EPA-330/9-74-001-C
NATIONAL FIELD INVESTIGATIONS CENTER
CINCINNATI
OPERATIONAL CONTROL PROCEDURES
for the
ACTIVATED SLUDGE PROCESS
PART IMA
CALCULATION PROCEDURES
DECEMBER 1973
UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF ENFORCEMENT AND GENERAL COUNSEL
-------
EQUIVALENTS USED FOR ACTIVATED SLUDGE CALCULATIONS
ft
inches
m
m
sq ft
sq m
cu ft
cu ft
cu ft
cu m
cu m
cu m
gal
gal
liter
mgd
cu m/day
gpd/sq ft
cu m/day/sq m
Ib
Ib
kg
kg
lbs/1000 cu ft
g/cu m
cu ft (H20)
gal (H?07
liter TH90)
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
0.3048
2.540
3.28083
39.37
0.0929
10.7639
28.3170
0.028317
7.48052
1000.0
35.3145
264.179
3.785
0.003785
0.26417
3785
0.000264
0.0408
24.51
0.453592
453.592
2.20462
1000.0
16.0
0.0625
62.4
8.345
1 .000
= m
= cm
ft
= in
= sq m
= sq ft
liter
= cu m
= gal
liter
cu ft
= gal
liter
= cu m
= gal
= cu m/day
= mgd
= cu m/day/sq m
= gpd/sq ft
= kg
g
Ib
g
= g/cu m
lbs/1000 cu ft
Ib (H90)
Ib (H,0)
kg (H,0)
Ib/day
kg/day
Ib
kg
English SLU
Metric SLU
= mgd x mg/1 x 8.345
= cu m/day x mg/1 /1000
= English SLU x (WCR*/1198)
= Metric SLU x (WCR/10)
= Metric SLU x 264.2
= English SLU x 0.003785
*WCR = sludge weight (mg/1)/centrifuged concentration
-------
NATIONAL FIELD INVESTIGATIONS CENTER - CINCINNATI
OPERATIONAL CONTROL PROCEDURES
FOR THE
ACTIVATED SLUDGE PROCESS
PART IIIA
CALCULATION PROCEDURES
by
Alfred W. West, P.E.
Chief, Waste Treatment Branch
DECEMBER 1973
UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF ENFORCEMENT AND GENERAL COUNSEL
RXOOOQ05335
-------
FOREWORD
The Waste Treatment Branch of the National Field In-
vestigations Center - Cincinnati is developing a series of
pamphlets describing Operational Control Procedures for the
Activated Sludge Process. This series will include Part I
OBSERVATIONS, Part II CONTROL TESTS, Part III CALCULATION
PROCEDURES, Part IV SLUDGE QUALITY, Part V PROCESS CONTROL,
and an APPENDIX. Each of these individual parts will be
released for distribution as soon as it is completed, though
not necessarily in numerical order. The original five-part
series may then be expanded to include case histories and
refined process evaluation and control techniques.
This pamphlet has been developed as a reference for
Activated Sludge Plant Control lectures I have presented at
training sessions, symposia, and workshops. It is based on
my personal conclusions reached while directing the
operation of dozens of different activated sludge plants.
This pamphlet is not necessarily an expression of
Environmental Protection Agency policy or requirements.
The mention of trade names or commercial products in
this pamphlet is for illustrative purposes and does not
constitute endorsement or recommendation for use by the
Environmental Protection Agency.
Alfred W. West
-------
TABLE OF CONTENTS
PAGE NO.
DATA SOURCES AND TEXT ORGANIZATION 1
ACTIVATED SLUDGE CHARACTERISTICS 4
Activated Sludge Concentrations - ATC £ RSC ..,. 4
Sludge Weight To Concentration Ratio - WCR 5
Sludge Units - SLU 6
Settled Sludge Concentration - SSC 9
SIMPLIFIED MIXING FORMULAS 12
CFP Examples 13
ATC Examples 15
RSC Examples 17
AERATION TANK CHARACTERISTICS 20
Aeration Tank Sludge Units - ASU 22
Return Sludge Units - RSU , . . . 23
Aeration Tank Detention Time - ADT 24
ORGANIC LOADING AND PURIFICATION PRESSURES 25
Aeration Tank Loading Factors 25
Relative Purification Pressures 25
FINAL CLARIFIER CHARACTERISTICS 28
Final Clarifier Sludge Units - CSU 28
Final Clarif ier Detention Time - CDT 32
Clarifier Sludge Detention Time - CSDT , 33
Clarif ier Surface Overflow Rate - OFR 35
PROCESS CHARACTERISTICS ...... 36
Sludge Aeration Hours Per Day - SAH 36
Sludge Age - AGE £ AAG 36
Sludge Concentration Ratio - SCR 39
CLARIFIER SLUDGE FLOW DEMAND - CSFD 40
MIXING FORMULA DEVELOPMENT 42
Simplified Mixing Formulas 42
Expanded Mixing Formulas 45
CLARIFIER SLUDGE FLOW DEMAND FORMULA DEVELOPMENT .... 47
-------
DATA SOURCES AND TEXT ORGANIZATION
Calculation procedures used by the Waste Treatment
Branch of the National Field Investigations Center
Cincinnati (NFIC-C) during technical assistance projects are
described in this Part III of the Operational Control
Procedures for the Activated Sludge Process. The suggested
types and frequency of observations and control tests have
been described in Parts I and II.
Essential flow data, such as waste water flow into the
aeration tanks (AFI), return sludge flow (RSF), excess
sludge wasted from the process (XSF), etc., are determined
from the plant flow meters at each test period. Sludge and
process characteristics, such as mixed liquor and return
sludge concentrations (ATC and RSC), settled sludge volume
(SSV), depth of sludge blanket in the final clarifier (DOB),
etc., are determined by the control tests that have been
described in Part II CONTROL TESTS.
These readings and control test results comprise the
"Observed:" data that are entered in the formulas to
determine the "Wanted;" information. Formulas and calcu-
lation examples are provided in this Part. The procedures
for using these calculated values to evaluate sludge quality
and process status, and to determine control adjustment
requirements are described in subsequent Parts.
All calculations are performed in step-by-step fashion
even though, in some cases, the end result could have been
determined by one longer equation containing all the vari-
ables. This step-by-step method is preferred because some
of the intermediate results are informative in themselves
and are frequently used directly in other equations to
calculate other process relationships. All examples are
expressed in both metric and English units and a table of
equivalents is printed inside the front cover. Figure 1
identifies tank sizes, flow rates and sludge concentrations
used in the calculation examples. A complete list of all
symbols and their definitions is included in the APPENDIX to
this series. For convenient referencing, each calculation
example is preceded by definitions of the symbols used in
the example.
Some sections also include brief discussions of certain
implicit assumptions, approximations, and use of the com-
puted relationships. It is hoped that such statements will
help clarify and add realism, even though they may be
repeated and expanded in subsequent Parts describing process
-------
AFI=23,100 cu m/day
= 6.10 mgd
IV)
.^ AERATION TANK
AVM=5,945 cu m
AVF=210,000 cu ft
AVG=1,571,000 gals
ASA=1,200 sq m
= 12,960 sq ft
AWD=4.94 m
= 16.2 ft
CFJ=AFi+RSF
= 34,080 cu m/day
=9.00 mgd
@ ATC = 5.0% CFO=22,720 cu m/day
= 6.00mgd
RSF=10,980 cu m/day
= 2.90 mgd
@ RSC=15.0%
XSF=380 cu m/day
=0.10 mgd
@ RSC=15.0%
FINAL CLARIFIER
CVM=2,970 cu m
CVF=105,OOO cu ft
CVG=785,000 gals
CSA=730 sq m
= 7854 sq ft
CWD-4.07 m
rCSF=RSF + XSF
= 11,360 cu m/day
= 3.00 mgd
F igu re 1
ACTIVATED SLUDGE SYSTEM
Volumes, Flows, and Sludge
Concentrations Used in the Examples
-------
evaluation and control. Finally, the development of the
mixing formulas and clarifier sludge flow demand formula are
included in the last section of this Part for those who may
be interested in their derivation.
Though the size of Part III may appear formidable, most
calculations, except those in Part III B - Step Aeration and
Contact Stabilization, are quite simple and straightforward.
Most of these routine process relationship calculations
that are based on the sludge unit concept were proposed
originally by E.B. Mallory. Some of the process loading
factors and purification pressures presented reflect
contemporary reaction kinetics principles.
The clarifier sludge flow demand formula (CSFD) and the
associated sludge concentration ratio (SCR) and sludge
weight-to-concentration ratio (WCR) that are used to
calculate process control adjustment requirements were
evolved by the author. He also developed the coordinated
testing, calculation, evaluation and control procedures
"NFIC-C Procedures" - described in this pamphlet series.
-------
ACTIVATED SLUDGE CHARACTERISTICS
ACTIVATED SLUDGE CONCENTRATIONS
ATC £ RSC
Sludge concentration values used for calculating
process relationships and control requirements are
determined by the centrifuge test that is described in Part
II, CONTROL TESTS.
Mixed liquor (ATC) and return sludge (RSC) concen-
trations are the most frequently used centrifuge values.
These symbols are defined as follows:
ATC = Aeration Tank Concentration
The mixed liquor concentration
determined by the standard 15-
minute centrifuge test, ex-
pressed as the percent of the
centrifuge tube occupied by the
compacted mixed' liquor sludge.
ATC=5%
RSC = Return S_ludge Concentration
The return sludge concentration
determined by the standard 15-
minute centrifuge test, ex-
pressed as the percent of the
centrifuge tube occupied by the
compacted return sludge.
RSC =
-------
SLUDGE WEIGHT-TO-CONCENTRATION RATIO - WCR
WCR = MLTSS/ATC
Mixed liquor concentration, expressed in percent and
identified as ATC, should be determined by the standard
centrifuge test during every control test period. At least
once every 24 hours the weight of mixed liquor total
suspended solids, expressed in mg/1 and identified as MLTSS,
should be determined by the laboratory balance from a
portion of one of the samples that had been used to measure
ATC.
Though the solids concentration by centrifuge is used
for most process control calculations discussed in these
pamphlets, the ratio of solids by weight to solids by
centrifuge (WCR) is one of the factors used to evaluate
sludge oxidation and relative age.
SYMBOLS
ATC = Aeration Tank Concentration (%)
MLTSS = Mixed Liquor Total Suspended Solids,
I"n mg/1, by laboratory balance.
WCR = Sludge Weight-to-Concentration Ratio
EXAMPLES
"Young" "Normal" "Old"
Sludge Sludge Sludge
Observed:
MLTSS = 4,000 mg/1 4,000 mg/1 4,000 mg/1
ATC = 8.0% 5.0% 4.0%
Wanted: WCR
Therefore:
WCR = MLTSS/ATC MLTSS/ATC MLTSS/ATC
4,000/8 4,000/5 4,000/4
500 800 1,000
-------
4'000 mg/i = 800 = WCR
5.0%
'5%
The WCR of a properly oxidized sludge will usually
approximate 800. The WCR for a young sludge will usually be
less than 600, and that for an old, or over-oxidized, sludge
may exceed 1,000.
The above examples also demonstrate that there is no
one common constant to convert ATC to MLTSS for all types of
sludges.
SLUDGE UNITS - SLU
SLU = Volume X Centrifuged Concentration/100
The number of sludge units in any tank, or portion of
any tank or container, is determined by multiplying the
volume occupied by the sludge (measured in cubic meters or
gallons) times the sludge concentration (measured by the
centrifuge test), but divided by 100 to convert the observed
percent concentration to a decimal fraction).
SYMBOLS
SC = SJLudge Concentration (!
*SLU = Sludge Units
by centrifuge)
-------
* Subscripts are not needed to distinguish between Metric
or English sludge units because the type of SLU will
obviously conform to the system (Metric or English) used by
the operator.
Formulas to convert sludge units to pounds or kilograms
and to convert Metric sludge units to English sludge units
are included in the Equivalents Table inside the front
cover.
SC
VOLUME
10,000 gals.
X
-f- 100 = SLU
10%
10,000 gals. X 10.0 -f- 100 = 1,000 SLU
EXAMPLES
Metric Units
Observed:
Volume = 5,945 cu m
SC = 5.095
Wanted; SLU
Therefore:
SLU = cu m x SC/100
= 5,945x5.0/100
= 297 SLU
English Units
Observed:
Volume = 1,571,000 gals
SC = 5.0%
Therefore:
SLU = gals x SC/100
= 1 ,571 ,000x5.0/100
= 78,550 SLU
-------
DISCUSSION
The sludge unit, which is based on the centrifuge test,
rather than the mass unit (expressed by weight - in
kilograms or pounds) which is determined by the laboratory
balance, is used for most process relationship calculations.
This is because many properties that govern the sludge's
purification capability also influence its compressibility
and the end point concentration in the centrifuge tube.
Additionally, the centrifuge test, which is also used to
calculate WCR, is more rapid, and can be performed
conveniently and more frequently than the suspended solids
test.
The advantage of using sludge units rather than sludge
weight can be illustrated by visualizing the different
trc.r.'-^nr ~,t capability of equal weights of different types of
mixed liquor sludges.
Assume that two identical 10,000 cu m aeration tanks
each contained an equal weight, but a different type or
quality of mixed liquor sludge solids. Then further assume
that Tank #1 contained a properly oxidized, highly active,
flocculant sludge with a large percentage of voids and
surface area. Let's also assume that the measured sludge
concentration, by weight, was 2,400 mg/1. An adsorptive
sludge of this type would have a WCR of about 800 and the
ATC by centrifuge would have approximated 3.0%.
Then for Tank #1 :
SLUDGE WEIGHT = cu m x mg/1 / 1,000
= 10,000x2,400/1,000 = 24,000 kg
SLUDGE UNITS = cu m x ATC/100
= 10,000x3.0/100 = 300 SLU
Now let's assume that Tank #2 contained an over-
oxidized less active, older, slightly knotted, dense floe
that settled more rapidly but.had less adsorptive capacity.
And assume that the sludge concentration, by weight, also
equaled 2,400 mg/1. A sludge of this type would have a WCR
of about 1,200 and the ATC by centrifuge would have
approximated 2.0%.
-------
Then for Tank #2:
SLUDGE WEIGHT = 10,000 x 2,400/1,000 - 24,000 kg
SLUDGE UNITS = 10,000 x 2.0/100 = 200 SLU
If evaluated on the basis of weight alone, it would
have appeared that both tanks provided equal purification
capabilities. (2,400 mg/1 and 24,000 kgs in each tank).
But from an evaluation of sludge units it is evident that
the first tank (300 SLU) contained 50% more sludge units
than the second tank (200 SLU). Although the highly active
sludge in the first tank would probably not perform 50% more
'?ork •!-.]-nr the equal vreirjht of leos active nnd po rer quality
sludge in the second tank, it certainly could produce a
significantly better quality final effluent.
No similar comparison is made with an exceptionally
young, fluffy, slowly settling bulking sludge since, in
actual practice, such a sludge could not be held in the
system. The WCR might be 300 and the centrifuged ATC of a
2,400 mg/1 mixed liquor would equal 8.0%. Such a slowly
settling sludge, though capable of producing a sparkling
settlometer supernatant, would be washed out of the final
clarifier long before ATC could be increased to the 8.0%
level.
In summary_, the sludge unit data would have indicated
the potential superiority of sludge in the first tank, while
the mass data, based on weight alone, would have erroneously
indicated that the treatment capability of both sludges was
equal.
SETTLED SLUDGE CONCENTRATION - SSC
SSC = 1 ,000 x ATC/SSV
Settled sludge concentration (SSC) values are
calculated from the centrifuged mixed liquor concentration
(ATC) and the settled sludge volume (SSV) values that are
observed during the 60 minute settlometer test. Sludge
quality, as determined by both the shape of the SSC curve
and the 60 minute SSC value is discussed in PART IV SLUDGE
QUALITY.
-------
A table of calculated SSC values and the SSV and SSC
curves are illustrated in the following example and in
Figure 2.
SYMBOLS
ATC = Aeration Tank Concentration (%)
SSC = Settled SJLudge Concentration (%)
SST = SjLudge S_ettling Time (minutes)
SSV = S~ettled"~S_ludge Volume (cc/1 in settlometer)
EXAMPLE
Observed:
ATC =3.0%
SSV = Values shown in Table 1.
Wanted: SSC Trend during the 60-minute test
Therefore:
ELAPSED TIME
SST
(min.)
0
5
10
15
20
25
30
40
50
60
OBSERVED
SSV
(cc/1)
1000
630
470
390
340
300
275
235
215
200
TABLE 1.
SSC = 1000 ATC/SSV
3000/1000
3000/630
3000/470
3000/390
3000/340
3000/300
3000/275
3000/235
3000/215
3000/200
CALCULATED
SSC
3
4
6.
7
8
10
10
12
13
15
00
76
38
69
82
00
91
76
95
00
10
-------
1000«
900
ssv & ssc
ATC=3.00
800
H 700
CO
CO
111
5
LU
O
Q
CO
O
LU
LU
CO
600
500
400
300
200
100
16
14
12
10
8
U
CO
CO
<
cc
LU
u
z
O
O
LU
O
Q
13
_J
CO
Q
LU
4 h-
LU
CO
0 10 20 30 40 50
SLUDGE SETTLING TIME SST (minutes)
0
60
Figure 2
SLUDGE SETTLING AND
CONCENTRATION VS. TIME
11
-------
SIMPLIFIED MIXING FORMULAS
CFP = ATC/(RSC-ATC)
ATC = (CFPXRSC)/(CFP+1.0)
RSC = ATC+CATC/CFP)
The mixing formulas based on the relationship between
ATC, RSC, and CFP are used to calculate many process
relationships and control adjustment demands needed to
maintain optimum process equilibrium. They are also used to
check waste water and return sludge flow meters, and can be
used to determine either of these two flows if one of the
two meters is missing or inoperative. At equilibrium, the
clarifier sludge flow percentage (CFP) calculated from the
mixed liquor and return sludge concentrations, and expressed
decimally, will equal the CFP value determined by dividing
the metered clarifier sludge removal flow rate (CSF) by the
metered clarifier flow rate (CFO).
The mixing formulas have been simplified by neglecting
final effluent suspended solids since that concentration is
usually very small compared to the mixed liquor and return
sludge concentrations. Development of the mixing formulas
and expansions to include either primary effluent or final
effluent suspended solids are included in the Derivation
Section.
SYMBOLS
AFI = Aeration Tank Waste Water Flow-Ir: (Usually
primary effluent flow)
ATC = Aeration Tank Concentration (%)
CFI = Final Clarifier Flow-In (Mixed liquor Flow
into Final Clarifier)
CFO = Final Clarifier Flow-Out (Final Effluent)
CFP = Final Clarifier Sludge Flow Percentage
(Expressed decimally)
CSF = Final Clarifier SJLudge Flow (Usually RSF+XSF)
RFP = Return Sludge Flow Percentage (As determined
from flow meter readings)
RSC = Return Sludge Concentration (55)
RSF = Return SJLudge F_low
XSF = Excess S~ludge Flow to Waste
12
-------
CFP EXAMPLES
CFP = ATC/(RSC-ATC)
To illustrate use of the CFP formula let's assume that
the return sludge flow (RSF) meter failed and was taken out
of service. In this case, the aeration tank flow-in (AFI)
meter and the excess sludge flow to waste meter (XSF) were
functioning and the operator could therefore calculate the
return sludge flow and other needed process relationships
from the ATC and RSC test data.
The measured flows and those flows calculated from the
CFP formula are shown in Figure 3 and the calculation
examples follow.
Metric Units English Units
Observed: Observed:
AFI = 23,100 cu m/day AFI = 6.100 mgd
XSF = 380 cu m/day XSF = 0.100 mgd
ATC = 5.0% ATC = 5.0%
RSC = 15.0% RSC = 15.0%
Wanted: CFP, CSF, RSF £ RFP
Therefore: Therefore:
CFP = ATC/(RSC-ATC) CFP = ATC/(RSC-ATC)
= 5.0/(15.0-5.0) = 5.0/(15.0-5.0)
= 0.50 = 0.50
or 50% or 50%
CFO = AFI-XSF CFO = AFI-XSF
= 23,100-380 = 6.100 - 0.100
= 22,720 cu m/day = 6.000 mgd
CSF = CFOxCFP CSF = CFOxCFP
= 22,720x0.50 = 6.000x0.50
= 11,360 cu m/day = 3 .000 mgd
RSF = CSF-XSF RSF = CSF-XSF
= 11 ,360-380 = 3 ,000-0.TOO
= 10,980 ca m/d = 2.900 mgd
13
-------
METERED AFI=6.10 mgd
CFI=AFI+RSF
= 6.10+2.90
= 9.00 mgd
AERATION TANK
ATC=5.0% %
METERED XSF
=0.10 mgd @ RSC=15.0%
M
RSC=15.0%
RSF METER OUT
M
CFO=AFI-XSF
= 6.1-0.1 = 6.0 mgd
FINAL CLARIFIER
RSF=CSF-XSF
= 3.00-0.10
= 2.90 mgd
RFP = RSF/AFI
= 2.90/6.10
=0.475
= 47.5%
MIXING FORMULA
CFP = ATC/(RSC-ATC)
= 5.07(15.0-5.0)
=0.50
CSF=CFOxCFP
= 6.0x0.5
= 3.0 mgd
Figure 3
CFP MIXING FORMULA USED TO
DETERMINE UNKNOWN FLOWS.
-------
RFP = RSF/AFI RFP = RSF/AFI
= 10,980/23,100 = 2.900/6.100
= 0.475 = 0.475
or 47.5% or 47.5%
ATC EXAMPLES
ATC = (CFPxRSC)/(CFP+1.0)
In this case assume that the maximum capacity of the
final clarifier sludge removal pump was 11,360 cu m/day
(3.000 mgd) and the waste water flow into the aeration tanks
(API) averaged 22,720 cu m/day (6.000 mgd) when sludge
wasting was cut back to zero.
Furthermore, the mixed liquor could concentrate to an
SSC of 15% after one hour in the Settlometer.
Then further assume that the operator wanted to know
the maximum mixed liquor concentration (ATC) his process
could maintain at equilibrium if he controlled his return
sludge concentration (RSC) to equal the one hour SSC of 15%.
These conditions are illustrated in Figure 4 and the
calculations follow.
Metric Units English Units
Observed: Observed:
AFI = 22,720 cu m/day AFI = 6.000 mgd
CFO = AFI CFO = AFI
CFO = 22,720 cu m/day CFO = 6.000 mgd
XSF =0.0 XSF =0.0
CSF = 11,360 cu m/day CSF = 3.000 mgd
RSC = 15% RSC = 15%
Wanted: ATC at process equilibrium.
Therefore: Therefore;
CFP = CSF/CFO CFP = CSF/CFO
= 11,360/22,720 = 3.00/6.00
= 0.50 = 0.50
15
-------
AFl=6.00 mgd
AERATION TANK
WANTED:
MAXIMUM ATC
FINAL CLARIFIER
MIXING FORMULA
ATC=(CFPxRSC)/(CFP+1.0)
= (0.5x15.0)7(0.50+1.0)
= 7.5/1.5 MAXIMUM PUMP
= 5.0% CAPAClTY=3.0mgd
RSC=15.0%
NOTE: XSF=0.0
MAXIMUM CFP=0.50
Fig u re 4
ATC MIXING FORMULA USED TO
DETERMINE MAXIMUM ATC
-------
ATC = (CFPxRSC)/(CFP+1.0)
= (0.5x15)/(0.5+1.0)
- 7.5/1.5
= 5.0%
ATC = (CFPxRSC)/(CFP+1.0)
= (0.5x15)7(0.5+1.0)
= 7.5/1.5
= 5.0%
If sludge quality remained the same, the clarifier
sludge pumping capacity would permit building ATC up to 5.0%
while maintaining process equilibirum.
RSC EXAMPLES
RSC = ATC + (ATC/CFP)
In this case let' r, assume that the operator, who had
been collecting clarifier sludge samples from near the
surface of the pump station wet well, suspected that the
solids content of these samples did not truly represent the
solids content of the return sludge being pumped to the
aeration tanks. He suspected solids-liquid separation in
the deep wet well and therefore feared that the
concentration of return sludge pumped from the bottom of the
wet well might be greater than the measured 10.0% RSC of the
sludge sample collected near the wet well surface.
He could check this out a number of ways, and one would
be by use of the RSC mixing formula.
The plant conditions are illustrated in Figure
the calculation examples follow:
and
Metric Units
English Units
Observed;
CFI
CSF
XSF
ATC
34,080 cu m/day
11,360 cu m/day
0.0
5.0%
Observed:
CFI
CSF
XSF
ATC
9.000 mgd
3.000 mgd
0.0
5.0%
Wanted: RSC
Therefore:
CFO = CFI-CSF
= 34,080-11,360
= 22,720 cu m/day
CFO = CFI-CSF
= 9.000-3.000
= 6.000 mgd
17
-------
CFP = CSF/CFO
= 1 1 ,36.0/22,720
- 0.50
RSC = ATC + (ATC/CFP)
= 5.0 + (5.0/0.5)
= 15.0%
CFP = CSF/CFO
= 3.000/6.000
= 0.50
RSC = ATC + (ATC/CFP)
= 5.0 + (5.0/0.5)
= 15.0%
The operator would now know that the RSC should
actually have approximated 15 instead of 10 percent. He
would then relocate his return sludge sampling point to the
sludge flow discharge channel or to some other location
where a truly representative sample could be collected.
-------
SAMPLE COLLECTED HERE
RSC = 10.0%
CFI=9.00mgd @ ATC =5.0%
XSF-0.0(pV
|lP=Io7j
^
• J
MIXING FORMULA
RSC=ATC+(ATC/CFP)
\ 1
FINAL Cl
^
= 5.0+(5.0/0.5) ^^te
= 15.0%
.". RELOCATE RSC SAMPLING '
STATION
CSF=RSF+XSF
= 3.0+0.0
CFO=CFI-CSF
= 9.0-3.0
= 6.00mgd
CFP=CSF/CFO
= 3.0/6.0
=0.50
PUMP STATION
=3.0mgd
Figure 5
RSC MIXING FORMULA USED TO
CHECK VALIDITY OF RSC TEST RESULTS
-------
AERATION TANK CHARACTERISTICS
This section contains aeration tank sludge unit and
detention time calculation examples. It also contains
supplementary formulas and calculated aeration tank loading
factors and purification pressures.
A coordinated evaluation of these with the final clari-
fier and process characteristics, that are defined in the
next two Sections, reveal process status and purification
potential.
This appears to be a good place to reemphasize that
optimum plant performance and best final effluent quality
are achieved by diligent, coordinated evaluation of all
interrelated and interacting sludge and process character-
istics. In all too many actual cases, activated sludge
plants produce effluents below the quality level they are
capable of achieving because process adjustments were aimed
at meeting only a few independent, preconceived objectives.
Best treatment cannot be achieved by exclusive attempts
to maintain either a constant mixed liquor sludge concen-
tration or sludge age level, for example, while neglecting
other coordinated process requirements needed to satisfy
such demands as return sludge flow and clarifier sludge
detention time.
Methods to determine the coordinated control adjust-
ments needed to meet the various interrelated process
requirements are discussed in Part V PROCESS CONTROL.
Aeration tank characteristics, flows and sludge concen-
trations used in the aeration tank calculations are illus-
trated in Figure 6.
20
-------
AFI=23,100 cu m/day
= 6.10 mgd
M
K)
a..!
\j*~ AVM=5,945 cu m
\ AVF=210,000 cu ft
\ AVG=1,571,000 gals
ASA = 1,200 sq m
12,960 sqft
AWD=4.94 m
\ 16.2 ft
///////S/S//////////////////////////////////////'//;
7
• ^
;
^
$
^
|
J
'/////{Vs
CFI = AFI+RSF
= 34,080 cu m/day
= 9.00 mgd
@ ATC=5.0%
TO FINAL CLARIFIER
RSF=10,980 cu m/day
= 2.90 mgd
@ RSC=15.0%
TO WASTE
XSF=380 cu m/day
=0.10 mgd
@ RSC=15.0%
« |M
FROM FINAL
CLARIFIER
Figure 6
AERATION TANK
Volumes, Flows, and Sludge Concentrations
Used in the Examples
-------
AERATION TANK SLUDGE UNITS - ASU
ASU = AVxATC/100
SYMBOLS
ASU = Aeration Tank S_ludge Units
ATC - Aeration Tank Concentration (%)
AV = Aeration Tank Volume
AVG = Aeration Tank Volume in gals
AVM = Aeration Tank Volume in cu m
ATC
AERATION TANK
VOLUME
1,571,000 gals.
-5- 100 = ASU
5%
1,571,000 gals. X 5.0-100 = 78,550 SLU
EXAMPLES
Metric Units
Observed:
AVM = 5,945 cu m
ATC = 5.0%
Wanted: ASU
Therefore:
ASU = AVMxATC/100
= 5,945x5.0/100
= 297
English Units
Observed;
AVG = 1,571,000 gals
ATC =5.0%
Therefore;
ASU = AVGxATC/100
= 1,571,000x5.0/100
= 78,550
22
-------
RETURN SLUDGE UNITS - RSU
RSU = RSF x RSC/100
SYMBOLS
RSC = Return S_ludge Concentration (%)
RSF = Return S_ludge Flow
RSU = Return Sludge Units (to aeration tanks)
RSC
RETURN
SLUDGE FLOW
-4- 100 = RSU
2,900,000 gals/day X 15.0^-100=435,000 RSU/day
EXAMPLES
Metric Units
Observed:
RSF = 10,980 cu m/day
RSC = 15.OX
Wanted: RSU
Therefore:
RSU = RSFxRSC/100
= 10,980x15/100
= 1650/day
English Units
Observed:
RSF = 2.900 mgd
RSC = 15.0%
Therefore:
RSU = RSFxRSC/100
= 2,900,000x15.0/100
= 435,OOP/day
23
-------
AERATION TANK DETENTION TIME IN HRS - ADT
ADT3AFI = (AVx24)/AFI
ADT3TFL = (AVx24)/(AFI+RSF)
SYMBOLS
ADT = Aeration Tank Detention Time (hrs)
AFI = Aeration Tank Waste Water Flow-In
(usually primary effluent flow)
AV = Aeration Tank Volume
AVG = Aeration Tank Volume in gals
AVM = Aeration Tank Volume in cu m
RSF = Return SJLudge Flow ~~
TFL = Total Flow to Aeration Tank (AFI+RSF)
EXAMPLES
Metric Units
Observed:
AVM = 5,945 cu m
AFI = 23,100 cu m/day
RSF = 10,980 cu m/day
Wanted; ADT3AFI 6 ADT3TFL
Therefore:
ADTSAFI = (AVMx24)/AFI
- (5,945x24)/23,100
- 6.18 hrs
ADT3TFL = (AVMx24)/(AFI+RSF)
= (5,945x24)7(23,100
+10,980)
=4.19 hrs
English Units
Observed:
AVG = 1.571 million gal
AFI = 6. 100 mgd
RSF = 2.900 mgd
Therefore;
ADT3AFI = (AVGx24)/AFI
= (1.571x24)76.1
= 6.18 hrs
ADT3TFL = (AVGx24)/(AFI+RSF)
= (1.571x24)7(6.1+2.9)
=4.19 hrs
24
-------
ORGANIC LOADING AND PURIFICATION PRESSURES
AERATION TANK LOADING FACTORS
The following monitoring type BOD loading factors, that
are calculated after the BOD test results are obtained, can
be used to evaluate certain historical cause-and-effect
relationships even though they cannot be used for day-to-day
process control. Such factors, when related to actual plant
performance, can be used to develop design criteria for
future plant modifications and additions. (All symbols have
been explained in previous sections.)
Metric Units English Units
kg BOD/1000 AVM Ibs BOD/1000 AVF
kg BOD/ASU Ibs BOD/1000 ASU
kg BOD/kg MLVSS Ibs BOD/lb MLVSS
Similar calculations may be based on COD, TOC or other
loading measurements.
RELATIVE PURIFICATION PRESSURES
When correlated with sludge quality •, the following
factors indicate process purification pressures. The first
three factors can be determined rapidly after each control
test. The last two factors, though more definitive, can
only be calculated after the BOD test data are available.
This section only introduces additional factors, which
when combined with other sludge quality indicators, can help
the operator interpret process responses to control
adjustments.
Metric Units English Units
ATCxADTSAFI ATCxADTSAFI
ATCxADT3TFL ATCxADT3TFL
RSU/1000 cu m AFI RSU/1000 gals AFI
ATCxADTSTFL/mg/l BODd ATCxADT3TFL/mg/l BODd
RSU/kg of BODi RSU/lb of BODi
25
-------
All symbols except the following have been defined in
previous sections .
BODi = Five-day biochemical oxygen demand
~ of the waste water entering (in) the
aeration tanks.
BODo = Five-day biochemical oxygen demand
~~ of the final clarifier effluent, (out)
BODd = Calculated net five-day biochemical
~~ oxygen demand of waste water and
the "liquid portion" of the return
sludge at the aeration tank
entrance, (diluted waste water)
= (BODi+(BODoxRFP) )/(1 .0+RFP)
Except for the following BODd calculation, examples are
not shown since all other intermediate calculations are
those conventionally used by plant operators and the loading
factors and purification pressure values are simple
fractions of previously defined characteristics. Aeration
tank detention times (ADT) are based on waste water flow
alone (3AFI), or waste water flow plus return sludge flow
(3TFL) .
BODd EXAMPLE
BODd = (BODi+(BODoxRFP) )
= (160+(10xO. 475) )/
= 1 12 mg/1
1 .0+RFP)
.0+0.475)
Note: Return sludge usually contains less than 2.0%
solids and the BOD 5 of the liquid portion (98%+ of the
total return sludge flow) should therefore approximate
the BOD 5 of the clarifier effluent. The entire, return
sludge flow, rather than the variable liquid fraction,
is used to calculate BODd. This facilitates using
normally available data directly rather than intro-
ducing additional required analyses and calculations.
The logic is in line with some contemporary kinetics
principles .
The following Metric and English unit results are
included to permit checking the formulas and the examples
given in previous pages.
26
-------
Test Results
AFI
RSF
BODi
BODo
MLVSS
RSTSS
ATC
RSC
AV
AV
Metric Units
23,100 cu m/d
10,980 cu m/d
160 mg/1
10 mg/1
3000 mg/1
12,000 mg/1
5.0%
15.0%
5945 cu m
5945 cu m
Results of Intermediate Calculations
BODd
BODi
ASU
MLVSS
RSTSS
ADT3AFI
ADT3TFL
RFP
RSU
Aeration Tank Loadings
BODi/AV
BODi/ASU
BODi/MLVSS
Purification Pressures
ATCxADTSAFI
ATCxADTSTFL
ATCxADTS)TFL/mg/l BODd
RSU/AFI
RSU/BODi
RSTSS/BODi
112 mg/1
3,700 kg/clay
297 SLU
17,835 kg
131,700 kg/day
6.18 hrs
4.19 hrs
0.475
1,650/day
622 kg/1000 AVM
12.4 kg/ASU
0.207 g/g
30.90
20.95
0. 187
71.3 RSU/1000 cu m
0.446 RSU/kg BODi
35.66 kg/kg
English Units
6.1 mgd
2.9 mgd
160 mg/1
10 mg/1
3000 mg/1
12,000 mg/1
5.0%
15.0%
0-210 million cu ft
1.571 million gals
112 mg/1
8,140 Ibs/day
78,550 SLU
39,300 Ibs
290,400 Ibs/day
6.18 hrs
4.19 hrs
0.475
435,000/day
38.76 lbs/1000 AVF
104 lbs/1000 ASU
0.207 Ibs/lb
30.90
20.95
0. 187
71.3 RSU/1000 gals
53.4 RSU/lb BODi
35.66 Ib/lb
27
-------
FINAL CLARIFIER CHARACTERISTICS
This section includes calculation procedures for the
following final clarifier characteristics that define proc-
ess equilibrium, permit clarifier and process performance
evaluation and dictate control adjustment requirements.
Final Clarifier Sludge Units - CSU
Final Clarifier Detention Time - CDT
Clarifier Sludge Detention Time - CSDT
Ci.arif.iar Surface Ov^rfl^-w Rate -• OFR
The clarifier sludge detention time (CSDT) should be
calculated after every control test for use along with the
CSFD (clarifier sludge flow demand - described later) to
determine the required clarifier sludge flow control
adjustment. The number of sludge units in the final
clarifier (CSU) is usually calculated from the 24-hour
average of test records to determine the aerator to
clarifier solids distribution ratio (SDR = ASU/CSU) and for
use in sludge age calculations. The other values, CDT and
OFR are used to document hydraulic and sludge loadings.
Final clarifier characteristics, flows and sludge
concentrations used are illustrated in Figure 7.
FINAL CLARIFIER SLUDGE UNITS - CSU
CSU = BLVxCSC/100
The sludge blanket volume (BLV) is readily calculated
from the depth of blanket (DOB) readings described in Part
II, CONTROL TESTS. For calculating the mean concentration
of the clarifier sludge (CSC), it is implicitly assumed that
sludge concentration will increase uniformly from a value
approximating ATC at the upper surface of the accumulated
sludge blanket to RSC at the bottom of the blanket. The
mean clarifier sludge concentration (CSC) will then
approximate the average of ATC and RSC.
The clarifier characteristics for the following CSU
calculation examples are shown in Figure 8.
28
-------
CFI=TFL=CFO+CSF
= 34,080 cu m/day
=9.00 mgd
@ ATC=5.0% |—i
FROM AERATION
TANK
to
V£>
CVM=2,970cum
CVF=105,000 cu ft
CVG=785,000 gals
CSA=730 sq m
= 7854 sq ft
CWD=4.07 m
= 13.37 ft
CFO=CFI-CSF
= 22,720 cu m/day
=6.00 mgd
-0
FINAL EFFLUENT
r
TO AERATION TANKS
RSF=10,980 cu m/day
= 2.90 mgd
/
I
XSF=380 cu m/day
=0.10 mgd r
"
TO WASTE
CSF=RSF+XSF
= 11,360 cu m/day
= 3.00 mgd
@ RSC=15.0%
Figure 7
FINAL CLARIFIER
Volumes, Flows, and Concentrations
Used in the Examples
-------
CFI @ ATC
(MIXED
SIDE WALL
(SWD)
HOPPER,
DEPTH (HOD)
'
LIQUOR INFLUENT)
1/3 HC
I
CV=FINAL CLARIFIER VOLUME
I •
SLUDGE BLANKET
SURFACE @ ATC
BLV=
BLANKET
)D^?LT/CW
VOLUME^,,
\ >
CO
O
Q
i
_l
\
i
O
^
O
\
„ (FINAL EFFLUENT)
Q
0
X
Q
V)
11
2/3 HOD -»^NX\
CSF @ RSC
(SLUDGE WITHDRAWAL) RSF + XSF
CLARiFIER
SLUDGE CONCENTRATION
= (ATC*RSC)/2
BOTTOM OF SLUDGE
BLANKET RSC
Figure 8
CSU = FINAL CLARIFIES? SLUDGE UNITS
CSU = BLVxCSC/100
-------
SYMBOLS
ATC = Aeration Tank Concentration (%}
BLT = Sludge Blanket Thickness (CWD - DOB)
BLV = Sludge Blanket Volume
CSA = Final Clarifier Surface Area
CSC = Mean C_larifier S_ludge Blanket Concentration
= (ATC+RSC)/2 ~ ~
CSU = Final Clarifier Sludge Units
CV = Final CJLarifier Volume
CVF = Final Clarifier Volume in Cubic Feet
CVG = Final Clarifier Volume in Gallons
CVM = Final Clarifier Volume in Cubic Meters
CWD = Final Clarifier Mean Water Depth
DOB = Depth of Sludge Blanket
TMeasured from water surface to upper surface
of the sludge blanket)
RSC = Return Sludge Concentration (%)
SWD = Clarifier Side Water Depth
EXAMPLES
Metric Units
Observed; Observed:
CVM = 2,970 cu m CVG
CWD = 4.07 m CWD
DOB = 2.71 m DOB
ATC =5.0% ATC
RSC = 15.0% RSC
Wanted: CSU
English Units
785,000 gals
13.37 ft
8.9 ft
5.0%
15.0%
Therefore:
BLT = CWD-DOB
= 4.07 - 2.71
= 1.36 m
BLV = (BLT/CWD)xCVM
= (1.36/4.075)x2970
= 990 cu m
Therefore:
BLT = CWD-DOB
= 13.37 - 8.9
= 4.47 ft
BLV = (BLT/CWD)xCVG
= (4.47/13.37)x785,000
= 262,400 gals
CSC = (ATC+RSO/2 CSC =
= (5.0+15.0)/2
= 10.0%
(ATC+RSO/2
(5.0+15.0)/2
10.0%
31
-------
CSU = BLVxCSC/100 CSU = BLVxCSC/100
- 990x10.0/100 = 262,400x10.0/100
= 99 SLU = 26,240 SLU
DISCUSSION
The mean sludge blanket concentration is calculated
from the implicitly assumed upper surface (ATC) and bottom
level (RSC) concentrations to eliminate the otherwise time
consuming and impractical task of collecting and centri-
fuging many additional sludge samples at one- or two-foot
depth intervals from each clarifier during each testing
period.
These assumptions are quite realistic for full-load,
optimum sludge quality and process balance. The actual
upper and lower level concentrations may not, however, equal
ATC and RSC when sludge settling and sewage flow rates
diverge widely from optimum. Though the value calculated
from each control test will not always be accurate, the
trend (-increasing or decreasing) of the calculated sludge
unit values will realistically represent the changes that
are occurring.
Since process evaluation and control policy are based
on the study of established trends, rather than upon obser-
vation of single test results, this simplified calculation
procedure is valid as well as convenient.
FINAL CLARIFIER DETENTION TIME - CDT
CDT = (CVx24)/CFI
SYMBOLS
CDT = Final CJLarifier Detention Time based
on CFI (hrs) ~
CFI = Final Clarifier Flow-In
CV = Final Clarifier Volume
CVG = Final Clarifier Volume in g_als
CVM = Final Clarifier Volume in cu m
32
-------
EXAMPLES
Metric Units
Observed:
CVM = 2,970 cu m
CFI = 34,080 cu m/d
Wanted: CDT
Therefore:
CDT = (CVMx24)/CFI
= (2.970x24)/34,080
= 2.09 hrs
English Units
Observed;
CVG = 0.7850 million gal
CFI = 9.000 MGD
Therefore:
CDT = (CVGx24)/CFI
- (0.7850x24)/9.0
= 2.09 hrs
CLARIFIER SLUDGE DETENTION TIME - CSDT
!CSDT = CSU/CSUO 1
-. I
The sludge detention time in the final clarifier is
determined by dividing the number of sludge units
accumulated in the clarifier by the rate at which sludge
units are removed from the clarifier. See Figure 9.
SYMBOLS
CSDT = Final Clarifier SJLudge Detention Time (hrs)
CSF = Final Clarifier S_ludge Flow
CSU = Final C_larifier S_ludge Units
CSUO = Final Clarifier Sludge Units-Out
RSC = Return S_ludge Concentration (%)
RSF = Return S_ludge Flow
XSF = Excess Sludge Flow to waste
EXAMPLES
Metric Units
English Units
Observed:
CSU
RSC
RSF
XSF
99
15.0%
10,980 cu m/day
380 cu m/day
Observed:
CSU =
RSC =
RSF =
XSF =
26,240
15.0%
2.900 ragd
0.100 mgd
33
-------
CSU = F!NAL
CLARIFIER
SLUDGE UNITS
= BLVxCSC/1pg
CSUO=CLAR!FIER SLUDGE
UNITS-OUT
= CSFxRSC/100
Figure 9
CSDT = CLARIFIER SLUDGE DETENTION TIME
CSDT = CSU/CSUO
-------
Wanted: CSDT
Therefore: Therefore:
CSF = RSF+XSF CSF = RSF+XSF
= 10,980+380 = 2.9+0.1
= 11,360 cu m/day = 3.000 mgd
CSUO = CSFxRSC/100 CSUO = CSFxRSC/100
= (11,360x15.0)/100 =3,000,000x15.0/100
= 1700 SLU/day = 450,000 SLU/day
- 1700/24 = 71 SLU/hr - 450,000/24 = 18,750 SLU/hr
CSDT = CSU/CSUO CSDT = CSU/CSUO
= 99/71 = 1.39 hrs -- 26,240/18,750 = 1.40 hrs
FINAL CLARIFIER SURFACE OVERFLOW RATE - OFR
OFR = CFO/CSA
SYMBOLS
CSA = Final Clarifier Surface Area
CFO = Final Clarifier Flow-Out (Final Effluent)
OFR = Final Clarifier Surface Overflow Rate
EXAMPLES
Metric Units English Units
Observed: Observed;
CFO = 22,720 cu ra/d CFO = 6.000 mgd
CSA = 730 sq m CSA = 7854 sq ft
Wanted: OFR
Therefore: Therefore:
OFR = CFO/CSA OFR = CFO/CSA
= 22,720/730 = 6,000,000/7,854
= 31.1 cu m/day/sq m = 764 gals/day/sq ft
35
-------
PROCESS CHARACTERISTICS
SLUDGE AERATION HOURS - SAH
SAH = (ADTx24)/(ADT+CSDT)'
Activated sludge oxidation is influenced by the number
of hours the sludge resides in the aeration tanks during
each 24-hour cycle.
SYMBOLS
ADT - Aeration Tank Detention Time
CSDT - Final Clarifier S_ludge Detention Time
SAH - S_ludge~Aeration Hours per day
EXAMPLES
Observed:
ADT =4.19 hrs (3TFL)
CSDT = 1.39 hrs
Wanted: SAH
Therefore:
SAH = (ADTx24)/(ADT+CSDT)
= (4.19x24)7(4.19+1.39)
= 18.0 hrs/day
SLUDGE AGE - AGE & AAG
AGE = (ASU+CSU) / TXU/day
AAG = AGExSAH/24
The following method of calculating sludge age is used
while the Waste Treatment Branch is developing an improved
method. The improved method will be included in a future
36
-------
issue of this pamphlet series if it proves practical and
more realistic.
Sludge age, being the average time that sludge solids
remain in the activated sludge plant, can vary from few to
many days. Using 2U-hour average data for each day's sludge
age calculation could obviously cause gross errors. If no
sludge were wasted on one day, for example, the calculation
would erroneously imply an infinite sludge age.
It is therefore suggested that the 7-day moving
averages of TSU, TXU etc, be used to compute sludge age.
Seven days is a reasonable time span and it includes all
data for every day in a calendar week. For instance, the
sludge age calculation on Thursday would be based on the
averages of all appropriate data collected during the
previous Friday, Saturday, Sunday, Monday, Tuesday,
Wednesday and the current Thursday. This procedure also
minimizes the discrepancy that can be introduced when no
sludge is wasted for a day or two. In this case, the one or
two zeros would be averaged in with the other TXU values for
the remaining 5 or 6 days in the 7-day moving average time
interval. The moving average concept is described and
illustrated in the Appendix.
Obviously, with a clear final effluent ESU becomes very
small. Under this condition TXU will nearly equal XSU.
But, the ESU term becomes significant under "bulking"
conditions, for example, as final effluent becomes degraded,
i.e solids are discharged with the final clarifier overflow.
SYMBOLS
AAG - Aeration Age. Number of days the sludge was
subjected to aeration.
AGE - Sludge Age in days.
ASU - Aeration Tank S_ludge Units
CFO - Final Clarifier Flow-Out
CSU - Final CJLarifier SJLudge Units
ESU - Final Effluent SJLudge Units
FEC - Final Effluent Concentration (%)
FETSS - Final Effluent Total Suspended Solids (mg/1)
SAH - S_ludge Aeration Hours per day
TXU - Total Excess Sludge Units removed (XSU+ESU)
WCR - S~ludge Weight-to-Concentration Ratio
XSC - Excess Sludge Concentration
XSF - Excess S_ludge Flow to Waste
XSU - Excess Sludge Units Wasted
37
-------
EXAMPLES
Metric Units
Observed:
ASU = 297 SLU
CSU = 99 SLU
XSF = 380 cu m/day
XSC = 15.0%
CFO = 22,720 cu m/day
FETSS = 10.0 mg/1
WCR = 800
SAH = 18 hrs/day
Wanted: AGE £ AAG
Therefore:
XSU = XSFxXSC/100
= 380x15.0/100
= 57 SLU/day
English Units
Observed:
ASU
CSU
XSF
XSC
CFO
FETSS
WCR
SAH
78,550 SLU
26,240 SLU
0.100 mgd
15.0%
6.0 mgd
10.0 mg/1
800
18 hrs/day
FEC =
FETSS/WCR
10/800
0.0125%
ESU = CFOxFEC/100
= 22,720x0.0125/100
= 2.84 SLU/day
TXU = XSU+ESU
- 57+3
=60 SLU/day
AGE = (ASU+CSU)/TXU/day
= (297+99)/60
= 6 . 6 days
AAG = AGExSAH/24
= 6.6x18/24
= 5.0 days
Therefore;
XSU = XSFxXSC/100
= 100,000x15.0/100
= 15,000 SLU/day
FEC = FETSS/WCR
= 10/800
- 0.0125%
ESU = CFOxFEC/100
= 6,000,000x0.0125/100
= 750 SLU/day
TXU = XSU+ESU
= 15,000+750
= 15,750 SLU/day
AGE = (ASU+CSU)/TXU/day
= (78,550+26,240)/15,750
= 6.6 days
AAG = AGExSAH/24
= 6.6x18/24
= 5.0 days
38
-------
SLUDGE CONCENTRATION RATIO - SCR
SCR = SSC60/RSC
The sludge concentration ratio reveals process balance
status, and indicates control adjustment needs. It shows
how closely the controlled return sludge concentration
approached the desired settled sludge concentration that had
been determined from the settlometer test.
The SSC settlometer test results should be plotted on a
trend chart as illustrated in the Appendix. The RSC values
should also be shown, as enlarged dots, on this trend chart
to indicate how far they may have strayed from the desired
SSC values.
The SCR, therefore, refines impressions received from
the trend chart and provides numerical values that can be
used to analyse process balance and to set target values for
return sludge flow demand calculations.
An SCR between 1.0 and 1.2 usually indicates good
balance. Values less than 0.9 or greater than 2.0 reveal
the need for process adjustment.
SYMBOLS
RSC = Return SJLudge Concentration (%)
SCR = Sludge Concentration Ratio
SSC60 = Settled S_ludge Concentration at 60 minutes
EXAMPLES
Observed: Case A Case B Case C
SSC60 = 15.0 8.0 16.5
RSC = 14.0 10.0 7.5
Wanted; SCR
Therefore;
SCR = SSC60/RSC SSC60/RSC SSC60/RSC
15.0/14.0 8.0/10.0 16.5/7.5
1.07 0.80 2.2
The SCR in Case A reveals good process balance, but the
SCR in Case B is too low and that in Case C is too high.
39
-------
CLARIFIER SLUDGE FLOW DEMAND - CSFD
CSFD = CSFx(RSC-ATC)/(SSC-ATC)
This CSFD Formula is used to determine the clarifier
sludge removal flow rate (CSF) needed to maintain proper
process balance. It should be computed at the end. of each
testing period, after which the operator should adjust the
CSF to equal the CSFD.
The operator should also compute the CSDT, as shown in
the final clarifier section, to determine whether the final
clarifier sludge residence time approximates 1.0 hour, or is
at least within the tolerable limits of from 0.75 to 1.5
hours.
The use of these formulas for process evaluation and
control is discussed in Part IV PROCESS CONTROL.
SYMBOLS
ATC = Aeration Tank Concentration (%)
CSF = Final Clarifier S_ludge Flow
CSFD = Clarifier Sludge Flow Demand
RSC = Return S_ludge Concentration (%}
SSC = Settled Sludge Concentration (%)
EXAMPLES
Metric Units English Unites
Observed: Observed;
CFO = 22,720 cu m/day CFO = 6.000 mgd
CSF = 11,360 cu m/day CSF = 3.000 mgd
ATC =5.0% ATC =5.0%
RSC = 15.0% RSC = 15.0%
SSC = 13.0% SSC - 13.0%
-------
Wanted: CSFD needed to reduce RSC from 15.0 to 13.0
Therefore: Therefore:
CSFD = CSFx(RSC-ATC) CSFD = CSFx(RSC-ATC)
/(SSC-ATC) /(SSC-ATC)
= 11,360 (15.0-5.0) = 3.0(15.0-5.0)
/(13.0-5.0) /(13. 0-5.0)
= 11,360x10.0/8.0 = 3.0x10.0/8.0
= 14,200 cu m/day = 3.75 mgd
-------
MIXING FORMULA DEVELOPMENT
SYMBOLS FOR MIXING FORMULAS
AFI = Aeration Tank Waste Water F_low-In
ATC = Aeration Tank Concentration (%)
CFI = Final Clarifier Flow-In
CFO = Final Clarifier Flow-Out (Final Effluent)
CFP = Final C~larifier Sludge F_low Percentage
(expressed decimally)
CSF = Clarifier SJLudge Flow (Usually = RSF+XSF)
FEC = Final Effluent Solids Cone. (%)
FETSS = Final Effluent Total Suspended Solids (mg/1)
MLTSS = Mixed Liquor Total Suspended S_olids (mg/1)
PEC = Primary Effluent Solids Cone. (%)
PETSS = Primary E_f fluent Total Suspended Solids (mg/1)
RSC = Return sludge Concentration (%)
RSF = Return S_ludge Flow
RSP = Return S_ludge Flow percentage based on
a mass balance around the inlet end of
the aeration tank (expressed decimally)
SLU = SJLudge Units
CSUI = Final Clarifier Sludge Units-In
CSUO = Final Clarifier Sludge Units-Out
WCR = Sludge Weight-to-Cpncentration Ratio
XSF = Excess Sludge Flow to Waste ~~
SIMPLIFIED MIXING FORMULAS
(See Figure 10)
A. Define the Flow Equality.
The sum of the final effluent and clarifier sludge
flow out of the final clarifier must equal the mixed
liquor flow into the clarifier.
Flow Out = Flow In
CFO + CSF = CFI
(D
Express CSF and CFI as functions of CFO and CFP.
CSF = CFO x CFP
CFI = CFO (1.0+CFP)
(2)
(3)
-------
Now substitute the right hand terms of equations (2)
and (3) for CSF and CFI in equation (1)
Flow Out = Flow In
CFO+(CFOxCFP) = CFO(1.0+CFP) (4)
B. Define the Sludge Unit Equality
The number of sludge units flowing out of the final
clarifier will be the sum of FEC/100 multiplied by the final
effluent flow plus RSC/100 multiplied by the clarifier
sludge flow. The number of sludge units entering the
clarifier will be ATC/100 multiplied by the mixed liquor
flow.
By multiplying the terms in equation (4) by the
appropriate concentrations, the sludge unit equality
becomes:
CFO X FEC/100 + (CFO x CFP) x RSC/100
= CFO (1.0 + CFP) x ATC/100 (5)
The final effluent suspended solids concentration is
exceedingly low compared to the mixed liquor and return
sludge concentrations in an activated sludge plant that is
performing properly. Under such conditions, the number of
sludge units carried out in the final effluent can be
neglected and equation (5) can be simplified to:
CFO x CFP x RSC/100 = CFO (1.0 + CFP) x ATC/100 (6)
After cancelling the common CFO and 100 terms from both
sides of equation (6) it can be further simplified to
include only ATC, RSC and CFP as follows:
CFP X RSC = (1.0 + CFP) x ATC
CFP x RSC = ATC + (CFP x ATC)
(CFP x RSC) - (CFP x ATC) = ATC
CFP (RSC - ATC) = ATC
CFP = ATC / (RSC - ATC) (7)
The CFP equation (7) can now be transformed to the
other two mixing formulas so that any single unknown can be
calculated from the other two known or measured values.
CFP = ATC/(RSC-ATC)
ATC = CFPxRSC/(CFP+1-0)
RSC = ATC+(ATC/CFP)
-------
SLUDGE UNITS IN (CSUI)=CFO(1.0+CFP )ATC/100
CFP =
CFI=CFO(1.0+CFP)
c- MIXED LIQUOR
FINAL
EFFLUENT
- -»
.
rCLARIFIER SLUDGE
CSFs^CFOxCFP
Fig ure 10
MASS BALANCE FOR
MIXING FORMULA DEVELOPMENT
CSUI= CSUO
CFO(1.0+CFP)ATC = CFOxCFPxRSC
-------
EXPANDED MIXING FORMULAS
TO INCLUDE SIGNIFICANT PRIMARY EFFLUENT (PEC) OR FINAL
EFFLUENT (FEC) SUSPENDED SOLIDS CONCENTRATIONS.
In high rate activated sludge plants for example, where
the primary effluent suspended solids concentration may be
significant compared to very low mixed liquor suspended
solids concentrations, it is usually necessary to use mixing
formulas that have been expanded to account for primary
effluent solids.
Recognition and use of final effluent solids concen-
trations in expanded mixing formulas may also be necessary
whenever significant amounts of sludge solids are washed out
of the process final effluent during sludge "balking".
In either case, a preliminary calculation is usually
necessary to convert the primary effluent or final effluent
suspended solids concentrations to equivalent centrifuge
values (PEC and FEC) before using the expanded formulas.
Since the sludge weight to centrifuged sludge concentration
ratio (WCR) is usually determined daily, these approximate
centrifuge concentration equivalents (PEC and FEC) can be
computed as follows:
Primary Effluent Final Effluent
PEC = PETSS/WCR FEC = FETSS/WCR
Observed: Observed:
PETSS = 240 mg/1 FETSS = 480 mg/1
WCR = 800 WCR = 800
Wanted: PEC Wanted: FEC
Therefore; Therefore:
PEC = PETSS/WCR FEC = FETSS/WCR
= 240/800 = 480/800
= 0.30% = 0.60%
The expanded formulas can then be derived according to
the same mass balance techniques that were described for the
Simplified Mixing Formula development.
CFO and FEC must, however, be included in the deri-
vation to account for sludge units in the final effluent.
45
-------
AFI and PEC must be included in the derivation of the
formulas that are expanded to include primary effluent
solids. Since these formulas are based on a mass balance of
solids entering and leaving the aeration tanks, AFI, RSF and
RSP are used instead of the CFO, CSF and CFP values that
were used in the mass balance around the final clarifier.
Such derivations will then provide the following two
sets of mixing formulas to include significant final
effluent or primary effluent suspended solids
concentrations:
FOR SIGNIFICANT FINAL EFFLUENT SOLIDS
CFP = (ATC-FEC)/(RSC-ATC)
ATC = (CFPxRSC)+FEC/(CFP+1.0)
RSC = ATC+ (ATC-FEC)/CFP
FOR SIGNIFICANT PRIMARY EFFLUENT SOLIDS
RSP = (ATC-PEC)/(RSC-ATC)
ATC = (RSPxRSC)+PEC/(RSP+1.0)
RSC = ATC+ (ATC-PEC)/RSP
-------
CLARIFIER SLUDGE FLOW DEMAND
FORMULA DEVELOPMENT
SYMBOLS FOR THE CLARIFIER SLUDGE FLOW DEMAND FORMULA
ATC = Aeration Tank Concentration (%)
CFO = Final Clarifier Flow-Out (Final Effluent)
CSF = Final Clarifier Sludge Flow
CFP = Final CjLarifier Sludge Flow Percentage
(expressed decimally) ~~
CSUI = Final Clarifier S_ludge Units-In (Mixed Liquor)
CSUO = Final Clarifier SJLudge Units-Out (Return plus
waste sludge)
CSFD = Clarifier SJLudge Flow Demand
RSC = Return SJLudge Concentration (%)
SSC = Settled Sludge Concentration (%)
DEVELOPMENT OF THE CLARIFIER SLUDGE FLOW DEMAND FORMULA
(SEE FIGURE 11)
The CSFD formula is developed by expressing the
clarifier sludge flow as a percent of the sewage flow.
CSF = CFOxCFP (1)
CFP is then expressed in terms of RSC and ATC according
to the mixing formulas.
CFP = ATC/(RSC-ATC) (2)
The solids concentration relationship in equation (2)
is now substituted for CFP in equation (1) and:
CSF = CFOxATC/(RSC-ATC) (3)
By transposing the terms in equation (3) it becomes:
CFOxATC = CSFx(RSC-ATC) (4)
Substituting the desired clarifier sludge concentration
(SSC) and the unknown clarifier sludge flow demand (CSFD),
-------
for RSC and CSF respectively in equations (1), (2), and (3)
will give:
CFOxATC = CSFD(SSC-ATC) (5)
Since the right hand terms in equations (4) and (5) are
each equal to (CFOxATC), they are equal to each other, and:
CSFD(SSC-ATC) = CSF(RSC-ATC)
CSFD = CSF(RSC-ATC)/(SSC-ATC)
DISCUSSION AND CHECK ON THE FORMULA
The number of sludge units in the mixed liquor entering
the final clarifier must equal, or approximate in actual
practice, the number of sludge units in the clarifier sludge
pumped out from the bottom of the clarifier.
Though the return sludge concentration (RSC) will
change rapidly in response to a clarifier sludge flow (CSF)
adjustment, the mixed liquor concentration. (ATC) entering
the clarifier will change only slightly, if at all, when the
process balance is near optimum equilibrium.
Following is a mass balance check on the results from
the CSFD example in the Process Characteristics Section.
CSUI must equal CSUO
Observed:
CSUI = (6.0+3.0)x5.0/100 - 0.450 million SLU/day
CSUO = 3.0x15.0/100 = 0.450 million SLU/day
The observed sludge units entering the final
clarifier equal those leaving the clarifier.
Demand:
CSUI = {6.0+3.75)x5.0/100 = 0.4875 million SLU/day
CSUO = 3.75x13,0/100 - 0,4875 million SLU/day
Sludge units entering the final clarifier will equal
those leaving the clarifier after the clarifier sludge is
increased from 3.0 mgd to meet the 3.75 mgd clarifier sludge
flow demand.
48
-------
CFO INCREASED CSF
CFO OBSERVED CSF
CFO REDUCED CSF
WWW NOTE: ATC AND CFO
" V " REMAIN CONSTANT
O O O
REDUCE CSF
TO INCREASE RSC
-CSUI
CFO
RSC
'
CSF
OBSERVED CSF & RSC
RSC
CSF
\ INCREASE CSF
\ TO REDUCE RSC
'/ '/' / / , ,- / ' /
•, //'f/// ////A
- '/ / ' •,-,••
RSC
-CSUO
CSF
Figure 11
MASS BALANCE FOR CSFD
CFD = CSF(RSC-ATC)/(SSC-ATC)
-------
SUMMARY OP
FORMULAS AND CALCULATED RESULTS
PARAMETERS
FORMULAS OR PROCEDURE
VALUES SHOWN IN EXAMPLE CALCULATIONS
METRIC UNITS ENGLISH UNITS
EXAMPLE
REFERENCE
ON PAGE
HYDRAULIC LOADINGS
ADT a AFI
ADT 3 TFL
CDT
OFR
BOD LOADINGS
BODi / AV
BODi / ASU
BODi / MLVSS
PURIFICATION PRESSURES
ATC X ADT 3 AFI
ATC x ADT 3 TFL
ATC x ADT / MG/L BODd
RSU / AFI
RSU / AFI BODi
RSTSS / BODi
SLUDGE
SSV 5
SSV60
* ATC
ssceo
SCR
WCR
SIMPLE MIXING FORMULAS
CFP
ATC
RSC
PROCESS RELATIONSHIPS
DOB
BLT
BLV
CSC
ASU
CSU
TSU
RSU
SDR
CSF
CSUI / DAY
CSUO / DAY
CSUO / HOUR
CSDT
CFP
CFP
RFP
SAH
XSU
PEC
ESU
TXU
AGE
AAG
(AV X 24) / AFI
(AV X 24) / (AFI + RSF)
(CV X 24) / CFI
CFO / CSA
WT OF BODi / 1000 AV
WT OF BODi / ASU
BT OF BODi / WT OF MLVSS
DIRECT CALCULATION
DIRECT CALCULATION
DIRECT CALCULATION
DIRECT CALCULATION
DIRECT CALCULATION
WT OF RSTSS / WT OF BODi
SETTLOMETER READING
SETTLOMETER READING
CENTRIFUGE READING
1000 X ATC / SSV60
SSC60 / RSC
MLTSS / ATC
ATC / (RSC - ATC)
(CFP X RSC) / (CFP +
ATC + (ATC / CFP)
1.0)
MEASURED
CWD - DOB
(BLT / CWD) X
(ATC + RSC) /
CV
2
AV x ATC / 100
BLV X CSC / 100
ASU +• CSU
RSF x RSC / 100
ASU / CSU
RSF + XSF
CFI X ATC / 100
CSF X RSC / 100
CSUO/DAY / 24
CSU / CSUO/HOUR
100 X CSF / CFO
100 x ATC / (RSC - ATC)
100 X RSF / AFI
(ADT X 24) / (ADT + CSDT)
XSF X XSC / 100
FETSS / WCR
CFO X FEC / 100
XSU + ESU
TSU / TXU/DAY
AGE x SAH / 24
CLARIFIER SLUDGE FLOW DEMAND
CSFD
CSF X (RSC - ATC) / (SSC - ATC)
6.18 HRS
4.19 HRS
2.09 HRS
31.1 CU M/DAY/SQ M
622 KG/1000 AVM
12.4 KG/ASU
0.207 KG/KG
30.90
20.95
0.187
71.3 RSU/1000 CU M
0.446 RSU/KG BODi
35.66 KG/KG
630 CC/L
200 CC/L
3 X
15 %
0.8 to 2.2
500 TO 1,000
0.50
5 *
15.0 %
2.71 M
1.36 M
990 CU M
10 %
297 SLU
99 SLU
396 SLU
1,650 SLU/DAY
3.0
11,360 CU M/DAY
1,700 SLU/DAY
1,700 SLU/DAY
71 SLU/HR
1.39 HRS
50.0 %
50.0 X
47.5 X
18 HRS/DAY
57 SLU/DAY
0.0125 X
2.84 SLU/DAY
60 SLU/DAY
6.6 DAYS
5 DAYS
14,200 CU M/DAY
6.18 HRS 24
4.19 HRS 24
2.09 HRS 33
764 GPD/SQ FT 35
38.76 LBS/1000 AVF 27
104 LBS/1000 ASU 27
0.207 LBS/LB 27
30.90 27
20.95 27
0.187 27
71.3 RSU/1000 GAL 27
53.4 RSU/LB BODi 27
35.66 LB/LB 27
630 CC/L 10
200 CC/L 10
3 % 10
15 % 10
0.8 to 2.2 39
500 TO 1,000 5
0.50 13
5 X 17
15.0 % 18
8.9 FT
4.47 FT
262,400 GALS
10 %
78,550 SLU
26,240 SLU
104,790 SLU
435,000 SLU/DAY
31
31
31
31
22
32
23
3.0
3.0 MGD
450,000 SLU/DAY
450,000 SLU/DAY
18,750 SLU/HR
1.40 HRS
50.0 %
50.0 X
47.5 X
18 HRS/DAY
15,000 SLU/DAY
0.0125 X
750 SLU/DAY
15,750 SLU/DAY
6.6 DAYS
5 DAYS
3.75 MGD
28
35
48
35
35
35
15
13
15
36
38
38
38
38
38
38
40
* ATC OF 3.0 USED IN THE SSC EXAMPLE.
------- |