The Calculation of Stage Efficiency and Its Application to Diffuser Design

The actual mechanism controlling the extraction of sucrose from cane in diffusers is still in dispute. It is generally believed that displacement washing or lixiviation is the governing process. Cane diffusers have been adapted from the vegetable oil extraction industry via the beet industry. A considerable portion of Chemical Engineering solid-liquid extraction design theory has been developed in the vegetable oil industry where it is generally accepted that molecular diffusion from within to the surface of the solid material is the rate controlling mechanism, followed by surface washing-eddy diffusion. In the present paper the McCabe-Smith calculation is used to determine the number of ideal stages for an average diffuser on the basis of constant underflow. The stage efficiency is calculated from a knowledge of the diffusion coefficient and particle size distribution in the feed. These data are available from laboratory and pilot scale tests. From the number of ideal stages and stage efficiency, the number of actual stages is calculated giving results which are in close agreement with the number of stages used in existing cane and first bagasse diffusers. It is concluded therefore that the theoryisapplicable to cane diffuser design and that molecular diffusion within the cane particles is the controlling mechanism.