Batch with attrition
The balance equation becomes:
This type of equation is resolved by the characteristic method [NOU 85].
We observe that n is an increasing function of L. Remember that the total number of crystals is:
Irrespective of whether this n is for continuous crystallization or for batch crystallization, both of these variables are the solutions of a differential equation that is linear in form.
For which the general solution is [SPI 92]:
In a crystallizer with a draft tube, we typically use marine impellers located on the lower part of the draft tube. The draft tube is the dispositive allowing the maximum flow for minimum energy. The drop in pressure through a draft tube is for the most part attributed to the turning at its ends.
where V is the velocity in the tube.
By shaping the lower part of the tube, that is, the tube entrance (where the impeller is present), coefficient k can be brought down to 1.4 (according to Oldshue [OLD 83]).
The role of agitation is, of course, to keep the crystals in suspension, but above all to homogenize the slurry and avoid excessive local supersaturation.
The agitator must not break the crystals, otherwise fines will appear, which will affect the size distribution. To address this, experience shows that the velocity at the blade ends must be limited. Nonetheless, while excessive velocity can damage crystals, vigorous agitation can round their aspect, making them purer and more robust.
In general, baffles are significant in the agitation process, while in crystallization, even if they are several centimeters from the wall, they can lead to the accumulation of crystals, provoking pipe blockages. This is one of the advantages of a draft tube system that avoids baffles.
In case of external recirculation, the circulation flow can reach several hundred or even several thousand cubic meters per hour.
The pumps used are axial with low manometric height and do not cause too much crystal damage.