A mathematical model of a raw sugar vacuum pan (a batch crystalliser) has been prepared. It predicts the parameters of the size distribution (mean size, CV) resulting from the batch operation of the pan.
The mathematical model is based on unsteady state material and population balances and on kinetic data for the crystallisation mechanism s involved. This model was solved on a digital computer by numerical methods, and also on a hybrid computer.
To obtain kinetic data a survey was made of the literature on the kinetics of crystal growth and nucleation under conditions similar to those prevailing in industrial raw sugar pans. This shows that relevant data is scant, especially in the areas of (a) the effect of impurity and circulation conditions, (b) nucleation phenomena in industrial practice, and (c) the spread of crystal size as crystals grow under industrial and laboratory conditions.
Data on the last mentioned aspect is practically non-existent, so this was singled out for intensive experimental investigation and analysis. The concepts involved are rather novel, and departures from the simple crystallisation laws are entailed. A size dispersion function was defined to describe the broadening of the crystal number size distribution as growth proceeds. Experimental measurements under controlled laboratory conditions and also under factory conditions were made to give an approximate form to the size dispersion function, and to estimate the influence of growth conditions.
An important area that was developed to enhance the accuracy of size distribution measurements was that of crystal sizing in the range up to 2000 microns. Sieve methods were first used, but crystal shape variations and problems with the preparation of crystal samples made these unreliable. A determined effort to use the Coulter Counter at the higher size ranges was not successful as the electronic system was not capable of performing with the long pulses from larger particles. The Counter was useful, however, for nuclei counts. A Zeiss-Endter Particle Size Analyser was automated for data punching on paper tape, and the distribution of projected area of crystals on photomicrographs of the sugar samples readily obtained. However the relationship of projected area to crystal volume is shape dependent. The crystal volume is the most appropriate measure of size for our purposes and this eventually was successfully measured for crystals larger than 250 microns by the use of an electronic microbalance giving an output which could be sensed and logged by a small digital computer.
With suitable estimates for the rates of other mechanisms and assumptions based on factory practice as to the behaviour of the vacuum, pan, the mathematical model of the batch sugar crystallisation process was set up. This predicted the mass and size distribution of the product crystals from information on the initial conditions and the progressive state and material feed variables. The model describes the crystal size distribution by its moments, and incorporates the size dispersion function in the second moment to predict the spread of sizes.
Although most of the many model parameters were chosen from the literature and some were estimated from pilot tests with the laboratory vacuum pan, the key growth parameters were set from the data gathered directly from a full scale factory unit (suitably instrumented with a computer data logging system). Direct search techniques were used to minimise the least square error between model predictions and the actual data for 10 batch crystallisations covering a range of industrial conditions. The model was verified against further data obtained from the factory unit, and against general batch crystallisation data and found to perform quite satisfactorily. With such a model, investigations were then carried out
(a) to show the operating performance of pans under altered initial and operating conditions
(b) to select control settings which would optimise the production performance of the pan
(c) to show the performance and product crystal quality which would result from the operation of pans as a series of continuous mixed suspension mixed product removal units.