# Calculation for continuous crystallizers

## Cooling

We can deduce the composition X_{s} of the exit liquor by:

- - knowing the composition X
_{e}and the temperature T_{e}of the supply, that is at the entry, and; - - providing ourselves with the mass of crystals to be produced W
_{E}(X_{e}-

Xs).

The temperature T* of this liquor must correspond to the exiting saturation equilibrium.

Thus, we know the entry temperature Te and exit temperature T* of the mass. We can deduce the thermal cooling power to be provided Q:

If the difference in concentration between equilibrium X* and the level of real solute on exit Xs is assumed to be zero, experience shows that this hypothesis is typically verified.

Q: thermal power (W)

T_{e}: entry temperature of the mother liquor (degrees Celsius)

T*: exit temperature of the slurry (degrees Celsius)

W_{E}: flow of water accompanying the product to be crystallized (kg.s^{-1})

X_{e}: level of solute in the mother liquor on entry (kg.kg^{-1})

X_{s}: level of solute on exit (kg.kg^{-1})

C_{E}: thermal capacity of water (J.kg^{-1}.°C^{-1})

C_{S}: thermal capacity of the product to be crystallized (J.kg^{-1}.°C^{-1})

Л,,: crystallization heat of the product (J.kg^{-1}).