 # Operative relationship of a CHC without attrition

Irrespective of the crystal size, the rate of increase in mass is: Therefore: However (see section 4.2.7): The crystallizer’s productivity is: The nucleation rate is equal to the productivity quotient (in kg.s-1) by the mean crystal mass (see section 4.2.7). However, we frequently write: e : agitation power per cubic meter of slurry (W.m-3).

By equating the two expressions of J, we obtain: Let us replace AX with its value in the expression of P: Or again: Lifting the two members of the previous equation to power i = comes

g

to: However, the Mc / P ratio is written: By eliminating P between [4. Ibis] and [4.2], we obtain the desired relationship: In general, j is close to i, and Mc scarcely intervenes in the equation [4.3]. Often, the value of i, greater than 1, is of the order of 2 and we have: We observe that the crystal size is far from proportional to the residence time. This can be explained by the supersaturation AX decreasing with residence time. 