Parameter unit Axial Radial

D0 cm2 · s–1·K–0.5 1.98*10–4 5.77*10–7

m 0.27 0.38

E kJ mol–1 1.235 2.700

tion energies for diffusion in the radial and axial directions are significantly lower

than those obtained by others (see Tab. 4.13). Several explanations for the low activation

energies have been put forward. First, when diffusion occurs from the

impregnated wood to the water solution surrounding the wood sample, the effective

surface area can be assumed to be significantly higher than the geometric

area due to surface roughness. Second the release of the diffusing substance from

the wood block comprises two process steps, namely desorption and diffusion.

Accounting for both the higher effective surface area and the elimination of the

desorption process step would eventually lead to lower activation energies.

The model also considers the influence of the pressure during impregnation of

wood chips. Such pressure may change the geometry of the pore system, and also

affect the diffusion coefficient for chemical diffusion into the wood chip. The diffusion

coefficient has been considered to be proportional to the dimensionless

pressure with a power factor m. The pressure power factor in the axial direction is

found to be smaller than that for the radial direction, which means that the influence

of pressure is more significant in the radial direction (see Tab. 4.15).

The established impregnation model is able to predict the required time to

reach a steady-state concentration distribution within the chips which is a prerequisite

for homogeneous delignification reactions. The point concentration from

the surface to the center of the chip can be simulated by considering both chip

length and thickness. The course of the average and the center NaOH concentration

in relation to the bulk concentration as a function of impregnation time were

calculated for two different impregnation conditions (Tab. 4.16).

The simulation result is shown in Fig. 4.17. Compared to the minimum concentration

at the chip center, the average concentration rises rapidly with increasing

impregnation time. The increase in impregnation pressure from 200 kPa to

2000 kPa reduces the impregnation time needed to reach an average concentration

of 99% (of the NaOH concentration in the bulk solution) from 15 min to only

8 min. The same concentration level at the chip center requires a prolongation of

the impregnation time of up to 5 min, depending on the applied pressure.

4.2 Kraft Pulping Processes 157

Tab. 4.16 Conditions for the impregnation of hardwood chips:

influence of pressure. Based an these conditions, the course of

average and minimum concentration in a chip are simulated by

the introduced impregnation model [56].

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