumed that there is no interaction

between radial and axial diffusion processes.

Дата добавления: 2015-10-21