A THEORETECM. AND EXPENMENTAL STUDY OF
FACTORS GC‘VERNING THE OPERA'FION OF
CONISNUOUS FLQW CULTURES WITH FEEDBACK

Thasis for the Degree of Ph. D.
MICE-{EGAN STATE UNIVERSITY
WilEiam A. Sack
1391543

ӣ615

This is to certify that the

thesis entitled

A THEORETICAL AND EXPERIMENTAL STUDY OF
FACTORS GOVERNING THE OPERATION OF
CONTINUOUS FLOW CULTURES WITH FEEDBACK

presented by

William A . Sack

has been accepted towards fulfillment
of the requirements for

Rh 2 degree in Sanitary Engineering

7; //é/4g

Major profeszg)

Date #249.»

LIBRARY

Michigan State
University

 

 

 

A THEORETICAL AND EXPERIMENTAL STUDY OF FACTORS
GOVERNING THE OPERATION OF CONTINUOUS FLOW

CULTURES WITH FEEDBACK

by

William A? Sack

AN ABSTRACT OF A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOC TOR OF PHILOSOPHY

Department of Civil and Sanitary Engineering

1964

ABSTRACT

A THEORETICAL AND EXPERIMENTAL STUDY OF FACTORS
GOVERNING THE OPERATION OF CONTINUOUS FLOW

CULTURES WITH FEEDBACK

by William A. Sack

A continuous flow culture with feedback was operated under
steady state conditions at growth rates ranging from 0. 009 to 0. 2.36.
For comparison. the system was also operated without feedback under
steady state conditions at three growth rates ranging from 0. 079 to
0. 292. An artificial sterile medium based on glucose served as the
feed. Substrate concentrations of 200, 400 and 1000 mg/l were used.
The majority of the runs were made at a concentration of 1000 mg/l.
A mixed culture of microorganisms was used in the system.

A mathematical model based on equations developed by
Herbert (1961) was presented to describe the operation of the system.
It was found that the experimental steady state cell concentration :5
was consistently greater than that predicted by the model. From a
material balance around the system and from direct measurements,

it was found that cells were being retained in the reactor longer than

Abstract 2 William A. Sack

predicted by the equation. for complete mixing conditions. This was
found to be due to evaporation, adhesion of cells to the vessel walls
and partial blockage of the effluent port. When the model was modi-
fied to include the increased retention of solids, good agreement was
obtained between measured and computed steady state reactor cell
concentrations. The correction of the model was expressed as a
retention factor L which varied from 0. 727 to 0. 999 during the runs.

The reactor cell concentration was largely dependent on a
parameter called the feedback factor A". A" is in turn a function of
the recycle ratio a. the cell concentration factor C and L. The value
of C was found to decrease from Z. 20 to 1. 28 when a was increased
from 0. 36 to 3. 37.

Daily fluctuations in 3E during a given run were due to
differences between the amount of cells produced and the amount of
cells discharged from the system. The daily fluctuations were pre-
dicted reasonably well using a transient condition analysis instead of
a steady state type of analysis.

The yield coefficient Y was found to increase as the rate of
growth was increased. For runs made at S' = 1000 mg/l, -Y- increased
from 0.413 to 0. 556 as k increased from 0. 01 to 0. 29. The variation

1

in Y for all runs was from 0. 2.52 to 0. 556.

Abstract 3 William A. Sack

The steady state reactor substrate concentration Swas
found to increase as k1 increased. The relationship between the

two parameters was correctly expressed by a first order equation

first suggested by Teissier (1936) as:

-cS
k1 — km(1-e )

where km = maximum growth rate ; 0.87 and c = 0. 02. When the

substrate consumption rate kc was plotted against k . a linear re-

1
lation was obtained. However. the curve showed that 15 mg glucose
per gram cell weight per hour were being consumed at a k1 of zero.
Hence a certain rate of substrate uptake was necessary to sustain
cell metabolism without producing growth.

The settling properties of the mixed culture were quite
variable. However flocculent growth was present during all the runs
with feedback.

Mixing studies conducted using the reaction chamber
showed that a dye solution exhibited perfect mixing while various
suspensions showed slight departures from theoretical complete mix-

ing. The departure from complete mixing was greatly influenced by

the Specific gravity of the particles in suSpension.

A THEORETICAL AND EXPERIMENTAL STUDY OF FACTORS
GOVERNING THE OPERATION OF CONTINUOUS FLOW

CULTURES WITH FEEDBACK

by

William A. Sack

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOC TOR OF PHILOSOPHY

Department of Civil and Sanitary Engineering

1964

ACKNOWLEDGEMENTS

The author wishes to eXpress his indebtedness and
appreciation to Dr. Karl L. Schulze whose generous help and
encouragement made this thesis possible.

The author would also like to thank Dr. Robert F. McCauley
and Dr. Walter L. Mallmann for their guidance concerning various
portions of this work.

Acknowledgment is made to the Division of Engineering
Research and to the National Institutes of Health for their support
during the course of this research.

I would like to eXpress my sincere gratitude to my wife
for her aid and understanding which made the years of my education

possible.

ii

II.

III.

IV.

TABLE OF CONTENTS

INTRODUCTION

LIT ER ATUR E REVIEW

THEORETICAL CONSIDERATIONS

A.

Flow or mixing pattern in aerator

Growth kinetics

Effect of basal matabolism

Mathematical model of the continuous flow system

Mathematical model of the continuous flow feedback
system

EXPERIMENTAL APPARATUS, CULTURE AND METHODS

A.

B.

C.

D.

E.

Description of apparatus
Sterilization of the apparatus
Culture

Nutrient medium

Analytical technique 5

RESULTS

A.

B.

C.

The yield factor
The reactor cell concentration
Relationship between Specific growth rate and reactor

substrate concentration

iii

10

13

l4

18

24

24

32

33

38

40

47

47

49

61

VI.

VII.

VIII.

IX.

D. Comparison of actual and predicted reactor cell
concentrations

E. Comparison of actual and predicted final effluent cell
concentrations

F. Relationship between feedback factor and reactor cell
concentration I

G. Relationship between recirculation ratio and cell
concentration factor

H. Effect of a negative feedback factor on system Operation

I. Relationship between Specific growth rate and Specific
substrate consumption rate

J. Relationship between growth rate and yield coefficient

K. Organic load on system

L. Transient condition analysis

M. Mixing studies

DISCUSSION

CONCLUSION

APPENDIX

BIBLIOGRAPHY

iv

66

68

69

7O

71

73

74

75

76

78

145

162

164

166

Table

10

11

12

13

14

15

16

17

18

19

20

LIST OF TABLES

Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data
Measured and computed data

Measured and computed data

- Run No.

- Run No.

- Run NO.

- Run No.

- Run No.

- Run No.

- Run No.

- Run No.

- Run No.

- Run No.

- Run No.

Run No.

Run No.

Run No.

Run No.

- Run No.

2a

2b

8a

9

10

11

12

Average values of measured and computed data

Run Nos. 1 to 5

Average values of measured and computed data

Run Nos. 6 to 12

Data obtained from Run Nos.

20 to 22

Average values of measured and computed data

Run Nos. 20 to 22

Page
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99

100

101

102

103

104

Table Page

21 Data obtained from evaporation experiments 105
22 Computed rate of evaporation assuming no

reactor effect 106
23 Comparison of measured reactor effluent concentration

and reactor cell concentration 107
24 Summary of data for batch determination of km 108
25 Data concerning rates of substrate supplied

and consumed 109
26 Comparison of experimental and computed variation

in reactor cell concentration - Runs 1 to 5 110
27 Comparison of experimental and computed variation

in reactor cell concentration - Runs 6 to 9 111
28 Comparison of experimental and computed variation

in reactor cell concentration - Runs 10 to 12 112
29 Data from washout Run W-l 113
30 Data from washout Run W-2 113
31 Data from washout Run W—3 114
32 Data from washout Run W-4 114
33 Data from washout Run W—5 115
34 Data from washout Run W-6 115
35 Inter-relation of E, C and (1 following a change in 132

vi

LIST OF FIGURES

Figure Page
1 The inter —re1ation of A, C and o. 20
2 Continuous flow feedback apparatus 25
3 Schematic diagram of continuous flow feedback apparatus 26
4 Culture aeration System 31
5 Standard glucose curve 43
6 The effect of L on the feedback factor 116
7 Relationship between k1, experimental and calculated-S

values 117
8 Determination of km 118
9 Comparison of Z and x" ; E and x'F; x8" and xer - Run No.
1 . 119
10 Comparison of 2 and 3;"; 3; and x'F; E6” and xer - Run No. 120
11 Dzaily variation in 2, comparison of 3:6" and Xer - Run No.
2a 121
12 Daily variation in 2, comparison of 3:8" and Xer - Run No.
2b 122
13 Daily variation in 3:, comparison of :6" and xer - Run No.
3 123

vii

Figure

14

15

16

17

18

19

20

21

22

23

24

Comparison
No. 4
Comparison
No. 4a
Comparison
No. 5
Comparison
No. 6
Comparison
No. 7
Comparison
No. 8
Comparison
No. 8a
Comparison
No. 9
Comparison
No. 10
Comparison
No. 11
Comparison

No. 12

of 3? and E";

of x and x”; x and x'F; x "

of x and x";

of x and x“;

of E and Qv;

of x and x";

of x and x";

of x and x";

of x and x";

of x and x";

of x and x";

x and x'F; x "

e

x and x'

E and X'F; § ”

xandx' ;x "

xandx' ;x"

viii

and x
er

and x
er

and x
er

and x
er

and x
er

and x
er

and x
er

and x
er

and x
er

and x
er

and x
er

- Run

- Run

- Run

- Run

- Run

- Run

- Run

- Run

- Run

- Run

- Run

Page

124

125

126

127

128

129

130

131

132

133

134

Figure

25

26
27
28
29
30
31-1
31-2
32
33
34
35
36
37

38

39

Comparison of average experimental and computed reactor
cell concentration

Relationship between E and A"

Experimental relationship between C and (1

Variation in a, A and C due to a negative A - Run No. 12
Comparison of kC and k1
Relationship between Y and k1
F diagrams of some continuous flow models

Comparison of completely and incompletely mixed models
F diagram for Run W-l

F diagram for Run W-2

F diagram for Run W-3

F diagram for Run W—4

F diagram for Run W-5

F diagram for Run W-6

Theoretical relationship between D and reactor and final
effluent cell concentration for systems with and without

feedback

Theoretical relationship between 3? and A"

ix

Page

135
136
137
138
139
140
141

141

142
142
143
143
144

144

156

157

I. INTRODUCTION

The activated sludge process has been used as a method of
sewage treatment in this country for nearly half a century. During this
time! the process has been refined and modified until today it is the most
popular method of waste treatment for cities of over 10, 000 population.
However, the design of the process is based largely on empirical
relationships which are known to have been successfully applied in the
past. In the conventional plant, the untreated waste and return sludge
enter at one end of the aeration tank and spend a theoretical detention
time of about 6 hours flowing through the tank. A bacterium moving
along with a given element of waste may initially find adequate food for
growth. However, by the time the element of waste reaches the outlet
end of the tank its substrate concentration is reduced to a low level and
the bacterium may be approaching the endogenous metabolism level.
Because of the variation in growth rate and the gradients in substrate
and cell concentration, this type of System does not lend itself well to
theoretical analysis. However, studies have shown (Kehr, 1936;
Sawyer and Rohlich, 1943) that’the hydraulic flow pattern of many of the
conventional plants is close to complete mixing. The completely mixed
process has found increased popularity in recent years in the treatment
of high concentration industrial wastes and in the small so-called
"package" plants. In these plants there are no appreciable substrate

or solids concentration gradients in the aeration tank.

A number of different experimental approaches have been
used to study the activated sludge process. They range from operation
of a laboratory-scale reactor to that of a full-scale plant or pilot plant.
These units may be operated as batch or continuous culture systems.

The term "batch system” will be used for a system to which
materials are added and reaction products withdrawn at relatively
large time intervals. Herbert (1961) points out that the term "con-
tinuous culture" is applied to almost any process involving passage of
fluids through a reactor system in which they are exposed to micro-
biological action.» The classification of continuous culture systems
may be made according to the nature of the overall metabolic reaction
taking place or the type of reactor operation. Because a system of
given operational type will behave much in the same way regardless of
its metabolic classification, the reactor operation designation system
is the most widely accepted and will be used in this paper.

Continuous culture systems may then be divided into open
and closed systems which are further subdivided into homogeneous
and heterogeneous systems with reference to mixing characteristics.
The terms open and closed refer respectively to those systems where
cells are discharged continuously in the effluent or wholly retained
within the system. The homogeneous designation refers to. the type
of reactor where no gradients exist with respect to cell or substrate

concentration. This is also referred to as a completely mixed system.

Ideal heterogeneous reactors are characterized by "piston" or "plug"
flow through the reactor with no inter-mixing of the contents. All
systems can further be subdivided into those with and without feedback
and into single and multi-stage systems. With regard to the type of
control, the systems can be classified as those subject to internal and
those subject to external control. In the internally controlled type,
nutrients are supplied in excess at all times. The organisms thus
grow at their maximum growth rate with the steady state concentration
of organisms being regulated by the nutrient feed rate. In the externally
controlled unit the nutrient supply is limited and thus determines
growth rate. These are the conditions most similar to those of the
activated sludge process and hence this type of control is almost ex-
clusively used to study this process.

The two system types pertinent to this investigation may be
described as (1) the homogeneous, single stage, open externally con-
trolled continuous flow system and (2) the homogeneous, single stage,
open externally controlled continuous flow system with feedback. For
the sake of expediency, (1) and (2) will be referred to respectively as
the continuous flow system without feedback and the continuous flow
feedback system. A third general type often used is the continuous
flow system with aeration and concentration combined in the same unit.

The completely mixed activated sludge plant may be considered

to be a continuous flow feedback system. This system has recently

been analyzed and mathematical equations have been developed which
may be used to describe its operation. It is the object of this thesis
to test the validity of these formulations by operation of a laboratory-
scale unit under controlled conditions. Two factors which are ex-
tremely important to the operation of the process are the recycle
ratio a and the solids concentration factor C. The latter is the ratio
of the cell concentration in the feedback to the reactor cell concen-
tration. The experimental program was especially designed to inves-
tigate the inter-relation between C, a and the reactor cell concentra-
tion. Very few data are available in the literature relating these

parameters under controlled conditions.

II. LITERATURE REVIEW

Batch fed units require relatively little attention and in-
strumentation and have therefore been extensively used to study the
bio-oxidation process and to establish design criteria for full-scale
continuous flow plants (Busch £131; , 1960; Weston and Stack, 1960;
Heukelekian _et_a_l., 1951; Busch, 1962; Quirk, 1959; Eckenfelder,
1956; Symons and Mckinney, 1958; Dryden _e_t_al. , 1956; Nemerow
and Ray, 1956; Gellman and Heukelekian, 1955; Candy 3311.. , 1963;
Weston, 1961; Sawyer e_tj_l., 1955; Zablatzky 921., 1959).

Although batch study is useful for determining the maximum
attainable growth rate or basic susceptibility to oxidation of a given
waste, it cannot duplicate steady state conditions produced by con-
tinuous organic and hydraulic loading and continuous solids wastage.
Busch 31331. , 1960 found significant differences in solids production
and settling characteristics of companion batch and continuous units
fed the same number of grams of glucose daily.

The single stage open system without feedback is the simplest
type of continuous flow system and probably has been the most widely
used constant flow unit to study bio-systems. As the name implies,
substrate is continuously fed at a given rate to a reactor containing
a stirred culture. The reactor volume is kept constant by a fixed

overflow line through which the reaction products leave the reactor.

Much of the basic theory concerning growth and substrate removal
has been derived using this type of unit (Monod, 1942, 1950; Novick
and Szilard, 1950; Herbert, 1956; Schulze and Lipe, 1963). Since
the system does not provide for concentration of the culture as in the
activated sludge process, it has been little used by sanitary engineers.
However, the growth of mixed cultures and BOD removal rates at
several different temperatures were studied by Garrett and Sawyer
(1952) with this type of system.

The continuous flow feedback system most closely simulates
the activated sludge process. It differs from the system described
above in that the cells in the reactor effluent are concentrated in a
separate unit and partly recycled to the reactor. Laboratory units
with separate concentration andlcell return facilities obviously present
operational difficulties and require close supervision. This is espe-
cially true at the low flow rates used in small scale operation. How-
ever, this type of apparatus allows study of the recycle ratio and cell
concentration factor. Both of these parameters vitally influence the
operation of the system.

The use of continuous culture units with feedback has been
reported by a number of workers. Gaudy£t_a_l. (1960) employed a
system featuring an air lift sludge return to study the efficiency of
removal of glucose at various organic loading rates. Kountz and

Fourney (1959) investigated sludge production by a metabolic energy

balance around a multiple unit total oxidation system. Pasveer

(1955) determined the feasibility of activated sludge treatment of citrus
wastes. Schulze (1963) developed a mathematical model for the con-
tinuous flow feedback system and applied it to operational data from
full-scale activated sludge plants.

Continuous flow culture systems with combined aeration and
concentration in the same vessel are designed to maintain a higher
level of suspended solids than would be possible with the normal
aeration unit. This is accomplished by the use of baffles which effec-
tively divide the unit into an aeration chamber and a sedimentation
chamber. Laboratory-scale plants of this type have been used for
basic study of the bio-oxidation phenomena as well as for investigation
and design of specific municipal and industrial waste problems (Coe,
1952; Busch and Myrick, 1960; Busch, 1954, 1959; Ludzack, 1960;
Stack and Conway, 1959; Orford Et_al_. , 1960; Hatfield and Strong,
1954; Washington and Symons, 1962).

The performance of plant-scale activated sludge units has
been widely studied both in pilot and full-scale investigations. How-
ever, a listing of the studies probably filling several pages would seem
to fulfill no purpose in connection with this dissertation. It is difficult
to obtain fundamental information from plant-scale studies because of
wide fluctuation in organic and hydraulic loading. In addition, the waste
itself is usually subject to continuous variation in its composition and

temperature.

III. THEORETICAL CONSIDERATIONS

The purpose of this investigation is to formulate and experi-
mentally test a mathematical model of the open type, single stage
continuous flow feedback system. The parameters on which the model
is based Should be fundamental and readily measurable. Various
approaches for this purpose have been suggested by a number of
authors (Busch, 1959, 1960a, b, 1962; Doshi, 1961; Eckenfelder,
1959, 1961; Eckenfelder and Porges, 1957; Garrett, 1958; Garrett
and Sawyer, 1952; Gaudy e_t_al. , 1960; Herbert g_t_a_l_. , 1956, Herbert,
1958a, b, 1960; McCabe, 1960; McKinney, 1962; Rich, 1963; Stack
and Conway, 1959; Washington g_t_a_l_., 1963; Weston, 1961; Weston
and Stack, 1960). Each approach is based on some type of material
balance around all or part of the system, and a mathematical state-
ment of Sludge growth-substrate removal relationships.

, A model representing any continuous flow culture system
must specify (1) the flow pattern expected to exist in the aerator, and
(2) a formulation relating cell growth to substrate concentration or the

kinetics of the growth process. These topics are considered below.

A. Flow or mixing pattern in aerator

 

Chemical engineering literature (Danckwerts, 1953; Green-
halgh et a1. , 1959; Levenspiel, 1962) lists two general types of steady

state continuous flow reactors. The ideal piston or plug flow type is

characterized by an orderly flow of fluid through the vessel with no
element of fluid overtaking any other element. This type of flow would
be approximated in a long tank having a relatively small cross section.
Each particle of fluid would have the same theoretical residence time.
The other type is called the backmix or completely mixed reactor.

The increments of the influent intermix immediately with the vessel
contents and lose their identity in every respect. Thus the exit stream
from the reactor has the same composition as that of the reactor fl‘aid.
Each element of fluid has an equal chance of being withdrawn from the
reactor at any instant and the residence time of any individual element
has little significance.

The standard vigorously aerated activated sludge tank
obviously does not completely conform to either the ideal piston flow
or ideal backmix flow model. However, studies by Kehr (1936) showed
that in a short mixing tank (6 feet wide by 15 feet long by 3 3/4 feet
deep) the detention or washout rate was reasonably close to that pre-
dicted by complete mixing theory. In a full-scale aeration tank, Sawyer
and Rohlich (1943) found that the back-flow was very significant when
practicing stage addition of activated sludge along the tank. The
existence of backflow suggests the tank contents were well mixed.
Obviously, to ascertain the degree of departure from complete mixing
would require specific studies in each case. However, it is felt that

the vigorous mixing provided in modern plants by either diffused air

10

or by mechanical aerators produces a flow pattern more closely

approximating backmix than plug flow.

The contents of the reactor used in this investigation were

continuously mixed by both a magnetic stirrer and by the air flow

used to aerate the culture. The incoming feed and the recycled flow

appeared to be quickly dispersed and intermixed throughout the vessel.

In order to determine how closely the flow pattern of the experimental

reactor conformed to the complete mixing model, a series of wash-

out experiments were conducted as will be reported in Section V.

B. Growth kinetic s

 

Symbols used in the following section are defined as follows:

X

S!

cell concentration, mg dry wt/liter, at time t
initial cell concentration

time , hr

average doubling time, that is, the time re—
quired for the concentration of organisms to
double

substrate concentration in reactor, mg/l
concentration of influent substrate , lug/1
saturation constant numerically equal to the
substrate concentration at which kl == 1/2km

dilution rate =4 Fi/v = number of complete

reactor volume changes per unit time

11

F1 = rate of flow of feed solution into the reactor
v = volume of reactor
Y = yield factor = net unit weight of cells formed

per unit weight of substrate used

. . 1 dx -1
k1 = spec1flc growth rate =- 3: 5:, hr
km = maximum growth rate for a given set of conditions
dx

overall growth rate.

Discussions of bacterial growth usually start with the familiar
relation:
dx/dt = klx 1

01‘

The specific growth rate may also be expressed in terms of the time

required for the concentration of organisms to double, t as:

d

The relationship between the specific growth rate and the concentration
of a substrate required for growth was first suggested by Monod (1942)

8.8:

 

km is the maximum growth rate obtained when substrate is present in

excess and Sn is a constant numerically equal to the substrate

12

concentration when k1 equals km/Z. According to equation 4, the

relation between k and S is hyperbolic with k

1 reaching km only at

l
infinity. The formulation also predicts that exponential growth can
occur at any value of k1 between zero and km if the substrate concen-
tration is held constant at its corresponding value. Equation 4 has
the form of an adsorption isotherm and is essentially the same as the
Michaelis-Menten equation used in enzyme kinetics. The bacterial
cell is thus considered as an enzyme molecule reacting with the sub-
strate at the reaction velocity k1.
Schulze and Lipe (1963), working with E. £o_l_i in continuous
flow culture, found a different type of equation also gave close agree-
ment between actual and theoretical reactor substrate concentration:
dk/dS = c(k — k)
m 1
In integrated form equation 5 becomes

k1 = km(l - e’CS)
where c is a constant computed from a series of experimental data.
This first order equation was first proposed by Teissier (1936) but
seems to have been largely neglected in recent years.. Equation 6
.predicts that the growth rate will approach its maximum value
asymptotically as S increases.

As first shown by Monod (1942), there is a direct relation

between cell growth and substrate consumption. For a medium con-

taining but a single organic substrate, the growth rate is directly

13

proportional to the organic substrate metabolized as expressed by
the equation:

dx dS
___ _ _ , 7
dt Y dt

The parameter Y is known as the economic or yield coefficient.

_ net weight of cell material formed

unit weight of substrate used

 

Using equation 7 and either equation 4 or 6 growth may be described
in batch or continuous culture if the appropriate constants can be

determined.

C. Effect of basal metabolism

 

In recent years, work by a number of authors has suggested
that, in addition to anabolic metabolism, organisms also exhibit a
basal or endogenous metabolism. Herbert (1958) found that the yield
coefficient decreased at low growth rates when working with Torula

utilis growing on a glucose-NH medium and A. aerogenes growing on

3

 

a glycerol-NH3 medium. These results were explained by postulating
a constant endogenous metabolism resulting in the oxidation of cell
substance. More direct evidence is provided from studies carried

out by Herbert (1959) on cell respiration at different growth rates.

Using _A_ aerogenes, the respiratory carbon dioxide production was

 

found to be a linear function of growth rate. However, when

extrapolated back to zero growth rate, a positive respiration rate was

14

noted, indicating the presence of a continuous endogenous respiration
in addition to the anabolic respiration. Using E_ EEO—ll in continuous
culture with glucose as the limiting carbon source, Schulze and Lipe
(1963) also found evidence for a basal rate of metabolism. Their work
again revealed a decrease in the yield constant as the growth rate
decreased and a positive respiration rate at a theoretical growth rate
of zero. In addition, when the rate of substrate uptake was plotted
against the growth rate, the intercept at zero growth rate showed a
substrate uptake rate of 55 mg glucose per gram cell weight per hour.
Hence both growth and substrate uptake was influenced by basal

metabolism.

D. Mathematical model of the continuous flow system

 

This dissertation deals primarily with the continuous flow feed-
back system. However, several short-duration runs were made with-
out feedback, and hence this system is also discussed. Assume the
growth chamber contains a culture of volume v, with cell concentration
X and substrate concentration S. Culture medium of substrate concen-
tration S' is fed at a steady flow rate Fi. The dilution rate is Fi/v =D.

The following assumptions are made as a basis for development
of the model:

1. The contents of the reactor are completely mixed.

2. The influent contains a single organic substrate which

15

is the sole growth-limiting factor. All other substances required for
growth, including oxygen, are present in excess.

Equations relating cell and substrate concentration in the
reactor at steady state have been developed by Monod (1950), Novick
and Szilard (1950) and Herbert 321i. (1956). However, the following
derivation of the fundamental equations describing continuous culture
behavior is based on that of Herbert _e_t__a_1. (1956). The material
balance equations around the reactor are as follows:

Cell balance

 

Increase = growth - outflow 8
dX
-— = X - DX
dt k1

Substrate balanc e

 

Increase = input - outflow - consumption 9
k X
9§ = DS' - DS — -——1
dt. Y

In equations 8 and 9, the terms k1X and le/Y representing cell
growth and substrate consumption respectively include both the anabol-
ism and catabolism processes. Since both of these processes are
functions of the cell concentration, X, the growth rate k1, may be

thought of as consisting of a term k ' representing cell formation and

1

k1" representing cell loss due to endogenous respiration. The yield

coefficient Y Should also be considered a net factor representing the

result of growth and loss of cell material due to endogenous respiration.

16

Steady state condition 5

 

As noted in equation 8, organisms in the reactor are growing
at a net rate k X and being washed out of the vessel at a rate DX.

1

Obviously, if k is greater than D, dX/dt is positive, and the reactor

1
cell concentration will increase. Conversely, if the dilution rate is
greater than k1, cell washout reduces the value of X. At a critical
dilution rate, Dc' the cells are growing at their maximum rate. Above
Dc’ complete washout occurs.

However, at D values below Dc’ the continuous flow system
has a built-in self-adjusting property which tends to influence k1 to
adjust itself to any given D value. Powell (1956) has shown that the
steady state is the only stable state of the system. For example, in a
system which has just been inoculated, X is small, S is nearly equal

to S', and k is greater than D. However, as the cell concentration

1
begins to increase, the value of 5' decreases, resulting in a decreasing
kl until the specific growth rate is equal to the dilution rate. At this
point the combined rates of substrate consumption and outflow just
balance the rate of inflow and there is no further tendency toward
change. Hence small fluctuations from steady state set up opposing
reactions and equilibrium is restored.

At steady state dX/dt and ds/dt equal zero, and equations 8 and

9 may be written respectively as:

17

and
X-zlP.(SI_§) 11
k
l
01‘
X=Y(S'-S) ' 12

Combining equations 4 and 10 gives a relation for steady state substrate

concentration as:

S:-——-— 13

or from 6 and 10:

1n

 

 

The parameters S and X refer to steady state substrate/and cell con-
centrations. The above equations describe the steady state operation
of the system for any value of D below Dc and of the substrate concen-
tration S'.

Schulze and Lipe (1963) have pointed out that there is also a
minimum dilution rate Dm' below which washout will occur. Apparently
below Dm there is not sufficient substrate supply to allow cell repro-

duction to keep pace with the dilution rate.

Transient conditions

 

Equations 8 and 9 may be solved simultaneously over a finite

period of time to give:

18

ax_ , YAS
At—Y(s.-S)D—DX- At 15

The term Y (S' - S) D is the actual rate of cell yield and DX is the rate

of loss of cells from the system.

E. Mathematical model of the continuous
flow feedback system

 

 

The following development of a mathematical model of the con—
tinuous flow feedback system is based on that of Herbert (1961). Figure
3 shows a schematic diagram of the continuous flow feedback system.
Substrate of concentration 5' enters the aerator containing culture of
volume v at a flow rate Fi° The concentrations of cells and substrate
in the vessel are respectively x and S. The culture leaves the aerator
at a flow rate (1 + a) F1 and is concentrated in a settling tank. The
concentrate is continuously returned to the reactor at a flow rate aFi,
where a is the ratio of the feedback flow to the influent substrate flow
and is called the recycle ratio. The cell concentration of the recycled
flow is Cx. The parameter C is defined as the ratio of the feedback
cell concentration to the reactor cell concentration and is thus called
the cell concentration factor. The clarified supernatant of the settling
tank flows to waste at a rate equal to Fi' The cell concentration of the
final effluent is xe. The dilution rate for the reactor is

D1 = (1 + a) Fi/v 16
whereas the dilution rate for the whole system is

D = Fi/v 17

19

The balance equations around the reactor are then:

Cell balance

 

Increase 2 feedback - outflow + growth
dx/dt==DCGC-XD(l-|-a)+xkl 18

Substrate balance

 

Increase 2 input + feedback - outflow - consumption
dS/dt : D8' + aDS — (1+a)DS - klx/Y 19

Steady state conditions

 

It was pointed out that for a system without feedback operating
at a given substrate concentration and dilution rate, the growth rate
would tend to adjust itself to the dilution rate fostering steady state
conditions or k1 = D. However, when equation 18 is solved for the
equilibrium condition of dx/dt = 0 , the following formulation is obtained:

k1=(l+a-aC)D=AD 20
where

A = (l + a - aC) . 21
The quantity (1 + a - aC) is called the feedback factor. The equilibrium
growth rate is now seen to be a function of the recycle ratio and cell
concentration factor as well as the dilution rate.

The theoretical inter-relations between the parameters A, C,
and a are depicted in Figure 1. The curves are plotted for values of A

ranging from 1. 0 to -1. 0, and for values of C and a from 0 to 11. 0

and 0 to 3.2. respectively. In actual practice C seldom exceeds about

Retycle ratio

3.2

2.8

2.4

 

 

20

A:1+CL—CLC

0
‘\
o v
\\ '51
‘f‘
(5‘
C’
\‘ “
1 a 2 _ \x .0
0 s
0.8 — \3, 0
_. \\i : 4. o \\\\
\\\ \\
0 '\\ \\‘
O4 ‘\_\c\r. 6. o \\ \\\ \\
\x \\ \~\\ \ \
C \\\ ‘\7\\ \\\\
NL‘mhg— \ \ \\
0 ' l _L‘ _ _ J l I I

 

 

-1.0 -0.8 -0.6A 1-0.4 -0.2 0 0.2 0.4 6.6

-A 1

Figure 1. The inter-relation of A, C and a .

 

 

21

5 or 6 and a is usually less than 1. O. Theoretically, A may have any
value from 1. O to minus infinity. However, negative feedback factors
are only transient and cannot exist for any significant length of time
as will be shown later.

Generally, Figure 1 shows that for large values of a, the
feedback factor will tend to decrease and that for small values of C it
will increase. However, a and C are not strictly independent of one
another. Hence a large change in a may bring about only a slight
modification in A due to an adjustment in C. Since the value of A is
usually less than unity, higher dilution rates may be used without
washout as may be seen from equation 20. Theoretically, D may
approach infinity as A approaches 0 without the product AD exceeding
the maximum growth rate of the culture and without resulting in com-
plete washout of the cells. In practice limitations in the concentration
factor and in the oxygen transfer rates impose practical restrictions
on the magnitude of D.

Solving equation 19 for dS/dt = O, and combining with equation
20 gives an expression for the steady state cell concentration:

5: = i— (s' - S) 22

From a consideration of the cell concentration and flow rates
in and out of the settling tank at equilibrium, the steady state system
effluent solids concentration, 528 may be found as:

Reactor solids effluent - system effluent - solids in feedback

22

Dx (1 +a) - Dxe =DaxC
or

xe=(l+a-aC)x=Ax 23

From this relation the feedback or A factor is seen to be simply the
ratio of the system effluent cell concentration and the reactor solids
concentration, 528/)": = A.
Using equations 4 and 20, the steady state reactor substrate
concentration becomes:
S AD
s = _’l____ 24

k -AD
m

or from equations 6 and 20

 

S: 25

The above formulations allow prediction of the steady state cell and
substrate concentrations of the system if values for the constants km,
Sn and C are known.

Transient conditions

 

Equations 18 and 19 may be solved simultaneously over a finite
period of time to give:

A A
X=Y(S'-S)D-ADx-YZ-ES- 26

23
Under most operating conditions the term Y 5-;- approaches zero and

equation 26 may be rewritten as

AX Y(S'-S)D - AxD

At
The term Y (S' — S) D is the actual rate of yield of cells and AxD is

the rate of loss of cells from the system.

27

IV. EXPERIMENTAL APPARATUS, CULTURE
AND METHODS

A. Description of the apparatus

The primary components of the apparatus were the reaction
chamber and the settling tank. Feed solution was pumped into the
reactor at a constant rate from storage bottles. The culture in the
constant volume reactor was aerated and mechanically mixed. Reactor
effluent was settled and the concentrate continuously recycled to the
reactor. The supernatant effluent from the settling tank was stored
in 20 liter bottles for analysis. A photograph of the apparatus is shown
in Figure 2, and a schematic diagram of the flow system is presented
in Figure 3.

1. Substrate feed system

Feed solution was made up and sterilized in batches of 20 liters
in pyrex bottles. The feed bottle was vented to the atmosphere and
protected against contamination by a cotton plug. A sigmamotor model
T-65 pump was used to pump the feed to the reactor through tygon
lines. The feed entered the reactor through a Kjeldahl bulb which
afforded an air break between the sterile feed and the aerosol which
existed in the reactor. Several sets of feed lines were held in abe yance
at all times in the event contamination developed in the feed lines or

bottle. When contamination was detected in the lines, a set was

24

25

 

 

continuous flow feedback apparatus.

Figure 2.

26

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V
; Pump “”7 ' ' '.
11 l Sterile.
feed,/',:
1’ solution
A B 1 /
, Compregged
TT* 1' air
1 -—-—1
1 4 L T
Reactor, ' '
Pump \\ .//
I I m '
‘ Magnetic
stirrer
v
1 3 Electric
; stirrer
%
l Itflnent
._Feedback stpfage

 

 

 

Figure 3. Schematic diagram of continous flow feedback apparatus

sterilized and aseptically installed in the system. If organisms had
developed in the lines and the feed bottle, both were replaced.
2. Reactor and reactor overflow

The reaction chamber was a pyrex glass container 12. 5 cm in
diameter and 32 cm deep. As may be seen in Figure 2, the bottom of
the vessel was shaped like an inverted dome so that almost no stagnant
pockets could develop.- The chamber was capped with a removable
pyrex cover having three 2.5 cm openings positioned around a 3. 5 cm
opening.

Overflow ports were located in the side of the vessel so that
culture volume could be maintained at one or two liters. However, it
was found that pieces of heavy floc collected around the port, seeming
to block the outlet. It was also felt that a top overflow might favor
the retention of the heavier flocs in the reactor. To minimize the
above effects, the effluent port was submerged to about the mid-depth
of the vessel by means of the "S" shaped effluent tube shown schemati-
cally in Figure 3.

Mixing in the reactor was accomplished by vigorous aeration
of the culture and by a magnetic stirrer. The stirrer was mounted
directly under the reactor and separated from it by a 3/16” glass plate
built into the bottom of the constant temperature bath tank. The reactor
was immersed in a water-filled galvanized tank for temperature control

(not shown in Figure 3). The temperature of the bath was maintained

28

at the desired temperature it 0. 50 C by means of a Fenwal thermo‘

regulator and heater.
3. Settling tank

Continuous concentration of the sludge in the settling tank and
its return to the reactor proved to be the most difficult problem en-
countered in operation of the laboratory-scale apparatus. Even if the
organisms were flocculating and settling well, great difficulty was
encountered in continuously removing the concentrated sludge from
the settling tank at the low flows used. It was also found that the floc
would ”bridge“ the opening of the sludge return line. Since no high
specific gravity inert suspended solids were mixed with the floc as in
full-scale plants, the floc usually settled quite slowly and often clung
to the sides of the settling tank. To overcome these difficulties, many
different sizes and shapes were tried for the settling tank. Various
types of stirrers and scrapers were installed in an attempt to stop the
bridging and still promote sedimentation. One unsuccessful innovation
was an apparatus to shake the whole settling tank. periodically to dis-
lodge the floc clinging to the walls of the tank.

The settling tank which finally evolved was an inverted two
liter erlenmeyer flask with the bottom removed (see Figure 2). The
clarified effluent overflowed through a 3/4 inch port into a 20 liter
bottle, thus maintaining the liquid volume of the settling vessel at

O. 60 liters. Sludge was drawn off at the bottom of the tank at a rate

29

of approximately 20 ml per minute by a model T-65 sigmamotor pump.
The sludge then passed through a glass "Y" which split the flow, chan-
neling most of it back to the settling tank. The remainder of the sludge
flow was fed back to the reaction chamber by another sigmamotor
pump. The main objective of the recirculation around the settling
tank was to create a flow high enough to keep in motion the settled
sludge. This also served to help eliminate stagnant sludge pockets
which tended to become septic. A thin plastic strip shaped to follow
the contour of the bottom and side of the settling tank served as a
scraping mechanism. It was attached to a vertical shaft which rotated
at one rpm driven by a small electric motor.

The return sludge went through a "T" connection just before
entering the reactor. By opening clamp B and closing A (see Figure 3)
samples for measuring the return flow rate and sludge concentration
were obtained.

The detention time in the settling tank (based on flow from the
reactor) varied from O. 3 to 3. 0 hours during the experiments.

4. Aeration system

A schematic diagram of the culture aeration system is given
in Figure 4. Air from the compressed air line was passed through
pressure reducing and needle valves. The air pressure to the reactor
was maintained at approximately 4 psi and the rate of air flow varied

between 1. O and 3. 7 liters per minute during the runs. The air was

30

filtered through a cotton plug to remove any oil or other impurities
from the air line. Finally the rate of flow was measured through a
Rotameter and the air saturated with water by passage through a water
filled gas saturator. The saturator (not used in runs 1 through 4)
was installed to replace moisture constantly escaping from the reactor
in the air stream. The air passed into the reaction chamber through
one or more fritted glass diffusers. At the highest k1 values, three
diffusers were used to maintain dissolved oxygen in the reactor.
5. Method of sludge wasting

As noted previously, the supernatant from the settling tank
was collected in a 20 liter bottle. For most of the runs cells were
allowed to build up in the settling tank until the sludge blanket was
slightly below the overflow. The overflow thus carried out a concen-
tration of cells approximately equal to that formed in the reactor.
However, due to fluctuation in the settling properties of the organ-
isms, the effluent cell concentration varied significantly as will be
discussed in Section V. Because of the significant variation in effluent
cell concentration, an attempt was made to adjust the cell loss from
the system by manually wasting sludge from the settling tank. This
procedure was practiced only in runs 2b through 6. In these runs, in
addition to the automatic wasting of cells in the effluent, cells were
withdrawn by pipette 4 to 6 times each day from the settling tank. The

quantity of cell material wasted was determined by calculations based

31

 

Cotton
filter

 

A

 

 

 

 

Rotsmeter

 

 

 

 

Gas
saturator

 

 

 

 

\ Reactor

 

 

Figure 4.

Noodle
valve

Pressure
gauge

Pressure
reducing

valve

Culture aeration system.

 

 

 

 

 

 

 

 

 

 

 

Compressed
air line

 

on cell production and cell loss in the system effluent. However, be—
cause of the difficulty of correctly estimating the quantity of cell
material to waste, the manual wasting procedure was abandoned after

run 6.

B. Sterilization of tire apparatus

 

The only part. of the apparatus routinely sterilized (in addition
to the media) was the substrate feed system. The glass and rubber
parts of this system were placed in a gas autoclave for at least 15
minutes at 15 pounds pressure. The tygon part of the system which
passed through the sigmamotor pump was sterilized using 4 per cent
per—acetic acid for at least one hour. Chemical sterilization of the
tygon was practiced since heat was found to deform and eventually
harden the tygon. It was usually necessary to sterilize a new set of
lines to replace a contaminated set every three or four days. Growth
in the lines was thought to originate from cells in the aerosol of the
reactor entering through the Kjeldahl bulb and growing back through
the lines. Line contamination may also have originated from accidental
contamination occurring during assembly of the sterilized lines. It was
necessary to sterilize the entire apparatus several times as a result of
the appearance of excessive populations of rotifers or protozoa devel-
oping in the reactor. In these cases all components (except the sub-
strate feed lines) were sterilized in a gas autoclave for at least 30

minutes at a pressure of at least 15 psi.

33

C. Culture

 

Organisms to be used in a feedback system employing gravity
separation must obviously settle and to some degree concentrate within
some given basin detention time. Most bacteria are just slightly larger
than the upper limit of the colloidal range and possess specific gravi-
ties close to that of water. Hence the settling velocity of a single
bacterium is usually too low for gravity separation. However, some
or perhaps all species agglomerate or flocculate under certain con-
ditions. Flocculation greatly increases settling velocity as may be

seen from Stoke's law

2
V:-&.(s_1).c_1_
18 z

In the above equation

V = settling velocity of the particle
z = the kinematic viscosity of water
g = the acceleration due to gravity
d -— particle diameter

5 =— specific gravity of the particle

In order to obtain flocculent species of bacteria, a 100 ml
sample of mixed liquor from the East Lansing Sewage Treatment Plant
was inoculated into one liter of the 200 mg/l feed solution in the reactor
and aerated for at least 24 hours to allow the culture to establish itself.

Feeding was then begun on a continuous basis and the system operated

34

in. an attempt to build up the reactor solids concentration. This pro-
cedure was tried several times without success. After about 36 hours
the floc which had been in the original inoculum was washed out of the
system and the remaining growth consisted of only dispersed organ-
isms. Failure of the above procedure to produce flocculent growth may
have been due in part to organic overload of the culture. McKinney
and Weichlein (1953) found that floc formation is correlated with meta-
bolic activity. Using both sewage and a synthetic medium based on
glucose, they observed that no floc was formed as long as the organ-
isms were actively metabolizing and reproducing. However, out of 72
isolates from activated sludge, all cultures had formed flocs within 17
days after inoculation into unaerated liquid media. Twenty-six of the
72 isolates were found to flocculate within 48 hours in an aerated cul-
ture. The authors concluded that floc formation was the result of com-
plete metabolism of the organic substrate and not caused by special
zooglea-producing bacteria.

Assuming that the organic load on the system had been too high
to allow the development of flocs, the system was again inoculated and
the feed rate reduced to load the reactor at about 0. 25 lbs of BOD5 per
pound of suspended solids per day (300 mg/l glucose equals approxi-
mately 224 mg/l BOD5)' This is a common load for small activated
sludge plants. The effluent from the settling tank was settled for 24

hours and floc which had formed during that time returned to the reactor.

35

Using these latter procedures a flocculent culture was developed from
a sewage inoculation. The above method for obtaining flocculent growth
was used successfully again during the course of the runs when it was
found necessary to develop a new culture from a small inoculum of the
reactor culture which had been stored in the refrigerator. . Four or
five days were required to build up a significant cell concentration in
thismanner because of the low organic load which could be placed on
the system.

It should be noted that no attempt was made to maintain a pure
culture because of the difficulty to Operate a feedback system in a
sterile condition. As might be expected, a heterogeneous population
developed in the system. Microscopic examination showed the culture
to consist mainly of bacteria intermixed with varying numbers of
vorticella, rotifers and other protozoa. The majority of the bacteria
were present in flocs. However, a certain amount of non-flocculent
bacteria was always in evidence. Several different types of flocs were
present at all times. Microscopic examination showed the predominant
type during most of the runs was a dense floc composed of bacilli and
giving a characteristic ”folded” appearance. The yellowish floc was
found to be composed of a coliform organism or organisms.

Several times during runs the protozoa became quite numerous
and forced termination of the run. It was found that by running for

several days with a low or zero concentration of dissolved oxygen in the

36

reactor, the protozoa population would be reduced to an insignificant

level and a new run could be started. However, when this procedure

was not effective, the apparatus was sterilized, and the reactor

inoculated with either cells which had been stored in a refrigerator

from earlier runs or from the stock culture of coliform organisms.
1. Identification of bacteria

During most of the runs a yellowish floc composed of baccilli
was predominant. A small piece of this floc was washed 9 times to
remove other organisms by vigorously shaking it in 100 m1 bottles of
sterile buffered tap water. The washed piece of floc was then streaked
out on a plate containing in a solidified form the glucose based media
described in part D of this section. One of the typical isolated
colonies which formed was re streaked in order to obtain a pure culture
of the organism. The organism thus isolated was found to be a small
Gram negative rod, occurring singly or in groups. The colonies were
mucoid, smooth, convex, regular, and white to cream.

The organism was also tested by the Michigan State University
Veterinary Diagnostic Laboratory and found to have the following fer-
mentation reactions:

1. Glucose Acid and gas

2. Lactose Acid and gas

3. Hydrogen sulfide Negative

37

4. . Indole production Positive
5. Methyl red test Positive
6. Voges-Proskauer test Positive
7. Citric acid or salts utilized Positive

The diagnostic laboratory identified the organism as a member of the
coliform group. Since no single member of this group ordinarily

shows positive reactions in all four tests of the IMViC Series (Nos. 4-7
above) it was assumed that the culture contained more than one coliform
organism. For instance, most varieties of _I:_3_._ ggliwould give a positive

reaction for tests 4 and 5 and most varieties of i aerogenes would

 

produce positive reactions for tests 6 and 7. In an attempt to separate
the organisms, they were plated out in tryptone-glucose extract media
using the pour plate technique. The organisms were vigorously shaken
in each dilution before plating. However, again all colonies which grew
appeared to be the same morphologically and a repeat of tests 4 through
7 using cells from 7 separate colonies again gave all positives. The
pour plate procedure was repeated two more times and tests 4 through
7 run once more with identical results.

The standard coliform test was also run on the organism as
given in Standard Methods (Standard Methods for the Examination of
Water and Waste-water, 11th edition, 1960). The test showed the

organism to be a member of the coliform group.

38

On the basis of the above tests, it would seem that two or more
members of the coliform group were growing so intimately together as
to preclude separation. It is, of course, also possible that a genetic
transformation had taken place, allowing one organism to give positive
results for tests 4 to 7.

It should be noted that when the isolated coliform organism was
later used for the km tests, the cells flocculated after several days
aeration. The floc thus formed was of the same yellowish folded type

present in the reactor.

D. Nutrient medium

 

The medium used was designed to contain amounts of nitrogen,
phosphorus , magnesium, iron, calcium, trace elements (tap water),
and nutriles (yeast extract) in excess of actual growth requirements.
Glucose was used as the carbon source and as the limiting substance
for growth.

A list of the components and their concentrations are given
below for the case when the glucose concentration was 1000 mg/l. For
runs where the glucose concentration was 400 or 200 ppm, the concen-
tration of the remaining components was reduced respectively to 2/5
and 1/5 of that shown below. One liter of tap water was added per 20

liters of feed solution.

39

 

 

Component Concentration mfl
Glucose 1000
(NH4)2 504 283
KHZ P04 140
FeSO4 10
CaCl2 10
Mg 504 75
Yeast extract 50

In addition to the above constituents, varying amounts of a
phosphate buffer (pH 7. 2) and a potassium hydroxide solution were added
to the feed for pH control. The amounts of base and buffer added as

well as the resulting feed pH after sterilization are shown below.

 

Glucose KOH
concentration Buffer Concentration Volume
mg/l ml (‘70) ml Feed pH
200 0 O 0 7. 0 - 7. 2
400 25 10 10 7. 6 - 7.9
1000 30 20 20 9. 4 - 9.8

The components of the phosphate buffer used are given in Standard
Methods (Standard Methods for the Examination of Water and Waste-

water, 11th edition, p. 319).

40

1. Preparation

Feed solution was prepared in batches of 20 liters. To prevent
precipitation of the salts and carmelization of the glucose, the sugar,
base and buffer were sterilized in separate flasks in a gas heated
autoclave for at least 20 minutes at 15 psi. Three ml of 0. 5 N sulfuric
acid were added to the glucose solution to prevent carmelization during
sterilization. The remaining constituents of the feed solution were
sterilized in 20 liter pyrex bottles in the autoclave for at least one hour
at 15 psi. The glucose, buffer, and base were added to the 20 liter

bottle containing the sterilized nutrients and salts'just prior to use.

E. Analytical technique 3

 

1. Measurement of cell concentration

Samples were taken each day for measurement of the cell con-
centration of the reactor, the return flow and the plant effluent. The
reactor effluent was also sampled during runs 10 through 12 and 20
through 22. The applicability of photometric, turbidimetric and
gravimetric techniques was investigated for cell concentration meas-
urement. The first two proved unsuitable due to the non-homogeneity
of the flocculated cell suspension. Some success was attained by
homogenizing cells in a Waring Blender for 10 minutes prior to
photometric examination. However, the method did not give consist-

ently reproducible results and was abandoned.

41

All the cell concentration determinations were made using a
modification of the membrane filter technique as suggested by Engel-
brecht and Mckinney, 1956.

The procedure used is as follows:

1. The membrane was dried for one hour at 103°C to drive
off substances volatile at this temperature (mainly glycerol).

2. After cooling for 10 minutes in a desiccator, the mem-
brane was weighed to the nearest tenth of a milligram.

3. The membrane was mounted in a Gelman Filter Apparatus
and a sample of between 10 to 30 ml put through the filter under vacuum.

4. The membrane was dried for one hour at 103° C and
weighed as in step 2.

2. Glucose determination

Samples were taken for determination ofglucose concentration
in the reactor and of the influent media at least once during each run.
The method used for determination of glucose concentration was a
modification of that used by Scott and Melvin (1953). In the presence
of glucose the anthrone reagent develops a blue-green color which is
proportional to the glucose concentration. _ The optical density of the
sample was read against a de-ionized water blank at 625 m using a
Bausch and Lomb Spectronic 20 colorimeter. The anthrone reagent was
made in the proportion of 0. 2 gm anthrone to 100 m1 of concentrated

sulfuric acid. The reagent darkens with age and was used only up to

42

eight days after preparation. A 20 mg/l glucose standard was in—
cluded with each set of samples for standardization.

In order to determine whether the blue-green color developed
would obey the Lambert-Beer law, the reagent was tested against a
series of known glucose concentrations using the procedure given

below. The following results were obtained.

 

Sample No. Glucose concentration mg/l Optical density
blank 0 O
2 2 0 . 021
3 10 0 . 160
4 15 0 . 252
5 22 O . 398

The above data are plotted in Figure 5 showing that the color develop-
ment followed the Lambert-Beer law when measured at 625 mu.
The procedure used was as follows:

1. The sample was taken and immediately filtered through
a membrane filter to remove bacteria. Approximately the first 5 ml
of the filtrate were discarded.

2. Five ml of each sample, a blank (de-ionized water), and
a glucose standard (20 ppm) were pipetted into test tubes which were
then immersed into a rapidly circulating cold water bath (approximately

60C and allowed to attain the temperature of the bath.

Optical density

0.5

0.4

0.3

O
o
N

0.1

 

43

 

! l

l

5 10 15 20

L.—

Glucoss concentration - mg/l

Figure 5. Standard glucose curve.

44

3. With the test tubes still in the bath, ten ml of cooled
anthrone reagent (approximately 6°C) were vigorously syringed into
the tubes, using a 10 cc syringe, with such force as to immediately mix
the sample and anthrone reagent.

4. The tubes were loosely covered with aluminum foil and
placed into a rapidly circulating 900- C water bath for 16 minutes to
allow color development.

5. Next the samples were cooled to approximately room
temperature for one minute in the 60 C bath and immediately trans-
ferred to matched cuvettes (1 cm in diameter). The optical density
was measured at 625 mu on the spectrophotometer against the de-
ionized water blank.

3. Flow rate measurement
The rates of influent and return flow were each checked

several times daily. The liquid collected in a graduate cylinder or
volumetric flask was read over a given period of time to determine the
rate. The influent was sampled and measured from the Kjeldahl bulb
which was first moved to a ringstand beside the reactor. The eleva-
tion of the bulb was not changed during the measurement so as not to
alter the head on the influent pump. The return rate was sampled by
closing clamp B and opening clamp A (see Figure 3). The head on the
return pump was also maintained at a constant level during measure-

ment.

45

4. Measurement and control of pH

ThepH of the reactor liquor was measured at least once daily
using a Beckman Model D-2 pH meter. Due to the production of acid
by the organisms, the pH of the reactor would drop if not adjusted.
The inclusion of base and buffer in the feed reduced significant pH
variation. However, pH adjustment was usually required once or twice
a day (depending upon the growth rate) and was made when the pH fell
below 6. 8 (except for run No. l) by addition of from 1 to 25 ml of a 1
per cent KOH solution to the reactor. The pH was maintained between
6. 6 and 7. 3 except for run number 1. In run No. 1, no buffer or base
was added to the feed solution and the pH in the reactor ranged as low
as 6. 3. The average pH for each run is given in column 18 of Tables
17 and 18.

5. Measurement of dissolved oxygen

It was desired to keep the (dissolved oxygen level in the reactor
between 0. 5 and 3. 5 ppm at all times in order to favor the growth of
aerobic organisms. The dissolved oxygen level was checked several
times each day upon initiation of a new run and approximately once a
day during the run. If the level of dissolved oxygen was below 0. 5 or
above 3. 5 ppm, the air rate was increased or decreased respectively.
The Alsterberg (Azide) Modification of the Winkler Method was used to
measure dissolved oxygen as given in Standard Methods (Standard

Methods for the Examination of Water and Wastewater, 11th edition,

46

1960). The procedure was slightly modified in that a 50 ml sample was
used instead of the 300 ml suggested and quantities of reagents added
to the sample reduced to 0. 5 ml instead of 2. 0 ml. The level of dis-
solved oxygen varied between 0. 2 and 4. 2 ppm during the runs. The
average concentration of dissolved oxygen for each run is recorded in
column 19 of Tables 17 and 18.
6. Microscopic examination

Samples were taken approximately once every two days from
the reactor and examined microscopically to determine the general
types and relative numbers of organisms present. The culture was
examined more-often during periods of high plankton population. If the
population of organisms other than bacteria (rotifers, protozoa, etc.)
was found to be increasing, the run was terminated and the rate of
aeration greatly reduced in order to obtain a zero value of the dissolved
oxygen in the reactor. It was found that running the system for a day
under these conditions was often effective in greatly reducing the
population of the intruders without materially harming the bacterial
floc present. If the lack of dissolved oxygen did not significantly re-
duce the percentage of intruders, the system was shut down, sterilized,

and reinoculated as previously noted.

v. RESULTS

The data presented herein were taken over a two year period
of almost continuous operation of the system. The majority of the
runs (sixteen) were carried out with feedback of the cells to the re-
actor. They were designed to test the validity of the formulations
proposed in Section III (equations 18 to 27) to analyze the operation of
a continuous flow feedback system. Three runs were also made with-
out feedback in order to compare results obtained from the two sys-
tems. - Elimination of the return flow allowed attainment of a higher
growth rate at a relatively lower dilution rate than could be obtained

with the feedback system.

A. The field factor

 

The yield factor Y must first be determined before the reactor
cell concentration can be computed. Since both substrate consumed
and cell weight produced were measured, the yield factor could be

computed for each day's run as:

__ net weight of cell material produced per unit time
weight of substrate used per unit time

 

The substrate consumed was determined from the measured influent
and steady state reactor substrate concentrations which are designated
as S' and S respectively. S is assumed to be equal to the substrate

concentration in the system effluent. The average values of S' and

47

48

S for a given run were used in the computation of Y and are recorded
in columns 4 and 16 respectively of Tables 17 and 18. The net weight
of cell material formed includes all cell material which left the sys-
tem in the effluent and that which was mechanically wasted in some
runs. In addition, it includes cell weight lost from the system due to
sampling. The net weight was also adjusted for any increase or de-
crease in the reactor solids concentration since the last measurement.

The average yield factor Y for each feedback run is given in
column 13 of Tables 17 and 18. Y is seen to vary from 0.252 to 0.556.
For the runs using 5' = 1000 mg/l, Y varies from 0. 413 to 0. 556.
Each average value is based on a series of daily measurements and is
felt to give the true yield factor under the conditions of the run. The
variation in Y from run to run will be related to growth rate in a later
section.

The daily yield factors Y are listed in column 12 of Tables 1 to
16. The value of Y is seen to vary by as much as 0.1 in many of the
runs and in the neighborhood of 0. 2 in two runs. Some fluctuation in
Y within a given run is to be expected because of the changing popula-
tion of organisms. However, it is felt that most of the variation is due
to fluctuation in the mass of cell material contained in the settling tank.
The settling properties of the floc fluctuated daily, resulting in alter-
nate periods of buildup and excessive loss of cells from the tank. The
effects of this buildup and excessive loss on system operation are

discussed in a later section.

49

For the runs without feedback, the substrate consumed was
again determined from measurement of S' and S. The average values
of S' and S are given in columns 3 and 12 respectively of Table 20.
The net weight of cell material formed was computed from measure-
ments of the reactor effluent solids concentration Re' As will be
discussed in more detail later, Re decreased if the reactor was al-

lowed to operate without scraping the cells from the walls. Hence

only those samples of Re taken at least three hours after scraping
were used in the computation. The values of Re and Y for each run

are shown in columns 7 and 9 respectively of Table 20. The average

yield factor may be seen to vary from 0. 483 to 0. 559.

B. The reactor cell concentration
Using equations 20 and 22, the steady state reactor cell con-

centration x' was computed for each day for the feedback runs as

Shown in column 7 of Tables 1 to 16. The daily measured values of the

Steady state cell concentration x are given in column 6 for comparison

The average values for x' and x for each run are presented in columns

8 and 7 respectively of Tables 17 and 18. It may be seen that the com—

puted cell concentrations are well below the actual measured values in

almost every case. The same result was found for the runs without

feedback as may be seen in columns 4 and 5 of Table 20.

50

1., Solids balance around settling tank
In an attempt to ascertain the reason for the above noted dis-
crepancy, a solids balance was established around the settling tank.

Rate of cells Rate of cells Rate of cells
entering from reactor “ returning to reactor + leaving in effluent

(F,+F)x x F,a + x F, 28
1 r r1 e1

Equation 28 relates the principal flow of cell mass in and out of the
settling tank. However, several additional terms are necessary to
include all the factors influencing the operation of the laboratory-scale
unit used in this investigation.

First, as will be discussed below, some evaporation occurred
in the system, reducing the hydraulic waste flow from the system to
SOme value less than Fi' The actual rate of cell mass leaving in the
effluent was determined by measurement of the concentration and

volume of the effluent over a given period of time. The total cell mass

in the effluent Wn divided by the elapsed time over which the sample
Was taken At gives the desired rate of cell mass leaving in the effluent.

Another modification of equation 28 is necessary to account for
the various samples taken which were not returned to the system.

Samples taken from the reactor or reactor effluent are designated as

Wr and those from the feedback flow as Wf.

As noted in the preceding section, there were alternate

periods of cell buildup and excessive cell loss from the settling tank.
This was reflected by variation in the yield factor. In order to make
a material balance around the settling tank, it is necessary to deter-
mine any changes in the weight of cells contained in the settling tank
over the given period of time. This may be done using the average
yield factor obtained over the entire length of the run. Using the
average yield factor 17 and the amount of substrate consumed, the
average actual weight of cells that must have been formed may be
found. When the average weight of cells formed found in this way is
greater than the daily measured weight of cells formed, the differ-
ence WC divided by the elapsed time is added to the right side of
equation 28. When the daily weight is greater than the average weight
the value WC /At is subtracted from the right side of equation 28.
The cell balance around the settling tank may be rewritten

incorporating the above modifications as:

Rate of Rate of Rate of Rate of Rate of Rate of
cells cells cells cells cells storage
entering - sampled = returned + leaving - sampled + or excess
from from to in from loss of
reactor reactor reactor effluent feedback cells
flow flow from
settling
tank
Wr Wn Wf WC
(FNFr’x ' z: - X.— F. + I. ' 2r. ”-5 A—t

or rearranging

Wn+ r- fiwc

 

(F.+F)x=xF + 29
1 r rr

By substitution of data from Tables 1 to 16 into equation 29, it
was found that the left hand side of the equation was larger than the
right hand side in almost every case. Each parameter in equation 29
is an experimentally measured quantity except WC , which evolves
directly from the data as shown above. However, the balance assumes
that the cell concentration x leaving the reactor is equal to that in the
reactor. It also assumes that the flow entering the reactor (F1 + Fr)
is the same as that leaving (no evaporation).

Since all quantities on the right hand side of equation 29 are
measured, it was concluded that either the cell concentration in the
reactor effluent was less than :2, or the effluent rate from the reactor
was less than F1 + Fr. The existence of either or both of the above
conditions would result in making the actual weight of cells in the
reactor effluent per unit time less than that as given by (F1 + Fr) (:2).
For purposes of comparison in later computations, the ratio of the
experimentally determined rate of cell mass leaving the reactor
(mg/min) to that given by (Fi + Fr) (:2) will be designated as L. All the
cell mass actually leaving the reactor went to the settling tank and
is accounted for by the terms of the right side of equation 29. The L

or retention factor may then be computed as:

53

 

 

Wn+Wr-Wf+Wc
xF + ‘
L= rr At 30
(Fi+Fr)x

The L values have been computed in this manner for each day of each
run and are presented in column 10 of Tables 1 to 16. The average L
for each run is presented in column 11 of Tables 17 and 18. The value
of L is seen to vary from 0. 727 to 0. 999 when computed using the
average data of each run. Several of the daily L values slightly ex-
ceed unity. It is felt that these cases represent small errors in the
data.

2. Evaporation

The volume of effluent from the system was measured routinely
for determination of the cell yield. By comparing this figure with the
volume of substrate used, evaporation for the system was found to
average about 200 ml per day.

In order to determine whether evaporation from the reactor
itself was sufficient to cause the imbalance noted above, the rate of
evaporation from the reactor was both measured and computed. Four
evaporation experiments were made with tap water in the reactor using
rates of aeration comparable to those used in actual growth experiments.
The data, which are presented in Table 21, Ashow an average evaporation
rate of 0.0165 ml/min at 280 C and 0. 016 ml/min at 240 C per liter of

air per minute (column 5). During the runs, the average air rate

54

varied from a low of 1. 0 l/min to a high value of 3. 7 l/min. Taking a
median value of about 2. 5 l/min, and using the rate of 0. 016 ml/min
per liter per minute of air obtained above, the evaporation rate per day
would be about 58 ml. This is much less than the measured value of
about 200 ml/day and shows that most of the evaporation occurred in
the settling and effluent systems which were not covered.

To determine what the maximum evaporation rate due to aera-
tion might be, computation was made based on the assumption that the
influent air was dry and that it became saturated in passing through the
reactor. The method of computation is shown in Appendix 1. At an
aeration rate of l. 0 l/min, one atmosphere pressure, and 240 C, the
rate of evaporation is predicted to be 0. 0234 ml per minute per liter of
air. This is, of course, higher than the measured rates noted above,
since the influent air actually contained some moisture, a factor which
reduced evaporation.

As noted in a previous section, the ratio of the actual weight of
cells in the reactor effluent per unit time to that given by (Fi + Fr) (52)
is denoted as L. Assuming that evaporation is the only factor causing
L to be less than unity, equation 29 may be solved for (F1 + Fr)° The
value thus obtained, (Fl + Fr )', should be the actual effluent flow from
the reactor at a cell concentration of )2 mg/l. The average values of
(F1 + Fr)' have been computed for runs 1 through 4 and are presented in

Table 22 along with those of (Fi + Fr). The difference between the two

55

quantities has been expressed as an evaporation rate for comparison
with the evaporation rate of 0. 016 ml/minute per liter per minute of air
as obtained by experiment. From Table 22 it may be noted that all
evaporation rates thus computed are considerably larger than 0. 016.
Hence, evaporation was not the only factor affecting L.
3. Reactor effect

In order to eliminate the evaporation effect, a gas saturator
was installed for runs 4a to 22. The influent air was saturated with
water so that there would be no evaporation loss. Since the L value
did not approach unity upon introduction of this correcting factor, it
was concluded that some other factor was tending to hold back cells in
the reactor. As noted previously, vigorous mixing in the reactor was
accomplished by at least two air diffusers and a magnetic stirrer. The
influent substrate and return cells appeared to be almost immediately
distributed throughout the vessel by the vertical and horizontal cur-
rents developed. However, it was noticed that significant quantities of
cells built up on the reactor walls and effluent tube as the run pro-
gressed. If the effluent tube was not cleaned at least twice a day, the
cells tended to build up around its mouth and would sometimes com-
pletely shut off the effluent until the head inside the reactor had in-
creased to 4 or 5 inches and had forced the plug of cells through the
effluent line. One or two runs had to be prematurely terminated due

to such sudden discharges of cells, which disrupted the equilibrium of

the system.

56

In order to determine whether the cells adhering to the reactor
walls and the partial blockage of the effluent tube could cause a signif-
icant differential between the reactor cell concentration and the reactor
effluent cell concentration Re, both quantities were measured in runs
10 through 22. Normally the cell walls were scraped and any plug
formed in the effluent tube removed about 5 times daily. However,
since the buildup of cells in the reactor was observed to increase as
the run progressed, samples were taken as follows:

1. The system was allowed to run various amounts of time
without scraping.
2. Next either procedure (a) or (b) was followed.

(a) The reactor effluent sample was taken first and the
reactor sample was taken after scraping the walls of
the reactor and the effluent tube.

(b) The reactor and effluent tube were first scraped

and then the samples taken.

The data are presented in Table 23. The heading “Hours after
scraping” refers to the time elapsed between the previous scraping of
the reactor and effluent tube and sampling as in procedure 2a or 2b.
The data show that Re was consistently lower than the reactor cell con-
centration and hence the ratio of Re/x was less than unity whereas the

theory of complete mixing assumes that both concentrations would be

equal. The ratio Re/x is then a measure of L since

__ actual rate of cell mass leaviii reactor _(Fi + Fr) Re

 

L

where lie is the average reactor effluent cell concentration. Re/x
is termed L' to differentiate it from the L computed using equation 30.
The values of L' are given in column 5 of Table 23. It may be noted
that they generally decrease as the length of time after scraping in-
creases indicating a buildup of cells in the reactor with time. Since
the value of L' is dependent upon when the reactor was last scraped,
the L computed using equation 30 is thought to give a better estimate of
the actual retention factor and will be used in subsequent calculations.

To theoretically estimate how many milligrams of cells might
adhere to the reactor walls, an analysis was made assuming a layer of
cells 0.05 mm thick on the walls of the reactor when the vessel con-
tained 2 liters of mixed liquor. A typical bacterium was assumed to
weigh (Lamanna and Mallette, 1959) l. 6 x 10-12 gms, occupy l. 5 cubic
microns, possess a 75 per cent. water content, and a density of 1.10
gms/cc.

Using the preceding values, it was found that a layer of cells
0. 05 mm thick would weigh approximately 935 mg and hence if com—
pletely scraped from the wall could increase the cell concentration in
the 2 liter reactor by 467 mg/l. The complete computation is given in

Appendix 2. The value of 467 mg/l assumes that the film covers the

58

entire surface of the reactor and that it is composed solely of cells.
Since there will obviously be void space between the cells filled with
water, the value is probably at least 50 per cent too high. However,
it would seem that a layer of cells clinging to the reactor wall could
significantly raise the actual concentration of cells in the reactor.
4. Modification of equations to include evaporation
and reactor effect for runs with feedback

It has been shown above that the weight of cells leaving the
reactor per unit time is actually smaller than would be given by
(F1 + Fr) (52). It is therefore necessary to rewrite equations 18 to 27
taking this factor into account. This may be done most conveniently
by including the L factor in the derivation.

Cell balance

 

Rate of Rate of Rate of Rate of
increase = feedback - outflow + growth
dx .
d-t— : aDCx - DLx(l +a) + xk1 31

At equilibrium 9}- = O and

(it
k1=D(L+La-aC)=A"D ‘ 32
where
(L+La-aC)=A" 33

The feedback factor has thus been modified to include L. The original

feedback factor was defined as:

59

(1 + a - aC) = A 21

It may be seen that equations 21 and 33 are identical when L = 1. O. In
order to portray the effect of L on the feedback factor, a, C, and A
have been related again in Figure 6 (see figures at end of this section)
as in Figure l for three values of C using equation 21. To see what
happens when L is reduced below 1. 0, the same curves were plotted
using equation 33 with L = 0.9. It may be seen that the effect is to
shift all the curves to the left. The value of A" at a = 0 is now 0. 9
instead of 1. 0. However, the same basic relations are seen to exist
between the parameters for A" as for A.

The substrate balance given by equation 19 remains unchanged.

Combining equations 32 and 19 under steady state conditions gives:

*4-

): 2:” (S'-S) 34
The formulations for the steady state cell concentration in the system

effluent and the steady state reactor substrate concentration become

 

respectively:

ice" = (L + L a - ecu" = An)?" 35
and

- sn A"D

5 ‘ m 36

m
or km
In R - A"D
s = m 37

 

 

60

The above equations are identical to equations 18 to 25 except for the
revised feedback factor. The formulations hold regardless of whether
correction is being made for the evaporation or reactor effect or both.
The value of L is computed using equation 30 as described in a pre-
vious section.
5. Modification of equations to include evaporation
and reactor effect for runs without feedback

Equations 8 to 15 for runs without feedback may also be modi-
fied to include the retention of solids in the reactor using the computed
L. If the terms representing feedback are dropped from equation 30,
L may be computed as:

W+W
r

Cell balance

 

Increase . growth - outflow

g3; . k1X - LDX 39
dt

At equilibrium dX/dt . O and

k LD 40

13

Combining equation 11 and 40 gives:

i' (s' - s)
L 41

i" .

61

The effluent cell concentration is no longer equal to the reactor cell

concentration, but now becomes:

Xe?! : Lil!

The steady state substrate concentration becomes:

 

_ SnLD
S = —_—'_ 43
km - LD
or
km
14 )
g = km- LD
C 44

C. Relationship betweengrowth rate and reactor
substrate concentration

 

The average measured values of the steady state reactor sub-
strate concentration for the runs with feedback S are recorded in column
16 of Tables 17 and 18. The average values of s for the runs without
feedback are listed in column 12 of Table 20. Since the reactor is as-
sumed to be completely mixed, S is also the effluent substrate concen-
tration. A plot showing the relationship between growth rate and reactor
substrate concentration is given in Figure 7. The data shown represent
the average measured S values from the continuous flow runs with and
without feedback. The growth rates were computed using equations 32
and 40. Figure 7 shows that the growth rate increases with increasing

substrate conc ent ration.

62

As noted in Section III, the Michaelis-Menten equation relates
growth rate to S as:

kl:

 

km s
§+Sn

Dixon and Webb (1958) suggest three methods of treating the data to
obtain the constants km and Sn° However, when tried, none of the
methods gave values of the constants which would yield a curve similar
to the experimental curve of Figure 7.

The Teissier equation (SchulZe and Lipe, 1963) also allows kl
to be expressed in terms of S as:

v

-S
k=km(l-ec) 6

1

Here again there is the problem of evaluating the constants km and c.
Reed and Theriault (1931) suggested a rather cumbersome method for
calculating the constants by relating the data in simultaneous equations.
Using this method, the values of km and c were found to be respectively

0. 869 and 0. 0201. Equation 6 would then be:

80. 02015) 45

k =0.869(I-

l

The curve predicted by equation 45 is plotted in Figure 7 showing a
good fit to the experimental data. However, the data extend to only
about 35 per cent of the computed maximum kl value. The feedback

runs were not made at higher growth rates because of the mechanical

63

difficulty of supplying the required large amounts of sterilized media.
Higherrates would also have made it difficult to maintain a sufficient
level of dissolved oxygen in the reactor.

The values of km and c as obtained from the preceding analysis
may be used to compute S by substitution in equation 37 to give for the

runs with feedback:

 

1 ( 0.869 )
n
S -

07869 - A" D
0.0201

46

 

Values of S have been computed using the above equation both for each
day as given in column 17 of Tables 1 through 16 and average values

for each run as presented in column 17 of Tables 17 and 18. The com-
puted values agree closely with the measured ones as would be expected.

For runs without feedback, equation 44 becomes:

 

 

( 0.869
g ; 1n(0.869 - LD 47
0.0201

Values of S computed from equation 47 are given in column 13 of Table
20. They are in fair agreement with those measured experimentally.
1. Experimental determination of km
In order to check the value of km obtained above using the Reed-
Theriault analysis, the maximum growth rate was determined from
batch tests. As noted previously, a mixed culture was used during the

continuous flow runs. Microscopic examination showed that many

64

species of bacteria and protozoa were present during the runs. It was
felt that if a sample of this heterogeneous culture taken from a sub-
strate limiting environment was allowed to grow under conditions of un-
limited substrate, the population would shift radically to favor those
organisms capable of the highest growth rate under the new conditions.
The value of km thus obtained would probably be meaningless.

It was found, however, that one type of yellowish ”folded" floc
made up a significant proportion of the culture during most of the runs.
The floc was found to consist of a member or members of the coliform
group. It was felt that determination of the km of this isolated organism
or organisms would give a value more representative of the actual
population than by using a sample of the mixed culture.

Two batch determinations of km were made using the isolated
coliform organisms. In each case, several loopfuls of cells were
inoculated into 2. 5 liters of sterile media. The growth of organisms
was followed by aseptically withdrawing samples for analysis of cell
concentration until logarithmic growth had ceased. The pH and dis-
solved oxygen of the culture were checked at intervals and adjusted when
necessary. The substrate concentration was determined initially and
near the end of the test in order to compute the yield factor. A sum-
mary of the data is given in Table 24. Figure 8 shows the resulting
growth curves. The slope of the straight line portion of the curve of

the logarithm of the organism concentration versus time gives the

65

desired value of km. The values of km obtained in tests 1 and 2 were
0. 454 and 0. 457. The respective values of Y were 0. 523 and O. 556
which are in the same range as the yield coefficients obtained during
the continuous flow runs. In both tests 1 and 2, the cells grew in a
dispersed manner at their maximum rates of growth. However, after
gently aerating the cultures for 4 or 5 days, partial flocculation
occurred. Microscopically, the floc was found to be the same yellow
"folded" type which was present during most of the runs.

The average km of 0. 456 does not agree with the value of O. 869
obtained by the Reed-Theriault analysis of the continuous flow data.
This is not too surprising when one considers the continuously changing
heterogeneous group of organisms cultured in the reactor. The con-
tinuous flow data actually reflect the'composite effect of all organisms
growing in the unit in 19 runs over a two year period. Another factor
contributing to the difference between the two maximum growth rates is
the comparatively small range of k1 values covered by the data. The
highest growth rate attained using the continuous flow system was 0. 29,
which is approximately only 1/3 of the km obtained from the Reed-
Theriault analysis. As may be seen from Figure 7 the relation between
k1 and S at this point was still close to a straight line and the value of
0. 869 may therefore be somewhat in error. However, since k1 = 0. 869
was obtained using data from the continuous flow runs, it is felt to be

the best estimate of the maximum growth rate available.

66

D. Comparison of actual and predicted reactor
cell concentrations

 

 

1. Runs with feedback
Equations 34 and 37 may be’c‘ombined to allow computation of

the steady state reactor solids concentration as:

k
S'-ln( m” )
km-A D

 

Y

AH c

 

Using equation 48, the daily values of the reactor solids concentration
i" have been computed and are presented in column 8 of Tables 1 to 16.
The daily values of a" are plotted in Figures 9 to 24. The measured
values of the reactor cell concentration x are also plotted for compari-
son. The agreement is seen to be good in the majority of cases.

Each feedback factor shown was computed using the average
values of x and xr found from two consecutive measurements. Each
feedback factor thus reflects two sets of data and gives a better estimate
of the actual trend of conditions between the two measurements. The
same may be said for the computed cell concentrations and k1 values,
since both parameters are computed using the feedback factor.

The average values of i" have been computed for each run and
are given in column 9 of Tables 17 and 18. The overall values of 52"
are plotted against 32 in Figure 25 for comparison. If 32 and 31" agreed
perfectly, a 45 degree line would be formed. The computed and meas-

ured values are seen to follow the 45 degree line quite well except for

67

1

runs 2a and 2b. It was to be expected that these two runs might yield
poor results, as only two values of‘xr were measured in each case.
No measurements of xr were made for run 3. However, the overall
value of xr has been estimated using the plot of C1 vs C given in Figure
27. Parameters computed using this estimated xr are marked with an
asterisk in Table 17.
2. Runs without feedback
Substitution of equation 47 into equation 41 gives an expression

which may be used to compute the steady state reactor solids concen-

tration as:

 

 

k
S'-1n m
.. k - LD
3.2;” : % m 49
C

Using the above formulation, the average cell concentration for each
run was computed and is presented in column 6 of Table 20. The com—
puted and measured concentrations show close agreement. This is to
be expected, since T was calculated using the same data and only a dif-
ference between the computed and measured values of the substrate con-
centration causes a difference between i and SC".

The yield factor was computed from the concentration of cells

in the reactor effluent, R Since Re decreased with the length of time

e.

after scraping the reactor, only values of Re taken 3 hours or more

after scraping were used in computing T or L.

68

E. Comparison of actual and predicted final
effluent cell concentrations

 

 

1. Runs with feedback
The steady state final effluent solids concentration 2e" may be

computed from equation 35 as:

ice": A"i"
Daily values of 2"6 are given in column 14 of Tables 1 through 16 and
are plotted in Figures 9 through 24. In addition, the average values for
each run are presented in column 15 of Tables 17 and 18. The computed
effluent cell concentration is seen to exhibit almost no variation within
a given run. This is to be expected since from equation 34

32m" = a? (s' - .6.)
Thus the steady state final effluent cell concentration is also equal to
the rate of cell production T (S' - S). Since T and S' are constants, and
the computed S values vary only slightly within a given run, xe“ will
show little variation. The actual daily system effluent concentration
x6 is presented in column 13 of Tables 1 through 16. The average value
of xe for each run is also given in column 14 of Tables 17 and 18. Xe is
the concentration of all cells lost from the system, including those lost
through sampling. The value of X6 varies significantly from day to day
and is sometimes greater and sometimes less than 326". Hence for

some periods more cells were being lost from the system than were

being produced (xe greater than x8") and during other periods more

69

cells were being produced than were lost from the system 62¢" greater
than xe). As will be discussed in Section VI, it is this fluctuation in X8
which was largely responsible for the daily variation in the reactor cell
concentration.
2. Runs without feedback

The equilibrium effluent cell concentration is given by equation
42 as:
ice" . Law
The values of Re” have been computed for the three runs and are re-
corded in column 11 of Table 20. is” is seen to agree with the meas-
ured value Re,(column 7). This is to be expected since the computa-
tions used to calculate Re" were dependent upon Re'

F. Relationship between feedback factor and
reactor cell concentration

 

One of the most important parameters influencing the operation
of the feedback system is the feedback factor A". The solids concentra-
tion in the aerator depends directly upon A” as may be seen from equa-
tion 34. A given value of A", producing a certain reactor cell concen-
tration, may result from an almost infinite combination of C, a. , and L
values, as may be seen from Figure 6. Hence if equation 34 holds, a
plot of the computed A” values and the respective measured cell concen-
trations should show a definite correlation with "x increasing as A" de-

creases. In Figure 26, A" has been plotted versus a. For comparison,

70

a curve has been drawn through the computed values of the reactor cell
concentration x" which are also plotted. The measured values of 32 are
seen to follow the curve closely, showing the expected correlation with
A". The cell concentration increases with decreasing A" and approaches
infinity as A" approaches zero. For the runs without feedback, the A"
factor is equal to L since a and C are zero. The points representing

the three runs without feedback are shown as squares on the figure.

G. Relationship between recirculation ratio
and cell concentration factor

 

 

The recirculation ratio and the cell concentration factors are
readily measurable basic system parameters. In this investigation, the
value of a could be easily manipulated by changing Fi or Fr' However,
the value of C was largely non-controllable. The feedback factor is, of
course, dependent upon both parameters.

In order to determine if a and C were inter-related, the two
parameters have been plotted against one another in Figure 27. It may
be seen that the data show C and a to be inversely related. This inverse
relation might be expected since as a is increased the detention time in
the final tank is decreased (assuming Fi remains constant) and C will
thus be reduced. The detention time in the settling tank varied from
O. 3 to 3. 0 hours during the experiments. The theoretical curves in
Figure 6 also suggest C will decrease with increasing a. For any

given value of A“, if a is increased, C will decrease. However, it

71

may be argued that A” will also change to maintain the same value of C
or even result in a larger C. The inter-relation between C and awill
be discussed more fully in Section VI.

H. Effect of a negative feedback factor
on system operation

 

 

As pointed out in a previous section, it is theoretically possible
to have a negative feedback factor A where A = 1 + a- a C. It may be
seen from Figure 1 that A will become negative if (I is increased and C
does not decrease. However, the experimental curve presented in Fig-
ure 27 indicates that C will decrease if ais increased.

Run No. 12 was designed to investigate what effect a negative A
might have on the system. After completion of run No. 11, run 12 was
begun by increasing the return rate, and data were taken immediately
without allowing the system to adjust itself to a new equilibrium. Just
prior to increasing the return rate, C, 0:, and A were 1. 732, 0. 538 and
0. 605 respectively. The variation in (I, C and A during run 12 is plotted
in Figure 28. Upon increasing the return rate and producing an aof
2.130, the A factor decreased to -0. 560. However, it may be seen that
one hour later A had become +0. 590, due to a decrease in C from 1. 732
to 1.193. The average value of C for run 12 is 1. 28 as compared to an
average C of l. 72 for run 11. The only condition changed was the in-
crease of the return rate, causing ato change from an average of 0. 549

in run 11 to 2.163 in run 12. The average A for run 12 is 0. 393. As

72

may be seen from Figure 28, the feedback factor did become slightly
negative a second time during run 12. However, it is felt that the
relatively high C value which caused the negative A was not repre-
sentative of actual conditions. No other negative values of A were
found during any of the runs except these two in run 12.

The above discussion has considered the effect of a negative A
on system operation. It is also theoretically possible to obtain a nega-
tive value of the modified feedback factor A" where A" -.- L + L 61- CC.

It may be seen from Figure 6 that A” will become negative if a is
increased and C does not decrease. However, the computation of A"

is based on L, which in turn is based on a calculation assuming an
equilibrium between cell mass flowing in and out of the settling tank as
shown in equation 30. In run 12, when the return rate was suddenly
increased, the settling tank was losing cells at a much higher rate than

it was receiving them from the reactor. This imbalance was soon re-
solved by the decrease in the return concentration which quickly occurred
as shown in Figure 28. The almost immediate increase in reactor cell
concentration as shown in Table 16 (column 6) also helped to resolve the
imbalance by increasing the concentration of cells going into the settling
tank. Immediately after a sudden increase of the return rate, the system
needs time to adjust itself. Since the balance around the final tank
assumes equilibrium, it predicts a higher reactor effluent cell concen-

tration, making the L value greater than 1. 0 and thus not allowing A" to

73

become negative. For example, in run 12, the L value increased to

l. 305 immediately upon increasing a, resulting in a positive A” of 0.395.

1. Relationship between specific growth rate
and specific substrate consumption rate

 

 

The specific substrate consumption rate kC (mg glucose consumed

per gram cell weight per hour) may be calculated as:

_ D(s'-§)
kc ““— 5°

The consumption rates for each run are given in column 4 of Table 25.
The specific growth rates as computed from equations 32 and 40 are

included for comparison in column 5. kc is plotted against the growth
rate in Figure 29. The value of kC is seen to increase directly with k1

as:

kc:n+hk 51

where n is the ordinate intercept representing the consumption rate
when k1 equals zero and h is a factor giving the milligrams of glucose

consumed per gram of cell weight formed. The method of least squares

was used to evaluate n and h giving:

k =15+1764k1 52
C

From equation 52 it is seen that a substrate consumption rate of 15 mg
glucose per gram cell weight per hour is occurring under conditions of

no growth.

74

Schulze and Lipe (1963), using 2 3313 and a glucose media, have
shown that their data follow equation 51. They found a value of n equal
to 55 mg glucose per gram cell weight per hour. The authors termed
n the maintenance supply since it is just sufficient to sustain cell
metabolism but mt enough to allow growth and reproduction.

The parameter h is by definition the inverse of the yield factor,
Y. Using the value of h obtaii‘led above, expressed as grams of glucose
consumed per gram of cell weight formed, the yield factor is computed
to be 1/1. 764 z 0. 567. The value of 0. 567 is slightly higher than the
highest value of Y measured during the continuous flow runs of 0. 556.
This would be expected since l/h gives 'a corrected yield factor which
does not include the substrate consumed just to maintain the cell

metabolism.

J. Relationship between growth rate and yield coefficient

 

The average yield coefficient for each run is given in column 13
of Tables 17 and 18 and column 9 of Table 20. i? is seen to vary from
0. 252 to 0. 559. When considering only the runs with feedback which
used an S' of 1000'mg/1, the variation is reduced to from 0. 413 to
O. 556. In Figure 30, T is related to the growth rate. It may be seen
that .1? increases sharply with k1 up to a growth rate of approximately
0. 06. As k1 increases above 0. 06, T increases much more slowly

and probably tends toward a maximum value of around 0. 56. The

75

organisms were therefore converting substrate into cell material at a
much higher efficiency at the higher k1 values. A similar relationship
has been noted by other workers (Herbert, 1958; Lipe, 1961; Orford
$11. , 1960). The reason for the sharp dropoff of T at low k1 values
is probably due to the influence of endogenous metabolism, as was dis-

cussed in Section 111.

K. Organic load on system

 

The organic loading rate is an important parameter to the opera-
tion of an activated plant. It is usually expressed as the unit weight of
substrate applied to the aeration tank per unit weight of suspended solids
per unit time. The average organic loading rate expressed in terms of

glucose and BOD for each run is given in column 3 of Table 25. The

5
BOD values have been calculated assuming that 1 mg/l of glucose equals

0. 746 mg/l of BOD Standard Methods, 11th Edition, 1960. The con-

5 (
sumption rate (column 4) and efficiency (column 6) are also listed. The
loading rate varies from 32. 0 to 532. 0 mg glucose per gram cell weight
per hour. Efficiency of substrate removal is above 98 per cent in all
runs.

The loading rate expressed in terms of BOD is seen to vary from
0. 57 to 9. 54 lbs BOD5 per lb of reactor cell material per day. These

loading rates are considerably higher than those used in practice and

yet did not impair the efficiency of BOD removal. The design organic

76

loading used in the conventional activated sludge process seldom ex-
ceeds 0. 5 lbs per lb of suspended solids per day. One purpose of
keeping the loading rate at this range is to promote the growth of
flocculent organisms as pointed out by Garrett and Sawyer (1952).
Pilot plant studies by Logan and Budd (1955) suggest that BOD load-
ing rates over 0. 38 or under 0. 22 lbs per lb of suspended solids per
day tend to increase the Sludge Volume Index and hence reduce the
floc settling properties. During the feedback runs flocculent growth
was obtained even at the highest loading rate (7. 96 lbs BODs/lb cell
material/day). However, there was‘also a high concentration (ap-
proximately 100 to 150 mg/l) of non-flocculent organisms in the ef-
fluent which would not have been an acceptable effluent from a full-

scale plant.

L. Transient condition analysis

 

The analysis of the data has thus far been based on equations
which were derived assuming steady state operation of the system.
These equations assume that there is no change in cell or substrate
concentration in the reactor. It has been shown that the steady state
equations predict the operation of the system quite well considering
the number of variables involved.

However, as may be seen from Tables 1 through 16, the

reactor cell concentration did vary from day to day for a given run.

77

In Section III, equations 26 and 27 were derived to describe operation
of the system under non-steady state or transient conditions. These

equations are given below using the modified feedback factor.

[AS—9%. ?D(s'-S)-A"Dx—?(%S-) 53
and

lift: ?D(S'-S)-A”Dx 54
or

Ax

At[?D(s'-'s) - A"Dx] 55

- S
Equations 54 and 55 are written assuming the term W43?) is close

to zero. This seems a reasonable assumption since the maximum
variation in S between two consecutive‘days in a given run is about

3 mg/l. The maximum value of the term T(%—§-) would then be only
about one per cent of the computed'variation inAx/At. If large varia-
tions in S occurred over short time intervals the term could not be
neglected.

Using equation 55, Ax has been computed for each day's data
and is recorded in column 5 of Tables 26 through 28. The actuale as
found from the measured initial (x1) and final (xF) cell concentrations
is also given for each day in column 4. It may be seen that the com-

puted and measured values ofo agree reasonably well in most cases.

However, in some instances they are widely divergent. In computing

78

Am, the average value of 3: between two measurements has been used.
Using the measured values of XI and the predictedAx values, the final
cell concentrations (xF') have been computed. These are given in col-
umn 7 of Tables 26 through 28 and are plotted in Figures 9 through 24
for comparison with the measured final cell concentrations. The com-
puted variation in cell concentration as given by Ax' follows the actual
variation in the majority of cases. That is, if the actual cell concen-
tration has increased during a given day, the computed variation fol-
lows this trend. In those few cases where the predicted and measured
variation are widely divergent, it is felt that the disagreement is due to
the influence of fluctuations in the cell mass in the settling tank on the

system.

M. Mixing studie s

 

The development of the equations used in this investigation
assumes that the contents of the reactor are completely mixed at all
times. In a completely mixed reactor the increments of the influent
completely intermix with the vessel contents. The concentration of
any reaction product in the exit flow from the reactor thus has the same
value as that of the reactor fluid. The washout rate of a suspension of
concentration, Q, from a completely mixed continuous flow unit may
thus be expressed as:

-dQ

- 56
dt ' DQ

79

Equation 56 may be integrated to yield an expression for the concen-
tration at any time as:

- -Dt
Q - Qoe 57

where 00 is the initial concentration at t s 0 and t is the time elapsed
since initiation of the flow. Since D equals Fi/v and is actually the

reciprocal of the nominal detention time, t the term Dt may also be

0'
written t/to.

It has already been shown that the cell concentration in the
reactor was different from that of the reactor effluent in the experiments
performed during this investigation. Thus one of the basic character-
istics of the complete mixing model described above did not hold for the
laboratory unit. To correct for this departure from the completely
mixed model, the theoretical analysis”Was modified and a correlation
factor L introduced as shown earlier.

In order to get a better understanding of the mixing character-
istics of the reactor, a series of washout tests were conducted. Tests
were made using a dye solution, mixed liquor from the East Lansing
Sewage Plant, cells from the reactor and Fuller's earth. The tests
were carried out in the same reaction vessel and under the same mixing
conditions used during the investigations already described. The reactor
was filled with a known concentration of one of the above substances and

tap water pumped in at a steady dilution rate. The decrease in concen-

tration of the substance in the reactor was checked periodically until it

80

became too small to be measured accurately. In order to determine if
the position of the overflow tube had any measurable effect on the mix-
ing pattern, runs were made with the overflow tube at mid-depth and at
the top of the liquid level.

If perfect mixing conditions prevailed in the reactor, the con-
centration would follow the negative exponential curve predicted by
equation 57. In chemical engineering literature, the curve represented
by equation 57 is usually presented in reduced or dimensionless units.
A plot of Q/Qo vs Dt is called the "F" curve. This curve depicts the
residence time distribution of labeled elements in the reactor. Figure
31-1 shows the shape of the F curve for some representative types of
mixing systems after Danckwerts (1953). The piston flow and the com-
plete mixing systems represent the'ideal types of flow.

Danckwerts (1953) pointed ‘out‘ that the F diagram may be used
to estimate the degree of departure of the system from complete mixing.
If the F diagrams of a completely mixed and an incompletely mixed
system are superimposed on each other, a result such as that shown in
Figure 31-2 may be obtained. The size of the shaded area (A1 + A2)
shows the departure from complete mixing.

1. Washout pattern of a dye solution (Run W- 1)

In order to investigate the flow pattern of a solution through the

reactor without the complicating effects of material sticking to the walls

of the reactor and the effluent tube, a dye was chosen. The washout of

81

the dye was followed with a Coleman Jr. Spectrophotometer set at a
wavelength for maximum absorption of the incident light. A calibration
curve of per cent transmittance vs concentration was made to allow
determination of the dye concentration in the reactor at any time.

A mixing experiment was’first conducted using methylene blue.
However, about two hours after the start of the run, it was noted that
the dye was coming out of solution and forming particles visible to the
naked eye. Since the calibration curve would no longer hold, the run
was discarded.

After unsuccessfully experimenting with several other dyes,
picric acid was found to remain in solution for prolonged periods de-
spite vigorous mixing. Using a dilution rate of 0. 271, a solution of
picric acid was washed out of the reactor and its concentration followed
as noted above. The pertinent data are given in Table 29 and the
theoretical and actual F curves are presented in Figure 32. It may be
seen that the two curves are essentially the same, showing that the
contents of the reactor were completely mixed.

2. Washout patterns of mixed liquor and reactor
cells (Runs W-Z, W-3 and W-4)

Two washout runs were carried out using mixed liquor from the
East Lansing Sewage Treatment Plant. The organisms were first
killed by addition of 300 mg/l of free chlorine in the form of sodium
hypochlorite. A side overflow was used for run W-3 and a top over-

flow for run W-2.

82

Run W-4 was carried out with a side overflow using cells from
the continuous flow experiments. 'The‘cells which had been stored in
the refrigerator for several weeks were first killed with 3 mg/l free
chlorine. Reactor solids concentration for the above runs was deter-
mined by the membrane filter technique. Since solids were necessarily
removed from the reactor for each sample, the measured concentra-
tion has been corrected to account for this removal in each case.

The data for runs W-Z through W-4 are given in Tables 30 to
32. The respective F diagrams are presented in Figures 33 to 35. The
curves show that the mixing conditions were close to perfect during the
three experiments. In run W-2 using mixed liquor and a top overflow
the solids were initially washed out of the vessel slightly faster than
predicted. However, toward the end of the run the measured reactor
concentration was slightly higher than theoretical and solids were re-
tained in the vessel. Mixed liquor‘was also used in run W-3, but the
solids left the vessel from a side overflow. Run W-3 exhibited perfect
mixing during most of the run. However, the data show that solids
were retained in the vessel toward the end of the run as in W-Z. The
data for run W-4 show that the washout’was close to theoretical. In
contrast during the continuous flow experiments, it was found that the
reactor effluent cell concentration was regularly lower than the cell
concentration in the reactor, indicating retention of cells in the vessel.

It was expected that the washout experiments might exhibit the same

83

tendency by showing a slower cell washout than was predicted by com-
plete mixing theory. The reason for the fact that runs W-Z to W-4 did
not show the expected retention is probably that the washout experiments
were conducted over much shorter periods of time than the actual growth
runs. Hence the cells did not build up on the reactor or the effluent tube
which was a major cause of solids retention in the continuous flow runs.
Killing the floc with chlorine was also observed to alter its appearance
and may have affected its washout. Finally, the washout runs were dif-
ferent from the growth runs in that cells were not fed back to the reactor.
The return of a high cell concentration to the unit may have had an in-
fluence on its overall mixing characteristics.

3. Washout patterns of Fuller’ 5 earth (Runs W-S and

W-6)

Fuller, 8 earth was used in two runs in order to determine what
effect a completely inert high specific gravity material might have on
mixing. Run W-5 was made using a side overflow and W-6 a top over-
flow. The data are given respectively in Tables 33 and 34. The F
diagram for run W-5 is presented in Figure 36 showing a faster rate of
washout than predicted over the entire curve. This would be expected
since the relatively heavy solids would tend to settle despite mixing
and thus be washed out faster due to the low position of the effluent port.
It would also be expected that such a suspension would wash out more

slowly than predicted if the overflow were at the top of the vessel.

84

This proved to be the case for run W-6 as shown in Figure 37. Using
a top overflow, the experimental washout curve lagged well behind the
complete mixing curve. Hence mixing of a suspension is greatly in-

fluenced by the specific gravity of the solids.

85

 

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103

 

 

 

 

Table 19. Data obtained from Run Nos. 20 to 22.
a? 3:153: 12.-1 .3: .27. 52:: 9% 3:221:21.
scraging gg/l ml
20
2h.00 0.105 612
37.25 0.105 sun #80 6 600
h9.25 0.105 652 588 0 6.2 800
59.75 0.105 520* u2u* 0 370
21
19.25 0.259 66h 52k 3 9.u 200
22
12.00 0.360 h5
29.00 0.357 668 600 0 19.3 8
35.50 0.357 680 6+0 0
72.50 0.3h5 66h 5u8 5 1

* Data not used in calculations

h2.6*

104

 

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105

 

Table 21. Data obtained from evaporation experiments.
Evaporation Elapsed Rate of Air rate Rate of Temp.
1033 time evap. 1/m1n 1evap. 00

ml min nil/min I§_I11____/

min 1air
#3 886 0.0h85 2.80 0.017 29.0
29 690 0 . 0h20 2 . 80 0 . 015 2+ . 0
20 936 0.0216 1.1+0 0.015 28.0
32 952 0.0390 1.90 0.018 28.0

106

Table 22. Computed rate of evaporation assuming no reactor effect.

 

 

Run Actual Computed Air rate Computed rate of
No. (F1 + Er) (F1 + F})' l/min evaporation
ml/min ml/min (F1 + Fr) - (F1 + Fr)
Air rate
1 9.37 9.30 1.0 0.070
2 12.97 12.95 1.0 0.020
23 3032 2092 lo]. 0036’4'
2b 6.71 6.68 1.1 0.031
3 8.6h 7.1a 1.8 0.833

n 11.7% 11.h3 1.7 0.19h

107

Table 23. Comparison of measured reactor effluent concentration and reactor

c all conc ent ration

 

Run. No. Length of Hours 7 Measured L' Reactor
run after Re cell conc.
hours scraping (mg/1) mg/l
10 21. 00 6 1050 0.482 2180
68.67 5 1395 0.664 2105
11 0 7 1225 0.867 1415
15. 50 0 1205 0.950 1270
23. 50 5 1345 0.910 1480
37. 00 0 1410 0.938 1505
48. 50 0 1200 0.924 1300
66. 25 0 1155 0.895 1290
12 31. 50 0 1075 0.844 1275
55. 50 4 1060 0.895 1185
80. 50 0 1665 0.969 1720
87. 50 0 1330 0.990 1345
20 37. 25 6 480 0. 747 644
47. 25 0 588 0.902 652
57.75 0 424 0.815 520
21 19. 25 3 524 0.790 664
22 29.00 0 600 0.926 668
35. 50 0 640 0.942 620
72. 50 5 548 0.824 644

108

Table 24. Summary of data for batch determination of k

 

Test No. 1 Test No. 2
k 0. 454 0.457
m
Generation time - hours 1. 528 1. 518
Y 0. 523 0. 556
Initial substrate conc. 1040 1092-

Temperature 250C 250C

109

 

 

 

 

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110

Table 26. Comparison of experimental and computed variation in reactor

cell concentration. - Runs 1 to 5.

 

Run Hours Actual Computed Actual Computed

No. of At Ax Ax XF xF'
Run

1 13. 50 13. 50 +36 ~54 460 478

37. 50 24. 00 ~52 ~31 408 429

61. 50 24. 00 + 4 ~14 412 422

2 26. 00 15. 50 ~62 - 6 586 642

48. 25 22. 25 +58 +62 644 648

73. 00 14. 25 ~16 - 8 596 604

84. 25 11. 25 ~56 ~10 540 586

98. 50 14. 25 + 4 - 2 544 538

192. 50 12. 75 ~32 ~19 580 593

4 15. 25 15. 25 +145 +63 2110 2028

42. 75 27. 50 ~75 +43 2035 2153

66. 75 24. 00 ~40 ~45 1995 1990

88. 25 21. 50 ~50 + 8 1945 2003

120. 25 32. 00 +40 + 3 1985 1948

133. 00 12. 75 ~135. ~16 1850 1969

162. 25 29. 25 +260 +431 2110 2281

186. 75 24. 50 +55 +82 2165 2192

213. 75 27. 00 +115 +95 2280 2260

233. 00 19. 25 +195 +199 2475 2479

4a 23. 50 8. 00 +20 +47 2335 2362

40. 50 17. 00 ~130 -743 2205 1592

47. 50 7. 00 +35 +73 2240 2278

91. 00 24. 00 +115 +116 2180 2181

14 6. 00 25. 00 +280 +387 2365 2472

5 20. 17 20.17 +110 +143 2475 2508

49. 75 29. 58 +25 +35 2500 2510

73. 50 23. 75 ~45 - 9 2455 2491

94. 25 20. 75 + 5 +43 2460 2498

118. 00 23. 75 ~65 ~49 2395 2411

111

Table 27. Comparison of experimental and computed variation in reactor

cell concentration ~ Runs 6 to 9.

 

Run. Hours Actual Compute (1 Actual Computed
No. of At Ax Ax xF xF'
Run
6 23. 25 23. 25 ~75 ~28 2965 3012
47. 25 24. 00 ~55 ~48 2910 2917
73. 75 26. 50 +15 +29 2925 2939
98. 00 24. 25 ~83 ~30 2842 2895
122.25 24.25 ~32 ~ 5 2810 2837
145. 00 22. 25 +30 +59 2840 2869
170. 50 25. 50 +115 +145 2955 2985
192. 00 21. 50 ~210 ~127 2745 2828
7 15. 00 15. 00 ~75 ~39 2630 2666
42. 50 27. 50 ~335 ~293 2295 2337
86. 50 12. 50 +160 +127 2685 2652
110. 00 13. 00 +85 ~33 2695 2577
8 38. 50 13. 50 ~40 ~21 3230 3249
65. 25 26. 75 +1370 +1350 4600 4580
84. 75 13. 75 ~250 ~203 4350 4397
108. 75 24. 00 ~4OO ~355 3950 3995
8a 22. 00 22. 00 +205 +865 1410 2070
45. 00 23. 00 -490 ~453 920 957
57. 00 12. 00 +355 +386 1255 1306
9 12. 75 12. 75 +75 +91 1520 1536
24. 25 11. 50 +110 +143 1630 1663
35. 75 11. 50 +85 +125 1715 1755
48. 75 13. 00 ~135 ~110 1580 1605
61. 25 12. 50 ~225 ~128 1355 1452
71. 25 10. 05 ~30 +10 1325 1365
86. 25 14. 50 ~110 ~30 1215 1295
96. 75 10. 50 ~120 +47 1095 1262
113. 25 16. 50 +210 +165 1305 1262
120. 25 7. 00 ~325 +156 1630 1461
134. 50 14. 25 ~165 +269 1465 1899

112

Table 28. Comparison of experimental and computed variation in reactor cell

comparison - Runs 10 to 12.

 

Run. Hours Actual Computed Actual Computed
No. of At Ax Ax x x '
F F
Run
10 21. 00 21. 00 +565 +578 2180 2193
39. 00 18. 00 ~655 -597 1525 1583
58. 67 19. 67 +470 +580 1995 2105
11 15. 50 15. 50 ~142 ~180 1270 1235
23. 50 8. 00 +210 +79 1480 1349
37. 00 13. 50 +25 +174 1505 1654
48. 50 11. 50 ~205 ~73 1300 1432
66. 25 17175 ~10 ~59 1290 1241
81. 75 15. 50 +30 +43 1320 1333
12 31. 50 31. 50 ~75 ~89 1275 1261
55. 50 24. 00 ~90 ~90 1185 1185
80. 50 25. 00 +535 +594 1720 1779
87. 50 7. 00 ~375 ~354 1345 1366

113

Table 29. Data from washout Run W-l.

Picric acid Side overflow v = 2.180 liters

D = 0.271 Air rate = 1.05 liters air/liter reactor vol./min

 

 

 

Dt measured Corrected Theoretical Q/qo
conc. conc. cone.
microgms/l microgps/l microgms/l
0 93.h 93.” 1.000
0.135 81.5 81.6 0.872
0.h16 62.h 61.7 0.668
0.61h 51.h 50.6 0.550
1.110 30.8 30.8 0.330
1.381 23.5 23.5 0.252
1.660 17.9 17.7 0.192
1.879 14.3 lh.h 0.153
1.973 13.0 13.0 0.139
2.0h0 12.2 12.1 0.131
2.109 11.5 11.3 0.123
Table 30. Data from washout Run W-2.
Mixed liquor pr overflow 'v = 1.9h5 liters
D = 0.323 , Air rate = 1.10 liters air/liter reactor vol./min
It. measured Corrected Theoretical Q/qD
cone. cone. conc
InEs/l ML 315/1
08 9780 9730 9730 1.000
0.1 3 7525 7525
0.595 11955 11987 $328 8'33
1.028 3190 3228 3880 0.332
1.328 2930 2h65 2585 0.253
2.180 1185 1220 1 8 .
09 0.125
2'763 6&5 625 613 0.071

114

Table 31. Data from washout Run W-3.

Mixed liquor Side overflow v = 2.038 liters

 

D = 0.297 Air rate = 1.08 liters air/liter reactor VOL/min
Dt Measured Corrected Theoretical 69/ Q0
cone 0 com: o cone o
2.8/1 Ins/1 mall
0 7655 7580 7580 1.000
0.158 6320 6320 6326 0.83u
0.h70 1290 A619 1740 0.609
0.801 3 00 3038 3398 0.h52
0.990 2880 2917 2803 0.38%
1 . 595 15 65 1608 15 30 0. 212
2.080 985 1007 9H6 0.183
2.h37 775 797 659 0.105

Table 32. Data from washout Run W~4.

Reactor cells Side overflow v = 2.095 liters

 

D = 0.377 Air rate = 1.1-+3 liters air/liter reactor VOL/min
Dt Measured Corrected Theoretical Q/ Q
conc. conc. cone. 9
ms/1 ms/l ms/1
0 885 877 877 1.000
0.311 610 610 621 0.695
0.722 #15 h19 #25 0.078
1.1-+1411- 168 173 208 0.197

2.262 83 87 91 0.099

115

Table 33. Data from washout Run W~5.

Fuller's earth Side overflow v = 2.310

 

D = 0.210 Air rate = 1.19 liters air/liter reactor VOL/min
Dt Measured Corrected Theoretical 0/ Q0
cone. conc. conc.
Lbs/1 lbs/1 12521
0 3#30 3#00 3#00 1.000
0.203 2608 2608 2777 0.76;
0.3#9 2220 2229 2399 0.65
0.751 1#15 1#3# 1606 0.#22
1.307 788 810 921 0.238
1.83# #36 #60 5## 0.136
2.##8 217 239 292 0.070

Table 34. Data from washout Run W-6.

Fuller's earth Top overflow v = 1.920

 

D = 0.21111 Air rate = 1.25 liters air/liter reactor vol./min
Dt Measured Corrected Theoretical 0/ Q0
conc. CODC. come.
the/1 Ins/l Ins/l
0 3875 3835 3835 1-000
0.305 3095 3095 2830 0.807
0.567 2520 25## 217# 0.66#
0.956 1723 1761 1#71 0.#59
1.300 1285 1323 10#6 0.3#5
2.010 760 760 513 0.208
2.773 #25 #52 238 0.118

116

 

k1 "' mg/l

0.9 ‘
‘5 117

‘1

0.7 L
0.6
k1 : 0.87(1 - 9-0-20 g)
0.5 E—
0.4 T
0.3 ~—

002 F—

0.1 _/

 

I 1 l J L
40 80 120 160 200

-S--mg/l

Figure 7. Relationship between k1, experimental and calculated 8' values.

240

Cell concentration - mg/l

600 [—

400

 

118

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Figure 31—1. F diagrams of some continuous flow models.

 

 

 

Figure 31-2. Comparison of completely and incompletely
mixed models.

142

 

 

1.00 Q9
1\
1H\\
! (2‘ Picric acid
1 \ Side overflow
0.75 1‘ ‘
1 "CD Experimental data CJ<01
1 *‘, Predicted curve ———
i "
0.50 i— O p
.l \.\‘ 3
o.m. 3
0.25 — ‘{§\\\
1()\\\C;3
O J 1 u 1 L 1
0 0.50 1.00 Dt 1.50 2.00 2.50 5.00

Figure 32. F diagram for Run lkl.

 

1.00 3}
1g

. 0‘ Mixed liquor
0.75 L— ~ Top overflow

Experimental data (Q g)

 

‘\\ Predicted curve ————
O a 50 i‘ O ,\\
Q/ \\
Q° " \e\
1 \\
00 25 _ O\‘\.
I \“\»\\3
l e\\
x-{3L3‘_ <3
0 _ I l g L 1 I
O 0.50 1.00 1050 2.00 2050 3000
Dt

Figure 33. F diagram for Run l-2.

143

 

 

 

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1 0 3?
\
\.
13‘ Mixed.liquor
\\ Side overtlow
0.75 h- \
\\ Experimental data 0 C)
Ci Predicted curve -——-
\1 '
0.50 - \\\1
cz/c.o
0025 h
0' 1 1 1 1 ' l
0 0.50 1.00 1.50 2.00 2.50

Dt
Figure 34. F diagram.for Run ILS.

1

1.00 (1?

 

 

 

 

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1 \
\\\ Reactor cells
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Q\
\\ Experimental data 0 O
\\ Predicted curve -————
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\\\\
Q/Qo ’\\
1 \\
i
0.25 b
9
O 1 1 1 1 I
0 0.50 1.00 Dt 1.50 2.00 2.50

Figure 35. F diagram for Run I;4.

 

 

 

1.00-g 144
Fuller's earth
Side overflow
0075 ‘— 0
Experimental data 7) 0
Predicted curve -—-‘
0.50 ~—
Q/Qo
0.25 c—
O
o 1 ' 1 1 1 1
0 0.50 1.00 1.50 2.00 2.50
Dt
Figure 36. F diagram for Run st.
1.o_o

   
    

Fuller's earth
Top overflow

1
1
1
0.75 1-

 

 

Experimental data (3 C)
Predicted curve -————
1
1
1
0.50 L
Q/Q
° 0
0025 H
O
\D
0 1 1 I I 1
0 0.50 1.00 1.50 2.00 2.50
Dt

Figure 37. F diagram for Run I;6.

VI. DISCUSSION

The purpose of this dissertation was to determine if the
mathematical model presented in Section III could be used to describe
the operation of the continuous flow feedback system. It was found
that the predicted values of Ewere less than the measured values in
each case due to evaporation and reactor effects. Other workers have
noted the same type of discrepancy. Herbert gal. (1956) and Herbert
(1959) working with a continuous flow system without feedback found
that at high dilution rates 3':- was greater than that predicted by theory.
The same type of relation was obtained by Schulze and Lipe (1963). It
is quite possible that the difference between theoretical and actual cell
concentration found by these workers was due to causes similar to
those found in this investigation. The original mathematical model
was modified as shown in Section V and it was shown that the behavior
of the system could be successfully analyzed.

It was found that the concentration factor decreased with
increasing recycle ratio. To see why this occurred, and to see what
are some of the practical limitations on the system, the inter-relations
of C and o. are discussed below using a hypothetical situation.

Assume a continuous flow feedback system is initially

operating under equilibrium conditions (condition A) as given in Table 35.

145

146

Table 35. Inter-relation of E, 'C and 0. following a change in a .

 

Given: ii: 0.5, s' = 1005 mg/1,S: 5,1, =1.0 (A = An)

Cell concentration produced = 0. 5(1000) = 500 mg/l

 

Condition Fi * Fr C o. A x xx.
mllmin ml/min mg/ml mg/ml
A 10 5.0 2.0075 0.50 0.500 1.000 2.000
B 10 7.5 2.00 0.75 0.250 1.000 2.000
C 10 7.5 1.75 0.75 0.438 1.142 2. 000
D 10 7.5 2.00 0.75 0.250 2.000 4. 000

The recycle ratio is then increased to 0. 75 by increasing Fr from

5. 0 to 7. 5 ml/min producing condition B. However, since cells are now
being returned to the reactor at a higher rate, state B is only a temporary
condition. To see what immediate effects the increase in Fr has on the
system, cell balances will be taken around the reactor and the settling
tank under condition B.

Reactor cell balance

 

Rate of return cells + rate of cells formed = rate of effluent cells

2.0(7.5) + 0.5(10.0) 1.0(17.5)

20. 0 mg/min 17. 5 mg/min
Hence the reactor is receiving cells at a faster rate than it is losing them

and the reactor solids will increase at a rate of 2. 5 mg/min.

147

Settling tank cell balance

Cells entering settling tank = cells returned to reactor + cells lost in effluent

1.0 (17.5)

2.0 (7.5) + 0. 5(10.0)
l7. 5 mg/min : 20. 0 mg/min

The settling tank is therefore losing cells at a rate of 2. 5 mg/min. The
above balances are made assuming that the cells produced in the reactor
will be lost in the effluent (no storage in the settling tank).

If the system is allowed to run as in condition B and there
are enough cells in the settling tank to maintain xr at 2000 mg/l, the
reactor will eventually come to a new equilibrium which may be found

by solving the above cell balance equation for a new E as

— _ [719-511
X — Frxr + Fi Fi+Fr

 

The new equilibrium condition is shown as condition C in Table No. 35.
It may be noted that the result of increasing a was to increase 32 to

1142 mg/l and to decrease C. The value of A also decreased slightly.
The same pattern of results was obtained experimentally as reported in
Section V. When a was increased from 0. 549 in run 11 to 2.163 in run
12, the value of C dropped from 1. 72 to 1. 28 while A" decreased slightly
from 0. 397 to 0. 393. A" is used instead of A since L is not equal to 1. 0
in run 12. The average reactor cell concentration increased slightly
from 1361 in runll to l866mg/1’in ruan, However, one important factor

observed in the experimental run was not considered in the above example.

148

The average return cell concentation decreased from 2337 mg/l in run 11
to 1780 mg/l in run 12. Thisreduction in xr is reSponsible for the large
reduction in C and the small reduction in A".

In the above hypothetical example, if it had been possible to
maintain C at 2. 0, the new equilibrium would be as in condition D in
Table No. 35. However, xr would have had to be doubled to 4000 mg/l.
One possible method of increasing xr would be to purposely waste less
solids than are being produced allowing the sludge blanket to increase in
the settling tank. Thismethod, of course, has limitations since the
properties of normal sludge allow only a limited range of compaction.

The above paragraphs have shown how C, A". and xwill
reapond to an increase in 0.. An equivalent decrease in a in the above
example situation would bring about the reverse sequence. That is, the
values of A" and C would increase, while E would decrease.

In operation of the experimental system, the value of E was
found to vary from day to day in Spite of a constant feed and return rate.
Equation 54 was derived for a non-steady state or transient type of
system Operation. The formulation predicts variation in x due to a dif-
ference between the concentration of cells in the effluent x"A” and the
concentration of cells produced 376". As reported in Section V, equation
54 was used to compute the daily variation in 3'5. The computed daily
cell concentration (termed x'F) was plotted against 32" in Figures 9 to 24
showing good agreement in most cases. It was also noted that the measured

system effluent concentration Xe varied significantly from day to day.

149

According to equation 54, when the concentration of cells produced is
greater than the concentration of cells in the effluent 58" greater than xe),
the reactor cell concentration will rise. When the reverse'is true the
value of x will fall. It was shown in Section V that the weight of cells in
the settling tank varied from day to day due to changes in the settling
properties of the floc. The weight of cells stored or the excess loss of
cells from the settling tank in a time At is termed WC. The weight of
cells ,Wc,stored in a given period has, in effect, been temporarily lost
from the system because it has not appeared in the system effluent as
measured by xe. The actual concentration of cells lost from use in the
system including storage or excess loss from the settling tank will be

termed xer' The value of xer can be determined by

J"er : xe i Wc/ Vs
where V8 is the volume of feed solution that passed through the system
during At. If cells were stored, the term Wc/ Vs is added to Xe and if
an excess of cells were lost, the term is subtracted. The computed
daily values of xer have been recorded in column 15 of Tables 1 to 16.
xer is also plotted vs 3E6“ in Figures 9 to 2.4. It may be seen that when
xer is greater than xe”, 2 falls proportionately. The reverse is also
true. Hence the plots of xer vs 378" give complete support for equation 54.
The above considerations show that the daily variations in

reactor solids concentration were due to wasting too much or too little

cell mass over a given period of time. The variation in the effluent

150
solids concentration is thought to be a result of the constantly varying
settling properties of the culture. An index of the settling properties is
given by the return cell concentration, xr. As may be seen in Tables 1
through 16 (column 5), xr varied widely throughout a given run.
The following sequence of events is suggested to describe the
effect of a change in the settling properties of the culture on system operation.

1. The system is initially in equilibrium.

2. The culture begins to lose some of its settling properties,

3. A concentration of cells begins to flow out in the system
effluent which is greater than that being formed in the
reactor.

4. The mass of cells in the final tank decreases.

5. The value of xr begins to decrease and as a result, 3.“
begins to fall.

6. The system may then level off at a new equilibrium with
a lower C and a slightly lower 3:.

7. At this new equilibrium, the system is again losing a

concentration of cells equal to that produced in the reactor.

Organisms other than bacteria were present during all of the
runs. These included Species of rotifers, vorticella and other protozoa.
As observed microscopically, the population of these organisms was
usually quite small when compared to that of the bacteria, as is normally
true in an activated sludge plant. However, at times, quite unpredictably,
one or more Species of the protozoa would increase to the point of des-
troying the floc either directly by preying upon it or indirectly by competing

with the bacteria for the substrate.

151

Macroscopically, the cultural variation could be noted from
a change in some physical floc characteristic such as its color, settling
property, degree of foaming, or tendency to adhere to the walls of the
apparatus. Two factors are thought to be reaponsible for the varying
organism population. First, both the reactor and settling tank were sub-
ject to airborne contamination, as well as contamination from equipment
routinely used for sampling and flow measurement. Secondly, as experi-
mental conditions were changed from run to run, it would be eXpected
that certain organisms would find the environment more favorable to
their growth than others. These variations in culture are thought to be
largely responsible for changes in the settling property of the floc, which
in turn affects the equilibrium of the system. Gaudy _e_t__a_l_._. (1960) also
reported that the settling characteristics of their mixed culture were
extremely variable during operation of a continuous flow feedback unit.
They used a glucose based medium.

Obviously, by returning to the reactor only those organisms
which would readily settle, flocculent Species would be favored over
those which are diSpersed. However, both flocculent and diSpersed
organisms were present at all times during the runs with feedback.
During some periods, the supernatant above the settled system effluent
was quite cloudy, showing a high concentration of diSpersed organisms,
while at other times the supernatent was relatively clear. It should be
also noted that the presence of various types of higher organisms probably
influenced the relative population of diSpersed and flocculent organisms

present.

152

The three runs without feedback were carried out with culture
formed during the feedback runs. During the three runs, the percentage of
flocculent growth in the system rapidly decreased. This is shown in column
8 of Table 19 under the heading of “Settled floc volume". The floc volume
was obtained by settling a one liter sample of the system effluent for 30
minutes in a one liter graduate and reading the volume of floc thus formed.
It may be seen that the settled floc decreased from 800 ml to almost zero
during the tests. It is felt that when the feedback was discontinued, the
growth of the flocculent bacteria was no longer favored and they were
displaced by diapersed types better adapted to the existing 0:) nditions.

In run 21, the protozoa population increased greatly, destroying some of
the flocculent growth.

A contributing factor to the loss of flocculent growth in run 22
may have been the inability of the organisms to produce flocs at a higher
growth rate of 0. 292. However, this could not explain the loss of floc
in runs 20 and 21. In both of these runs the growth rate was below that
used in run 10, in which no loss of floc was observed.

The temperature of the reactor was controlled by immersing
the vessel in a water bath. During a given run the temperature was
maintained at the desired level i 0. 50C by means of a Fenwal thermo-
regulator and heater. Temperatures of 24, 25, and 27°C were used during
the course of the experiments. The temperature used for each run as
well as the range of growth rates during the reSpective runs are given in

the following table.

153

 

Run Nos. Tern perature C)C Range of growth
rate - hr"-1
l-.- 4a 27 0. 009 - 0. 028
5 - 8 24 0.029 - 0.048
8a - 22 25 0.079 - 0.292.

The first temperature change (from 27°C to 240C ) was made in an
attempt to reduce evaporation from the system. The second change
(24°C to 250C ) was necessitated when it was found that the room tem-,-
perature sometimes approached 25°C (77°F) during the night due to
a faulty heating system. It is well known that temperature influences
biological activity. A 10 degree rise in temperature is often found to
approximately double the rate of growth if substrate is present in
excess. However, as may be seen in the above table, the maximum
value of k1 at the 270 C temperature was only 0. 028. During the rest
of the runs (runs 5 - 22), k1 varied from 0. 029 to O. 292 and the temp-
erature from 24 to 250 C. Since the bath temperature has a i 0. 50 C
variation, runs 5 to 22 may be considered to have been performed at
essentially the same temperature. Because of this and because k1
reached a value of only 0. 028 in runs 1 to 4, it is not felt that an
attempt to adjust the data for temperature variation is justified.

The theoretical relation between-the dilution rate and the
reactor and effluent cell concentrations is plotted in Figure 38 for the

continuous flow systems with and without feedback. The curves have

been plotted using equations 35, 42, 48 and 49. Curves showing the

154

rate of cell loss have also been included for both systems. The curves
for the system without feedback are shown using dashed lines. It may be
seen that the cell concentration for the feedback system is twice that for
the system without feedback due to the use of an A" value of 0. 5. Since
A" is O. 5, the growth rate for the feedback system is 0. 5 D while k1=D
for the system without return. Hence the former system may be operated
at twice the dilution rate and still maintain a much lower effluent substrate
concentration. This characteristic is of paramount importance to the
operation of the activated sludge process. Since k1 and S are directly
related (see Figure 7), an effluent low in BOD may be produced by keeping
A" small which in turn lowers the value of the growth rate. It should

also be noted that the initial BOD or substrate concentration will not
affect the effluent concentration as long as A‘is not changed. The effect

of a higher or lower 5' is merely to vary the concentration of solids

carried in the aerator as may be seen from equation 34

2 = 775' -5”)
All

Thus doubling of S' will approximately double E. In the experimental runs,
values of S' of 200, 400 and 1000 mg/l were used. However all but three

of the runs were made at the highest influent substrate concentration.

Because of variation in both A" and Y from run to run, no quantitative
conclusion can be reached concerning the relation between S' and E. However,
as may be seen from Tables 17 and 18, as S' was increased from 200 to

1000 mg/l, 3: increased from 426 to a maximum of 3822 mg/l. Hence the

general trend was as expected.

155

It is possible to have complete washout of the culture in the reactor
at a given A" as shown in Figure 38. Theoretically, it is also possible to
run the unit at any dilution rate without washout by decreasing the value of
A". The theoretical relation between E and the feedback factor has been
plotted in Figure 39 using equation 48. The curve has been plotted for
a dilution rate of 0. 5. It may be seen that the cell concentration approaches
infinity as A" decreases toward zero and that 3; approaches zero as A"
increases past 1. 0. However, high values of E are limited in actual operation
by the transfer rate of dissolved oxygen. It should also be noted that the
only way that A" may become greater than unity is for the cell concentration
factor to become less than 1. 0. Hence A" values above 1. 0 seem of little
practical significance.

In addition to these practical restrictions, there are a number of
other basic factors to be considered before applying the analysis used in
this dissertation to the full-scale plant. One of the most obvious is that
in formulatio n of the models, it has been assumed that the influent contained
only dissolved substances. However, in almost all domestic wastes, there
is a significant concentration of suSpended organic and inorganic solids.
Fair and Geyer (1958) state that the average domestic sewage contains
235 mg/l of suSpended solids. Even assuming 50 per cent of the above
solids are removed during primary sedimentation the remaining approxi-
mately 100 mg/l of solids will certainly have a large effect on the con-

centration of solids in the system.

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In the following analysis, Si is the incoming solids concentration
and Ss is solids concentration in the reactor exclusive of the cell contri-
bution, x. The total reactor solids concentration is thus T5 2 SS + x.

The following balance is taken around the aerator.

Solids balance

 

Increase = feedback - outflow + growth + incoming
dTS
'71:- = DC (X+Ss)-(1+G)DL(X+SS)+k1X+DSi 58

The correSponding substrate balance (equation 19) would be unchanged.
At equilibrium, equation 58 may be solved for k1 as :
D
: —- N -
k1 x (TsA Si) 59
The steady state value of TS may be found by combining equations 59 and 19

as:

T = S,+Y(S' -'§)
8 1

 

A" 60
The effluent solids concentration at equilibrium Te, may be found from
a solids balance around the settling tank as
Reactor solids effluent - system effluent = cells in feedback
LDT (l + a) - DTe = O. DCT
or
T = A"? 61
e

Expressions for the equilibrium substrate concentration in the
aerator may be obtained by substitution of equation 59 into equation 6 to

give:

159

 

 

'5": m 62

From equation 60, it may be seen that a suSpended solids concentra-
tion of 100 mg/l entering the aerator will have a large effect on the con-
centration of suSpended solids in the aerator. The magnitude of the in- .1

crease will depend on the value of thefeedback factor.

Another important consideration in using the preceeding analysis
is the magnitude or even the existence of the retention factor, L for full- 1
scale -plants. The L factor was introduced in Section V to include the
effects of evaporation and the reactor effect. The reactor effect is the
term applied to the retention of solids in the aerator due to a film of cells
clinging to the walls and to the partial plugging of the reactor effluent
tube. The relatively large surface area and high aeration rates charac-
teristic of activated sludge plants would suggest that evaporation may be
a significant factor. The film of sludge on the tank walls would probably
be negligible because of the relatively large volume per unit of wall sur-
face. On the other hand, the higher overall Specific gravity (due to
influent suSpended solids) might lead to a solids concentration gradient
in some areas of the aeration tanks particularly near the tank bottom.
This lack of complete mixing would result in retention of solids in the
tank and could be analyzed using a retention factor in the same manner as

was done for the laboratory-scale unit.

160

In the theoretical analysis, it has been assumed that a concen-
tration of cells equal to that formed will be continuously wasted from the
system. The effect of wasting too low or too high a concentration of cells
from the laboratory—scale unit was to produce variation in the reactor cell
concentration. In most full-scale plants, sludge is wasted only inter-
mittantly from the settling tanks. "Bulking" of sludge is also a common
problem which would tend to cause fluctuation in the settling properties
and hence the concentration of return sludge. However, over a period
of time, the sludge carried in the system will be approximately constant.
It is also very probable that because’of the large quantity of solids car-
ried in a full-scale plant, minor short duration variations in return cell
concentration would have little effect on the aerator solids concentration.
Hence, it is felt that in most cases, intermittant sludge wasting will not
seriously limit the applicability of the proposed equations.

The relation between growth and reactor substrate concentration
was found to follow the Teissier equation for the experimental unit. The
use of this equation for computing substrate concentration depends on the
determination of the constants km and c. The Michaelis-Menten equation
has been used to relate kl and Sby most authors. In the application of
this equation the value of km and Sn have to be known. The problems
associated with the determination of km for a mixed culture from batch
tests have already been discussed in Section V. It was found that the

batch value of km determined using one of the pre-dominant organisms

161

of the culture did not agree with the km obtained from continuous flow
data. The maximum growth rates of pure cultures have been widely
studied. However, it would seem that there is need for more work in
the area of growth of heterogeneous cultures at high rates.

In many cases, the most expedient approach to obtain the
relation between kl and S might be to operate a continuous flow bench-
scale unit without feedback. The unit would be loaded with the waste
to be treated in the full-scale plant and an acclimated mixed culture. The
experimental systems with and without feedback were found to have

approximately the same S at a given growth rate. In addition, at the

low growth rates used in sewage treatment, the relation between kl and

S is approximately linear. Hence the experimental data obtained from
such a unit would supply the needed relation and theconstants km and c
would not be required. It is obvious that some of the above consider-
ations relating to the application of the the) ry discussed in Section V

to full-scale plants will require further study.

VII. CONCLUSIONS

A continuous flow system with feedback was constructed
and operated under steady state conditions at growth rates ranging from
0. 009 to 0. 236. The system was also operated without feedback under
steady state conditions at three growth rates ranging from 0. 079 to
0. 292.

The steady state cell concentration E in each case was found to
be greater than that predicted by the mathematical model based on the
equations of Herbert (1961). From a material balance around the system
and from direct measurements, it was found that cells were being re—
tained in the reactor due to their sticking to the walls and due to a partial
blocking of the effluent port. Evaporation tended to have the same effect
in that it increased reactor cell concentration. When the model was
modified to include the retention of solids, good agreement was obtained
between measured and computed steady state reactor cell concentrations.
The retention of solids in the reactor was eXpressed as a retention factor
L which varied from 0. 727 to 0. 999 during the runs.

It was found that 3; varied inversely with the feedback factor A"
as was expected. A" in turn was a function of the recycle ratio a , the

cell concentration factor C and L as expressed in equation 33. Values of

A" ranging from 0.120 to O. 480 were produced during the runs by adjusting

a . The value of C was found to decrease from 2. 20 to l. 28 when a: was

increased from 0. 36 to 3. 37.
162

- ‘__._-._‘

41__I4.¢¢1-4-

163

It was found that daily fluctuations in 32 during a. given run were
due to differences between the weight of cells produced and that lost from
the system. The daily fluctuations were predicted reasonably well using
a transient condition analysis instead of a steady state type of analysis.
The yield coefficient Twas found to increase as the rate of growth in-
creased. For runs made at S' = 1000 mg/l, Tincreased from 0.413 to
0. 556 as k increased from 0.01 to 0. 29. A sharp decrease in V'occurred

l

at low growth rates reaching a value of 0. 25. With increasing k1 values

Y probably tended toward a maximum value of 0. 56.
The steady state reactor substrate concentration Swas found

to increase as k1 increased. The relationship between the two parameters

was correctly expressed by a first order equation by Teissier (1936) as

_ -cS)
k1 — km(1 — e
where km = 0.87 and c = 0. 02. When the substrate consumption rate kC

was plotted against k , a linear relation was obtained. The curve showed

1
that 15 mg glucose per gram cell weight per hour were being consumed
at a k1 of zero. Hence a certain rate of substrate uptake was necessary
to sustain cell metabolism without producing growth.

The settling properties of the mixed culture were quite variable.
However flocculent growth was present during all the runs with feedback.

Mixing studies conducted using the reaction chamber showed that
a dye solution exhibited perfect mixing while various suSpensions showed
slight departures from theoretical complete mixing. The departure from

mixing was greatly influenced by the Specific gravity of the particles in

suSpens ion.

VIII. APPENDIX

1. Computation of evaporation
When dry air is bubbled through liquid at constant temperature,
the gas becomes saturated with the liquid and the partial pressure of the
vapor in the resulting mixture is equal to the vapor pressure of the liquid.

If Dalton's law of partial pressure holds, then

 

n1 P
P '-' + 63
n1 n2
where p 2 partial vapor pressure
P = total pressure of air and vapor
n1 2 moles of vapor
n2 = moles of air in gas leaving saturator

The value of n2 may be calculated assuming the ideal gas law holds as:

PV
n2 ' if? 64
where R = the ideal gas constant = 0. 082 liter-atm
mole-degree Kelvin

 

Using t = 2970K, V = 1.0 liters, and P = 1. 0 atm, n equals 0.0411 moles.

2
At 24°C (2970K) the vapor pressure of water is 23. 24 mm or

0. 0306 atm. Substituting into equation 63 then yields a value for n equal

1
to O. 0013 moles or 0. 0234 gms of vapor. Since the computation is based

on 1. 0 liters of air passing through the reactor per minute, the evapor-

ation rate is 0. 0234 mllminute per liter of air.

164

165

2. Estimate of weight of cells adhering to reactor walls

In the following computations, a typical bacterium is taken to
have a wet weight of 1.6 x 10-2 gms and have a volume of 1. 5 x 10-9mm
(Lamanna and Mallette, 1959). The layer of cells adhering to the reactor
wall could readily be observed with the naked eye. Hence it is conser-
vatively assumed to be 0. 05 mm thick. Assuming the reactor to contain
2 liters of culture, a volume of cell material equal to 3504 mm3 would
be contained in a layer 0. 05 mm thick adhering to the reactor walls.
There would then be 2338 x 109 bacteria contained in this layer since

3
3504 mm = 2338 x109

 

l. 5x10-9mm

Taking the cells to have a water content of 75 per cent, there would be

2 -
2338x109x0. 25xl.6 x10.1 =9352x10 4 gm

or 935 mg of bacteria on a dry weight basis. If all these cells were
scraped from the walls, it would add 935 mg/2 liters = 467 mg/l to the
reactor concentration.
The calculation was checked by assuming that the density of cell
mass is 1.1 gm/cc (Lamanna and Mallette, 1959). Then
3. 504 cc x1. 1 gm/cc x . 25 (per cent dry weight) = 962 mg
In two liters there would be 481 mg/l added to the reactor cell concentration

which checks with the above figure of 467 mg/l.

10.

11.

IX. BIBLIOGRAPHY

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BUSCH, A. W. and MYRICK, N., 1960, Food-population equilibria
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BUSCH, A. W., MYRICK, N., MCKINNEY, K. W. and PETERSON,
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59.

171

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1959, An application of biological engineering to

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31/1281-1287.

Sewage and Ind. Wastes

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