the theory and design of aerobic biological treatment

The Theory and Design of Aerobic Biological Treatment

V. A. VAVILIN, Water Problems Institute, USSR Academy of Sciences, 1313 Sadovaya-Chemogryazskaya Street, 103064 Moscow, USSR

S-m=Y

The processing of numerous experimental data shows that the high-level and rough treat- ments of multicomponent sewage water follow different laws. In the case of rough treatment, the classical Monod‘s model is fairly adequate to the experiment. High concentrations of a pollutant “saturate” the complex of microorganisms (activated sludge or biofiim) and the general oxidation process follows a zero order for the substrate. In the case of high-level treatment, the model of an n order (n > 1) for the substrate is adequate to the experiment. Generalized models of aerobic treatment, independent of the reactor type (an aeration tank, trickling filter, rotating disk), are proposed.

INTRODUCTION

Aerobic biological treatment using microorganisms ensures destruction of a broad range of organic pollutants. Based on the processing of numerous data, a unified approach to the description of aerobic biological treatment processes in different reactors-aeration tanks, trickling filters, and rotating disks-is proposed.

MAIN CONCEPTS

Reactors, performing the process of aerobic biological treatment, oxidize a certain range of substrate pollutants, being components of a complex pollutant. The rate of treatment depends on the rates of oxidation of individual components and on their contribution to the total rate of oxidation. As the time of sewage water retention in a reactor T and the concentration of microorganisms X increase, the role of oxidized hardly oxidizable components of a complex pollutant increases. As the influent sewage water concentration So increases the range of oxidized compounds shifts towards easily oxidizable compounds.

The concentration of a multicomponent pollutant is measured, as a rule, in units of biochemical oxygen demand (BOD) and chemical oxygen demand (COD). The CODIBOD ratio increases in the course of biological treatment because the range of remaining compounds tends to hardly oxidizable com-

Biotechnology and Bioengineering, Vol. XXIV, Pp. 1721-1747 (1982) 0 1982 John Wiley & Sons, Inc. CCC 0006-3592/82/081721-27$03.70

1722 VAVILIN

ponents. Hence, respective rate constants for COD appear to be much smaller than those for BOD.

In accordance with the range of oxidized compounds, the microbiological composition of sludge flocs or biofilm is formed in an aeration tank, trickling filter, and rotating disk. Thus, the species composition of microorganisms depends not only on the type of sewage water but also on the regime of operating of the reactor treating sewage water.

The key variable, governing the law that is followed by the treatment process, is the pollutant concentration in a reactor with which the effluent pollutant concentration S, is connected. At large S, values and So values (rough treatment), the microorganisms of sludge or biofilm are “saturated” with the most representative components of the substrate pollutant, and the treatment rate becomes maximal, corresponding to the zero-order reaction for a multicomponent substrate S. In this case, the increment of the biomass of microorganisms is maximal. At small S, values (high-level treatment), the treatment process is subjected to the n-order reaction (n > 1) for a multicomponent substrate S.

If S, values are far from saturation, the range of oxidized compounds tends towards hardly oxidizable components. In this case, the dependence of the treatment efficiency on the concentration of microorganisms X and the temperature t o is poor, since their increase results in the “capture” of more hardly oxidizable components, and this decreases the respective rate constant. In the case of s, values near to saturation, the range of oxidized compounds tends to easily oxidizable. Here, the treatment efficiency strongly depends on the microorganisms’ concentration and temperature; in addition, the treatment rate may be governed by the dissolved oxygen concentration.

In the case of a wide variation range of S, values, generalized models of the treatment process of a special type are adequate to the experiment; these models give a zero order at large S, values and an n order at small S, values for the multicomponent concentration pollutants. The biological treatment process models, proposed earlier, are either particular cases of a generalized model or its approximations. Traditional models have, as a rule, a systematic error, Within a narrow range of variations in S, values, different models “work” approximately similarly.

The type of a reactor-a plug-flow reactor or a completely mixing reactor-is of no substantial importance, at the first approximation, in the treatment of multicomponent sewage water, as in the course of treatment the dominating role is played by the zero-order reaction in the oxidation of individual components of a multicomponent pollutant.

The S, values for municipal sewage water are, as a rule, far from saturation, and therefore an n-order model is true for them as far as the multicomponent pollutant concentration is concerned.

Proposed generalized models are unified for the design of different microbiological reactors, i.e., an aeration tank, trickling filter, or rotating disk.

AEROBIC BIOLOGICAL TREATMENT 1723

A FO-D SCHEME AND GENERALIZED MODEL OF BIOLOGICAL TREATMENT

The aerobic biological treatment process, performed by the microorganisms of activated sludge or biofilm, and occurring in such reactors as an aeration tank, trickling filter, and rotating disk, may be roughly presented in the form of a scheme in Figure 1.

Sewage liquid flows to a reactor with a concentration So and leaves it with a concentration S, , with the concentrations being measured in BOD, COD, or TOC units. The sewage water discharge is q , the reactor volume is V; hence, the time of retention of sewage liquid in the reactor is T = V/q. In the case of a trickling filter T is T = V/q = DA/q = D/Q, where D is the depth of a filter, A is the cross-sectional area of a filter, and Q is the specific hydraulic loading. The T value is connected to the mean contact time. The mean contact time TH depends on the holdup of liquid by media of the trickling filter (TH - arD/Qm, where a is the specific surface of media, r, m are positive constants). For a trickling filter it is more correct to use TH instead of T = D/Q.

Fig. 1. Graphical presentation of the aerobic biological treatment process in keeping with the generalized model (1). 1, high-level treatment; 2, rough treatment. Explanations are in the text.

1724 VAVIUN

In the reactor, a certain concentration X of microorganisms exists as sus- pended activated sludge particles (in the case of aeration tanks) or as biofilm, fastened to the fixed surface of media, in trickling filters or rotating disks. It is evident that for biofilm the X value is proportional to the specific surface of media or rotating disks in a reactor (surface per reactor volume unit).

The treatment process occurs at some temperature t o ; in a number of cases nutrients are necessary to add to the original sewage liquid for a successful treatment process.

The numerous data, treated by the author, have shown that the specific rate of aerobic biological treatment of different sewage waters in different reactors (aeration tanks, trickling filters, and rotating disks) is well described by eq. (l), given in ref. 1:

where prn, is the maximal specific rate of the treatment process, and n, p , and k , are positive constants.

The increment of microorganisms biomass is

X , - Xo = Y(S0 - S,) - bXT (2)

where X is the average microorganisms concentration, Y is the yield coefficient of microorganisms, and b.is the constant of the rate of the autooxida- tion of microorganisms biomass. As a rule, in treatment processes, the microorganisms’ biomass increment for the time T is much smaller than that of the average microorganisms’ biomass in a reactor (AX = X , - Xo << X).

The treatment process, described by the generalized model (1) is plotted in Figure 1. One may conclude that the law governing the treatment process depends on the position of the point S, = S,* on the curve p = p(S,) , which in turn depends on the range of oxidized compounds-their concentrations and oxidation rates, and the reactor oxidize a certain range of substrate pollutants.

It is evident that v = v,,/2 takes place if

s, = m = i , ( s o ) (3)

i.e., when the half-saturation constant &, is the increasing function of the influent pollutant concentration. The above is true only for multicomponent pollutants. For single substratesp = 0 and k, = constant.

At large S,* values and So values (rough treatment), the process rate becomes maximal and is practically independent of the substrate concentration:

= p(S,) = prn, - const (4) SO - S e v =

X T

From (4),

AEROBIC BIOLOGICAL. TREATMENT 1725

In this case, microorganisms are saturated with substrate components, which predominate in original sewage water, and these components are oxidized, in keeping with the zero-order kinetics. There will be a maximal increment of microorganisms biomass in this case.

At small S, values (high-level treatment), the oxidation rate is governed by an n-order reaction (n > 1) for the substrate

The coefficient n shows the degree of difference in the rates of oxidation of individual pollutant components. Larger n values correspond to a sharper transition to hardly oxidizable components. The analysis of a number of data has shown p = n - 1 to be a good approximation. Thus, the proposed generalized model has three coefficients-n, k,, and pmax.

Figure 2 shows the "origin" of different orders in the oxidation of a multicomponent pollutant, when the oxidation of separate components is governed by a zero-order reaction. It is easy to understand that with fairly large So values at the initial intercept of the kinetic curve a zero order for a multicomponent pollutant is valid. As the treatment duration increases, the reaction order also increases, since more hardly oxidizable compounds are processed.

The value of F = So/XT is called the organic loading on a complex of microorganisms; v = (So - S, /XT) is the specific oxidation capacity. We may say that large loading values F are roughly consistent with readily oxidizable compounds, while small F values with hardly oxidizable compounds.

0 1 2 0 1 3 2 J

Fig. 2.

t t

Kinetic cumes for a first-order reaction (a) and second-order reaction (b) for the generalized pollutant S in the case of oxidation of a three-component pollutant. Separate components are oxidized according to a zero order: (a) Sol = 40, ko,X = 40, So, = 30, kO2X = 15,

-

So3 = 30, k,X = 8.6, So = Sol + So2 + So3 = 100, kX = 1. (b) So, = 63, kolX = 126, So2 = 20, k,X = 13.3, So3 = 17, k,X = 3.5, So = So, + So2 + S, = 100, kX = 5.

1726 VAVILIN

In keeping with the range of oxidized compounds, the species composition of microorganisms, contained in activated sludge or biofilm, also changes. For example, Gyunter2 discusses the dependence of the species composition and the abundance of activated sludge microorganisms on the value of sludge loading. A large number of active microorganisms and a large sludge biomass increment are observed with an increase in F values.

If the reactor operating regime changes, the species composition of microorganisms adapts the new range of oxidizable compounds in a certain period of time (the adaptation time).

If n = 1 and p = 0, we have a classical Monod's relationship, for which

Monod's relationship describes well the biological treatment process at fairly large Se values, which are not far from saturation. Model (7) holds for a trickling filter as well.

The retention time of sewage water in the reactor is found using formula (1):

(8) SO - Se T =

while the value of Se = S,* is determined from

P,axX{ S: /(k,"-'s[ + S: I}

S:+' - S,"(So - pmaxXT) + Sek:-pS$ - k:-PS$-l = 0 (9)

In the case of any n, it is necessary to use the numerical or graphical solution (9). At n = 2, an analytical expression for Se may be obtained from the cubic equation (9).

It is evident that instead of eq. (1) it is possible to propose a number of other relationships of the same type. For instance,

- - p ( S ) = -pma,Sn/(k:-"SOp + S " ) 1 dS X dt

If eq. (1) describes the average specific treatment rate, then eq. (10) describes the instant rate. Integrating eq. (10) from 0 to T , we obtain

We have, from eq. ( l l ) , for the average rate

= P(Se) SO - S e v = X T


Formula (8) complies with a completely mixing reactor, while formula (11) with a plug-flow reactor. However, here, these types of reactors are not dis- tinguished. If it is considered that the reaction of oxidation of individual components largely follows a zero order for substrate, then the transfer function S, = f( So, X, T) is the same for both a completely mixing reactor and a plug-flow reactor.

BIOCHEMICAL OXIDATION OF SINGLE SUBSTRATES

Activated sludge and biofilm are structural formations with a size on the order of 100 pm, while the size of individual microorganisms is about 1 pm. Under these conditions, the processes of mass transfer of substrate from solution to the complex of microorganisms become important. This results in some distribution of substrate concentration within a particle of sludge and biofilm. It is evident that the maximal substrate concentration value is observed at the surface of a particle of sludge or biofilm, while small particles or a thin biofilm have the greatest activity. The oxidation rate for them is limited by intracellular biochemical transformations.

Vavilii, Vasiliev, and Kuzmin3 consider stationary diffusion models for particles of sludge and biofilm. Monod’s model is a fairly good approximation to the solution of diffusion models. If some characteristics of particles of sludge and biofilm are known, it is possible to estimate the half-saturation constant k,. The k, value for large particles and a thick biofilm is much larger than that for small particles.

The k , value also depends on the concentration of active forms of microorganisms oxidizing a simple substrate; the concentration is governed, in turn, by the conditions of preliminary growing of activated sludge or biofilm. Ac- cording to Rao and Gaudy,4 the linear glucose consumption rate is 0.310- 0.965 g/h/g sludge for a sludge, grown on glucose, with a load of 5 g/L/day, and at the same time it is equal to 0.288-0.548 g/h/g sludge for a sludge, grown on glucose, with a load of 1 g/L/day. Thus, activated sludge adapts itself to consumption of high substrate concentrations due to the increase in the number of active forms of microorganisms.

The small k, values, sometimes observed for activated sludge (e.g., Wurh- mann gives k, = 0.2 mg/L for glucose; see ref. 5), are explained mainly by small concentrations of active microorganisms that also influences the maximal substrate consumption rate.

According to Tischler and E~kenfelder ,~ the average linear rate of consumption of a number of single substrates for filamentous sludge is larger than that for nonfilamentous sludge. This is easily explained by the large value of the surface/volume ratio for filamentous particles.

In the case of high substrate concentrations, the process of oxidation may be limited by the dissolved oxygen concentration.

A formal sorption model, describing the effect of saturation by high substrate concentrations, may be proposed6 instead of diffusion models.

1728 VAVILIN

Figure 3 shows the Monod relationship for glucose, oxidized by activated sludge and biofdm.

The analysis of some data6 shows that at small S, values a second order, rather than the first order used in Monod’s model, is adequate to the experiment. Figure 4 shows kinetic curves for oxidation of a number of simple substrates. It is easy to see that at some S values the reaction rate decreases sharply. The reaction kinetics may be described fairly well (Fig. 4) by Moser’s model:

For n = 2, the solution of (13) is

S = P + W

where p = (So - kf/So - p,,XT)/2. Moser’s model has been proposed for pure cultures. In the case of acti-

vated sludge, the sharp decrease in the reaction rate at small S values may be explained by, e.g., “disengaging” of a number of microorganisms actively consuming fairly high substrate concentrations S.

For generalized models (1) and (10) used in description of the process of oxidation of simple substrates, p is considered to be equal to zero. If we take n = 2, we have the following equation instead of eq. (1):

Fig. 3. Monod’s relationship (7) for activated sludge and biofdm in the case of glucose oxidation. Activated sludge: u = 24 mg/L. Experimental data are from ref. 7. Biofdm: the figure was taken from ref. 8 with permission of Professor J. Andrews.

AEROBIC BIOLOGICAL TREATMENT

s, m g / l

1729

300.

230

130

gluco E e \ - =--z-

k, + S dt

0 I 2 3 4 5 t,

Fig. 4. Kinetic curves of oxidation of glucose and aniline by activated sludge in keeping with eq. (14). Glucose: X = 2870 mg/L, pmax = 0.046 h-', R , = 20 mg/L. Aniline: X = 2960 mg/L, p- = 0.0089 h-', k, = 6 mg/L. Experimental data are taken from ref. 5. Aniline has been measured in TOC units.

At large S, values, the classical Monod relationship (7) is fairly adequate to the experiment. For instance, the following values are obtained for glucose (Figure 3): 3, = 291 mg/L, u = 24 mg/L, pmax = 1 h-l, k , = 190 mg/L.

At small S, values, the following relationship describes the experiment well.

= p(S,) = kS,' SO - S e v = X T

(16)

where k = pmax/k j . The following values are obtained for glucose (Fig. 5): 3, = 7 mg/L, u = 1 mg/L, k = 1.35 X (L/mg)2 h-l. Here, 5, is the average value of the effluent substrate concentration, and

1730 VAVILIN

0 5

Fig. 5. A second-order relationship for glucose oxidized in an aeration tank. R = 1.35 X (L/mg)2/h-', u = 1 mg/L. Experimental data are taken from ref. 9.

is the root-mean-square deviation of measured and estimated Se values (N is the number of measurements and $ is the number of coefficients in the model). The found coefficients correspond to minimal u values.

The total data series shows that model (15) is adequate to the experiment. Its coefficients may be roughly estimated from the linear form

For example, for the above two data series, for glucose, the values pmax = 0.886 h-', k , = 102 mg/L were obtained, with the u value equal to 39 mg/L for the first series and 2.3 mg/L for the second series. The numerical search for the minimum (17) for the generalized model (1) at p = 0 gave pmax = 0.936 h-', k , = 168 mg/L, n = 1.43, and u = 19.8 mg/L for the first series and u = 2.1 mg/L for the second series.


THE OXIDATION KINETICS OF MULTICOMPONENT POLLUTANTS

As stated earlier, multicomponent pollutants are measured in BOD, COD, and TOC units. Because in the course of treatment the number of hardly oxidizable compounds increases in the treated water, the increase in the COD/ BOD ratio is fairly evident. Respective constants of oxidation rates for COD are appreciably smaller than those for BOD.

The oxidation kinetics of a multicomponent organic component may be a sum of oxidation kinetic curves for single substrates, which is experimentally shown in ref. 5. Then

N

I= 1 s = c S&) (19)

and for the rate

where I is the order number of a single substrate and N is their total number. For example, model (13) at n = 2 with the respective solution of (14) may be used for individual components.

The following equation may be written for the concentration of a multicomponent pollutant:

- = -Xp(S) dS dt

which is certainly a mere formal approximation of eq. (20). The empirical function, instead of an equation of the type (21), may be directly sought:

which is an approximation of eq. (19). The relationship p(S) = C p l [ S l ( t ) ] is the function of the initial concentra-

tions of single pollutants and, therefore, of the initial concentration of the multicomponent pollutant. At large So and Sol values, respectively, there is a zero order for the concentration S :

The following form of eq. (21) has been proposed by the authorlo:

which is a modification of Fair and Geyer's model"

1732 VAVILIN

and that of Grau, Dohanyos, and Chudoba's modelI2

The solution of eq. (24) is

s = S ~ / " ~ I + k(n - 1)s;-1-pxt (27)

Taking into account eq. (27), we write eq. (24) as

S" + k(n - l ) X t ] (28)

Equation (28) shows that the constant of the rate of the pseudo-first-order is a decreasing function of time at n > 1 . This may be explained by the supposi- tion that in the course of oxidation the process tends to more hardly oxidizable components.

Model (10) is a generalization of eq. (24). Figure 6 shows an example of a kinetic curve for municipal sewage water oxidation.

Activated sludge, adapted to the oxidation of a certain range of pollutants (hardly oxidizable ones in the case of small loading values F and readily oxidizable ones in the case of large values F), requires a certain adaptation

- = -kX- = -kXS/[S{-"+' dS

dt so"

0 2

I

4 6 t, hr

Fig. 6. Kinetic curves of sewage water oxidation and their description by model (10). X = 1250 mg/L (original sewage water). X = 1560 mg/L (twice-concentrated sewage water). X = 2920 mg/L (four-times concentrated sewage water). Experimental data are taken from ref. 13. The (I value may be made smaller, if the parameter n increases.


period in order to oxidize a different range of pollutants. It is due primarily to the change in the type composition of sludge in the course of adaptation.

TRADITIONAL MODELS OF BIOLOGICAL TREATMENT

The most frequently used model in description of the treatment process in a completely mixing reactor is the first-order Eckenfelder model l4 :

= p(Se) = kSe SO - S e

X T v =

Eckenfelder's model has been modified by Grau, Dohanyos, and Chudoba12:

In turn, model (30) has also been subjected to modificati~n'~:

where Sh is a correction for hardly oxidizable compounds. Table I shows a review of the frequently used models as well as a number of

new ones. It is easy to be convinced that traditional models are either particular cases of generalized models (1) and (10) or their various approximations. Figure 7 shows, as an example, the approximation (30) of the generalized model (1).

It should be noted that a number of models, proposed for design of completely mixiing reactors, may be also used for design of plug-flow reactors. For instance, model (7) may be applied to design of trickling filters and rotating disks, where the liquid flow regime approaches the plug-flow regime.

DESIGN OF REACTORS OXIDIZING MULTICOMPONENT SEWAGE WATERS AT SMALL S, VALUES

(HIGH-LEVEL TREATMENT)

A particular case of generalized models (1) and (10) for high-level treatment is

1 dS S" - --p(S) = -k-

X dt S;-' (33)

where k = pm,/ks. Thus, we have only two coefficients-k and n. Figure 8 shows that, according to eq. (32), an increase in the influent pollutant concentration SO results in an increase of s,* and v* (greater contribution of more

TA

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1)

than

mod

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6). I

t m

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de

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s so

met

imes

app

lied

to d

esig

n of

plug

-flo

w

!-ac

tors

. It

may

be

used

for

rou

gh t

reat

men

t des

ign.

Con

tois

’s m

odel

is

a m

odif

icat

ion

of M

onod

’s m

odel

. It

im

prov

es M

o-

nod’

s m

odel

in

the

case

of

tran

sitio

n to

tre

atm

ent

at a

hig

her

leve

l, si

nce

it co

nsid

ers

the

low

erin

g of

the

“act

ivity

” of

mic

roor

gani

sms w

ith

an i

ncre

ase

in t

heir

con

cent

ratio

n. I

f fa

ct,

it is

a be

tter

appr

oxim

atio

n of

the

gene

raliz

ed m

odel

(1)

as

com

pare

d to

Mon

od’s

mod

el.

se -

sh

P(S

,) =

Pnl

ax -

SO

k p

(S,)

= kS:/So

rn fr

om “

satu

ratio

n.”

g s

e

P(S

,) =

Pm

ax _

__

k,

+ S,

S k,

+ S s,

k,X

+ s,

Fi P

(S) =

Pm

ax ~

P(S

,>) =

Pm

ax -

5 5 3

Hal

f-or

der

mod

el d

escr

ibes

wel

l th

e ex

peri

men

t in

the

cas

e of

roug

h tr

eatm

ent

and

larg

e S:

valu

es.

It m

ay b

e us

ed f

or a

n ae

ratio

n ta

nks,

tr

ickl

ing

filte

rs, a

nd r

otat

ing

disk

s.

Fair’

s m

odel

has

bee

n pr

opos

ed f

or d

esig

n of

plu

g-flo

w r

eact

ors.

It

de-

scri

bes

wel

l hi

gh-le

vel

trea

tmen

t at

sm

all S:

valu

es. F

air’

s fu

nctio

n fo

l- lo

ws f

rom

the

gene

raliz

ed m

odel

(10

) at k

a-”

Si >

> St

: an

dp =

n - 1

. 3 VI

TA

BL

E I (continued)

Expression for treatment rate:

p(S

,) according to (I), p

(S) according to (10)

No.

= type of transfer function s, =f(So, x, n

Com

ments

Particular case of 14 has been used by the author."

Modification of 14 has been proposed by the author."

17. S

, = y + (a

+ Q1'2)1/3 + (a

- Q

1/2)1/3 Pm

axSpZ G

eneralized model (1) at n =

2 and p =

1. P

(S,) =

kSS0 + s,'

at Q =

(y2

+ p3 2 0, w

here

2 p =

-7

+ k,So/3; S, =

y + y1,2,3 at Q <

0 (in this case <

0). It is necessary to select S

, > 0

.yl =

2(-~

)'/~

cos ~/

3

at cos Q =

a

/[

(-

~)

~]

~/

*,

y2,3 =

-2

(--~)'/~

cos(Q

/3 * 2?r/3). The sign of

the square root is the sam

e as with a

.

aFor trickling filters or rotating disks the X value is proportional to specific surface of media or rotating disks; for trickling filters it is m

ore correct to use the m

ean contact time T

H - arD

/Qm

instead of aT = d

/Q.


O <I s:2 SO ‘e

Fig. 7. Approximation (30) of the generalized model (1).

readily oxidizable compounds to the general process of oxidation), while an increase of the parameter /3 = XT leads to the “capture” of a larger quantity of hardly oxidizable compounds by the reactor and the v* and S,* values decrease, respectively.

Analysis of some data on oxidation of municipal sewage water in aeration tanks has shown that n = 2 in eq. (32) and n = 3 in eq. (33) are fairly adequate to the experiment. It is easy to obtain the following from eqs. (32) and (33):

S, = So/d + 2kXT (35)

Note that models (34) and (35) lead approximately to the same u values.

F1=2S0/XT

F2=So/XT

B -s0/2m 3-

-3

Fig. 8. The effect of the concentration So and the parameter /3 = XT on the treatment process (high-level treatment). Explanations are in the text.

1738 VAVILIN

Routine first-order models (n = 1) give

s, = SO/(l + RXT)

S e O = S B-kXT

(36)

(37)

Figures 9-11 show examples of processing the data on the oxidation of municipal sewage waters in an aeration tank, trickling filter, and rotating disk.

0 , m c

3 , m 5

0

0,015

0,010

0,005

S, = Soe-m

0 20 40 60

S,, W/lBOD

Fig. 9. The dependence of the constants of rate of models (37) and (35) in the case of oxidation of municipal sewage water in 36 plug-flow aeration tanks on the S, value (high-level treatment). Experimental data are taken from ref. 18; r is the correlation coefficient.


W

'e

Fig. 10. The dependence of the constants of the rate of models (37) and (35) in the case of oxidation of municipal sewage water in a trickling filter with a gravel media on the S, value (high- level treatment). Experimental data are taken from ref. 19; r is the correlation coefficient.

VAVILIN

I Fig. 11. The dependence of the constants of the rate of models (36) and (34) in the case of

oxidation of municipal sewage water in a rotating disk on the S, value (high-level treatment). Ex- perimental data are taken from ref. 20: So = 150 + 36 mg/L BOD, T = V/q = 11.2 5z 10.6 h, S, = 25.2 +. 10.7 mg/L BOD, and r is the correlation coefficient. The processing of data contained in ref. 20 for five different rotating disks (N = 40) has given k = 5.6 h-’ for model (34), u = 4.5 mg/L, and average S, = 24.8 mg/L BOD.

Figure 12 shows the compliance of function (32) at n = 2 with the process of peptone oxidation in an aeration tank.

As the processing of some data on oxidation of municipal sewage water in completely mixing and plug-flow aeration tanks, the rate constants, estimated for the same transfer characteristics S, = S, (So, X , T), are approximately equal. For instance, k = 9 X L/mg/h for model (34), k = 5 X L/mg/h for model (35), and k = 1 X lop3 L/mg/h for model (36). The above becomes evident if one considers that in the course of oxidation of municipal sewage water the removal of individual components mainly follows a zero order.

The models “work” approximately equally, with a fairly narrow range of variations of So, X , T, and S, .lo

The increase in the microorganisms’ concentration X results in a more rapid transition to hardly oxidizable components, which naturally diminishes the process rate constant. This is why McKinney’s model” does not yield to Eckenfelder’s model (see Table I) and the fairly poor dependence Of the efficiency of the process on the microorganisms’ concentration is evident. On the


0 1 2

2 ',/So, w/l mc

Fig. 12. Relationship (32) in the case of peptone oxidation (n = 2). Experimental data are taken from ref. 15: So = 353 & 269 mg/L TOC, X = 2745 rfi. 290 mg/L, T = 0.77 f 0.35 day, S, = 24.9 f 12.7 mg/L TOC, and u = 1.8 mg/L.

whole, first-order models introduce a systematic error (they underestimate the treatment rate at large S, values and overestimate at small S, values). The systematic error is eliminated if models of a higher order, e.g., (34) and (35), are considered.

The temperature increase also leads to a more rapid transition to hardly oxidizable components. Novak2' indicates that, while applying models of the Monod type, it is necessary to consider

Roe C 1 f "S ksOeC2" + S

v =

where v is the specific treatment rate; ko, ksO, C1, and C2 are constants. It is evident that with a decrease of S values, the specific treatment rate depends on temperature increasingly less.

If first-order models (36) and (:7) are applied, the correction for temperature is usually introduced:

kr0 = k 200 ~ ( t " - m " ) (39)

where k,. and kmo are rate constants at some temperature and at to = 20°C,

1742 VAVILIN

respectively, 0 is the constant called the temperature coefficient (0 = 1.0-1.1).

It was shown that the correction for temperature decreases with diminishing organic loading F, which is equivalent to the transition to a treatment at a higher level. Thus the 8 value depends not only on the sewage-water type but also on the operating conditions of the treatment system.

The data on high-level sewage water treatment in five rotating disks (the experimental data are taken from ref. 20, with n = 41), processed by the author, have shown the practical independence of rate constants from temperature in models (34) and (35).

The excessive mass of microorganisms may be estimated from eq. (2). If the flow recirculation is taken into consideration, it is easy, using eq.

(33), to obtainlo

(40) SO se =

(1 + R)"-Vl + k(n - 1)XT - R

at

V T =

q ( 1 + R )

where R is the recirculation coefficient. The analysis of some data has shown that the consideration of circulation

does not lead to an appreciable decrease in the root-mean-square deviation u [eq. (17)] in the case of aeration tanks, which oxidize municipal sewage water. It is more important to trickling filters.

DESIGN OF REACTORS OXIDIZING MULTICOMPONENT SEWAGE WATERS AT LARGE S, VALUES

(ROUGH TREATMENT)

As was said above, at large S,* and, hence, So values, microorganisms are saturated by the most abundant substrate components in original sewage water, and these components are oxidized, in keeping with the zero-order kinetics. In this case, a maximal increment of microorganisms biomass is observed.

With diminishing S$ values, the classical Monod model (7) becomes more adequate to the experiment. A good approximation of it is the n-order model (n < 1) and its particular case-the half-order model

Figure 13 shows that the effect of the parameter 0 = XT on the specific oxidation capacity V* and on the effluent concentrations S,* in keeping with eq. (42). A comparison of Figures 8 and 13 shows that in the case of rough


Fig. 13. The effect of the concentration So and the parameter f l = XT on the treatment process (rough treatment). Explanations are in the text.

treatment a close dependence of the efficiency of the treatment process on the microorganisms’ concentration and retention time of sewage (appreciable variations in Sz values) is observed. The deviation from the zero-order kinetics means that in the course of the treatment process, a fairly rapid “disappear- ance” of the mostly oxidized pollutant components occurs, and this results in a substantial decrease in the treatment rate.

Figure 14 shows examples of processing of some data on sewage-water oxidation in a trickling filter at fairly large S,* values. Model (42) describes the process much better than the frequently applied model (29) that underesti- mates the treatment rate at small Se values and overestimates it at large S, values.

With decreasing S,* values, when the transition to a treatment at a higher level takes place, Monod’s model becomes inadequate to the experiment. The Contois model, its modification,

describes the treatment process much better, since it formally takes into account the decrease in the activity of microorganisms with an increase in their concentration X. In fact, with an increase in X values, the transition to the oxidation of hardly oxidizable compounds is more rapid, which is considered by generalized models (I) and (10).

The coefficients of models (43) may be approximately estimated from the linear form of eq. (43)

1744 VAVLIN

SO s, = 1 + kD/p

0 500 loo0

S,, %A BOD Fig. 14. The dependence of the constants of the rates of models (36). (37). (42) in the case of

oxidation of sewage water from hydrolysis production on the S, value (rough treatment). Q = q/A is the specific discharge of sewage liquid ( A is the cross-sectional area of the trickling filter) and D is the filter depth. Experimental data are taken from ref. 22.

Figure 15 shows the results of processing of data on oxidation of sewage water from yeast production, in keeping with eq. (44).

In the case of rough treatment, a closer dependence of the process rate on temperature is observed. This follows from, e.g., eq. (38).

Large pollutant concentrations may lead to the oxidation rate beginning to govern the dissolved oxygen concentration C. SkirdovD underlines the fact that the increase in the treatment rate due to the increase in C is possible only under rough treatment conditions. In the case of rough treatment, the efficiency of multistage schemes of treatment with different dissolved oxygen


0 %4

‘ e n

Fig. 15. Processing of data on oxidation of sewage water from yeast production for the Con- tois model in keeping with eq. (44). Experimental data are taken from ref. 23 and r is the correlation coefficient: So = 3850 1293 mg/L BOD, X = 3728 k 799 mg/L, T = 17 k 3.2 h, S, = 280 k 253 mg/L BOD, and u = 130 mg/L BOD. The numerical estimation of the minimum_ u is a more accurate procedure for determining coefficients; this resulted in pmax = 0.096 h-’, k, = 0.041, u = 116 mg/L.

contents increases. It is possible to show24 that the limiting concentration of dissolved oxygen increases proportionally to the S, value.

The excessive biomass of microorganisms may be estimated from eq. (2). The S, value for municipal sewage water is, as a rule, far from saturation,

and a high-level treatment is employed. In exceptional cases, e.g., Figure 6, S, may “saturate” a complex of microorganisms. These may be described by generalized models (1) and (10).

SOME CONSEQUENCES

It is well known that an important characteristic, governing the settling capacity of activated sludge, is the sludge index SVI. With large SVI values,

1746 VAVILIN

slowly settling sludge does not concentrate on the settling basin bottom and the treatment system fails. Fairly low values of SVI (100 cm3/g) are main- tained within a certain range of organic load values F. At small as well as large F values, sludge bulks and SVI values increase.

Sludge bulking is associated with disproportionate development of filamentous microorganisms, which gain an advantage over zooglea microorganisms. At small F values, hardly oxidizable components predominate among oxidizable substrates, which results in excessive development of some forms of filamentous microorganisms. At large F values, the dissolved oxygen concentration restrains the treatment process. Lack of oxygen also leads to excessive development of filamentous microorganisms. The maximum concentration of dissolved oxygen, below which sludge bulks, increases with increasing F value^.^

In the case of rough treatment (large So and S, values), a close dependence of the treatment efficiency on the microorganisms concentration, sewage liquid retention time, temperature, and concentration of dissolved oxygen is observed. The above causes the obtained experimental results to become less reproducible than in the case of high-level treatment.

CONCLUSIONS

The processing of numerous experimental data shows that there are general regularities of the biological treatment process independent of the reactor type (an aeration tank, trickling filter, rotating disk). Particular models of treatment processes, given earlier by different researchers, may follow from generalized models of a certain type. The use of routine models leads, as a rule, to systematic errors. The design but not the dynamic models of aerobic treatment processes are considered in the article. The latter are pref- erable for management purposes. For design good simple models with a minimum number of coefficients are important. There are only three coefficients pma, k,, and n for generalized models (1) and (10) at p = n - 1.

Some known phenomena are not described with the approach suggested in the article, e.g., the organic substance reservation by the aggregate of microorganisms. Experimental data treated in the article are usually unfiltered BOD or COD. It is well-known that in some cases different models are pref- erable for soluble and particulate organic matter. However, for the rough evaluation of treatment efficiency the total BOD or COD can be considered.

References

1. V. A. Vavilin, Dokl. ANSSSR, 258, 1269 (1981). 2. L. I. Gyunter, Doctoral thesis, K. D. Pamfiiov Academy of Municipal Economy, Mos-

3. V. A. Vavilin, V. B. Vasiliev, and S. S. Kuzmin, Ecol. Mod., 10, 105 (1980). 4. B. S. Rao and A. F. Gaudy, J. Water Pollut. Control Fed., 38, 794 (1%).

cow, 1973, in Russian.


5. L. T. Tischler and W. W. Eckenfelder, h e e d i n g s of the 4th Industrial Waste Confer-

6. V. A. Vavilin, Dokl. ANSSSR. 256, 759 (1981). 7. P. Krishnan and A. F. Gaudy, -dings of the 21st Purdue Industrial Waste Confer-

8. B. H. Kornegay and J. F. Andrews, J. Water Pollut. Control Fed., 40, 460 (1968). 9. S. Siber and W. W. Eckenfelder, Water Res., 14, 471 (1980).

ence on Water Pollution Research (Pergamon, London, 1968), p. 361.

ence, 1966.

10. V. A. Vavilm, Acta Hydrochem. .Hydmbwl., to appear. 11. G. M. Fair and J. C. Geyer, Water Supply and Waste Water Disposal (Wiley, New York,

12. P. Grau, M. Dohanyos, and J. Chudoba, Water Res., 9, 637 (1975). 13. J. Chudoba, Proceedings of the 4th Industrial Warte Conference on Water Pollution Re-

14. W. W. Eckenfelder, Industrial Water Pollution Control (McGraw-Hill, New York, 1966). 15. C. E. Adam, W. W. Eckenfelder, and J. C. Hovious, Water Res., 9, 37 (1975). 16. R. E. Mc-Kinney, J. Sanit. Eng. Div. ASCE, 88, 87 (1%2). 17. J. Oleszkievicz, Env. Prot. Eng.. 2, 85 (1976). 18. T. R. Haseltine, Water Sewage Works, 102, 487 (1955). 19. C. E. Keefer and J. Meisel, Sewage Works, 99, 277 (1952). 20. H. H. Benjes (Design seminar handout), Small wastewater treatment facilities (USEPA,

21. J. T. Novak, J. Water Pollut. Control Fed., 46, 1984 (1974). 22. Yu. V. Voronov, A. L. Ivchatov, V. A. Vavilin, and S. S. Kuzmin, Hidmiiznoje proiz-

23. I . V. Skirdov, Doctoral thesis, VNIIVODGEO, Moscow, 1976, in Russian. 24. V. A. Vavilin and V. B. Vasiliev, Mathematical Modeling of Processes of Biological

25. J . C. Palm, D. Jenkins, and D. S. Parker, J. Water Pollut. Control Fed., 52, 2484 (1980).

1954).

search, (Pergamon, London, 1968), p. 375.

Cincinnati, 1979).

wdstvo. N6, 19 (1981).

Sewage Water Treatment by Activated Sludge (Nauka, Moscow, 1979), in Russian.

Accepted for Publication November 17, 1981; corrected proofs received April 21, 1982

the theory and design of aerobic biological treatment

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