MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

The fraction of the carbon content of the particle converted to CO 2 is denoted as and
determined from the CO/CO 2 product ratio (MR):
= 1/(1 + MR). (6.4)
The mass diffusion outside the particle is (Frank-Kamenetskii, 1969):
qdiff = kDP ⎛ 1− Ps / P⎞
ln⎜ ⎟ when γ ≠ 0 (6.5a)
⎝ 1 − P / P g ⎠
q diff = k D(P og − P os ) when γ = 0 (6.5b)
where the mass transfer coefficient is given by:
k D = M cD ox Sh
d p ′
R T m o
71
(6.6)
o = 0.5(1+ ) (6.7)
=
− 1
+ 1
This assumes, of course, that oxygen is the only oxidizer and that pyrolysis reactions
have been completed. Slightly different and iterative forms can be used to account for
(6.8)
these effects, such as those in PCGC-3 (Smoot and Smith, 1985; Smith et al., 1994). The
quasi-steady state assumption leads to
q diff = q rxn (6.9)
If the particle temperature is known or guessed, Eqs. (6.9), (6.1) and (6.5) can be used to
determine the value of P s. Numerically, a value is guessed for P s, Eqs. (6.1) and (6.5) are
used to compute q rxn and q diff, and then the difference q 1 = (q rxn - q diff) is driven to zero
by changing the value of P s using the Newton-Raphson method. This procedure for
computing P s is referred to in this study as the P s loop.