CEE 633 Physical & Chemical TreatmentLecture 18. Ch. 10

Prof. Albert S. Kim

Civil and Environmental Engineering, University of Hawaii at Manoa

Thursday, October 18, 2011

1 / 12

Circular Sedimentation Tankh 0

r0

ri

vf

The fluid velocity vf

vf =Q

2π (r − ri)h0

as r → r0, vf (↓). The distance a particle has set-tled

h = t · vc =(r2 − r2i

)h0

Qvc

where t is the settling time. The particle travelingvelocity vc is equal to overflow rate (OR)

vc =h0τ

= h0Q

π(r20 − r2i

)h0

=Q

π(r20 − r2i

) =Q

A= OR

Particles of settling velocity greater than or equal to vc are all removed.

2 / 12

Therefore,

h =π(r2 − r2i

)h0

Q

Q

π(r20 − r2i

) =

(r2 − r2ir20 − r2i

)h0

In other wordsh

r2 − r2i=

h0r20 − r2i

Interpretation,1 Given h, if the particle’s radial distance < r,⇒ settled.2 Given r, if the particle’s depth > h,⇒ settled.

3 / 12

Basin ConditionsCritical scour velocity by Camp

vsc =

√8k

fg

(ρp − ρfρf

)dp

The width-to-length ratio of a basin is related to the travel velocity of thewater for excess velocity values that would result in scour.

Horizontal velocity to cause scouring

k =

{0.04 mono-dispersed0.06 sticky

f = Darcy Weisbach friction factor ~ 0.03For a basin with length/width≥ 5

horizontal velocity < 18m/h = 5mm/sec.Since scour velocity is usually of ' O(0.1)m/s = O(100)mm/s

Conditions1 overflow rate = settling velocity of particles (to be removed)2 The horizontal fluid velocity < scour velocity

4 / 12

10-3 Flocculant settling in sedimentation basins

Type I: Individual (stabilized) particle (low concentration water surface)

Type II:

particle flocs formed (orthokinetic or differential settling)Settling velocity (↑) as time (↑) by adding coagulant (slow→ fast settling)Capturing of small/tiny particles (or aggregates) by big aggregates. Tinyparticles (which did not participate in initial aggregation) are effectivelyremoved due to

1 Fast settling velocity (↑) due to increased mass (↑) by capturing2 Sweeping effects: scavenging

5 / 12

Type III:1 hindered settling - near the bottom of basin2 blanket of particles formed , which traps particles below it as it settles (i.e.,

clear-cut interface between turbid and clean regions)3 called zone-settling when the particle settling velocities are affected by

presence of other particles4 concentration is high enough to provide strong drag forces on settling flocs5 settling velocity (↓) as concentration (↑) near the bottom of a basin

Type IV:1 compression settling at high concentration2 particle suspension is consolidated: phase transition from liquid to solid,

e.g., in sludge thickening dewatering processes.3 Water passes through a mat of particles near underdrain.

6 / 12

Solid flux analysis

Solid fluxGT = Gs +Gb

whereGT = total solid flux toward underdrain [kg/m2 · s]Gs = settling flux in basin due to gravity [kg/m2 · s]Gb = bulk fluid flux due to underflow [kg/m2 · s]

7 / 12

Settling flux1. Calculation of Gs (with initial particle concentration, Ci )

Settling velocity is defined as

vi =ddblanket

dt|t=0

where dblanket is the (measured) depth of the blanket as a function of time.Then, the settling flux is a product of settling velocity (i.e., downward velocityof the blanket) and the initial concentration Ci: Gs = viCi

8 / 12

Bulk flux and Total flux2. Calculation of Gb

Qb

A

A'

Qu, C

u

The bulk flux is

Gb =QCi

A=Qu

ACi = ubCi

where ub is the bulk downward velocity.

Because Qb = Qu, ubA = uuA′, because

A > A′ ⇒ ub < uu

3. Then, the total flux is a sum of settling and bulk fluxes:

GT = Gs +Gb = (vi + vb)Ci

where vi and vb are settling velocities of flocs (blanket) and suspension,respectively.

9 / 12

Analysis of zone settling

10 / 12

Settling velocity and solid flux values

Table 10-1. p 801.

Figure: Settling velocity

The solid flux, Gs is a product of solid concentration Ci and initial settlingvelocity vi [m/s].

11 / 12

Limiting Flux RateIf solid loading > limiting flux rate, then solid will accumulate & overflow

1 Select Cu, the underdrain solidconcentration due to the requirementsof downstream residuals.

2 Obtain GL by drawing a tangent line3 Calculate the downward velocity at

bulk fluid: ub = GL/Cu

Required area for settling: because ub =Q

A=Qu

A=GL

Cu, the area is

A=QuCu

GL

(See Example 10-6, p. 803)12 / 12