Parametric study of the nonisothermal n th-order distributed activation energy model involved the Weibull distribution for biomass pyrolysis

Cai, Junmeng; Liu, R. H.

doi:10.1007/s10973-006-8266-y

Cited by 23 publications

(16 citation statements)

References 20 publications

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“…On the other hand, the results obtained by the symmetrical distribution functions (Cai et al, 2006;Dhaundiyal and Singh, 2016 a;Dhaundiyal and Singh, 2017;Dhaundiyal and Tewari, 2017) for the upper limit of activation energies E ∞ (kJ·mol -1 ) are very close to the range of activation energies derived for the asymmetrical function, Rayleigh distribution. In case of another asymmetric function, Weibull distribution, the obtained value of activation energies differ from Rayleigh distribution through appreciable margin (Cai and Liu, 2007;Dhaundiyal and Singh, 2016 b). So, it is not necessary that the outcome of two asymmetrical functions may exhibit the same behaviour with the skewness of thermoanalytical data.…”

Section: Application Of Biomassmentioning

confidence: 93%

Approximations to the Non-Isothermal Distributed Activation Energy Model for Biomass Pyrolysis Using the Rayleigh Distribution

Dhaundiyal

Singh

2017

Acta Technologica Agriculturae

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The Distributed Activation Energy Model (DAEM) or Multiple Reaction Model (MRM) applies either to the total amount of volatiles released or to the amount of an individual volatile constituent like carbon monoxide or tar (Howard, 1981). It is also called the Distributed Rate Model, and uses Vand's treatment of independent parallel processes (Vand, 1943) in modelling the resistance of metallic films. The detailed study includes the total amount of volatiles released during the pyrolysis process (Howard, 1981;Donskoi and McElwain, 1999). Originally, the coal devolatilization, however, was considered first to develop the Distributed Activation Energy Model (Pitt, 1962), yet the DAEM also applies to the pyrolysis of other materials, including biomass, residual oils, resin char (Teng and Hsieh, 1999), and kerogen (Lakshmanan and White, 1994). Calculations of solutions to this model involve evaluations of double integrals, which vary rapidly and hence create significant numerical difficulties. In order to tackle the integral complication, asymptotic expansion has been adopted for the accurate approximation to our problem. The solution for the DAEM model is given by Eq. (1): (1) where:-the time varying absolute temperature of the biomass R -the universal gas constant E -the activation energy k 0 -the pre-exponential or frequency factor β (β >0) -the scale parameter of initial distribution function respectivelyThe aim of this paper is to use asymptotic methods to make accurate approximations to the integrals and thereby evaluate the influence of relevant parameters on the biomass pyrolysis. Asymptotic expansionThe relationship between the DAEM and the single first order reaction model have been explored by Niksa and Lau (1993), which is based on the approach of holding the activation energy fixed, and defining an effective or nominal rate constant (Niksa and Lau, 1993). They also gave an analytical approximations to the DAEM for the exponentially and the linearly varying temperature profiles. The basis of approach lies on exploiting the rapid changes occurring in the double exponential term in Eq. (1). The procedure adopted by Niksa and Lau (1993) provides accurate approximations to the DAEM for all the relevant parameters for the kinetic mechanism of biomass pyrolysis. The modification done by them is simply refinement of the concept applied by Suuberg (1983), who used unit step function approximation to Double exponential term (DExp) (Howard, 1981;Vand, 1943;Pitt, 1962). In the subsequent sections, a more accurate approximation to DExp has been developed, which is implemented in the two different types of distribution cases (Narrow and Wide distribution). Acta Technologica Agriculturae 3 Nitra, Slovaca Universitas Agriculturae Nitriae, 2017, pp. 78-84 ApproximAtions to the non-isothermAl DistributeD ActivAtion energy moDel for biomAss pyrolysis using the rAyleigh Distribution This paper deals with the influence of some parameters relevant to biomass pyrolysis on the numerical solutions of the nonisothermal n th ...

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Section: Application Of Biomassmentioning

confidence: 93%

Approximations to the Non-Isothermal Distributed Activation Energy Model for Biomass Pyrolysis Using the Rayleigh Distribution

Dhaundiyal

Singh

2017

Acta Technologica Agriculturae

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“…Cai and Liu [18] developed a new DAEM, which considering the reaction order and the dependence of frequency factor on temperature. And parametric study of the nth-order Gaussian DAEM and nth-order Weibull DAEM also been performed [19,20]. After the heating rate was specified and kinetic parameters were available, computer codes based on DAEM, such as FG-DVC [21,22] and FLASHCHAIN [23][24][25], can be used to predict the yield of individual pyrolysis products.…”

Section: Introductionmentioning

confidence: 99%

Analysis of volatile species kinetics during typical medical waste materials pyrolysis using a distributed activation energy model

Yan

Zhu

Jiang

et al. 2009

Journal of Hazardous Materials

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“…The WPPs evaluated for the thermo-oxidative degradation process of Native Cassava starch, at different heating rates(10,20,30, and 40 C min 21 ). The corresponding conversion fraction regions (Da) for every identified stage are also shown.…”

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“…The WPPs evaluated for the thermo-oxidative degradation process of Native Cassava starch, at different heating rates(10,20,30, and 40 C min 21 ). The cumulative probability functions for the standard Weibull model in the case of the first thermo-oxidative degradation stage (Stage 1) of Native Cassava starch at different heating rates(10,20,30, and 40 C min 21 ). The cumulative probability functions for the standard Weibull model in the case of the first thermo-oxidative degradation stage (Stage 1) of Native Cassava starch at different heating rates(10,20,30, and 40 C min 21 ).…”

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Kinetic modeling of native Cassava starch thermo‐oxidative degradation using Weibull and Weibull‐derived models

Janković

2013

Biopolymers

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A new approach in kinetic modeling of thermo-oxidative degradation process of starch granules extracted from the Cassava roots was developed. Based on the thermoanalytical measurements, three reaction stages were detected. Using Weibull and Weibull-derived (inverse) models, it was found that the first two reaction stages could be described with the change of apparent activation energy (Ea) on conversion fraction (α(T)) (using "Model-free" analysis). It was found that first reaction stage, which involves dehydration and evaporation of lower molecular mass fractions, can be described with an inverse Weibull model. This model with its distribution of Ea values and derived distribution parameters includes the occurrence of three-dimensional diffusion mechanism. The second reaction stage is very complex, and it was found to contain the system of simultaneous reactions (where depolymerization occurs), and can be described with standard Weibull model. Identified statistical model with its distribution of Ea values and derived distribution parameters includes the kinetic model that gives the variable reaction order values. Based on the established models, shelf-life studies for first two stages were carried out. Shelf-life testing has shown that optimal dehydration time is achieved by a programmed heating at medium heating rate, whereas optimal time of degradation is achieved at highest heating rate.

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Parametric study of the nonisothermal n th-order distributed activation energy model involved the Weibull distribution for biomass pyrolysis

Cited by 23 publications

References 20 publications

Approximations to the Non-Isothermal Distributed Activation Energy Model for Biomass Pyrolysis Using the Rayleigh Distribution

Approximations to the Non-Isothermal Distributed Activation Energy Model for Biomass Pyrolysis Using the Rayleigh Distribution

Analysis of volatile species kinetics during typical medical waste materials pyrolysis using a distributed activation energy model

Kinetic modeling of native Cassava starch thermo‐oxidative degradation using Weibull and Weibull‐derived models

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