Approximate solution technique for nonisothermal, gaussian distributed activation energy models

Abstract

The literature on combustion and pyrolysis contains many references to pyrolytic reaction models based on the concept of a Gaussian distribution of activation energies. Such models have been used to describe the pyrolysis of coal [1-12], oil shale [13], and cellulose [14] ; they are seen as particularly appropriate for describing the pyrolysis of certain natural products containing a variety of chemically distinct functional groups. It has been pointed out that the use of a single first-order reaction rate model to describe overall volatiles formation can give rise to activation energies which are too low to be realistic for chemical processes (even in situations in which transport limitations play no role) [2, 6]. As a compromise between detailed individual product evolution models [1, 7, 10, 13 15-17] and the single pseudoreaction models, a few groups have modeled the overall rate of weight loss during pyrolysis as being governed by a Gaussian distribution of activation energies [4-6, 8, 9, 14]. This approach recognizes the fact that there are many distinct chemical pathways available for formation of volatiles, but does not get involved with the actual identification of all volatile species. In one test case, analysis of detailed product formation kinetics has shown the Gaussian distribution concept to be reasonable [17]. It is sometimes necessary to use models which distinguish between the evolution of different types of volatiles. Among the detailed individual volatile product formation models, a growing