The advent of additive manufacturing has revolutionized the design and fabrication of chemical reactors. Previously impractical geometries are now achievable, leading to significantly larger design spaces. However, exploring these spaces efficiently poses a significant challenge for traditional design methodologies. Existing parameterizations are often low-dimensional, leading to expensive optimization processes and limiting the exploration of more complex and potentially superior designs. Data-driven design tools, such as multi-fidelity Bayesian optimization, offer a promising pathway to navigate these high-dimensional design spaces. Multi-fidelity methods leverage lower-fidelity simulations during optimization, drastically reducing computational costs while still achieving high-quality solutions. This is especially beneficial when gradients are unavailable or a more global solution is needed compared to gradient-based approaches. This research introduces an augmented intelligence framework that integrates data-driven optimization, machine learning, CFD, and additive manufacturing to design high-performance reactors. The coiled-tube reactor, known for its desirable mixing and heat transfer properties, serves as a case study to illustrate the effectiveness of the proposed framework. Coiled-tube reactors have garnered significant attention in various chemical engineering applications due to their efficient mixing and heat transfer capabilities. They have been successfully employed in flow chemistry, bioprocesses, and chemical kinetic experiments, demonstrating versatility across different scales and applications. At the mesoscale, they combine the benefits of microreactors with the economic advantages of larger-scale reactors. Previous work has shown that improvements in plug flow performance at low flow rates can be achieved by introducing pulsed-flow conditions to enhance radial mixing through the generation of Dean vortices. However, inducing these vortices at low flow rates under steady-state conditions without pulsed flow remains a challenge. This study aims to improve plug flow performance by identifying optimal geometric parameterizations through the application of machine learning techniques and CFD simulations. The subsequent designs will then be 3D-printed and experimentally validated, showcasing the efficacy of the proposed approach.

The literature extensively covers the design and optimization of chemical reactors, focusing on various reactor types and optimization techniques. Existing work on coiled-tube reactors highlights their advantageous mixing and heat transfer characteristics. Studies explore modifications to enhance performance, often involving pulsed flow to induce Dean vortices at low Reynolds numbers. However, these methods may not be suitable for all applications. The application of multi-fidelity Bayesian optimization to reactor design is a relatively recent development, with studies demonstrating the potential for significant computational savings and improved solution quality. This work builds on the existing literature by developing a novel framework that combines advanced manufacturing, machine learning, and multi-fidelity optimization to explore the high-dimensional design space of coiled-tube reactors, potentially uncovering designs that surpass traditional approaches.

This study employs a novel augmented intelligence framework that combines several advanced techniques to optimize the design of coiled-tube reactors. The framework comprises three main stages: **1. Parameterization:** Two distinct parameterizations are defined to describe the reactor geometry: one for the cross-section and one for the coil path. * **Cross-section Parameterization:** A polar Gaussian process (GP) is used to model the cross-sectional shape, allowing for smooth variations along the reactor length. The GP uses a polar kernel function that handles the angular coordinates appropriately, ensuring smooth transitions. The hyperparameters of the GP control the complexity of the cross-sectional profile. The number of interpolation points for both the angular and radial directions affects the dimensionality of the design problem. * **Coil Path Parameterization:** The coil path is parameterized using cylindrical coordinates, where deviations from a nominal coil are introduced through interpolation points. This parameterization ensures that the coil does not self-intersect. The number of interpolation points along the path is a hyperparameter influencing the flexibility of the parameterization. **2. Simulation and Optimization:** Computational fluid dynamics (CFD) simulations using OpenFOAM are employed to evaluate the performance of each reactor design. The simulations solve the transport equations for an impulse tracer to obtain the residence time distribution (RTD). Multi-fidelity Bayesian optimization, specifically the DARTS framework, is employed to optimize the parameters of both the cross-section and coil path parameterizations. This allows for utilizing lower-fidelity simulations early in the optimization process to reduce computational cost, while higher-fidelity simulations are used to refine the optimal design in later stages. The optimization aims to maximize plug flow performance, while simultaneously penalizing non-ideal RTDs (e.g., bimodal or highly skewed distributions) using a composite objective function. Gaussian processes are used to model both the simulation cost and the objective function. t-distributed stochastic neighbor embedding (t-SNE) is used to analyze the convergence of the optimization process in the high-dimensional parameter space. **3. Experimental Validation:** The optimized designs are 3D-printed using a FormLabs Form3+ printer. Experimental residence time distribution (RTD) experiments and Villermaux-Dushman reaction experiments are conducted at Re = 50 to validate the performance of the designs. Data are analyzed using a tanks-in-series model to estimate plug flow performance. The experiments measure the concentration profiles at the reactor outlet, providing quantitative data for comparing the performance of the optimized reactors with a conventional design. A comprehensive analysis is provided, including convergence analysis, hyperparameter sensitivity analysis, and experimental uncertainty analysis.

The key findings of this study are: 1. **Optimal Design Features:** The optimization identified key features responsible for improved plug flow performance, including periodic expansions and contractions of the reactor cross-section, distinct pinches within the cross-section, and controlled variations in the coil path. These features lead to the generation of enhanced Dean vortices, even at low Reynolds numbers (Re=50), improving radial mixing. 2. **Improved Plug Flow Performance:** The optimized reactor designs demonstrated significant improvements in plug flow performance compared to the conventional design. Experimental RTD measurements showed a 55-62% increase in the equivalent number of tanks in series (N), indicating significantly reduced axial dispersion. 3. **Enhanced Reactive Flow Performance:** The Villermaux-Dushman reaction experiments validated the improved mixing capabilities of the optimized designs. The optimized reactors showed higher absorbance values at 353nm (indicating higher conversion of the limiting reactant), confirming superior performance for mass transfer limited reactions. 4. **Convergence Analysis:** The t-SNE analysis provided insights into the convergence of the optimization process, revealing systematic changes in design parameters indicative of convergent behavior. Lower-fidelity simulations were effectively utilized during the exploration phase of optimization, saving computational time. 5. **Interpretability of Results:** The framework's design ensured interpretability of the results. This approach enables identification of key driving characteristics responsible for improved reactor performance, rather than merely relying on black-box optimization results. 6. **Benchmarking:** The generated parameterizations and simulations are shared openly as benchmark problems, supporting algorithm development for high-dimensional, expensive, black-box optimization problems. 7. **Impact:** The optimized reactors exhibited a 29.3% higher pressure drop than the standard coil for a single coil turn, a trade-off that can be considered in future multi-objective optimizations. This research represents a significant advance in chemical reactor design. It highlights the potential for machine learning methods to discover superior designs exceeding the capabilities of traditional techniques.

This work addresses the challenge of efficiently exploring high-dimensional design spaces for chemical reactors by integrating advanced manufacturing, machine learning, and multi-fidelity Bayesian optimization. The results demonstrate the effectiveness of the proposed augmented intelligence framework in identifying reactor designs with significantly improved performance. The observed performance enhancements stem from the optimized geometry's ability to induce Dean vortices at lower Reynolds numbers, thereby improving radial mixing under steady-state conditions. The experimental validation using both tracer and reacting flow experiments confirms the computational findings. The interpretability of the results further strengthens the framework's value, allowing for understanding the underlying physical mechanisms driving the enhanced performance. The open-source nature of the data and code contributes to the broader chemical engineering community by providing valuable resources for benchmarking optimization algorithms and advancing research in reactor design. Future work could explore incorporating additional factors such as pressure drop and different operating conditions (multiphase flows, reactive systems) into the optimization problem to further refine the design methodology. The principles demonstrated here are potentially transferable to other classes of chemical reactors, enabling efficient exploration and optimization of novel designs.

This study presents a novel augmented intelligence framework that successfully integrates advanced manufacturing, machine learning, and multi-fidelity Bayesian optimization for the design of high-performance chemical reactors. The framework identified key design features leading to improved plug flow characteristics and reactive flow performance in coiled-tube reactors, validated through 3D-printing and experimentation. The work demonstrates the potential of machine learning to accelerate the discovery of advanced reactor designs exceeding traditional methods. The open-source release of data and code promotes further research and algorithm development in high-dimensional optimization for chemical engineering applications. Future directions include extending the methodology to multi-objective optimization incorporating pressure drop and exploring various reactor types beyond coiled designs.

While the study demonstrates significant improvements in reactor performance, several limitations should be considered. First, the optimization may not have found the absolute global optimum due to the complexity of the search space. Second, the experimental validation was conducted at a single Reynolds number (Re=50). Further experiments across a wider range of Reynolds numbers would strengthen the generalizability of the findings. Finally, the pressure drop in the optimized designs was not directly measured but estimated computationally and is a factor that may need further investigation or optimization.