Page 270 - Biomass Gasification, Pyrolysis And Torrefaction Practical Design and Theory

246 Biomass Gasification, Pyrolysis and Torrefaction

char particle, λ g is the thermal conductivity of the gas, and σ is the
Stefan Boltzmann constant.
A similar heat balance for the gas in an element dz in length can be car-
ried out as:

0 1
" #
9
P
j F gj C pg T g X
d @ A 52 A ξ ΔH k ðT g Þ
k
dZ
k56
2 3
(7.91)
4
2
2 4πr N c A 4 λ g ðT g 2 T c Þ 1 e p σðT 2 T Þ
c g c
4 5
r c
4 4
2 ½h conv ðT g 2 T w Þ 1 e w σðT 2 T ފπD r
g w
where ξ k is the extent of the gas-phase kth reaction with the heat of reaction,
ΔH k (T g ); h conv is the gas-wall convective heat transfer coefficient; and D r is
the reactor’s internal diameter.
The first term on the right of Eq. (7.91) is the net heat absorption by the
gas-phase reaction, the second is the heat transfer from the gas to the char
particles, and the third is the heat loss by the gas at temperature T g to the
wall at temperature T w .
The equations are solved for an elemental volume, A r dL r , with boundary
conditions from the previous upstream cell. The results are then used to solve
the next downstream cell.
SYMBOLS AND NOMENCLATURE
2
A cross-sectional area of bed or reactor (m )
21
preexponential coefficient in Eq. (7.42) (s )
A 0
preexponential coefficients in Eqs. (7.44) and (7.47), respectively
A b , A w
s )
(bar 2n 21
total number of atoms of element j entering the reactor ( )
A j
number of atoms of jth element in ith species ( )
a i,j
mass of jth gas, required for the kth reaction (kg)
a jk
3
molar concentration of ith gas (mol/m )
C i
specific heat of char (kJ/kg K)
C pc
specific heat of the bulk gas
C pg
internal diameter of the reactor(m)
D r
D g,j diffusion coefficient of the jth gas in the mixture of gases
2
(m /s)
d b diameter of the bubble (m)
E activation energy (kJ/mol)
e p emissivity of char particle ( )
F gl0 initial flow-rate of the gas (mol/s)
F gl molar flow-rate of the lth gas (mol/s)