The aim of this paper is to present a simple model, based on a time and space integral method, for prediction of preheating and conversion time of a charring solid particle exposed to a non-oxidative hot environment. The main assumptions are 1) thermo-physical properties remain constant throughout the process; 2) temperature profile within the particle is assumed to obey a quadratic function with respect to the space coordinate; 3) pyrolysis initiates when the surface temperature reaches a characteristic pyrolysis temperature; 4) decomposition of virgin material occurs at an infinitesimal thin layer dividing the particle into char and virgin material regions; 5) the volume of the particle remains unaltered; 6) volatiles escape through the pores immediately after formation.
Employing assumption (2) allows one to convert the energy conservation equation of the particle, which is basically described in the form of a partial differential equation (PDE), into an ordinary differential equation (ODE) by performing space integration. Next, by applying approximate time integration the ODE is transformed into an algebraic equation. Applying this approach to the preheating and pyrolysis stages of a thermally thin charring solid particle leads to a set of algebraic equations which provides reactor designers with a convenient means for computation of the heating up time, mass loss history and total conversion of particle. The accuracy of the simple model is assessed by comparing its prediction with that of a one-dimensional detailed pyrolysis model. Overall, good agreement is achieved indicating that this new model can be used for engineering and design purposes.