Optimal Design of a Two-Stage Membrane System for Hydrogen Separation in Refining Processes

This paper fits into the process system engineering field by addressing the optimization of a two-stage membrane system for H-2 separation in refinery processes. To this end, a nonlinear mathematical programming (NLP) model is developed to simultaneously optimize the size of each membrane stage (membrane area, heat transfer area, and installed power for compressors and vacuum pumps) and operating conditions (flow rates, pressures, temperatures, and compositions) to achieve desired target levels of H-2 product purity and H-2 recovery at a minimum total annual cost. Optimal configuration and process design are obtained from a model which embeds different operating modes and process configurations. For instance, the following candidate ways to create the driving force across the membrane are embedded: (a) compression of both feed and/or permeate streams, or (b) vacuum application in permeate streams, or (c) a combination of (a) and (b). In addition, the potential selection of an expansion turbine to recover energy from the retentate stream (energy recovery system) is also embedded. For a H-2 product purity of 0.90 and H-2 recovery of 90%, a minimum total annual cost of 1.764 M$year(-1) was obtained for treating 100 kmolh(-1) with 0.18, 0.16, 0.62, and 0.04 mole fraction of H-2, CO, N-2, CO2, respectively. The optimal solution selected a combination of compression and vacuum to create the driving force and removed the expansion turbine. Afterwards, this optimal solution was compared in terms of costs, process-unit sizes, and operating conditions to the following two sub-optimal solutions: (i) no vacuum in permeate stream is applied, and (ii) the expansion turbine is included into the process. The comparison showed that the latter (ii) has the highest total annual cost (TAC) value, which is around 7% higher than the former (i) and 24% higher than the found optimal solution. Finally, a sensitivity analysis to investigate the influence of the desired H-2 product purity and H-2 recovery is presented. Opposite cost-based trade-offs between total membrane area and total electric power were observed with the variations of these two model parameters. This paper contributes a valuable decision-support tool in the process system engineering field for designing, simulating, and optimizing membrane-based systems for H-2 separation in a particular industrial case; and the presented optimization results provide useful guidelines to assist in selecting the optimal configuration and operating mode.