A new device of a double-pass mass exchanger is a circular tube divided by inserting a permeable barrier into two subchannels with uniform wall concentration, resulting in considerable improvement of the device performance in mass transfer compared with that in an open conduit. Efficiency improvement in mass transfer has been studied analytically by using eigenfunction expansion in power series. Analytical results show that a suitable adjustment of the permeable-barrier position can effectively enhance the mass transfer efficiency, leading to an improved performance. A numerical example in mass transfer efficiency of the two flow patterns of double-pass devices has been illustrated with the mass-transfer Graetz number as a parameter. The effects of the permeable-barrier position on the mass transfer efficiency and on the increment of power consumption have been also delineated.