Global J. of Engg. & Appl. Sciences, 2012: 2 (2)
Research paper: Pushpendra Kumar Sharma et al., 2012: Pp.178-182
MODELLING OF COD REDUCTION IN A UASB REACTOR
Pushpendra Kumar Sharma, Nasim Ahmad Khan* and Sohail Ayub*
Dept. of Env. Engg., HCST, Mathura.
*Dept. of Civil Engg., AMU, Aligarh
ABSTRACT
In the present study an attempt has been made to develop a mathematical model for COD reduction in an
UASB reactor. The reactor is operated at steady state under a given set of process conditions and the reactor
contents are completely mixed. For successful operation of a UASB reactor the operational parameter specific
substrate utilization rate kept in the range of 0.30-0.36 kg COD/kg V ss d. which is used in the model
development to evaluate effluent substrate concentration. The values of COD removal efficiency predicted by
the proposed model are in close agreement with the experimental results available in the literature.
INTRODUCTION
UASB reactor is getting wide applications during
recent years for the treatment of a variety of
industrial wastewaters. Over 300 full scale plants
have been installed and commissioned in various
parts of the world (Chui and Fang, 1994) there is a
continuous need for a better understanding of their
mechanisms. In this respect mathematical modeling
offers a number of potential benefits. A review of
literatures reveals scanty informations available
regarding the modeling aspects of the process. COD
removal is an important parameter to evaluate the
performance of the process. Therefore, in the
present study an attempt has been made to develop
a mathematical model for COD reduction in an
UASB reactor. The reactor usually consists of three
parts, sludge bed, sludge blanket and the settler. On
this basis a COD reduction model can be visualized
and presented through Fig. 1. The wastewater
enters the reactor at the bottom and flows upwards
through a bed of relatively dense sludge and a
blanket of sludge particles. The substrate comes in
contact with the biomass and eventually gets
converted into biogas and cells (Bhatia et al., 1985;
Bolle et al., 1986a and Bolle et al., 1986b). The gas
bubbles thus produced pass through the bed and
cause excellent mixing so that adequate contact is
made available between the biomass and the
substrate. The fluid flow in the settler can be
described as plug flow. The rising gas bubbles,
produced in the sludge bed strengthen the
bypassing effects but reduce the dead spaces. In the
sludge bed, the bacteria are sufficiently supplied, so
that enough gas is produced for mixing. In the lower
parts of the bed the gas bubbles rise slowly because
of the compactness of the bed. At higher places in
the sludge blanket, the gas bubbles will rise faster,
giving better mixing. The back mix flow from the
blanket to the bed is generalized to replenish the
volumes of the gas bubbles (plus their wake) that
have already left the sludge bed. The flow rate is
dependent on the flow rate of gas (Heertjes et al.,
1978).
For the model shown in Fig 1 the following
notations may be considered. Suffix d represents
178
the ideally mixed region in the sludge bed and t
represents the same in the blanket and pf
represents the plug flow (settler) region.
Q
= Wastewater flow entering and leaving the
reactor. (m3/d).
Qbp = The part of flow (Q), bypassing the sludge bed.
Qd = The part of flow (Q), entering the sludge bed.
Qdt = The liquid flow from bed to blanket. (m3/d)
Qtd = Backmix flow of liquid from blanket to bed.
(m3/d)
So = Influent substrate concentration. (kg/m3)
Xo = Influent biomass concentration. ( kg/m3)
V d = Volume of sludge bed. (m3)
Sd = Substrate concentration in bed. (kg/m3)
Xd = Biomass concentration in bed. (kg/m3)
rsd = Rate of substrate conversion per unit vol. in
bed. (kgCOD/m3.d)
rst = Rate of substrate concentration per unit vol. in
blanket. (kgCOD/m3.d)
V t = Volume of sludge blanket. (m3)
St = Substrate concentration in blanket.(kg/m3)
Xt = Biomass concentration in blanket. (kg/m3)
Xe = Effluent biomass concentration. (kg/m3)
Se = Effluent substrate concentration. (kg/m3)
D
= Specific substrate utilization rate (kg
COD/kg.VSS.d)
Model Development: Substrate conversion and
COD reduction are closely related to each other. To
evaluate COD reduction efficiency of the UASB
system, mass balance for substrate utilization is
carried out around the bed and blanket (Fig.1),
resulting in equations (1) and (2) (Bowker, 1983;
Hulshoff Pol and Lettings, 1986).
Sludge bed:
V d. . dSd = Qd.So + Qtd.St – Qdt.Sd – qd.Xd.Vd…(1)
dt
Sludge blanket
V t . dSt = Qbp.So + Qdt.Sd – Qtd.St – Q.St – qt.Xt.Vt…(2)
dt
Under pseudo – steady state conditions,
dSd = 0 and dSt = 0
dt
dt
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Global J. of Engg. & Appl. Sciences, 2012: 2 (2)
From Eqn.(1),
0 = Qd.So + Qtd.St – Qdt.Sd – qd.Xd.Vd. ……(3)
Vd = Qd.So + Qtd.St – Qdt.Sd ………(4)
qd.Xd
Also from Eqn.(3),
St = Qdt.Sd + qd.Xd.Vd – Qd.So……(5)
Qtd
Now from Eqn.(2)
O = Qbp.So + Qdt.Sd – Qtd.St – Q.St – qt.Xt.Vt …(6)
Therefore,
Vt = Qbp.So + Qdt.Sd – Qtd.St. – Q.St ……(7)
qt.Xt
Also from Eqn.(6) we get ,
St = Qbp.So + Qdt.Sd – qt.Xt.Vt …… (8)
Qtd + Q
Equating Eqn. (5) and (8),
Qdt.Sd + qd.Xd.Vd – Qd.So = Qbp.So + Qdt.Sd - qt.Xt.Vt
Qtd
Qtd + Q
or,
Qdt.Sd.Qtd + qd.Xd.Vd.Qtd - Qd.So.Qtd + Q.Qdt.Sd +
Q.qd.Xd.Vd – Q.Qd.So =
Qtd .Qbp.So + Qtd.Qdt.Sd – Qtd.qt.Xt.Vt
or,
Q.Qdt. Sd = Qtd.Qbp.So – Qtd.qt.Xt.Vt – qd.Xd.Vd.Qtd +
Qd.So.Qtd – Q.qd.Xd.Vd +
Q.Qd.So
= So(Qtd.Qbp + Q.Qd + Qd.Qtd) – qd.Xd.Vd(Q+Qtd) –
Qtd.qt.Xt.Vt
Hence,
Applying mass balance for flow around sludge bed
and at point A (Fig.1),
Qdt = Qd + Qtd…… (10)
Q = Qd + Qbp……… (11)
Or, Qd = Q – Qbp … (12)
Using Equations (10) and (12) can be further
modified as given below ,
So[Qtd.Qbp + Q(Q-Qbp) + (Q – Qbp) Qtd]
Sd = - qd.Xd.Vd(Qd+Qbp+Qtd) – Qtd.qt.Xt.Vt
Q.Qdt
So (Qtd.Qbp + Q2 – Q.Qbp + Q.Qtd – Qbp.Qtd)
Or, Sd = - qd.Xd.Vd(Qd+Qbp+Qtd) – Qtd.qt.Xt.Vt
Q.Qdt
= Q.So.(Q-Qbp+Qtd) – qd.Xd.Vd(Qbp+Qdt) – Qtd.qt.Xt.Vt
Q.Qdt
Or,
Experimental observations reveal that most of the
influent COD is removed in sludge bed which has a
very high concentration of biomass as compared to
179
that in the sludge blanket. It implies that the most of
the substrate is converted to methane, carbon
dioxide and biological solids in the bed itself rather
than blanket. Specific substrate utilization rate in
the blanket may be considered to be negligible
because no appreciable substrate conversion is
accomplished in the blanket due to absence of a
high concentration of viable biomass. Keeping these
in view, following assumptions may be adopted. (i)
Xt is very very small as compared to Xd. (ii)
Substrate utilization rate (qt) in blanket is very very
small as compared to that (qd) in sludge bed. (iii) Sd
remains unchanged in blanket and settler i.e (Jewell
and Switzenbaum, 1980; Jewell, 1981 and Jones and
Hall, 1989).
Sd ≈ St ≈ Se
Applying these assumptions to equations (13),
Sd = Q.So.Qdt – qd.Xd.Vd (Qbp + Qdt) ……… (14)
Q.Qdt
Assuming that the reactor is operating at steady
state under a given set of process
conditions and if the reactor contents are
completely mixed Qbp may be negligible
(i.e. Q = Qd). Thus equation (14) can be further
simplified as,
Sd = Q.So.Qdt – qd.Xd.V d.Qdt
Q.Qdt
Sd = Q.So – qd.Xd.Vd ……(15)
Q)
i.e. Se = Q.So – qd.Xd.vd........ (16)
Q
Equation (16) represents a simplified mathematical
model to evaluate effluent substrate
concentration from the reactor. For a reactor under
consideration the values of various parameters
such as flow rate (Q), influent substrate
concentration (So), volume of sludge bed (Vd),
biomass concentration in the sludge bed (Xd),
hydraulic retention time (HRT), organic loading
rate (OLR), sludge loading rate (SLR), etc. affecting
the reactor performance are available (Table 1)
(Mosey, 1983; Parkin and Owen, 1986).
Volume of the reactor = 11.4 l
Hydraulic retention time (HRT) = 4 hrs
Biomass concentration in sludge bed (Xd) =
70.68 g/l
 Average values are shown in parentheses
These parameters can be used to estimate the value
of effluent substrate concentration.



Manjunath (1987) suggested that the reactor
should be operated at specific substrate utilization
rate. (q) values above the limiting values (i.e.q>qlim).
The limiting values of substrates utilization rat
(qlim) were reported in the range of 0.059 – 0.174 kg
COD/kg Vss.d. Keeping this in view various values
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Global J. of Engg. & Appl. Sciences, 2012: 2 (2)
of specific substrates utilization rate were selected
in the range of 0.05 – 0.38 kg COD/kg Vss.d to
evaluate the corresponding values of effluent
substrate
concentration/treatment
efficiency
(Table (1) and (2))
Equations (17) – (19) represent the regression
analysis of the data presented, through Table (2).
So = 1350 mg/1: y = - 3.937x + 1.351; (r =
0.999)…(17)
So = 1800 mg/1: y = - 4.692x+1.799; (r =
0.999)……(18)
So = 2100 mg/1: y = - 5.529x+ 2.101; (r =
0.999)……(19)
Where y = Effluent substrate concentration (kg.m3)
x= Specific substrate utilization rate (kg COD/kg Vss
d)
r= coefficient of correction
For successful operation (i.e. COD removal
efficiency ≈ 85-95%) of a UASB reactor it has been
observed (Table (2) ; Equations (17 –19) that the
operational parameters (Table 1), the values of
specific substrates utilization rate should be kept in
the range of 0.30 – 0.36 kg COD/kg Vss d. The values
of specific substrate utilization rate may be adopted
as 0.31 kg COD/kg V SS.d (for SO = 1350 mg/1), 0.35
kg COD.kg VSS.d (for SO = 1800 mg/1) and 0.35 kg
COD/kg VSS.d (for SO = 2100 mg/1) and Used in the
model developed to evaluate effluent substrate
concentration (Table 2) (Pol et al., 1983; Van der
Meer and Heertjes, 1983 and Lettings et al., 1984).
Model Verification
Model proposed in the preceding section (Eqn.16)
is verified with the help of data available in (Table1).
For Influent substrate concentration
SO = 1350 mg/1> = 1.35 kg/m3
Organic loading rate (OLR) = 8.1 kg COD.m3d
Qd = 0.31 kg COD/kg VSS d
Xd = 70.68 kg/m3
Vd = 3.80 x 10-3 m3 (from Table 6.1)
Q = V = 11.4 x 10 -3 m3 = 68.4 x 10 3 m3/d
T
4/24
d
From Eqn(16)
Se = 68.4 x 10 -3 x 1.35 – 0.31 x 70.68 x 3.8 x 10-3
68.4 x 10 -3
= [ 92.84 – 83.26] x 10-3]
68.4x 10-3
= 0.13275 Kg/m3
= 132.75 mg/1
COD removal efficiency (%) =
(1350 – 132.75) x 100 = 90.0%
1350
For influent substrate concentration
SO = 1800 mg/1 = 1.8 kg/m3
Organic loading rate (OLR) = 10.80 kg COD/m3.d
Qd = 0.35 kg COD/kg VSS.d
Xd = 70.68 kg/m3
180
V d = 4.54 x 10-3 m3 (table 6.1)
Q = 68.4 x 10-3 m3/d
Se = 68.4x10-3 x 1.8 – 0.35x70.68x4.54x10-3
68.4 x 10-3
= 123.12 x 10-3 – 112.31 x 10-3
68.4 x 10-3
3
= 0.1580 kg/m
= 158 mg/1
COD removal efficiency
= [1800 – 158] x 100 = 91.0%
1800
And
For influent substrate concentration (Table 3)
So = 2100mg/1 = 2.1 kg/m3
Organic loading rate (OLR) = 12.60 kg COD/m3.d
Qd = 0.35 kg COD/kg VSS.d
Xd = 70.68 kg/m3
V d = 5.35 x 10-3 m3 (Table 6.1)
Q = 68.4 x 10-3 m3/d
Se = 68.4x10-3 x 2.1 – 0.35 x 70.68 x 5.35 x 10-3
68.4 x 10-3
= 143.64x10-3 – 132.35 x 10-3
68.4x 10-3
= 0.1651 Kg/m3 = 165.1 mg/1
COD removal efficiency =
[2100-165.1] x 100 = 92.0%
2100

Volume of the reactor = 11.4 1

Hydraulic retention time (HRT) = 4 hrs

Biomass concentration in Sludge bed (Xd) =
70.68 kg/m3

Average values are shown in parentheses
CONCLUSIONS
The present study can be concluded as follows:
1. A mathematical model for COD reduction in an
UASB reactor is obtained as :
Se = Q.So.Qdt – qd.Xd.Vd(Qbp+Qdt)
Q.Qdt
When the reactor contents are completely mixed
then Qbp may be negligible (i.e. Q = Qd). Thus the
model can be further simplified as
Se = Q.So – qd.Xd.Vd
2. For successful operation (i.e. COD removal
efficiency = 85 – 95%) of a UASB reactor it has
been observed that for the operational parameters
the values of specific substrate utilization rate
should be kept in the range of 0.30-0.36 kg COD/kg
V ss d. The value of specific substrate utilization rate
may be adopted as 0.31 kg COD/kg V SS.d (for So =
1350 mg/1), 0.35 kg COD/kg VSS.d (for So = 1800
mg/1) and 0.35 kg COD/Kg VSS.d (for So = 2100
mg/1) and used in the model developed to evaluate
effluent substrate concentration.
3. Table-3; compares the values of COD removal
efficiency obtained by the proposed model with
those obtained experimentally. The values of COD
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Global J. of Engg. & Appl. Sciences, 2012: 2 (2)
removal efficiency predicted by the proposed model
are in close agreement with the experimental
results available in the literature.
REFERENCES
Bhatia, D., Vieth, W.R and K. Vankatasubramaniant.
1985. Steady-state and transient Behavior in
Microbial Methanification. Mathematical
Modeling and Verification Biotechnology and
Bioengineering. XXVII: 1199-1207.
Bolle, W.L., Van Breugel, J., Van Eybergen, G.C.,
Kossen, N.W.F and R.J. Zoe Te Meyer. 1986a.
Modelling the liquid Flow in Up-Flow
Anaerobic
Sludge
Blanket
reactors.
Biotechnology
and
Bioengineering.
XXVIII:1615-1620.
Bolle, W.L., Van Breugel, J., Van Eybergen, G.C.,
Kossen, N.W.F and W. Van Gills. 1986b. An
Integral Dynamic model for the UASB
Reactor. Biotechnology and Bioengineering.
XXVIII: 1621-1636.
Bowker, R.P.G. (1983). New wastewater Treatment
for Industrial Applications. Environment
Progress, 2(4):235-242.
Graef, S.P and J.F. Andrews. 1974. Stability and
control of Anaerobic Digestion. J.Water Poll.
Control. Fed, 46:666-683.
Heertjes, P.M. and R.R. Van der Meer. `1978.
Dynamics of liquid flow in an Up-flow reactor
used for Anaerobic Treatment of wastewater.
Biotechnology and Bioengineering. XX: 15771594.
Hulshoff Pol, L and G. Lettings. 1986. New
Technologies for Anaerobic Wastewater
Treatment. Wat. Sci. Tech. 18(12): 41-53.
Jewell, W.J and M.S. Switzenbaum. 1980. Anaerobic
Attached Film Expand Bed Reactor
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Treatment. J. Water Pollut. Control, 52(7):
1953-65.
Jewell W.J. 1981. Development of the Attached
Microbial Film Expanded Bed process for
Aerobic and Anaerobic Waste Treatment.
Biological Fluidized Bed Treatment of Water
and Wastewater. Cooper, P.F. and Atkinson,
B. (eds.) Ellis Horwood, Chichester, England.
Jones, R.M. and Hall, E.R. (1989). Assessment of
Dynamic Models for a High Rate Anaerobic
Treatment Process. Env. Tech. Letters,
10(6):551-556.
Lettings, G., Pol, L.W.H., Koster, I.W., Homba, W.M.,
Dezeeuw, W.J., Rinzema, A., Grin, P.C.
Roersma, P.E and S.W. Homba. `1984. High
Rate Anaerobic wastewater Treatment using
the UASB reactor under a wide range of
Temperature conditions. Biotechnology and
Genetic Engineering. Reviews, II: 392-399.
Mosey, F.E. 1983. New Development in the
anaerobic treatment of industrial Wastes.
Effluent and Waste Treatment Journ. XXIII(5):
85-93.
Parkin, G.F and W.F. Owen. 1986. Fundamentals of
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Pol, L.H.W., Dezeeuw, W.J., C.T.M and G. Lettings.
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Biotechnology and Bioengineering, XXV:25312556.
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Global J. of Engg. & Appl. Sciences, 2012: 2 (2)
Table-1: Analysis of effluent substrate
Influent
substrate
concentration
(mg/l)
Organic
loading rate
(OLR)
(kg COD/m3d)
COD removal
efficiency
(%)
Effluent
substrate
concentration
(mg/l)
Volume of
sludge bed (Vd)
(l)
Sludge loading
rate (SLR)
kg COD/kg Vss d
1350
1800
2100
8.10
10.80
12.60
90-92 (91)
94-96 (95)
94-97 (95)
135-108 (121.5)
108-72 (90)
126-63 (94.5)
3.80
4.54
5.35
0.339
0.391
0.372
Table-2: Evaluation of the Specific Substrate Utilization Rate
Influent Substrate
Concentration
So = 1350 mg/l
Influent Substrate
Concentration
So = 1800 mg/l
Influent Substrate
Concentration
So = 2100 mg/l
Specific
Substrate
Utilization
rate qd
(kgCOD/kg
Vss d)
Effluent
substrate
concentration Se
(kg/m3)
COD
removal
efficiency
(%)
Specific
Substrate
Utilization
rate qd
(kgCOD/kg
Vss d)
Effluent
Substrate
Concentration
Se
(kg/m3)
COD
removal
efficiency
(%)
Specific
Substrate
Utilization
rate qd
(kgCOD/kg
Vss d)
Effluent
Substrate
concentration Se
(kg/m3
COD
removal
efficiency
(%)
0.05
0.10
0.20
0.30
0.31
0.32
0.33
0.34
1.150
0.960
0.560
0.170
0.132
0.092
0.050
0.014
15
29
56
87
90
93
96
99
0.05
0.10
0.20
0.30
0.31
0.32
0.33
0.34
0.35
1.565
1.330
0.860
0.390
0.346
0.299
0.250
0.200
0.160
13
26
52
78
81
83
86
89
91
0.05
0.10
0.20
0.30
0.31
0.32
0.33
0.34
0.35
1.824
1.548
0.996
0.444
0.390
0.330
0.280
0.200
0.170
13
26
52
79
81
84
87
90
92
0.36
0.37
0.38
0.110
0.060
0.020
94
97
99.9
0.36
0.37
0.38
0.110
0.060
0.002
95
97
100
Table-3: Comparison between COD removal efficiency (Verification)
Influent
Substrate
Concentration
So (mg/1)
1350
1800
2100
Organic
Loading rate
(OLR)
(Kg COD/M3d)
8.10
10.80
12.60
COD removal
Efficiency
(Experimental)
(%)
90-92(91)
94-96 (95)
94-97(95)
Fig.1 COD reduction model
COD removal
Efficiency
Predicted by the
Model (%)
90
91
92
************
182
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