Indian Journal of Engineering & Materials Sciences Vol. 10, October 2003, pp. 397-402

Activated sludge process - A rationality in design

Devendra Swaroop Bhargavaa & Anirudh Prakashb

"Bhargava Lane, Devpura, Haridwar 249 401, India

bInsti tute of Engineering & Technology, Sitapur Road, Lucknow 226010, India

Received 30 September 2002; accepted 5 August 2003

An attempt has been made here to determine the various conditions of operating variables that innuence the design and efficiency of the process. Nomographs have been evolved for a handy and quick aid in the design of an ASP under the varying conditions and values of the parameters that significantly affect the performance of the ASP.

Activated sludge process (ASp(3 is the most significant process for the stabilization of wastewaters containing high organic load. It is a biological process where an active biomass consisting of healthy and living aerobes is utilized to convert the unstable organic matter into a stable form. There are numerous factors which severely affect the efficiency of performance of the ASP. A judicious choice of the affecting variables has a significant effect not only on the performance of the process but also on the economy of the design .

Design of ASP has long been an utopia due to the involvement of a very large number of variables and also due to the often unpredictable nature of the microorganisms. Monod's equation had been the key concept in the stated design. In the ASP design, the volume of the aeration tank unit (the main reactor of the process) is over-emphasized while the secondary sedimentation tank, a vital unit of the whole process, most often gets ignored. Mc Harg4

, and Jenkins and Garrison5 have emphasized the importance of 9c (the mean cell residence time, or the solids retention time, or the sludge age) as a major control variable in the operation of an ASP. Considering 9c as the control as well as the operational parameter, Busby and Andrews6 have developed a dynamic model. Buhr et al. 7 correlated the residual organic content and solids retention time while keeping the mean cell residence time as the control and operational variable. Chi-Yuan LeeS developed a steady state model for suspended growth with bacterial supplements as a process variable, following the Monod's kinetics and mass­conservation principles while maintaining the conventional solids retention time. They however, ignored mass-balance around the clarifier. According

to Metcalf and Eddy Inc l, waste stabilization by the microorganisms occurring in the reactor unit. leads to a conservative design. McHarg4 derived equations considering separate mass-balance of biological solids around the clarifier and the aeration tank, to develop a simple spread sheet model. Tackas et al. 9 treated secondary clarifiers as a separate unit while giving steady as well as unsteady solution for secondary clarifiers. Henze et al. lo gave steady as well as unsteady solution only for the reactor (aeration tank), through highly complicated sophisticated computer simulation for control of the ASP. Linderbergll analyzed the reactor tank and settler tank separdtely and their results combined to achieve optimum control for the ASP. He however, did not use XR

(return sludge rate) as a control variable but stated it to be an effective control variable which needed further study and emphasized stress on nitrogen removal by the ASP for control of eutrophication. Gaudy and Gaudy3 advocated that the design of an ASP essentially consist of aeration tank and settling tank, done simultaneously involving mass-balance around both, thus accounting for waste stabilization in settling tank as well. Their equations were used for the second and the third approaches presented in this paper. Gaudy and Gaudi derived equations using mass balance of microbial solids around both the settling as well as aeration (reactor) tank (making the process more rational and non-conservative). The operational parameter was chosen as XR (return sludge volume) which can be varied during the operational phase for checking variation of biochemical oxygen demand (BOD) contribution during the year [instead of 9c (mean cell residence time)], the operational and control parameters (which can not be varied during the operational phase) resulting in a rigid design.

398 INDIAN J. ENG. MATER. SCI., OCTOBER 2003

Theoretical An ASP consists of an aeration tank where

effective waste stabilization of organic wastes takes place by a controlled amount of aerobes, and a settling unit where the bio-flocculated biological solids are concentrated to desired levels for recirculation and removed from the flow. Some amount of the settled but active solids is returned back to the aeration tank, while another part, though also active, is wasted to maintain the desired concentration of the active solids in the aeration tank. For high efficiency, steady state conditions for the active solids are to be maintained in the aerations tank. Growth of aerobes in the aeration tank is a function of only substrate amount although nutrients, aeration, pH, temperature, etc, also affect the functioning.

While applying the mass balance equation for the ASP, it is assumed that: (1) The growth of aerobes occurs only in the aeration tank (the reactor); (2) The amount of substrate concentration in the returned sl udge is same as in the effluent; (3) Volume used in calculation of mean cell residence time for the system includes only the volume of the reactor unit; (4) Amount of active sludge in the effluent is Iflegligible, i.e, Xe=::O; and, (5) Amount of active solids=::O.

Applying the mass balance equation 1.2 for b ~ ological solids, we have:

... (1)

For steady state, dX/dt tends to be zero. 8c, the mean cell residence time and control parameter [(mass of cells in the reactor)/(mass of cells wasted each day)]=V.X/[(F-Fw).xe+Fw.eX.]. Using it along with Monod's equation, /-l=(/-lmax.Se)/(Ks+Se) in Eq.(1) equated to zero, we get:

... (2)

12 Applying the mass balance for the substrate' "We get:

... (3)

As before, for steady state conditions, putting dS/dt=O, in Eq . (3), value of /-l (obtained by using 8c

value in Eq. (1» and D for FIV, we get:

... (4)

The first approach shown in Fig. la using Eqs (1)-(4), is quite conservative as the first assumption is not

satisfied. Hence, instead of applying mass balance for the entire system, a more logical approach is to apply the mass balance only across the aeration tank" (the reactor) where most of the stabilization and growth of aerobes occur. This second approach shown in Fig. lb. Applying mass balance for active solids across the aeration tank (reactor) only, we have:

V.(dX/dt)=/-l.x. V-Kd.x. V-(1 +a.).F.X +a..F. ex. . .. (5)

For steady state, dX/dt=O and equating with Monod' s equation for /-l, we get:

Se=[(l +a.-a..C).D+kd].Ks/[/-lmax-{ (I +a.-a..C).D+kd) J ... (6)

Applying mass balance for substrate concentration in the aeration tank, we get:

V(dS/dt)=F.Sj-(/-l.x. V)/Yl-( I +a.).F.Se+a..F.Se ... (7)

Equating Eq. (7) to zero for steady state and substituting the /-l value obtained from Eq . (5) at steady state, we get:

In the second approach (taking C as constant and control parameter), the system becomes somewhat unstable. Let us assume that there is dec rease in ' X' in

r. - - - - - - - - - - - - - - _t_ - - - - - - - _ • . - - - - - - - -,

IA x ; I IF,Sj V ( l+a )F , X . 5 ~ J Sq:ttli ng \ ( F-Fw ),X""sl!

S. I un ; t I \ rF

Atrotion tank I I aF.CX.S~ FWlC:.S",

i . L _________________ ...... _____ . ___ _ - - - - ..J

B r-------- -, I I I X • I I

F, Si I V 1 ( 1 + a ) F, X I SI! ---'---,~ S. I

..----f.lAuation : of. ex. S~ tank I

I I

L. _________ J

C r----------~

I I I I

F, Sj : IU+O)F. X,51!:

S. I A~rotion :

ta n k I I

Q F, XR. St :

Fig. I-Flow diagram for (A) 0" (B) C and (C) XR as control parameters

BHARGAVA & PRAKASH: ACTIVIATED SLUDGE PROCESS 399

the reactor, then to keep C as constant, XR (the return active sludge) has to decrease and this will further decrease ' X' because the net inflow of'X' decreases.

Hence, to make the system stable, we will treat XR

as the control variable (i.e. C varies) in the next third approach 3 shown in Fig. Ic. Here, we have:

v. (dXldf)=~. V.X -kd' V.X +a.F.XR-( 1 +a)F.X ... (9)

For steady state, dXldt=O. Thus, we get:

... (10)

Likewise, applying the substate mass balance3

around the aeration tank, we get,

V.(dS/df)=F.Sj-(~.x. V)IY,+a.F.Sc(l+a).F,Se . . . (II)

For steady state, dS/dt=O . Thus, we get:

.. . (12)

Solving Eq. (12) after substituting Monod ' s equation

[~=(Se ' ~l11ax)/(K,+Se)], we get:

... (13)

Using Eq. (10) for~, and Eq. (13) for X in Eq. (12), we get:

[~l11ax/( I +a)-D-kd/(l +a)]Se2 + Se[D.(Sj-Ks) -{ ~l11aJ( I +a} {Sj+(a.XR)/Y,}+{kd/(l+a) }(Sj-Ks)] +(Ks.D.Sj+Ks·kd.S;)-=O ... (14)

Denoting the coefficients of Se2 , Se and the constant

term in Eq. (\4) respectively by A, Band C, quadratic Eq. ( 14) yields:

Se=[-B±~4AC ]/(2.A) ... (15)

Substituting the value of ~ from Eq. (10) in Eq. (12), we get:

... (16)

ASP design considerations

A successful design of any process incorporates efficiency and economy. Efficiency in ASP would depend mainly on the effluent substrate concentration (lower the concentration, higher the effic iency). The

amount of the active sludge to be wasted has some effect on the overall efficiency of the plant. Hence. S" is chosen as one of the output variables on which th e effeet of different input variables are studied. Th e second most important output variable IS X (concentration of the active solids in the aerati on tank) such that more the concentration of X, hi gher the oxygen requirements and thus higher the cos t. bu t higher the efficiency. Another important variabl e affecting the cost is the dilution rate, D (fl ow rate/volume) . Higher the dilution rate, lower will he the volume requirement and hence lower the cost.

The control parameters are mainly the amount or

solids to be wasted (Oe), recycle concentration rati o (C) and the recycled microbes concentration (XR).

These variables are hydraulically and manuall y controllable, whereas the other control parameters include the kinetic properties of a particular microbi al culture.

Results ASP design nomographs - A study of the

variations of these manually controllable parameters

is carried out. Taking Oe, C and XR. as control parameters, their variation effects on Sc and X are evaluated for two extreme conditions of the influent substrate concentration, i.e . at Sj of 250 mg/L and 2500 or 25000 mg/L, respectively representing a domestic sewage and an industrial waste. For each or the stated control parameters, the values of cost affecting (X) and efficiency affecting (SJ are evaluated at different values of D (cost affecting) for the varying values of the stated control parameters

(Oe, C and XR)' These variation effects are depic ted graphically. For the entire evaluations, the followin g kinetic coefficients are assumed for a typica l microbial culture generally found in an ASP: Y,=O .6 mg/mg; kd=0.0025 h- 1

; ~l11ax=0.125 h- 1; K,=60 mg/L:

a=0.5 (also 0.75). Oe has been varied from 0 .5 to 25 days, D from 0 to 2.5 h- 1

, C from I to 2.95 , and XI{ from 2000 to 25,000 mg/L. The result as obta ined from the computer programs (as wa developed in C­language, by the second author for thi s paper) for the stated evaluations, are plotted as design nomograph s in Figs 2 to 6 .

Discussion From the first approach , the results of variations in

the Oe values from 0.5 to 25 days on the values o r X and Se against the different D values (up to 2.5 ) are shown in Fig. 2 for the Si values of 250 and 2500

400 INDIAN 1. ENG. MATER. SCI., OCTOBER 2oo3

25000

~~~ _______________________ s,

~~~ ________________________ s.

1--2.:.''----------------------- 5 ,

, ~ X

I---~-~.L__;,.L--,r__--~~ 5 ,

!_- X

~~IO~~7S~--~~--~~~~---_~:

--I~;- XSt

__ ___ _____ _ __ _ _ 0:..5_ ... X

0. 4 0 ·8 \ ·2 \ ·6 2·0 1·4

0 , h .- 1

Fig. 2- Variation of 8c on X and Se with D [Sj=250 mg/L (a 0.5); dotted lines for Sj=2500 mg/L for X 10 times]

mg/L. The concentration of X increases with 8e at all values of D, Sj and 8e. The concentration of X increases also with ' D. The X values negligibly increase when Sj increases from 250 to 2500 mg/L. In the higher ranges of 8e, the rate of increase in X per unit increase of D is larger when compared to the lower ranges of 8e . Se increases with decreasing values of 8e at any value of D and Sj. The value of Se is independent of D (for both the Sj valUJes) and is maintained at constant values as per the Se versus 8e

variation plot shown as the inset of Fig. 2 suggesting that 8e> 1 0 days is appropriate. Thus, for a desired va lue of Se (manifesting efficiency), the 8e value can be chosen (using these nomographs) for the design of the aeration tank. Once the 8e value is chosen, the X value for a given Sj value can be easily ascertained from the use of the nomographs contained in Fig. 2, after adopting an appropriate value of D or 8. As an example, if for sewage (Sj=250 mg/L) treatment, desired Se is 2 .6 mg/L [efficiency of treatment= {(250-2.6)/250} .100=99%]. This would need a 8e value of 15 days (vide nomographs in Fig. 2) and this would provide a X value of 4000 mg/L at a o value of 0.15 h- 1 or 8 value of (1/0.15)=6.6 h, the aeration time.

From the second approach, the results of the variations in the C values from 1 to 2.95 Ont the values

3000 300

2500 250

2000 200

1500 150

~ ~ ------ E '" E -.: .

'" 1000 100

500 50

-- X.I .S

_-x X , '--C: 2 .3

r2 . '5 I IS. : C: I : St I \ ·5 I S,

2S, 2 .5

/

/

0 .4

S,

2· 7

/

/ /

/

/ /

0 . 8 1.2 -I

O. h .

/ /

...........: . - . - --- ,C: 2.95 /' S. "-

/ ' 2.9 \

2.0 2· 1.

Fig. 3-Variation of C on X and Se with D [Sj=250 mg/ L (a 0.5. dotted lines a 0.75); chain-dotted lines for Sj=2500 mg/L a 0.75 for X 20 times]

of X and Se corresponding to the different D values (up to 2.5) are presented as nomographs in Fig. 3 for a Sj value of 250 and 2500 mg/L. Se increases with D (for any C value), but decreases with increasi ng C values (for any value of D) or with increasing a values (for any C value). The rate of increase in So value per unit increase of D value, is very high in the lower ranges of C. X however, attains an optimum (maximum) value at a particular D value (for any C value) and the magnitude of this optimum/max imum X value increases with C values corresponding to any Sj value. This particular D value also increases with C. However, when Sj increases, for the same C value, the said maximum X value reduces and occurs at higher D value. Also, for the same Sj valee, an increase of a will result in an increase of this optima value and occurs at a larger D value. From the nomographs presented in Fig. 3, C can thus be evaluated for a desired value of X at a predecided D value or can be evaluated for the desired val llJes of Xe and D. Once C(=XR IX) is evaluated, the XR v8.lue (used for design

BHARGA V A & PRAKASH: ACfIVIATED SLUDGE PROCESS

of secondary clarifier) can be fixed for the pre-fixed value of X. Thus, in the above stated example, X was 4000 mg/L and D was 0.15 h- I

, giving a value of C as 2.95, and thus XR=2.95x4000=11,600 mgIL.

From the third approach, the results of variations in the XR values of 2000, 5000, 10,000, 15,000 and 20,000 mg/L on the values of X and Se corresponding to the different D values (up to 2.5) are shown as design nomographs in Figs 4-6 for the respective Sj values of 250, 2500 and 25000 mglL. X increases with Se (at any value of D), and the increase in the X values are negligible with respect to the D values at any value of XR showing that the values of X are almost independent of the D values for any XR value (except at the very low value of D at around and up to 0 .1 when the X values increase with the D values) and mainly depend on the XR value. X also increases with a (at the same XR values). The X values as well as the Se values also increase with increasing Sj values at any XR and/or D values. The values of Se increase with decreasing values of XR (at any D) and corresponding to any XR value, the Se values increase with D such that in the lower ranges of XR, Se increases very rapidly with D or rate of increase of Se per unit of D

7000 140

6000 12 0

5000 100

4000

J 0 00

2 000

1000

BO

-'

'" E

X R: 20000

5000

10000

15000

20000

0 . 4 0 . 8 1.2 1.6 2.0 2 . 4 0 , ... - 1

Fi g. 4-Variation of XR on X and Se with D [S;=250 mgIL (a 0.5); dotted lines a 0.75]

15000 )00

'R~:4~O~OOO~ ______________________ ,

".( 12500

o 4 os o . D. ,., - 1

Fig. 5- Variation of XR on X and Sc with D [S;=2500 mg/L a 0.5]

6 !.OOO 1600

56 000 1400

(. &000 1200

40000 1000

)2000

~ ~

E ><

24JOO

16000

BOOO

XR : 160000

5,

sooo

5,

BOooO

0·)

o. h - 1

"

0·1. o 5

Fig. 6-Vari ation of XR on X and Sc with D [S;=25000 mg/L a 0.5)

40 1

5,

!.ooo

0 1

0.'

402 INDIAN 1. ENG. MATER. SCI. , OCTOBER 2003

va lue is hi gher in the lower ranges of XR when compared LO the higher ranges of XR. The Se values are lower when a increases at any XR and/or D values. Th us, it is easy to fix up XR for any desired value of X. In the above mentioned example, X=4000 mg/L. This corresponds to the X versus D curve (nomographs show n in Fig. 4) of XR= I 1,600 mg/L al most at any D va lue above 0.1 (say 0.15). Likewise, knowing Se and [I. XR can be evolved. In the stated case example, corresponding to Se of 2.6 mg/L and D of 0.1 5 h- I

, the corresponding So versus D curve (nomographs shown in Fig. 4) belongs to XR=II,600 mg/L again.

Thus, for the stated case example, the reactor (or th e aerati on tank) need be designed for D=O.I 5 (or the hydraulic retention time of 6.6 h or 13 h if D is taken as 0. 1, and a return sludge concentration (XR) of I 1,600 mg/L with 8c= IS days and X=4000 mg/L such that C=XR/X=11600/4000=2.95. 8c of IS days will prov ide Se of 2.6 mg/L (Fig. 2), all at a=0.5. As an example, for a flow rate of say 2250 m3 /day (or 93.75 m.\ Ih) , Sj of 250 mgfL, a value of 0.5, the Se value works out to be 2.645 mg/L using Eq. (2), and the X value works out to [using Eq. (4)] 28, 120.4 D from whi ch D works out to be 0.1423 when X=4000 mg/L. Th us, the hydraulic reten tion time (8) equals 1/0.1423 h- I=7 h giving the reactor (aeration tank) volume as 7x93.75=659 m3

.

Conclusions A rational design methodology and nomographs for

the des ign of an aeration tank (the reactor of an ASP) are presented for an economical and efficient design. These investigati ons would benefit the field engineers and designers to design , operate and control the ASP at minimal cost and maximum efficiency.

Acknowledgment The authors are grateful to the Institute of

Engineering and Technology, Sitapur Road, Lucknow, fo r providing opportunity to prepare this paper materi al as part of the class course work.

Nomenclature C = (XRIX), the recyc le concentrat ion factor D = (FIV), the dilution rate (h- I) F . = flow rate (m 3/h) FR = fl ow in recycle (m)/h) Fw = flow wasted ( m3/h) FIM = food to microorgan isms rati o

Ks = concentration o f substrate at which 11 = I1m.J2 (lIlg/LJ kd = speci fic decay rate (h - I) SR = recycle substrate concentration (mg/L) Sc = effl uent substrate concentratio n (mg/L) Sj = influent substrate concentration (mg/L) U = maximum substrate utili zati on rat,; (clay- I) V = volume o f ae rat~m tank, the reactor (m ') X = concentra tion o f microorgani sms in the reatcor (lIlg/Ll XR = recycle microorgani sm concentraion (mg/L ) Y, = true cell y ield (mg/mg) 8 = (VIF), the hydraulic retention t ime (11)

8e = mean cell res idence time (day) 11 = specific growth rate of microorgani sms (h- ' ) 11m., = maximum specific growth rate (h- I)

a = (FR/F) the hydraulic recycle ratio

References I Wastewater engilleerillg treatlllellt, disposal, Cilld rellse (T ;ila

McGraw Hill Publi sing Company Ltd, New De lhi ). (Metca l,. & Eddy, Inc. rev ised by George Tchubanoglous & Frank li en L Burton), 199 1.

2 Arceivala S J. Wastewater treatlll elll Jill' po/llfl ifl/l mll/rol (Tata McGraw Hill Publishing Company Limited. 'ell De lhi ), 1998.

3 Gaudy A F & Gaudy E T, Microbiologv for I' II Virollllll'lIl11l scientists alld ellg ineers (McGraw Hill In terna tional. New York), 198 1, p.255.

4 McHarg W H, Chemical Ellg . 80 (1973 ) 46; 100 ( 1993) 1:1 :1: 10 1 (1994) 153.

5 Jenkins 0 & Garri son W E. J Wat Poilul COll lrol Fed ... W. Ptl (1968) II.

6 Bushy J B & Andrews J F, J Wat Pol/ III Cumrol Fed. 47 (1975) 1055 .

7 Buhr H, Lee M & Narayan B, Wat Enviroll Res. 517 CWO I ) 73.

8 Chi-yuen L, J Env Ellg, Alii Sue Civil Ellgr, 123 ( 1997) g09. 9 Takas I, Patry G G & Walasco 0 , Wal Res. 25 ( 199 1) 126:1 .

10 Henze M, Grady Jr C P L, Gujer W. Marais G V R & Matsuo T, Wat Res, 2 1 (1987) 50S.

II Linderberg C F, COlltrol of estimaiol1 strateg ies applied III

the activated sludge process, PhD T hes is. Department of Materi als Science Systems & Cont ro l Group. Up,a la University, 1997.