Entropy Generation Rate Minimization for Methanol Synthesis via a CO₂ Hydrogenation Reactor

The methanol synthesis via CO₂ hydrogenation (MSCH) reaction is a useful CO₂ utilization strategy, and this synthesis path has also been widely applied commercially for many years. In this work the performance of a MSCH reactor with the minimum entropy generation rate (EGR) as the objective function is optimized by using finite time thermodynamic and optimal control theory. The exterior wall temperature (EWR) is taken as the control variable, and the fixed methanol yield and conservation equations are taken as the constraints in the optimization problem. Compared with the reference reactor with a constant EWR, the total EGR of the optimal reactor decreases by 20.5%, and the EGR caused by the heat transfer decreases by 68.8%. In the optimal reactor, the total EGRs mainly distribute in the first 30% reactor length, and the EGRs caused by the chemical reaction accounts for more than 84% of the total EGRs. The selectivity of CH₃OH can be enhanced by increasing the inlet molar flow rate of CO, and the CO₂ conversion rate can be enhanced by removing H₂O from the reaction system. The results obtained herein are in favor of optimal designs of practical tubular MSCH reactors.