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Abstract  

This paper describes the influences of some parameters relevant to biomass pyrolysis on the numerical solutions of the nonisothermal n th-order distributed activation energy model (DAEM) involved the Weibull distribution. Investigated parameters are the integral upper limit, the frequency factor, heating rate, the reaction order and the shape, scale and location parameters of the Weibull distribution. Those influences can be used for the determination of the kinetic parameters of the nonisothermal n th-order Weibull DAEM from thermoanalytical data of biomass pyrolysis.

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Abstract  

The dependence of the frequency factor on the temperature (A=A 0 T m) has been examined and the errors involved in the activation energy calculated from some integral methods without considering such dependence have been estimated. Investigated integral methods are the Coats-Redfern method, the Gorbachev-Lee-Beck method, the Wanjun-Yuwen method and the Junmeng-Fusheng method. The results have shown that the error in the determination of the activation energy calculated ignoring the dependence of the frequency factor on the temperature can be rather large and it is dependent on x=E/RT and the exponent m.

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Abstract  

The pyrolysis of wheat straw has been carried out by means of thermogravimetric analysis in inert atmosphere. The samples were heated over a range of temperatures that includes the entire range of pyrolysis with three different heating rates of 5, 10 and 20 K min−1. The activation energy values as a function of the extent of conversion for the pyrolysis process of wheat straw have been calculated by means of the Flynn–Wall–Ozawa isoconversional method, the Vyazovkin–Sbirrazzuoli isoconversional method and an iterative isoconversional method presented in this article. The results have showed that there are small differences between the activation energy values obtained from the three methods, and the pyrolysis process reveals a dependence of the activation energy on conversion and have indicated the validity of the iterative integral isoconversional method. The effective activation energy for the pyrolysis of wheat straw is 130–175 kJ mol−1 in the conversion range of 0.15–0.85. Furthermore, the prediction of the pyrolysis process under isothermal conditions from the dependence of the activation energy on the extent of conversion has been presented.

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Non-isothermal kinetics in solids

The precision of some integral methods for the determination of the activation energy without neglecting the temperature integral at the starting temperature

Journal of Thermal Analysis and Calorimetry
Authors: J. Cai and R. Liu

Abstract  

The integral methods, which are obtained from the various approximations for the temperature integral, have been extensively used in the non-isothermal kinetic analysis. In order to obtain the precision of the integral methods for the determination of the activation energy, several authors have calculated the relative errors of the activation energy obtained from the integral methods. However, in their calculations, the temperature integral at the starting temperature was neglected. In this work, we have performed a systematic analysis of the precision of the activation energy calculated by the integral methods without doing any simplifications. The results have shown that the relative error involved in the activation energy determined from the integral methods depends on two dimensionless quantities: the normalized temperature θ=T/T 0, and the dimensionless activation energy x 0=E/RT 0 (where E is the activation energy, T is the temperature, T 0 is the starting temperature, R is the gas constant).

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Abstract  

Recently, Órfão obtained two simple equations for the estimation of the relative error in the activation energy calculated by the integral methods [2]. In this short communication, the validity of the equations has been evaluated by comparing the results calculated by the equations with the results calculated by the equation from theoretical derivation without introducing any assumption.

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Abstract  

In this paper, a systematic analysis of the errors involved in the determination of the kinetic parameters (including the activation energy and frequency factor) from five integral methods has been carried out. The integral methods analyzed here are Coats-Redfern, Gorbachev, Wanjun-Yuwen-Hen-Zhiyong-Cunxin, Junmeng-Fusheng-Weiming-Fang, Junmeng-Fang and Junmeng-Fang-Weiming-Fusheng method. The results have shown that the precision of the kinetic parameters calculated by the different integral methods is dependent on u (E/RT), that is, on the activation energy and the average temperature of the process.

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Abstract  

A new approximation has been proposed for calculation of the general temperature integral
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int\limits_0^T {T^m } e^{ - E/RT} dT$$ \end{document}
, which frequently occurs in the nonisothermal kinetic analysis with the dependence of the frequency factor on the temperature (A=A0Tm). It is in the following form:
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int\limits_0^T {T^m } e^{ - E/RT} dT = \frac{{RT^{m + 2} }} {E}e^{ - E/RT} \frac{{0.99954E + (0.044967m + 0.58058)RT}} {{E + (0.94057m + 2.5400)RT}}$$ \end{document}
The accuracy of the newly proposed approximation is tested by numerical analyses. Compared with other existed approximations for the general temperature integral, the new approximation is significantly more accurate than other approximations.
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Summary

Silica-gel column chromatography and preparative reversed-phase high-performance liquid chromatography (RP-HPLC) were sequentially employed for the isolation of two antioxidants including gallic acid and methyl gallate from Folium Toonea Sinensis. An RP-HPLC-UV method was then developed and validated to rapidly determine their content in this herb with ethyl gallate as internal standard. The quantitation was performed on an XBridge Shield RP18 column (150 mm × 4.6 mm, 5 μm) under 40°C. The mobile phase consisting of acetonitrile and 0.1% formic acid aqueous solution was driven at 1.0 mL min−1 under gradient elution, and 270 nm was selected to monitor the separation. To evaluate the fitness for purpose of the method and to investigate the difference in the content of analytes among different samples, the leaves collected from five production sites were analyzed. The newly established method is suitable for routine analysis of gallic acid and methyl gallate in the herb and, hence, can assist in its quality assessment. It was also found that not only the content of two antioxidants but also the ratio varied significantly among different geographical origins. In addition, three samples from Yantai, Zumadian, and Zhenjiang were distinguished as they have a much higher content ratio than the other two.

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