Daliborka Nikolić

This study evaluates the intensification potential of forced periodic operation (FPO) for methanol synthesis performed in a cooled continuous stirred tank reactor (CSTR) using nonlinear frequency response (NFR) methodology. A comprehensive dynamic reactor model incorporating the mass and energy balances, temperature-dependent kinetics, and dynamic changes of different active centres was used. The theoretical approach enables time-saving prediction of time-averaged reactor performance under periodic modulation of single and simultaneous input variables. Single-input forcing of inlet temperature and H2 resulted in modest improvements in methanol production, whereas modulation of CO, CO₂, or volumetric flow rate predominantly caused performance deterioration. In contrast, simultaneous two-input modulation (CO & flow rate, CO2 & flow rate and H2 & flow rate) generated substantially stronger positive effects. Modulation of CO & flow rate increased the methanol productivity and yield based on hydrogen up to 33.1%, while deteriorating yield based on total carbon. Hereby, the yield of methanol based on total carbon was predicted to increase most pronouncedly in the case of H2 & flow rate modulations (up to 28.6%). Multi-objective optimisation showed that it is also possible to select points on the resulting Pareto front at which the system can be improved in terms of both productivity and yield compared to the steady state. The results of the present study demonstrate that dynamic reactor operation can surpass steady state limitations. NFR analysis is an analytical and efficient tool for a priori screening and design of intensified operating strategies. It is applicable to other reactions and operating concepts.

Forced periodic operation (FPO) has emerged as a promising process intensification strategy for nonlinear catalytic reactors. In this study, the nonlinear frequency response (NFR) methodology was applied to investigate square-wave FPO of an isothermal CSTR for methanol synthesis. The analysis focused on periodic modulation of the inlet CO and flow rate, considering both single-input and simultaneous-input forcing. The reactor response was evaluated using higher-order frequency response functions (FRFs) to quantify the non-periodic component responsible for time-averaged process enhancement. The results showed that individual modulation of either inlet CO or flow rate doesn't provide significant improvement in reactor performance and may even reduce methanol productivity. In contrast, simultaneous modulation of both inputs generates a strong positive nonlinear interaction that substantially enhances reactor performance. Under optimal forcing conditions, methanol productivity increased from 336.9 mmol min⁻¹kgcat-1 at steady-state to 553.6 mmol min⁻¹kgcat-1, corresponding to a 64.3% improvement. Compared with previously reported cosine forcing, square-wave modulation nearly doubled the attainable productivity enhancement while also improving hydrogen utilisation efficiency. The results demonstrate that square-wave FPO represents a highly effective strategy for methanol synthesis intensification and confirm the capability of the NFR methodology for a priori evaluation and optimisation of periodically operated catalytic reactor systems.

Focus of this paper is the experimental demonstration of forced periodic operation applied to the synthesis of methanol. A theoretical analysis using the nonlinear frequency response (NFR) method and rigorous mathematical optimization provide a general guideline for analyzing simultaneously carried modulations of inlet composition and total volumetric flow rate. Influences of the forcing parameters (amplitudes, frequencies, phase differences, and shapes of forcing functions) were studied for well‐mixed reactors (CSTR) and theoretically for tubular reactors. Predictions of promising operating conditions were made exploiting a kinetic model developed and validated for an industrial Cu/ZnO/Al ₂ O ₃ catalyst. Confirming the trends of the theoretical results, in an experimental study using a laboratory CSTR, higher time‐averaged product amounts and improved yields were achieved compared to conventional steady state operation applying the optimized phase‐shift. Hereby, square wave modulations of the inputs outperformed sinusoidal modulations. A severe and unsolved problem concerns the deactivation of the catalyst observed in the course of the three months experimental campaign, which caused performance reductions for both steady state and periodic operation.

Traditionally, methanol is produced in large amounts from synthesis gas with heterogeneous Cu/ZnO/Al₂O₃ catalysts under steady state conditions. In this paper, the potential of alternative forced periodic operation modes is studied using numerical optimization. The focus is a well-mixed isothermal reactor with two periodic inputs, namely, CO concentration in the feed and total feed flow rate. Exploiting a detailed kinetic model which also describes the dynamics of the catalyst, a sequential NLP optimization approach is applied to compare optimal steady state solutions with optimal periodic regimes. Periodic solutions are calculated using dynamic optimization with a periodicity constraint. The NLP optimization is embedded in a multi-objective optimization framework to optimize the process with respect to two objective functions and generate the corresponding Pareto fronts. The first objective is the methanol outlet flow rate. The second objective is the methanol yield based on the total carbon in the feed. Additional constraints arising from the complex methanol reaction and the practical limitations are introduced step by step. The results show that significant improvements for both objective functions are possible through periodic forcing of the two inputs considered here.