Overall balance of the crystallizer population
Band (L, L + AL) sees its population varying during time 5t.
Crystals of length L grow from G(L)5t and enter the number section of n(L) G(L) 5t = nGSt.
n(L)AL is the number of crystals present in 1 m3 of slurry, between length L and L + AL.
Crystals of length L + AL also grow, leaving their section. Their growth is:
They leave their section at number:
Therefore, disregarding infinitely small terms of the second order:
The overall balance of the band is (entry minus exit):
Assuming a homogenous crystallizer, the population variation of the preceding band over time St is:
V is the crystallizer volume (m3).
If there is vaporization, the variation is:
The balance for the device is written:
However, this balance is incomplete.
We must account for:
- 1) the disappearance of D crystals per unit of time and unit of volume of the crystallizer. This disappearance is due to dissolution;
- 2) the apparition J of crystals per unit of time and unit of volume of the crystallizer. This apparition is due to primary and/or secondary nucleation (attrition);
- 3) the extraction of production qs (L) ns(L). The extracted flow varies with the size of crystals as their residence times are not necessarily identical;
- 4) the arrival of supply qana(L). However, most of the time, supply does not include crystals unless there is inflow of recycling returns;
The complete balance is written as:
The dimensions in this balance are as follows: