Mathematical models have been developed to optimize three configuratio
ns for membrane gas separation modules. The three systems include the
single stage, the two stage, and the continuous membrane column (CMC).
Analysis of the three systems is carried out for the case of enrichin
g a binary mixture of methane and carbon dioxide, where the reject str
eam is the desired product. The cost optimization function includes th
e capital cost for compressors and membranes as well as the energy ope
rating cost. The cost function is solved subject to a set of equality
and inequality constraints. The equality constraints include the modul
e balance equations and the permeation fluxes across the membrane. The
inequality equations include constraints on mole fractions in permeat
e and reject streams, operating pressure, membrane area, and the amoun
t of methane recovered in reject stream. Model equations for the three
systems are solved using GINO, a program for nonlinear optimization.
A quasi-Newton search method is selected and found quite efficient for
solution of the equations. Over the range of parameters considered in
the analysis, results show that the two stage configuration has a low
er production cost than the other two systems. In addition, the operat
ing cost for the CMC and the single stage systems are found to be comp
arable. Irrespective of this, the optimum amount of methane recovered
is the highest for the CMC system. Although the optimum operating cost
s for the CMC and the single stage systems are higher than the two sta
ge system, comparison should consider other factors including higher m
ethane recoveries generated by the CMC system and the simplicity of de
sign and operation for the single stage system.