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This work deals with the optimization of two-stage membrane systems for H2 separation from off-gases in hydrocarbons processing plants to simultaneously attain high values of both H2 recovery and H2 product purity. First, for a given H2 recovery level of 90%, optimizations of the total annual cost (TAC) are performed for desired H2 product purity values ranging between 0.90 and 0.95 mole fraction. One of the results showed that the contribution of the operating expenditures is more significant than the contribution of the annualized capital expenditures (approximately 62% and 38%, respectively). In addition, it was found that the optimal trade-offs existing between process variables (such as total membrane area and total electric power) depend on the specified H2 product purity level. Second, the minimization of the total power demand and the minimization of the total membrane area were performed for H2 recovery of 90% and H2 product purity of 0.90. The TAC values obtained in the first and second cases increased by 19.9% and 4.9%, respectively, with respect to that obtained by cost minimization. Finally, by analyzing and comparing the three optimal solutions, a strategy to systematically and rationally provide ‘good’ lower and upper bounds for model variables and initial guess values to solve the cost minimization problem by means of global optimization algorithms is proposed, which can be straightforward applied to other 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 kmol·h −1 with 0.18, 0.16, 0.62, and 0.04 mole fraction of H 2 , CO, N 2 , CO 2 , 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.

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