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

Abstract

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 <k> (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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