Minimum amount of extracting solvent of AB/BC countercurrent extraction separation using organic feed

For an AB/BC countercurrent extraction separation using organic feed, the conditions to have minimum amount of extracting solvent (S_min) and minimum amount of scrubbing agent solution (W_min) were discussed, and the formulae of both S_min and W_min were deduced. It was shown that only when the ratio of flowrate of central component B leaving aqueous outlet to that leaving organic outlet took a certain optimal value, the AB/BC separation could have S_min as well as W_min, and this optimal ratio was decided by the separation factors between the three components but independent of feed composition. S_min was only relative to the separation factor of A/C pair but regardless of the separation factors of other pairs as well as feed composition, whereas W_min was determined by the separation factors between the components together with feed composition. Meanwhile it was also found that the organic stream out of feed stage was same composition as the initial organic feed when the separation system was given by the two minimum amounts and its steady state was achieved. Finally the results above were used to design a LuYb/YbTm separation case and the stage-wise compositions of each component in both the organic and the aqueous phase at steady state were given by computer simulation.