Consider a hypothetical ternary mixture of components

,

, and

fed into a membrane separation module. The feed composition is

mole % of

,

mole % of

, and

mole % of

. This Demonstration computes the permeate (

,

, and

), and reject compositions (

,

, and

) for user-set values of the reject mole fraction of component

. The membrane area and stage cut,

, are also calculated. Complete mixing is assumed. The built-in
Mathematica function
FindRoot is used to readily solve seven simultaneous equations with seven unknowns. Values of the thickness of the membrane, pressures in both sides of the membrane, feed flow rate, and the permeabilities of the components are all taken from [1].