Process synthesis and optimization based on multi-stage membrane superstructure for helium extraction from natural gas

In the traditional design method based on the experience of a hybrid multi-stage membrane process in helium extraction from natural gas, it is difficult to ensure synchronous optimization of processes and parameters owing to complex configurations and interdependent parameter relationships. In this study, a novel superstructure is proposed for the optimal synthesis of a multi-stage membrane process. A comprehensive mixed-integer nonlinear programming (MINLP) mathematical model was developed. More feasible process structures were included in this model, and both process parameters and structures could be optimized simultaneously. The particle swarm optimization algorithm was employed to minimize the separation cost and systematically identify the optimal number of membrane stages, membrane areas, interstage pressures, and recirculation stream locations. To enhance the simulation accuracy and simplify the model complexity, Python interfacing with UniSim Design via ActiveX was employed to facilitate the acquisition of calculation data and process condition configuration. First, the ability to obtain optimal process configurations was validated through comparison with a reference case in this field. Subsequently, the model was applied to helium extraction in a natural gas plant. The optimal process configurations and operating variables were determined for the different recovery rates and purities. Additionally, the optimal process configurations and operating variables were also solved for different helium feed concentrations (700–9000 ppm). The model validation results show that the applied model solution reduces the separation cost by 18.2 %, which proves that the application of this model can enhance the economic efficiency of membrane separation technology for helium extraction from natural gas.