Dried sugar cane billets are shredded and conveyed to a diffuser, which consists of a stainless steel

mesh conveyor belt on which the shredded solids sit and which moves slowly and continuously

under a series of stationary hot liquid sprays. The sugar in the shredded solid is gradually leached

out. The spray spacing permits sufficient time for the liquid to drain through the solid and be

collected, where it is then pumped counter$-$currently to the solid shredded cane and is sprayed on

"fresher" cane. Hence, each spraying and draining may be considered as one stage of a counter$-$

current leaching operation.

Experiments were performed to assess the carryover of liquid in the shredded cane solids $($the

underflow$)$ on the belt after the draining time between stages. The results are:

The cane billets enter the diffuser with a sugar content of $20wt.\%$ and must be extracted to a final

exhausted content of less than $0\mathrm{.}5wt.\%$ on a solvent$-$free basis $($i$.$e$.$ after drying$).$ Assume the billets

entering the diffuser initially have zero moisture content. Pure hot water is used as the solvent feed

to the diffuser. $1kg$ of water is used per $kg$ of fresh cane billet.

The solution draining from the mesh belt $($overflow$)$ is generally free of solids, except at the first

stage $($where solid enters$),$ in which the overflow contains a suspension of shredded solids at a

concentration $($inert solid$)$ of $10wt.\%.$

Calculate the number of spray stations $($stages$)$ required to obtain the desired performance. Perform

your calculations on a right$-$angle triangle diagram with inert fibre at the bottom$-$left corner, pure

sugar up at the top left apex, and pure water at the bottom right vertex. Use a basis of $1kg$ of cane

billet $($i$.$e$.1kg$ of feed containing inert solid and sugar$).$