Modelling of Mass and Heat Transport in Paper - Evaluation of Mechanisms and Shrinkage

Abstract: In this work a one-dimensional model for the mass and heat transport in the thickness direction of paper has been developed. Solid-based coordinates were applied to simplify incorporation of shrinkage. Liquid diffusion, gas convection and vapour and air diffusion were incorporated as mass transport mechansims. In the heat balance the convective heat transport and heat conduction were included. Specific models for the transport parameters were developed from data in the literature. The model was evaluated for four cases of drying where moisture and temperature distribution data through the thickness of paper are available. An algorithm was proposed to calculate unknown parameters directly from the experimental data. Three remaining parameters were obtained by non-linear regression of calculated moisture and temperature distribution to the experimental data. Simulations showed that the model can predict the drying behaviour and the moisture and temperature gradients for convective drying of kraft, and hot surface drying of kraft and sulphite pulp sheets with low density. For high-density sheets the general behaviour was correctly predicted, but moisutre and temperature gradients deviated more from the experimental data, than in the case of low-density sheets. The mechanisms governing the drying behaviour were investigated. Shrinkage behaviour and volume fractions of solid, liquid and gas in kraft and CTMP sheets have been measured using the mercury displacement technique. The gas volume fraction increases continuously with decreasing moisture ratio. Influence of basis weight, pressing and beating was also investigated. A triangular phase diagram was developed in which the phase development and shrinkage behaviour of paper can be studied. Analysis showed that kraft sheets shrink continuously in the moisture ranges investigated, while highly refined CTMP sheets showed a region with no shrinkage. Analysis and modelling of the shrinkage behaviour showed that the shrinkage is higher than ideal shrinkage for moisture ratios below approximately 1.0 kg water/kg DS.