Optimization of module configuration in membrane gas separation

Mathematical models have been developed to optimize three configurations 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 enriching a binary mixture of methane and carbon dioxide, where the reject stream is the desired product. The cost optimization function includes the capital cost for compressors and membranes as well as the energy operating cost. The cost function is solved subject to a set of equality and inequality constraints. The equality constraints include the module balance equations and the permeation fluxes across the membrane. The inequality equations include constraints on mole fractions in permeate and reject streams, operating pressure, membrane area, and the amount 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 lower production cost than the other two systems. In addition, the operating cost for the CMC and the single stage systems are found to be comparable. Irrespective of this, the optimum amount of methane recovered is the highest for the CMC system. Although the optimum operating costs for the CMC and the single stage systems are higher than the two stage system, comparison should consider other factors including higher methane recoveries generated by the CMC system and the simplicity of design and operation for the single stage system.