A nonstandard membrane process is described that involves, highly selective sorption of a compound "A" at a large absolute weight fraction w(A). coupled with a significant diffusionally induced flux of a second component "B." The flux of B convectively moves A from a dilute external mass fraction relative to component B upstream to an enriched mass fraction downstream. The general form of the process has potential applications involving dilute feeds where current membranes processes perform poorly for such removal as a result of excessive solubility of the smaller component B. The most important widespread application is expected to be the separation of small organic solutes from supercritical carbon dioxide to facilitate the recycling and reuse of CO2 while minimizing costly and energy-intensive recompression steps. We consider the utility of this concept by modeling the separation efficiency of phenol from supercritical carbon, dioxide. (c) 2005 American Institute of Chemical Engineers.