Diffusion and Reaction in Isothermal Pulping Digesters

Abstract

A mathematical model describing isothermal alkali diffusion and reaction with acetyl groups in moist wood chips was derived and validated against experiments. A coupled mass balance for the acetyl groups and the alkali was posed and solved numerically. Differences observed earlier between model-predicted and experimentally obtained alkali concentration profiles demonstrated that the diffusion coefficient D is not a constant but a certain function of alkali concentration C. A model for this dependence was developed on the basis of theoretical principles. The function C→D plays a key role in the qualitative form of the resulting alkali profiles, especially in terms of changes in the sign of the curvature that were not explained by other approaches in the literature. A new parameter, the “deacetylation index”, was introduced as an observable quantity that is useful for tracking the end of the impregnation stage in pulping processes.