Sedimentation - Tech Alive

trextemperMechanics

Feb 22, 2014 (3 years and 1 month ago)

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Sedimentation


Type I Sedimentation


This is
discrete particle settling
, i.e. each particle settles as a separate entity and there is no inter
-
particle
bridging o
r

flocculation. The particles intended for capture in grit chambers settle

as discrete particles. Design
for unit operations based on Type I Sedimentation is based on Stokes' Law:


where:


v
s

=


particle settling velocity, m
∙s
-
1




g =


acceleration due to gravity, 9.81 m∙s
-
2




ρ
p

=


density of the particle, kg∙m
-
3




ρ
w

=


density of the fluid, ~1000.0 kg∙m
-
3

@ 20°C




d =


diameter of the particle, m




μ =
=
=
摹湡浩c⁶楳捯獩=yⰠㄮ〰㉸㄰
-
3

Pa∙s (= kg∙m
-
1
∙s
-
1
) @ 20°C



Type II Sedimentation


This is
flocculant settling
, i.e the particles have a natural (or chemically enhanced) tendency to agglomerate as
they settle. These particles grow in size as they coalesce and water is squeezed out increasing their density.
There i
s no theoretical basis for predicting these changes in size and density, so design calculations for Type II
sedimentation are based on laboratory batch settling tests. The particles captured in primary treatment follow
Type II sedimentation.


Type III Sed
imentation


This is
zone settling
, i.e. at high particle densities interparticle forces hinder individual particle settling and the
entire suspension settles
en masse
. This type of settling is characteristic of intermediate depths in secondary
clarifiers
and in the gravity thickeners used for sludge treatment.


Type IV Sedimentation


This is
compression settling
, i.e. settling of particles that are of such a high concentration that the particles
touch each other and settling can only occur by compression
of the compacting mass. This type of settling is
observed in the lower depths of secondary clarifiers and in gravity thickeners.




2
p w
s
g ( - )
d
=
v
18
 

 


Stokes' Law


Stokes' Law
relates particle size and settling velocity. There are three
forces which act on a particle: the

downward gravitational force (F
g
), an
upward buoyancy force (F
b
) and an upward drag force (F
d
). The
gravitational force is a function of "g" and the mass of the particle, thus
diameter and particle density. The buoyancy force is a function of the fluid
mass displaced by the particle and thus diameter and fluid density. And the
drag force is a function of particle size and viscosity and thus diameter and
fluid viscosity.

2
p w
s
g ( - )
d
=
v
18
 

 



Specific gravity
: the ratio of the mass of a given volume of a
ny substance to that of an equal volume
of water, taken at 4

C. The specific gravity of platinum is 21.5 because any volume of platinum
weighs 21.5 times more than an equal volume of water at 4

C.


Particle density:
calculated as the product of the specif
ic gravity of the particle (e.g. 1.9) and the
density of water at 4 °C (1000 kg∙m
-
3
). Variation in particle density over the range of environmental
temperatures is negligible.


Liquid density:

calculated as the product of the specific gravity of water (1.
0, by definition) and the
density of water at the environmental temperature. The density of water decreases above and below
4 °C and the changes may be significant over the range of environmental temperatures.


Dynamic viscosity:
decreases with increasing

temperature
-

by a factor of three over the range 0
-
35
°C.















0
500
1000
1500
2000
2500
0
10
20
30
40
Temperature
Settling Velocity (m/d)
F
b

F
g

F
d

F
d

Settling Tank Design



The fundamental consideration is that the water residence time (

) be greater than the particle settling time (t
s
),


s
t












[1]


i.e. the particle gets to the bottom before it exits the tank.


The water residence time

is given by,


V
Q












[2]


The particle settling time is given by,








s
s
h
t
v











[
3
]


substituting Equation
s
2

and
3

to Equation 1 yields,


s
V h
Q v


and
dividing both sides by
h,






[
4
]


1
surface
s
A
Q v


and inverting and multiplying both sides by Q,



[5]


surface
s
Q
A
v










[6]


This is the basic design equation for a grit
chamber, with vs calculated using Stokes Law.

In application to primary treatment (Type II or
flocculent settling),
we define the surface
overflow rate (m
3
∙m
-
2
∙d
-
1
) based on Equation
6

and relate SOR to removal

efficiency
empirically through laboratory tests.


top
Q
SOR
A




[12]