Total entropy generation rate minimization configuration of a membrane reactor of methanol synthesis via carbon dioxide hydrogenation

The total entropy generation rate, internal exergy loss and exergy efficiency of the membrane reactor of methanol synthesis via carbon dioxide hydrogenation are compared, and the results show that the total entropy generation rate minimization is equivalent to the internal exergy loss minimization and the exergy efficiency maximization under the fixed inlet exergy. Therefore, this paper optimizes the membrane reactor with total entropy generation rate minimization as an optimization objective under a fixed methanol production rate. The optimal temperatures curves of exterior walls for three optimal membrane reactors with different boundary conditions are obtained by using optimal control theory and nonlinear programming. The influences of other geometric and operating parameters on optimization results of optimal membrane reactors are analyzed. The results indicate that when inlet temperatures of the reaction mixture and mixture in the permeable tube are unfixed, the optimizing curve of exterior wall temperature makes the total entropy generation rate of membrane reactor reduce by 12.39% compared with the total entropy generation rate of a reference membrane reactor with a linear exterior wall temperature. Decreasing the inlet molar flow rate of sweep gas and gas hourly space velocity and increasing inlet pressure of reaction mixture, the inlet pressure of mixture in the permeable tube and heat transfer coefficients are favorable for decreasing the total entropy generation rate in the membrane reactor. As the porosity of catalyst bed and reactor length increases, the minimum total entropy generation rate decreases first and then increases. From the perspective of engineering application, this paper establishes two membrane reactors (membrane reactor heated by three-stage furnaces of the same length and membrane reactor heated by three-stage furnaces of different lengths), respectively. The minimum total entropy generation rates of the two reactors are reduced by 11.67% and 11.79% compared with the total entropy generation rate in the reference membrane reactor, respectively. The obtained results are beneficial to the optimal design of energy-efficient membrane reactors.

Automated summary

This study compares the total entropy generation rate, internal exergy loss, and exergy efficiency of a membrane reactor used for methanol synthesis via carbon dioxide hydrogenation. The results indicate that minimizing the total entropy generation rate is equivalent to minimizing the internal exergy loss and maximizing the exergy efficiency under fixed inlet exergy. To optimize the membrane reactor, the total entropy generation rate is minimized as the objective while maintaining a fixed methanol production rate. The optimal temperature curves of the exterior walls for different boundary conditions are obtained using optimal control theory and nonlinear programming. Other geometric and operating parameters are analyzed to determine their influences on the optimization results. The study finds that optimizing the exterior wall temperature reduces the total entropy generation rate of the membrane reactor. Additionally, two different types of membrane reactors are established, and their minimum total entropy generation rates are reduced compared to the reference membrane reactor. These findings are valuable for the optimal design of energy-efficient membrane reactors.