MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

At time zero the function f E is assumed to be a normalized log-normal distribution in E d
and integration of Eq. (6.28) yields a value of unity. In Zone I,
A(t)
A 0
= N(t)
N 0
∞
[ ∫0
] (6.29)
= f E (t,E d )dE d
In Zone II, classical Thiele theory leads to (Hurt et al., 1998):
A(t)
A 0
= N(t) ⎡
⎣ N 0
⎢
⎤
⎥
⎦
1/2
The Ash Encapsulation Submodel
∞
[ ∫0
] 1/2
= f E (t,E d )dE d
77
(6.30)
Mineral matter inhibits combustion in the late stages by one of several physical
mechanisms. First, an ash film can pose an additional resistance to oxygen transport to
the reacting surface; second, the existence of the inert ash layer outside the particle
increases the diameter of the particle, reducing the global rate expressed on an external area
basis.
The ash encapsulation submodel assumes the presence of a porous ash film
surrounding a carbon-rich core. The core region is assumed to have a constant local mass
fraction of mineral matter equal to the overall mineral mass fraction in the unreacted char.
This assumption of “shrinking core” is obviously not realistic for Zone I combustion.
Therefore, this ash encapsulation submodel is not ideally suited for modeling char
oxidation under Zone I conditions, which is recognized by Niksa and Hurt (1999).
The detailed description of the ash encapsulation submodel can be found
elsewhere (Hurt et al., 1998)