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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  

Slow pyrolysis of walnut shell which is a cheap and abundantly available solid waste was carried out using thermogravimetric analysis. The effects of raw material heating rate on the pyrolysis properties and kinetic parameters were investigated. A two-step consecutive reaction model were used to simulate the pyrolysis process. The kinetic parameters were established by using the pattern search method. Comparison between experimental data and the model prediction indicated that the two-step consecutive reaction model can better describe the slow pyrolysis of walnut shell as the formation of an intermediate during the pyrolysis process was taken into account.

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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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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=A 0 T m). 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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Abstract  

INAA was used to determine 32 major and trace elements in 21 soil samples collected from the Loess Plateau, China, and Ontario, Canada. The elemental concentrations determined in different layers of each soil, have been used for comparison in order to find out the general characteristics and any significant differences between Canadian and Chinese soils which developed from similar parent materials. This data can be useful to pedologists and geochemists to study the elemental behaviours and the influences of climate and environment on soil formation. Effort is directed to applying a statistical factor pattern recognition method to these soils for possible use in future soil erosion and transport studies in China. From this study, four soil factors were resolved each for the Chinese and Canadian soils.

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Abstract  

The radiochemical method has been used for investigation of the adsorption of radium on eighteen inorganic ion exchangers. The distribution coefficient of radium obtained are as follows: barite 2955, celestite 2420, BaSO4 4350, BaCrO4 5245, Ba3(PO4)2 5775, MnO2·nH2O 1681, La2O3·nH2O 4150, Zerolit S/F 2920, etc.

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Abstract  

The kinetics of direct reduction of artificial chrome iron ore was studied by isothermal and non-isothermal methods. In the initial, middle and final periods, the reaction is controlled by nucleation and growth, a phase boundary reaction, and diffusion, respectively. In the main reaction region, the kinetic equation is 1–(1–)1/3=kt and the apparent activation energy is 270 kJ mol–1. The kinetic mechanisms found with the isothermal and non-isothermal methods do not differ, and the activation energy values are approximately the same. However, the non-isothermal method can demonstrate the kinetic process completely.

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