Question

A master chemical engineer student has designed a pilot plant for the production of sugar. It is a continuous crystallization vessel containing 130 liters of sucrose slurry fed with 65 liters/hr of supersaturated solution. The withdrawal rate of product slurry is also 65 liters/hr. A nucleation rate B of 9.72 x 10⁷nuclei/liters hr, and growth rate G of 0.035 mm/hr are expected. Calculate the anticipated crystal size distribution of the slurry on different standard screens.

Mesh number	Screen size (mm)
20	0.85
25	0.71
35	0.5
50	0.3
100	0.15
120	0.125

Answer 1

The number of crystals N between I1 and I2 crystal size, Ni=BV/Q*(exp(-I1Q/(GV))-exp(-I2Q/(GV)))

Nuclear rate, B = 9.72*10^7 nucleir/l/hr

Vessel volume,V = 130 litre

Q, supersaturation solution flowrate = 65 l/hr

G, growth rate = .035 mm/year

mi, crystal fraction at ith mesh = Ni/?Nj

Mesh Number,i	I1	I2	Ni	mi
120	.125	.15	9769468	.3
100	.15	.3	20089743	.61
50	.3	.5	2516819	.07
35	.5	.71	145720	.004
25	.71	.85	6601	.0002
20	.85	Infinity	1033	3.1*10^-5
		?Nj	32529386