MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

where
and
An energy balance is used to relate the particle temperature to the reaction rate:
− mC p, p
S g
dTp dt + qheatΔH = − Nu
d (1− e ) p (T 4 4
p − Tg) + (Tp − Tw ) (6.10)
= C p, g d p o q heat
M C Nu
ΔH = 1
M C
72
(6.11)
[ (1 − )ΔH CO + ΔH CO2]
(6.12)
where ΔH CO and ΔH CO2 are the heats of reaction per mole carbon for the reactions C + 0.5
O 2 = CO and C + O 2 = CO 2, respectively. In some cases T p is measured or controlled
(e.g., fixed bed combustion) and the energy balance step can be skipped. The procedure
for solving the energy balance equation is:
1. guess a value for T p;
2. go through the P s loop and compute the converged value of reaction rate
(denoted as q ps here): q ps = q rxn = q diff;
3. compute the value of q heat from the energy equation (6.10);
4. calculate the difference between the value of q ps from the P s loop and q heat from
the energy equation;
5. Guess a new value for T p using Newton-Raphson method so that the difference
q = (q – q heat) is zero. Notice that this new T p changes the value of q from the
P s loop.