MODELLING OF WASHING OF BROWN STOCK ON ROTARY VACUUM WASHER

Abstract

Brown stock washing is the key operation controlling the cleanliness of pulp with least carryover of dissolved solids on one hand and separating the maximum black liquor at as high a concentration as possible on the other. Any carryover of black liquor solids with the washed pulp leaving for bleaching and paper making is a source of BOD, COD and other toxic pollution parameters harmful to the environment and subsequent processing. The washing process needs optimization with respect to equipment, operating cost and environmental factors. To achieve these objectives the primary step is to optimize the parameters for a desired degree of separation and to control them if any deviation occurs from the set values. For this development of mathematical modelling is imperative necessity. Several washing equipments are in use for pulp washing. But, rotary vacuum filters are most important equipments used for brown stock washing. Though some mathematical models are available in the literature for different pulp washing systems, still there is enough scope to deal with this system with a view to achieve more realistic models. The present investigation deals with pulp washing under the influence of longitudinal dispersion coefficient(DL) and accumulation capacity of fibers, which leads to adsorption and desorption dynamics in a rotary vacuum washer. In a rotary vacuum washer several zones are formed during one rotation of drum. No two zones of a rotary vacuum washer have similar mechanism. Therefore mathematical model for each zone varies significantly. In this investigation a systematic approach for developing a mathematical model for all zones of a rotary vacuum filter, considering both macroscopic and microscopic interpretations has been followed. For cake formation zone mathematical models in terms of pertinent parameters are available in literature. However, models for the prediction of filtrate flow rate of a rotary filter from constant pressure filtration data are rarely available. In this investigation filtrate flow rate is proposed with or without the consideration of filter medium resistance. The solution of the equations are given. The derived equations can be used for designing such filter from laboratory data on constant pressure filtration as well as for scaling up. For cake washing zone non homogeneous, non linear, first order, second degree, partial differential equations are developed. Eight washing models are taken in hand with or without consideration of longitudinal dispersion coefficient (DL) and different boundary conditions based on the earlier worker's models. Before solving, these differential equations are converted into dimensionless form by using Peclet number, dimensionless concentration, dimensionless time and dimensionless thickness. These equations are solved by applying Laplace transform technique. Inverse has been taken by using the method of residues. Dimensionless expressions are given for exit concentration of solute leaving the bed, average concentration of solute in discharged pulp and mean concentration of filtrate collected through the washing zone. The solution technique for models 1 to 6 are identical (except boundary conditions and adsorption isotherm) but the solution technique for models 7 and 8 are different.