Derivation and Properties of Membrane Residue Curve Maps

Residue curve maps have been developed for membrane permeation systems. A “thought experiment” was conducted whereby a fluid mixture was allowed to permeate through a diffusion membrane in a batch still. The differential equations which describe any residue curve are derived from mass balances, implying that membrane residue curve maps (M-RCM's) can be used for any type of membrane, provided the appropriate permeation (flux) model is used. In this paper, a simple constant relative permeability model is used for demonstration purposes, and as an example, an M-RCM is plotted for methanol/butene/methyl tertiary butyl ether (MTBE) using the appropriate flux data. The curves in an M-RCM trace the change in composition of the residual retentate in the batch still. At any time during batch permeation, the permeate composition is related to that of the retentate at that particular time, thus allowing a membrane separation vector to be defined as the vector difference between the two compositions.