who’s afraid of the settling flux?
TRANSCRIPT
Who’s Afraid of the Settling Flux?
M.TRUETT GARRETT, JR., Sc.D, P.E.
Click on View, Notes page, to see
references and comments.
Who’s afraid of the settling
flux?
• The ATV, Abwassertechniche Vereinigung,
in Germany 1991. Currently DWA, 2007.
• WEF Publication Committee, Manual of
Plant Operation does not mention flux.
• Ekama, et al, Secondary Settling Tanks,
1997, cite “…a lack of confidence in the
predictive power of the flux theory.”
Who’s afraid of the settling
flux?
• “Flux theory” may not be well understood
so that many are hesitant, afraid, to use it,
being concerned that their results may not
be correct.
ACTIVATED SLUDGE SETTLING
VELOCITY VS. CONCENTRATION
0
1
2
3
4
5
6
0 1 2 3 4 5 6
SOLIDS CONCENTRATION, g/L
SE
TT
LIN
G V
EL
OC
ITY
, m
/hr
ACTIVATED SLUDGE SETTLING
VELOCITY VS. FLOC VOLUME
0
1
2
3
4
5
6
0 20 40 60 80 100
FLOC VOLUME, DSV30, %
SE
TT
LIN
G V
EL
OC
ITY
, m/h
r
Illustration Of Terms
Overflow
Inflow
Underflow
Inflow = Overflow + Underflow
Area of the tank
Definition Of Terms
Overflow rate = V = Qo/A, m/hr
Underflow rate = U = Qu/A, m/hr
Inflow rate = (V + U) = (Qo+Qu)/A
Feed concentration = C, g/dL, percent
Underflow concentration = Cu, g/dL
Settling velocity of solids = Vs, m/hr
Definition Of Terms, cont’d.
• Feed Floc Volume = FV, mL/dL, percent by volume.
• FV = DSV30 = DSVI x C
• DSVI = SVI of mixed liquor
sample diluted so that sludge volume after 30 min. < 30%.
• Michaels and Bolger showed that flocculated kaolin slurries settle as flocs.
• Scott found the Richardson and Zaki relationship applicable to settling data for calcium carbonate slurries.
Vs = Vso x (1- kc)4.65
Where kc is the floc volume, k has the dimension mL/g, the same as the SVI, c is the solids concentration, g/mL.
• Vso is the Stokes settling velocity of the average floc.
• Scott found that the R-Z relationship
applied for values of kc less than about
0.4.
• Since we defined C as percent solids,
g/dL, and Scott’s concentration was
g/mL, the R-Z equation, using n
instead of 4.56, becomes,
Vs = Vso x (1-FV/100)n.
Dick and Young used the log-log
equation to fit higher concentrations.
Vs = a * FV-n
SETTLING AND UNDERFLOW
VELOCITY VS. FLOC VOLUME
0.01
0.10
1.00
10.00
10 100 1000
Floc Volume, DSVI*C, Percemt
Se
ttlin
g V
elo
cit
y a
nd
Un
de
rflo
w V
elo
cit
y, m
/hr
(100 - FV)
U vs Xu, POWER
U vs Xu, EXP.
Sims Bayou
Thickener
Richardson & Zaki
POWER EQUATIONS FITTED
TO THE SETTLING DATA
• For FV < 40,
• Vs = 8.58 * (1 - FV/100)3.83 m/hr
• For FV > 40,
• Vs = 15,300 * FV-2.56 m/hr
EXPONENTIAL EQUATION
FITTED TO THE SETTLING
DATA
• Vesilind proposed plotting the
logarithm of the settling velocity
against the arithmetical value of
concentration. This gives a
single exponential equation.
• Vs = 9.38 * exp(-0.0494*FV) m/hr
Exponential Correlation of
Settling Velocity and Floc Volume
0
0
1
10
0 10 20 30 40 50 60 70 80 90 100
FLOC VOLUME, PERCENT
SE
TT
LIN
G V
EL
OC
ITY
, m
/hr
Formulas At A Settling Tank
1. (V + U)*FV = U*FVuThis is limited by,
2. (Vs + U)*FV = U*FVu How can we rearrange this to
plot the relationships?
Limiting Formulas At The Settling
Tank
2. (Vs + U)*FV = U*FVu Multiply left side of equation.
3. Vs*FV + U*FV = U*FVuVelocity times Concentration
is a FLUX by definition.
Preparing a total flux plot
• Label ordinate as FLUX, m/hr * Floc
Volume
• Label abscissa as Floc Volume = FV,%
• Plot U*FV vs FV, a straight line from 0,0
• Fit an equation to the settling data,
Vs=f(FV)
• From the equation, plot Vs*FV vs FV
3. Vs*FV + U*FV = U*FVu
Total Flux Versus FV Plot
• The concern is for the Floc Volume as it increases from Feed FV to Underflow FV at the same Total Flux.
• If the Feed FV is less than FVB, the maximum flux is limited by the minimum in the Total Flux curve.
U=0.34 m/hr
0
20
40
60
80
0 25 50 75 100 125 150
Feed Floc Volume, percent
Flo
c V
olu
me F
lux, F
V x
m/h
r
Total Flux (Vr+U) Flux
Underflow Flux FVB
Vr Ext. Underflow FV
3. Vs*FV + U*FV = U*FVu
Total Flux Versus FV Plot
• If the Feed FV is greater
than FVB, the Total Flux
is limited only by the
Total Flux curve.
• The Underflow FV will
be greater than the value
obtained when Feed FV
is less than FVB.
U=0.34 m/hr
0
20
40
60
80
0 25 50 75 100 125 150
Feed Floc Volume, percent
Flo
c V
olu
me F
lux, F
V x
m/h
r
Total Flux (Vr+U) Flux
Underflow Flux FVB
Vr Ext. Underflow FV
3. Vs*FV + U*FV = U*FVu
Total Flux Versus FV Plot
Result when Loading Point is in the various areas
• C. On (Vr+U) curve it issteady state. Below the curve, no blanket forms, existing is depleted
• B. Thick blanket forms at conc. FVB. Thin blanket, if any, settles into the thick blanket.
• A. Thin blanket forms at feed solids concentration also thick blanket forms if FV is less than FVB.
C
B
A
U=0.34 m/hr
U=0.34 m/hr
A
B
C
3. Vs*FV + U*FV = U*FVu
Total Flux Versus FV Plot
Result when State Point is in the various areas
• If a sludge blanket
persists, the State
Point is either on or
oscillates around the
green line of (Vr+U)
Flux.C
B
A
U=0.34 m/hr
A
B
C
U=0.34 m/hr
3. Vs*FV + U*FV = U*FVu
Yoshioka Flux Plot
0
20
40
60
80
0 25 50 75 100 125 150
Feed Floc Volume, percent
Flo
c V
olu
me F
lux, F
V x
m/h
r
Settling Flux, FV*m/h Vr Flux, FV*m/h
FVB Vr Ext
Underflow FV
• The Settling Flux is plotted versus the Feed Floc Volume.
• For Feed FV < FVB, the Maximum Flux that can be removed is shown by a line with slope –U tangent to the Settling Flux curve.
U=0.34 m/hr
3. Vs*FV + U*FV = U*FVu
Yoshioka Flux Plot
Result when State Point is in the various areas
U=0.34 m/hr
C. On Vr curve it is steady
state. Below the curve, no
blanket forms, existing is
depleted.
B. Thick blanket forms at
conc. FVB. Thin blanket, if
any, settles into the thick
blanket.
A. Thin blanket forms at
feed solids concentration
plus thick blanket if FV is
less than FVB.
AB
C
3. Vs*X + U*X = U*Xu
Yoshioka Flux Plot
YOSHIOKA Et Al.
FLUX PLOTS
Alternate Limiting Formulas At
The Settling Tank
3. (Vs + U)*FV = U*FVu
Divide by FV, subtract U
4. Vs = U*FVu*(1/FV) – U
Plot Vs versus (100/FV)
Plot U on the Y-axis
4. Vs = U*FVu*(1/FV) - U
Velocity Versus 100/FV Plot
ABA
C. No blanket forms,
existing is depleted. The
only steady states are on
the Vr max curve.
B. Thick blanket forms.
Thin blanket, if any, settles
into the thick blanket.
A. Thin blanket forms at
feed solids concentration
plus thick blanket 1/Xu
1/Xb
AB
C
A B
C
Real, non-steady state equation
• (U + V) FV = U FVu + rate of
change in sludge blanket
• If the rate of change of the blanket
is zero, V becomes Vrmax.
• (U+Vrmax)FV = U FVu
• Vrmax = U FVu(1/FV) - U
4. Vrmax = U*FVu*(100/FV) - U
• Points on a velocity
vs. reciprocal of
concentration chart
indicate the derivative
of the sludge blanket
height, NOT the
blanket height.
Results of Blanket Formation
• In an activated sludge plant, formation of a sludge blanket in the settler depletes solids in the mixed liquor aeration tank.
• The change in feed solids depends on the size and arrangement of aeration tanks.
• Due to the dynamics of the process a simulation program is needed to follow the changes in blanket height from storm flow.
Danger!
Sedimentation programs that do not have
mixed liquor aeration tanks are worthless!
In an activated sludge plant, formation of a
sludge blanket in the settler depletes solids
in the mixed liquor aeration tank and
reduces the solids in feed to the settler.
Review of Coe And Clevenger,
1916
C = 62.35 R/(F – D)
C = capacity in pounds per sq. foot per hour.
R = rate of settling in feet per hour at
consistency F.
F = ratio of fluid to solids in pulp tested.
D = ratio of fluid to solids in discharge req’d.
Coe And Clevenger
C = 62.35 R/(F – D)
Upper chart
R= C(F – D)/62.35
Lower chart, line added
Coe And Clevenger, Figure 6
Coe And Clevenger, Figure 13
Coe and Clevenger
• The chart illustrates the
calculation of C for point j
at F=3.0, R=0.62, and
D=1.0
• C=62.35*0.62/(3-1)=19.3
• The calculation may be
repeated for each point for
the Capacity Curve, or
• Since the line is tangent to
the curve, it is the Capacity
Replot of Figure 13.
0
0.5
1
1.5
2
2.5
3
3.5
4
0246810
Consistency, lb H2O/lb pulp
R, ft
/hr
F D
R
Coe and Clevenger
Omitting the weight of water per cubic foot,
R = C*(F-D)/62.35 is equal to
• V= U*Xu*(1/X – 1/Xu)
• V= U*Xu*1/X – U*Xu/Xu
• V= U*Xu*(1/X) – U
• Thus the Coe and Clevenger lower chart is
equivalent to the Velocity vs 1/X plot.
• The line may be started from the underflow
rate or 1/underflow concentration.
Discussion
• Coe and Clevenger called X*Xu the capacity of a thickener, not the limiting flux.
• The term flux was later applied to the product of concentration and velocity to aid in the explanation of the thickening phenomenon.
• The mathematics is the same regardless of the name applied to the terms.
Summary
• The Flux Curve is not theory, but an analytical tool. You can use it to see the effect of various operating conditions.
• The curve of V vs Reciprocal of X has real coordinates and the flux terminology is not required.
• The plots of Total Flux vs X and the V vs Reciprocal of X have origins in the paper by Coe and Clevenger, 1916.
Deviations
• If the sludge blanket gets into the underflow
then the underflow concentration is less
than predicted and extra solids accumulate
in the settling tank.
• Sawyer, Two Rivers WI Plant
• Munch, Calumet IL Plant
• Billmier, use deeper scraper blades
Operation Problem
Municipal plants must treat high flow
during rain storms, bypass not allowed.
The plant must be operated so that high
flow can be received without upset.
The problem requires a dynamic
solution, therefore a simulation model
aids understanding of the solutions.
Solution
The City of Houston and The University of Texas conducted research at the city’s 12 MGD Turkey Creek plant.
The research is reported in the Masters Thesis of William T. Manning, Jr. and in WER, July/Aug 1999, p 234.
The original 1.2 MGD plant (idle) was modified for the study and effluent was returned to the main plant.
A spreadsheet model was developed to simulate operating results.
DESCRIPTION OF PLANT
USED FOR STUDY
Aeration Tanks, two at 26,880 cf each,
operated in series.
Clarifier, circular,13.5 side water depth,
area 4,800 sf.
An idle aeration basin of the main plant
was used to store effluent for storm flow
simulation.
SCHEMATIC OF WASTEWATER FLOW
Test Initial Conditions
0
10,000
20,000
30,000
40,000
50,000
60,000
0 50 100 150 200
FV
Flo
c V
olu
me
Flu
x, g
pd
/sf
*FV
Floc Vol. Flux Curve Tests, Initial FV FluxU=100 gpd/sf U=200 gpd/sfU=300 gpd/sf
8/23
8/27
Power Equations Fitted To
Settling Data
• For FV < 40,
• Vs = 8.58 * (1 - fv/100)^3.83 m/h
• For FV > 40,
• Vs = 15,300 * fv^-2.56 m/h
Exponential Equation Fitted
To Settling Data
• Vs = 9.38 * exp(-0.0494*FV) m/h
Comparison Of Power And
Exponential Flux Curves
8/23
8/27
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100 120 140 160
Floc Volume, DSV30, percent
Flo
c V
olu
me
Flu
x, D
SV
30
*m/h
Flux Curve, Power Flux Data Flux Curve, Exponential
Test Results 8/23
V=2.12 M/h, U=0.42 M/h, FV=24%
Note: Overflow Rate Less Than Settling Rate, Model Tracks Blanket
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 1 2 3 4 5 6
Time From Start, Hours
Bla
nket
Heig
ht,
m
-1
0
1
2
3
4
5
6
Sett
lin
g a
nd
Overf
low
Rate
s, m
/h
Bkt. Sl. Judge BLKT-MODEL 1
Settling Rate Overflow Rate
A Flux Plot of Manning Test 8/23
Figure 1. Floc Volume Flux Curve
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Floc Volume, percent
Flo
c V
olu
me F
lux,
Settling Flux, FV*m/h Vr Flux, FV*m/h Storm Result 1st hr
Storm Result 2nd hr Storm Result 3rd hr Storm Result 4+ hrs
"Start of Storm" VrExt
Garrett et al, DSVI POWER EQ UR OK
Test Results 8/27
V=2.54 M/h, U=0.34 M/h, FV=38%
Note: Overflow Rate Exceeds Settling Rate, Model I Does Not
Track the Blanket
0.0
0.5
1.0
1.5
2.0
0 1 2 3 4 5 6
Time From Start, Hours
Bla
nk
et
He
igh
t, m
0
1
2
3
4
5
6
Se
ttlin
g a
nd
Ov
erf
low
Ra
tes
,
m/h
Bkt. Sl. Judge Bkt Meter Bkt. Model 1
Settling Rate Overflow Rate
A Flux Plot of the Manning Test 8/27
Figure 1. Floc Volume Flux Curve
0
20
40
60
80
100
120
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Floc Volume, percent
Flo
c V
olu
me F
lux,
Settling Flux, FV*m/h Vr Flux, FV*m/h Storm Result 1st hr
Storm Result 2nd hr Storm Result 3rd hr Storm Result 4+ hrs
"Start of Storm" VrExt
Garrett et al, DSVI POWER EQ UR OK
4. Vrmax = U*FVu*(100/FV) - U
• Model I did not
consider Vo>Vs and
formation of a thin
blanket.
• Model II by Manning
includes formation
of a thin blanket at
rate dHa/dt = Vo-Vs
Test Results 8/27 + Model 2
V=2.54 M/h, U=0.34 M/h, FV=38%
Note: Model 2 (With Ha) Tracks the Blanket Height
0.0
0.5
1.0
1.5
2.0
0 1 2 3 4 5 6
Time From Start, Hours
Bla
nket
Heig
ht,
m
Bkt. Sl. Judge Bkt. Model 2, Power Bkt Meter
Summary
• The use of the spreadsheet with
Model II allows rapid evaluation of
the effect of storm flows. The safe
maximum floc volume may be
determined for the peak overflow rate
and the maximum allowable sludge
blanket height. This may exceed the
Flux Curve.
