Mathematical modelling of in-situ microaerobic desulfurization of biogas from sewage sludge digestion

Abstract

Microaeration can be used to cost-effectively remove in-situ H2S from the biogas generated in anaerobic digesters. This study is aimed at developing and validating an extension of the Anaerobic Digestion Model n°1 capable of incorporating the main phenomena which occurs during microaeration. This innovative model was implemented and tested with data from a pilot scale digester microaerated for ∼ 200 d. The results showed that despite the model's initial ability to predict the digester's behavior, its predicted performance was improved by calibrating the most influential parameters. The model's prediction potential was largely enhanced by adding retention parameters that account for the activity of sulfide oxidizing bacteria retained inside the anaerobic digester, which have been consistently shown to be responsible for a large share of the H2S removed.

Full text

Mathematical
modelling
of
in-situ
microaerobic
desulfurization
of
biogas
from
sewage
sludge
digestion
Andrés
Donoso-Bravo
a,
*,
M.
Constanza
Sadino-Riquelme
b
,
Israel
Díaz
d,c
,
Raul
Muñoz
c,d
a
Cetaqua,
Centro
Tecnológico
del
Agua,
Los
Pozos
7340,
Santiago,
Chile
b
Department
of
Chemical
and
Materials
Engineering,
University
of
Alberta,
Edmonton,
AB,
Canada
c
Institute
of
Sustainable
Processes,
Universidad
de
Valladolid,
Spain
d
Department
of
Chemical
Engineering
and
Environmental
Technology,
School
of
Industrial
Engineering.
Universidad
de
Valladolid,
Dr.
Mergelina
s/n,
47011,
Valladolid,
Spain
A
R
T
I
C
L
E
I
N
F
O
Article
history:
Received
27
September
2018
Received
in
revised
form
31
October
2018
Accepted
16
November
2018
Keywords:
Biogasin-situdesulfurization
H
2
S
Modeling
Simulation
A
B
S
T
R
A
C
T
Microaeration
can
be
used
to
cost-effectively
remove
in-situ
H
2
S
from
the
biogas
generated
in
anaerobic
digesters.
This
study
is
aimed
at
developing
and
validating
an
extension
of
the
Anaerobic
Digestion
Model
n

1
capable
of
incorporating
the
main
phenomena
which
occurs
during
microaeration.
This
innovative
model
was
implemented
and
tested
with
data
from
a
pilot
scale
digester
microaerated
for

200
d.
The
results
showed
that
despite
the
model’s
initial
ability
to
predict
the
digester’s
behavior,
its
predicted
performance
was
improved
by
calibrating
the
most
influential
parameters.
The
model’s
prediction
potential
was
largely
enhanced
by
adding
retention
parameters
that
account
for
the
activity
of
sulfide
oxidizing
bacteria
retained
inside
the
anaerobic
digester,
which
have
been
consistently
shown
to
be
responsible
for
a
large
share
of
the
H
2
S
removed.
©
2018
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY-NC-ND
license
(http://
creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
Microaeration,
which
consists
of
dosing
of
a
limited
amount
of
air
to
anaerobic
digesters,
has
emerged
as
one
of
the
most
cost-effective
technologies
for
H
2
S
removal
from
biogas.
The
microaerophilic
conditions
created
by
air
supply
support
the
partial
oxidation
of
H
2
S
to
S

by
the
action
of
sulfide-oxidizing
bacteria.
In
Europe,
this
process
is
gaining
increasing
attention
and
several
full-scale
plants
have
already
implemented
this
technology
to
remove
H
2
S
from
biogas
[1].
Indeed,
microaeration
has
been
traditionally
employed
to
control
H
2
S
in
full-scale
digesters
treating
agricultural
waste.
Recently,
this
technology
has
been
successfully
applied
to
the
treatment
of
a
broad
range
of
biogas
flow
rates
(7
L
d
1
-
250
m
3
h
1
),
H
2
S
concentrations
(2500
-
67,000
ppm
v
)
[2]
and
substrates
(from
industrial
wastewaters
to
WWTP
sludge)
[3,4].
Interestingly,
microaeration
does
not
inhibit
organic
matter
removal
nor
CH
4
productivity
[5,6].
On
the
contrary,
significant
enhancements
in
organic
matter
hydrolysis
and
methanogenic
activity
have
been
reported,
likely
due
to
the
suppression
of
the
inhibition
caused
by
sulfide
[1,7,8].
Both
air
and
O
2
can
be
used
to
support
biogas
desulfurizationwith
similar
H
2
S
removal
efficiencies.
In
this
context,
the
use
of
concentrated
O
2
resulted
in
lower
operating
costs
when
compared
to
ferric
salt
addition
for
biogas
desulfurization
in
wastewater
treatment
plants
(WWTP)
[9].
Mathematical
modeling
of
(bio)chemical
processes
is
nowadays
considered
of
paramount
importance
for
process
analysis,
control
and
optimization.
Modeling
anaerobic
digestion
(AD)
allows
us
to
get
more
insight
on
process
performance,
evaluate
different
scenarios
and
hypotheses,
facilitates
a
virtual
plant
for
assessment
and
training,
and
represents
a
valuable
tool
for
process
control
or
experimental
design.
Therefore,
process
modelling
helps
minimize
the
experimental
work
needed,
which
translates
into
resource
savings
and
risk
minimization.
Furthermore,
modeling
is
recog-
nized
as
one
the
future
needs
to
be
addressed
in
AD
[10].
Recent
studies
have
developed
models
for
the
microaerobic
process
in
AD,
for
both
liquid
effluents
and
for
systems
with
immobilized
biomass,
UASB
[11 ]
and
biotrickling
filters
[12].
Therefore,
to
the
best
of
our
knowledge,
no
mathematical
model
has
been
so
far
adapted
and
implemented
for
the
microaerobic
H
2
S
removal
during
sewage
sludge
AD
in
a
continuous
stirred
reactor.
The
anaerobic
digestion
model
1
(ADM1)
developed
by
the
IWA
task
group
[13]
is
the
most
recognized
and
widely
used
model
to
describe
the
AD
process.
In
this
context,
extensions
of
the
ADM1
have
also
been
published
in
order
to
describe
particular
processes
not
considered
in
the
original
model.
These
extensions
have
tackled
biological
sulfate
reduction
[14,15],
inorganic
compounds
and
solid
precipitation
[16]
and
phenolic
compounds
biodegrada-
tion
[17],
among
others.
*
Corresponding
author:
E-mail
address:
andreseduardo.donoso@cetaqua.com
(A.
Donoso-Bravo).
https://doi.org/10.1016/j.btre.2018.e00293
2215-017X/©
2018
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY-NC-ND
license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Biotechnology
Reports
20
(2018)
xxx–xxx
Contents
lists
available
at
ScienceDirect
Biotechnology
Reports
journal
homepage:
www.else
vie
r.com/locat
e/btre

This
study
is
aimed
at
developing,
implementing
and
testing
a
mathematical
model
of
the
microaerobic
digestion
process
based
on
the
ADM1
model
using
experimental
data
from
pilot-scale
anaerobic
digesters
operated
under
microaerobic
conditions.
2.
Material
and
methods
2.1.
Experimental
data
The
pilot-plant
scale
digester
(working
volume
of
200
L)
was
operated
under
mesophilic
conditions
with
thickened
mixed
sewage
sludge
at
a
hydraulic
retention
time
(HRT)
of
20
d.
Microaeration
was
performed
in
the
sludge
recirculation
line.
The
O
2
flow
rate
(Fig.
1a)
was
manually
adjusted
to
the
variable
biogas
production
rate
resulting
from
the
unsteady
organic
load
of
sludge
feeding.
Fluctuations
in
the
organic
loading
rate
of
anaerobic
digesters
are
inherent
to
the
variations
in
sludge
compositions
in
WWTPs
and
were
here
observed
in
all
parameters
monitored,
namely,
total
COD
(between
70
and
37
g
COD
L
1
),
soluble
COD,
TS,
VS
(Fig.
1b)
and
VFA
concentrations
(Fig.
1c).
Additionally,
Na
2
SO
4
was
added
to
the
sludge
feed
(1090
mg
L
1
)
with
the
aim
of
increasing
the
formation
of
H
2
S
during
anaerobic
digestion.
Therefore,
the
concentration
of
sulfate
and
dissolved
sulfide
were
monitored
(Fig.
1d).
First,
the
digester
was
in
operation
for
70
d
in
strict
anaerobic
conditions
(data
not
shown)
before
the
micro-
aerobic
period
began.
More
details
about
the
experimental
set-up
and
operation
can
be
found
elsewhere
[18].
The
biogas
production
was
measured
by
liquid
displacement
and
the
biogas
composition
was
determined
by
GC-TCD.
Sulfate
concentration
was
measured
by
HPLC-IC.
VFA
concentrations
were
quantified
by
GC-FID.
Alkalinity,
ammonium,
TKN,
COD,
TS,
VS,
total
dissolved
sulfide,
pH
and
ORP
were
determined
according
to
standard
methods
[19].
2.2.
Model
description
2.2.1.
Model
implementation
and
ADM1
modification
ADM1
was
implemented
and
solved
in
Matlab12015b
along
with
the
general
modification
suggested
by
Rosen
and
Jeppsson
[20].
Suggested
parameters
by
the
ADM1
report
[21]
were
maintained,
although
the
minimum
and
maximum
values
of
the
pH
inhibition
function
for
H
2
consumers
were
adapted
to
the
primary
sludge.
Additionally,
a
VS
output
was
also
included,
together
with
the
COD
output,
by
using
a
conversion
COD/mass
ratio
derived
from
the
generalized
mineralization
equation
[22].
The
composite
concentration
(Xc)
was
set
equal
to
zero
so
that
the
particulate
carbohydrates,
proteins,
lipids
and
inerts
were
the
input
conditions
to
the
ADM1
model.
The
elimination
of
the
disintegration
step
originally
considered
in
the
ADM1
has
been
lately
suggested
as
necessary
based
on
the
recently
reported
drawbacks
derived
from
the
use
of
a
two-hydrolysis
step
during
the
anaerobic
digestion
of
sewage
sludge
[10]
2.2.2.
Assumptions
and
microaeration
process
rationale
The
mathematical
description
of
the
sulfide
oxidation
process
involves
the
following
assumptions:
&
The
levels
of
dissolved
oxygen
are
always
maintained
below
the
inhibition
threshold.
Therefore,
no
inhibition
function
due
to
the
presence
of
oxygen
was
added.
In
fact,
the
redox
potential
of
the
pilot
digester
cultivation
broth
remained
always
below
494
mV
under
process
operation
with
and
without
microaeration
[23].
&
Sulfide
oxidizing
bacteria
X
SOB
is
the
only
microbial
community
that
consumes
oxygen.
&
The
conversion
of
H
2
S
to
S

is
the
only
reaction
considered.
In
this
context,
the
conversion
of
H
2
S
to
SO
42
requires
4-fold
Fig.
1.
Time
course
of
(a)
the
sludge
feeding
rates
and
O
2
flow
rate,
(b)
solids
and
COD
concentrations,
(c)
VFA
concentrations
and
(d)
S
2
and
SO
42
concentration
in
the
digester.
2
A.
Donoso-Bravo
et
al.
/
Biotechnology
Reports
20
(2018)
e00293

more
O
2
than
the
oxidation
to
S

,
and
therefore
the
O
2
limiting
conditions
prevailing
in
the
cultivation
broth
of
the
digester
do
not
promote
the
complete
oxidation
of
H
2
S.
&
No
spontaneous
H
2
S
or
S

chemical
oxidation
(redox)
reactions
occur.
&
The
dissolved
oxygen
present
in
the
sludge
feeding
is
negligible
compared
to
the
O
2
transferred
from
the
gas
phase,
which
governs
the
growth
of
X
SOB
.
&
The
new
process
included
into
the
ADM1
along
with
its
stoichiometry
are
shown
in
Table
1
based
on
the
findings
of
[24].
The
sulfur
oxidation
process
involves
elemental
sulfur
(S),
sulfide
oxidizing
bacteria
(X
SOB
),
dissolved
oxygen
and
oxygen
in
the
gas
phase
as
new
state
variables
(ordinary
differential
equations,
ODE).
The
kinetic
parameters
of
the
sulfate
reducing
bacteria
(SRB)
were
taken
from
Barrera
et
al
[14].
&
An
O
2
laden
gas
stream
is
injected
into
the
digester
and
partially
transferred
to
the
liquid
phase
according
to
Eq.
(1),
where
K
H
stand
for
the
Henrys
law
constant
(K
H
=
0.0013
at
37

C),
k
L
a
the
volumetric
mass
transfer
coefficient,
p
pO2
the
O
2
partial
pressure
and
S
O2
the
dissolved
O
2
concentration
in
the
anaerobic
broth:
O
2
Transf
er
rate
¼
k
L
aðK
H
p
pO
2

S
O
2
l
Þ
ð1Þ
&
The
value
of
the
volumetric
mass
transfer
coefficient,
k
L
a,
depends
on
reactor
design
and
operating
conditions.
A
unique
k
L
a
value
was
assumed
because
the
HRT
and
mixing
rate
were
constant
in
the
experimental
period
considered,
so
were
the
temperature
and
the
operating
pressure.
Changes
in
mixing
conditions,
such
as
switching
sludge
for
biogas
recirculation,
would
result
in
a
different
k
L
a
value.
&
Two
additional
ODEs
were
added
to
describe
the
O
2
mass
balance
in
the
anaerobic
cultivation
broth
(Eqs.
(2),
(3)
dS
02
l
dt ¼
O
2
Transf
er
rate

SOB
consumption

S
O
2
l
ð2Þ
Where
SOB
consumption
stands
for
the
O
2
consumption
rate
by
X
SOB
and
S
O2
_l
the
O
2
mass
flow
rate
in
the
effluent
of
the
anaerobic
digestion.
&
Similarly,
the
O
2
mass
balance
in
the
headspace
of
the
digester
can
be
described
as
follows:
dS
02
g
dt ¼
S
02in
g

O
2
Transf
er
rate

S
02
g
ð3Þ
Where
S
O2_g
represents
the
O
2
concentration
in
the
gas
phase,
S
O2in_g
the
gas
phase
O
2
mass
flow
rate
supplied
to
the
digester
and
S
O2_g
the
gas
phase
O
2
mass
flow
rate
leaving
the
digester
together
with
the
biogas
effluent.
2.3.
Model
implementation
A
manual
calibration
of
the
most
sensitive
model
parameters
was
carried
out.
Several
simulations
were
performed
in
order
to
identify
the
parameters
that
would
influence
the
experimental
outputs
the
most.
The
initial
conditions
of
the
model
resolution
were
obtained
from
simulations
until
steady
state
conditions
were
reached
and
process
parameters
(mainly
COD
concentrations
and
pH)
were
similar
to
the
initial
values
of
the
experimental
data.
This
is
a
widely
accepted
method
for
estimating
the
initial
conditions
in
anaerobic
digesters
[25].
2.4.
Input
conditions
A
complete
characterization
of
the
sewage
sludge
was
carried
out
weekly,
along
with
the
collection
of
fresh
sludge
from
Valladolid
WWTP.
This
characterization
was
assumed
to
hold
until
the
next
characterization
and
only
the
inlet
flow
was
measured
daily.
The
concentrations
of
H
2
S
and
HS

were
estimated
from
the
measurement
of
the
total
sulfur
and
the
equilibria
equation
as
a
function
of
the
pH.
The
content
of
carbohydrates,
proteins
and
lipids
was
assumed
to
correspond
to
20%,
65%,
15%
of
the
degradable
organic
matter,
respectively
[26].
Similarly,
inerts
were
assumed
to
be
30%
of
the
total
COD.
The
dissolved
VFAs,
inorganic
nitrogen,
sulfate,
sulfide
and
oxygen
concentrations
were
taken
directly
from
the
weekly
experimental
characterization
of
the
sewage
sludge.
3.
Results
and
discussion
3.1.
Reactor
operation
conditions
Fig.
1
shows
the
characteristics
of
the
feed
to
the
anaerobic
digester
throughout
the
period
modelled.
The
sludge
flow
rate
averaged
9
-
12
L
d
1
,
although
significant
drops
and
peaks
occurred
during
digester
operation.
These
fluctuations
are
neces-
sary
in
order
to
test
the
model’s
response
to
transient
conditions
and
unstable
reactor
loads.
Likewise,
the
solid
content
and
the
organic
matter
concentration
inside
the
digester
showed
varia-
tions
during
the
experimental
period.
Although
the
total
COD
concentration
seems
to
experience
the
greatest
fluctuation,
this
variability
is
strongly
related
to
the
experimental
error
of
the
COD
measurement
method
when
analyzing
a
semi-solid
substrate
such
as
sewage
sludge.
The
VS
concentration
was
correlated
to
the
total
COD
concentration.
It
is
worth
stressing
that
the
sewage
sludge
used
in
this
study
exhibited
a
significant
concentration
of
VFAs
and
sulfur
compounds,
which
are
crucial
to
generate
an
adequate
environment
for
SRB
bacteria
to
thrive.
Dissolved
sulfide
was
present
in
the
sewage
and
consequently
in
the
sludge.
3.2.
Parameters
calibration
The
sensitivity
analysis
(data
not
shown)
indicated
that
only
few
parameters
could
be
calibrated
in
a
dependable
way.
Thus,
Table
1
Petersen
matrix
of
the
new
biochemical
reactions
added
to
the
ADM1.
Process
S
H
2S
S
S
S
02_l
S
IC
S
IN
X
C
X
SOB
Rate
Uptake
of
H
2
S
by
SOB
1
(1-
Y
SOB
)
-
(1-Y
SOB
)/64
-
S
C
i
v
i
-Y
SOB
*N
BAC
Y
SOB
k
mSOB
*(S
H
2S
/(Ks
H
2S
+
S
H
2S))*(S
02
/(Ks
O2
+
S
02
))*
X
SOB
;
Decay
of
SOB
-C
BAC
+
C
XC
-N
BAC
+
N
XC
1
1
k
decSOB
*
X
SOB
Hydrogen
sulfide
(kmol
m
3
)
Elemental
sulfur
(S

)
(kmol
m
3
)
Dissolved
oxygen
(kmol
m
3
)
Inorganic
carbon
(kmol
m
3
)
Inorganic
nitrogen
(kmol
m
3
)
Composites
(
kg
COD
m
3
)
Sulfur
oxidizing
bacteria
(kg
COD
m
3
)
A.
Donoso-Bravo
et
al.
/
Biotechnology
Reports
20
(2018)
e00293
3

some
kinetic
parameters
of
X
SOB
were
set
as:
K
S_H2S
and
K
S_O2
(affinity
constants)
=
310
3
g
L
-1
;
Y
SOB
(biomass
yield)
=
0.25
g
g
-1
;
k
dec
(decay
coefficient)
=
0.02
d
-1
.
These
values
were
chosen
based
on
previous
simulations
in
order
to
avoid
the
washout
of
the
SOB
from
the
digester
and
lied
in
the
same
order
of
magnitude
as
those
microorganisms
present
in
the
anaerobic
digestion
process.
Furthermore,
these
values
were
in
agreement
with
the
fact
that
a
significant
fraction
of
the
SOB
population
was
present
over
the
layers
of
sulfur
accumulated
in
the
digester
headspace
according
to
a
DGGE
analysis
[23].
The
hydrolysis
parameters
were
optimised
by
trial
and
error
to
minimize
the
squared
value
of
the
difference
between
predicted
and
experimental
methane
production
curves.
The
values
of
the
calibrated
parameters
are
presented
in
Table
2,
which
compiles
five
stoichiometric
coefficients
and
one
kinetic
parameter
calibrated.
This
difference
was
induced
by
the
type
of
experimental
data
since
a
continuous
operation
without
controlled
changes
in
the
inlet
conditions
(such
as
hydraulic
or
organic
overloads)
suits
better
the
estimation
of
stoichiometric
parameters
compared
to
that
of
kinetic
parameters
[25].
Indeed,
a
stable
continuous
operation
is
basically
driven
by
process
stoichiometry
rather
than
by
process
kinetics.
The
calibrated
parameter
k
m_SOB
,
related
to
the
maximum
growth
rate
of
sulfur
oxidizing
bacteria,
showed
that
this
type
of
microorganism
grows
5–6
and
10-12-fold
faster
than
acidogenic
and
methanogenic
communities,
respectively,
which
is
in
agree-
ment
with
the
difference
between
the
metabolism
of
aerobic
and
anaerobic/facultative
microorganisms.
The
stoichiometric
value
of
the
methane
conversion
(C
CH4
)
increased
by
20%
compared
to
the
reference
value
[20]
since
a
constant
bias
was
observed
in
regards
to
the
methane
composition
of
the
biogas
generated
in
our
pilot
digesters.
The
coefficient
parameters
associated
to
N
metabolism
were
also
calibrated
due
to
different
properties
of
sludge
used
in
this
study
compared
to
those
used
in
the
original
ADM1
model.
In
fact,
several
authors
recommend
the
calibration
of
the
stoichio-
metric
parameters
associated
to
the
N
metabolisms
for
every
substrate
fed
into
the
digester
[21].
The
only
physical-chemical
parameter
calibrated
was
the
pipe
resistance
coefficient
(k
P
),
which
governs
the
biogas
flow
estimation
and
determines
the
head
loss
of
the
outlet
gas.
This
expression,
which
assumes
an
overpressure
in
the
headspace
of
the
digester,
represents
the
preferred
expression
since
it
yields
smoother
values
of
the
biogas
flow
than
the
original
one
[20].
The
value
of
this
parameter
depends
on
the
physical
properties
of
the
digester
and
should
be
modified
according
to
the
specific
properties
of
the
target
set-up.
In
our
particular
case,
overpressures
ranging
from
10
to
20
mbar
were
recorded
throughout
the
digester’s
operation,
which
resulted
in
a
k
P
of
7

10
4
(Table
2).
3.3.
Model
performance
Figs.
2
and
3
show
the
simulation
results
of
the
modified
ADM1
model
along
with
the
experimental
offline
(i.e
measurements
in
the
anaerobic
broth)
and
online
data
(biogas
production
and
composition
data
and
pH
in
the
anaerobic
broth),
respectively.
The
online
data
corresponds
to
the
composition
of
the
biogas
produced
and
the
pH
of
the
anaerobic
broth
in
the
digester.
Both
the
methane
and
CO
2
content
simulation
matched
the
experimental
data
(Figure
a,b)
as
well
as
the
pH
value
and
remained
constant
because
microaeration
did
not
affect
them
significantly.
Even
though
the
pH
was
slightly
overestimated
by
the
model’s
predictions,
it
remained
at

7.5
(close
to
the
typical
pH
value
of
anaerobic
digesters)
(Fig.
2e).
The
biogas
flow
rate
was
very
well
predicted
by
the
model’s
simulation,
although
there
were
some
random
under
and
overestimation
of
this
variable
during
digester
operations
(Fig.
2f).
Therefore,
the
model
was
able
to
reproduce
the
most
common
on-line
variables
monitored
during
AD
operation.
On
the
other
hand,
the
average
H
2
S
and
O
2
concentrations
predicted
in
the
gas
phase
was
in
agreement
with
the
average
empirical
concentrations
measured
(Fig.
2c
and
d).
However,
the
model
was
not
able
to
reproduce
the
random
H
2
S
peaks
observed
during
the
period
evaluated.
Interestingly,
those
H
2
S
peaks
did
not
match
any
sudden
rise
in
the
sulfate
inlet
concentration
or
in
soluble
H
2
S
concentrations
in
the
digester
broth
(Fig.
3).
Previous
works
have
hypothesized
that
the
biological
oxidation
of
H
2
S
may
also
occur
in
the
headspace
of
the
digester
and
in
the
superior
layer
of
the
anaerobic
broth
based
on
the
high
abundance
of
SOB
bacteria
recorded
by
the
DGGE
analysis
[23].
A
simple
consider-
ation
of
biomass
retention
was
consequently
proposed
to
partially
overcome
the
limitation
identified,
while
maintaining
the
model’s
complexity.
The
biomass
retention
approach,
which
is
presented
in
the
next
section,
separates
the
hydraulic
retention
time
and
the
biomass
retention
time,
in
this
case,
for
the
SOB
microorganism.
The
decreasing
trends
in
total
organic
matter
(measured
as
total
COD
and
VS
concentrations)
observed
up
to
day
115th
as
well
as
the
slight
bounce
back
from
this
day
onwards
were
both
properly
represented
by
the
model
(Fig.
3a,
c).
Likewise,
the
simulation
of
the
evolution
of
the
soluble
COD
concentration
was
in
agreement
with
the
empirical
values
throughout
the
entire
operational
time
(Fig.
3b).
Likewise,
the
inorganic
nitrogen
concentration
was
also
properly
predicted
by
the
model,
thus
validating
the
calibration
of
the
stoichiometric
parameters
conducted
in
the
previous
section.
Fig.
3e
also
confirmed
the
ability
of
the
ADM1
extension
to
describe
the
soluble
H
2
S
concentration
in
the
anaerobic
broth.
In
contrast,
the
soluble
sulfate
concentration
in
the
anaerobic
broth
was
overpredicted
and
only
matched
when
values
were
above
0.3
kmol
L
1
,
which
were
in
agreement
with
the
results
reported
by
[14].
3.4.
Effect
of
the
biomass
retention
Empirical
observations
of
anaerobic
digesters
operated
under
microaerobic
conditions
have
shown
that
SOB
may
form
a
biofilm
inside
the
digester
headspace,
thus
part
of
H2S
oxidation
may
be
carried
out
at
the
biofilm
surface.
Hence,
Kobayashi
et
al
[27]
identified
SOB
in
microbial
mats
located
on
the
top
of
the
biodigester,
where
elemental
sulfur
accumulated.
Therefore,
a
new
parameter
in
the
S
mass
balance
equation
was
proposed
in
order
to
take
this
biofilm
based
H
2
S
oxidation
into
account.
This
parameter,
defined
as
“alpha”,
multiplies
the
X
SOB
leaving
the
system
and
thus
modifies
the
retention
time
of
this
microbial
population.
This
is
conceptually
described
in
the
mass
balance
shown
in
Eq.
(4)
dX
SOB
dt ¼
alphaDX
SOB
þ
growth
rate

decay
ð4Þ
Where
D
is
the
dilution
rate
or
the
inverse
of
the
hydraulic
retention
time
(HRT)
Fig.
4
depicts
the
new
model
predictions
of
the
soluble
and
gaseous
H
2
S
as
a
function
of
different
alpha
values
compared
to
the
experimental
data.
The
influence
of
the
presence
of
SOB
(blue
line)
Table
2
Calibrated
parameters
of
the
model.
Type
of
parameter
Units
Calibrated
value
Kinetic
k
m
_
SOB
d
1
160
Stoichiometric
C
ch4
kmole
C
kg
COD1
0.0187
N
xc
kmole
N
kg
COD1
0.001
N
I
kmole
N
kg
COD1
8

10
4
N
aa
kmole
N
kg
COD1
6

10
3
N
bac
kmole
N
kg
COD1
0.019
Physical-chemical
k
P
m
3
d
1
bar
1
7

10
4
4
A.
Donoso-Bravo
et
al.
/
Biotechnology
Reports
20
(2018)
e00293

Fig.
2.
Time
course
of
the
online
measurements
of
the
concentration
of
methane
(a),
carbon
dioxide
(b),
hydrogen
sulphide
(c)
and
oxygen
(d)
in
the
biogas,
pH
in
the
anaerobic
digestion
broth
(e)
and
biogas
flow
rate
(f).
Experimental
data
(circles),
model
simulation
(continuous
line).
Fig.
3.
Time
course
of
the
offline
measurements
of
the
total
COD
(a),
soluble
COD
(b),
volatile
solids
(c),
sulfate
(d),
soluble
hydrogen
sulfide
(e)
and
inorganic
nitrogen
(f)
in
the
digester.
Experimental
data
(circles),
model
simulation
(continuous
line).
Fig.
4.
Time
course
of
the
H
2
S
concentration
in
the
liquid
(a)
and
gas
(b)
phases
at
different
alpha
values.
Experimental
values
(symbols),
Black
line
=
No
SOB,
blue
line
=
alpha
1
(no
retention),
Green
line
=
alpha
0,4,
orange
line
=
alpha
0.25
and
grey
line
=
alpha
0.1
(For
interpretation
of
the
references
to
colour
in
this
figure
legend,
the
reader
is
referred
to
the
web
version
of
this
article).
A.
Donoso-Bravo
et
al.
/
Biotechnology
Reports
20
(2018)
e00293
5

in
the
anaerobic
broth
compared
to
the
scenario
without
these
H
2
S
oxidizing
microorganisms
(black
line)
in
both
soluble
and
gas
phases
was
significant.
These
new
simulations
also
showed
the
impact
of
variations
in
biomass
retention
on
the
soluble
and
gas
H
2
S.
Model
simulation
of
these
two
variables
improved
signifi-
cantly
when
the
alpha
value
decreased
(=
enhanced
retention
of
the
SOB
in
the
digester).
Hence,
the
formation
of
biofilms
at
the
digester
headspace
maybe
partially
modeled
by
adding
this
biomass
retention
artifact.
This
model
approach
has
been
successfully
performed
in
anaerobic
filters
treating
vinasse
wastewater
[28].
In
brief,
despite
more
physico-chemical
reactions
should
be
considered
when
describing
H
2
S
oxidation
in
anaerobic
digesters
operated
under
microaerobic
conditions
[16,29];
the
approach
here
validated
represents
a
good
trade-off
between
complexity
and
reality.
3.5.
Elemental
sulfur
accumulation
It
is
known
that
one
of
the
main
shortcomings
of
the
application
of
microaeration,
as
a
H
2
S
removal
method,
is
the
accumulation
of
elemental
sulfur
in
the
digester.
The
build-up
of
this
compound
may
lead
to
multiple
operational
hurdles
such
as
pipeline
clogging,
hindered
mixing
or
even
digester
damage
due
to
an
excessive
weight
increase.
Based
on
the
negligible
aqueous
solubility
of
elemental
sulfur,
an
estimation
of
the
accumulation
of
this
element
in
the
reactor
can
be
carried
out
using
the
ADM1
extension
developed
here.
Fig.
5
shows
the
time
course
of
the
mass
of
S

generated
in
the
pilot
reactor
during
the
operational
period
analyzed
here.
Five
kg
of
elemental
sulfur
could
have
potentially
accumulated
in
the
pilot
digester
over
a
period
of

200
days
of
operation.
This
number
should
be
deemed
as
a
theoretical
maximum
since
part
of
the
S

produced
was
dragged
out
with
the
outlet
digestate.
This
estimation
of
the
S

accumulation
in
the
digester
can
be
used
to
plan
the
necessary
maintenance
measures.
Therefore,
the
model
developed
in
this
study
represents
a
useful
operational
tool
for
AD.
4.
Conclusions
An
extension
of
the
ADM1
capable
of
describing
H
2
S
removal
from
biogas
based
on
microaeration
was
developed
and
evaluated
using
experimental
data
from
a
pilot
anaerobic
digester.
The
maximum
specific
growth
rate
of
the
SOB
along
with
four
stoichiometric
coefficients
involved
in
nitrogen
metabolism
were
estimated
during
model
calibration.
The
model
accurately
described
the
most
conventional
variables
monitored
in
anaerobic
digestion
processes
(i.e
biogas
flow,
CH
4
and
CO
2
concentrations,
pH
and
organic
matter
removal).
The
average
concentrations
of
the
S-related
compound
(i.e.
soluble
SO
4
and
H
2
S
in
the
gas
and
liquid
phase)
were
properly
described.
Unfortunately,
the
model
exten-
sion
provided
a
poor
description
of
the
variations
in
the
concentration
of
S
compounds
under
transient
conditions.
Further
model
improvements
may
be
carried
out
by
separating
biological
H
2
S
oxidation
in
different
sections
of
the
digester
or
by
even
considering
H
2
S
oxidation
in
the
headspace
biofilm
on
top
of
the
digester.
Acknowledgment
University
of
Valladolid
is
also
gratefully
acknowledged
from
the
post-doctoral
grant
of
Israel
Diaz.
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