On the Modelling of Mechanical Dewatering in Papermaking

Abstract: Most of the water fed into a paper machine is removedmechanically in the forming and press sections. One of thefactor which has an important influence on mechanicaldewatering, i.e. in both forming and pressing, is thestress-strain behaviour of the fibre network.The focus of this thesis is on the development of improvedmathematical descriptions of the stress-strain behaviourexhibited by fibre networks in the forming and press sections.The first part of the thesis presents a physically based modelof the forming and densification of fibre mats in twin-wireformers. The model can calculate the ecect of the applicationof a varied load through the forming section. It was developedfrom mass and momentum balances of the fibre and liquid phases,the fibre mat stress-porosity relation and an expression forthe permeability as a function of the porosity. The fibre-matstress-porosity relation used is rate-independent and presentshysteresis. Simulations have been conducted to study theeffects of roll pressure, blade pulses, wire tension andbeating. The effect of sequential blade pressure pulses afterthe forming roll on the dewatering and the concentrationgradients could be characterised. The simulations alsoexhibited rewetting by expansion when the fibre mats left theforming roll. Increasing wire tension resulted in increaseddewatering, but the rate of increase diminished rapidly withincreasing tension. The simulation results also indicated thatbeating has a large influence on dewatering.The second part of the thesis presents two models of therate-dependent stress-strain behaviour of the fibre networkthat is observed in wet pressing. The first model was based onthe approach pioneered by Perzyna (1966) for strain-ratedependent plasticity and was quite satisfactory for calculatingthe stress-strain behaviour of the fibre network in singlepress nips. It was successfully applied for studyingdensification and dewatering in both normal wet pressing andhigh temperature wet pressing. However, the first model onlyincludes rate dependence in the compression phase of thecompressionexpansion cycle; the expansion phase is treated asbeing rate independentThe second model of the stress-strain behaviour of the fibrenetwork treats both compression and expansion as being ratedependent, according to experimental observations. It is basedon the idea that the wet fibre web may be conceived as alayered network of restricted swelling gels. A swollen fibre isa restricted gel, the inner swelling pressure in a swollenfibre wall being balanced by the stresses in the fibre wallstructure. The observed rate dependence of wet webs in bothcompression and expansion phases was attributed to the flow ofwater out of and into the fibre walls. The second model gavepredictions that are in good agreement with results fromuniaxial experiments using pressure pulses of arbitrary shapefor both a single pulse and a sequence of pulses. It maytherefore be used as a general model for the rheologicalbehaviour of the wet fibre network in wet pressing, providedthe model parameters are estimated from experimental data withsmall experimental error.KEYWORDS:Paper, modelling, dewatering, forming, wetpressing, fibre network stress, rheology, hysteresis,intra-fibre water, compressibility, structural stress,stress-strain, restricted gels, swelling.