Environmental Engineering Reference
In-Depth Information
(m
3/
/day); and t
res,X
is the solid retention time (SRT) exceeding HRT (day),
i.e. if t
res,X
=0, SRT=HRT (Thamsiriroj and Murphy, 2011).
Acid-base equations
The pH of the fermenting liquor can be simulated using six physicochemical
processes that describe the acid-base equilibrium of CO
2
/HCO
3
,NH
4
þ
/
NH
3
, HAc/Ac
(acetate), HPr/Pr
(propionate), HBu/Bu
(butyrate) and
HVa/Va
(valerate). If strong bases or acids are present in the feed influent
or if biocarbonate is added, the model allows them to be accounted through
the components S
cat
þ
and S
an
representing cations and anions respectively.
Equations 5.7 and 5.8 are required for determining pH (Thamsiriroj and
Murphy, 2011).
;
dS
liq
;
i
dt
¼
q
liq
V
liq
S
in
;
i
S
liq
;
i
i
¼
25-26
ð
cations and anions
Þ½
5
:
7
2
4
3
5
K
a
K
a
dS
an
dt
IN
K
a
;
IN
þ
;
dS
IN
dt
þ
CO2
K
a
;
CO2
þ
;
dS
IC
dt
þ
ðÞ
ac
K
a
;
ac
þ
Ka
;
ðÞ
1
64
d
Sac
dt
þ
1
112
þ
ð
Þ
ð
Þ
ð
Þ
S
H
þ
S
H
þ
S
H
þ
K
a
dS
cat
þ
dt
K
a
dS
pro
dt
þ
d
S
bu
dt
þ
K
a
d
S
IN
dt
pro
K
a
;
pro
þ
S
H
þ
;
;
bu
ðÞ
va
K
a
;
va
þ
S
H
þ
;
dS
va
dt
1
160
1
208
dS
H
þ
dt
¼
ð
Þ
ð
Þ
ð
Þ
K
a
bu
þ
S
H
þ
;
2
4
3
5
½
5
:
8
K
a
;
IN
S
IN
K
a
;
IN
þ
S
H
þ
K
a
;
CO2
S
IC
K
a
;
CO2
þ
S
H
þ
ðÞ
K
a
;
ac
S
ac
K
a
;
ac
þ
S
H
þ
ðÞ
K
a
;
pro
S
pro
K
a
;
pro
þ
S
H
þ
1
64
1
112
1
þ
2
þ
2
þ
2
þ
2
ð
Þ
ð
Þ
ð
Þ
ð
Þ
K
a
;
bu
S
bu
K
a
ðÞ
ðÞ
K
a
;
va
S
va
K
a
;
va
þ
1
160
1
208
K
w
S
H
þ
þ
þ
þ
ð
Þ
2
2
2
ð
Þ
ð
Þ
S
H
þ
bu
þ
S
H
þ
;
where pH= log
10
(S
H
þ
); S
H
þ
is the concentration of hydrogen ions (kmole
H
þ
/m
3
); dS
i
/dt is rate of change of component i as defined in equation 5.5;
K
a,i
is the equilibrium constant of component i (kmole/m
3
) and K
w
is the
equilibrium coefficient of H
2
O (kmole/m
3
).
Gas phase equations
Biogas considered in the ADM1 model is composed of methane, carbon
dioxide and hydrogen. The transformation of biogas from liquid to gaseous
form is considered in equation 5.9 based on the ideal gas law (Batstone
et al., 2002)
S
gas
;
i
q
gas
V
gas
þ r
T
;
i
dS
gas
;
i
dt
V
liq
V
gas
;
¼
i
¼
H
2
;
CH
4
and CO
2
½
5
:
9
where S
gas,i
is the concentration of gas component i (H
2
and CH
4
in
kg COD/m
3
and CO
2
in kmole C/m
3
); V
gas
is digester headspace (m
3
); q
gas
is
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