Studies on plant-scale, continuous, countercurrent, solid-liquid extractors have shown that axial dispersion occurs in both the solid and liquid phases. This reduces extraction efficiency. Mathematical models which predict solute concentration profiles for both the solid and liquid phases and extraction efficiency in the presence of axial dispersion have been developed.
Diffusion-partial-differential-equation solutions which account for liquid axial dispersion and surface mass-transfer resistance were obtained for different types of solid particle geometries. The validity of predicted solute concentration profiles was checked by comparing such profiles with experimental data from the literature. When liquid dispersion effects were included in the models, better agreement was found than when models were used that did not include these effects. The diffusion-partial-differential-equation solutions were extended to deal with solid particles with non-uniform sizes and with particles that have non-uniform velocities. The effect of particle size non-uniformity on extraction efficiency is illustrated by numerical examples.
Effects of flow maldistribution in the solid phase were modeled in terms of equivalent, multistage, countercurrents, continuous-stirred-tank extractors, where solid-flow non-uniformity was characterized by a residence time distribution function, and liquid dispersion by liquid backmixing flows. The models showed that extraction efficiency decreased when solid dispersion occurred, but the effect became insignificant when the dimensionless solid axial-dispersion coefficient, D(,s), was less than 0.01.
