The fuel particle can be simplified as a sphere that undergoes an endothermic process that is regulated by the equation of thermal exchange (Tillman, 1991):

Q = (A x A)/r x (T1 — T2) (5.13)

where:

A = thermal conductivity [W/mK]

A = area [m2] r = radius [m].

The temperature of the process varies, as a function of three steps:

(i) heating from ambient temperature to 105°C, to reach evaporation temperature that is higher than 100°C because of inter-molecular forces that bind water inside the woody cell;

(ii) drying at 105°C: this is an isothermal phase in which water leaves the woody particle, the evaporation front moves to the center of the particle generating a series of pores through which water and volatiles produced by pyrolysis will pass. The drying will continue until all the water contained in the biomass will evaporate. It is not a simultaneous process for all the layers of the sphere; in particular the external layer undergoes an immediate drying and it is not affected by pyrolysis but undergoes immediate combustion generating a layer of ashes that isolates from oxygen and heats the particle; the steam escaping from the particle contributes to the evacuation of ashes from the particle.

(iii) heating at temperatures higher than 105°C. The heat is exchanged to particles through:

• Radiation: from the flame and from the walls of the combustion chamber;

• Conduction: from adjacent particles and from the walls of the combustion chamber;

• Convection: due to turbulence and convective motions inside the combustion chamber.

As a result of this phase:

(i) the wood particle shrinks by 7-17% in volume (Haygreen and Bowyer, 1982) and the material begins to crumble and crack; this produces an important reduction of the size (shrinkage) of the fuel;

(ii) the diameter of the fuel pores also decreases reaching even 5-10 A (Skaar, 1972).

The governing equation of the drying phenomenon is Ficks second law of diffusion (Chen et al., 2012):

V( Deff(V MR))

where:

MR represents the moisture ratio of biomass (Vega-Galvez et al., 2011), expressed by the following equation: MR = (M — Me)/(M0 — Me) where M0 is the initial moisture content of the sample and Me is the equilibrium moisture content of the sample Deff represents effective diffusivity of moisture [m2/s] (Vega-Galvez et al., 2010).

Effective diffusivity (Deff) is generally determined using experimental drying curves; on the other hand the temperature dependence of the effective moisture diffusivity can be represented by an Arrhenius relationship and derived using TGA analysis:

where:

D0 = pre-exponential factor of the Arrhenius equation [m2/s]

Ea = activation energy for the moisture diffusion [kJ/mol]

R = ideal gas constant [J/mol x K]

T = drying temperature [°С].

The activation energy can be calculated by plotting ln(Deff) vs. the reciprocal of the temperature 1/(T + 273.15).