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.

Use the several programs of ASLO

E-mail: mtg@mtgarrett.net