Inverse Problems Of Chemical Kinetics Research Articles

Advanced Fitting Method for the Kinetic Analysis of Thermogravimetric Data.

The article considered the solution of the inverse problem of chemical kinetics of the analysis of experimental data of a thermogravimetric experiment at a constant sample heating rate. The fitting method for identifying the parameters of a kinetic triplet using the integral method for a model of a solid-state reaction based on the modified Arrhenius equation is described. The effectiveness of the proposed approach was confirmed by solving test cases for low, medium, and high rates of material conversion. Unlike other methods, setting the parameters of the reaction mechanism is not required, as they are determined by the solution. Solutions for real data of TGA studies with high and low sample heating rates were compared with the results obtained by other authors and experimental data. A description of the full cycle of calculations used to identify kinetic parameters from thermogravimetric experimental data is given, from the derivation of calculated relationships to the implementation of a short (three to five formulas) program code for MS Excel spreadsheets. The presented code is easy to verify and reproduce and can be modified to solve various problems.

Solving inverse problems of chemical kinetics by metaheuristic methods

Solving inverse problems of chemical kinetics by metaheuristic methods

INFLUENCE OF ADDITIONAL SLOW STAGES ON KINETIC REGULARITIES OF CHEMICAL REACTIONS

It is known that mechanisms with a different set of elementary stages are alternatively used to describethe kinetic patterns of chemical reactions involving the same reagents. In this regard, the article introduces two concepts–the "initial" reaction mechanism, which is obtained as a result N.I. Kol’tsovChemChemTech. 2022. V. 65. N 833of experimental studies, and alternative reaction mechanisms thatcan demonstrate dynamic be-havior close to the original mechanism. Alternative mechanisms include all stages of the original mechanism and additional slow stages satisfying certain stoichiometric constraints. The influence of additional dependent and independent slow stages on the patterns of chemical reactions in closed and open reactors of ideal mixing is investigated. It is established that the introduction of slow linearly dependent stages into the reaction mechanism does not significantly affect its kinetic pat-terns. The addition of the reaction mechanism by slow linearly independent stages leads to a change in its dynamics, which does not allow them to be used as part of alternative mechanisms. The article describes an approach that allows us to detectdependent stages, check the possibility of their im-plementation by comparing stationary and non-stationary characteristics (coordinates of stationary states, linear and nonlinear relaxation times, etc.), analyzing the properties of the matrix of stoi-chiometric coefficients (the number of rows and columns) and its rank (the maximum number of independent rows or columns). In this case, the main role is played by stoichiometric conservation laws (stationary and non-stationary), taking into account the peculiarities of their implementation in closed, quasi-open and fully open reactors of ideal mixing. Examples are given demonstrating the influence of additional dependent and independent slow stages on the dynamics of reactions. The results obtained can be useful in practice when solving inverse problems of chemical kinetics to clarify the mechanisms of specific complex reactions.

Application of the genetic algorithm method in the problem of chemical kinetics of the oxidative regeneration process

Annotation. One of the main problems in chemical kinetics is the establishment of the mechanisms of complex chemical reactions. The inverse problem of chemical kinetics is understood as the determination of the dependence of the concentration of the participating components on the basis of experimental data obtained from a laboratory installation for the oxidative regeneration of coked catalysts. One of the main methods used in inverse problems the genetic algorithm. The algorithms considered in the article make it possible to determine the values of the rate constants of the considered chemical stages.

Gravitational search algorithm for determining the optimal kinetic parameters of propane pre-reforming reaction

The article describes the gravitational search algorithm and its application to solve the inverse problem of chemical kinetics. It is shown that metaheuristic algorithms have become more and more popular recently. In this regard, it is logical to apply these algorithms to various optimization problems. The optimization problem is formulated on the example of solving the inverse problem of chemical kinetics. The process under study is the pre-reformation of propane into a methane-rich gas on a Ni catalyst, which is an industrially important chemical process. The article briefly describes the algorithm and its pseudocode, and then compares the performance of the gravitational search algorithm with other metaheuristic methods. The algorithm showed adequate results and was applied to solve a specific technological problem. Using this algorithm, the inverse problem of chemical kinetics was solved and the optimal values of the kinetic parameters of the reaction were found. It was proved that the model correctly described the available experimental data. Moreover, the sensitivity analysis of the algorithm parameters was performed.

Method for Solving the Inverse Problem of the Chemical Kinetics of Multistage Reactions

A method for solving the inverse problem of chemical kinetics based on the data of non-stationary experiments for multistage reactions is described. The method is based on the use of splines, which take into account the relaxation features of reactions with monotone kinetics. Examples of using the method to determine the intervals of physical values of the rate constants of two- and three-stage reactions are given. The influence of the spline structure on error in the determination of rate constants of stages is estimated. The effectiveness of the method for solving the inverse problem of chemical kinetics for multistage reactions is shown with consideration for errors in the determination of experimental data.

A Method for Solving the Inverse Problem of Chemical Kinetics for a Nonisothermal Gradientless Reactor Based on Steady-State Data

A method has been presented for solving the inverse problem of chemical kinetics based on steady-state experimental data with different initial conditions (multiexperiments) taking into account measurement errors in an open nonisothermal gradientless reactor. Examples of using the method to determine the intervals of the physical values of rate constants for the stages of multistage nonlinear reactions have been given. The effect of measurement errors on the accuracy and stability of the method has been evaluated.

SOLVING INVERSE PROBLEM OF CHEMICAL KINETICS WITH USE OF CUBIC SPLINES

A simple effective method for solving the inverse problem of chemical kinetics based on non-stationary experiments for multistage reactions occurring in an isothermal reactor of ideal mixing is described. The idea of the method is based on taking into account the distinctive features (informativeness) of different fragments of relaxation curves for chemical reactions with arbitrary (non-monotonic) kinetics and their as accurate approximation as possible. For this purpose, non-linear (cubic) splines are used to describe different informative fragments of relaxation curves, which allow to approximate and interpolate experimental data as accurately as possible. An additional advantage of cubic splines, from the point of view of the implementation of the described method, is their continuity at all given points up to and including second-order derivatives (smoothness). This allows us to calculate with good accuracy not only the concentration of reagents, but also the instantaneous rate of change at any time. The consequence of this is the possibility of a sufficiently accurate solution of the inverse problem based on the data of non-stationary experiments. The correctness of the mathematical model used and the stability of the method were tested using variations of the original data. An example of using the method for determining the intervals of physical values of the rate constants of the stages of a two-stage reaction is given. The influence of the method of selecting the reference points (structure) of the spline and measurement errors (noise) of experimental data on the error of determining the speed constants of the stages is estimated. The efficiency of application and good accuracy of the method for solving the inverse problem of chemical kinetics of multistage reactions occurring in non-gradient systems with taking into account of noise is shown.

Autonomous Kinetic Invariants of Linear Chemical Reactions

A method has been developed for calculating the exact autonomous kinetic invariants of multistage linear chemical reactions occurring in a gradientless isothermal reactor via any number of elementary stages and involving an arbitrary number of reagents within the framework of mass-action law. These invariants are functions that remain strictly constant throughout the reaction (i.e., are time-independent), although they depend on the nonequilibrium reagent concentrations measured in two experiments with different initial conditions (dual experiments). For the dynamic models of linear reactions, one can always find general and particular analytical solutions expressed explicitly in terms of the initial conditions. The idea of the method is based on choosing the initial conditions that allow the nonequilibrium reagent concentrations to be expressed in terms of constant kinetic parameters (stage rate and flow rate constants). An applicability criterion of the method was formulated. The number of different invariants was shown to be equal to the number of reagents. The relations obtained in this study were used to investigate the relaxation properties of multistage linear reactions occurring in closed and open isothermal systems. The invariant curves found for these reactions were compared with the concentration curves measured in two nonequilibrium experiments throughout the transition process. For these reactions, the time dependences of the invariants remained strictly constant, while the reagent concentrations continuously changed (including nonmonotonously) during the reaction. The results give new insight into the relaxation of linear chemical reactions and can be used to solve the inverse problems of chemical kinetics under the conditions of an isothermal perfect-mixing reactor.

Optimization algorithms for the conditions of complex catalytic reactions

A procedure was developed for the investigation of complex catalytic reactions using optimization algorithms. The first stage is a solution of the inverse problem of chemical kinetics involving the recovery of unknown parameters by single-objective optimization algorithms. In the second stage, based on the kinetic model, we solved the problem of determining the optimal conditions for the reaction resorting to multi-objective optimization algorithms. Parallelization models of computing for solving the multi-objective optimization problem are considered.

KINETICS QUASIINVARIANTS OF CHEMICAL REACTIONS IN OPEN SYSTEMS

The methods of nonequilibrium multi-experiments are one of the new approaches to solving inverse problems of chemical kinetics and optimization of chemical reactors. Currently, these methods are developed only for closed isothermal systems. In this paper, a generalization of the dual-experiment method and its extended version of the multi-experiment method for open systems is obtained, which allows to determine the approximate kinetic invariants (quasiinvariants) of chemical reactions in open continuous stirred tank reactor. The multi-experiment method for open systems is based on conducting two or more special nonequilibrium (unsteady) experiments under certain conditions. For nonlinear reactions of arbitrary complexity (multi-step, multi-equilibria), simple relations are obtained that allow to calculate the conditions for nonequilibrium experiments necessary for the identification of the reaction mechanism under study. The method allows to use any permissible values, except equilibrium ones, as initial values of reagent concentrations. The technique of carrying out multi-experiments and performing the necessary numerical calculations based on the multiple integration of systems of ordinary differential equations under different initial conditions is developed. The examples of using the developed method for one-stage linear and two-stage nonlinear reactions with two and three reagents are given. Found with the help of this method, the kinetic curves of the nonequilibrium quasiinvariants compared with the nonequilibrium curves of change of concentrations during the whole reaction. It is shown that quasiinvariant curves change within narrower limits than concentrations in different experiments, i.e. remain practically constant in time. The obtained results are also applicable for open nonisothermal systems.

Development and automation of algorithm for determining basis of nonlinear parameter functions of kinetic constants

Mathematical modeling of catalytic processes is necessary for the complete and accurate description, as well as for controlling the quality and physicochemical studied of catalysts. In the paper, theoretical issues of industrial catalysis are discussed. The work is devoted to theoretical graph analysis of informativity of kinetic parameters of the model of a complex chemical reaction. The aim is the development and automation of algorithm for determining basis of nonlinear parameter functions in solving inverse problems of chemical kinetics in order to define the number and form of independent combinations of rate constants of elementary stages. A program package for analysis of informativity of kinetic parameters of the mathematical model of a complex catalytic reaction is developed and described. The obtained functional relations between the kinetic parameters can be useful for experimentalists in physicochemical interpretation and analysis of mechanisms of chemical reactions. In other words, the proposed method allows independent combinations of kinetic constants to be distinguished that results in shortening the number of the model parameters and, as a consequence, enhance the accuracy of the mathematical model. The mechanism of hydrogen oxidation over a platinum catalyst is given as an example of the use of the software.

Interval Algorithm for the Global Search of Uncertainty Domains in Simulating the Kinetics of Complex Chemical Reactions

This study is devoted to the mathematical description of a kinetic experiment under the setting of multiple solutions to the inverse problems of chemical kinetics. A new algorithm for the global search of uncertainty domains is proposed, which represents a symbiosis of the methods of global optimization with an interval evolutionary approach. Chemical reaction models built using the kinetic parameters of these areas describe experimental data within an acceptable measurement error specified by the researcher. The use of this algorithm allows a complex multidimensional domain in the global space of kinetic parameters, whereas the local solution sets describing the experimental data with near equal accuracy are searched or the one-, two-, or three-dimensional projections of uncertainty domains are separately built in many other studies. The proposed algorithm has been tested using a reaction simulation of n-decane inhibited oxidation. Since this structure has a formal parallelism, parallel computing techniques are applied to speed up calculations.

Binary correspondences and the inverse problem of chemical kinetics

We show how binary correspondences can be used for simple formalization of the notion of problem, definition of the basic components of problems, their properties, and constructions. In particular, formalization of the following notions is presented: condition, data, unknowns, and solutions of a problem, solvability and unique solvability, inverse problem, composition and restriction of problems, isomorphism between problems. We also consider topological problems and the related notions of stability and correctness. A connection is indicated between the stability and continuity of a uniquely solvable topological problem. The definition of parametrized set is given. The notions are introduced of parametrized problem, the problem of reconstruction of an object by the values of parameters, as well as the notions of locally free set of parameters and stability with respect to a set of parameters. As an illustration, we consider a singularly perturbed system of ordinary differential equations which describe a process in chemical kinetics and burning. Direct and inverse problems are stated for such a system. We extend the class of problems under study by considering polynomials of arbitrary degree as the right-hand sides of the differential equations. It is shown how the inverse problem of chemical kinetics can be corrected and made more practical by means of the composition with a simple auxiliary problem which represents the relation between functions and finite sets of numerical characteristics being measured. For the corrected inverse problem, formulas for the solution are presented and the conditions of unique solvability are indicated. Within the study of solvability, a criterion is established for linear independence of functions in terms of finite sets of their values. With the help of the criterion, realizability is clarified of the condition for unique solvability of the inverse problem of chemical kinetics.

Mathematical model of obtaining a hydrocarbon fuel based on the fischer­tropsch pathway in a stationary layer of the cobalt­based catalyst

Studying the kinetics of the Fischer-Tropsch process is a rather important task, since this process is very sensitive to the temperature mode, as well as to the characteristics of the catalyst. In addition, a given process is accompanied by many side reactions that negatively affect the rate and selectivity of the reaction. The Fischer-Tropsch synthesis is an alternative source for obtaining high-quality fuel from coal or biomass rather than petroleum. Therefore, investigating the kinetics of the Fischer-Tropsch reaction, in order to improve the selectivity and activity of catalysts, and to determine the rate constants of chemical reactions, is a relevant problem. The choice of the catalyst is one of the main factors affecting the quality and product yield for the Fischer-Tropsch synthesis. We fabricated two samples of cobalt catalysts for conducting the experiments. The first sample of the catalyst Со/γ-Al 2 O 3 contains cobalt nanoparticles of the same size. The second sample of the catalyst (Со)/γ-Al 2 O 3 was obtained by the method of impregnating the carrier with a solution of cobalt nitrate. The catalyst, obtained through the method of impregnation of (Со)/γ-Al 2 O 3 , demonstrated a higher activity, larger by an order of magnitude than the monodispersed catalysts. However, the monodispersed catalyst showed high selectivity for the lower hydrocarbons. In order to calculate the kinetics of the Fischer-Tropsch process and to find the reaction rate constants, we developed a software module in the programming environment MS Visual Studio 2017 in the programming language C# using the .NET Framework v4.6 technologies. By using the developed program module, we calculated reaction rate constants of the Fischer-Tropsch process. After analyzing the data obtained, one can see that the relative error is within 2…3 %, demonstrating the adequacy of the proposed model to solve the inverse problem of chemical kinetics. Therefore, we can state that a given model for the calculation of rate constants could be applied to study the Fischer-Tropsch process.

STUDY OF CARBON DIOXIDE ADSORPTION ON CHROMOXIDE CATALYST ON NON-STATIONARY CONCENTRATIONS

Investigation of the regularities of chemical processes, not only near but also far from the stationary state, gives additional information on their mechanisms. In this paper, we present a new method for estimating rate constants of adsorption-desorption processes from the experimentally measured values of the nonstationary concentrations of an adsorbed substance, based on calculating the instantaneous rates of the adsorption (or desorption) process. This method allows to connect unknown kinetic parameters of adsorption (desorption) of a substance on the catalyst surface for various most probable assumed mechanisms with the calculated values of the instantaneous rates of adsorption-desorption processes. As a consequence, the method makes it possible to solve two types of inverse problems of chemical kinetics: calculate point and interval values of rates constants of adsorption and desorption; determine the most likely mechanism from several proposed mechanisms of implementation of these processes. Using this method, point and interval values of the rates constants of adsorption and desorption of carbon dioxide were determined on the base of nonstationary experimental data on adsorption on the assumption of carbon dioxide adsorption on a chromoxide catalyst to three proposed mechanisms: linear, bimolecular and dissociative. Based on the results of calculations, the corresponding non-stationary dependences of carbon dioxide adsorption were restored, which were compared with the experimental data. The obtained results confirm that the previously established dissociative mechanism of adsorption of carbon dioxide on the chromoside catalyst is the most probable. The developed simple method does not require the use of complex optimization calculations and can be used to solve the inverse problem of chemical kinetics associated with the determination of mechanisms and the estimation of the rates constants of adsorption and desorption of substances on various catalysts.Forcitation:Kol’tsov N.I., Fedotov V.Kh. Study of carbon dioxide adsorption on chromoxide catalyst on non-stationary concentrations. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2018. V. 61. N 7. P. 37-42

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.

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.

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.

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.