Equations Of Chemical Kinetics Research Articles

Prediction of the optimal speed of an aerospace vehicle by aerothermochemical analysis of hypersonic flow during atmospheric re-entry

The objective of this work is to predict the optimal speed of an aerospace vehicle by aerothermochemical analysis of the hypersonic flow during atmospheric re-entry, out of equilibrium vibrational and chemical behind a detached strong shock. This study focuses on the influence of the ionization process that plays a significant role in the absorption of heat, because the characteristics of hypersonic flows are that molecules behind a strong shock wave become vibrationally excited, partially or completely dissociated and ionized depending on their bond energy, and the velocity of flow. On the other hand, we present the mathematical model that governs the flow of reactive gas mixture out of vibrational and chemical equilibrium that is composed of 79% nitrogen N2 and 21% oxygen O2. Conservation and relaxation equations (chemistry-vibration) are presented with particular importance to the expression of source terms. The numerical resolution method used is based on physical modeling, governed by the Euler equations, supplemented by the equations of chemical kinetics using the finite difference method. The results obtained are in good agreement with the specialized literature.

Reduction of the Complete System of Chemical Kinetics Equations for Multicomponent High Temperature Gas Flows Based on the Partial Local Equilibrium Method

The paper presents a method to reduce the complete system of equations of chemical kinetics from a large number of equations to the final one, which can be solved with available computing tools without a noticeable loss of accuracy, e.g., to model chemical combustion reactions. The paper presents the theory and examples of the application of the partial local chemical equilibrium method for the calculation and modeling of subsonic and supersonic flows of reacting media for the reduction of kinetic schemes of complete chemical reactions in the case of incomplete local chemical equilibrium.

Sulfur and nitrogen doped-titanium dioxide coated on glass microspheres as a high performance catalyst for removal of naphthalene (C10H8) from aqueous environments using photo oxidation in the presence of visible and sunlight

Naphthalene is a toxic aromatic compound whose presence in aqueous environments is very hazardous. In this research, naphthalene removal from wastewater using titanium dioxide-nitrogen-sulfur (TiO2-N-S) photocatalyst immobilized on glass microspheres was investigated. Additionally, the effect of visible and sunlight, radiation time, pH, and initial concentration of naphthalene on photocatalytic removal of naphthalene were studied. Scanning electron microscope images revealed nanoparticles with an average size between 10 and 15 nm, and X-ray diffraction pattern revealed nano-photocatalyst with an average size of 11 nm. Energy-dispersive X-ray showed the presence of two elements, that is, sulfur and nitrogen in the crystalline structure of TiO2 powder, and diffuse reflectance spectroscopy showed the energy bandgap narrowing and transfer of photocatalytic activity of TiO2-N-S to the visible region. Chemical kinetic equation of naphthalene removal was second-order kinetic. The maximum level of naphthalene removal in the presence of visible and sunlight was obtained at a concentration of 25 mg/L (94.29%) and 40 mg/L (93.24%), respectively. Therefore, the immobilized TiO2-N-S on glass microspheres can be used as a new, effective, and functional method in treating water and industrial wastewater containing naphthalene in the presence of visible and sunlight.

Effect of CO2 diluent on the formation of pollutant NOx in the laminar non-premixed methane-air flame

In this paper, the effects of changes in the concentration of diluent CO2 in methane and air fuels are investigated. A finite volume method (FVM) with staggered grids is used for numerical solution. Equations of continuity, momentum, energy, ideal gas state and kinetic equations with thermodynamic and thermo-chemical information of chemical species are solved using the numerical method of SIMPLE. The convective terms are discretized using Power Law scheme (PLS). The under-relaxation factor dependent on temperature has been utilized to solve the chemical kinetic equations. In this research, by increasing the diluent mass fraction, the mass fraction of the fuel is diminished to the same extent. Therefore, the sum of the diluent and fuel mass fraction values remains constant. The results depicted that as the amount of CO2 diluent in the fuel increases, the total lift-off height and flame length decreases linearly, and the maximum temperature in the combustion chamber becomes smaller than that at the inlet of the chamber. When the concentration of CO2 increases in the fuel, the temperature changes become negligible at the inlet of the combustion chamber. By using the CO2 diluent, shorter combustion chambers can be used. While the diluent is used, the increase in the length of the combustion chamber will not have any effect on the NOx emissions reduction. Therefore, the more concentration of the diluent is used, the smaller the combustion chamber can be selected. Moreover, by increasing the diluent, NOx pollutant decreases in the combustion chamber.

Impact of atmospheric ionization by delayed radiation from high-altitude nuclear explosions on radio communication

In this study, we investigated the motion, shape, and delayed radiation intensity of a radioactive cloud by establishing a volume-source model of delayed radiation after high-altitude nuclear explosions. Then, the spatial distribution of electron number density at different moments on the north side of the explosion point generated by delayed γ-rays and delayed β-rays from the radioactive cloud under the influence of the geomagnetic field was calculated by solving chemical reaction kinetics equations. The impact of radio communication in the different frequency bands on the process of atmospheric ionization was also studied. The numerical results of the high-altitude nuclear explosion (120 km high and with a 1 megaton equivalent at 40° N latitude) indicated that the peak of electron number density ionized delayed γ-rays is located at a height of approximately 100 km and that of electron number density ionized delayed β-rays is about 90 km high. After 1 min of explosion, the radio communication in the medium frequency (MF) and high-frequency (HF) bands was completely interrupted, and the energy attenuation of the radio wave in the very high-frequency (VHF) band was extremely high. Five minutes later, the VHF radio communication was basically restored, but the energy attenuation in the HF band was still high. After 30 min, the VHF radio communication returned to normal, but its influence on the HF and MF radio communication continued.

Influence of reactor temperature conditions on the recycle flow rate

Objectives. The problem of optimizing chemical flow sheets according to energy costs associated with recycling flows is at present quite relevant. The current article investigates the influence of temperature conditions on the recycle flow rate, securing the specified conversion of the recycled flow sheet “reactor – separation unit.”Methods. The study’s main method is the mathematical simulation of a recycled flow sheet based on material balance and chemical kinetics equations. This model assumes that the separation unit can form the recycle and outlet flows of any specified compositions.Results. The mathematical model recycle flows provides the full reagent conversion of recycled flow sheet depends on the reactor type and the temperature conditions in it. It was established that the dependence of the recycle flow rate on the reactor temperature for endothermic reactions has monotonously decreasing shape. The most interesting are exothermic reactions for which the dependence of the recycle flow rate on the reactor temperature curve has a minimum. It is proved that the “reactor – separation unit” system with the plug flow reactor has lower optimal recycle flow rate than the recycled system with the continuous stirred tank reactor. For the adiabatic reactor the dependence of total conversion recycle flow rate on the inlet reactor temperature was investigated. It has been proven that the optimal recycle flow rate is equal to the minimum recycle flow rate for total conversion in the “reactor – separation unit” system.Conclusions. It has been established that isothermal operation conditions are the best in terms of the recycle flow rate, securing the specified conversion for the system.

On the peculiar properties of initiation and propagation of multifront detonation

At initiation an external source must initiate a chemical reaction in the combustible mixture and ensure its self-sustaining propagation over the whole volume of the mixture. Traditionally, the critical energy is considered as the measured value of successful initiation of a mixture, providing 100% excitation of the process – combustion or detonation. Actually, the initiation of combustion or detonation process has a “threshold” nature (“yes” – “no”). The spatial-temporal law of initiator energy allocation has a noticeable effect on the critical initiation energy. The instability of the system of equations of gas dynamics and chemical kinetics is manifested in the multifront nature of the detonation front and the cellular structure of the trajectories of the transverse waves. The important question is the moment and place of occurrence of such a structure, especially for expanding waves. Along with the kinetic- gasdynamic instability of the combustible mixture, a certain role is played by the instabilities introduced by the initiator: for example, the constrictive (sausage) electromagnetic instability of an electric conductor with a current, the Meshkov-Richtmeier instability at the expanding boundary of the liquid metal of the exploding wire, etc. In this report the existing problems of initiation and propagation of detonation are discussed based on modern data, including the results of the author’s research on these issues.

Kinetic studies on toluene removal from aqueous solutions using carbon nanotubes

The effectiveness of Taunit-M carbon nanotubes in removing toluene from aqueous media was studied. Adsorption kinetic data were analyzed implementing the simple Weber-Morris diffusion model and very common phenomenological models (Lagergren and Ho-McKay) which simulate mass transfer processes through using formal equations for chemical kinetics. Investigating the correspondence of the experimental data to different models as regards adsorption kinetics, it can be should assumed that the toluene adsorption on the carbon nanotubes represents a two-stage process consisting of the phenomena of diffusive transfer and adsorption itself. The analysis of the temperature effect on the equilibrium sorption shows that the Gibbs free energy (ΔG°) values vary in the range typical of adsorption interactions.

Probe supply of methane in gas-jet synthesis of diamond structures

The present work is devoted to a numerical and experimental investigation of the probe supply of “cold” methane on the growth of diamond structures during gas-jet deposition. The analysis of results of experiments on the diamond gas-jet synthesis from methane and hydrogen mixture flows are presented. The direct simulation Monte Carlo method for numerical analysis of gas-dynamic aspect of these experiments was applied. A one-dimensional approach based on the solution of equilibrium chemical kinetics equations was used to analyze gas-phase methane decomposition. The obtained results can be useful for investigation of gas-jet deposition of diamond structures.

Study of physico-chemical phenomena in a non-equilibrium hypersonic air flow behind a strong shock wave

In this study, the effects of different thermo-chemical models on the macroscopic parameters of the flow behind a strong shock wave have been examined. The effect of the geometric average temperature proposed by Park and the effect of the electronic energy are also presented, and two CVD vibration-dissociation coupling models including those of Park and Kuznetsov are also examined and used for comparison. The Park93 chemical kinetic model with 11 species and 49 elementary reactions was used to describe the non-equilibrium air chemistry. The energy exchange model between translational and vibrational modes is described by the Landau-Teller formula, where the species relaxation time is based on the Millikan-White formula including Park’s high-temperature correction. The theoretical model consisting of the Euler equations supplemented with the equation of molecular vibration and the equations of chemical kinetics using a two-temperature model (translational-rotational temperature and vibrational-electron-electronic temperature) is discretized by a finite difference scheme. Good agreement is found for the relaxation zone between the present results and those obtained by Panesi for the two trajectory point (1634 s and 1643 s) for the FIRE II reentry capsule.

Chemical Kinetics Analysis of Strength Development of Mortar Containing Fly Ash Based on Various Curing Temperatures

Due to large size and high internal temperature of hydraulic dams, the strength development process of damming materials is often faster than those under standard curing conditions. In order to further study the strength development features of damming materials under internal temperature conditions, two kinds of fly ash mortars were investigated, of which fly ash content is 40% and 30%. The compressive strength of mortars under three curing temperatures containing 20, 30 and 38°C was tested at 3 days, 7 days, 14 days, 28 days, 56 days and 90 days, respectively. Then chemical kinetics equation was employed to describe the strength development features under different temperature conditions. The results show that the compressive strength of fly ash mortar increases with the increase of curing temperature in the range of 20 to 38 °C. The main reason is that the chemical reaction rate of cementitious materials is accelerated by increasing curing temperature. For example, the hydration rate at 30° is 1.6 to 1.9 times of that at 20°, and the hydration rate at 38° is 3.1 to 3.9 times of that at 20°. In addition, the hydration rate of mortar with higher fly ash content is accelerated more. It can be seen that the apparent activation energy of mortar containing 40% of fly ash is 1.2 times of that with 30% of fly ash, and its chemical reaction barrier is higher. Therefore, the equivalent age of mortar with 40% of fly ash is longer and its compressive strength is improved more greatly under temperature-raising conditions.

Protobiotic Systems Chemistry Analyzed by Molecular Dynamics.

Systems chemistry has been a key component of origin of life research, invoking models of life’s inception based on evolving molecular networks. One such model is the graded autocatalysis replication domain (GARD) formalism embodied in a lipid world scenario, which offers rigorous computer simulation based on defined chemical kinetics equations. GARD suggests that the first pre-RNA life-like entities could have been homeostatically-growing assemblies of amphiphiles, undergoing compositional replication and mutations, as well as rudimentary selection and evolution. Recent progress in molecular dynamics has provided an experimental tool to study complex biological phenomena such as protein folding, ligand-receptor interactions, and micellar formation, growth, and fission. The detailed molecular definition of GARD and its inter-molecular catalytic interactions make it highly compatible with molecular dynamics analyses. We present a roadmap for simulating GARD’s kinetic and thermodynamic behavior using various molecular dynamics methodologies. We review different approaches for testing the validity of the GARD model by following micellar accretion and fission events and examining compositional changes over time. Near-future computational advances could provide empirical delineation for further system complexification, from simple compositional non-covalent assemblies towards more life-like protocellular entities with covalent chemistry that underlies metabolism and genetic encoding.

Modeling the Process of Sorption for the Purification of Waste Water from Petroleum Products and Heavy Metals

Fixed-bed adsorption is widely applied for the purification of liquid mixtures, including industrial waste water. The adsorption purification of waste water from petroleum products and heavy metals with the use of peat is modeled. A process model taking the longitudinal stirring of the liquid-phase flow, the outer- and inner-diffusion resistance of flow in sorbent grains, and the phenomena of adsorption on the peat surface into account is constructed. The results of experimental studies are presented. The effect of the abnormal diffusion of heavy metal ions in peat has been revealed and explained. Based on these studies, the isotherm of petroleum product adsorption from waste water and the change in the mass transfer coefficient depending on the adsorption value were plotted. The effect of chemical kinetics on the ion-exchange rate has been experimentally determined. The experimental curves of the adsorption of heavy metal ions are processed using the equations of diffusion and chemical kinetics. Based on these results some conclusions have been made.

Modeling the Effect of the Operating Temperature on the Performance of a Zinc/Bromine Flow Battery

The zinc/bromine (Zn/Br2) flow battery is an attractive rechargeable system for energy storage because of its inherent chemical simplicity, high degree of electrochemical reversibility at the electrodes, good energy density, and abundant low-cost materials. Because the performance of a Zn/Br2 flow battery depends strongly on the operating temperature, it is important to develop a mathematical model to predict the performance of the battery as a function of the operating temperature in order to estimate such quantities as current efficiency and conversion per pass. This information can be used to design both of bench and production scale cells and to select the operating conditions for optimum performance. In this work, a method of modeling the dependence of the charge and discharge curves of a Zn/Br2 flow battery on its operating temperature is presented. This work adopts a simple modeling approach by considering Ohm’s law and charge conservation on the electrodes based on the simplified polarization characteristics of the electrodes. To accommodate the temperature dependence, the key modeling parameters are expressed as the functions of temperature based on the well-known principles of the Arrhenius equation of chemical kinetics and the Nernst equation of electrochemical thermodynamics. The model is validated by comparing the modeling results with the experimental measurements.

Probing the Impact Energy Release Behavior of Al/Ni-Based Reactive Metals with Experimental and Numerical Methods

Reactive metals (RMs) are a new class of material that can withstand mechanical loads and chemically react to release large amounts of heat under strong impact loading. They are gradually becoming widely used in defense and military fields, including for high-efficiency warheads and reactive armor. For the numerical simulation method considering the combined mechanical-thermo-chemical process for the impact energy release behavior of the RMs, the Al/Ni-based RMs were investigated in this work by combining experiments, theoretical calculations and a numerical simulation. Three kinds of Al/Ni-based RMs (Al-Ni, Al-Ni-CuO and Al-Ni-MoO3), were prepared using the hot-pressing forming process. Firstly, the compressive behavior and the parameters of the Johnson-Cook constitutive model were obtained using a mechanical testing machine and split Hopkinson pressure bars (SHPB). Secondly, the parameters of the equation of state (EOS) under the medium and low pressure conditions of the Al/Ni-based RMs, which were was seen as porous mixtures with high theoretical material density percentages (TMD%), were calculated based on the cold-energy superposition theory and the Wu-Jing method. Third, the impact energy release behaviors of the three RMs were studied with direct ballistic tests. The shock temperatures at different impact velocities were calculated based on the existing shock-induced chemical reaction thermo-chemical model while considering the chemical reaction efficiency, the relationship between the shock temperature and the extent of the chemical reaction was established, and the parameters of the relevant chemical kinetic equations were fitted. Finally, the user’s subroutines defining the material model were implemented to update the stresses in the solids elements in LS-DYNA. The model was based on the Johnson-Cook constitutive model with consideration of the mechanical-thermo-chemical coupling effect, which was verified by the experimental results. The results show that the constitutive model developed in this work can describe the impact energy release behavior of the Al/Ni-based RMs.

CFD Design of Hydrogenation Reactor for Transformation of Levulinic Acid to γ-Valerolactone (GVL) by using High Boiling Point Organic Fluids

Levulinic acid (LA) has been ranked as one of the “Top 10” building blocks for future bio-refineries as proposed by the US Department of Energy. It is considered one of the most important platform molecules for the production of fine chemicals and fuels based on its compatibility with existing processes, market economics, and industrial ability to serve as a platform for the synthesis of important derivatives. Hydrogenation of LA to produce γ-valerolactone (GVL) is an active area of research due to the potential of GVL to be used as a biofuel in its own right and for its subsequent transformation into hydrocarbon fuels. This paper contains a new design for a simple, cost effective, and safe hydrogenation reactor for the transformation of levulinic acid to γ-valerolactone (GVL) by utilizing high boiling point organic fluid. The hydrogenation reactor is composed of a heating source—organic fluid (called “DOWTHERM A” or “thermex”) and the catalytic reactor. The advantages of high boiling temperature fluids, along with advances in hydrocracking and reforming technologies driven by the oil and gas industries, make the organic concept more suitable and safer (water coming in contact with liquid metal is well understood in the metallurgical industry to be a steam explosion hazard) for heating the hydrogenation reactor. COMSOL multi-physics software version 4.3b was applied in this work and simultaneously solves the continuity, Navier-Stokes (fluid flow), energy (heat transfer), and diffusion with chemical reaction kinetics equations. It was shown that the heat flux supplied by the DOWTHERM A organic fluid could provide the necessary heat flux required for maintaining the hydrogenation process. It was found that the mass fractions of hydrogen and levulinic acid decreased along the reactor axis. The GVL mass fraction increased along the reactor axis.

SimKinet: A free educational tool based on an electrical analogy to solve chemical kinetic equations.

In this article we introduce the software SimKinet, a free tool specifically designed to solve systems of differential equations without any programming skill. The underlying method is the so-called Network Simulation Method, which designs and solves an electrical network equivalent to the mathematical problem. SimKinet is versatile, fast, presenting a real user-friendly interface, and can be employed for both educational and researching purposes. It is particularly useful in the first courses of different scientific degrees, mainly Chemistry and Physics, especially when facing non-analytic or complex-dynamics problems. Moreover, SimKinet would help students to understand fundamental concepts, being an opportunity to improve instruction in Chemistry, Mathematics, Physics and other Sciences courses, with no need of advanced knowledge in differential equations. The potency of SimKinet is demonstrated via two applications in chemical kinetics: the photochemical destruction of stratospheric ozone and the chaotic dynamics of the peroxidase-oxidase reaction.

Kinetics of Siderite Ore Roasting in the Shaft Furnace

Kinetics of the siderite ore roasting in the air, helium and hydrogen flows has been studied in a gasometrical unit with continuous mass variation logging. We have derived the expression for determination of an apparent degree of calcination and identified its dependence on the size of the prill, the heat treatment duration, and gas-phase composition. Using a generalized chemical kinetics equation, we have obtained a formula for calculation of the decomposition period for siderite ore samples. It has been found that calcination rate increases with the temperature rise, irrespective of the sample size and atmospheric composition. Calcination process has been studied at low temperatures. We have demonstrated that it is feasible to describe the process of siderite ore thermal dissociation by a first-order kinetics equation. We have obtained the expression to calculate the duration of this process depending on different parameters. Using a generalized chemical kinetics equation, we have obtained a formula for checking the expressions that describe the experimental data. We have studied kinetics of the reduction of roasted ore samples at various temperatures using different sizes of the samples. The obtained results have been applied for optimization of the design values and operating conditions of the siderite ore roasting in shaft furnaces. These will also be used for designing a shaft furnace consisting of a calcination zone, reduction zone (metallization zone) and metallized product cooling zone, which will increase iron content in the end-product to 65-70%.

Recasting the mass-action rate equations of open chemical reaction networks into a universal quadratic format

Recasting the rate equations of mass-action chemical kinetics into universal formats is a potentially useful strategy to rationalize typical features that are observed in the space of the species concentrations. For example, a remarkable feature is the appearance of the so-called slow manifolds (subregions of the concentration space where the trajectories bundle), whose detection can be exploited to simplify the description of the slow part of the kinetics via model reduction and to understand how the chemical network approaches the stationary state. Here we focus on generally open chemical reaction networks with continuous injection of species at constant rates, that is, the situation of idealized biochemical networks and microreactors under well-mixing conditions and externally controllable input of chemicals. We show that a unique format of pure quadratic ordinary differential equations can be achieved, regardless of the nonlinearity of the kinetic scheme, by means of a suitable change and extension of the set of dynamical variables. Then we outline some possible employments of such a format, with special emphasis on a low-computational-cost strategy to localize the slow manifolds which are indeed observed also for open systems.

Application of Chemical Kinetics Methods to the Study of Iodonitrotetrazolium Chloride Reduction in the Presence of Bacillus subtilis Cells

It is demonstrated that the reduction of iodonitrotetrazolum chloride in the presence of a Bacillus subtilis suspension in a physiological solution can be described using chemical kinetics equations. The effective kinetic parameters are determined and the role of the diffusion of iodonitrotetrazolium chloride in the process of its reduction involving bacterial cell components is described.