Problems Of Chemical Kinetics Research Articles

Modeling the heterogeneous catalytic recovery processes of aldehydes and ketones

Mathematical models of the recovery reactions of cyclohexanone and anise aldehyde with subsequent esterification by the Meerwein-Ponndorf-Verley mechanism are constructed. Experimental research was conducted into recovery reactions of aldehydes and ketones in order to find the optimal catalyst for the recovery reaction of cyclohexanone and to establish the limiting stage in the recovery process of anise aldehyde. We analyzed the activity of three catalysts, in the presence of which the recovery reaction of cyclohexanone proceeded, and selected for further calculations and studies the most active zeolite – SnMgAl(СО3). By using the MathCad 15.0 programming environment, we solved the inverse problem of chemical kinetics for the examined reactions. It was found that the value of rate constant of the recovery reaction of cyclohexanone in the presence of zeolite SnMgAl(СО3) is the largest and reaches 0.2544 s-1, in other words, this is the most effective catalyst. As far as the recovery reaction of aldehyde anise is concerned, it was established that the first stage of this reaction (anise aldehyde recovery) proceeds slower than the second stage (anise alcohol esterification) and it is the limiting stage of the reaction. Results obtained in the course of experimental research might be used to solve the direct and inverse problems of chemical kinetics.

Features of calculating contrast structures in the Cauchy problem

In solving stiff Cauchy problems, regions of a very rapid change in the solution, which are called boundary layers, arise. In nonlinear problems, there may be several such regions and not only at the initial moment but at different times when they are called contrast structures. It is shown that in the numerical solution of contrast structures, round-off errors can become so great that even a significant increase in the digit capacity is unable to resolve the situation. In this case, approximate analytical methods developed in boundary layer theory turn out to be more effective. As an applied problem, we consider a numerical solution of a real problem of chemical kinetics, i.e., combustion of hydrogen in oxygen. It is shown that this process involves the emergence of a contrasting structure due to the production of transitional chemical components. Therefore, the actual flare of the flame occurs not at the initial moment but after a delay.

Estimating rare events in biochemical systems using conditional sampling.

The paper focuses on development of variance reduction strategies to estimate rare events in biochemical systems. Obtaining this probability using brute force Monte Carlo simulations in conjunction with the stochastic simulation algorithm (Gillespie's method) is computationally prohibitive. To circumvent this, important sampling tools such as the weighted stochastic simulation algorithm and the doubly weighted stochastic simulation algorithm have been proposed. However, these strategies require an additional step of determining the important region to sample from, which is not straightforward for most of the problems. In this paper, we apply the subset simulation method, developed as a variance reduction tool in the context of structural engineering, to the problem of rare event estimation in biochemical systems. The main idea is that the rare event probability is expressed as a product of more frequent conditional probabilities. These conditional probabilities are estimated with high accuracy using Monte Carlo simulations, specifically the Markov chain Monte Carlo method with the modified Metropolis-Hastings algorithm. Generating sample realizations of the state vector using the stochastic simulation algorithm is viewed as mapping the discrete-state continuous-time random process to the standard normal random variable vector. This viewpoint opens up the possibility of applying more sophisticated and efficient sampling schemes developed elsewhere to problems in stochastic chemical kinetics. The results obtained using the subset simulation method are compared with existing variance reduction strategies for a few benchmark problems, and a satisfactory improvement in computational time is demonstrated.

Modeling of chemical kinetics in gases

Some temperature dependences of reaction rate constants have been derived from the laws of quantum mechanics. Chemical reference data have been revealed to be usually dissatisfied with these laws. It is shown how similar reference data should be corrected. The constants for the kinetics of hydrogen combustion in oxygen are corrected as an example. A specialized method for the numerical solution of chemical kinetics problems has been developed. It represents an explicit algorithm, which appreciably surpasses the known methods in simplicity, precision, and robustness.

Nonlinearity problem in the numerical solution of superstiff Cauchy problems

For the numerical solution of Cauchy stiff initial problems, many schemes have been proposed for ordinary differential equation systems. They work well on linear and weakly nonlinear problems. The article presents a study of a number of well-known schemes on nonlinear problems (which include, for example, the problem of chemical kinetics). It is shown that on these problems, the known numerical methods are unreliable. They require a sufficient step reducing at some critical moments, and to determine these moments, sufficiently reliable algorithms have not been developed. It is shown that in the choice of time as an argument, the difficulty is associated with the boundary layer. If the length of the integral curve arc is taken as an argument, difficulties are caused by the transition zone between the boundary layer and regular solution.

Method of solving the inverse problem of chemical kinetics for catalytic reactions in which each step involves main reactants

A new method is suggested for solving the inverse problem of chemical kinetics. This method provides means to derive, from unsteady-state experimental data, the rate constants of catalytic reactions in which each step involves at least one main reactant. Examples of applying this method to two- and three-step reactions are presented.

A semi-analytical iterative technique for solving chemistry problems

The main aim and contribution of the current paper is to implement a semi-analytical iterative method suggested by Temimi and Ansari in 2011 namely (TAM) to solve two chemical problems. An approximate solution obtained by the TAM provides fast convergence. The current chemical problems are the absorption of carbon dioxide into phenyl glycidyl ether and the other system is a chemical kinetics problem. These problems are represented by systems of nonlinear ordinary differential equations that contain boundary conditions and initial conditions. Error analysis of the approximate solutions is studied using the error remainder and the maximal error remainder. Exponential rate for the convergence is observed. For both problems the results of the TAM are compared with other results obtained by previous methods available in the literature. The results demonstrate that the method has many merits such as being derivative-free, and overcoming the difficulty arising in calculating Adomian polynomials to handle the non-linear terms in Adomian Decomposition Method (ADM). It does not require to calculate Lagrange multiplier in Variational Iteration Method (VIM) in which the terms of the sequence become complex after several iterations, thus, analytical evaluation of terms becomes very difficult or impossible in VIM. No need to construct a homotopy in Homotopy Perturbation Method (HPM) and solve the corresponding algebraic equations. The MATHEMATICA® 9 software was used to evaluate terms in the iterative process.

Спецификация прямой задачи химической кинетики с участием веществ, допускающих изомерные соединения

Спецификация прямой задачи химической кинетики с участием веществ, допускающих изомерные соединения

Predicting pressure-dependent unimolecular rate constants using variational transition state theory with multidimensional tunneling combined with system-specific quantum RRK theory: a definitive test for fluoroform dissociation.

Understanding the falloff in rate constants of gas-phase unimolecular reaction rate constants as the pressure is lowered is a fundamental problem in chemical kinetics, with practical importance for combustion, atmospheric chemistry, and essentially all gas-phase reaction mechanisms. In the present work, we use our recently developed system-specific quantum RRK theory, calibrated by canonical variational transition state theory with small-curvature tunneling, combined with the Lindemann-Hinshelwood mechanism, to model the dissociation reaction of fluoroform (CHF3), which provides a definitive test for falloff modeling. Our predicted pressure-dependent thermal rate constants are in excellent agreement with experimental values over a wide range of pressures and temperatures. The present validation of our methodology, which is able to include variational transition state effects, multidimensional tunneling based on the directly calculated potential energy surface along the tunneling path, and torsional and other vibrational anharmonicity, together with state-of-the-art reaction-path-based direct dynamics calculations, is important because the method is less empirical than models routinely used for generating full mechanisms, while also being simpler in key respects than full master equation treatments and the full reduced falloff curve and modified strong collision methods of Troe.

Computer Simulation Approach in Development of Propane-air Combustor Microreactor

A mathematical model and simulation results of a new microreactor for propane-air combustion are presented. In this article we review 3D model of microreactor and solve problems of gas dynamics, heat transfer and chemical kinetics. The model is based on Navier-Stokes equations for a transient laminar flow of a compressible chemically reacting gas mixture, together with the mass transfer and energy balance equations. The simulation results were applied under development of microreactor geometry to solve a problem of fuel burning process stability. As a main result we have obtained temperature distribution in the microreactor during a fuel combusting process under different mass flow rates of propane and air. Flame shape and its long term stability were also investigated. To validate the model, we developed a microreactor prototype and performed a series of experiments varying fuel consumption. Experimental data have a high correlation to the simulation results and our model correctly predicts gas flows, flame shape and long term stability of oxidation process. The validated computational model will be used to investigate more complex microsystems base on combustion microreactors

Particle Swarm Optimization for Inverse Chemical Kinetics Problem Solving as Applied to n-hexane Isomerization on Sulfated Zirconia Catalysts

An attempt was made to use particle swarm optimization (PSO) method for solving the inverse chemical kinetics problem for the n-hexane isomerization process on a sulfated zirconia catalyst sample. A perspective supported isomerization catalyst based on sulfated zirconia supported on alumina was chosen. Also the optimal coefficients for this problem were chosen. Method of determining the kinetic rate constants for the hexane isomers interconversion was tested. Model of hexanes interconversion based on calculated kinetic rate constants was built.

Kinetic model of the catalytic hydroalumination of olefins with organoaluminum compounds

The purpose of this study was to develop a kinetic model for the Cp2ZrCl2-catalyzed hydroalumination of olefins with organoaluminum compounds HAlBu 2 i , AlBu 3 i , ClAlBu 2 i (Bu = C4H9, Cp = C5H5). Experimental data were taken from previous investigations in which the catalytic reaction was carried out with various olefins and different initial amounts of the catalyst in the temperature range from 0 to 40 °C. A mathematical model of the process was developed taking into account the material balance. The rate constants and activation energies for process steps were determined by solving the inverse problem of chemical kinetics. The kinetic patterns of the catalytic hydroalumination of olefins with organoaluminum compounds were studied in terms of the constructed reaction model.

Numerical optimisation for model evaluation in combustion kinetics

Numerical optimisation related to the estimation of kinetic parameters and model evaluation is playing an increasing role in combustion as well as in other areas of applied energy research. The present work aims at presenting the current probability-based approaches along applications to real problems of combustion chemical kinetics. The main methods related to model and parameter evaluation have been explicated. An in-house program for the systematic adjustment of kinetic parameters to experimental measurements has been described and numerically validated. The GRI (Gas research institute) mechanism (version 3.0) has been shown to initially lead to results which are greatly at variance with experimental data concerning the combustion of CH3 and C2H6. A thorough optimisation of all parameters has been performed with respect to these profiles. A considerable improvement could be reached and the new predictions appear to be compatible with the measurement uncertainties. It was also found that neither GRI 3.0 nor three other reaction mechanisms considered during the present work should be employed (without prior far-reaching optimisation) for numerical simulations of combustors and engines where CH3 and C2H6 play an important role. Overall, this study illustrates the link between optimisation methods and model evaluation in the field of combustion chemical kinetics.

Kinetic model of isolated reactions of the catalytic hydroalumination of olefins

The reaction of α-olefin hydroalumination by alkylalanes HAlBu 2 i , ClAlBu 2 i , AlBu 3 i catalyzed by Cp2ZrCl2 was studied. The kinetic model for the reaction steps isolated from the detailed mechanism of Cp2ZrCl2-catalyzed olefin hydroalumination were constructed. The inverse problem of chemical kinetics has been addressed in order to determine the kinetic parameters of the reactions. The estimation of rate coefficients has been performed by fitting the model outputs with available experimental data. The comparison between experimental data and simulated results with kinetic parameters validated the effectiveness of the developed model. The constructed mathematical model was used to study the mechanism of the isolated reactions of olefin hydroalumination.

Analysis of the informativity of kinetic measurements in solving inverse problems of chemical kinetics for multi-route reactions

Inverse problems of chemical kinetics that are solved in terms of a set of nonlinear ordinary differential, algebraic-differential, and algebraic equations corresponding to unsteady-state, steady-state, and equilibrium experimental conditions have been investigated. An algorithm has been devised for the analysis of the informativity of kinetic measurements in solving inverse problems of chemical kinetics for multi-route reactions.

Ya B Zeldovich and equation of state problems for matter under extreme conditions

In the amazing range of Yakov Borisovich Zeldovich's research interests—from general problems of chemical physics, kinetics, combustion, detonation, and shock waves to elementary particles and cosmology—the physics of matter under extreme conditions occupies a special position. This paper reviews some of Ya B's work on shock waves and equations of state of matter. Among Ya B's basic ideas are the utilization of shock data to develop thermodynamically complete equations of state; the shock compression of porous matter, and the adiabatic expansion of shock-compressed materials. The widespread use and development of these ideas as tools for the present-day studies of extreme conditions are illustrated with examples.

The Kinetic Model of n‐Decane Oxidation in the Presence of Inhibitory Composition

ABSTRACTThis article addresses mathematical modeling of the reaction of inhibited organic compounds oxidation. It was proposed to solve the inverse problems of chemical kinetics by using the index method of constrained global minimization of the deviation between the calculated and experimental data. This approach allows us to use more complete information about the chemical process which, in its turn, reduces the range of possible solutions, narrows down the domain of uncertainty, and improves the quality of mathematical model of chemical reactions. The index method was applied to solving inverse kinetic problem for the reaction of n‐decane oxidation in the presence of a p‐oxydiphenylamine/n‐decyl alcohol inhibitory composition.

基于随机模拟算法的激光辐照固体材料的温升研究

The complexity of the heat exchange equation brings difficulties to study laser-damage etc.A kind of stochastic simulation algorithm(SSA)which treats the energy input and redistribution process as a chemical kinetics problem is used.The complex system is easy to simulate.Temperature distribution of Gauss laser-silicon irradiation is studied by stochastic simulation.The simulation result is compared with the traditional calculation method.The results show that the stochastic method is reasonable to treat heat exchange,and stochastic simulation algorithm is useful to study Gauss laser-solid material irradiation.The beginning of laser irradiation,laser-damage is relations with wavelength,and low absorption coefficient can reduce damage probability of basement,but the late of laser irradiation,laser-damage is not obvious to reduce the absorption coefficient.

Near critical catalyst reactant branching processes with controlled immigration

Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk catalyst evolution is that of a classical continuous time branching process; in addition there is a specific form of immigration. Immigration takes place exactly when the catalyst population falls below a certain threshold, in which case the population is instantaneously replenished to the threshold. Such models are motivated by problems in chemical kinetics where one wants to keep the level of a catalyst above a certain threshold in order to maintain a desired level of reaction activity. A diffusion limit theorem for the scaled processes is presented, in which the catalyst limit is described through a reflected diffusion, while the reactant limit is a diffusion with coefficients that are functions of both the reactant and the catalyst. Stochastic averaging principles under fast catalyst dynamics are established. In the case where the catalyst evolves "much faster" than the reactant, a scaling limit, in which the reactant is described through a one dimensional SDE with coefficients depending on the invariant distribution of the reflected diffusion, is obtained. Proofs rely on constrained martingale problem characterizations, Lyapunov function constructions, moment estimates that are uniform in time and the scaling parameter and occupation measure techniques.

Model reductions with special CSP data

The model reduction methodology of computational singular perturbation (CSP) is enhanced for chemical kinetics problems. The leading order converged CSP-refined fast basis vectors are obtained analytically by exploiting the special format of the given reaction-specific chemical kinetics data. The leading order net reaction rates of the fast reactions (after they are exhausted) are also obtained analytically. Taking advantage of these leading order analytical results, a new model reduction strategy is advocated. The implementation of this new strategy is very straightforward, and extraction of general insights on the reaction system is also easier.