MIXING FORMULAE
FOR
ACTIVATED SLUDGE CHARACTERISTICS
ADAPTED BY
A. W. West, P.E.
Chief, Sewage Treatment Plant
Operations & Design Branch
ENVIRONMENTAL PROTECTION AGENCY
WATER QUALITY OFFICE
OFFICE OF ENFORCEMENT & STANDARDS COMPLIANCE
DIVISION OF FIELD INVESTIGATIONS - CINCINNATI CENTER
APRIL 1971
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33IVIRONMENTAL PROTECTION AGENCY
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305R71101
MIXING FORMULAE
FOR ACTIVATED SLUDGE CALCULATIONS
CASE A
CASE B
General - When
Significant Amounts of
Solids are drawn out
in the Clarifier Effluent
Usual Practice
with Clear
Clarifier Effluents
(FEC o)
CSP
ATC - FEC
RSC - ATC
ATC
RSC - ATC
RSC
ATC +
ATG - FEC
CSP
ATC
ATC
CSP
ATC
(CSP x RSC) + FEG
CSP + 1.0
CSP x RSC
CSP -t- 1.0
EXAMPLES
CSP
RSC
ATC
3.2
WHEN
ATC = 3-2
RSC =10.7
FEC = 0.2
(CSP = O.UO)
3'2 - °'2 o ho
10.7 - 3.2 - U>4U
- , 3.2 - 0.2
| .„_.„ .JM.n. JJJ f f(J
x 10.7) + 0.2 _ pn
WHEN
ATC = 3-
RSC = 11.
FEC = 0.
(CSP = 0.
3.2
11.2 - 3-2
3-2 + Si)-
O.U x 11.2
2
2
0
k(
20
* °
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ABBREVIATIONS
for
MIXING FORMULAE
FLOWS (WASTE WATERS, MIXED LIQUOR, & EFFLUENT)
PFO PRIMARY GIARIFIER FLOW (OUT OF)
TFO SLUDGE THICKENER FLOW (OUT OF)
AFI AERATOR FLOW (WASTE WATER I_N)
TFL TOTAL FLOW (OUT OF AERATOR)
CFI FINAL GIARIFIER FLOW (IN TO)
GFO FINAL CLARIFIER FLOW (OUT OF)
SLUDGE FLOWS
CSF FINAL CIARIFIER SLUDGE FLOW
RSF RETURN SLUDGE FLOW
XMF EXCESS MIXED LIQUOR FLOW TO WASTE
XRF EXCESS RETURN SLUDGE FLOW TO WASTE
CSP CIARIFIER SLUDGE FLOW PERCENT OF CFO
CONCENTRATIONS ($ by CENTRIFUGE)
ATC AERATION TANK CONCENTRATION(MIXED LIQUOR)
RSC RETURN SLUDGE CONCENTRATION
FEC FINAL EFFLUENT CONCENTRATION(EQUIV. CENTR.)
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CHECK MIXING FORMULAE BY MASS BALANCE
CUT A SECTION AROUND THE FINAL CLARIFIER, AND THE SIUDGE
UNITS COMING OUT MUST EQUAL (OR APPROXIMATE IN ACTUAL
PRACTICE) THE SLUDGE UNITS ENTERING THE CLARIFIER.
1) ONE SLUDGE UNIT (SLU) IS DEFINED AS THE AMOUNT
OF SLUDGE IN ONE GALLON AT A ONE PERCENT CON-
CENTRATION (EXPRESSED AS A DECIMAL) BY CENTRI-
FUGE, i.e., 10.0 mg at 4.0$ by CENTRIFUGE =
10 x 0.04 = 0.40 MILLION SLUDGE UNITS.
2) THE EQUIVALENT CENTRIFUGE CONCENTRATION OF LOW
LEVEL SOLIDS IN CLARIFIER EFFLUENTS CAN BE CAL-
CULATED FROM THE MEASURED TSS AND THE DAILY
MLTSS/ATC RATIO.
i.e., IF THE MIXED LIQUOR CONCENTRATED TO 4.2$
IN THE CENTRIFUGE, AND MEASURED 3360 mg/1 by
WEIGHT: - THE MLTSS/ATC RATIO = 3360/4.2 = 800.
THEN IF THE CLARIFIER EFFLUENT CONTAINED SOLIDS
CONCENTRATIONS BELOW THE RANGE FOR ACCURATE
CENTRIFUGE DETERMINATIONS, - THE EQUIVALENT
CENTRIFUGE CONCENTRATION IS: -
FEC = (TSS) -f (MLTSS/ATC RATIO)
i.e., FEC at 160 mg/1 at ESTABLISHED RATIO
FEC = 160/800 = 0.20$
CHECK CASE A
SLU IN = 14.0 x 0.032 = 0.448
SLU OUT = (4.0 x 0.10?) + (10.0 x 0.002)
= 0.428 + 0.020 = 0.448
CHECK CASE B
SLU IN = 14.0 x 0.032 = 0.448 MILLION SLU/DAY
SLU OUT = (4.0 x 0.112) + (10.0 x 0.0) = 0.448
NOTE: - AT CONSTANT CSP, THE EFFLUENT SOLIDS LOSS WOULD REDUCE THE AMOUNT
AND CONCENTRATION OF SLUDGE WITHDRAWN FOR RETURN. THIS COULD ALSO
DECREASE ATC IN THE NEXT PROCESS CYCLE.
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Environmental Prctaotlon Agency
Library, HegIon V
1 North 18 acker Drive
Chicago, Illinois 60606
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