The dispersion free membrane extraction through a cross-flow rectangular membrane module with arbitrary location of an impermeable plate placed for double-pass and external-recycle operations in raffinate phase, has been investigated. Theoretical treatment was analogous to the heat transfer in heat exchangers for the mass transfer in mass exchangers. An experiment was carried out in a cross-flow conduit of stainless steel inserted with a membrane sheet made of microporous polypropylene to extract acetic acid from aqueous solution by methyl iso-butyl ketone. Theoretical predictions are in agreement with the experimental results. Considerable improvement in mass-transfer performance is obtainable if the width of the first-pass subchannel, ΔB decreases, as well as the width of the second-pass subchannel, (1−Δ)B increases. The mass-transfer rate increases also when the reflux ratio increases. Based on the economic point of view, the suitable value of Δ (B is the width of a membrane sheet) may be 0.2.