Bayesian chemical reaction neural network for autonomous kinetic uncertainty quantification

Chemical reaction neural network (CRNN), a recently developed tool for autonomous discovery of reaction models, has been successfully demonstrated on a variety of chemical engineering and biochemical systems. It leverages the extraordinary data-fitting capacity of modern deep neural networks (DNNs) while preserving high interpretability and robustness by embedding widely applicable physical laws such as the law of mass action and the Arrhenius law. In this paper, we further developed Bayesian CRNN to not only reconstruct but also quantify the uncertainty of chemical kinetic models from data. Two methods, the Markov chain Monte Carlo algorithm and variational inference, were used to perform the Bayesian CRNN, with the latter mainly adopted for its speed. We demonstrated the capability of Bayesian CRNN in the kinetic uncertainty quantification of different types of chemical systems and discussed the importance of embedding physical laws in data-driven modeling. Finally, we discussed the adaptation of Bayesian CRNN for incomplete measurements and model mixing for global uncertainty quantification.

Adaptability of different mechanisms and kinetic study of methane combustion in steam diluted environments

The chemical kinetics of methane oxidation in a steam-diluted environment are studied in the present study. Various well-validated mechanisms for methane combustion are adopted and compared with experimental data. Ignition delay, laminar flame speed, and emissions for CH₄ combustion with steam dilution are discussed. Cumulative relative error parameter was determined for all mechanisms considered in this study to evaluate the prediction level in quantifiable terms. Reaction pathways under no and steam-diluted environments are analyzed, and key elementary reactions and species are identified in these conditions. The analysis gives a relative idea of the applicability of some of the reduced mechanisms for the diluted steam conditions. This study aims to guide future computational fluid dynamics simulations to accurately predict combustion characteristics in these conditions. Computations of laminar flame speed from GRI-3.0, Aramco3.0, Curran, and San Diego mechanisms were the most precise under diluted steam conditions. Similarly, for the calculation of ignition delay of methane under the steam dilution, the Aramco mechanism and the Curran's mechanism were able to predict the experimentally observed values most closely. Sensitivity study for the OH concentrations shows that the H-abstraction of methane from OH radicals has an opposing trend with dilution for Aramco and GRI-3.0 mechanism. On the other hand, CO and NO emissions were reduced significantly, with the dilution increased from 0 to 20%. The third-body effect of steam is observed to dominate the deviation observed between the detailed and reduced mechanism. For low operating pressure conditions, the GRI-3.0 mechanism gives an excellent prediction, whereas, for applications like gas turbines and furnaces, Aramco-3.0 and Curran mechanisms can be adopted to give good results. The San Diego mechanism can be chosen for low computational facility purposes as it shows very good predictions for ignition delay and laminar flame speed computations.

Statistical Analysis on Rate Parameters of the H2-O2 Reaction System

Quantitative rate determination of elementary reactions is a major task in the study of chemical kinetics. To ensure the fidelity of their determination, progressively tightened constraints need to be placed on their measurement, especially with the development of various notable experimental techniques. However, the evaluation of reaction rates and their uncertainties is frequently conducted with substantial subjectivity due to data source, thermodynamic conditions, sampling range, and sparsity. To reduce the extent of biased rate evaluation, we propose herein an approach of uncertainty-weighted statistical analysis, utilizing weighted average, and weighted least-square regression in statistical inference. Based on the backbone H₂/O₂ chemistry, rate data for each elementary reaction are collected from the time-history profile in shock tube experiments and high-level theoretical calculations, with their assigned weight inversely depending on uncertainty, which would overall avoid subjective assessments and provide more accurate rate evaluation. Aided by sensitivity analysis, the rates of a few key reactions are further constrained in the less investigated low- to intermediate-temperature conditions using high-fidelity flow reactor data. Good performance of the constructed mechanism is confirmed with validation against the target of the high-fidelity flow reactor data. This study demonstrates a systematic approach for reaction rate evaluation and uncertainty quantification.

Dual Fuel Reaction Mechanism 2.0 including NOx Formation and Laminar Flame Speed Calculations Using Methane/Propane/n-Heptane Fuel Blends

This study presents the further development of the TU Wien dual fuel mechanism, which was optimized for simulating ignition and combustion in a rapid compression expansion machine (RCEM) in dual fuel mode using diesel and natural gas at pressures higher than 60 bar at the start of injection. The mechanism is based on the Complete San Diego mechanism with n-heptane extension and was attuned to the RCEM measurements to achieve high agreement between experiments and simulation. This resulted in a specific application area. To obtain a mechanism for a wider parameter range, the Arrhenius parameter changes performed were analyzed and updated. Furthermore, the San Diego nitrogen sub-mechanism was added to consider NOx formation. The ignition delay time-reducing effect of propane addition to methane was closely examined and improved. To investigate the propagation of the flame front, the laminar flame speed of methane–air mixtures was simulated and compared with measured values from literature. Deviations at stoichiometric and fuel-rich conditions were found and by further mechanism optimization reduced significantly. To be able to justify the parameter changes performed, the resulting reaction rate coefficients were compared with data from the National Institute of Standards and Technology chemical kinetics database.

Global Sensitivity Analysis of Large Reaction Mechanisms Using Fourier Amplitude Sensitivity Test

Global sensitivity analysis (GSA) of large chemical reaction mechanisms remains a challenge since the model with uncertainties in the large number of input parameters provides large dimension of input parameter space and tends to be difficult to evaluate the effect of input parameters on model outputs. In this paper, a criterion for frequency selection to input parameter is proposed so that Fourier amplitude sensitivity test (FAST) method can evaluate the complex model with a low sample size. This developed FAST method can establish the relationship between the number of input parameters and sample size needed to measure sensitivity indices with high accuracy. The performance of this FAST method which can allow both the qualitative and quantitative analysis of complex systems is validated by a H2/air combustion model and a CH4/air combustion model. This FAST method is also compared with other GSA methods to illustrate the features of this FAST method. The results show that FAST method can evaluate the reaction systems with low sample size, and the sensitivity indices obtained from the FAST method can provide more important information which the variance-based GSA methods cannot obtain. FAST method can be a remarkably effective tool for the modelling and diagnosis of large chemical reaction.

Influence of oxygen on generation of reactive chemicals from nitrogen plasma jet

A nonthermal plasma jet is operated at atmospheric pressure inside a vacuum chamber filled with nitrogen gas. Various chemical compounds are fabricated from nitrogen and water molecules in plasma jet with varying oxygen content. Detailed theoretical investigation of these chemical compounds is carried out in terms of different oxygen ratio ξ. Experimental measurements are also carried out for comparison with theoretical results. Hydroxyl molecules are mostly generated at surface of water, and some of them can penetrate into water. The density of hydroxyl molecules has its maximum without oxygen, and decreases to zero as ξ increases to 0.25. The density of the ammonia of NH₃ also deceases as ξ increases to 0.25. On the other hand, theory and experiment show that the density of the NO₃ increases drastically as ξ increases to 0.25. The hydrogen peroxide density in plasma activated water deceases, reaches its minimum value at ξ = 0.05, and then increases again, as ξ increases from a small value to a large value. The pH value of the plasma activated water, which is slightly changed to alkali without oxygen, decreases as ξ increases.

Chemical kinetic model uncertainty minimization through laminar flame speed measurements

Laminar flame speed measurements were carried for mixture of air with eight C_3-4 hydrocarbons (propene, propane, 1,3-butadiene, 1-butene, 2-butene, iso-butene, n-butane, and iso-butane) at the room temperature and ambient pressure. Along with C_1-2 hydrocarbon data reported in a recent study, the entire dataset was used to demonstrate how laminar flame speed data can be utilized to explore and minimize the uncertainties in a reaction model for foundation fuels. The USC Mech II kinetic model was chosen as a case study. The method of uncertainty minimization using polynomial chaos expansions (MUM-PCE) (D.A. Sheen and H. Wang, Combust. Flame 2011, 158, 2358-2374) was employed to constrain the model uncertainty for laminar flame speed predictions. Results demonstrate that a reaction model constrained only by the laminar flame speed values of methane/air flames notably reduces the uncertainty in the predictions of the laminar flame speeds of C₃ and C₄ alkanes, because the key chemical pathways of all of these flames are similar to each other. The uncertainty in model predictions for flames of unsaturated C_3-4 hydrocarbons remain significant without considering fuel specific laminar flames speeds in the constraining target data set, because the secondary rate controlling reaction steps are different from those in the saturated alkanes. It is shown that the constraints provided by the laminar flame speeds of the foundation fuels could reduce notably the uncertainties in the predictions of laminar flame speeds of C₄ alcohol/air mixtures. Furthermore, it is demonstrated that an accurate prediction of the laminar flame speed of a particular C₄ alcohol/air mixture is better achieved through measurements for key molecular intermediates formed during the pyrolysis and oxidation of the parent fuel.

Development of a Joint Hydrogen and Syngas Combustion Mechanism Based on an Optimization Approach

A comprehensive and hierarchical optimization of a joint hydrogen and syngas combustion mechanism has been carried out. The Kéromnès et al. (Combust Flame, 2013, 160, 995-1011) mechanism for syngas combustion was updated with our recently optimized hydrogen combustion mechanism (Varga et al., Proc Combust Inst, 2015, 35, 589-596) and optimized using a comprehensive set of direct and indirect experimental data relevant to hydrogen and syngas combustion. The collection of experimental data consisted of ignition measurements in shock tubes and rapid compression machines, burning velocity measurements, and species profiles measured using shock tubes, flow reactors, and jet-stirred reactors. The experimental conditions covered wide ranges of temperatures (800-2500 K), pressures (0.5-50 bar), equivalence ratios (ϕ = 0.3-5.0), and C/H ratios (0-3). In total, 48 Arrhenius parameters and 5 third-body collision efficiency parameters of 18 elementary reactions were optimized using these experimental data. A large number of directly measured rate coefficient values belonging to 15 of the reaction steps were also utilized. The optimization has resulted in a H2/CO combustion mechanism, which is applicable to a wide range of conditions. Moreover, new recommended rate parameters with their covariance matrix and temperature-dependent uncertainty ranges of the optimized rate coefficients are provided. The optimized mechanism was compared to 19 recent hydrogen and syngas combustion mechanisms and is shown to provide the best reproduction of the experimental data.

Global Uncertainty Propagation and Sensitivity Analysis in the CH3OCH2 + O2 System: Combining Experiment and Theory To Constrain Key Rate Coefficients in DME Combustion

Statistical rate theory calculations, in particular formulations of the chemical master equation, are widely used to calculate rate coefficients of interest in combustion environments as a function of temperature and pressure. However, despite the increasing accuracy of electronic structure calculations, small uncertainties in the input parameters for these master equation models can lead to relatively large uncertainties in the calculated rate coefficients. Master equation input parameters may be constrained further by using experimental data and the relationship between experiment and theory warrants further investigation. In this work, the CH3OCH2 + O2 system, of relevance to the combustion of dimethyl ether (DME), is used as an example and the input parameters for master equation calculations on this system are refined through fitting to experimental data. Complementing these fitting calculations, global sensitivity analysis is used to explore which input parameters are constrained by which experimental conditions, and which parameters need to be further constrained to accurately predict key elementary rate coefficients. Finally, uncertainties in the calculated rate coefficients are obtained using both correlated and uncorrelated distributions of input parameters.

Few-Step Kinetic Model of Gaseous Autocatalytic Ethane Pyrolysis and Its Evaluation by Means of Uncertainty and Sensitivity Analysis

A kinetic scheme of radical chain reactions in autocatalytic pyrolysis of ethane was studied using a sensitivity analysis method, bringing in the experimental data. In the gas-phase kinetic experiments, ethane pyrolysis was carried out in laboratory reactors with the reaction mixture heated by CO2 laser irradiation. It was shown that the scheme with autocatalytic routes includes as few steps as possible and adequately describes the ethane pyrolysis with high ethylene yield at 900–1,150 K. Admissible variation ranges of preexponential factors and activation energies for the kinetic model of the reactions were found using the Monte Carlo statistical method. Reducibility of the scheme was examined by means of the Sobol’s variance based strategy applied for the sensitivity analysis evaluation.

Direct measurements of the total rate constant of the reaction NCN + H and implications for the product branching ratio and the enthalpy of formation of NCN

The high-temperature rate constant of the reaction NCN + H, a key reaction for modelling NO_x formation in flames, has been directly measured for the first time.