TRANSFER: BASICS OF MASS AND HEAT TRANSFER - Biomass as a Sustainable Energy Source for the Future - page 119

Q r = A d

V d E a σ

T ext ð Eq : 4 : 50 Þ

and contains the absorption efficiency factor E a = a r d whose coefficients a and b
need to be estimated from experiments.
5. Complex fuels such as diesel, kerosene, and biofuel contain many components,
and the evaporation of the corresponding fuel droplets cannot accurately be
described using single-component representation. Instead, models for multi-
component fuels are needed. When the number of components is low, e.g.,
two components in methanol droplets that have absorbed water from the envi-
ronment, all present species can be described by an individual mass fraction.
However, if the number of components is much higher like in biofuel, it is
not effective to consider transport equations for each component. Then it is bet-
ter to use a statistical approach based on continuous thermodynamics. The the-
ory of continuous thermodynamics describes the mixture in terms of a
probability density function (PDF) of the composition, e.g., of the molar mass
of the components. Predictions of continuous thermodynamic models differ
depending on the submodel for this PDF. A good introduction and further refer-
ences on the application of continuous thermodynamic methods for spray evap-
oration can be found in Le Clercq and Bellan (2004).

4.5.2 Devolatilization of a Biomass Particle

To further illustrate the heat and mass transfer processes taking place during biomass
conversion processes, we here consider a simple model for devolatilization of a bio-
mass (wood) particle in a hot environment without oxygen. The particle receives heat
from the surroundings, causing the release of volatile matter (tar and light gases).
More detailed models describing this phenomenon are considered in Chapter 11.
Here, we restrict ourselves to the description of the inside of the particle and treat heat
and mass exchange with the surroundings as a boundary condition, following the
approach presented in Lu et al. (2010).
Five species are included in the model: biomass, char, light gas, tar, and inert gas.
The first two are in the solid phase and have densities

ρ C . The other species are
in the gas phase. The additional complexity caused by the presence of moisture and
generation of water vapor is not included in this simple model. The volume of the
particle is occupied by solid material and by gases. The porosity

ρ B and

ε by definition is

the fraction of the total volume occupied by gases. The fraction (1 ) then consists

of solids. The partial density of the gaseous species in the pores are denoted

− ε

ρ g . The
partial density of the gaseous species in a volume containing both solid and gas then
is given by ε ρ g .

In the model description (see Figure 4.3), biomass is converted to light gas, tar, or
char, respectively, with rate coefficients k 1 ,k 2 , and k 3 . The tar is further converted to
light gas and to char, respectively, with rate coefficients k 4 and k 5 .