Equations Of Chemical Kinetics Research Articles

Adsorption of Bichromate and Arsenate Anions by a Sorbent Based on Bentonite Clay Modified with Polyhydroxocations of Iron and Aluminum by the "Co-Precipitation" Method.

The physicochemical properties of natural bentonite and its sorbents were studied. It has been established the modification of natural bentonites using polyhydroxoxides of iron (III) (mod.1_Fe_5-c) and aluminum (III) (mod.1_Al_5-c) by the "co-precipitation" method led to changes in their chemical composition, structure, and sorption properties. It was shown that modified sorbents based on natural bentonite are finely porous (nanostructured) objects with a predominance of pores of 1.5-8.0 nm in size. The modification of bentonite with iron (III) and aluminum compounds by the "co-precipitation" method also leads to an increase in the sorption capacity of the obtained sorbents with respect to bichromate and arsenate anions. A kinetic analysis showed that, at the initial stage, the sorption process was controlled by an external diffusion factor, that is, the diffusion of the sorbent from the solution to the liquid film on the surface of the sorbent. The sorption process then began to proceed in a mixed diffusion mode when it limited both the external diffusion factor and the intra-diffusion factor (diffusion of the sorbent to the active centers through the system of pores and capillaries). To clarify the contribution of the chemical stage to the rate of adsorption of bichromate and arsenate anions by the sorbents under study, kinetic curves were processed using equations of chemical kinetics (pseudo-first-order, pseudo-second-order, and Elovich models). It was found that the adsorption of the studied anions by the modified sorbents based on natural bentonite was best described by a pseudo-second-order kinetic model. The high value of the correlation coefficient for the Elovich model (R2 > 0.9) allows us to conclude that there are structural disorders in the porous system of the studied sorbents, and their surfaces can be considered heterogeneous. Considering that heterogeneous processes occur on the surface of the sorbent, it is natural that all surface properties (structure, chemical composition of the surface layer, etc.) play an important role in anion adsorption.

Математическое моделирование пиролиза резиновых отходов в горизонтальном цилиндрическом реакторе

Recycling of cushioned rubber products is an important environmental and technical-economic issue. Among the various methods of processing such waste, one of the most effective is the pyrolysis process, since it allows us to obtain fuel and energy, and provides the possibility of secondary use of carbon black and metal. Mathematical modeling of this process is necessary to solve problems of optimization and automated control. Thus, the purpose of this study is to simulate the pyrolysis process in a horizontal cylindrical batch reactor, which is currently becoming increasingly widespread. To mathematically describe the process, a model with distributed parameters is used in the form of a two-dimensional thermal conductivity equation and a system of equations of chemical kinetics of polymer thermal destruction reactions. The problem is solved numerically using the finite element method. As a result of the numerical solution of the equations of the mathematical model, non-stationary distributions of temperature and degree of conversion over the cross section of the reactor with non-uniform filling have been obtained. The authors have studied the kinetics of the reaction of polymer thermal destruction in reactors of different diameters. The results obtained can be used to predict the kinetics of material destruction under given reactor heating conditions, which can be useful when we design reactors and automate pyrolysis process control.

Experimental and simulation study on the expansion mechanism of polyurethane grout

Understanding the expansion mechanism of polyurethane polymer grout can supply guidance for accurate grouting. However, most of the polymer grout expansion calculations were defined simplistically by the polymer density-expansion pressure empirical relationship expression, which failed to meet the time history of the expansion pressure during the polymer reaction process. The objective of this paper was to investigate the expansion mechanism of polyurethane foam in various constraint conditions during the whole polymer reaction process. A model describing the expansion mechanism of polyurethane foam was established based on the energy conservation principle, the chemical reaction kinetic equation solved by the Runge-Kutta method, and the ideal gas state equation. The model was proved applicable compared to the experiments under fixed volume and fixed confining pressure boundaries. In addition, the effects of grouting quantity, confining pressure, initial temperature, and physical foaming agent content on the grout expansion pressure, density, and components conversions were discussed. The results showed that the expansion pressure of polymer grout gradually increased with time under the fixed volume conditions, and the grout expansion pressure increased as the density increased. The final grout expansion pressure will increase with the increase of initial temperature or the content of physical blowing agent. Under the fixed confining pressure condition, the polymer grout density gradually decreased with time, the grout density increased as the confining pressure increased while the conversions of the two components alcohol and isocyanate increased. The final density decreases with the increase of initial temperature or the content of physical blowing agent.

Impact of Composition Ratio on the Expansion Behavior of Polyurethane Grout.

Different formulations of foaming polyurethane grout offer controlled expansion rates. This is crucial for precision in filling voids without exerting excessive pressure on surrounding structures, which could potentially cause damage. This study focuses on the impact of composition on the expansion performance of tailor-made polyurethane grouting materials. Initially, multiple unknown chemical reaction kinetic parameters were identified by combining free expansion tests, which involved measuring density and temperature changes, with the particle swarm optimization algorithm. A numerical simulation, integrating chemical kinetic models and fluid flow equations, was established to replicate the free expansion process of polyurethane grout in a cup, aligning with our experimental results. Subsequently, we analyzed the polymerization process of polyurethane grout with varying compositions to determine the effect of composition ratios on grout expansion. Our findings reveal that the expansion ratio of foaming polyurethane is predominantly influenced by the concentrations of physical and chemical foaming agents, followed by isocyanate concentration. Polyol, in contrast, exerts a relatively minor influence. Furthermore, the solubility of the physical foaming agent in the grout determines both its maximum allowable concentration and its maximum contribution to volume increase. This study provides valuable insights for the design and selection of polyurethane grout components tailored to diverse applications.

Optimal Temperature Calculation for Multicriteria Optimization of the Hydrogenation of Polycyclic Aromatic Hydrocarbons by NSGA-II Method

Introduction. Multicriteria optimization, taking into account contradicting criteria, is used to improve production efficiency, reduce costs, improve product quality and environmental safety of processes. The literature describes the application of multicriteria optimization for production purposes, including the selection of reaction conditions and improvement of technological processes. In the presented paper, the object of research is the process of hydrogenation of polycyclic aromatic hydrocarbons (PAH) in the production of high-density fuels. To determine the optimal conditions of the process, the problem of multicriteria optimization based on the kinetic model is solved. The criteria include maximizing the yield of targeted naphthenes and conversion of feedstock. The research objective is to create a program implementing the multicriteria optimization non-dominated sorting genetic algorithm-II (NSGA-II). Due to this, it is possible to calculate the optimal temperature for the PAH hydrogenation process on the basis of the kinetic model.Materials and Methods. The NSGA-II genetic algorithm was used to solve the multicriteria optimization problem. Modified parental and survival selection within the Pareto front was also used. If it was necessary to divide the front, solutions based on the Manhattan distance between them were selected. The program was implemented in Python.Results. In the system of ordinary nonlinear differential equations of chemical kinetics, the concentration was designated yi, the conditional contact time of the reaction mixture with the catalyst — τ. The system was solved for the hydrogenation reaction of polycyclic aromatic hydrocarbons. The calculations showed that at τ = 0 y1(0) = 0.025; y2(0) = 0.9; y6(0) = 0.067; y9(0) = 0.008; yi(0) = 0, i = 3–5, 7, 8, 10–20; Q(0) = 1. The process temperature was considered as a control parameter according to two optimality criteria: maximizing the yield of target naphthenes (f1) at the end of the reaction, and maximizing the conversion of feedstock (f2). Values f1 were in the range of 0.43–0.79; conversion — 0.01–0.03; temperature — 200–300 K. The growth of temperature was accompanied by an increase in the yield of target naphthenes and a decrease in the conversion of feedstock. Each solution obtained was not an unimprovable one. When modeling the process of hydrogenation of PAH, an algorithm was launched with a population size of 100 and a number of generations of 100. A program implementing the NSGA-II algorithm was developed. The optimal set of values of the PAH hydrogenation reaction temperature was calculated, which made it possible to obtain unimprovable values of the optimality criteria — maximizing the yield of target naphthenes and conversion of feedstock.Discussion and Conclusion. The NSGA-II algorithm is effective for solving the problem of non-dominance, and deriving the optimal solution for all criteria. Future research should be devoted to the selection of optimal algorithm parameters to increase the speed of the solution. Based on the obtained theoretical optimal conditions of the PAH hydrogenation reaction, it is possible to implement the process in industry

О математической модели взаимодействия высокотемпературного потока плазмы с поверхностью древесины

In this study, the processes of thermal decomposition of wood during its treatment with a plasma flow are considered. To develop a mathematical model of these processes, a differential thermogravimetric analysis of the heating of larch samples in an argon atmosphere at a rate of 10–20 degrees/min is carried out. Based on the results obtained, a mathematical model of thermal decomposition is proposed, including four stages. The wood during heating is represented by a mixture of six components. At each stage, the kinetic parameters of the reactions are determined by processing measurements at a heating rate of 20 degrees/min. The equations of chemical kinetics describing changes in the mass of wood components are numerically solved using the finite-difference implicit Euler method and the obtained reaction parameters. The numerical solution to the equations of chemical kinetics with these parameters shows satisfactory agreement with the data from the corresponding experiment. The calculation performed at a heating rate of 10 degrees/min with the same kinetic parameters also shows satisfactory agreement with the measurements. Thus, the obtained reaction parameters do not depend on the heating rate in the considered range. The proposed model can be used in the mathematical description of changes in the structure and thermal state of wood samples exposed to high-temperature plasma flow treatment.

Numerical Study of Methane Mixtures' Conversion Under the Influence of Laser Radiation

The article presents a study of methane mixtures' laser conversion under various conditions of the computational experiment. Such flows are characterized by sharp local changes in the gas dynamic characteristics and the mixture components' concentrations. Their dynamics and mutual transformations are described by a stiff system of Navier-Stokes equations and chemical kinetics, which imposes serious restrictions on the choice of a computational algorithm. Numerical experiments were carried out using previously developed 2D code for modeling subsonic axisymmetric flows of a multicomponent medium, supplemented by modules that take into account laser radiation and solve equations of methane conversion's chemical kinetics. Verification of the results was made by calculating the conversion of methane under the influence of walls' external heating. Comparison of the substances' concentrations at the pipe outlet with the direct solution of the chemical kinetics system at different reaction temperatures showed a good agreement of the results. Computational experiments on the laser radiation's effect on the flow of a chemically active absorbing medium have been completed. It is shown that the laser radiation introduced into the mixture and absorbed by ethylene, changes the flow pattern and significantly increases the temperature of the gas mixture. An increase in temperature contributes to an increase in the yield of target products (ethylene, acetylene, hydrogen) at the reactor shorter length, while in the absence of radiation, the maximum concentrations of products appear at the reactor's outlet. The effect of the initial composition of the gas mixture on the methane's conversion is investigated, and it is concluded that the presence of ethylene significantly increases the formation of target products at moderate reactor walls' temperatures in the presence of laser radiation.

Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows

This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate’s architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: (i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; (ii) It accelerates the prediction step by enabling adaptivity as the surrogate’s evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0-textrm{D} scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1-textrm{D} shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations.

TUMME 2023: Tsinghua University Minnesota Master Equation program. New version announcement

This is an updated version of TUMME (Tsinghua University Minnesota Master Equation program), which is a computer program for setting up and solving master equations for chemical kinetics of unimolecular and bimolecular reactions. The master equation is discretized in terms of energy bins, and rate constants are calculated from chemically significant eigenmodes. TUMME has interfaces to Gaussian 16, Polyrate 2023, and MSTor 2023 output files that allow the master equation code to obtain the microcanonical flux coefficients needed for the kernel of the master equation as calculated by conventional transition state theory (TST), variational transition state theory (VTST) with various tunneling methods, or multi-structural or multi-path VTST (MS-VTST or MP-VTST) with various tunneling methods. The tunneling methods supported include zero-curvature tunneling (ZCT), small-curvature tunneling (SCT), large-curvature tunneling (LCT), and microcanonically optimized multidimensional tunneling (μOMT). For mechanisms involving only unimolecular isomerization (no bimolecular pairs), TUMME can set up and solve a conservative master equation for both rate constants and time-dependent energy-bin populations. For mechanisms involving bimolecular pairs, TUMME 2023 can set up and solve two kinds of master equation: (i) a nonconservative master equation for calculating rate constants of bimolecular reactions and (ii) a conservative master equation that includes bimolecular association in the transition matrix and that can be used for calculating the time evolution of the concentration of a pseudo-first-order bimolecular reactant. TUMME is written in double precision with Python 3; quadruple and octuple precision are also available for some subtasks in C++. The Python code can run in serial or parallel (MP or MPI), and C++ code can run on a single processor or on multiple processors with OpenMP. The program includes a manual and a tutorial. New version program summaryProgram Title: TUMME 2023CPC Library link to program files:https://doi.org/10.17632/whcnvm2mc9.2Developer's repository link:https://doi.org/10.5281/zenodo.7943283Licensing Provisions: Apache-2.0 for the program and CC-BY-4.0 for the manualProgramming languages: Python 3 and C++Does the new version supersede the previous version?: YesJournal reference of previous version: Comput. Phys. Commun. 270 (2022) 108140 [1]External libraries: Numpy, Scipy, Numba, mpi4py (optional), modified mpack (optional), qd (optional), omp (optional)Interfaces to other programs: Gaussian 16 [2], Polyrate 2023 [3], and/or MSTor 2023 [4]Nature of problem: Characterize and calculate rate constants for a temperature-dependent and pressure-dependent complex reaction systemSolution method: Solve the energy-grained master equation based on the chemically significant eigenmodes to get phenomenological rate constants and time evolutions of the populations [1,5–7].Reason for new version: The new version increases the functionality and accuracy, and it offers an easier way to run the program. In addition, some bugs have been corrected.Summary of revisions:1.Added an option (available in high precision) to treat pseudo-first-order bimolecular reactions to obtain the time evolution of the reactants and intermediates. [8]2.Added an inverse-Laplace-transform option in the REACTION block.3.Abandoned rounding the sizes of energy bins to an integer wavenumber (ESOT).4.Changed the way to run TUMME by providing an executable bash script.5.Slightly adjusted the strategy for eigenmode mergers to deal with some unexpected cases.6.Adjusted the output for the partition functions.7.Added options for large-curvature tunneling (LCT) and microcanonically optimized multidimensional tunneling (μOMT).8.Added the keyword pyrfile to support a Polyrate 2023 [3] file that ends with a suffix .fu100.9.Fixed some bugs.10.Updated the manual and added a tutorial to the program distribution, so the distribution now has both a manual and a tutorial.

Oxidation of TiAl alloy by oxygen grain boundary diffusion

Ti–Al intermetallic alloys have a number of advantages for the manufacture of aviation and car details. The use of these alloys is limited by their oxidation at high temperatures, which is associated with structural features and the presence of micro and nanosized grains. In such materials, grain boundary diffusion of oxygen can be active, which contributes to the acceleration of oxidation upon heating. In this paper, we present a two-dimensional model for research the diffusion which is accompanied by oxidation. The structure of TiAl is specified as symmetrically alternating grains with a clear separation of boundaries and triple junctions between them. Diffusion and chemical properties of grains and boundaries are different. The problem is formulated in a two-dimensional formulation and solved numerically. The influence of changes in the composition over time on the penetration of oxygen is taken into account. For the convenience of numerical research and analysis of the results, dimensionless variables are used. To solve the diffusion equation, an implicit difference scheme of splitting in coordinates is used. The equations of chemical kinetics are solved using an algorithm similar to the implicit Euler method using an iterative procedure. The results demonstrate the influence of different variants of kinetic regimes on the concentration distribution and integral concentrations of reagents and oxides.

Modeling of the Electronic Structure of Semiconductor Nanoparticles

This paper deals with the mathematical modeling of the electronic structure of semiconductor particles. Mathematically, the task is reduced to a joint solution of the problem of free energy minimization and the set of chemical kinetic equations describing the processes at the surface of a nanoparticle. The numerical modeling of the sensor effect is carried out in two steps. First, the number of charged oxygen atoms on the surface of the nanoparticle NO− is determined. This value is found by solving a system of nonlinear algebraic equations, where the unknowns are the stationary points of this system describing the processes on the surface of a nanoparticle. The specific form of such equations is determined by the type of nanoparticles and the mechanism of chemical reactions on the surface. The second step is to calculate the electron density inside the nanoparticle (nc(r)), which gives the minimum free energy. Mathematically, this second step reduces to solving a boundary value problem for a nonlinear integro-differential equation. The calculation results are compared with experimental data on the sensor effect.

Kinetics of diffusion-influenced multisite phosphorylation with enzyme reactivation.

The simplest way to account for the influence of diffusion on the kinetics of multisite phosphorylation is to modify the rate constants in the conventional rate equations of chemical kinetics. We have previously shown that this is not enough and new transitions between the reactants must also be introduced. Here we extend our results by considering enzymes that are inactive after modifying the substrate and need time to become active again. This generalization leads to a surprising result. The introduction of enzyme reactivation results in a diffusion-modified kinetic scheme with a new transition that has a negative rate constant. The reason for this is that mapping non-Markovian rate equations onto Markovian ones with time-independent rate constants is not a good approximation at short times. We then developed a non-Markovian theory that involves memory kernels instead of rate constants. This theory is now valid at short times, but is more challenging to use. As an example, the diffusion-modified kinetic scheme with new connections was used to calculate kinetics of double phosphorylation and steady-state response in a phosphorylation-dephosphorylation cycle. We have reproduced the loss of bistability in the phosphorylation-dephosphorylation cycle when the enzyme reactivation time decreases, which was obtained by particle-based computer simulations.

Discussion on Electron Temperature of Gas-Discharge Plasma with Non-Maxwellian Electron Energy Distribution Function Based on Entropy and Statistical Physics

Electron temperature is reconsidered for weakly-ionized oxygen and nitrogen plasmas with its discharge pressure of a few hundred Pa, with its electron density of the order of 1017m-3 and in a state of non-equilibrium, based on thermodynamics and statistical physics. The relationship between entropy and electron mean energy is focused on based on the electron energy distribution function (EEDF) calculated with the integro-differential Boltzmann equation for a given reduced electric field E/N. When the Boltzmann equation is solved, chemical kinetic equations are also simultaneously solved to determine essential excited species for the oxygen plasma, while vibrationally excited populations are solved for the nitrogen plasma, since the EEDF should be self-consistently found with the densities of collision counterparts of electrons. Next, the electron mean energy U and entropy S are calculated with the self-consistent EEDF obtained, where the entropy is calculated with the Gibbs's formula. Then, the "statistical" electron temperature Test is calculated as Test=[∂S/∂U]-1. The difference between Test and the electron kinetic temperature Tekin is discussed, which is defined as [2/(3k)] times of the mean electron energy U=⟨ϵ⟩, as well as the temperature given as a slope of the EEDF for each value of E/N from the viewpoint of statistical physics as well as of elementary processes in the oxygen or nitrogen plasma.

Effect of Operating Parameters on Agricultural Biomass Mixture Pyrolysis Process in a Batch Reactor

Many phenomena affect devolatilization of biomass particles, including mass and heat transfer, chemical reactions and physical transformation. Mathematical models that are capable to describe pyrolysis phenomena can greatly assist the large-scale development and optimization of pyrolysis processes, but to be implemented into large-scale simulation the models need to be simplified at a certain degree. In the present study, an existing mathematical model is used to describe the pyrolysis of a single particle of biomass. It couples the heat transfer equations with the chemical kinetics equations. The common Euler explicit method is used for solving the heat transfer equation and the two-step pyrolysis kinetics equations. The model equation is solved for a sphere particle with a radius of 0.001 m and temperature ranging from 300 to 923 K. An original numerical model for the pyrolysis of agricultural biomass mixture is proposed and relevant equations solved using original program realized in MATLAB. Simplified particle model was validated with the experimental data in a non-isothermal pyrolysis reactor. The sample was heated in the temperature range of 300–923 K at average heating rates of 21, 30 and 54 K/min. The model results showed reasonable agreement with experiments. The difference (between the experimental and model results) is slightly more prominent with decreasing heating rate (21 and 30 K/min), but model results are in much better agreement with the experimental date for higher heating rate (54 K/min). It is demonstrated that a constitutive equation can be used to express devolatilization rate for higher heating rates.

Method for calculating the pyrolysis zone in the production unit activated carbon

Activated charcoal can be obtained in many ways. The most promising in terms of resource saving and economic benefits is the method of obtaining activated carbon from organic waste by slow conductive pyrolysis. As a result of such thermochemical conversion, biochar and volatile products - condensable and non-condensable are formed, which are used as fuel for the operation of pyrolysis reactors. Modeling of slow thermal decomposition is carried out using finite difference schemes for heat and mass processes described by differential equations and equations of chemical kinetics. The pyrolysis process equipment is a complex and expensive mechanism, therefore, when developing equipment for pyrolysis, it is necessary to carry out calculations related to the optimization of the equipment design. In this work, as applied to an energy- and resource-saving plant for the production of activated carbon, analytical calculations were carried out and a universal calculation method was developed for the zone of conductive pyrolysis of crushed waste. A mathematical model of the process of conductive slow pyrolysis is presented, which consists of heat and mass transfer equations and equations of chemical kinetics. An algorithm for calculating the pyrolysis zone has been developed. A kinetic dependence of the specific gravity of the solid residue of wood particles during pyrolysis is obtained, which characterizes mass transfer during the thermochemical transformation of waste into a carbonaceous residue, this dependence shows the dynamics of the change in the mass of the solid fraction over time during the decomposition of waste, the kinetic curves show: the rate of chemical reactions occurring during pyrolysis, as well as the final specific gravity of coal.

Об одном подходе к нахождению сумм кратных числовых рядов

An approach to calculating sums of some types of multiple numerical series is presented. This approach is based on using the formula for the resultant of a polynomial (or an entire function with a finite number of zeros) and an entire function obtained earlier by A.M. Kytmanov and E.K. Myshkina. This formula does not require values of the roots of the functions under study and is a combinatorial expression. By calculating the resultant of a polynomial and an entire function in two different ways, it is possible to obtain a relation for multiple numerical series. For the second way to find the resultant, we use the product of one function at the roots of another. In this article, the sums of some types of multiple numerical series that were previously absent in known reference books are found. They are expressed in terms of well-known special functions such as the Bessel function. This approach to calculating the sums of multiple numerical series differs significantly from the method based on the use of residue integrals associated with a system of equations. The relevance of this problem is determined by the fact that in applied problems, for example, in the equations of chemical kinetics, there are functions and systems of equations consisting of exponential polynomials.

A Data-Driven Framework for Computationally Efficient Integration of Chemical Kinetics Using Neural Ordinary Differential Equations

AbstractA data-driven methodology is introduced for computationally efficient integration of systems of stiff rate equations in chemical kinetics using neural ordinary differential equations (NODE). A systematic algorithm is developed for training data generation and sampling. Subsequently, a novel transformation technique for sampled training data is designed to regularize the neural network parameters, leading to a stable training process. Finally, the NODE network is iteratively trained to learn the accurate neural network representation of chemical kinetics source terms by minimizing the mean absolute error between the true and predicted solutions. The computational efficiency and accuracy of the NODE network are evaluated by simulating the evolution of the thermochemical state of a constant pressure homogeneous hydrogen-air reactor. The combustion of hydrogen in air is described by a finite-rate mechanism including 9 chemical species and 21 reaction steps. The NODE network shows excellent multi-step prediction accuracy for a wide range of initial temperatures and equivalence ratios, spanning the composition space of real flames. The NODE also exhibit a significant reduction in numerical stiffness of the system, enabling the utilization of explicit solvers for integration. The present simulation results using NODE demonstrate up to 70% speed up in computation time compared to direct integration of the chemical mechanism with at most 3.16% relative error in ignition delay time.

On geometry of multiscale mass action law and its fluctuations

The classical mass action law in chemical kinetics is put into the context of geometric multiscale thermodynamics, which allows for description of chemical reactions with inertial effects. The kinetics is extended to an enlarged state space with reaction rates as new state variables, and it has the structure a Lie-algebroid dual. Subsequently, the dynamics is lifted to the Liouville description within kinetic theory of the enlarged state space, so that we can include also dynamics of fluctuations. The lifted kinematics has the geometric structure of a matched pair, which allows for reduction to moments by a Lie-algebra homomorphism, as in the Grad hierarchy. In particular, the first and second moments then lead to evolution equations for chemical kinetics with inertia and for correlations between composition and reaction rates. Finally, dissipation is added in the extended state space which leads to the classical mass action law when the moments relax to their respective quasi-equilibria. We demonstrate, for instance, the possibility of oscillating homogeneous chemical reactions, and how correlations between composition and reaction rates contribute to the chemical kinetics.

A practical Approach to predict Service Life and Re-lubrication Rate of Grease in Rolling Bearings

Lubrication is crucial for a sustainable operation of any machinery. A sustainable application of lubricants requires the avoidance of any waste, lubricants should not be exchanged long before their service life has ended. This refers especially to those applications where high operation temperatures are reducing the service life and require a huge consumption of lubricants. Therefore, to fulfil the requirement of sustainability a prediction of the service life at elevated temperatures is crucial. At elevated temperatures the service life of lubricants is limited by thermal aging. This results from a chemical reaction of components of the grease with the oxygen of the ambient air. Such a process follows the Arrhenius equation of chemical kinetics and is given by a straight line in a so-called Arrhenius plot. The slope of the line in the Arrhenius plot is given by the activation energy EA. The FAG FE9 test run is a typical method to assess the service life of a lubricating grease in bearings at elevated temperatures. The test is performed at the upper temperature limit of the grease and gives the service life at this maximum temperature. Once the activation energy EA is available the service life at any other temperature may be calculated. Since the temperature of Abstract *Frank Reichmann CARL BECHEM GMBH, Hagen, Germany the FE9 test run is usually the upper temperature limit the operation temperature is usually lower. Once the calculation start from a high temperature in direction a lower temperature low figures of activation energy EA are resulting in conservative service lives, as it is displayed in in this paper. In case of high figures of the activation energy EA the calculated service life becomes too high what may result in bearing failures. With FE9 test runs at different temperatures an activation energy EA = 75 kJ/mol was found for a reference grease. Laboratory methods to determine the activation energy do usually result is much higher figures. For example, HP-DSC test with this reference grease resulted in an activation energy EA > 100 kJ/mol, mostly it was even EA > 120 kJ/mol. Such a result will lead to unrealistic high calculated service lives. An activation energy of EA = 75 kJ/mol is basically a proper assumption for the calculation of service life of most greases. Generally it is always recommended to estimate a low activation energy.

Correlation between antioxidant depletion kinetic model and ageing behaviour of cross‐linked polyethylene cable insulation

AbstractA concise kinetic model catering for the antioxidant reaction of thermally aged cross‐linked polyethylene (XLPE) cable insulation before its abrupt performance deterioration is proposed for life prediction and condition assessment. The alternating current breakdown strength, elongation at break, carbonyl index, and pyrolysis activation energy of XLPE insulation are found to consistently display an abrupt change at a certain point of ageing time. This is strongly correlated to the depletion of the antioxidant whose content gradually decreases with ageing time and drops to a critical value, after which the abrupt degradation of the above macroscopic performances happens. Based on the simplified chain reactions of XLPE during thermal‐oxidative ageing, a concise kinetic model about antioxidant prediction is accordingly established by solving the chemical kinetics equations. It indicates that the antioxidant content decays with the reciprocal of time before the abrupt degradation occurs. Results of antioxidant content predicted by the kinetic model at different temperatures matches well with the experimental results, and its reliability can also be proved by the Arrhenius relationship of the obtained results. The kinetic model proposed herein demonstrates satisfying conciseness and thus can be highly feasible in ageing condition assessment and life predicting of XLPE insulation.