MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

Introduction
4. Analytical Solutions of the Effectiveness Factors
Pore diffusion effects can be treated with either a full numerical solution radially
through the porous char matrix (Reade, 1996), or treated using the analytical Thiele
modulus approach (Thiele, 1939). Since the char particle reactivity is often sought for
inclusion into a comprehensive model of a coal combustor, an analytical solution is
preferred here over the full numerical solution.
It was shown in the literature review that the effectiveness factor can be
approximately predicted by the asymptotic solution in spherical coordinates (Thiele,
1939; Bischoff, 1965):
= 1
M T
⎛ 1
⎝ tanh(3MT ) ⎜
where M T is the general Thiele modulus, which is
M T = L
(m + 1)
2
for the m-th order rate equation, and
M T = L
o k 1
2D e
1 ⎞
− ⎟ (4.1)
3MT ⎠
okmC m −1
s
De 27
(4.2)
KCs (1 + KCs ) [KCs − ln(1 + KC 1
2
s )]− (4.3)
for the Langmuir rate equation. It was also shown that the classic asymptotic solution of
the effectiveness factor is inaccurate when the general Thiele modulus is in the
intermediate range, and the error can be up to 24% in Cartesian coordinates, as shown in