Membrane extraction in rectangular modules with external recycle

The analysis of solvent extraction in the membrane modules of cocurrent, countercurrent and cross-flows with external recycle, has been carried out by mass-transfer theory, analogous to heat transfer in recycled heat exchangers. Considerable improvement is achievable by recycle operation if the increase in mass-transfer coefficient by applying the recycle effect can compensate for the decrease in the driving force of mass transfer due to the dilution of inlet feed solution. Under comparable conditions most solute is extracted in countercurrent-flow arrangement, the least in cocurrent-flow. However, the separation efficiencies of the three flow-type devices approach in unity for lower feed concentration and/or larger flow rate and/or larger reflux ratio.