sedimentation settling velocity column analysis

Crispen Mutsvangwa: Water Engineering, Education & Applications, www.weea.co.za of 11

Water Engineering, Education & Applications Email: [email protected] Website www.weea.co.za or [email protected] Paper No. WT 2/11: Determination of Terminal Settling velocity for discrete and flocculent particles Crispen Mutsvangwa MSc (Eng.,); MSc Water & Environmental Management © Copyright 2011. Water Engineering, Education & Applications

1 Determination of Terminal settling velocities for discrete and

flocculent particles Sedimentation is the downward movement of small suspended particles by gravity. Sedimentation is classified upon the characteristics and concentration of suspended materials:

• Discrete particles • Flocculent

1.1 Discrete particles (Type 1) Discrete particles are particle whose size, shape and specific gravity do not change with time i.e. non-interactive settling of particles from a dilute suspension. Examples are grit and sand, and their mass is constant. 1.2 Flocculant particles (Type 2) Particles which agglomerate (coalesce/flocculate) during settling i.e. no constant characteristics. Their mass varies during the process of settling and an increase in mass causes a faster rate of settlement. 2 Settling in an ideal settling basin for Type 1/discrete particles An ideal horizontal settling zone is free from inlet and outlet disturbance, in which particles settle freely at terminal settling velocities in quiescent conditions without any disturbances and flocculation is absent (Fig. 1). The particles are distributed uniformly In the design of sedimentation basins, the usual procedure is to select a particle with a terminal velocity vs and to design the basin so that all the particles that have a terminal velocity equal to or greater than vs will be removed.

sAvQ = (1) Where: A =surface area of sedimentation basin

vs =settling velocity or surface loading, m3/m2.day (AQvs = )


Fig. 1 Type I settling in a horizontal basin

Design velocity for a continuous flow sedimentation:

TH

timeention

depthvs ==det

The length of basin and the time a unit of water spends in the basin (detention time) should be such that all particles with velocity vs will settle at the bottom of basin, but adjustments must be made for:

• Effects of inlet and outlet • Turbulence • Short circuiting • Sludge storage

Particles with velocity less than vs will not be removed during the detention time, but some particles with velocity less than vs which enter the tank at distance from the bottom not greater than H will be removed e.g. at h. Assuming that particles of various sizes are uniformly distributed on the entire depth H, at inlet, then particles with settling velocity vp less than vs will be removed in the ratio:

s

pr v

vX =

Where: Xr =fraction of particle with settling velocity vp that are removed To determine the efficiency of removal for a given settling time, t it is necessary to consider the entire range of settling velocities present in the tank.

Particle trajectory

Settling zone

Outlet zone Inlet

zone vp

vs

vp

H

h


2.1 Determination of settling velocities

• Sieve analysis and hydrometer test combined with Newton and Stokes Law:

( )wd

wss C

gdv

ρρρ

34 −

= (Newton’s law for all regimes of flow)

Or ( )

µρρ

18

2ws

sgd

v−

= (Stokes Law for laminar flow)

Where:

sρ =density of particle

wρ =density of fluid Cd =Newton’s drag coefficient vs =settling velocity of particle µ =dynamic viscosity

2.1.1 Settling column analysis

• A settling column 2 to 3m deep, and diameter at least 100 times the largest particle size to prevent wall effects

• The initial suspended solid concentration of the suspension is noted, Co in mg/l

• A sample is placed in a jar and mixed completely to ensure uniform distribution of particles

• Suspension is allowed to settle quiescently • Samples are drawn at time intervals at a point h (one point) discrete

settling particles, the depth of sampling will not affect the resultant

distribution curves of the settling velocities: i

i th

v =

• The procedure is repeated for time intervals t2, t3; t4; t5……..tn, and these values of settling velocities are plotted against mass fraction remaining to give the settling velocity characteristic distribution curve for the suspension.


Fig. 2 Column analysis for discrete particles

Fig. 3: Settling velocity distribution curve for the mass fraction remaining

The total removal is given as: ( ) ∫+−=sx

s

ps dx

vv

xR0

1

Where; Xs =particles with vp=vs 1=Xs =fraction of particles with vp≥vs removed

Sampling point h

vp>vs

vp<vs

Xs

Xp

1-Xs

vs vp

Pro

porti

on o

f par

ticle

s w

ith le

ss

than

sta

ted

settl

ing

velo

city

1.0

Suspension settling velocity distribution curve for the mass fraction remaining

Removed particles

Settling velocities


∫sx

s

p dxvv

0

=fraction of particles with vp<vs removed

2.2 Example Determine the total removal efficiency given the following data:

o settling analysis results Table 1 o column is 1.6m deep o surface loading is 30m/day o Co=200mg/l

Table 1

Time, min 0 40 80 120 160 200 240 280 Conc, Ci, mg/l 200 175 170 160 155 110 80 35

Solution 1. Compute mass fraction remaining and corresponding velocities (Table 2) Table 2 Time, (min)

40 80 120 160 200 240 280

Mass fraction remaining, o

ii C

Cx = 0.88 0.85 0.8 0.78 0.55 0.4 0.175

thvs = , m/min

0.04 0.02 0.013 0.01 0.008 0.0067 0.0007


3 Type II settling (flocculent particles)

• settling is a result of inter-particle collisions • density of particles change because flocculating particles are continually

changing in size, shape and settling velocities • due to the above factors, Stokes law cannot be applied

3.1 Analysis of settlement for Type 2 particles

• analysis performed in column at least 300mm in diameter • depth equal to the proposed sedimentation tank • samples are withdrawn at regular time intervals from multiple ports or

different sampling heights and analyzed to determine the reduction in suspended solids

• the % removal is plotted as a numerical value against the depth and time • the concentrations obtained are used to compute mass fraction removal

instead of he mass fraction remaining • from the plot removal at various times, the theoretical efficiency is predicted

and a theoretical surface loading is established • the design surface loading should be 1/3 of that suggested by the settling

tests (theoretical), to get similar solids removal results to those obtained from a settling column

10010

×⎟⎟⎠

⎞⎜⎜⎝

⎛−=

CC

x ijij , %

Where: xij =mass fraction is % that is removed at the ith depth at jth time interval Co =initial solid concentration Cij =concentration at ith depth and jth depth time interval

• the values Cij and time are plotted to give isoremoval lines, lines with the

same concentration • the slope at any point on any given isoremoval line is the instantaneous

velocity of the fraction of particles represented by the line • velocity becomes greater at greater depth (the slope of the isoremoval

lines becomes steeper), a common characteristic of flocculating suspensions, reflecting and increase in particle size and settling velocity because of continued collision and aggregation with other particles.

The % removal is given as:

⎟⎠⎞

⎜⎝⎛ +∆

++⎟⎠⎞

⎜⎝⎛ +∆

+⎟⎠⎞

⎜⎝⎛ +∆

= +

2.....

22% 1322211 nnn RR

hhRR

hhRR

hhremoval

Where: h =column height


R1 =see diagram ∆h =see diagram Example Determine the overall removal efficiency of the sedimentation tank and surface loading given the following g data:

• initial solid concentration of sample Co =200mg/l • results of column analysis of flocculating suspension =Table 3 • height of sedimentation tank =2.4m • detention time =1 hr 20min

Table 3

Table 4

Solution


• compute 10010

×⎟⎟⎠

⎞⎜⎜⎝

⎛−=

CC

x ijij (Table 4)

• plot iso-concentration lines (isoremoval lines), Fig. 4 • plot vertical line at t =1 hr 20 mins (80 mins, i.e. retention time) • from the graph at 80 mins, about 45% of the solids reach the floor i.e. 100%

removed • determine h∆ • Overall removal, R

Fig. 4 Plot of the iso-concentration curves

%76.73210090

4.24.0

29080

4.23.0

28070

4.25.0

27060

4.23.0

26050

4.26.0

25045

4.25.0%

=⎟⎠⎞

⎜⎝⎛ +

+⎟⎠⎞

⎜⎝⎛ +

+⎟⎠⎞

⎜⎝⎛ +

+⎟⎠⎞

⎜⎝⎛ +

+⎟⎠⎞

⎜⎝⎛ +

+⎟⎠⎞

⎜⎝⎛ +

=removalOveral

Surface loading = ( )( ) 2

3

,/

mBLAreadaymQ

×

Detention time, Q

kofvolumet tan=


Q

AreaQ

heighArea 4.280 ×=

×=

Q

Aream

=4.2min80

Surface loading daymmdaymmareaQ ./2.43/2.43min/03.0

804.2 23====

Adjustment for full scale ( )daymmdaymSL ./8.28/8.285.12.43 23==

The surface loading for continuous flow tank should be 1/3 of that suggested by the settling column tests to get similar solids removal results to those obtained from a settling column. The optimum removal efficiency can be obtained by trying several detention times and then computing the surface loadings. The one which gives the maximum removal efficiency will be the one corresponding the maximum optimum surface loading.

sedimentation settling velocity column analysis

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