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At least 1,045 records · Page 58
All sourcesNASA NTRSDOE OSTI
NASA NTRS2026

A Modular Conjugate Heat Transfer Optimization Framework for Thermal Management of Electric Aircraft

Conjugate heat transfer (CHT) analysis and optimization is a powerful method for improving thermal management, as it simultaneously resolves the temperature distribution in both fluid and solid domains. This paper presents a modular, discrete adjoint-based CHT optimization capability integrated within the OpenMDAO/MPhys framework. A unique feature of the proposed framework is its flexibility to extend to multidisciplinary optimization, including aero-structural-thermal applications. The fluid domain is modeled using a finite-volume Computational Fluid Dynamics (CFD) solver, and the solid domain with a conduction heat transfer solver. A mixed Neumann-Dirichlet boundary condition is developed to enable full submersion of the solid geometry within the fluid domain, while ensuring consistent temperature and heat flux coupling at the CHT interface. Gradient-based optimization is performed; the gradients are efficiently computed using the discrete adjoint solvers implemented in DAFoam. To demonstrate the method, this paper considers two cases related to electric aircraft thermal management: a U-bend heat exchanger and an actively cooled battery pack. The U-bend case aims to minimize pressure loss while maximizing heat flux by changing the pipe geometry. The optimized design reduces pressure loss by 52.7% and increases total heat flux by 2.3%. In the battery pack case, a 3-by-3 cell configuration is cooled by ambient airflow, with constant heat generation prescribed in the cells. The battery casing shape serves as the design variable, and the objective function is a weighted sum of pressure loss and pack weight, subject to a maximum temperature constraint. The optimized design achieves a 44.6% reduction in pressure loss and a 1.5% reduction in weight, while satisfying the thermal constraint. To ensure the reliability of the optimized designs, this study validates coarse-mesh, steady-state predictions against fine-mesh unsteady simulations, demonstrating consistency within acceptable errors. This work demonstrates the potential of the developed framework to enable rapid, high-fidelity design of thermal management systems for electric aircraft.

heat transfer↗
NASA NTRS2026

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗
DOE OSTI2023

Digital Twin for Optimizing Real-time Economy of the Integrated Energy Systems

Economic and safe operation of integrated energy systems (IES) requires real-time optimization (RTO) of the control and actions conducted on each system component. In this regard, digital twins (DTs), which consist of a physical system, a virtual system, and the data communication that occurs between the two, are essential for effective RTO. Through the data warehouse, the virtual system is constantly updated with real-time data from the physical system, and functions as the model in the optimization framework. The reduced-order model of the dynamic process model in the virtual system is used in the optimization framework. The optimization results are then returned, via the data warehouse, as control actions to the physical system. This work demonstrates the software capabilities of DT assets for an IES in the context of preparing a DT for an experimental system comprised of Idaho National Laboratory (INL)’s Thermal Energy Delivery System and battery system. For the virtual demonstration, the DTs encompass (1) a physical system, including the Modelica models of the Thermal Energy Delivery System and the battery system; (2) virtual optimization via the Optimization of Real-Time Capacity Allocation (ORCA) platform; and (3) the open-source data warehouse software DeepLynx. This work assesses the performance of ORCA, which utilizes a reduced-order model built using the Risk Analysis Virtual Environment (RAVEN) and trained on the Modelica models and real-time data pipeline through the graph database hosted in DeepLynx. The proposed optimization workflow will be an RTO model based on DTs and the data they generate.

25 ENERGY STORAGE↗
DOE OSTI2013

On the use of genetic algorithm to optimize industrial assets lifecycle management under safety and budget constraints

The purpose of this paper is to describe the method and tool dedicated to optimize investments planning for industrial assets. These investments may either be preventive maintenance tasks, asset enhancements or logistic investments such as spare parts purchases. The two methodological points to investigate in such an issue are: 1. The measure of the profitability of a portfolio of investments 2. The selection and planning of an optimal set of investments 3. The measure of the risk of a portfolio of investments The measure of the profitability of a set of investments in the IPOP tool is synthesised in the Net Present Value indicator. The NPV is the sum of the differences of discounted cash flows (direct costs, forced outages...) between the situations with and without a given investment. These cash flows are calculated through a pseudo-Markov reliability model representing independently the components of the industrial asset and the spare parts inventories. The component model has been widely discussed over the years but the spare part model is a new one based on some approximations that will be discussed. This model, referred as the NPV function, takes for input an investments portfolio and gives its NPV. The second issue is to optimize the NPV. If all investments were independent, this optimization would be an easy calculation, unfortunately there are two sources of dependency. The first one is introduced by the spare part model, as if components are indeed independent in their reliability model, the fact that several components use the same inventory induces a dependency. The second dependency comes from economic, technical or logistic constraints, such as a global maintenance budget limit or a safety requirement limiting the residual risk of failure of a component or group of component, making the aggregation of individual optimum not necessary feasible. The algorithm used to solve such a difficult optimization problem is a genetic algorithm. After a description of the features of the software a test case is presented showing the influence of the optimization algorithm parameters on its efficiency to find an optimal investments planning. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Multi-objective optimization of a PCHE-type intermediate heat exchanger using genetic algorithms

For the advanced nuclear reactor systems and power conversion units, it is important to optimize the design of intermediate heat exchangers (IHXs) which transfer heat from the primary loop to the secondary or intermediate loop. For a multi-objective optimization problem, a printed circuit heat exchanger-type IHX with zigzag and S-shaped fin channels is selected to be optimized in terms of both the total cost and the heat exchanger thermal effectiveness using genetic algorithms. A computer code is developed to search a set of optimized designs of the zigzag channel geometry. It is found that among the Pareto-optimal solutions, the total cost is approximately linearly related to the thermal effectiveness between 88 and 95% while it rises rapidly after the effectiveness exceeds 95%. An optimal flow channel diameter is also determined through the optimization. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Optimization of a dry, mixed nuclear fuel storage array for nuclear criticality safety - 14339

A dry storage array of used nuclear fuel at the Idaho National Laboratory contains a mixture of more than twenty different types of research and test reactor fuels. Significant neutronic interaction occurs between fuel canisters within this large storage arrangement of 636 fuel storage canisters. Nuclear criticality safety is maintained primarily by moderation control and through control of neutron interaction and leakage provided by the credited geometry. Over the nearly forty years of operation the collected fuels are now arranged in a configuration that does not minimize the system neutron multiplication factor (k{sub eff}). This creates a concern since the entire remaining facility storage capacity cannot be utilized without exceeding the system minimum subcritical state (k{sub safe}) for ensuring nuclear criticality safety. This work determines a more optimal arrangement for the stored fuels with a goal to minimize the system k{sub eff}, but also with a minimum of potential fuel canister relocation movements. The ultimate goal is to establish a solution for this multiple-objective optimization problem by finding the Pareto Front for maximum k{sub eff} reduction versus the number of canister relocations. The process first required additional analysis of the array by Monte-Carlo neutron transport codes (specifically, MCNP) to gain a greater understanding of the interaction characteristics of the disparate fuel types. Some stored fuels are composed of primarily metallic and oxide components that provide very little inherent moderation, while other fuel types contain graphite or zirconium-hydride which can contribute a significant amount of moderation. These factors cause a complex relationship within a fuel arrangement with respect to thermal utilization and axial leakage probability. The new MCNP analysis was utilized to develop a simplified spreadsheet-based empirical model which simulates the array k{sub eff} result. This empirical model was benchmarked against additional MCNP calculations for various arrangements and then employed in the optimization analysis. A Tabu metaheuristic and stochastic approximation optimization was applied to the empirical model with the optimization function to minimize the array k{sub eff}. The optimization algorithm interrogated the empirical model to determine the optimal rearrangement for up to sixty canister movements. The Pareto Front was found, which shows that a limited number of canister relocation movements could allow the existing thirty-one empty array positions to be filled with common research reactor fuels while also yielding a reduction in the overall array k{sub eff} relative to the current arrangement. This will impart an improvement in the facility utilization while also offering an enhancement in the safety margin. The reduction in array reactivity has been confirmed by a final set of MCNP calculations with the proposed new arrangements. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Particle Swarm Optimisation for group structure optimization for radiotherapy shielding

Neutron transport simulations are ubiquitous in nuclear engineering because they allow one to model experimental systems and render a model platform for easy perturbation of experimental designs. In addition, simulations allow one to gain experimental insight without actually having to go through the trouble of building a physical experiment. Neutron transport simulations can be stochastic or deterministic based. Stochastic neutron transport simulations are typically simulated using the Monte Carlo method and yield very accurate solutions but are computationally expensive, while deterministic methods are typically faster but can be less accurate. Here we focus on optimizing the accuracy of deterministic neutron transport simulations for radiotherapy simulations. Deterministic neutron transport requires discretization of angle, energy, and space to appropriately analyze the system one is trying to model. Discretization of energy is challenging because of the highly variable neutron flux at certain neutron energies. Improper discretization of energy in the transport model can lead to erroneous results and therefore inaccurate interpretations of the solution. In this study, we evaluate Particle Swarm Optimization (PSO) as a mechanism for selecting optimal group structures for radiotherapy shielding. We tested the particle swarm optimization algorithm on radiotherapy shielding problems using Los Alamos National Laboratory's (LANL) main deterministic transport code PARTISN. Results show that the optimized energy group structures generated from the optimization algorithm outperformed LANL's standard energy group structures, and therefore demonstrate utility in using PSO to expedite computation times due to the increased accuracy obtained with a smaller but optimized group structure. (authors)

43 PARTICLE ACCELERATORS↗
DOE OSTI2018

Asynchronously parallel optimization solver for finding multiple minima

This paper proposes and analyzes an asynchronously parallel optimization algorithm for finding multiple, high-quality minima of nonlinear optimization problems. Our multistart algorithm considers all previously evaluated points when determining where to start or continue a local optimization run. Theoretical results show that, under certain assumptions, the algorithm almost surely starts a finite number of local optimization runs and identifies, or has a single local optimization run converging to, every minimum. The algorithm is applicable to general optimization settings, but our numerical results focus on the case when derivatives are unavailable. In numerical tests, a PYTHON implementation of the algorithm is shown to yield good approximations of many minima (including a global minimum), and this ability scales well with additional resources. Our implementation’s time to solution is shown also to scale well even when the time to evaluate the function evaluation is highly variable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.

distributionally robust optimization↗
DOE OSTI2020

Nonlinear Multiobjective MPC-Based Optimal Operation of a High Consistency Refining System in Papermaking

As one of the most important unit in the papermaking industry, the high consistency (HC) refining system is confronted with challenges such as improving pulp quality, energy saving, and emissions reduction in its operation processes. Here in this correspondence, an optimal operation of HC refining system is presented using nonlinear multiobjective model predictive control strategies that aim at set-point tracking objective of pulp quality, economic objective, and specific energy (SE) consumption objective, respectively. First, a set of input and output data at different times are employed to construct the subprocess model of the state process model for the HC refining system, and then the Wiener-type model can be obtained through combining the mechanism model of Canadian Standard Freeness and the state process model that determines their structures based on Akaike information criterion. Second, the multiobjective optimization strategy that optimizes both the set-point tracking objective of pulp quality and SE consumption is proposed simultaneously, which uses NSGA-II approach to obtain the Pareto optimal set. Furthermore, targeting at the set-point tracking objective of pulp quality, economic objective, and SE consumption objective, the sequential quadratic programming method is utilized to produce the optimal predictive controllers. In conclusion, the simulation results demonstrate that the proposed methods can make the HC refining system provide a better performance of set-point tracking of pulp quality when these predictive controllers are employed. In addition, while the optimal predictive controllers orienting with comprehensive economic objective and SE consumption objective, it has been shown that they have significantly reduced the energy consumption.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗
DOE OSTI2022

HOPP - Hybrid Optimization and Performance Platform

The Hybrid Optimization and Performance Platform, HOPP, is a wind + solar + battery + X design software for optimizing co-located, utility-scale hybrid plants down to the component level for different markets and technoeconomic objectives. Key technology and financial inputs to the HOPP model that inform the objective to be optimized are presented. The layout and performance integration is combined with optimal dispatch and full financial modeling within an optimization framework. With an example scenario, optimal sizing and layout results are shown in a sensitivity analysis of prices for two hybrid configurations.

batteries↗
DOE OSTI2021

Analysis of Hydrocyclone Geometry via Rapid Optimization Based on Computational Fluid Dynamics

Abstract Hydrocyclones exploit density gradients for the centrifugal separation of dispersions in a continuous liquid. Selection of the geometrics for optimal separation is case specific, like the media characteristics. The existing optimization method based on computational fluid dynamics (CFD) provides a powerful analytical tool but requires long computational times. The most common praxis for CFD optimization is via the single‐factor optimization method (SFOM). In this study, a novel approach is presented as an improved rapid optimization method that implements a dynamic‐mesh and user‐defined function optimization method (DUOM). The DUOM adapts the dynamic‐mesh approach from other applications to the optimization analysis of hydrocyclones. The DUOM reduced the computational time by 31.1 %, compared to the SFOM.

Liu, Lin↗
DOE OSTI2024

Stochastic Optimization and Uncertainty Quantification of Natrium-based Nuclear-Renewable Energy Systems for Flexible Power Applications in Deregulated Markets

Rapid integration of variable renewable energy sources (VRES) has made modeling and stochastic optimization of hybrid energy systems crucial for studying their long-term performance and viability. However, most studies have focused on just historical data, which may be unreliable for capturing short-term fluctuations, rare events, and long-term patterns of energy demand, price, and the variability of renewable energy sources. For this study, optimal synthetic time series models were developed using Wasserstein distance. The models were validated by comparing the key statistical measures against those of the historical data. They were then used to optimize the integrated Natrium-style advanced energy systems and their long-term (30 years) economics. The stochastic model performs bi-level optimization to find the optimal sizes for the balance of plant and thermal energy storage, while also optimizing energy dispatch to achieve the maximum net present value. In studies of two deregulated markets (California ISO and the Electric Reliability Council of Texas), the integrated Natrium-style system performed better in CAISO than in ERCOT, given higher and more consistent electricity prices during peak-demand periods. The potentially enlarged cost associated with the variable operation and maintenance of the TES system also plays a significant role in driving the system sizing, thus its impacts on the system are investigated in detail through comparison against a baseline case. The study also finds that the bi-level optimization results based on stochastic gradient descent closely match the grid search results. The uncertainty quantification of the stochastic signals provides further NPV-related insights and probability distributions for the case studies. The normal standard error of the mean of NPV for the case with and without TES VOM for CAISO were found to be 7.73M (plus-minus sign) 1.09M USD and 104.99M (plus-minus sign) 1.25M USD, respectively based on a 95% confidence. Given the relatively small NPV variance based on 150 samples, the analysis affords the most robust possible prediction of the techno-economic performance of the integrated Natrium-style energy systems.

25 ENERGY STORAGE↗
DOE OSTI2023

Optimized thermodynamic properties of REE aqueous species (REE 3+ and REEOH 2+ ) and experimental database for modeling the solubility of REE phosphate minerals (monazite, xenotime, and rhabdophane) from 25 to 300 °C

Rare earth elements (REE) are critical elements found in monazite, xenotime, and hydrated REE phosphates which typically form in hydrothermal mineral deposits. Accurate predictions of the solubility of these REE phosphates and the speciation of REE in aqueous fluids are both key to understanding the controls on the transport, fractionation, and deposition of REE in natural systems. Previous monazite and xenotime solubility experiments indicate the presence of large discrepancies between experimentally derived solubility constants versus calculated solubilities by combining different data sources for the thermodynamic properties of minerals and aqueous species at hydrothermal conditions. In this study, these discrepancies were resolved by using the program GEMSFITS to optimize the standard partial molal Gibbs energy of formation (Δ f G° 298 ) of REE aqueous species (REE 3+ and REE hydroxyl complexes) at 298.15 K and 1 bar while keeping the thermodynamic properties fixed for the REE phosphates. A comprehensive experimental database was compiled using solubility data available between 25 and 300 °C. The latter permits conducting thermodynamic parameter optimization of Δ f G° 298 for REE aqueous species. Optimal matching of the rhabdophane solubility data between 25 and 100 °C requires modifying the Δ f G° 298 values of REE 3+ by 1–6 kJ/mol, whereas matching of the monazite solubility data between 100 and 300 °C requires modifying the Δ f G° 298 values of both REE 3+ and REEOH 2+ by ~15–31 kJ/mol and ~2–10 kJ/mol, respectively. For xenotime, adjustments of Δ f G° 298 values by 1–26 kJ/mol are only necessary for the REE 3+ species. The optimizations indicate that the solubility of monazite in acidic solutions is controlled by the light (L)REE 3+ species at <150 °C and the LREEOH 2+ species at >150 °C, whereas the solubility of xenotime is controlled by the heavy (H)REE 3+ species between 25 and 300 °C. Based on the optimization results, we conclude that the revised Helgeson-Kirkham-Flowers equation of state does not reliably predict the thermodynamic properties of REE 3+ , REEOH 2+ , and likely other REE hydroxyl species at hydrothermal conditions. We therefore provide an experimental database (ThermoExp_REE) as a basic framework for future updates, extensions with other ligands, and optimizations as new experimental REE data become available. As a result, the optimized thermodynamic properties of aqueous species and minerals are available open access to accurately predict the solubility of REE phosphates in fluid-rock systems.

58 GEOSCIENCES↗
DOE OSTI2021

Combined plasma–coil optimization algorithms

Combined plasma–coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi-free-boundary optimization, and the free-boundary (coil) optimization. These are described using the MRxMHD energy functional, the Biot–Savart integral, the coil-penalty functional and the virtual casing integral and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma–coil optimization algorithms, we emphasize the importance of the stability matrix.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Machine Learning Optimization of p-Type Transparent Conducting Films

p-Type transparent conducting materials (p-TCMs) are important components of optoelectronic devices including solar cells, photodetectors, displays, and flexible sensors. Cu–Zn–S thin films prepared by chemical bath deposition (CBD) can have both high transparency in the visible range (>80%) as well as excellent hole conductivity (>1000 S cm –1 ). However, the interplay between the deposition parameters in the CBD process (metal and sulfur precursor concentrations, temperature, pH, complexing agents, etc.) creates a multidimensional parameter space such that optimization for a specific application is challenging and time-consuming. Here we show that strategic design of experiment combined with machine learning (ML) allows for the efficient optimization of p-TCM performance. The approach is guided by a figure of merit (FOM) calculated from the film conductivity and optical transmission in the desired spectral range. A specific example is shown using two steps of optimization using a selected subset of four experimental CBD factors. The ML model is based on support vector regression employing a radial basis function as the kernel function. 10-fold cross-validation was performed to mitigate overfitting. After the first round of optimization, predicted areas in the parameter space with maximal FOMs were selected for a second round of optimization. Films with optimal FOMs were incorporated into heterojunction solar cells and transparent photodiodes. Here, the optimization approach shown here will be generally applicable to any materials synthesis process with multiple parameters.

14 SOLAR ENERGY↗
DOE OSTI2022

Throughput Optimization of Molybdenum Carbide Nanoparticle Catalysts in a Continuous Flow Reactor Using Design of Experiments

Transition metal carbides (TMCs) have attracted significant attention because of their applications toward a wide range of catalytic transformations. However, the practicality of their synthesis is still limited because of the harsh conditions in which most TMCs are prepared. Recently, a solution-phase synthesis of phase-pure a-MoC1-x nanoparticles was presented. While this synthetic route yielded nanoparticles with exceptional catalytic performance, the reaction parameter space was not explored, and catalyst throughput was not optimized for scale-up. Continuous flow platforms coupled with statistical design of experiments (DoE) can provide a powerful method for understanding the reaction parameter space for optimizations. Here, we demonstrate the use of statistical DoE in tandem with response surface methodology for a parametric screening analysis to optimize the throughput of a MoC1-x nanoparticle synthesis utilizing a millifluidic flow reactor. A full factorial design was implemented to evaluate four input variables (reaction temperature, flow rate, solvent fraction of oleylamine, and precursor concentration) that carry statistically significant effects on three responses (throughput, residence time, and isolated yield). A Doehlert matrix was implemented to investigate each significant variable at a higher number of levels to optimize throughput. Our results give a nonintuitive set of experimental conditions that resulted in an optimized throughput of 2.2 g h-1. This translates to a 50-fold increase in throughput compared to the previously reported batch method. The catalytic performance of the MoC1-x nanoparticles produced under optimized throughput was demonstrated in the CO2 hydrogenation reaction. This DoE screening analysis and throughput optimization of MoC1-x synthesis open the door to an increased feasibility for scale-up.

design of experiments↗