Development of a Surface Area Dependent Rate Expression for Soot Oxidation in Diesel Particulate Filters

We collected soot from diesel engine exhaust on miniature particulate filter samples and evaluated soot oxidation rates on an automated flow reactor system. A series of isothermal pulsed oxidation experiments quantified reaction rates as a function of gas composition, temperature, flow rate, and soot consumption. An O₂ chemisorption method measured the soot active surface area as filter regeneration progressed. We developed a rate law with an explicit dependence on carbon surface area and estimated the associated kinetic parameters from the pulsed oxidation data. The resulting rate expression successfully captures the soot oxidation behavior over a wide range of operating conditions.     

Differential thermal analysis of reaction kinetics in pseudo-isothermal state Part 1. Simple reaction

A new method for the evaluation of kinetic parameters is proposed, in which differential thermal analysis (DTA) is carried out under psuedo-isothermal conditions, that is, both sample and reference materials are not heated and the temperatures remain as isothermal as possible. The hydrolysis of acetic anhydride was used as a model of simple reaction for the DTA experiment. The kinetic parameters such as the rate constant, the heat of reaction and the activation energy, evaluated from the proposed method were in good agreement with those obtained from conventional titration measurements. Systematic errors in the rate constant evaluation are discussed in order to enable the kinetic parameters to be evaluated accurately.     

Esterification of ethanol with sulfuric acid: A kinetic study

Experiments were conducted in a stirred batch reactor under isothermal conditions for obtaining kinetics of the esterification reaction between ethanol and sulfuric acid. Reactive adsorption technique was employed to enhance the conversion. Anhydrous sodium sulfate was used as an adsorbing agent to remove the water formed during the reaction. The variables include the mole ratio of ethanol to sulfuric acid, reaction temperature, purity of the reactants, and the amount of adsorbing agent. The reaction was found to be reversible and second order at low mole ratios, and irreversible and first order at high mole ratios. The kinetic parameters of the rate law were estimated. A possible reaction mechanism was proposed and validated with the experimental data. The effect of the mole ratio of reactants, anhydrous sodium sulfate loading, and purity of the reactants on the yield of ethyl hydrogen sulfate was studied, using full‐factorial search and optimized conditions were obtained by the method of steepest ascent. More precise optimum conditions were obtained using the Box‐Wilson composite method.     

Kinetics of calcium carbonate decomposition

Experiments on thermal decomposition of calcium carbonate were carried out in a thermogravimetric analyser under non-isothermal conditions of different heating rates (10 to 100°C/ min). A new technique for determining the kinetic parameters from non- isothermal thermogravimetric data was described. The activation energy and frequency factors were determined from the proposed method and also by the widely used Coats and Redfern method. The kinetic compensation effect between the activation energy and frequency factors obtained from both the methods were found to be very consistent and are in very good agreement with the literature values. The activation energy and frequency factors were also determined from isothermal experiments in the temperature range from 680 to 875°C. The activation energy and frequency factors determined from isothermal data using initial rate method were also found to be in very good agreement with the above results. It is also found that the kinetic parameters determined by isothermal analysis were consistent with the values determined by non-isothermal analysis.     

Cure kinetics and modeling the reaction of silicone rubber

The kinetics of the crosslinking reaction of polydimethylsiloxane (PDMS) was studied by differential scanning calorimeter (DSC). The kinetic parameters of the reaction were calculated from the Kissinger, the Ozawa, the Flynn–Wall–Ozawa, and the Friedman methods. The Chang method was also used to determine reaction order and to compare with other methods. To improve the accuracy, the autocatalytic model and the modified-Chang method were introduced. The theoretical heat generation against temperature curves, calculated by the estimated kinetic parameters, well fit the experimental data, which indicated that the analysis method used in this work was valid. The processing time and temperature was predicted by the direct integration of the kinetic equation with the data from isothermal runs. It would give a valuable guide for the thermal processing of silicone rubber.     

Kinetic studies of alkyl formate hydrolysis using formic acid as a catalyst

BACKGROUND: The hydrolysis of methyl formate is the major industrial process for the production of formic acid. The aim of the work is to determine the reaction kinetics quantitatively in the presence of formic acid catalyst, develop a mathematical model for the reaction system and estimate the kinetic parameters for the purpose of optimization. RESULTS: Liquid phase hydrolysis kinetics of alkyl formates (ethyl and methyl formate) was studied in an isothermal batch reactor at 80–110 °C and 20 bar nitrogen pressure. The catalyst of choice was formic acid. The reaction rate was enhanced but the formic acid product yield was slightly suppressed relative to the uncatalysed system. A kinetic model comprising mass balances and rate equations was developed and the kinetic and equilibrium parameters included in the rate equations were estimated from the experimental data with non‐linear regression analysis. CONCLUSION: The model was able to predict the experimental results successfully. The results obtained were compared quantitatively with an earlier model involving alkyl formate hydrolysis in a neutral aqueous solution. Copyright © 2011 Society of Chemical Industry     

Optimization of cure kinetics parameter estimation for structural reaction injection molding/resin transfer molding

A numerical method is proposed for polymer kinetic parameter estimation of either Structural Reaction Injection Molding (SRIM) or Resin Transfer Molding (RTM). The method simulates either radial flow or axial flow of reactive resins through a fiber preform inside a mold cavity. This method considers a non‐isothermal environment with different inlet boundary conditions. Based on the molding conditions, this method can find the best values of chemical kinetic parameters by comparing the simulated temperature history and the experimental temperature history. Since the kinetic parameters are estimated with the real molding conditions, the simulations using these parameter values can have better agreement with molding data than those parameters which are obtained from idealized conditions such as Differential Scanning Calorimeter (DSC). The optimization approach was verified by estimating kinetics parameters for RTM data available in the literature. Temperatures predicted by the optimized kinetics parameters are compared with experimental data for two different molding conditions: injection of a thermally activated resin into a radial mold under constant pressure flow, and injection of a mix activated resin into a radial mold under constant volume. In both cases, the optimized kinetics parameters fit the temperature data well.     

Cure kinetics of epoxy resin used for advanced composites

The cure kinetics of an epoxy resin used for the preparation of advanced polymeric composite structures was studied by isothermal differential scanning calorimetry (DSC). A series of isothermal DSC runs provided information about the kinetics of cure over a wide temperature range. According to the heat evolution behavior during the curing process, several influencing factors of isothermal curing reactions were evaluated. The results showed that the isothermal kinetic reaction of this epoxy resin followed an autocatalytic kinetic mechanism. In the latter reaction stage, the curing reaction became controlled mainly by diffusion. Cure rate was then modeled using a modified Kamal autocatalytic model that accounts for the shift from a chemically controlled reaction to a diffusion‐controlled reaction. The model parameters were determined by a nonlinear multiple regression method. Copyright © 2004 Society of Chemical Industry     

Comparative DSC kinetics of the reaction of DGEBA with aromatic diamines. II. Isothermal kinetic study of the reaction of DGEBA with m-phenylene diamine

In the first part of the present series the non-isothermal kinetics of the reaction of an epoxy resin based on diglycidyl ether of bis-phenol A (DGEBA) with m-phenylene diamine (mPDA) was studied. A four step kinetic analysis was applied using differential scanning calorimetry (DSC) data. It allowed us to confirm the validity of the three molecular autocatalytic model of this reaction, as well as to obtain reliable kinetic data in programmed temperature mode.The isothermal study of the DGEBA-mPDA reaction was performed applying a similar kinetic approach: (i) analysis at the peak maximum of the DSC curves; (ii) apparent activation energy analysis of the isothermal DSC data; (iii) integral and differential curve fitting methods; and (iv) modeling of the reaction and comparison of the model with the experiment.It was established that the overall kinetic parameters measured under programmed temperature conditions sufficiently well described the isothermal shift of the DSC curves along the logarithmic time scale, especially the initial stage of the reaction. A more precise analysis of the data showed that the isothermal DSC kinetics obeyed a formal model whose power exponent was approximately 2.5, or it was not well represented by the mechanistic-like three molecular autocatalytic velocity equation. Nevertheless, the activation energy of the autocatalytic rate constant determined at constant temperature mode, i.e. was found out in close agreement with the one obtained previously in programmed temperature mode, On the contrary, the ratio of the impurity catalytic to autocatalytic rate constant was slightly temperature dependent.     

Reaction kinetics of phenol synthesis through one-step oxidation of benzene with N<Subscript>2</Subscript>O over Fe-ZSM-5 zeolite

Based on the information from GC-MS on-line measurement and thermodynamic analysis, the reaction network of gas-phase hydroxylation of benzene with nitrous oxide over Fe-ZSM-5 zeolite was systematically investigated. The main reactions and side reactions were identified, and a kinetic reaction network was proposed as follows: benzene+N₂O→phenol→CO/CO₂. According to the mechanism, the experimental results were interpreted reasonably. The hydroxylation kinetic experiments were carried out in an isothermal integral microreactor under the conditions of n(benzene)/n(N₂O)=8–12, T=663–763 K and atmospheric pressure. Based on the reaction network proposed, the parameters in the rate model of power-law were estimated by means of Gauss-Newton optimal method with the Levenberg-Marquardt modifications, and the results were in good agreement with the experimental data.     

Dehydrogenation kinetic model of heavy paraffins

Based on the dehydrogenation mechanism of heavy paraffins under industrial conditions, the intrinsic reaction kinetic model and catalyst deactivation model were established considering the influence of side reactions with different carbon‐number heavy paraffins. Based on the experimental data of dehydrogenation reactions with different carbon‐number paraffins in an axial continuous‐flow isothermal fixed‐bed microreactor, Powell optimization method was used to estimate the model parameters. The results show that there is a liner relationship between the activation energies and pre‐exponential factors of homologous reactions and carbon number of paraffins. A correlation model about the deactivation rate constants under different conditions was established. The validation of kinetic model showed that the model could be used to predict detailed product distribution with different feedstocks under different reaction conditions. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Kinetic studies of wheat straw hydrolysis using sulphuric acid

The kinetics of cellulose and hemicellulose hydrolysis of wheat straw was studied using both isothermal and non-isothermal techniques in a batch reactor. Reactions were carried out between 100 and 210°C and product sugars were analyzed using a Bio-Rad HPX-87P liquid chromatographic column. A simple first order series reaction model was used for both cellulose and hemicellulose hydrolysis reactions and kinetic parameters were obtained for the Arrhenius rate equations for three different sulphuric acid concentrations (0.5, 1.O and 1.5%). Activation energies remained constant with acid concentration but the pre-exponential factors showed an increase with acid concentration. To minimize the amount of experimental data required and to achieve a unique solution to the kinetic parameters, the technique of combining isothermal and non-isothermal reaction data was studied.     

绝热加速量热无模型方法动力学预测

绝热加速量热主要采用基于单一实验数据的模型拟合方法进行动力学预测,难以应用于未知机理反应和复杂反应。为此,通过数值模拟方法在绝热条件下产生n级反应与Kamal自催化反应数据,采用Vyazovkin和Friedman等转化率方法进行动力学求解;然后在不同起始温度和等温条件下,采用无模型动力学参数进行绝热和等温动力学预测,并与模拟数据对比。结果表明,绝热加速量热采用Vyazovkin方法预测最大相对误差为39.9%,Friedman方法预测最大误差超100%,前者更适合进行预测;建议在预测温度±40℃范围内进行实验测量。这为未知化学物质和复杂反应热失控风险评估及化工事故模拟等提供了有效手段。     

Kinetic parameters estimation for unsaturated polyester‐styrene systems

A model modified from the traditional kinetic model is proposed for the determination of the kinetic parameters describing the autocatalytic reaction of polyesterstyrene systems. The proposed method utilizes three experimental data values from the $ \frac{{d\alpha }}{{dt}} $ vs. α curve—the initial value, the peak value, and the maximum value—to solve the kinetic parameters. The curing reaction of a thermosetting polyester was investigated by using the isothermal and dynamic techniques of differential scanning calorimetry (DSC). The results show that the reaction orders m, n and the ultimate conversion are not constant, and instead are functions of temperature. The estimated kinetic curves agree well with the experimental DSC data.     

Thermal decomposition kinetics of sodium perborate tetrahydrate to sodium metaborate by using model-fitting and model-free methods

Model-free and model-fitting methods have been applied to data for nonisothermal and isothermal decomposition of sodium perborate tetrahydrate to sodium metaborate. The kinetic triplet (f(a), A and E) of sodium perborate tetrahydrate was found by model fitting method defined with a single step reaction, which has an excellent fit for nonisothermal data and obeys different kinetic models and yields highly uncertain values of Arrhenius parameters. The isothermal and nonisothermal data for thermal decomposition of sodium perborate tetrahydrate to sodium perborate monohydrate and sodium metaborate were evaluated by model-free isoconversional method. The complex nature of multi-step process of sodium perborate tetrahydrate to sodium metaborate was more easily indicated by using wide temperature range in nonisothermal isoconversional method.     

Estimation of kinetic parameters associated with the curing of thermoset resins. Part I: Theoretical investigation

This is a two-part theoretical and experimental study on the estimation of kinetic parameters associated with the curing of a thermoset epoxy resin. In Part I, the estimation procedure is presented. This estimation procedure is based on a method referred to as the Box-Kanemasu method, which involves the minimization of a least squares function, and it represents a new application of this method. The kinetic parameters under consideration were the Arrhenius constants associated with two rate constants in a kinetic model used to describe the curing rate of an amine epoxy resin. The use of differential scanning calorimetry (DSC) and dielectric data assuming isothermal and dynamic experimental conditions was first investigated in a sensitivity study. It was determined that the degree of cure should be treated as the dependent variable and that data from isothermal experiments should be used. The estimation procedure was then used to estimate the Arrhenius constants from simulated degree of cure data with added errors. These results compared favorably with those found using a linear regression method.     

硝酸胍型产气药热分解动力学研究

采用TG-DSC技术研究了受热条件下硝酸胍型产气药的热稳定性、分解动力学和贮存期,并利用Kissinger法、Ozawa法计算了硝酸胍型产气药的热分解表观活化能(Ea)、指前因子(A)和速率常数(k),结果表明Kissinger法与Ozawar法所得动力学参数较为相近。采用恒温法预估了其使用寿命。     

Mass transport effects during measurements of gas-solid reaction kinetics in a fluidised bed

Design, modelling and scaling of many gas-solid reaction processes in a fluidised bed (FB) require reliable intrinsic kinetic data obtained under conditions similar to those in industrial-scale units. The determination of such data in a laboratory-scale FB seems to be the best route. Despite this, owing to practical difficulties, few experimental reactivity data are available from FB. One of the drawbacks of FB reactors is the plausible interference of physical processes on kinetic measurements. In this work a simple methodology is developed for the assessment of fluid-dynamic and mass transport effects during kinetic experiments in FB (FBKE). A modelling approach is proposed, which combines a kinetic particle model with a simple two-phase flow model. The parameters resulting from the model are expressed in terms of three observable quantities, making it possible to evaluate the transport effects in a straightforward way from gas concentration measurements. Charts for direct evaluation of transport effects in FBKE are included. The analysis presented aims at facilitating the selection of optimum operating conditions for FB tests to determine gas-solid kinetics. Moreover, it may support dimensioning of new rigs designed for this purpose. This study primarily aims at the assessment of transport effects in batch-operated laboratory FBKE, where isothermal conditions are assumed and only one reaction occurs: the reaction between CO₂ and char is taken as an example. The methodology developed can be applied to other isothermal systems to estimate the influence of diffusional effects on the observed reaction rate, i.e., char oxidation and other catalytic or non-catalytic systems.     

Cure kinetics of neat and carbon-fiber-reinforced TGDDM/DDS epoxy systems

The cure kinetics of neat and carbon fiber-reinforced commercial epoxy systems, based on Tetraglycidyl-4,4′-diaminodiphenylmethane (TGDDM) and 4,4′-diaminodiphenylsulfone (DDS) were studied by means of differential scanning calorimetry (DSC). Analysis of DSC data indicated that the presence of the carbon fibers has a very small effect on the kinetics of cure. A kinetic model, arising from an autocatalyzed reaction mechanism, was applied to isothermal DSC data. The effect of diffusion control was incorporated into the reaction kinetics by modifying the overall rate constant, which is assumed to be a combination of the chemical rate constant and the diffusion rate constant. The chemical rate constant has the usual Arrhenius form, while the diffusion rate constant is described by a type of the Williams-Landel-Ferry (WLF) equation. The kinetic model, with parameters determined from isothermal DSC data, was successfully applied to dynamic DSC data over a broad temperature range that covers usual processing conditions. © 1996 John Wiley & Sons, Inc.     

The characterization of thermoset cure behavior by differential scanning calorimetry. Part I: Isothermal and Dynamic Study

A study of the isothermal cure kinetics of an unsaturated polyester resin by differential scanning calorimetry is described. An autocatalyzed second order kinetic model is adopted to elucidate the cure reaction and also assess the kinetic parameters. The rate constant, the maximum cure rate, the extent of cure, and the degree of conversion at the maximum cure rate, all increase with increasing cure temperature, while the half-life and the time required to reach the maximum cure rate both decrease. Discrepancies between the experimental results and the predicted values of some of the kinetic parameters, especially at high degrees of conversion, are attributed to the highly different-controlled cure reaction following the gel point. The activation energy (E) and the pre-exponential factor (1n A) of the polyester cure reaction were estimated, using differential graphical techniques, to be 131 ± 4 kJ/mol and 39 ± 1 respectively. An ASTM method (E698) produces erroneously low values of the Arrhenius parameters, suggesting that the assumptions of the method may be overly simplified.