Asymptotic approximations to the Distributed Activation Energy Model Original Research Article

We present approximations to the Distributed Activation Energy Model (DAEM), also known as the Multiple Reaction Model (MRM), which is widely used in complex chemical systems such as coal pyrolysis. MRM assumes that the process can be represented by a continuum distribution in activation energy of individual reactions. An individual reaction is characterised by a pre-exponent coefficient and an activation energy. The distribution, usually Gaussian, is over the activation energy. The solution for the amount of product requires the evaluation of a double integral. This paper develops asymptotic approximations to this double integral, based on the assumptions that the mean of the Gaussian is large and that its standard deviation is small. The method will have wide applicability in situations, such as computational fluid dynamics modelling of coal-fired boilers, where it is important to be able to evaluate this double integral quickly. It also provides analytical insights into solution behaviour, since the asymptotic forms are explicit.