Reaction Rate Expression Research Articles

Fenton and photo‐Fenton processes for the degradation of atrazine: a kinetic study

AbstractBACKGROUNDThis study is focused on the kinetic modelling of the Fenton and photo‐Fenton degradation of a model pollutant (atrazine) in aqueous solution. The effects of hydrogen peroxide and ferric ion concentrations as well as those of radiation level on the atrazine degradation processes have been investigated.RESULTSThe experimental work was performed in a well‐stirred tank laboratory reactor irradiated from both sides with two tubular UV‐lamps. The reaction rate expressions were derived from an accepted reaction mechanism, explicitly taking into account the local volumetric rate of photon absorption inside the photoreactor. The proposed kinetic model was able to reproduce the combined effects of changing the ferric iron concentrations, hydrogen peroxide to atrazine molar ratios and radiation level on the pollutant degradation rate. Model predictions were compared with experimental data and good agreement was obtained. The maximum root mean square error (RMSE) for all the estimations was < 2.5%.CONCLUSIONSThe results obtained indicate that Fenton and photo‐Fenton processes are possible ways to improve the biodegradability of water containing commercial atrazine. © 2014 Society of Chemical Industry

Kinetic Parameters Optimization and Modeling of Catalytic Dehydrogenation of Heavy Paraffins to Olefins

A mathematical model for a fixed bed radial flow catalytic reactor was developed for dehydrogenation of heavy paraffins over Pt-Sn/Al2O3 catalyst. The model included appropriate kinetic rate expressions for the main dehydrogenation reaction as well as side reactions and catalyst deactivation. The reactor model consisted of a set of partial and ordinary as well as algebraic equations that were solved numerically to determine the concentration of various species along the radius of the bed as a function of time. The Nelder-Mead optimization method was used to obtain the optimum kinetic parameters. The validity of the model was demonstrated by comparing the predicted paraffin conversion and product distributions with experimental values reported in the literature.

Commemorating the 1913 Michaelis–Menten paper Die Kinetik der Invertinwirkung: three perspectives

Methods and equations for analysing the kinetics of enzyme-catalysed reactions were developed at the beginning of the 20th century in two centres in particular; in Paris, by Victor Henri, and, in Berlin, by Leonor Michaelis and Maud Menten. Henri made a detailed analysis of the work in this area that had preceded him, and arrived at a correct equation for the initial rate of reaction. However, his approach was open to the important objection that he took no account of the hydrogen-ion concentration (a subject largely undeveloped in his time). In addition, although he wrote down an expression for the initial rate of reaction and described the hyperbolic form of its dependence on the substrate concentration, he did not appreciate the great advantages that would come from analysis in terms of initial rates rather than time courses. Michaelis and Menten not only placed Henri's analysis on a firm experimental foundation, but also defined the experimental protocol that remains standard today. Here, we review this development, and discuss other scientific contributions of these individuals. The three parts have different authors, as indicated, and do not necessarily agree on all details, in particular about the relative importance of the contributions of Michaelis and Menten on the one hand and of Henri on the other. Rather than force the review into an unrealistic consensus, we consider it appropriate to leave the disagreements visible.

Time-on-stream stability of new catalysts for low-temperature steam reforming of biogas

Time-on-stream stability of six different steam reforming catalysts has been tested at 500 °C under a simulated biogas feed. The catalysts are based on different combinations of Ni, Pt and Rh as active species, and CeO₂, ZrO₂ and La₂O₃ as support. In order to perform a conservative analysis, biogas was simulated with a 50 % v/v CO2-CH4 mixture; furthermore a steam to methane ratio as low as 2.5 has also been used. All the samples containing CeO₂ in the support proved fairly stable up to 50 h on stream. Therefore, these catalysts are worth being further investigated to assess their activity and determine appropriate reaction rate expressions.

Improvement of NOx formation model for pulverized coal combustion by increasing oxidation rate of HCN

The NOx formation simulation during pulverized coal (PC) combustion has been studied for several decades. In these studies, the global reaction rate expressions for N intermediates (HCN and NH3) proposed by De Soete were frequently used. Using De Soete’s expressions, the calculated reaction rates of HCN and NH3 in the typical temperature range of 1750–2000K for PC combustion show that HCN has obviously lower conversion rate to NO (or oxidation rate of HCN, HCN+O2→NO+⋯) than that to N2 (HCN+NO→N2+⋯) as well as obviously lower conversion rate to NO than NH3 does (NH3+O2→NO+⋯). This is completely in contradiction with the well-recognized conclusions in the publications. Thus, in this study, the oxidation rate of HCN is recommended to be increased by about 13 times according to related literature data. The modified NOx model was integrated into coal combustion model to simulate the NOx concentration distribution for three coals (two sub-bituminous coals and one lignite) in a down-fired autothermal test furnace. The input kinetic data of coal devolatilization and char combustion for coal combustion model were all obtained from the experiments in a drop tube furnace, which ensured the good agreements of gas temperatures and compositions between prediction and measurement in the test furnace. According to the simulated results, it was nearly impossible to accurately reproduce the NOx concentration profile in pc furnace using the original De Soete’s HCN oxidation rate, since the NOx concentrations in the high-temperature flame zone were greatly underestimated. Nevertheless, a satisfactory agreement for the NOx concentration distributions between prediction and measurement could be obtained using the increased HCN oxidation rate, if proper char surface area (S) values were chosen. Via using different S values, it was found that the S leading to the best simulation results for three coals were all about 17.5 times higher than those measured by Hg porosimetry (SHg), but they could not correlated well with that measured with low-temperature N2 adsorption (SBET). This indicated that SHg was a better surface basis for normalizing char reactivity with NO than SBET for different coals in the NOx simulation under the conditions of PC combustion.

Theoretical Investigations on the Kinetics of H-Abstraction Reactions from CF3CH(OH)CF3 by OH Radicals

The kinetic studies of the H-abstraction reaction of CF3CH(OH)CF3 with the OH radical, which is predicted to have two classes of possible reaction channels, were carried out. The minimum energy path and energetics were calculated at M062X/6-31+G (d,p) method. The rate coefficients for each reaction channels were evaluated by canonical variational transition state theory (CVT) with the small-curvature tunneling correction (SCT) and zero-curvature tunneling over the wide range of temperature of 200-3000 K. The temperature-dependent rate expression for the title reaction is obtained to be k(Total) = 2.60 × 10(-22)T(3.04) exp(372.45/T) cm(3) molecule(-1) s(-1); with k(298) = 3.54 × 10(-14) cm(3) molecule(-1) s(-1). The global warming potentials (GWPs) and atmospheric lifetimes of CF3CH(OH)CF3 are computed in the present investigation. The atmospheric implications and the degradation mechanism of CF3CH(OH)CF3 are discussed. It is concluded that this compound can be suggested as an acceptable substitute to HFCs in terms of its atmospheric lifetime and GWPs.

Sulfation of Condensed Potassium Chloride by SO2

The interaction between alkali chloride and sulfur oxides has important implications for deposition and corrosion in combustion of biomass. In the present study, the sulfation of particulate KCl (90–125 μm) by SO2 was studied in a fixed bed reactor in the temperature range 673–1023 K and with reactant concentrations of 500–3000 ppm SO2, 1–20% O2, and 4–15% H2O. The degree of sulfation was monitored by measuring the formation of HCl. Analysis of the solid residue confirmed that the reaction proceeds according to a shrinking core model and showed the formation of an eutectic at higher temperatures. On the basis of the experimental results, a rate expression for the sulfation reaction was derived. The model compared well with literature data for sulfation of KCl and NaCl, and the results indicate that it may be applied at even higher SO2 concentrations and temperatures than those of the present study. Simulations of sulfation of KCl particles with different size indicate that only for very small KCl particle...

Power-law type rate expression for WGS reaction over Au–Re/CeO2 catalyst under realistic fuel processor conditions

Abstract The kinetic behavior of 1Au–0.5Re/CeO 2 catalyst was investigated at 280–325 °C as a function of temperature and partial pressures of reactants and products of the forward WGS reaction under realistic feed conditions. Parameters estimated by non-linear regression analysis were found to predict the overall CO conversion rate within a 10% error margin.

From Detailed Description of Chemical Reacting Carbon Particles to Subgrid Models for CFD

This work is devoted to the development and validation of a sub-model for the partial oxidation of a spherical char particle moving in an air/steam atmosphere. The particle diameter is 2 mm. The coal particle is represented by moisture- and ash-free nonporous carbon while the coal rank is implemented using semi-global reaction rate expressions taken from the literature. The submodel includes six gaseous chemical species (O 2 , C O 2 , CO, H 2 O , H 2 , N 2 ). Three heterogeneous reactions are employed, along with two homogeneous semi-global reactions, namely carbon monoxide oxidation and the water-gas-shift reaction. The distinguishing feature of the subgrid model is that it takes into account the influence of homogeneous reactions on integral characteristics such as carbon combustion rates and particle temperature. The sub-model was validated by comparing its results with a comprehensive CFD-based model resolving the issues of bulk flow and boundary layer around the particle. In this model, the Navier-Stokes equations coupled with the energy and species conservation equations were used to solve the problem by means of the pseudo-steady state approach. At the surface of the particle, the balance of mass, energy and species concentration was applied including the effect of the Stefan flow and heat loss due to radiation at the surface of the particle. Good agreement was achieved between the sub-model and the CFD-based model. Additionally, the CFD-based model was verified against experimental data published in the literature (Makino et al. (2003) Combust. Flame 132, 743-753). Good agreement was achieved between numerically predicted and experimentally obtained data for input conditions corresponding to the kinetically controlled regime. The maximal discrepancy (10%) between the experiments and the numerical results was observed in the diffusion-controlled regime. Finally, we discuss the influence of the Reynolds number, the ambient O 2 mass fraction and the ambient temperature on the char particle behaviour.

Application of a non-asymptotic approach to prediction of the propagation of a flame through a fuel and/or oxidant droplet cloud

The mathematical analysis of laminar premixed spray propagation has generally been based on exploiting the inverse of the large chemical activation energy as an appropriate parameter for asymptotic analysis. In the current work we apply a modification of a recently suggested non-asymptotic approach for gaseous flames which makes use of a different approximation. In it, only the Arrhenius exponential term in the reaction rate expression is approximated using a step function chosen so that the two functions are in proximity in an integral sense. Application of this approach is more amenable and is shown to yield a simple formula for the burning velocity of a flame propagating through a cloud of fuel and/or oxidant droplets, for the fuel rich off-stoichiometric case in which the only reactant present in the chemical reaction term is the deficient oxidant which appears linearly. Results computed with the new analytical solutions are presented and a comparison is made with the predictions using the usual large activation energy approach. In addition, a double spray is considered for the first time in which both liquid oxidant and liquid fuel feature as sprays of droplets in the unburned pre-mixture. Such a situation arises in rocket engines in which two initially separate spray streams mix in a turbulent shear flow so that locally one dimensionally propagating double spray premixed flames are created. The analysis leads to an analytical expression for the laminar burning velocity dependent on the spray- and gas-related parameters. Typical thermal and velocity maps in parametric space are presented.

Hydrodeoxygenation of 4-Propylguaiacol (2-Methoxy-4-propylphenol) in a Microreactor: Performance and Kinetic Studies

Catalytic hydrodeoxygenation of 4-propylguaiacol, a model compound for lignin-derived components of pyrolysis oil, was performed in a packed-bed microreactor. The effects of various processing conditions were investigated using presulfided NiMo/Al2O3 catalyst. The conversion of 4-propylguaiacol is highly influenced by temperature. Although many products were formed, 4-propylphenol predominated under the operating conditions selected with presulfided NiMo catalyst. External and internal mass-transfer resistances and heat-transfer resistance were investigated and found to be negligible. Reaction rate expressions were based on proposed reaction mechanisms using the Langmuir–Hinshelwood approach. Nonlinear regression was performed to obtain kinetic constants. The best-fitting rate equations were further validated by comparing experimental data obtained from an integral reactor with predictions obtained using the Runge–Kutta method based on the rate equations. A difference of less than 10% between the experimental data and the predicted data for the integral reactor was found.

Kinetic study for the direct synthesis of dimethyl carbonate from methanol and CO2 over CeO2 at high pressure conditions

The kinetics for the direct synthesis of dimethyl carbonate was studied over CeO2 at high pressure conditions in a batch reactor. Langmuir–Hinshelwood and Eley–Rideal mechanisms were proposed and compared by the performance of the respective reaction rate expression in fitting to the experimental kinetic data. The reactions were held at different temperatures (378–408K), CO2/methanol molar ratios (1.1–4.0) and pressures (15–20MPa) in order to adjust the kinetic parameters. An activation energy of 106kJmol−1, as well as the standard enthalpy and Gibbs energy of reaction (−20.10 and 31.50kJmol−1) were calculated from experiments. Furthermore, the changes in pressure revealed an effect on the kinetic constant, with an activation volume equal to −0.208cm3mol−1.

New insight into the ZnO sulfidation reaction: mechanism and kinetics modeling of the ZnS outward growth

Zinc oxide based materials are commonly used for the final desulfurization of synthesis gas in Fischer-Tropsch based XTL processes. Although the ZnO sulfidation reaction has been widely studied, little is known about the transformation at the crystal scale, its detailed mechanism and kinetics. A model ZnO material with well-determined characteristics (particle size and shape) has been synthesized to perform this study. Characterizations of sulfided samples (using XRD, TEM and electron diffraction) have shown the formation of oriented polycrystalline ZnS nanoparticles with a predominant hexagonal form (wurtzite phase). TEM observations also have evidenced an outward development of the ZnS phase, showing zinc and oxygen diffusion from the ZnO-ZnS internal interface to the surface of the ZnS particle. The kinetics of ZnO sulfidation by H(2)S has been investigated using isothermal and isobaric thermogravimetry. Kinetic tests have been performed that show that nucleation of ZnS is instantaneous compared to the growth process. A reaction mechanism composed of eight elementary steps has been proposed to account for these results, and various possible rate laws have been determined upon approximation of the rate-determining step. Thermogravimetry experiments performed in a wide range of H(2)S and H(2)O partial pressures have shown that the ZnO sulfidation reaction rate has a nonlinear variation with H(2)S partial pressure at the same time no significant influence of water vapor on reaction kinetics has been observed. From these observations, a mixed kinetics of external interface reaction with water desorption and oxygen diffusion has been determined to control the reaction kinetics and the proposed mechanism has been validated. However, the formation of voids at the ZnO-ZnS internal interface, characterized by TEM and electron tomography, strongly slows down the reaction rate. Therefore, the impact of the decreasing ZnO-ZnS internal interface on reaction kinetics has been taken into account in the reaction rate expression. In this way the void formation at the interface has been modeled considering a random nucleation followed by an isotropic growth of cavities. Very good agreement has been observed between both experimental and calculated rates after taking into account the decrease in the ZnO-ZnS internal interface.

Development of Rate Expression for Glycerol Hydrogenation Reaction

This paper highlights various routes for glycerol reaction and also pathway for heterogeneous catalyst and also being obtained as by product of biodiesel making it cost effective and easy availability. Whereby it also aims at development of rate model and compares values of calculated and experimentally obtained rate constant. It also aims at hydrogenation carried out at liquid phase and gas phase and also various types of catalyst, support and promoter that can be used in hydrogenation of glycerol, and also advantage of various by-products and intermediate formed by glycerol hydrogenation reaction. It also aims at various intermediate formed by acid/solid base catalyst.

Planned Experimental Studies into the Nucleation and Precipitation Kinetics of Sulfate-bearing Minerals under Conditions Relevant to CO2 Geological Storage

Carbon Capture and Storage (CCS) has been widely recognized as one of the main technologies to mitigate climate change. Deep-saline aquifers are among the preferred potential repositories for CO2 currently being emitted to the atmosphere from burning of fossil fuels. Large-scale injection of supercritical CO2 into subsurface reservoirs induces a complex interplay of multiphase flow, capillary trapping, dissolution and chemical reactions that may have significant impacts on both, short-term injection performance and long-term fate of CO2 storage. To ensure the viability of geological CO2 storage, a holistic understanding of reactions at supercritical CO2-water-rock interfaces and the environmental factors affecting these interactions is required.The major objectives of this contribution are to study the kinetics of CO2 brine-rock interactions and derive respective chemical reaction rate expressions under the typical conditions of CO2 storage sites. These rate laws may be used in modeling the storage sites and operating them in a way that will minimize scaling and thus potential reduction of injectivity.A new experimental system was set up at the Water-Rock interaction laboratory, Ben-Gurion University of the Negev that allows studying the interaction between CO2, brine, and minerals under CO2 supercritical conditions. All equipment is fully capable to deal with adjustable PTX conditions enabling continuous and computerized data acquisition of various variables including pressure, temperature, stirring speed, in-situ measurement of pH and redox potential. The experimental setup allows the measurement of dissolution and precipitation rates of diverse minerals under a wide range of environmental conditions as found in CO2 storage sites offering the possibility to collect liquid and solid samples for further chemical and morphological analyses.

Supercritical Water Oxidation Kinetics of Textiles Dyeing Wastewater

Oxidation of the textiles dyeing wastewater was studied in a continuous-flow reactor that was operated between 400 and 650°C at a fixed pressure of 25 MPa. The total organic carbon (TOC) concentration of the raw wastewater was in the 112.52 mmol/L . Hydrogen peroxide (H2O2) was used as an oxygen source. According to the wastewater and oxidant concentrations, the global rate expression was regressed from the complete set of data under various conditions of the reaction. The reaction rate expression for the oxidation of the textiles dyeing wastewater was determined with the activation energy of 39.908 (±1.99) kJ/mol and the pre-exponential factor of 114 (±7.5) /s; and the reaction orders for the TOC and the oxidant were 0.896±0.01 and 0.061±0.01 at a 95% confidence level.

Modeling of the Regeneration Processes in Diesel Particulate Filters

New simulation algorithm of soot oxidation in diesel particulate filter (DPF) is proposed. Two-dimensional finite differences scheme is used for calculation of the heat transfer in DPF (macro-scale). One dimensional model for treatment of the soot oxidation process in a separate filter channel (micro-scale) is based on a new expression for the oxidation reaction rate that is a modification of the known Bissett's equation. This expression allows consideration of the non-linear dependence of oxidation reaction rate on a reagent concentration. For cases of catalytic coating a modification of the known two-layer model is suggested. A fraction of soot that has been oxidized with the help of the catalyst is not invariable in the first layer, but it exponentially depends on the distance from a channel wall of the particle trap. Soot oxidation by O2 and/or NO2 in diesel particulate filters is investigated for various cases of non-catalytic and catalytic oxidation. The filter clogging propagation from its periphery to the center at critical temperature is described theoretically at first. A comparison between various types of DPF regeneration methods is performed by using the proposed simple simulation algorithm and appropriate computer code.

Influence of inert gas sparging on fatty acid lactylate esterification kinetics

I have proposed a novel reaction mechanism for the formation of acyl lactylate esters of fatty acids, and have determined the absolute esterification and reverse rate constants at several reaction temperatures, as well as having derived with rigor from basic physical chemistry precepts the gas-sparge dependent overall reaction rate expressions and rate constants of lactylate formation. Examples are given of acid values calculated from the derived rate expressions, compared to experimental values obtained as a function of time, during laboratory ester preparations. These fatty acid acyl lactylate esters and their salts have important commercial applications in both the food and non-food industries as emulsifiers, and their manufacture and sale is highly competitive. Therefore, an understanding of the cost versus benefit curve of sparge gas rates provided by this paper is highly desirable.

Numerical study of the influence of heterogeneous kinetics on the carbon consumption by oxidation of a single coal particle

This work is devoted to the numerical study of the influence of heterogeneous kinetics on the oxidation rates of a single carbon particle in quiescent and non-quiescent environments. The coal particle is represented by moisture- and ash-free nonporous carbon while the coal rank is implemented using several kinetic rate expressions. The model includes six gaseous chemical species (O2, CO2, CO, H2O, H2, N2). Three heterogeneous reactions are employed (C+O2, C+CO2 and C+H2O), along with two homogeneous semi-global reactions, namely carbon monoxide oxidation and the water–gas shift reaction. Several semi-global reaction rate expressions taken from the literature are utilized. The Navier–Stokes equations coupled with the energy and species conservation equations are used to solve the problem by means of the pseudo-steady state approach. At the surface of the particle, the balance of mass, energy and species concentration is applied including the effect of the Stefan flow and heat loss due to radiation at the surface of the particle. The model and the code used are validated against an analytic two-film model. Good agreement is observed. The numerical simulations performed reveal that the origin of heterogeneous kinetics has a significant effect on the carbon consumption rates of the particle. In particular, the maximal discrepancy between results is achieved in a kinetically controlled regime and is proportional by a factor of 10 in respect to carbon mass flux on the particle surface. Additionally, the influence of the particle Reynolds number referring to the laminar flow regime, the ambient O2 mass fraction and the temperature on the regimes of combustion and gasification is discussed.

Gas-dynamic equations for spatially inhomogeneous gas mixtures with internal degrees of freedom. II. General representation for one-temperature reaction rates

In our previous paper (Kolesnichenko and Gorbachev, 2010) [1] the general approach for solving kinetic equations for gas mixtures with internal degrees of freedom and for getting corresponding gas-dynamic equations was developed. In the present article we continue our studies and focus on formulating expressions for reaction rates arising in zero-order (Euler) gas-dynamic equations for a one-temperature case. Derived expressions take into account all non-equilibrium effects, that we understand as deviation of the distribution function from its quasi-equilibrium value. As was shown in Kolesnichenko and Gorbachev (2010, 2011) [1,2], for zero-order approximation these effects can be subdivided into two groups. The first group contain the effects caused by the perturbation of quasi-equilibrium distribution function by the physical–chemical processes. We call them “scalar” non-equilibrium effects. Only these effects remain in the spatially homogeneous case. The second group consists of the terms proportional to the velocity divergence and therefor is indicated as spatially inhomogeneous. Both the above-mentioned effects are described via additive corrections to the quasi-equilibrium distribution function. Thus they can be treated separately and give rise to the corresponding terms in the expressions for reaction rates. Those non-equilibrium reaction rates are functions of concentrations of all species presented in the mixture and of the whole set of equilibrium rate constants. This leads to the necessity of developing new approaches to obtaining the reaction rates from experimental data. Traditionally defined an equilibrium constant, that is the function only of the thermodynamic state of the system, can be introduced only in a spatially homogeneous case. It can partially simplify the problem of getting information on reaction rates. In general no such value can be introduced. Final expressions show strong correlations between parallel reactions. One such reaction can affect another one until it vanishes. This can be caused not only by the “scalar” non-equilibrium effects, as it was shown in Kolesnichenko and Gorbachev (2011) [2], but also by spatially inhomogeneous. This means that the derived non-equilibrium terms are not small corrections, but can dramatically change chemical kinetics of the reacting mixture.