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Steady state analysis of the coupling aerator and secondary settling tank in activated sludge process
~
Wat. Res. Vol. 30, No. 11, pp. 2601-2608, 1996
Pergamon PII: S0043-1354(96)00158-3
Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0043-1354/96 $15.00 + 0.00
STEADY STATE ANALYSIS OF THE COUPLING AERATOR AND SECONDARY SETTLING TANK IN ACTIVATED SLUDGE PROCESS S. H. C H O ' , H. N. C H A N G 2 a n d C. P R O S T 3 ~Korea Institute of Energy Research, 71-2, Jang-dong, Yusung-gu, Taejon, 305-343, Korea, 2Korea Advanced Institute of Sciences & Technology, 373-1, Kusung-dong, Yusung-gu, Taejon, 305-701, Korea and 3Laboratoire des Sciences du Grnie Chimique, CNRS-ENSIC-INPL B.P.451, 54001, Nancy, France
(First received May 1995; accepted in revised form May 1996) Abstract--The steady state analysis of coupling the function of aerator and secondary settling tank in activated sludge process for wastewater treatment is carried out to obtain appropriate responses of output variables and to decide optimum operating parameters. To consider the effect of the secondary settling tank, limit flux theory is applied and the aerator is assumed to be a continuous flow stirred tank reactor. By using sludge recycle ratio and sludge waste ratio as the operating parameters, the responses of the output variables--biomass concentration in aerator, dissolved pollutant and solid concentration in effluent--are represented as response surfaces and isoresponse curves. Acceptable operating zone can be obtained from the curves and optimum parameters can be determined. Coupling the function of aerator and secondary settling tank is important to consider the appropriate control of an activated sludge process. Copyright © 1996 Elsevier Science Ltd
Key words--activated sludge process, wastewater treatment, control, limit flux, response surface, isoresponse curve, acceptable operating zone
INTRODUCTION
NOMENCLATURE A= C= G= h= H = k= k0 =
surface area of settling tank (m 2) solid concentration factor solid flux in settling tank (kg/hm 2) height in settling tank (m) settling tank height (m) constant in settling model combined coefficient of mass transport and reaction rate (d- ~) k~ = endogenous decay coefficient (d-~) K, = half velocity constant (kg m -3) n = constant in settling model Q = input wastewater flowrate or effluent flowrate (m 3 dor m 3 h -I) R0 = substrate consumption rate (kg/hm 3) R, = biomass increasing rate (kg/hm 3) s = dissolved pollutant (substrate) concentration (kg m -3) t = time (h or d) u = underflow velocity (Q~IA) (mh -t) v = sludge settling velocity (m d -t or m h - ' ) V = aerator volume (m 3) X = biomass concentration (kg m -3) Y --- maximum yield (kg kg- ') ~t = sludge recycle ratio fl = sludge waste ratio 0~ --- mean solid retention time (h or d) Oh = mean hydraulic retention time (h or d)
t
Subscripts e= i= 1= o= u=
supernatant input to settling tank limit flux input to aerator bottom down stream of settling tank
Activated sludge system for biological wastewater t r e a t m e n t consists essentially o f a n a e r a t o r a n d a secondary settling tank. M a n y a u t h o r s studied the activated sludge system, b u t a few o f them considered the role o f the secondary settling t a n k by coupling it with the function of the aerator. M o s t o f them consider that the a e r a t o r works well w i t h o u t any p r o b l e m whether the conditions of sludge thickening or clarification in the secondary settling t a n k are good or not. It is generally t h o u g h t t h a t the p e r f o r m a n c e o f a e r a t o r is i n d e p e n d e n t o f t h a t o f the secondary settling tank. Lawrence a n d M c C a r t y (1970) studied the steady state system o f activated sludge. They o b t a i n e d substrate a n d biomass c o n c e n t r a t i o n s according to the variations of m e a n solid retention time by taking the m a x i m u m recycle c o n c e n t r a t i o n with (Xu)max = 106/SV1. On the other h a n d , Tucek et al. (1971) used (Xu)max= (Ct/(Ct + 1))I06/SVl to calculate the steady state. Brett et al. (1973) designed a model by using Westwerg's results (1967) to control a n activated sludge system. They introduced a modifying function in the balance e q u a t i o n of biomass which consisted o f sludge recycle ratio a n d sludge waste ratio, But they did not consider sludge settling characteristics. S h e r r a r d a n d K i n c a n n o n (1974) correlated m e a n solid retention time with sludge recycle ratio a n d
2601
2602
S.H. Cho et al.
sludge concentration factor in secondary settling tank experimentally. Riddell et al. (1983) tried to combine the functions of secondary settling tank and aerator in order to choose the allowable flowrate of a wastewater treatment plant. They used mean solid retention time and solid yield relative to corresponding effluent flowrate. Sheintuch (1987a, b) introduced the concept of system response for analysing the interactions of the functions of the two units. Many researchers worked on modeling the aerator by using various kinds of biological reaction kinetics in which they considered substrate consumption rate, cell growth and endogenous decay rate, inhibitions, lysis of cells, etc. On the other hand, others studied the role of secondary settling tank independently. And a few of them investigated the interaction between both units, but these are not sufficient to obtain appropriate data to control the system properly. In this paper, the coupled system of aerator and secondary settling tank will be studied using M o n o d - H e r b e r r s simple reaction kinetic model and limit flux theory. The analysis of steady state responses of the system will show a method to obtain the optimum operating parameters; sludge recycle ratio and sludge waste ratio. SYSTEM
ANALYSIS
An activated sludge system can be represented simply in Fig. 1. The material balance on the aerator can be represented as follows by assuming that the aerator is a continuous flow stirred tank reactor. For substrate Qso + otQs, = (1 + ~t)Qs + VRo + V(ds/dt)
(1)
For biomass Qxo + ctQx. + VRg = (1 + ot)Qx~ + V(dxddt)
(2)
The biological reaction kinetics can be used with a simple form of M o n o d - H e r b e r s model: The substrate consumption rate, Ro = (kosxi)/(Ks + s)
Qj So, X 0
( 1 +a)O~ S t X I
The biomass increasing rate, Rg = YRo
- kdXi
The material balance on the secondary settling tank is represented as follows, on the assumption that the biological reaction is negligible in the tank, therefore the substrate concentration is constant (s° = s): (1 + a)Qx, = (ct + fl)Qx. +(1 - ~)Qxe + d dt
foH xAdh
For steady state, from the above equations of material balance, the substrate and biomass concentrations in the aerator can be obtained as follows, by assuming that the entering solid concentration is negligible: Ks(1 + kdOc) s -- YkoOc -- kdOc -- 1
r
oc
Xi--kdOc + 1 ~ ( s ° -
s)
Oc = Oh
Xi
([3Cx, + (1 - fl)x0)
C - ((1 + ~)xi -- (1 -- ]~)Xe) (~ +/~)x~
dG,/dx = (1 - n)kx-" + Qo/A
Fig. 1. Activated sludge system.
(6)
(7)
In equations (4) and (5), 0c is unknown, for 0c and C can be determined according to the performance of the secondary settling tank. To represent the relation between the sludge settling velocity and the concentration, in general, a power model and an exponential model have been used empirically. But the power model does not fit well in dilute solid concentration range, and the application of the exponential model is very complicated. Cho et al. (1993) showed that a pseudo-fluid model (v = k ( e x p ( - n x ) / x ) agrees well with the experimental data, and its application is not quite complex. First, let us try the case of the power model; v = kx-". The total solid flux is the sum of the solid flux due to gravity settling and the convection solid flux due to underflow,
ctQ, Su, Xu sludge waste
(s)
mean solid retention time with C = x,/x~. The solid concentration factor C can be written as follows:
The first derivative of Gt to concentration x is
sludge recyc}e
(4)
where Oh = V/Q; mean hydraulic retention time
Gt = x(kx-" + Q,/A)
Input
(3)
and the second derivative is, d2G,/dx 2 = - n(1 - n)kx -("+ i)
Steady state analysis In the case where n is greater than 1, the second derivative is always positive. Therefore G, passes through a minimum at x = x, where the first derivative is zero. Then the limit flux concentration is:
xI = ((n-Q;)kA)-"" If there is a limit flux layer, the underflow flux will be equal to the limit flux,
=
(iA+(&q
As the limit flux layer, dG,/dx = 0, so kx;” = (QJA).(l/(n - 1)). By applying this to the above equation, G,(G, at x = xl), x, becomes x,(n - 1)/n. By applying the equation for x, and xU = Cx,, into the above equation, the limit solid flux and its concentration can be represented as follows: G, = k(n - I)(+
- l))“(Cu,) -”
x, = Cx,(n -
1)/n
(9) (10)
For the limit flux to be a criterion of thickening operation, its concentration should be greater than the initial solid concentration.
This condition gives the following constraint applying the limit solid flux as criterion:
The solid concentration
in the supernatant
x = ((1 + a) - (a + e
will be
P)Q
(13)
(1 - P)
But in the other case where the initial concentration is greater than the limit flux concentration (xi < x,), i.e. (n - 1)/n < (a + /?)/(I + a), the solid entrainment in the supernatant would depend on the initial flux (G,(x,)) and the applied flux (G,): (clarification criterion). When the applied flux is not larger than the initial flux, G, < G,(x,), there will be no entrainment in the supernatant, and then the concentration factor is equal to equation (11). In an actual activated sludge system, it might not be possible to be a clarification criterion condition. But as a theoretical consideration, all of the case that can be thought with an activated sludge characteristics and concentration, shall be investigated. For the other condition, G, > G,(x), the concentration factor can be obtained from the solid balance C=&+l
(14)
and the solid concentration in the supernatant is equal to equation (13). Now C, x,, 8,, s, x, can be calculated simultaneously. For the case of using the pseudo-fluid model (a = k exp( -nx)/x) for settling, the limit flux and its concentration can be obtained as follows. The equation of solid flux due to gravity is given by an exponential form
for
G = k exp( -nx) and the total flux is
(n - 1)/n > (c( + P)/(l + CI) In this case, two types of activated sludge charge on the settling tank can be considered: G, < G, and G, > G,. If the applied solid flux (G,) is larger than the limit solid flux, the difference between the two flux will be entrained in the supernatant stream and the thickening function will not be sufficient. Let us call this region as thickening criterion boundary. For the first type of charge, G, < G,, the solid content in the supernatant can be considered to be negligible, xe z 0, then the solid concentration factor becomes C = (1 + a)/(cl + B)
2603
G, = k exp( -nx) The first derivative is
dG,/dx = - nk exp( -nx)
+ Qu/A
and the second derivative is d2G,/dxZ = n2k exp( - nx)
Since d2G,/dx2 is positive, G, passes through a minimum G, at point xl where dG,/dx = 0. At this point (x,) G, = k exp(-nxl)
(11)
On the other hand, if the applied solid flux is larger than the limit solid flux, the amount of solid flux at the bottom is equal to the limit solid flux. Then the solid concentration factor is
+ xQu/A
(dG,/dx),,
+ x,Q./A = xuQ./A
r, = - nk exp( -nx,)
+ Qu/A = 0
From the above two equations, x, becomes (x, - l/n), and the concentration of the limit flux layer and the limit flux are obtained as follows: G, = nkCx, exp(1 - nCx,) x, = Cx, - l/n
And
in
the
thickening
criterion
boundary,
nx, 2 (c( + fi)/( 1 - /I), if the applied flux is larger than
2604
S.H. Cho et al. 10
the limit flux, the concentration factor can be represented as
l-
9 8
ln((~ ~ fl~)Q.'~
\
c =
Ank J
(15)
7
In the other Case, C and xo are represented as being the same as the expressions of the power model. For the exponential model, the approaching procedure is similar to the others. But the application is more complicated, because the concentration factor should be calculated using the trial and error method, and the constraints are more complex than the case of the other models.
6
nxi
.2
5
ct = 0.2
o
4
ct = 0.3 ct = 0.4
3 ct = 0.5 ~=0,6 0.=0.8--
2
__ i
c t = 1.0 RESULTS
AND
l
DISCUSSION
To investigate the responses of the output variables---concentrations of solids and dissolved organics in the supernatant and the biomass concentration in the a e r a t o r - - a n d to decide optimum conditions of the operating parameters, the calculation was carried out by using the operating parameters as recycle sludge ratio and waste sludge ratio. The parameters used for this calculation are as follows: Ks; 0.06 g/l; half-velocity constant k0; 5.0 d-~; combined coefficient of mass transport and reaction rate Y; 0.6 g g-~; maximum yield kd; 0.06 d-~; endogenous decay coefficient V; 13,600 m3; aerator volume A; 2750 m2; surface area of settling tank Q; 54,400 m 3 d - I ; entering wastewater or effluent flowrate so; 0.5 g 1 t; entering dissolved pollutant concentration k; 375; constant of power model (when the velocity is represented in m d -~ and the concentration in g 1-~) n; 2.3; index of the power model
o
L
0
0.02
i
i
0.04
0.06
0,1
waste sludge ratio, 13 Fig. 2. Sludge concentration factors in sample case study (k = 375 m d -L, n = 2.3 for power model).
But the limit flux concentrations seen in Fig. 3 does not show such phenomena. This can be understood by equation (8). These limit flux concentrations might be meaningless in the range where any limit flux layer cannot exist. The calculated results are shown in Figs 4--6. Figure 4 shows the responses on the dissolved pollutant concentrations in the aerator or in the supernatant. The tridimensional diagram is the
~2
10 0.=0.1
~
s
0.=
o
In Smollen and Ekama (1984), k values were from 1.5 to 60 m h -~. They used 325 m d-~ for their sample calculation. As our measurement in a wastewater treatment plant, those were between 65 and 460 m d - ' , and the index n was between 1 and 5. Settling characteristics are changed continuously. Here 375 m d -t for k, and 2.3 for n were selected for sample calculation. Before the investigation of responses, the variations of sludge concentration factor and limit flux concentration were calculated for the sample plant conditions with a power model. As can be seen in Fig. 2, concentration factor increases according to the decrease of recycle ratio, or decrease of waste sludge ratio. The rate of increase of the concentration factor becomes quite small after a limit flux layer occurs.
t
0.08
~
0.2
0.=0.3
6
0.=0.4
0.=0.5 r~ = 0.6 "~
0.=0.8 ~=1.0
4
2
0 0
i
)
t
I
0.02
0.04
0.06
0.08
O.I-
waste sludge ratio, p
Fig. 3. Limit flux concentrations in sample case study (k = 375 m d -~, n = 2.3 for power model).
Steady state analysis
2605
V, 375- x'2"3 m/day 100
g
V,3./S.x~Z3m/day
02S
s.SOmg/l
o 0,20
o
~, SO ,."
cl
o
uT 0
,o
2 23.7-
-~
a
40
t.
3O
•*' 0.15
-20
g 0.10
c
"o
O.OS
355
I
I
I
1.0 sludge recycle ratio,
~005 0.035 0.15 sludge waste ratio,
A. Response surface
I
2.0
B. Isoresponse curves
Fig. 4. Responses of the substrate concentration in aerator (k = 375 m d ), n = 2.3 for power model). A, Response surface; B, isoresponse curves.
response surface. If the recycle sludge ratio diminishes or the waste sludge ratio increases, the biomass retention time decreases, accordingly the pollutant concentrations in the supernatant increase. If the biomass retention time becomes smaller than the critical value, the biomass cannot persist in the system and the entering pollutant cannot be diminished. But in Fig. 4, the responses superior to 0.1 g !-) were eliminated to show clearly the responses in the interesting zone. From the response surface diagram, the isoresponse curves were obtained by cutting the response surface with the same concentration. The curves indicate that if the sludge recycle ratio and the waste sludge ratio under the curve are controlled, the pollutant concentration can be maintained to a value inferior to that of the curve.
Figure 5 shows the biomass concentration responses in the aerator. If one decreases the waste sludge ratio down to a value less than 0.035, the entering solid flux into the settling tank becomes superior to the limit flux, therefore the biomass concentration in the aerator does not increase to the solid loss in the supernatant, and the pollutant concentration cannot be decreased any more. Similarly if the operating parameters are controlled to be under the curve, the biomass concentration superior to the value of the curve can be obtained. By decreasing the waste sludge ratio, the biomass concentration can be increased, but there is a limit to decreasing the waste sludge ratio, which is the result of considering settling effect. If the applied solid flux to the settling tank becomes larger than the limit flux due to increasing the biomass concentration, a
V.-375 • x'Z3m/day .
0.2S
V= 375-x'2.3 m/day
•
o-1or "
,,.~"
0.005 0.085 OJS~' ~ sludge ~ a s t e r a t i o ,
A. Response surface
/
/
~
x,
0 __.
sludge
B.
tO recycle
2.0 ratio,
Isoresponse curves
Fig. 5. Responses of the biomass concentration in aerator (k = 375 m d -), n = 2.3 for power model). A, Response surface; B, isoresponse curves.
2606
S.H. Cho et al.
0.06 V : 37S-x"2-3m/day,
V" 375.x"2"3 m/day
0.0.5
X e : l ~
o"
'-i~'z°ss I:~°° l'~2]-°°/
, ~., ~=-o."o~'z,~0".03o.oz "~ 0.01
o.oo 0.035
%o
I
I
I
1.0
I
2.0
sludge recycle ratio,
sludge waste ratio,
A. Response surface
B. Isoresponse curves
Fig. 6. Responses of the solid concentration in supernatant (k = 375 m d -~, n = 2.3 for power model). A, Response surface; B, isoresponse curves.
part of the solid begins to overflow through the weir. Therefore the biomass concentration in the aerator cannot increase any more. As for the solid concentration in the effluent (Fig. 6), if the operating parameters are maintained above the isoresponse curve, the concentration inferior to the value of the curve can be obtained theoretically, with the exception of the solid amount that overflows as small isolated particles. Consequently, if the three kinds of the isoresponse curve are combined, the operating diagram can be obtained (Fig. 7), which can be used to determine the operating parameters to obtain the desirable responses, e.g. s < 30 mg 1-~, x > 3 g 1-~, xe < 30 mg !- ~. Therefore in the crossed line zone in Fig. 7 the minimum recycle sludge ratio and the waste sludge ratio can be determined. The crossed line zone can be called an acceptable operating zone.
0.20
V, 375 • X'2"3m/day
• 0.15-
o.lo
-g 0.0.5
I
I
I
1.0 Sludge recycle ratio.
In Fig. 8, the acceptable operating zones were compared by changing the settling characteristics for pseudo-fluid model. The settling characteristics of Fig. 8(B) for pseudo-fluid model is similar to the characteristics of power model with k = 375 m d -~, and n = 2.3. If the settling characteristics of activated sludge become poor, the zone becomes smaller and narrower (Fig. 8). In particular, if the settling tank is studied separately from the aerator, no solid entrainment can be observed in the supernatant by increasing the recycle ratio, but in Fig. 7 it can be observed easily that if the recycle ratio is increased, the biomass concentration in aerator increases and finally some part of the solid begins to overflow the weir. This means that the secondary settling tank should be studied by combining it with the role of the aerator. As mentioned previously, if the sludge retention time is increased, the biomass concentration increases in the aerator. But if the applied solid flux to the settling tank becomes superior to the limit solid flux, the biomass concentration in the aerator cannot increase any more. However, this point cannot be observed by studying the aerator, like Lawrence and McCarty (1970), without considering activated sludge settling characteristics. This means that the aerator should be studied by coupling it with the settling tank. This steady state analysis will give some tendency of an activated sludge process. Unfortunately since sludge settling characteristics change continuously in activated sludge process, it is difficult to obtain a steady state. In practical wastewater plant, it is impossible to obtain steady state experimental results.
2.0
Fig. 7. Acceptable zone of operating parameters (k = 375 m d -~, n = 2.3 for power model).
CONCLUSIONS The steady state responses of activated sludge process for biological wastewater treatment were
"u
tJ
w
0 e..
° ~o
0.0!
0;10
0.15
0.20
I
I 20
g,
~
t~
o
0
0.05
0.I0
0.15
I 1.0 (131
Sludge recycle
I
•
ratio,
V= 253-exp(-O.344-X)/ X, mid
1
amy
2.0
.0.15
0.05
~, o.1o
&.
o
0.20
Sludge
IC)
recycte ratio,
• 1.0
I
V--Z S3.exp (-O.IG2-X }/X,m/d
Fig, 8. Variation of acceptable operating zone according to the change of settling characteristics (pseudo-fluid model).
(A)
Sludge recycle ratio.
1.0
!
V:379.5 •exp(- 0.344.X1/ X ,m/d
0.Z0
!
o.,
Z.O
eh
2608
S.H. Cho et al.
investigated theoretically by coupling the functions of aerator and secondary settling tank. The responses on biomass concentration in aerator, dissolved pollutant concentration in supernatant and solid entrainment in effluent were represented on the response surface diagrams and the isoresponse curves. By combining the isoresponse curves of the three output variables, the acceptable operating zone was obtained, and the optimum operating parameters (recycle ratio and waste sludge ratio) can be decided. REFERENCES
Brett R. W. J., Kermode R. I. and Burrus B. G. (1973) Feed forward control of an activated sludge process. War. Res. 7, 525-535. Cho S. H., Colin F. and Prost C. (1993) Settling velocity model of activated sludge. Wat. Res. 27(7), 1237-1242.
Lawrence A. W. and McCarthy P. L. (1970) Unified basis for biological treatment design and operation. J. of Sanitary Eng. Div., ASCE SA3, 757-778. Riddell M. D. R., Lee J. S. and Wilson T. E. (1983) Method for estimating the capacity of an activated sludge plant. J. WPCF 55(4), 360-368. Sheintuch M. (1987a) Steady state modeling of reactorsettler interaction. Wat. Res. 21(12), 1463-1472. Sheintuch M. (1987b) Species selection in a reactor-settler system. Biotech. Bioeng. 30, 598-606. Sherrard J. H. and Kincannon D. F. (1974) Operational control concepts for the activated sludge processes. War. & Sewage Works, March, 44-66. Smollen M. and Ekama G. (1984) Comparison of empirical settling velocity equations in flux theory for secondary settling tanks. War. SA 10(4), 175-184. Tucek F., Chudoba J. and Madera V. (1971) Unified basis for design of biological aerobic treatment process. Wat. Res. 5, 647-680~ Westwerg N. (1967) A study of the activated sludge process as a bacterial growth process. War. Res. l, 795-804.
Wat. Res. Vol. 30, No. 11, pp. 2601-2608, 1996
Pergamon PII: S0043-1354(96)00158-3
Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0043-1354/96 $15.00 + 0.00
STEADY STATE ANALYSIS OF THE COUPLING AERATOR AND SECONDARY SETTLING TANK IN ACTIVATED SLUDGE PROCESS S. H. C H O ' , H. N. C H A N G 2 a n d C. P R O S T 3 ~Korea Institute of Energy Research, 71-2, Jang-dong, Yusung-gu, Taejon, 305-343, Korea, 2Korea Advanced Institute of Sciences & Technology, 373-1, Kusung-dong, Yusung-gu, Taejon, 305-701, Korea and 3Laboratoire des Sciences du Grnie Chimique, CNRS-ENSIC-INPL B.P.451, 54001, Nancy, France
(First received May 1995; accepted in revised form May 1996) Abstract--The steady state analysis of coupling the function of aerator and secondary settling tank in activated sludge process for wastewater treatment is carried out to obtain appropriate responses of output variables and to decide optimum operating parameters. To consider the effect of the secondary settling tank, limit flux theory is applied and the aerator is assumed to be a continuous flow stirred tank reactor. By using sludge recycle ratio and sludge waste ratio as the operating parameters, the responses of the output variables--biomass concentration in aerator, dissolved pollutant and solid concentration in effluent--are represented as response surfaces and isoresponse curves. Acceptable operating zone can be obtained from the curves and optimum parameters can be determined. Coupling the function of aerator and secondary settling tank is important to consider the appropriate control of an activated sludge process. Copyright © 1996 Elsevier Science Ltd
Key words--activated sludge process, wastewater treatment, control, limit flux, response surface, isoresponse curve, acceptable operating zone
INTRODUCTION
NOMENCLATURE A= C= G= h= H = k= k0 =
surface area of settling tank (m 2) solid concentration factor solid flux in settling tank (kg/hm 2) height in settling tank (m) settling tank height (m) constant in settling model combined coefficient of mass transport and reaction rate (d- ~) k~ = endogenous decay coefficient (d-~) K, = half velocity constant (kg m -3) n = constant in settling model Q = input wastewater flowrate or effluent flowrate (m 3 dor m 3 h -I) R0 = substrate consumption rate (kg/hm 3) R, = biomass increasing rate (kg/hm 3) s = dissolved pollutant (substrate) concentration (kg m -3) t = time (h or d) u = underflow velocity (Q~IA) (mh -t) v = sludge settling velocity (m d -t or m h - ' ) V = aerator volume (m 3) X = biomass concentration (kg m -3) Y --- maximum yield (kg kg- ') ~t = sludge recycle ratio fl = sludge waste ratio 0~ --- mean solid retention time (h or d) Oh = mean hydraulic retention time (h or d)
t
Subscripts e= i= 1= o= u=
supernatant input to settling tank limit flux input to aerator bottom down stream of settling tank
Activated sludge system for biological wastewater t r e a t m e n t consists essentially o f a n a e r a t o r a n d a secondary settling tank. M a n y a u t h o r s studied the activated sludge system, b u t a few o f them considered the role o f the secondary settling t a n k by coupling it with the function of the aerator. M o s t o f them consider that the a e r a t o r works well w i t h o u t any p r o b l e m whether the conditions of sludge thickening or clarification in the secondary settling t a n k are good or not. It is generally t h o u g h t t h a t the p e r f o r m a n c e o f a e r a t o r is i n d e p e n d e n t o f t h a t o f the secondary settling tank. Lawrence a n d M c C a r t y (1970) studied the steady state system o f activated sludge. They o b t a i n e d substrate a n d biomass c o n c e n t r a t i o n s according to the variations of m e a n solid retention time by taking the m a x i m u m recycle c o n c e n t r a t i o n with (Xu)max = 106/SV1. On the other h a n d , Tucek et al. (1971) used (Xu)max= (Ct/(Ct + 1))I06/SVl to calculate the steady state. Brett et al. (1973) designed a model by using Westwerg's results (1967) to control a n activated sludge system. They introduced a modifying function in the balance e q u a t i o n of biomass which consisted o f sludge recycle ratio a n d sludge waste ratio, But they did not consider sludge settling characteristics. S h e r r a r d a n d K i n c a n n o n (1974) correlated m e a n solid retention time with sludge recycle ratio a n d
2601
2602
S.H. Cho et al.
sludge concentration factor in secondary settling tank experimentally. Riddell et al. (1983) tried to combine the functions of secondary settling tank and aerator in order to choose the allowable flowrate of a wastewater treatment plant. They used mean solid retention time and solid yield relative to corresponding effluent flowrate. Sheintuch (1987a, b) introduced the concept of system response for analysing the interactions of the functions of the two units. Many researchers worked on modeling the aerator by using various kinds of biological reaction kinetics in which they considered substrate consumption rate, cell growth and endogenous decay rate, inhibitions, lysis of cells, etc. On the other hand, others studied the role of secondary settling tank independently. And a few of them investigated the interaction between both units, but these are not sufficient to obtain appropriate data to control the system properly. In this paper, the coupled system of aerator and secondary settling tank will be studied using M o n o d - H e r b e r r s simple reaction kinetic model and limit flux theory. The analysis of steady state responses of the system will show a method to obtain the optimum operating parameters; sludge recycle ratio and sludge waste ratio. SYSTEM
ANALYSIS
An activated sludge system can be represented simply in Fig. 1. The material balance on the aerator can be represented as follows by assuming that the aerator is a continuous flow stirred tank reactor. For substrate Qso + otQs, = (1 + ~t)Qs + VRo + V(ds/dt)
(1)
For biomass Qxo + ctQx. + VRg = (1 + ot)Qx~ + V(dxddt)
(2)
The biological reaction kinetics can be used with a simple form of M o n o d - H e r b e r s model: The substrate consumption rate, Ro = (kosxi)/(Ks + s)
Qj So, X 0
( 1 +a)O~ S t X I
The biomass increasing rate, Rg = YRo
- kdXi
The material balance on the secondary settling tank is represented as follows, on the assumption that the biological reaction is negligible in the tank, therefore the substrate concentration is constant (s° = s): (1 + a)Qx, = (ct + fl)Qx. +(1 - ~)Qxe + d dt
foH xAdh
For steady state, from the above equations of material balance, the substrate and biomass concentrations in the aerator can be obtained as follows, by assuming that the entering solid concentration is negligible: Ks(1 + kdOc) s -- YkoOc -- kdOc -- 1
r
oc
Xi--kdOc + 1 ~ ( s ° -
s)
Oc = Oh
Xi
([3Cx, + (1 - fl)x0)
C - ((1 + ~)xi -- (1 -- ]~)Xe) (~ +/~)x~
dG,/dx = (1 - n)kx-" + Qo/A
Fig. 1. Activated sludge system.
(6)
(7)
In equations (4) and (5), 0c is unknown, for 0c and C can be determined according to the performance of the secondary settling tank. To represent the relation between the sludge settling velocity and the concentration, in general, a power model and an exponential model have been used empirically. But the power model does not fit well in dilute solid concentration range, and the application of the exponential model is very complicated. Cho et al. (1993) showed that a pseudo-fluid model (v = k ( e x p ( - n x ) / x ) agrees well with the experimental data, and its application is not quite complex. First, let us try the case of the power model; v = kx-". The total solid flux is the sum of the solid flux due to gravity settling and the convection solid flux due to underflow,
ctQ, Su, Xu sludge waste
(s)
mean solid retention time with C = x,/x~. The solid concentration factor C can be written as follows:
The first derivative of Gt to concentration x is
sludge recyc}e
(4)
where Oh = V/Q; mean hydraulic retention time
Gt = x(kx-" + Q,/A)
Input
(3)
and the second derivative is, d2G,/dx 2 = - n(1 - n)kx -("+ i)
Steady state analysis In the case where n is greater than 1, the second derivative is always positive. Therefore G, passes through a minimum at x = x, where the first derivative is zero. Then the limit flux concentration is:
xI = ((n-Q;)kA)-"" If there is a limit flux layer, the underflow flux will be equal to the limit flux,
=
(iA+(&q
As the limit flux layer, dG,/dx = 0, so kx;” = (QJA).(l/(n - 1)). By applying this to the above equation, G,(G, at x = xl), x, becomes x,(n - 1)/n. By applying the equation for x, and xU = Cx,, into the above equation, the limit solid flux and its concentration can be represented as follows: G, = k(n - I)(+
- l))“(Cu,) -”
x, = Cx,(n -
1)/n
(9) (10)
For the limit flux to be a criterion of thickening operation, its concentration should be greater than the initial solid concentration.
This condition gives the following constraint applying the limit solid flux as criterion:
The solid concentration
in the supernatant
x = ((1 + a) - (a + e
will be
P)Q
(13)
(1 - P)
But in the other case where the initial concentration is greater than the limit flux concentration (xi < x,), i.e. (n - 1)/n < (a + /?)/(I + a), the solid entrainment in the supernatant would depend on the initial flux (G,(x,)) and the applied flux (G,): (clarification criterion). When the applied flux is not larger than the initial flux, G, < G,(x,), there will be no entrainment in the supernatant, and then the concentration factor is equal to equation (11). In an actual activated sludge system, it might not be possible to be a clarification criterion condition. But as a theoretical consideration, all of the case that can be thought with an activated sludge characteristics and concentration, shall be investigated. For the other condition, G, > G,(x), the concentration factor can be obtained from the solid balance C=&+l
(14)
and the solid concentration in the supernatant is equal to equation (13). Now C, x,, 8,, s, x, can be calculated simultaneously. For the case of using the pseudo-fluid model (a = k exp( -nx)/x) for settling, the limit flux and its concentration can be obtained as follows. The equation of solid flux due to gravity is given by an exponential form
for
G = k exp( -nx) and the total flux is
(n - 1)/n > (c( + P)/(l + CI) In this case, two types of activated sludge charge on the settling tank can be considered: G, < G, and G, > G,. If the applied solid flux (G,) is larger than the limit solid flux, the difference between the two flux will be entrained in the supernatant stream and the thickening function will not be sufficient. Let us call this region as thickening criterion boundary. For the first type of charge, G, < G,, the solid content in the supernatant can be considered to be negligible, xe z 0, then the solid concentration factor becomes C = (1 + a)/(cl + B)
2603
G, = k exp( -nx) The first derivative is
dG,/dx = - nk exp( -nx)
+ Qu/A
and the second derivative is d2G,/dxZ = n2k exp( - nx)
Since d2G,/dx2 is positive, G, passes through a minimum G, at point xl where dG,/dx = 0. At this point (x,) G, = k exp(-nxl)
(11)
On the other hand, if the applied solid flux is larger than the limit solid flux, the amount of solid flux at the bottom is equal to the limit solid flux. Then the solid concentration factor is
+ xQu/A
(dG,/dx),,
+ x,Q./A = xuQ./A
r, = - nk exp( -nx,)
+ Qu/A = 0
From the above two equations, x, becomes (x, - l/n), and the concentration of the limit flux layer and the limit flux are obtained as follows: G, = nkCx, exp(1 - nCx,) x, = Cx, - l/n
And
in
the
thickening
criterion
boundary,
nx, 2 (c( + fi)/( 1 - /I), if the applied flux is larger than
2604
S.H. Cho et al. 10
the limit flux, the concentration factor can be represented as
l-
9 8
ln((~ ~ fl~)Q.'~
\
c =
Ank J
(15)
7
In the other Case, C and xo are represented as being the same as the expressions of the power model. For the exponential model, the approaching procedure is similar to the others. But the application is more complicated, because the concentration factor should be calculated using the trial and error method, and the constraints are more complex than the case of the other models.
6
nxi
.2
5
ct = 0.2
o
4
ct = 0.3 ct = 0.4
3 ct = 0.5 ~=0,6 0.=0.8--
2
__ i
c t = 1.0 RESULTS
AND
l
DISCUSSION
To investigate the responses of the output variables---concentrations of solids and dissolved organics in the supernatant and the biomass concentration in the a e r a t o r - - a n d to decide optimum conditions of the operating parameters, the calculation was carried out by using the operating parameters as recycle sludge ratio and waste sludge ratio. The parameters used for this calculation are as follows: Ks; 0.06 g/l; half-velocity constant k0; 5.0 d-~; combined coefficient of mass transport and reaction rate Y; 0.6 g g-~; maximum yield kd; 0.06 d-~; endogenous decay coefficient V; 13,600 m3; aerator volume A; 2750 m2; surface area of settling tank Q; 54,400 m 3 d - I ; entering wastewater or effluent flowrate so; 0.5 g 1 t; entering dissolved pollutant concentration k; 375; constant of power model (when the velocity is represented in m d -~ and the concentration in g 1-~) n; 2.3; index of the power model
o
L
0
0.02
i
i
0.04
0.06
0,1
waste sludge ratio, 13 Fig. 2. Sludge concentration factors in sample case study (k = 375 m d -L, n = 2.3 for power model).
But the limit flux concentrations seen in Fig. 3 does not show such phenomena. This can be understood by equation (8). These limit flux concentrations might be meaningless in the range where any limit flux layer cannot exist. The calculated results are shown in Figs 4--6. Figure 4 shows the responses on the dissolved pollutant concentrations in the aerator or in the supernatant. The tridimensional diagram is the
~2
10 0.=0.1
~
s
0.=
o
In Smollen and Ekama (1984), k values were from 1.5 to 60 m h -~. They used 325 m d-~ for their sample calculation. As our measurement in a wastewater treatment plant, those were between 65 and 460 m d - ' , and the index n was between 1 and 5. Settling characteristics are changed continuously. Here 375 m d -t for k, and 2.3 for n were selected for sample calculation. Before the investigation of responses, the variations of sludge concentration factor and limit flux concentration were calculated for the sample plant conditions with a power model. As can be seen in Fig. 2, concentration factor increases according to the decrease of recycle ratio, or decrease of waste sludge ratio. The rate of increase of the concentration factor becomes quite small after a limit flux layer occurs.
t
0.08
~
0.2
0.=0.3
6
0.=0.4
0.=0.5 r~ = 0.6 "~
0.=0.8 ~=1.0
4
2
0 0
i
)
t
I
0.02
0.04
0.06
0.08
O.I-
waste sludge ratio, p
Fig. 3. Limit flux concentrations in sample case study (k = 375 m d -~, n = 2.3 for power model).
Steady state analysis
2605
V, 375- x'2"3 m/day 100
g
V,3./S.x~Z3m/day
02S
s.SOmg/l
o 0,20
o
~, SO ,."
cl
o
uT 0
,o
2 23.7-
-~
a
40
t.
3O
•*' 0.15
-20
g 0.10
c
"o
O.OS
355
I
I
I
1.0 sludge recycle ratio,
~005 0.035 0.15 sludge waste ratio,
A. Response surface
I
2.0
B. Isoresponse curves
Fig. 4. Responses of the substrate concentration in aerator (k = 375 m d ), n = 2.3 for power model). A, Response surface; B, isoresponse curves.
response surface. If the recycle sludge ratio diminishes or the waste sludge ratio increases, the biomass retention time decreases, accordingly the pollutant concentrations in the supernatant increase. If the biomass retention time becomes smaller than the critical value, the biomass cannot persist in the system and the entering pollutant cannot be diminished. But in Fig. 4, the responses superior to 0.1 g !-) were eliminated to show clearly the responses in the interesting zone. From the response surface diagram, the isoresponse curves were obtained by cutting the response surface with the same concentration. The curves indicate that if the sludge recycle ratio and the waste sludge ratio under the curve are controlled, the pollutant concentration can be maintained to a value inferior to that of the curve.
Figure 5 shows the biomass concentration responses in the aerator. If one decreases the waste sludge ratio down to a value less than 0.035, the entering solid flux into the settling tank becomes superior to the limit flux, therefore the biomass concentration in the aerator does not increase to the solid loss in the supernatant, and the pollutant concentration cannot be decreased any more. Similarly if the operating parameters are controlled to be under the curve, the biomass concentration superior to the value of the curve can be obtained. By decreasing the waste sludge ratio, the biomass concentration can be increased, but there is a limit to decreasing the waste sludge ratio, which is the result of considering settling effect. If the applied solid flux to the settling tank becomes larger than the limit flux due to increasing the biomass concentration, a
V.-375 • x'Z3m/day .
0.2S
V= 375-x'2.3 m/day
•
o-1or "
,,.~"
0.005 0.085 OJS~' ~ sludge ~ a s t e r a t i o ,
A. Response surface
/
/
~
x,
0 __.
sludge
B.
tO recycle
2.0 ratio,
Isoresponse curves
Fig. 5. Responses of the biomass concentration in aerator (k = 375 m d -), n = 2.3 for power model). A, Response surface; B, isoresponse curves.
2606
S.H. Cho et al.
0.06 V : 37S-x"2-3m/day,
V" 375.x"2"3 m/day
0.0.5
X e : l ~
o"
'-i~'z°ss I:~°° l'~2]-°°/
, ~., ~=-o."o~'z,~0".03o.oz "~ 0.01
o.oo 0.035
%o
I
I
I
1.0
I
2.0
sludge recycle ratio,
sludge waste ratio,
A. Response surface
B. Isoresponse curves
Fig. 6. Responses of the solid concentration in supernatant (k = 375 m d -~, n = 2.3 for power model). A, Response surface; B, isoresponse curves.
part of the solid begins to overflow through the weir. Therefore the biomass concentration in the aerator cannot increase any more. As for the solid concentration in the effluent (Fig. 6), if the operating parameters are maintained above the isoresponse curve, the concentration inferior to the value of the curve can be obtained theoretically, with the exception of the solid amount that overflows as small isolated particles. Consequently, if the three kinds of the isoresponse curve are combined, the operating diagram can be obtained (Fig. 7), which can be used to determine the operating parameters to obtain the desirable responses, e.g. s < 30 mg 1-~, x > 3 g 1-~, xe < 30 mg !- ~. Therefore in the crossed line zone in Fig. 7 the minimum recycle sludge ratio and the waste sludge ratio can be determined. The crossed line zone can be called an acceptable operating zone.
0.20
V, 375 • X'2"3m/day
• 0.15-
o.lo
-g 0.0.5
I
I
I
1.0 Sludge recycle ratio.
In Fig. 8, the acceptable operating zones were compared by changing the settling characteristics for pseudo-fluid model. The settling characteristics of Fig. 8(B) for pseudo-fluid model is similar to the characteristics of power model with k = 375 m d -~, and n = 2.3. If the settling characteristics of activated sludge become poor, the zone becomes smaller and narrower (Fig. 8). In particular, if the settling tank is studied separately from the aerator, no solid entrainment can be observed in the supernatant by increasing the recycle ratio, but in Fig. 7 it can be observed easily that if the recycle ratio is increased, the biomass concentration in aerator increases and finally some part of the solid begins to overflow the weir. This means that the secondary settling tank should be studied by combining it with the role of the aerator. As mentioned previously, if the sludge retention time is increased, the biomass concentration increases in the aerator. But if the applied solid flux to the settling tank becomes superior to the limit solid flux, the biomass concentration in the aerator cannot increase any more. However, this point cannot be observed by studying the aerator, like Lawrence and McCarty (1970), without considering activated sludge settling characteristics. This means that the aerator should be studied by coupling it with the settling tank. This steady state analysis will give some tendency of an activated sludge process. Unfortunately since sludge settling characteristics change continuously in activated sludge process, it is difficult to obtain a steady state. In practical wastewater plant, it is impossible to obtain steady state experimental results.
2.0
Fig. 7. Acceptable zone of operating parameters (k = 375 m d -~, n = 2.3 for power model).
CONCLUSIONS The steady state responses of activated sludge process for biological wastewater treatment were
"u
tJ
w
0 e..
° ~o
0.0!
0;10
0.15
0.20
I
I 20
g,
~
t~
o
0
0.05
0.I0
0.15
I 1.0 (131
Sludge recycle
I
•
ratio,
V= 253-exp(-O.344-X)/ X, mid
1
amy
2.0
.0.15
0.05
~, o.1o
&.
o
0.20
Sludge
IC)
recycte ratio,
• 1.0
I
V--Z S3.exp (-O.IG2-X }/X,m/d
Fig, 8. Variation of acceptable operating zone according to the change of settling characteristics (pseudo-fluid model).
(A)
Sludge recycle ratio.
1.0
!
V:379.5 •exp(- 0.344.X1/ X ,m/d
0.Z0
!
o.,
Z.O
eh
2608
S.H. Cho et al.
investigated theoretically by coupling the functions of aerator and secondary settling tank. The responses on biomass concentration in aerator, dissolved pollutant concentration in supernatant and solid entrainment in effluent were represented on the response surface diagrams and the isoresponse curves. By combining the isoresponse curves of the three output variables, the acceptable operating zone was obtained, and the optimum operating parameters (recycle ratio and waste sludge ratio) can be decided. REFERENCES
Brett R. W. J., Kermode R. I. and Burrus B. G. (1973) Feed forward control of an activated sludge process. War. Res. 7, 525-535. Cho S. H., Colin F. and Prost C. (1993) Settling velocity model of activated sludge. Wat. Res. 27(7), 1237-1242.
Lawrence A. W. and McCarthy P. L. (1970) Unified basis for biological treatment design and operation. J. of Sanitary Eng. Div., ASCE SA3, 757-778. Riddell M. D. R., Lee J. S. and Wilson T. E. (1983) Method for estimating the capacity of an activated sludge plant. J. WPCF 55(4), 360-368. Sheintuch M. (1987a) Steady state modeling of reactorsettler interaction. Wat. Res. 21(12), 1463-1472. Sheintuch M. (1987b) Species selection in a reactor-settler system. Biotech. Bioeng. 30, 598-606. Sherrard J. H. and Kincannon D. F. (1974) Operational control concepts for the activated sludge processes. War. & Sewage Works, March, 44-66. Smollen M. and Ekama G. (1984) Comparison of empirical settling velocity equations in flux theory for secondary settling tanks. War. SA 10(4), 175-184. Tucek F., Chudoba J. and Madera V. (1971) Unified basis for design of biological aerobic treatment process. Wat. Res. 5, 647-680~ Westwerg N. (1967) A study of the activated sludge process as a bacterial growth process. War. Res. l, 795-804.