MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

6. Return to step 2 and repeat the process until the P s loop and the energy balance
are both converged. That is, q 1 = (q rxn - q diff ) = 0 and at the same time q 2 =
(q – q heat) = 0.
A set of equations was derived to describe the evolution of particle size and
density during combustion. The char particle is assumed to consist of two components: a
combustible component whose density changes with burnout and a non-combustible
inorganic component whose density is constant. The apparent density is defined as:
p
= totalweightof particle
volumeof particle
= m c + m a
V p
where the particle volume includes the voids between the solid matrix. Rewriting this
equation in terms of (a) the apparent densities of the combustible material and the ash,
and (b) the volumes they occupy yields:
p = m c
V p
+ m a
V p
= vc mc Vp v c
+ v a
V p
m a
v a
73
= v c
V p
c + v a
V p
The weights of the combustible material and ash in the particle can be expressed as:
a
(6.13)
(6.14)
m a = x a V p p = v a a (6.15)
m c = (1− x a )V p p = v c c (6.16)
Utilizing Eqs. (6.15) and (6.16) to eliminate v a and v c from Eq. (6.14) yielded the
following relationship for apparent density of the coal char particle:
1
p
= x a
a
+ (1− x a )
c
The change of apparent carbon density is related to burnout by:
c
c ,o
(6.17)
= m ⎛
c
⎝
⎜
⎞
⎟ (6.18)
⎠
m c,o