Formal Kinetics Research Articles

Kinetics of chemical reactions in spray

The number of observations demonstrating a significant effect of droplet sizes on the kinetics of chemical processes has increased with the expansion of the scope of application of spray technology. The equations linking the concentrations of reagents, the volume of droplets, the initial composition of the solution, the composition of the gas medium and the speed of processes are formulated within the framework of formal chemical kinetics. Using the example of second-order reactions (coupling, exchange, condensation, polymerization, polycondensation), it is shown that size kinetic effects occur when chemical processes are accompanied by changes in the droplet sizes in equilibrium with the gas medium. The results of computer simulation of condensation reaction and polycondensation process reproducing size effects are presented. Kinetic curves obtained by modeling the polycondensation process are compared with experimental data.

Formal kinetics of catalytic oxidation of diesel paraffin-naphthenic fraction in the presence of carbon nanotubes containing Co, Mn and Fe

This study identified the formal kinetics of aerobic oxidation of the paraffin-naphthenic fraction of diesel fuel in the presence of multi-walled carbon nanotubes (MWCNTs) containing three transition metals—Fe, Co, and Mn. The synthesis of metal-containing multi-walled carbon nanotubes (M@MWCNTs) was carried out by pyrolysis of cyclohexane in the presence of ferrocene (CVD synthesis), followed by sequential doping of the resulting iron-containing carbon nanotubes Fe@MWCNTs with Co and Mn clusters. The resulting Fe–Co–Mn@MWCNT samples were identified using electron microscopy (SEM, TEM) and elemental analysis. The resulting carbon nanotubes were found to have a diameter of 30–60 nm and length of 500–800 μm. Iron clusters were observed to be present within the channels, while Co and Mn particles were observed to be present in the outer space of the nanotubes. The formal kinetic regularities of the dearomatized diesel fraction aerobic oxidation promoted by M@MWCNT additives were studied. It has been demonstrated that metal-nanocarbon additives effectively catalyze the oxidation process in the absence of hydroperoxides, resulting in thermal decomposition. The introduction of Co and Mn clusters into the nanotube structure has been observed to enhance catalytic activity. A catalytic oxidation scheme is currently under consideration, with corresponding effective oxidation rates being determined. It is postulated that these findings may prove useful in the estimation of effective nano-catalytic systems for the oxidative conversion of multicomponent hydrocarbon feedstocks.

INVESTIGATION OF THE KINETICS OF THE COAL PYROLYSIS PROCESS

The study of the processes occurring in the temperature range of the main decomposition of the organic mass of coal (OMC) makes it possible to understand both the general patterns and the specifics of the decomposition of solid fuels. This temperature interval is used to calculate the kinetic parameters of the process, which carry important information both about the nature of the structural-chemical transformations and about the structure and direction of thermal destruction of OMC. In this article, to study the kinetics of pyrolysis of coal, the method of thermogravimetric analysis was used, in which heating of coal samples was carried out in ceramic crucibles in the temperature range of 25-900 °C at different heating rates (5-25 deg/min) in nitrogen and oxygen media. Coal from the Kenderlyk deposit was chosen as the object of study. Based on the constructed differential DTG curves (dependence of the sample mass change rate on time) at different heating rates, the kinetic parameters of pyrolysis of coal were calculated using the equations of non-isothermal formal kinetics. The effect of the rate and temperature of coal heating on the kinetic parameters of pyrolysis of coal has been studied. The main stages of OMC decomposition are revealed. It has been found that the heating rate of coal samples significantly affects the temperature and process rate corresponding to the main decomposition maxima on the differential DTG curves. The dependence between the kinetic parameters of pyrolysis of coal in the temperature range of the main decomposition of OMC on the rate and temperature of heating, as well as between the kinetic parameters at different stages of the main decomposition of coal, is analyzed.

Effect of preparation method of pyrolysis liquid mixed with coal on its ignition and combustion characteristics

Relevance. The need to develop technological solutions to increase the competitiveness of pyrolysis processing of various wastes. Combustion of pyrolysis liquid in a mixture with coal is one of these solutions, which makes it possible to stabilize the properties of the obtained fuel and use in standard energy equipment. Aim. To determine the influence of the method of preparing a mixture of pyrolysis liquid and low-grade coal on its ignition and combustion characteristics, as well as on composition of the released gas-phase products, depending on the temperature of heating medium and concentration of the additive. Methods. Pyrolysis and oxidation characteristics were studied using thermogravimetric analysis, and formal kinetic constants were calculated using the Coates–Radfern method. Samples of mixed fuels were prepared by the methods of homogeneous mixing and surface wetting of pyrolysis liquid of rubber processing and low-grade coal. Ignition and combustion characteristics were determined using an experimental stand, and composition of gas-phase combustion products was determined using once-through gas analyzer. Results. The authors have determined the features of pyrolysis and oxidation of the pyrolysis liquid as well as the values of formal kinetics constants, indicating the physical nature of the factors that defining the rate of these processes. It was found that at 600 °C the ignition of the studied mixtures weakly depended on concentration of the additive, while at 700 and 800 °C the dependence was linear, and the differences between the samples prepared using different methods were insignificant. For samples obtained by the method of surface wetting, combustion of the additive occurred in the gas phase near the surface of the sample. For the samples obtained by the method of uniform mixing, it occurred predominantly in the bulk of the backfill. This led to more intense and complete coal combustion in these compositions due to more uniform releasing of heat and initiation of coal particles. The concentration curves of the NO, CO and CO2 release demonstrated, that behavior of the fuel mixture components was additive in terms of released gas-phase combustion products, as well as the absence of significant nonlinear effects over the entire studied range of temperatures and additive concentrations.

GRINDING OF FIBROUS SEMI-FINISHED PRODUCTS AS A MECHANOCHEMICAL PROCESS. MATHEMATICAL MODELING

It is known that the process of grinding fibrous semi-finished products proceeds in the form of four successive stages, accompanied by complex processes of fibrillation and hydration of fibers subjected to mechanical action. The development of these processes over time determines the dynamics of changes in cellulose fiber, which ultimately leads to the formation of the necessary paper-forming properties. The paper shows that the representation of the grinding of fibrous semi-finished products as a mechanochemical process makes it possible to formulate a mathematical model of the grinding dynamics based on the principles of formal kinetics. The latter makes it possible to single out the stages of the milling process in the form of a standard kinetic mechanism of successively occurring reactions. The corresponding model is presented as a system of ordinary differential equations with constant coefficients, the solution of which presents no fundamental difficulties. Since it is not the degree of destruction that is determined experimentally, but the degree of grinding, it is proposed to present the relationship between these values as a power series with a limitation in the form of a linear approximation. However, due to the large dimension, the parametric identification of the model has fundamental difficulties. The paper proposes a reduction method that allows overcoming the problem. The corresponding parameters are identified by comparing the model and the array of experimental data. The presented approach makes it possible to obtain an adequate closed mathematical description of the dynamics of grinding fibrous semi-finished products.

On a special class of gibbs hard-core point processes modeling random patterns of non-overlapping grains

Inspired by issues of formal kinetics in materials science, we consider a class of processes with density with respect to an inhomogeneous finite Poisson point process, which may be regarded as a generalization of the classical Strauss hard-core process. We prove expressions for the intensity measure and the void probabilities, together with upper and lower bounds. A discussion on some special cases of interest, links with literature and a comparison between Matérn I and Strauss hard-core process are also provided. We apply such a special class of point processes in modeling patterns of non-overlapping grains and in the study of the mean volume density of particular birth-and-growth processes.

Моделирование управляемого синтеза интерметаллидного композита с разными способами описания кинетики фазообразования

Currently, multilevel (multilevel), multiscale (multiscale) and multiphysical (multi-physical) approaches to modeling the synthesis of new materials are of great interest. The purpose of this work is to compare two modeling approaches to the synthesis of coatings from Ti and Al powders on a substrate under the condition that the process is controlled by a moving heat source. The first approach consists in a formal description of the reactions sequence based on formal kinetics. The result is the composite coating composition depending on the parameters of the movable heat source. The second way of describing phase formation leads to a two-level model, in which the separation by description levels is associated with the separation of physical processes. The macrolevel problem includes the thermal part. The problem at the meso level gives the phase composition at each point of the macrosample and is solved in the quasi-stationary approximation. Based on the solution of the problem in each reaction cell, the distribution of aluminum and titanium concentrations, the phase boundaries position and the volume fractions of all phases in the cells at an arbitrary point in time, corresponding to the volume fractions of the phases at each point of the macrosample, are found. The resulting volume fractions of the phases are converted into mass concentrations of intermetallic compounds for comparison with the model of the first type. It is shown that both approaches lead to close values of the average integral concentrations of the phases. However, the dynamics of phase formation can differ significantly.

Diffusion Kinetics Theory of Removal of Assemblies’ Surface Deposits with Flushing Oil

The diffusion kinetics theory of cleaning assemblies such as combustion engines with flushing oil has been introduced. Evolution of tar deposits on the engine surfaces and in the lube system has been described through the erosion dynamics. The time-dependent concentration pattern related to hydrodynamic (sub)layers around the tar deposit has been uncovered. Nonlinear equations explaining the experimentally observed dependences for scouring the contaminants off with the oil have been derived and indicate the power law in time. For reference purposes, a similar analysis based on formal chemical kinetics has been accomplished. Factors and scouring parameters for the favor of either mechanism have been discussed. Any preference for either diffusion or chemical kinetics should be based on a careful selection of washing agents in the flushing oil. Future directions of studies are proposed.

Processing of Phosphoric Solid Waste by Humic Acid Leaching Method

This article presents the results of research on the leaching of solid phosphorus-containing waste with humic acid. Such waste includes the by-products of the electrothermal processing of phosphate raw materials—phosphorus sludge and cottrel dust. Chemical and X-ray diffraction analyses have been used to study their composition and phase structure, according to which these substances have an amorphous structure. The leaching of phosphoric sludge and cottrel dust was investigated by varying the main parameters. The obtained data were processed using the method of formal kinetics to study the features of the process. The reaction rate constants and the apparent activation energy were calculated, and the values found made it possible to determine that the process under study is limited by diffusion. The scientific novelty of the article is the use of humic acid for leaching phosphoric solid waste as opposed to traditional methods. This new method may offer improved efficiency, reduced environmental impact, and a potential alternative solution for the processing of phosphoric waste.

Changing the paradigm in modelling the Bray-Liebhafsky oscillatory chemical reaction.

The Bray-Liebhafsky (BL) reaction is one of the simplest chemical oscillators consisting initially of only three components. Despite this, its mechanism is unknown for more than 100 years due to the absence of selective, sensitive, and fast experimental techniques for following all of the involved intermediates. The modeling of the BL mechanism assumes presumably mass action kinetics "adjustable" to oscillatory solutions by the application of mathematical stability analysis and treating the system as homogeneous. Such a basically mathematical approach need not suggest physically realistic kinetic parameters and is not unique since a number of models can be proposed. Based on recent experimental and computational results, a new model of the BL oscillatory reaction mechanism is constructed by including heterogeneous processes occurring in the system. The same set of equations is able to demonstrate not only the oscillatory evolution but also mixing effects on the oscillatory dynamics, and non-oscillatory stepwise-iodine oxidation and can rationalize other effects described in literature. Thus, the paradigm of treating the BL oscillatory system as a homogeneous one, described by formal kinetics only, is extended for a better understanding of the chemistry of this apparently simple system. The introduced ideas of energy redistribution may contribute to establishing an improved conceptual base for considering other complex oscillators in various fields of science.

Acceleration of chemical processes in aerosol

The evolution of the state of aerosol droplets containing a reaction mixture with volatile components is accompanied by a change in the size and composition of the droplets, changes in the concentrations of reagents and the rates of chemical reactions. The methods of formal chemical kinetics and equilibrium thermodynamics describe size effects that lead to a significant acceleration of chemical processes in aerosols. The dependence of the rate of chemical processes on the initial size and composition of droplets, as well as on the composition of the gas phase, is described. The main regularities are modeled on the example of the condensation reaction of glycine with glucose (Maillard reaction). Keywords: aerosol, size effect, chemical kinetics, spray technology.

Ускорение химических процессов в аэрозоле

The evolution of the state of aerosol droplets containing a reaction mixture with volatile components is accompanied by a change in the size and composition of the droplets, changes in the concentrations of reagents and the rates of chemical reactions. The methods of formal chemical kinetics and equilibrium thermodynamics describe size effects that lead to a significant acceleration of chemical processes in aerosols. The dependence of the rate of chemical processes on the initial size and composition of droplets, as well as on the composition of the gas phase, is described. The main regularities are modeled on the example of the condensation reaction of glycine with glucose (Maillard reaction).

Multi-fractal modeling of curcumin release mechanism from polymeric nanomicelles

The physicochemical properties of “smart” or stimuli-sensitive amphiphilic copolymers can be modeled as a function of their environment. In special, pH-sensitive copolymers have practical applications in the biomedical field as drug delivery systems. Interactions between the structural units of any polymer-drug system imply mutual constraints at various scale resolutions and the nonlinearity is accepted as one of the most fundamental properties. The release kinetics, as a function of pH, of a model active principle, i.e., Curcumin, from nanomicelles obtained from amphiphilic pH-sensitive poly(2-vinylpyridine)-b-poly(ethylene oxide) (P2VP-b-PEO) tailor-made diblock copolymers was firstly studied by using the Rietger-Peppas equation. The value of the exponential coefficient, n, is around 0.5, generally suggesting a diffusion process, slightly disturbed in some cases. Moreover, the evaluation of the polymer-drug system’s nonstationary dynamics was caried out through harmonic mapping from the usual space to the hyperbolic one. The kinetic model we developed, based on fractal theory, fits very well with the experimental data obtained for the release of Curcumin from the amphiphilic copolymer micelles in which it was encapsulated. This model is a variant of the classical kinetic models based on the formal kinetics of the process.

Using the Intelligent System to Improve the Delivered Adequacy of Dialysis by Preventing Intradialytic Complications

Acute kidney failure patients while detoxificated by hemodialysis (HD) mostly or continuously faced regular problems such as low blood pressure (hypotension), muscle cramps, nausea, or vomiting. Higher intradialytic symptom leads to low-quality HD treatment. Although more known therapeutic interventions are used to relieve the HD side effects, this study was designed to investigate how intelligent systems can make highly beneficial alterations in dialysis facilities and equipment to ease intradialytic complications and help the staff deliver high-quality treatment. A search was performed among relevant research articles based on nonpharmacological intervention methods considered to prevent adverse effects of renal replacement therapy until 2020 in the PubMed databases using the terms “intradialytic complications,” “intradialytic complication interventions,” “nonpharmacological interventions,” “intradialytic exercises,” and “adequacy calculation methods.” Studies included the prevalence of intradialytic complications, different strategies with the aim of preventing complications, the outcome of intradialytic exercises on dialysis symptoms, and dialysis dose calculation methods. The results showed the incidence of hypotension varying between 5% and 30%, fatigue, muscular cramps, and vomiting as the most common complications during dialysis, which greatly affect the outcome of HD sessions. To prevent hypotension, ultrafiltration profiling, sodium modeling, low dialysate temperature, and changing the position to Trendelenburg are some strategies. Urea reduction ratio (URR), formal urea kinetic modeling (FUKM), formal single-pool urea kinetics, and online clearance monitoring (OCM) are methods for calculating the delivered dose of dialysis in which OCM is a low-cost and accessible way to monitor regularly the quality of dialysis delivered. Integration of the chair and HD machine which is in direct contact with the patient provides an intelligent system that improves the management of the dialysis session to enhance the quality of healthcare service.

Use of the Taylor theorem to predict kinetic curves in an arbitrary mechanism

This work serves as a proof of concept by reporting the development of a novel method for the solution of kinetic rate equations based on Taylor polynomials. The key observation is that mass action type rate equations are autonomous ordinary differential equations, which give the first derivative of a concentration as the polynomial of the concentrations of all substances appearing in the system. Two time scale transformations (based on first order and second order formal kinetics) are introduced to provide bounded polynomials in a way that the polynomial nature of the ordinary differential equation obtained with the transformed variable is conserved. Three chemical systems are used to test the performance of the method. The first system is a series of two consecutive reactions in which the first process is second order and the second process is first order with respect to its sole reactant. Kinetic curves in this scheme could be described by this method with a suitably chosen time transformation and a 100-degree polynomial with an accuracy better than 0.1%. The second system is a series of three reactions containing an autocatalytic step, it produces three extrema on the kinetic curve of one of the species (oligooscillation). The third system is the parallel-consecutive bimolecular reaction, for which high simulation accuracy was achieved with minimal effort. The simulations show that the time transformation used in the calculations has a central role, and the second order transformations typically works better than the other one. Also, the examples confirm that extrema on the kinetic traces are the problems.

A model-free sparse approximation approach to robust formal reaction kinetics

Accurate and transferable models of reaction kinetics are of key importance for chemical reactors on both laboratory and industrial scale. Usually, setting up such models requires a detailed mechanistic understanding of the reaction process and its interplay with the reactor setup. We present a data driven approach which analyzes the influence of process parameters on the reaction rate to identify locally approximated effective rate laws without prior knowledge and assumptions. The algorithm we propose determines relevant model terms from a polynomial ansatz employing well established statistical methods. For the optimization of the model parameters special emphasize is put on the robustness of the results by taking not only the quality of the fit but also the distribution of errors into account in a multi-objective optimization. We demonstrate the flexibility of this approach based on artificial kinetic data sets from microkinetic models. This way, we show that the kinetics of both the classical HBr reaction and a prototypical catalytic cycle are automatically reproduced. Further, combining our approach with experimental screening designs we illustrate how to efficiently explore kinetic regimes by using the example of the catalytic oxidation of CO. • Data driven approach for robust kinetic modeling. • Algorithm automatically determines functional form of model to avoid bias. • Effective kinetic models do not require mechanistic understanding. • Automatic discovery of kinetic regimes.

Ignition and burning of the composite sample impacted by the Bunsen burner flame: A fully coupled simulation

Experimental study and three-dimensional simulation of warming up, ignition, and subsequent burning out of the composite material impacted by the attached Bunsen burner flame is presented. The specimen is the fiberglass-reinforced composite with the epoxy resin binder. In the experiment, vertical specimen was located above the laminar diffusion flame, and transient variation of specimen mass and surface temperatures was recorded until the matrix polymer burned out. In the simulations, thermal decomposition of the composite was evaluated by the in-house pyrolysis model Pyropolis coupled with the general-purpose CFD solver, which simulated the flames generated by the burner and by the combustible volatiles. Formal kinetics of thermal decomposition of matrix polymer and the heat of combustion of volatiles have been derived from the microscale combustion calorimetry measurements. The simulation results include favorable comparisons of experimental and predicted dynamics of material degradation and flame behavior. Transient spatial distributions of surface temperature, burning rate, and heat fluxes (net, radiative and convective) are demonstrated. This study is the step towards developing the computational framework capable of replicating and predicting the outcome of standard fire tests UL94 and VBB.

A study on the effect of the number of clusters at the phase transformation kinetics

This work aims to study cluster nucleation, whose solid–solid phase transformation kinetics considerably deviates from that forecasted by the Kolmogorov–Johnson–Mehl–Avrami (KJMA) model. In this scenario, nuclei do not appear homogeneously within the matrix; however, they appear in preferred regions called clusters. One of the principal parameters of this nucleation is the number of clusters in the matrix. This work uses a numerical model to simulate nucleation and growth reactions, which occur explicitly in spherical clusters. It was thus possible to analyze the cluster number variation affecting the microstructural evolution. During the numerical experiments, we compare the simulation outcomes with the analytical model from Villa & Rios. It was possible to observe that analytical solutions from Villa & Rios equations corroborated the numerical results. The computational model of this study agrees with the analytically exact modeling. This study expanded the analytical solution showing the microstructural evolution in 3D. The simulations also proved that the slower the phase transformation reaction occurs, the fewer clusters per unit volume. Also, the generated microstructures have their particular characteristics. Studies in cluster matrices that use only qualitative and visual analyses can lead to wrong interpretations regarding microstructural evolution when using conventional models of formal kinetics. Thus, the computer simulation study presented that Villa & Rios model is the most suitable for this case involving clustering nucleation. The research shows that clustering introduces microstructural heterogeneity into the matrix. This heterogeneity can be harmful to the materials' final properties that underwent a microstructural transformation with these characteristics.

Mathematical modeling and analysis of operation of cylindric pyrolysis reactor with radial heating

The vector of development of solid-fuel energy is currently directed towards expanding the range of renewable fuels used. Along with the direct combustion of fuel, the processes of controlled thermal transformation of the raw biomass in an oxygen-free surrounding to obtain a new fuel based on it (liquid, solid, gaseous) are widely spread. A significant part of research in this sphere is related to the study of the formal kinetics of such processes, at the same time, the hardware design of the process is no less important, but less studied. Thus, development of mathematical models of pyrolysis equipment operation is relevant. A decisive difference approximation of these processes in the framework of an axisymmetric formulation of the problem is chosen as a mathematical basis for modeling physical and chemical transformations and transfer processes in the radial direction of a cylindrical pyrolysis reactor. The material constants of the processes are borrowed from the well-known literature references The authors studied the modes of reactor operation not covered by a full-scale experiment, using the previously proposed and verified one-dimensional mathematical model of a cylindrical pyrolysis reactor. The issues of the influence of the dimensionless kinetic function of the process (reaction model) on the thermal transformation of the material in the apparatus are considered. The significant influence of the chosen reaction model on the kinetic nature of the process is pointed out. The mutual influence of drying and pyrolysis the presence of which is due to the energy effects of the processes is considered. A significant spatial heterogeneity of the process is defined and the possibility of the existence of a non-trivial effect of advanced heating of the internal zones of the apparatus in comparison with the peripheral ones is specified. The paper shows that a computational experiment can help to detect non-trivial effects and identify the variability of the process implementation even within the framework of a single design and technological solution of the pyrolysis process. According to the authors, the results of the obtained numerical experiments indicate that mathematical modeling can be the basis of making technological solution. However, further research is also needed to determine reliably the material constants of the process.

Photochemical study of interaction of chromium (III) with EDTA reaction kinetics: a chemical kinetics laboratory experiment

Abstract: The kinetics of the complex ion of chromium (III) with EDTA formation reaction in a water solution was studied. The possibility of simultaneous determination of partial reaction orders with respect to all reactants was shown. The influence of temperature and hydrocarbonate-ions as a catalyst on the reaction rate was studied. It was shown that this reaction is very suitable for the experimental demonstration of formal kinetics regularities and can be used in a university laboratory practice course. The methodical instructions for students were developed.