Agriculture Reference
In-Depth Information
where
V
is the rate of Reaction (5.1), and the ratio of these rates is
V
CH
4
V
CO
2
=
4
b
+
c
4
b
−
c
+
4
d
φ
=
(
5
.
2
)
Similarly the fractions of CH
4
produced in Reactions (5.1b) and (5.1a) are
c
4
b
+
c
4
b
4
b
+
c
R
H
2
=
and
R
Ac
=
1
−
R
H
2
=
and the ratio of these fractions is
R
H
2
R
Ac
=
c
4
b
ψ
=
(
5
.
3
)
If the composition of SOM
0
is
SOM
0
=
x
C
+
y
H
+
z
O
then
SOM
1
=
(x
−
2
b
−
d)
C
+
(y
+
2
a
−
4
b
−
+
(z
+
a
−
2
b
−
2
c)
H
2
d)
O
−
+
Taking O to be in oxidation state
1 and ignoring all other SOM
elements, the charges on SOM
0
CandSOM
1
Caretherefore
2, H in state
Z
0
=
2
z
−
y
and
Z
1
=
2
z
−
y
+
2c
−
4
d
and the change in total SOM C charge per mole of C consumed,
Z
,is
Z
=
Z
1
−
Z
0
=
2
c
−
4
d
(
5
.
4
)
These equations can be combined to give
Z
in terms of
φ(
=
V
CH
4
/V
CO
2
)
:
Z
=
4
φ
−
1
φ
+
1
(
5
.
5
)
This relation is plotted in Figure 5.4(a). Negative values of
Z
indicate a deficit
of electrons in the gaseous products of SOM decomposition and that SOM
1
is
more reduced than SOM
0
; positive values indicate a surplus of electrons in the
gaseous products and that SOM
1
is more oxidized than SOM
0
.
Substituting for
c
from Equation (5.3) and for
d
from
d
=
1
−
2
b
in
Equation (5.2) gives the following expression for
b
in terms of
φ
and
ψ
:
φ
(
1
+
φ)(
1
+
ψ)
b
=
(
5
.
6
)
Here
b
is the number of moles of acetate produced per mole of SOM carbon
decomposed. From Equation (5.3), the number moles of H
2
produced is
4
φψ
(
1
+
φ)(
1
+
ψ)
c
=
4
bψ
=
(
5
.
7
)
