Discussion by G.v.R. Marais
O'Connor and Eckenfelder
1 in 1960 proposed the first model for aerated lagoons. They assumed
complete mixing and first order degradation of total BOD5 in the lagoons.
Let R = retention time in days Sj = influent BOD5 S = lagoon BOD s , K = first order kinetic
constant in log e -days
The differential equation for BOD5 in the lagoon can then be written
dS/dt = S./R + (K + l/R)S
(1)
which has the steady state solution, when dS/dt = 0:
S =Sj/(KR + 1)
( 2 )
One may extend the solution to a series of lagoons with retention times Ri, R 2
R n :
S n = Si / [ (KRj + 1) (KR 2 + 1)
(KR n + 1)] ( 3 )
where S n = BOD 5 from the nth lagoon.
If the lagoons in series all have the same retention time, R:
S n = Si/(KR + l)n
( 4 )
As the number of lagoons in series increases, for the same total retention time, the effluent from
the series can be shown to approach the value for a plug flow or batch system:
Let Rj = nR. For a fixed Rj as n ->°°, R - > 0 and writing t = R j then in the limit.
S = S i e "
K t
( 5 )
One can now show that for the same total retention time plug flow gives the highest reduction and
the single lagoon the lowest reduction of BOD 5 . In a series system as the number of lagoons increases
per fixed total retention time, the reduction increases from that of a single lagoon to approach the
value for the batch configuration. Consequently, the single lagoon and batch configuration defines two
reduction limits and the series of two or more lagoons intermediate reduction conditions.
If one can show that experimentally the batch and single lagoon configurations give results
kinetically consistent it seems reasonable to conclude that the results will also be consistent for
intermediate series operation: referring to O'Connor and Eckenfelder's paper
1 , batch and single pond
data are presented for cannery wastes. The data was adjusted to a common temperature of 25°C (using
Θ = 1,085) and the single lagoon values plotted Sj/s versus R to give an estimate of K
2 (Figure 1).
Using this value of K the theoretical reductions were calculated for both the single lagoon, equation
(2), and the batch condition, equation (5), and the experimental results superimposed (Figure 2). It is
evident that for this waste the two configurations are kinetically consistent so that one may conclude
that there will also be consistency for the series configuration.
Bratsch and Randall
3 attempted to fit equation (2) to effluent data from a series of 5 lagoons with
retention times of 2, 1, 1, 1 and 1 days. They found that for the summer conditions a value of K = 2,5
was necessary to give the measures effluent BOD5. This value of K is so far outside the range of
expected values (0,3 to 1,0 at 20°C) that an explanation must be sought. The most likely one is that K
was calculated from the single lagoon formulation, equation (2). If the series equation (3) is used, a
value of K = 0,6 gives the same reduction; this value is much more reasonable. If one should
accept the value K = 0,6 it serves as confirmation of the advantage of series operation predicted
theoretically for first order type reaction: for example if these lagoons were consolidated into a single
lagoon of 6 days retention the percentage BOD remaining would be about 22% instead of 7% from the
series. On the basis of these observations the writer questions the Authors' statement that there is no
advantage in series operation.
A further point needs to be mentioned regarding series operation. During winter months when the
K value decreases to low values, say 0,2, unless the lagoons have been designed to give at least 70%
reduction of BOD at the low temperature there is little merit in series operation. Assume a series of
two lagoons is designed to give 60% reduction in winter with K = 0,2, then from equation (4) one may
deduce the following equation to determine the total retention time:
R T = n [(So/S)
l / n - l ] /K
(6)
499
O'Connor and Eckenfelder
1 in 1960 proposed the first model for aerated lagoons. They assumed
complete mixing and first order degradation of total BOD5 in the lagoons.
Let R = retention time in days Sj = influent BOD5 S = lagoon BOD s , K = first order kinetic
constant in log e -days
The differential equation for BOD5 in the lagoon can then be written
dS/dt = S./R + (K + l/R)S
(1)
which has the steady state solution, when dS/dt = 0:
S =Sj/(KR + 1)
( 2 )
One may extend the solution to a series of lagoons with retention times Ri, R 2
R n :
S n = Si / [ (KRj + 1) (KR 2 + 1)
(KR n + 1)] ( 3 )
where S n = BOD 5 from the nth lagoon.
If the lagoons in series all have the same retention time, R:
S n = Si/(KR + l)n
( 4 )
As the number of lagoons in series increases, for the same total retention time, the effluent from
the series can be shown to approach the value for a plug flow or batch system:
Let Rj = nR. For a fixed Rj as n ->°°, R - > 0 and writing t = R j then in the limit.
S = S i e "
K t
( 5 )
One can now show that for the same total retention time plug flow gives the highest reduction and
the single lagoon the lowest reduction of BOD 5 . In a series system as the number of lagoons increases
per fixed total retention time, the reduction increases from that of a single lagoon to approach the
value for the batch configuration. Consequently, the single lagoon and batch configuration defines two
reduction limits and the series of two or more lagoons intermediate reduction conditions.
If one can show that experimentally the batch and single lagoon configurations give results
kinetically consistent it seems reasonable to conclude that the results will also be consistent for
intermediate series operation: referring to O'Connor and Eckenfelder's paper
1 , batch and single pond
data are presented for cannery wastes. The data was adjusted to a common temperature of 25°C (using
Θ = 1,085) and the single lagoon values plotted Sj/s versus R to give an estimate of K
2 (Figure 1).
Using this value of K the theoretical reductions were calculated for both the single lagoon, equation
(2), and the batch condition, equation (5), and the experimental results superimposed (Figure 2). It is
evident that for this waste the two configurations are kinetically consistent so that one may conclude
that there will also be consistency for the series configuration.
Bratsch and Randall
3 attempted to fit equation (2) to effluent data from a series of 5 lagoons with
retention times of 2, 1, 1, 1 and 1 days. They found that for the summer conditions a value of K = 2,5
was necessary to give the measures effluent BOD5. This value of K is so far outside the range of
expected values (0,3 to 1,0 at 20°C) that an explanation must be sought. The most likely one is that K
was calculated from the single lagoon formulation, equation (2). If the series equation (3) is used, a
value of K = 0,6 gives the same reduction; this value is much more reasonable. If one should
accept the value K = 0,6 it serves as confirmation of the advantage of series operation predicted
theoretically for first order type reaction: for example if these lagoons were consolidated into a single
lagoon of 6 days retention the percentage BOD remaining would be about 22% instead of 7% from the
series. On the basis of these observations the writer questions the Authors' statement that there is no
advantage in series operation.
A further point needs to be mentioned regarding series operation. During winter months when the
K value decreases to low values, say 0,2, unless the lagoons have been designed to give at least 70%
reduction of BOD at the low temperature there is little merit in series operation. Assume a series of
two lagoons is designed to give 60% reduction in winter with K = 0,2, then from equation (4) one may
deduce the following equation to determine the total retention time:
R T = n [(So/S)
l / n - l ] /K
(6)
499