Removal of dilute bioproducts from fermenter broths is a major challenge both to avoid microbe inhibition and to recover solutes economically without water loss. We analyze a proposed new process, membrane vapor extraction (MVE), where semi-volatile dilute aqueous solutes vaporize at the upstream side of an omniphobic, microporous membrane and dissolve into a nonpolar solvent highly favorable to the solutes but not to water. A new membrane-process analysis is outlined and applied to the countercurrent recovery of 2 wt % aqueous butanol by a prototype solvent (dodecane) at 40 degrees C. Thermodynamic phase equilibria, pioneered by the Prausnitz school, are crucial to MVE process design. Over 90% of the feed butanol is recovered with essentially no water loss giving a separation factor of over 1000. Energy requirements in MVE are low. Our design calculations demonstrate that MVE is a viable separation process to remove and recover dilute aqueous biosolutes. (c) 2015 American Institute of Chemical Engineers AIChE J, 61: 2795-2809, 2015