The mass-transfer flow of a multi-pass counterflow laminar mass exchanger by inserting three permeable barriers with external refluxes was investigated theoretically, and the mathematical formulation was developed as well. With the use of an orthogonal expansion technique and the eigenfunction expanding in power series, the analytical solutions were obtained for finding the outlet concentration and mass transfer efficiency. The influences of the design parameters, the channel thickness ratio (β) and barrier characteristics (γ), and the operating parameters, the mass-transfer Graetz number (Gz m ) and recycle ratio (R), are examined. Theoretical predictions of the new multi-pass operations are compared with those in the single- (without the permeable barrier inserted) and double-pass operations under the same working dimensions and represented graphically. The results show that the influences of the recycle ratio and channel thickness ratio in the present device with external refluxes are dominant in low and high mass-transfer Graetz number regions, respectively. Therefore, an optimal economic feasibility of multi-pass mass exchangers was found when the recycle ratio and channel thickness ratio are suitably selected under the operating conditions of interest.
Chemical engineering Communications 193(2), pp.246-271