Biomass (B)
Volatiles + Gases (G)
(R1)
Char (C)
(R2)
For reaction (R1),
À
dC B
dt
¼ k 1 :C
n1
B
ð12:1Þ
where n 1 and k 1 are the order and rate constant of reaction (R1), respectively.
For reaction (R2),
À
dC B
dt
¼ k 2 :C
n2
B
ð12:2Þ
where n 2 and k 2 are the order and rate constant of reaction (R2), respectively.
Combining Eqs. (12.1) and (12.2)
À
dC B
dt
¼ k 1 :C
n1
B þ k 2 :C
n2
B
ð12:3Þ
According to Shafizadeh (1981), n 1 ¼ n 2 ¼ 1.
Substituting the above condition in Eq. (12.3),
À
dC B
dt
¼ k 1 :C B þ k 2 :C B
¼ C B k 1 þ k 2
ð
Þ
À dC B =C B
ð
Þ¼dt k 1 þ k 2
ð
Þ
ð12:4Þ
ln C B
½
Š
C B
1 ¼ k 1 þ k 2
ð
Þt
½
Š
t
0
À ln 1 À ln C B
ð
Þ¼ k 1 þ k 2
ð
Þ0 À t
ð
Þ
ln C B ¼ À k 1 þ k 2
ð
Þt
C B ¼ e
À k 1 þk 2
ð
Þ t
ð12:5Þ
Equation 12.5 is used to predict the concentration of biomass as a function of
time:
dc c
dt
¼ k 2 :C B
n 2
¼ k 2 :e
À k 1 þk 2
ð
Þ t
dC c ¼ k 2 e
À k 1 þk 2
ð
Þ t
:dt
C C
½ Š ¼À k 2 : e
À k 1 þk 2
ð
Þ t
À
Á = k 1 þ k 2
ð
Þ
Â
Ã
ð12:6Þ
Equation 12.6 is used to calculate the concentration of char as a function of time.
328
S. Aswin et al.