2.3.1 Introduction

Mathematical modelling may be defined as the art of obtaining a solution, given specified input data, that is representative of the response of the process to a corresponding set of inputs (54). The development of a mathematical model can be mechanistic (theoretical) using physico-chemical principles, empirical based on experimental data, statistical or judgmental as in an expert system or a combination of the above.

2.3.2 Pyrolysis Modelling Objectives

Mathematical modelling is utilised in pyrolysis to account for the effects of the interaction of the parameters on the end products. The objectives of a mathematical pyrolysis model should include:

1 the development of a diagnostic tool in order to evaluate the importance of the various process parameters such as particle size, heat of pyrolysis (reaction) and thermal properties of the feedstock and products;

2 the prediction of the effects of process parameters, i. e. heating rate, reactor temperature, particle size, moisture content, on the product yields and characteristics in order to aid optimisation of the pyrolysis process;

3 the development and establishment of better reactor design techniques in order to specify reactor type and size.

There are four types of pyrolysis model: empirical, kinetic, analytical and stagewise. All models basically derive energy and mass balances across a particle of biomass as shown in Figure 2.6.

where:

Te: environment temperature T§: surface temperature

Tq: char temperature Ту/: biomass temperature

The pyrolysis of a single particle represented above is not however applicable to conditions where particle ablation is significant or the primary method used to achieve pyrolysis. A typical example is that of Diebold’s vortex reactor where the particle is in contact with a heated surface under conditions of high applied pressure and high relative motion where conductive heat transfer is the dominant mode (48).