Page 261 - Biomass Gasification, Pyrolysis And Torrefaction Practical Design and Theory

Chapter | 7 Gasification Theory 237

@L
5 0 (7.76)
@n i
Substituting the value of G total from Eq. (7.73) in Eq. (7.75), and then
taking its partial derivative, the final equation is of the form given by:
!
0 N K N
@L ΔG f;i X n i 1 X X
5 1 ln 1 λ j a ij n i 5 0 (7.77)
@n i RT n total RT
i51 j51 i51
7.5.2.4 Kinetic Models
Gas composition measurements for gasifiers often vary significantly from
those predicted by equilibrium models (Kersten, 2002; Li et al., 2001;
Peterson and Werther, 2005). This shows the inadequacy of equilibrium
models and underscores the need of kinetic models to simulate gasifier
behavior.
A kinetic model gives the gas yield and product composition a gasifier
achieves after a finite time (or in a finite volume in a flowing medium).
Thus, it involves parameters such as reaction rate, residence time of particles,
and reactor hydrodynamics. For a given operating condition and gasifier con-
figuration, the kinetic model can predict the profiles of gas composition and
temperature inside the gasifier and overall gasifier performance.
The model couples the hydrodynamics of the gasifier reactor with the
kinetics of gasification reactions inside the gasifier. At low reaction tempera-
tures, the reaction rate is very slow, so the residence time required for com-
plete conversion is long. Therefore, kinetic modeling is more suitable and
accurate at relatively low operating temperatures (,800 C) (Altafini et al.,

2003). For higher temperatures, where the reaction rate is faster, the equilib-
rium model may be of greater use.
Kinetic modeling has two components: reaction kinetics and reactor
hydrodynamics.

7.5.2.5 Reaction Kinetics
Reaction kinetics must be solved simultaneously with bed hydrodynamics
and mass and energy balances to obtain the yields of gas, tar, and char at a
given operating condition.
As the gasification of a biomass particle proceeds, the resulting mass loss
is manifested either through reduction in size with unchanged density or
reduction in density with unchanged size. In both cases the rate is expressed
in terms of the external surface area of the biomass char. Some models,
where the reaction is made up of char alone, can define a reaction rate based
on reactor volume. There are thus three ways of defining the char gasifica-
tion reaction for biomass: (i) shrinking core model, (ii) shrinking particle
model, and (iii) volumetric reaction rate model.