MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

where r p1 is the macro-pore radius, r p2 is the micro-pore radius, M is the macro porosity,
is the micro porosity, and is the roughness factor.
Thermodynamic and Transport Properties
CBK model uses the following correlations for thermal conductivities
(cal/cm/sec/K) and molar heat capacities (cal/mol/K) of nitrogen and oxygen (Mitchell et
al. 1992):
N 2 = 7.6893 ×10−7 0.7722
Tm O2 = 7.1352 × 10 −7 0.7968
Tm CpN 2 = 7.7099 − 5.5039 × 10 −3 Tm +13.1214 ×10 −6 2 −9 3
Tm −11.68 × 10 Tm
+5.2340 ×10 − 12 4 −15 5 −18 6
Tm − 1.1732 ×10 Tm − 0.1039 ×10 Tm
CpO2 = 7.3611− 5.3696 ×10 −3 Tm + 20.542 ×10 −6 2 −9 3
Tm − 25.865 ×10 Tm
+15.946 ×10 − 12 4 −15 5 −18 6
Tm − 4.8589 ×10 Tm − 0.5862 ×10 Tm
In the CBK model the thermal conductivity of a gas mixture is assumed to be the linear
combination of the thermal conductivities of the component gases (mainly nitrogen and
oxygen):
84
(6.53)
(6.54)
(6.55)
(6.56)
= (1 − P O2 ) N 2 + P O2 O 2 (6.57)
Similarly, the molar heat capacity of a gas mixture is
C P = (1 − P O 2 )C P, N2 + P O 2 C P,O 2 (6.58)
Eq. (6.53) to (6.56) are adopted in the HP-CBK model. However, Eq. (6.57) and (6.58)
will undoubtedly fail at high pressures since the partial pressure of oxygen is often greater
than 1 atm. These equations are modified to: