Modelling of the periodic anaerobic baffled reactor (PABR) based on the retaining factor concept

Article abstract of DOI:10.1016/S0043-1354(00)00137-8

The fact that the active biomass is continuously removed from the continuously stirred anaerobic digesters, leading to long retention times, has been overcome in a number of high rate systems based on immobilization of the active biomass, such as the Upflow Anaerobic Sludge Blanket Reactor (UASBR) and the Anaerobic Baffled Reactor (ABR). A kinetic model of glucose consumption, which was developed based on a batch kinetic experiment, was used for the development of a dynamic model for the prediction of the behaviour of the recently developed flexible reactor called the Periodic Anaerobic Baffled Reactor (PABR). The PABR may be operated as a UASBR, an ABR or at an intermediate mode. The key assumption of the model is that the hydraulic behaviour of a PABR is equivalent with the behaviour of CSTRs in series as concerning the dissolved matter, whereas the biomass is allowed to be retained in the PABR through a retention factor accounting for precipitation. The model adequately predicted the experimental behaviour of a glucose fed PABR. The model was subsequently used to examine the behaviour of the PABR as a function of operating conditions, both for constant and varying loading rates. It was shown that for different cases, the reactor should best be operated as a UASBR or as an ABR. The fact that the active biomass is continuously removed from the continuously stirred anaerobic digesters, leading to long retention times, has been overcome in a number of high rate systems based on immobilisation of the active biomass, such as the Upflow Anaerobic Sludge Blanket Reactor (UASBR) and the Anaerobic Baffled Reactor (ABR). A kinetic model of glucose consumption, which was developed based on a batch kinetic experiment, was used for the development of a dynamic model for the prediction of the behaviour of the recently developed flexible reactor called the Periodic Anaerobic Baffled Reactor (PABR) [(1998) Wat. Sci. Technol. 38(8-9), 401- 408]. The PABR may be operated as a UASBR, an ABR or at an intermediate mode. The key assumption of the model is that the hydraulic behaviour of a PABR is equivalent with the behaviour of CSTRs in series as concerning the dissolved matter, whereas the biomass is allowed to be retained in the PABR through a retention factor accounting for precipitation. The model adequately predicted the experimental behaviour of a glucose fed PABR. The model was subsequently used to examine the behaviour of the PABR as a function of operating conditions, both for constant and varying loading rates. It was shown that for different cases, the reactor should best be operated as a UASBR or as an ABR. (C) 2000 Elsevier Science Ltd.

Full text of DOI:10.1016/S0043-1354(00)00137-8

Wat. Res. Vol. 34, No. 15, pp. 3725±3736, 2000
7
2000 Elsevier Science Ltd. All rights reserved
Printed in Great Britain
0043-1354/00/$ - see front matter
PII: S0043-1354(00)00137-8
www.elsevier.com/locate/watres
MODELLING OF THE PERIODIC ANAEROBIC BAFFLED
REACTOR (PABR) BASED ON THE RETAINING FACTOR
CONCEPT
$
$M
M
I. V. SKIADAS , H. N. GAVALA
and G. LYBERATOS*
Laboratory of Biochemical Engineering and Environmental Technology, Department of Chemical
Engineering, University of Patras, 26500, Rion, Greece
(
First received 1 June 1999; accepted in revised form 1 January 2000)
AbstractÐThe fact that the active biomass is continuously removed from the continuously stirred
anaerobic digesters, leading to long retention times, has been overcome in a number of high rate
systems based on immobilisation of the active biomass, such as the Up¯ow Anaerobic Sludge Blanket
Reactor (UASBR) and the Anaerobic Ba‚ed Reactor (ABR). A kinetic model of glucose consumption,
which was developed based on a batch kinetic experiment, was used for the development of a dynamic
model for the prediction of the behaviour of the recently developed ¯exible reactor called the Periodic
Anaerobic Ba‚ed Reactor (PABR) [(1998) Wat. Sci. Technol. 38(8±9), 401±408]. The PABR may be
operated as a UASBR, an ABR or at an intermediate mode. The key assumption of the model is that
the hydraulic behaviour of a PABR is equivalent with the behaviour of CSTRs in series as concerning
the dissolved matter, whereas the biomass is allowed to be retained in the PABR through a retention
factor accounting for precipitation. The model adequately predicted the experimental behaviour of a
glucose fed PABR. The model was subsequently used to examine the behaviour of the PABR as a
function of operating conditions, both for constant and varying loading rates. It was shown that for
di€erent cases, the reactor should best be operated as a UASBR or as an ABR. 7 2000 Elsevier
Science Ltd. All rights reserved
Key wordsÐmodelling, periodic anaerobic ba‚ed reactor, PABR, anaerobic digestion, biomass reten-
tion factor, kinetics
INTRODUCTION
The Anaerobic Ba‚ed Reactor (ABR), initially
developed by McCarty and coworkers (Bachmann
The main problem of the continuously stirred tank
reactor (CSTR) during the anaerobic treatment of
wastewaters, i.e. the fact that the active biomass is
through a bed of anaerobic sludge after being trans-
continuously removed from the system leading to
long retention times, has been overcome in a num-
ABR does not require the sludge to granulate in
ber of systems based on immobilisation of the
et al., 1982, 1985), consists of a cascade of ba‚ed
compartments where the wastewater ¯ows upward
ported to the bottom of the compartment. The
order to perform e€ectively, although granulation
does occur over time (Barber and Stuckey, 1999).
active biomass. Such a typical reactor (Lettinga,
1
980) is the Up¯ow Anaerobic Sludge Blanket
Experiments with lab-scale reactors have shown
that the ABR is very stable under shock loads due
to its compartmentalised structure (Nachaiyasit and
Stuckey, 1997a, b). In addition, the ABR has many
potential advantages, i.e. no requirement of biomass
with unusual settling properties and low capital and
operating costs coupled with mechanical simplicity
Reactor (UASBR). In the UASBR the microorgan-
isms are kept in the reactor due to the production
of the highly ¯occulated, well settled, compact
sludge granules which develop. Granular UASBR is
the system of choice for low to medium-high
strength wastewaters containing low or easily
hydrolysable solids.
(
Barber and Stuckey, 1999). From a reactor design
point of view a UASBR resembles a well-mixed
reactor, whereas an ABR resembles a plug-¯ow
$Current address: Anaerobic Microbiology/Biotechnology
Research Group, Department of Biotechnology, reactor (Grobicki and Stuckey, 1991, 1992).
Technical University of Denmark, Building 227, DK-
2
Author to whom all correspondence should be addressed.
Tel.: +30-61-997-573; fax: +30-61-993-070; e-mail:
lyberatos@chemeng.upatras.gr
The Periodic Anaerobic Ba‚ed Reactor (PABR)
800, Lyngby, Denmark.
was initially developed by Skiadas and Lyberatos
1998) and consists of two concentric cylinders. The
area between the cylinders is compartmentalised so
*
(
3725

3
726
I. V. Skiadas et al.
that the reactor resembles an ABR with the com- it behaves as a UASBR; and (b) for smaller values
partments arranged in a circular manner in the of the organic loading the PABR should be oper-
annular region (Fig. 1(a)). The wastewater enters ated at smaller frequencies approaching that of an
the digester at the down¯ow section of the feeding ABR (Skiadas and Lyberatos, 1998). In addition,
(
®rst) compartment, comes up at the up¯ow section when a PABR is operated without switching of the
of the same compartment and passes on to the next feeding point (namely as an ABR), it fails when a
second) compartment through the outer tubing. relatively high step increase in the hydraulic reten-
(
The ¯ow pattern is repeated at the third and fourth tion time (HRT) is imposed. The PABR, when
compartments. Wastewater eventually leaves the operated with periodic switching of the feeding
system after passing through the up¯ow part of the point, is able to approach a stable periodic state
e‚uent compartment, which is the fourth one in (SPS) when exposed to the same step change (Skia-
counterclockwise order. The role of the four com- das and Lyberatos, 1998). The above simulation
partments is periodically changed by proper switch- predicted that for a four day HRT and 16 g/l in¯u-
ing (on or o€) the 12 valves of the outer tubing, in ent Chemical Oxygen Demand (COD) concen-
a clockwise manner. For instance, when A is the tration, the PABR performance in SPS was
feeding compartment (Fig. 1(b)), D will be the e‚u- optimum when operated at the UASBR mode (high
ent one and valves 1, 3, 6, 9, 11 are switched on, switching frequency) with 12 g/l e‚uent COD con-
while valves 2, 4, 5, 7, 8, 10, 12 are switched o€. centration and 2.4 g/l biomass concentration. In
Likewise, whenever the feeding compartment is the contrast, experiments with a 15 l PABR, fed with a
B, C or D, the e‚uent one will be the A, B or C, glucose-based synthetic wastewater of the same
respectively. In the extreme of zero switching fre- in¯uent COD concentration and at the same HRT,
quency (no switching) the reactor behaves as an resulted in about 1 g/l e‚uent COD concentration
ABR. In the other extreme (in®nite frequency) the with a biomass concentration varying between 31
compartments become identical so that the reactor and 57 g/l (Skiadas, 1998). The di€erence between
should behave like a UASBR. By setting the switch- the model prediction and the experimental results is
ing frequency, a great ¯exibility is obtained, taking attributed to the high biomass retention in the com-
advantage of the optimal reactor con®guration partments of the PABR, that a simple CSTR model
(UASBR, ABR or ``something in between'') neglects. The objective of this work is the develop-
depending on the loading conditions. ment of an appropriate new model that will ade-
The fact that the PABR has residence time distri- quately describe the anaerobic digestion of glucose
bution equivalent to four well mixed reactors in in the PABR.
series (Skiadas and Lyberatos, 1998) allows simu-
lation of the PABR, using kinetic models that were
developed for the anaerobic digestion in continu-
ously stirred tank anaerobic digesters. Simulation
employing the model of Smith et al. (1988) (acido-
genesis of glucose and methanogenesis are taken iment was carried out in a continuously stirred batch an-
into account considering unionised volatile fatty aerobic digester. The digester was inoculated with 1900 ml
MATERIALS AND METHODS
In order to determine the microbial growth constants
under mesophilic conditions (358C), a batch kinetic exper-
of inoculum preadapted to a glucose-based synthetic med-
acids (VFAs) concentration as a key parameter and
ium (Skiadas and Lyberatos, 1998). The adaptation took
methanogenesis as the rate limiting step) showed
that: (a) for large values of organic loading, the
place in a 15 l anaerobic digester fed in a draw and ®ll
manner (once a day an amount of supernatant anaerobic
PABR is expected to perform better when operated liquor was replaced by the same amount of synthetic med-
ium). Thus, the biomass was allowed to accumulate in a
period of 100 days up to a concentration of 14 g/l (Skia-
das, 1998). The batch digester was fed with 100 ml glucose
at a high frequency of switching feed point, namely
medium containing 30 g/l C
casein, 4 g/l yeast extract, 5 g/l NaHCO
6
H
12
O
6
ÁH
2
O, 4 g/l hydrolysed
and trace min-
3
erals. Measurements included concentration of dissolved
carbohydrates, lactic acid, VFAs, volatile suspended solids
(
VSS), dissolved COD, biogas production and composition
and pH.
In order to verify the predictions of the simulations, a
four compartment PABR was constructed out of stainless
steel with a total useful volume of 15 l. The PABR was
inoculated with 15 l of the glucose preadapted inoculum
which was used for the above kinetic experiment, and it
was started up at 0.2 g COD/l d organic loading rate
(
1
OLR) and a switching period of 1 day. During a time of
00 days the OLR was increased gradually to 4.55 g
COD/l d at a four day HRT and the biomass concen-
tration reached the value of 31 g/l due to its accumulation
in the compartments of the PABR. The digester behaviour
Fig. 1. (a) Front view of a four compartment PABR. (b)
Top view of a four compartment PABR. 1, 2, . . ., 12 was examined under three di€erent SPSs at switching
valves. wÁ Up¯ow, ꢀ Down¯ow.
periods of 1, 1.5 and 2 days, respectively. Once the diges-

Modelling of the PABR
3727
ter approached a SPS, dissolved COD and VFAs concen-
tration were measured in each compartment during a time
of one switching period. Biogas composition and pro-
duction rate were measured as well. The digester was
maintained under mesophilic (358C) conditions.
batch experiment, the total carbon of the consumed
glucose is greater than the total carbon of the pro-
duced VFAs, lactate and biogas. Furthermore, the
2
measured dissolved COD value (1600 mg O /l) is
Determinations of dissolved COD and VSS were carried greater than the sum of the COD values of the
out as described in Standard Methods. Glucose concen-
2
VFAs and lactate (500 mg O /l), but the di€erence
tration was measured colorimetrically according to Josefs-
son (1983). Lactic acid concentration was measured using
the diagnostic kits and reagents of ``Sigma Chemical Com-
(
sumed glucose in 1 h. These observations indicate
1100 mg O
2
/l) is smaller than the COD of the con-
pany, Sigma DiagnosticsÐUSA''. VFAs were measured that accumulation of some undetermined intermedi-
by a Flame Ionisation Gas Chromatograph. The biogas
production rate was measured by displacement of a dilute
olism), as well as accumulation of intracellular
sulphuric acid solution. The biogas composition was calcu-
ate products (as the end product of bacterial metab-
intermediate products of bacterial metabolism, is
lated from the volume of the remaining methane gas after
the proper injection of speci®c volume biogas samples into taking place during batch anaerobic digestion of
a system of communicating vessels containing a sodium glucose. Hence, an important improvement to a
hydroxide solution (Skiadas, 1998).
model for the anaerobic digestion of glucose would
be the assumption of this intermediate accumu-
lation.
RESULTS AND DISCUSSION
Batch experiment
Kinetic model development
The present kinetic study showed (Fig. 2) that
It has been reported (Pullammanappallil, 1993)
the anaerobic decomposition of glucose to methane that the response of continuously stirred tank an-
and carbon dioxide passes through the production aerobic digesters to an increase of OLR cannot be
of lactic, acetic and propionic acid. The concen- predicted precisely enough by mathematical models
trations of other VFAs such as butyrate were negli- developed so far and describing the anaerobic diges-
gible, compared to those of acetate and propionate tion of carbohydrates in suspended growth. Such
(data not shown). In addition, despite the complete models predict that the VFAs accumulation takes
consumption of glucose during the ®rst hour of the place earlier than it is observed. This happens
Fig. 2. Batch experimental results as well as model predicted values of glucose, lactate (a), propionate,
acetate, IP (b) concentration, biogas production (c) and COD concentration (d) vs time.

3
728
I. V. Skiadas et al.
mediate (®nal and/or intracellular) product, from
now on referred to as IP. Subsequently, di€erent
groups of acidogenic bacteria convert lactate and IP
(rate r2 and r3, respectively) to a mixture of acetate
and propionate. The propionate is converted by the
acetogenic bacteria to acetate (rate r4) and ®nally
4 2
the methanogens produce CH and CO (rate r5)
using acetate as substrate. Also, it is assumed that
all the above ®ve consumption rates follow simple
Monod kinetics:
mmax i ‰Ci Š
ri ˆ
X
ꢁ1†
Ksi ‡ ‰Ci Š
where mmax i is the maximum speci®c consumption
rate of the component i, [=]mg Ci=g biomass h, Ksi
is the saturation constant of the component i, [=]
mg/l, i = 1, 2, 3, 4 and 5 for the glucose, lactate,
IP, propionate and acetate, respectively, ‰Ci Š is the
Fig. 3. Anaerobic bioconversion of glucose to biogas.
component
i concentration, [=]mg/l for com-
because these models do not take in consideration: ponents 1, 2, 4, 5 and mg carbon/l for component
a) the accumulation of the intracellular intermedi- 3, X is the total biomass concentration, [=] g/l, and
(
ate products of bacterial metabolism (Pullamma- ri is the consumption rate of component i for pro-
nappallil, 1993); and (b) the consumption of ducts formation and cell synthesis.
carbohydrates by bacteria producing substances
The fact that only part of the total biomass is re-
other than VFAs (such as lactate) and the sub- sponsible for the degradation of a speci®c com-
sequent conversion of these substrates to VFAs by ponent is included in the mmax i constants expression
di€erent groups of bacteria (Costello et al., 1991).
The kinetic model developed in this work is sche-
matically shown in Fig. 3. The conversion of glu-
cose to biogas is completed according to the
stoichiometric reactions shown in Table 1. It is
(Gavala et al., 1999):
mmax i fi
Yx=i
mmax i ˆ
ꢁ2†
assumed that the anaerobic biodegradation of glu- where mmax i is the maximum speci®c growth rate of
cose is completed in ®ve steps: in the ®rst step the the bacteria consuming the component i, Yx=i is the
acidogenic bacteria consume glucose (rate r1) and substrate i biomass yield coecient and fi is the
produce lactic acid, as well as an unknown inter- fraction of the bacteria consuming component i.
Table 1. The substrate consumption and the biomass synthesis stoichiometric reactions used in the model for the anaerobic degradation
of glucose, as well as the resultant stoichiometric biomass yield coecients assuming that one mole of produced ATP provides sucient
energy for the formation of 10 g of biomass (Bauchop and Elsden, 1960)
First and third step. Glucose consumption and production of lactate either
VFAs through IP or lactate
1
X Lac
3
X Ac
� 4
C
C
C
6
6
6
H
H
H
12
12
12
O
O
O
6
6
6
4 2CH
3
CHOHCOOH+2ATP
O 4 2CH COOH+2CO
4 2CH CH COOH+2H
4 6C N+12H
Y
Y
Y
Y
ˆ 1:1111  10 gr biomass/mg produced Lac
� 4
+2H
+2H
2
2
3
2
+4H
2
+4ATP
ˆ 3:3333  10 gr biomass/mg produced Ac
3
X Pr
3
� 4
3
2
2
O+2ATP
ˆ 1:3514  10 gr biomass/mg produced Pr
� 4
5
C
6
H
12
O
6
+6NH
3
5
H
9
O
3
2
O
ˆ 4:2117  10 1 CO
2
/mg produced Ac
CO2 Ac
Second step. Lactate consumption
2
X Pr
2
X Ac
2
CO2 Lac
� 4
CH
CH
3
CHOHCOOH+H
CHOHCOOH+H
2
4 CH
O 4 CH
4 3C
3
CH
COOH+CO
N+6H
2
COOH+H
2
O+0.5ATP
Y
Y
Y
ˆ 0:6577  10 gr biomass/mg produced Pr
� 4
3
2
3
2
+2H
2
+1ATP
ˆ 1:6667  10 gr biomass/mg produced Ac
� 4
5
CH
3
CHOHCOOH+3NH
3
5
H
9
O
3
2
O
ˆ 2:4909  10 1 CO
2
/mg consumed Lac
Fourth step. Propionate consumption (acetogenesis)
CH CH COOH+2H O 4 CH COOH+CO +3H
CH CH COOH+CO +2NH 4 2C N+2H
4
Ac Pr
4
X Pr
3
2
2
3
2
2
+1ATP
Y
Y
Y
ˆ 0:7275 mg produced Ac/mg consumed Pr
� 4
3
3
2
2
3
5 9
H O
3
2
O+H
2
ˆ 1:2126  10 gr biomass/mg consumed Pr,
4
� 4
ˆ 2:9471  10 1 CO
2
/mg consumed Pr
CO2 Pr
Fifth step. Acetate consumption (acetoclastic methanogenesis)
CH COOH 4 CH +CO +0.25ATP
CH COOH+2NH 4 2C N+4H
5
X Ac
5
� 5
3
4
2
Y
Y
Y
ˆ 3:9772  10 gr biomass/mg consumed Ac
� 4
5
3
3
H
5 9
O
3
2
O
ˆ 4:0199  10 1 CH
4
/mg consumed Ac,
CH4 Ac
5
� 4
ˆ 4:0199  10 1 CO
2
/mg consumed Ac
CO2 Ac

Modelling of the PABR
3729
According to this kinetic model, the mass bal- perimentally measured concentrations of the glu-
ances for the anaerobic biodegradation of glucose cose, lactate, propionate and acetate and the
to biogas in a batch continuous stirred digester take respective predicted concentrations. Biogas pro-
the form:
duction was not included in the least-squares objec-
tive equation because this model aims only at the
prediction of the dissolved COD removal. The
GAMS modelling language was used to formulate
the optimisation problem (Brooke et al., 1996).
The proposed model was solved assuming that
the biomass concentration remained constant
during the batch experiment. This is a reasonable
assumption, given the fact that the expected bio-
d‰GlŠ
dt
ˆ
� r1
ꢁ3†
ꢁ4†
d‰LacŠ
ˆ
CE1 Á r1 � r2
dt
d‰IPŠ
dt
ˆ
DE1 Á r1 � r3
ꢁ5† mass growth attributed to the consumption of glu-
cose fed (with the low biomass yield of the
anaerobic bacteria) was negligible compared to the
d‰PrŠ
dt
initial biomass concentration (14 g VSS/l). Also, the
duration of the experiment was comparatively small
ˆ
AL2 Á r2 ‡ AL3 Á r3 � r4
ꢁ6†
(
48 h). The model exhibited a mathematically stable
d‰AcŠ
convergence, yielded reasonable kinetic parameter
values and adequately matched the concentration
response curves for glucose, lactate, propionate and
acetate (Fig. 2(a) and (b)).
The predicted biogas production at time t of the
batch experiment is equal to:
4
Ac Pr
ˆ
BE2 Á r2 ‡ BE3 Á r3 ‡ Y
Á r4 � r5 ꢁ7†
dt
dX
dt
1
X Lac
3
X Pr
ˆ
CE1 Á r1 Á Y
‡ AL3 Á r3 Á Y
2
X Pr
2
X Ac
‡
‡
AL2 Á r2 Á Y
‡ BE2 Á r2 Á Y
ꢀ
t
5
5
4
3
X Ac
4
X Pr
PBP ˆ ꢁY CH Ac Á r5 ‡ Y CO Ac Á r5 ‡ Y CO Pr
BE3 Á r3 Á Y
‡ r4 Á Y
‡ r5
4
2
2
0
5
X Ac
3
2
Á Y
ꢁ8†
Á r4 ‡ Y CO Ac Á BE3 Á r3 ‡ Y CO Lac Á r2†dt ꢁ9†
2
2
where [Gl], [Lac], [IP], [Pr] and [Ac] are the glucose,
lactate, IP, propionate and acetate concentrations,
respectively.
where PBP is the model prediction for the biogas
production, [=]
volume.
l of produced biogas/digester
The factor fi in equation (2) corresponds to a
group of bacteria, the component i consuming bac-
teria, as a fraction of the total biomass. Such a
group consists of bacteria which are using the same
substrate i for their growth, but do not necessarily
lead to the same metabolic end-product. The latter
is re¯ected by the products between the consump-
tion rates (ri) and the parameters CE1, DE1, AL2,
AL3, BE2 and BE3 in the above di€erential
equations, where CE1 is the produced lactic acid
per unit of consumed glucose, [=] mg lactate/mg
glucose, DE1 is the produced IP per unit of con-
sumed glucose, [=] mg carbon of IP/mg glucose,
AL2 is the produced propionic acid per unit of con-
sumed lactic acid, [=] mg propionate/mg lactate,
BE2 is the produced acetic acid per unit of con-
sumed lactic acid, [=] mg acetate/mg lactate, AL3
is the produced propionic acid per unit of con-
sumed IP, [=] mg propionate/mg carbon of IP, and
BE3 is the produced acetic acid per unit of con-
sumed IP, [=] mg acetate/mg carbon of IP.
The model predicts less methane production than
it is experimentally observed (Fig. 2(c)). This hap-
pens because the model does not consider the pro-
2
duction of methane by H -utilising methanogens.
Optimal kinetic parameters obtained from the
simulation process are given in Table 2. Typical
values (according to the literature) for the maxi-
mum speci®c consumption rates are: 1800 mg/g h
for glucose consumption (Ghosh and Klass, 1978);
Table 2. Estimated values of the kinetic parameters
Parameter
Value
Units
� 1
m
max1
mmax2
197.94
2.88
4.82
0.52
1.87
46
11
31
14
32
0.137
0.345
0
0.41
0.66
0.61
mg Gl (g biomass h)
mg Lac (g biomass h)
mg C IP (g biomass h)
�
�
1
1
m
m
m
max3
max4
max5
�
� 1
1
mg Pr (g biomass h)
mg Ac (g biomass h)
mg Gl l
�
1
Ks1
Ks2
Ks3
Ks4
Ks5
CE1
DE1
AL2
AL3
BE2
BE3
�
1
mg Lac l
mg C IP l
mg Pr l
mg Ac l
mg Lac (mg Gl)
mg C IP (mg Gl)
�
1
� 1
�
1
The data from the batch experiment were used to
estimate the values of the kinetic parameters in the
model. A modi®ed non-linear least squares ®tting
method was used and the least-squares objective
was to select the best kinetic parameter values so as
to minimise the squared residuals between the ex-
�
1
� 1
1
�
mg Pr (mg Lac)
�
mg Pr (mg C IP)
1
1
�
mg Ac (mg Lac)
mg Ac (mg C IP)
� 1

3
730
I. V. Skiadas et al.
1912 mg/g h for lactate utilisation (Lee et al., 1974); the total biomass concentration (as VSS) even if a
2
12 mg/g h for propionate (Lawrence and McCarty, considerable portion of the digester VSS content is
1969); and 150 mg/g h for acetate consumption non-viable biomass (which is the case for the an-
(
van den Berg, 1977). Expectedly, the latter values aerobic digesters with high solids retention time), or
are signi®cantly higher in comparison with the re- is the biomass of di€erent bacterial groups than
spective values given in Table 2 because the mmax i these taken into consideration in this model.
values obtained from the literature are equal to Finally, the optimal value of coecient AL2 was
mmax i=Yx=i and do not include the factor fi: The found to be zero, suggesting that the biodegrada-
above typical values are expressed in mg/(g bio- tion of lactate leads only to the production of acet-
mass) h, where biomass is only a speci®c group of ate.
bacteria such as methanogens. On the contrary, the
values for the present simulation process were
based on the assumption that biomass is the total
PABR experimental results
The measured dissolved COD concentration in
bacterial mass contained in the batch digester. In each of the four compartments during a switching
addition, the values given in Table 2 are related to period of one, 1.5 and two days is shown in Fig. 4
Fig. 4. Experimental results for the COD concentration in each compartment of the PABR under SPS
at switching periods (T) of one, 1.5 and two days and the respective model predicted values. For T =
1
d, compartment no. 3 was the e‚uent one between time 0 and 6, compartment no. 2 between time 6
and 12, compartment no. 1 between time 12 and 18 and compartment no. 4 between time 18 and 24.
Similarly, compartment no. 3 was the e‚uent one between time 0 and 9, compartment no. 2 between
time 9 and 18, compartment no. 1 between time 18 and 27 and compartment no. 4 between time 27
and 36 for T = 1.5 d. For T = 4 d, compartment no. 1 was the e‚uent one between time 0 and 12,
compartment no. 4 between time 12 and 24, compartment no. 3 between time 24 and 36 and compart-
ment no. 2 between time 36 and 48.

Modelling of the PABR
3731

3
732
I. V. Skiadas et al.
and the VFAs concentration in each of the four concentration of the e‚uent stream from the same
compartments during a switching period of one and compartment. In contrast, the biomass concen-
two days is shown in Fig. 5. The values at the start tration of the e‚uent stream from each one of the
of a period are equal with those at the end of the four compartments will be equal to ꢁ1 � d†X if the
same period (stable periodic state, SPS). For each biomass concentration in the same compartment is
compartment the COD and the VFAs values are X, where d is a real number (with values between 0
located on a wave-like curve. The four curves are and 1) from now on called the biomass retention
almost identical verifying an SPS. Each curve is factor.
transposed for T/4 in relation with the curve that
Figure 6 shows a circular series of four CSTR,
corresponds to the previous compartment, because which is assumed equivalent to a four compartment
four changes of the in¯uent and e‚uent compart- PABR. Fj is the in¯uent stream of the PABR when
ment occur during a time of one switching period the compartment j is the feeding one ꢁ j ˆ 1, 2, 3 or
(
four compartment PABR). Note that higher 4), Ej is the e‚uent stream of the PABR when the
switching periods lead to larger amplitude oscil- compartment j is the e‚uent one, and Ej, ꢁ j‡1† is
lation of the COD (Fig. 4) and the VFAs (Fig. 5) the ¯ow stream between compartment j and com-
concentrations in each compartment. Note (Fig. 4) partment j + 1. Because of the circular ¯ow pattern,
that the COD concentration at the e‚uent is almost one should have in mind that j + 1 is equal to 1 for
always equal to the lowest COD value in the four j = 4, and j � 1 is equal to 4 for j = 1. The values
compartments (the COD value of the harvesting of the dimensionless factors Fj, Ej and Ej, ꢁ j‡1† may
compartment).
be either 0 or 1 and are switched periodically with
time as the role of the four compartments changes
periodically.
Model development for the PABR
Subsequently, the kinetic model for glucose con-
sumption, which was developed based on the batch E E E E E E2,3 E3,4 E4,1). Then:
1 2 3 4
Consider the parameter vector VF=(F F F F
1
2
3
4
1,2
kinetic experiment, was used for the development of
a dynamic model for the prediction of the PABR
behaviour under constant operating conditions
1
2
3
4
. VF=(1 0 0 0 0 0 0 1 1 1 1 0) when the ®rst com-
partment (Fig. 6) is the feeding and the fourth is
the e‚uent one.
. VF=(0 1 0 0 1 0 0 0 0 1 1 1) when the second
compartment is the feeding and the ®rst is the
e‚uent one.
. VF=(0 0 1 0 0 1 0 0 1 0 1 1) when the third
compartment is the feeding and the second is the
e‚uent one.
. VF=(0 0 0 1 0 0 1 0 1 1 0 1) when the fourth
compartment is the feeding and the third is the
e‚uent one.
(
SPS), as well as of the response of the PABR to
organic loading disturbances. The key assumption
of the dynamic model is that the hydraulic beha-
viour of a four compartment PABR is equivalent
with the behaviour of four CSTRs in series as far
as the substrates and products are concerned,
whereas the biomass is assumed to be retained in
the compartments of the PABR by precipitation.
According to this assumption the glucose, lactate,
IP, propionate and acetate concentration in each
one of the four compartments equals the respective
Consequently, the mass balances for the anaerobic
biodegradation of glucose to biogas in a PABR
simulated with four CSTR type digesters in series
(
Fig. 6) may be compactly written in the form:
2
3
0
j
Gl
‰
GlŠ ‰GlŠj
‰GlŠj
‰LacŠj
‰GlŠj� 1
‰LacŠj� 1
� R
R
6
6
6
7
7
7
j
Lac
0
0
0
0
0
‰LacŠj
‰IPŠj
6
6
6
7
7
7
j
IP
‰IPŠj
‰IPŠj� 1
R
R
R
6
7
6
6
7
7
j
Pr
6
‰PrŠj
‰PrŠj
‰PrŠj� 1
7
6
7
6
6
4
j
7
7
5
‰AcŠj
‰AcŠj
‰AcŠj� 1
Ac
j
ꢁ1 � d†Xj ꢁ1 � d†Xj ꢁ1 � d†Xj� 1 RX
2
3
2
3
d‰GlŠ =dt
j
4
Á D Á Fj
6
6
6
6
6
7
d‰LacŠ =dt 7
6
6
6
6
6
6
4
7
7
7
j
7
7
7
7
� 4 Á D Á Ej
d‰IPŠ =dt
j
7
Â
� 4 Á D Á Ej, j‡1 ˆ 6
ꢁ10†
7
7
5
6
6
6
4
d‰PrŠ =dt 7
j
7
7
5
4 Á D Á Ej� 1, j
Fig. 6. A circular series of four CSTRs that is assumed
equivalent to a four compartment PABR as far as the sub-
strates and products are concerned.
d‰AcŠ =dt
dXj=dt
j
1

Modelling of the PABR
3733
The value of d was estimated by ®tting the above
mathematical model to the values of the e‚uent
COD concentration of the 15-l PABR under three
di€erent SPSs at switching periods of one, 1.5 and
two days, respectively.
A least squares ®tting
method was used, where the system of di€erential
equations [equation (10)] was solved by a fourth-
order Runge±Kutta routine. Since the kinetic par-
ameters of the model had already been determined
during the simulation process of the batch kinetic
experiment, the least-squares objective was to select
the best d value (with no kinetic parameters ma-
nipulation), so as to minimise the squared residuals
between the experimentally measured and the re-
spective predicted values of the mean e‚uent COD
concentration for the three di€erent SPSs. In Fig. 7
the optimal values of the calculated e‚uent COD
concentrations during the time of one period are
graphically compared with the experimental results
Fig. 7. The optimal values of the calculated e‚uent COD from the anaerobic digestion of glucose in the 15 l
concentrations during the time of one period are graphi- PABR. The optimal d value (with a precision of
cally compared with the experimental results from the an-
three decimal digits) obtained from the ®tting pro-
cess was 0.936.
aerobic digestion of glucose in the 15 l PABR. (a) T = 1 d,
(
b) T = 1.5 d and (c) T = 2 d.
The developed dynamic model was validated by
comparing its predictions for the anaerobic diges-
tion of glucose in the PABR with the experimental
results for the COD and VFAs concentration. The
model is capable of predicting adequately the ampli-
tude oscillation of the COD (Fig. 4) and the VFAs
0
where [Gl] is the in¯uent glucose concentration,
Gl] , [Lac] , [IP] , [Pr] , [Ac] and Xj are the glucose,
lactate, IP, propionate, acetate and biomass concen-
[
j
j
j
j
j
trations in the compartment j, D is the dilution rate
j
(
Fig. 5) concentrations in each compartment of the
PABR in SPS for a biomass retention factor d ˆ
:936: Finally, the prediction of the model for the
�
1
(
of glucose consumption in the compartment j),
the inverse of the HRT), [=] h , R ˆ r1j (rate
Gl
0
j
Lac
R
ˆ CE1 Á r1j � r2j (rate of lactate production in
biomass concentration is about 34 g/l and thus in
good correspondence with the aforementioned ex-
perimental results (31 g/l).
j
IP
the compartment j ), R ˆ DE1 Á r1j � r3j (rate of
j
Pr
IP production in the compartment j ),
R
ˆ
AL2 Á r2j ‡ AL3 Á r3j � r4j (rate of propionate pro-
Ac
j
duction in the compartment j), R ˆ BE2 Á r2j ‡ Simulation of the PABR behaviour
4
Ac Pr
BE3 Á r3j ‡ Y
Á r4j � r5j (rate of acetate pro-
j
X
Next, the model was used for the simulation of
the PABR behaviour for several SPSs, as well as
for the prediction of the PABR response to changes
of the HRT. For assessment of the PABR perform-
ance and stability characteristics, the mean rate of
organic matter (COD) removal as a function of the
HRT for a given feed concentration is shown in
Table 3. It can be seen that an optimum value for
the HRT exists for every value of the period. In ad-
ꢁ11† dition, for small enough HRTs, the mean COD
duction in the compartment j ) and R ˆ CE1 Á r1j Á
1
X Lac
3
X Pr
2
X Pr
Y
‡ AL3 Á r3j Á Y
X Ac
‡ AL2 Á r2j Á Y
X Ac
‡ BE2 Á
‡ r5j Á
2
3
4
X Pr
r2j Á Y
X Ac
‡ BE3 Á r3j Á Y
‡ r4j Á Y
5
Y
(rate of biomass production in the compart-
ment j).
The methane production rate may be calculated
by:
X
1
CH4
5
QCH ˆ
ꢁY
Á r5j †, ‰ˆŠ
4
CH4Ac
1
d
j
removal rate is greater at shorter periods of switch-
Table 3. The mean methane production rate and the mean rate of COD removal (optimum values in bold letters) as a function of the
HRT of a four compartment PABR for di€erent values of period (T [=] d). In¯uent COD concentration 15 g/l
T=<<
T = 1
T = 4
T = 12
T=>>
HRT (d)
T=<<
T = 1
T = 4
T = 12
T=>>
0.4156
0.4895
0.5711
0.5977
0.5689
0.4198
0.4973
0.5798
0.5984
0.5687
0.4206
0.4991
0.5826
0.5967
0.5579
0.4206
0.4974
0.5760
0.5862
0.5288
0.4211
0.4786
0.4504
0.3387
6
5
4
3
2
2483
2941
3513
4153
5259
2498
2963
3532
4143
5216
2501
2969
3540
4137
5187
2501
2962
3520
4104
5121
2503
2877
3114
3363
Methane production rate (l/l d)
Mean rate of COD removal (mg/l d)

3
734
I. V. Skiadas et al.
Fig. 8. Predicted response of: (a) an ABR to a step decrease in the HRT from 10 to two days; (b) a
PABR (with a switching period of one day) to the same step decrease in the HRT; (c) a PABR to the
same step decrease in the HRT without switching (ABR), as well as with a switching period of one day
and to the reverse step change after 100 days operation at two days HRT; (d) a PABR to a step
increase of the HRT (from two to 10 days) without switching, as well as with a switching period of one
day.
ing, whereas for large HRTs it is larger at longer PABR when it comes to stability, the following
switching periods. Finally the PABR tends to simulations were undertaken. When a PABR is
behave as a UASBR, as the switching frequency operated without switching of the feeding point
becomes high enough (T= << ). The equivalent (namely as an ABR), it fails when a step decrease
UASBR is then of equal volume to the total volume in the HRT from 10 to two days is imposed, due to
of the four individual compartments. The same methanogen washout (see Fig. 8(a)). The PABR,
exact behaviour is predicted for the mean methane however, when operated with periodic switching of
production rate (see Table 3), whereas again for the feeding point (T = 1 d), approaches an SPS
every value of the period there is an optimum when exposed to the same step change. Thus, it is
HRT. Here, it may also be seen that for small possible to maintain a continued operation in spite
values of the HRT, the mean methane production of the large drop of the HRT (see Fig. 8(b)). When
rate is greater at shorter periods of switching and the same PABR is exposed to the reverse step
exactly the reverse is true for large values of the change in the HRT after 100 days operation at two
HRT. Finally, these conclusions and general trends days HRT (before the methanogens have com-
are valid regardless of the in¯uent COD concen- pletely washed out), it returns back to the initial
tration (see Table 4).
steady state. This reversion is more ecient if the
In order to assess the relative merits of the PABR is operated with periodic switching of
the feeding point (Fig. 8(c)). In the case of zero
switching frequency, the methanogens have almost
Table 4. The mean methane production rate (l/l d) as a function
of the in¯uent COD concentration of a four compartment PABR
for di€erent values of switching period (T ) and HRT
completely washed out from the ®rst three compart-
ments and they need more time to recover. On the
contrary, the response of a PABR at SPS, which is
exposed to the same step increase of the HRT, is
more ecient if it simultaneously will start to be
operated without switching of the feeding point
(Fig. 8(d)). There will be enough time for the bac-
teria to remove more organic content from the ®rst
three compartments.
T = 1
T = 4 T = 12 COD (g/l) T = 1 T = 4 T = 12
0
0
0
.2529 0.2531 0.2533
.5060 0.5063 0.5068
.7591 0.7595 0.7604
15
30
45
0.5687 0.5579 0.5288
1.1495 1.1268 1.0695
1.7293 1.6957 1.6104
HRT=10 d
HRT=2 d

Modelling of the PABR
3735
The predictions of the above developed model for centration, as well as the biomass concentration in
the performance of the PABR in SPS, as well as for the reactor.
the reactor response in a step change of the HRT,
The simulations of the PABR behaviour employ-
are qualitatively similar to those using Smith's ing the new model for the anaerobic digestion of
model (Skiadas and Lyberatos, 1998). This proves glucose in the PABR showed that for large values
that the predictions for the behaviour of the PABR of organic loading, the PABR is expected to per-
are not sensitive to the particular model structure, form better when operated at a high frequency of
at least qualitatively. Given that a series of several switching feed point, namely it behaves as
a
CSTRs provides greater substrate conversion than a UASBR, whereas for smaller values of the organic
CSTR of equal volume for reactions with Monod loading the PABR should be operated at smaller
kinetics (Bailey and Ollis, 1986), the compartmenta- frequencies approaching that of an ABR. Also, the
lised structure of the PABR gives the possibility of simulations showed that depending on the loading
optimising the COD removal rate as a function of rate, which in principle may be variable, it is poss-
the OLR by the manipulation of the switching fre- ible that the switching frequency should be manipu-
quency. When the resulted biomass dilution rate is lated accordingly, allowing for the PABR to be
smaller than the maximum biomass growth rate in operated as an ABR, a UASBR or at an intermedi-
each of the four PABR compartments, the COD ate mode. Consequently, the PABR is best suited
removal is higher at a PABR operated at zero fre- for handling time-varying loading rates since it
quency of switching the feed point (as a ABR). In allows for maximal conversion rates at all times.
contrast, when the biomass dilution rate is relatively
The PABR should prove a useful high rate an-
high but not higher than the overall biomass pro- aerobic system of high ¯exibility and it deserves
duction rate, the COD removal is higher at a further study and characterisation. On the other
PABR operated at high frequency of switching the hand, the above developed model should be a useful
feed point (as an UASBR). For every intermediate tool for the future designing of a pilot scale PABR;
value of the OLR there is a value of the switching despite that, its validity and prediction capacity are
frequency (between zero and in®nite) for which the limited to the conditions under which the exper-
COD removal rate is maximised (see Tables 3 and iments were conducted. Apparently, the constant d
4
). assumption over the four compartments is not quite
The model predicts less methane production than precise. Further experiments need to be carried out
it was experimentally observed due to the neglected (preferably in pilot scale) to determine the par-
production of methane from H2 and CO . Never- ameter d as a function of the PABR operational
2
theless, the usefulness of this model is not reduced parameters such as volumetric and organic loading
since it aims at the prediction of the COD removal rate.
during the anaerobic wastewater treatment in
PABR.
AcknowledgementsÐThe authors wish to thank the
Commission of the European Communities for the ®nan-
cial support of this work under Grant No. BRE2-CT92-
0355.
CONCLUSIONS
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