Agriculture Reference
In-Depth Information
Consumption, Q
. Methane oxidation is described with dual-substrate Michae-
lis-Menten kinetics:
Q
CH
h
=
V
O
C
LCH
4
K
O2
+
C
LCH
4
C
LO
2
K
O1
+
C
LO
2
(
8
.
12
)
where
V
O
(
z, t
) is the oxidation potential and
K
O1
and
K
O2
are Michaelis con-
stants. Oxygen is consumed in respiration and CH
4
oxidation, the latter requiring
two molecules of O
2
per molecule of CH
4
. Hence, assuming Michaelis-Menten
kinetics and no carbon limitation:
Q
O
2
=
V
R
C
LO
2
K
R
+
C
LO
2
+
2
Q
CH
4
(
8
.
13
)
where
V
R
(
z, t
) is the respiration potential and
K
R
a Michaelis constant.
Reaction Potentials
. The reaction potentials
V
M
,V
O
and
V
R
are the rates at
which methanogenesis, CH
4
oxidation and oxic respiration would proceed
in situ
were all enzymes saturated with the necessary substrates. They depend on
in situ
enzyme concentrations and hence on
in situ
microbial populations. They change
over time.
Equations (8.1)-(8.13) can be solved to provide transient- or steady-state pro-
files of O
2
and CH
4
concentration, reaction rates and surface fluxes for any
combination of the controlling variables
θ
G
,θ
L
,v,κ,σ,V
M
,V
O
and
V
R
.Where,
as is usual, one or more of the controlling variables may be further simplified,
approximated or neglected, process-based simulation of CH
4
emission becomes
possible using a relatively limited set of input data.
Simplified Model Focusing on Effects of the Plant
Arah and Kirk (2000) make the following assumptions to develop a simpli-
fied model:
(1) the soil is saturated and air-filled porosity external to roots is negligible, i.e
θ
G
=
0;
(2) water content,
θ
L
, is uniform with depth;
(3) leaching is negligible, i.e.
v
=
0;
(4) root transmissivity is proportional to root-length density, i.e.
κ
=
k
T
L
V
;
(5) ebullition is negligible, i.e.
σ
=
0;
(6) oxidation potential,
V
O
, is constant;
(7) CH
4
production potential is proportional to respiration potential,
V
M
=
V
R
/ 50;
(8) respiration potential is proportional to root-length density, i.e.
V
R
=
k
V
L
V
;
(9) root-length density is normally distributed with depth, with maximum value
L
Vmax
at depth
z
max
, and standard deviation equal to
z
max
/2.
