Environmental Engineering Reference
In-Depth Information
biogas flow rate (m
3
/day), defined by
RT
P
gas
P
gas
;
H2O
V
liq
r
T
;
H2
16
þ
r
T
;
CH4
q
gas
¼
64
þ r
T
;
CO2
P
gas
is total headspace pressure (bar), defined by P
gas
=p
gas
,
H2
þ
p
gas
,
CH4
þ
p
gasCO2
þ
ρ
T,i
is kinetic gas
transfer rate of gas component i (kg COD/m
3
/day); R is the gas law constant
(bar m
3
/kmole/K); and T is operating temperature (K).
Combining equations 5.5 to 5.9 yields a set of 30 differential equations in
total for the simulation of a single CSTR digester system. More details on
the construction of these differential equations can be found in Rosen and
Jeppsson (2006). In the case where the system includes for recirculation of
digestate as input together with the feedstock, equations 5.10 and 5.11 are
added to the model
p
gas
,
H2O
; p
gas
,
H2O
is water vapour pressure (bar);
S
in
;
i
¼
S
feed
;
i
f
feed
þ
S
liq
;
i
1
ð
f
feed
Þ
;
i
¼
1-12
;
25-26
½
5
:
10
;
X
in
;
i
¼
X
feed
;
i
f
feed
þ
X
liq
;
i
1
ð
f
feed
Þ
i
¼
13-24
½
5
:
11
where S
feed,i
and X
feed,i
are the concentrations of component i in feedstock
input and f
feed
is the fraction of feedstock input to total inflow.
5.8.4 Initial conditions and digester input
Solving differential equations requires values for initial conditions. In the
case of a CSTR the initial conditions are the conditions of the components
within the digester. There are 30 variables included in the model: 12 liquid
and 12 particulate variables (as described in Table 5.5); 3 ion state variables
(cations, anions and hydrogen ions); and 3 gas phase variables (methane,
carbon dioxide and hydrogen). It may not be practical to determine the
initial condition of each variable based on laboratory measurement. A more
effective approach is to allow an initial period of digester operation to serve
as model calibration. Samples of initial digester content are required for the
measurement of dry solids (DS) and volatile solids (VS) content. The DS are
assumed to be composite particulate material (X
c
), which are further
subdivided into inerts (ash), carbohydrates, proteins and lipids. Inert
material is the ash content calculated from the difference between %DS and
%VS. The fraction of carbohydrates, proteins and lipids can be measured or
initially assumed. The simulation results in the early part of the calibration
period will not be accurate. However, accuracy will improve as the contents
of the digester are gradually replaced by new input feed. As the
characteristics of the input feed are sufficiently known, the simulation in
the later part of calibration period will gradually increase in accuracy when
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