TRANSFER: BASICS OF MASS AND HEAT TRANSFER - Biomass as a Sustainable Energy Source for the Future - page 120

Light gas

k 1

k 4

k 2

Biomass Tar

k 5

k 3

Char

FIGURE 4.3 Global lumped component scheme for devolatilization (of wood).

Arrhenius expressions describe the temperature dependence of the kinetic rate
coefficients:

E a , i
R u T

k i =k 0 , i exp − ð Eq : 4 : 51 Þ

The pre-exponential factor k 0,i and the activation energy E a,i have to be determined
experimentally for the type of biomass considered.
In a reference frame for the description of the biomass particle, the transport equa-
tions for species mass, momentum, and total energy can be formulated as follows.
Assuming that the solid is not moving (i.e., neglecting particle swelling), the transport
equations for solid species only contain a transient term and source or sink terms.
Using subscripts B, C, and T to denote biomass, char, and tar, the mass conservation
for biomass and char is given by

∂ ρ B
∂

ð

k 1 +k 2 +k 3

Þ ρ B ð Eq : 4 : 52 Þ

= −

t

∂ ρ C
∂ t =k 3 ρ B +

ε k 5 ρ T ð Eq : 4 : 53 Þ

The porosity factor in front of k 5 represents the fact that the rate constants refer to the
conversion per unit volume of the biomass particle, whereas ρ T is the tar density in the

pores. In a similar manner, strictly speaking, a factor (1 − ε ) should appear in front of

k 3 , but since usually is a small number, this factor is omitted.

The transport equations for gaseous species also contain convective and diffusive
terms. Gas is leaving the particle generating an outward convection velocity. In gen-
eral, the equations are three-dimensional, but for particles having symmetry, the
description can be simplified. The transport model described here is one-dimensional
in the sense that it is assumed that only one spatial direction is important. This coor-
dinate is called r and, for spherical, cylindrical, and flat particles, respectively, has the
meaning distance from the center of the sphere, distance from the axis of the cylinder,
and distance from the midplane of the flat disk. When formulating the transport equa-
tions, the three different possible shapes of the particle are distinguished by the value
of a parameter n. A spherical particle is described by n = 2, a cylinder particle by n = 1,
and a flat plate particle by n = 0. The species mass conservation equation for gas-phase
species takes the form

ε