Water and Wastewater Engineering
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6-26 WATER AND WASTEWATER ENGINEERING
circuiting because of uneven inlet or outlet conditions, and local turbulence or dead spots in the
reactor corners. The mean detention time in real tanks is generally less than the theoretical deten-
tion time calculated from Equation 6-13 .
Selection of G and Gt Values
Both G and the product of the velocity gradient and time ( Gt ), serve as criteria for the design of
mixing systems. The selection of G and Gt values for coagulation is dependent on the mixing
device, the chemicals selected, and the anticipated reactions. As noted previou
sly, coagu lation
occurs pred ominately by two mechanisms: adsorption of the soluble hydrolysis species on the
colloid and destabilization or sweep coagulation where the colloid is trapped in the hydroxide
precipitate. Jar test data may be used to identify whether adsorption/
destabilization or sweep
coagulation is predominant using the following procedure:
• Determine the optimum pH and dose from plots of settled turbidity (see, for example,
Figure 6-11 ).
• Plot the optimum pH and dose on Figure 6-9 .
• Determine which is the predominant mechanism from the plotted position.
G values in the range of 3,000 to 5,000 s
1
and detention times on the order of 0.5 s are
recommended for adsorption/destabilization reactions. For sweep coagulation, detention times of
1 to 10 s and G values in the range of 600 to 1,000 s
1
are recommended (Amirtharajah, 1978).
6-7 MIXING PRACTICE
Although there are some instances of overlap, mixing equipment may be divided into two broad
categories: equipment that is applicable to dispersion of the coagulant into the raw water and that
used to flocculate the coagulated water. Dispersion of the coagulant into water is called flash
mixing or rapid mixing.
Flash Mixing Design Criteria
This equipment is designed to produce a high G. The order of preference in selec tion of equip-
ment type is based on effectiveness, reliability, maintenance requirements, and cost. Common
alternatives for mixing when the mechanism of coagulation is adsorption/destabilization are:
1 . Diffusion mixing by pre
ssured water jets.
2. In-line mechanical mixing.
3. In-line static mixing.
Common alternatives for mixing when the mechanism of coagulation is sweep coagulation are:
1 . Mechanical mixing in stirred tanks.
2. Diffusion by pipe grid.
3. Hydraulic mixing.
COAGULATION AND FLOCCULATION 6-27
The focus of this discussion is on the following three mixing alternatives: in-line mechanical
mixing, in-line static mixing, and mechanical mixing in stirred tanks.
In-Line Mechanical Mixing. Also know as an in-line blender ( Figure 6-13 ), this in-line sys-
tem overcomes some of the disadvantages of the
static mixer.
The following design criteria may be used in selection of in-line mechanical mixers: (1) G in
the range 3,000 to 5,000 s
1
, (2) t of about 0.5 s, and (3) headloss of 0.3 to 0.9 m (Amirtharajah,
1978).
An example of the information manufacturers provide for the selection of an in-line blender
is given in Table 6-4 and Figure 6-14 .
TABLE 6-4
Representative in-line blender data
Model
Weight
Motor
a
kg
power,
W
Dimensions
b
ABCDEF
AZ-1 6535085 12 11 3064 23
AZ-2 8555090 15 17 35 68 30
AZ-3 140 75095 17 22 40 68 30
AZ-4 230750
1,000 110 20 27 5071 30
AZ-5300 1,100
1,500 125 2332 55 76 30
AZ-6 325 1,500 1302536607630
AZ-7 400 1,500
2,250135 27 41 65 76 30
AZ-8 425 2,250 140 3046 707630
AZ-9 500 2,25014533 51807630
AZ-10 600 3,700 150 33 51708844
AZ-11 7507,500 160 3861 908853
AZ-12 1,200 15,000 190 48 71 120 9558
AZ-13 1,600 22,000 210 5691125 95 68
a
Where two values are given, alternate motors are available for the model.
b
These are noted in Figure 6-14. All are in cm.
NOTE: these data are hypothetical and do not represent actual choices. Manufacturers’ data must be used to select a blender.
6-28 WATER AND WASTEWATER ENGINEERING
C
D
B
A
E
F
FIGURE 6-14
Dimension notation for in-line blenders given in Table 6-4.
Chemical
feed line
Motor
Propeller
Gear
drive
Stator
Raw water
FIGURE 6-13
Typical in-line blender.
COAGULATION AND FLOCCULATION 6-29
Example 6-5. Using Table 6-4 select an in-line blender for an alum coagulant. The jar test
data resemble that shown in Figure 6-11 . The design flow rate is 383 m
3
/h, and the design water
temperature is 17 C.
Solution:
a . Based on the jar test results, it appears that adsorption/destabilization is the predominant
mechanism of coagulation. G values in the range of 3,000 to 5,000 s
1
and detention
times on the order of 0.5 s are recommended for adsorption/destabilization reactions.
b. As a first trial, select mod el AZ-6, with a reaction chamber diameter of 36 cm (dimen-
sion C in Table 6-4 ) and a length of 60 cm (dimension D in Table 6-4 ) and calculate the
volume of the reaction c
hamber.
()
()
36
4
60 61 072
2
3
cm
cm cm,
V
c. Check the detention time using Equation 6-13
t
()( )61 072 10
383
1 5910
3 6 33
3
,
.
cm m /cm
m /h
4
0 57hor s.
This is sufficiently close to the 0.5 s guideline to be acceptable.
d. Estimate the value of G a ssuming that the water power is 80% of the motor power. From
Table 6-4 find the motor power is 1,500 W
P ()( )08 1500 1 200., ,WW
Using Appendix A, find the viscosity of the water is 1.081 10
3
Pa · s at 17 C.
From Equation 6-12
G
0 5
33
1 200
1 081 10 61 072
.
,
.,
W
Pa scm()()
(()10
4263
6 33
1
m /cm
s
⎛
⎝
⎜
⎞
⎠
⎟
,
This meets the velocity gradient criteria.
Comment. If either the detention time or the velocity gradient criteria had not been met, an-
other trial model would have been selected and checked. In an actual design, more than one
manufacturer’s models may have to be examined to find a satisfactor
y match.
In-Line Static Mixing. A s shown in Figure 6-15 , this mixer consists of a pipe with in-line heli-
cal vanes that rotate and split the flow to increase turbulence. The vanes are segmented so that
the number of vanes may be adjusted to fit local conditions. These segments are called elements.
The element size is specified in terms of the diameter of the pipe they are in, that is, the length of
element divided by the pipe diameter ( L / D ). This is called the aspect ratio. Generally, the aspect
ratio varies from 1.0 to 1.5. The mixers come in sizes as small as 0.5 cm for research application
6-30 WATER AND WASTEWATER ENGINEERING
1 Ele
m
ent
FIGURE 6-15
Static mixer.
to as large as 300 cm for industrial and water treatment use. Generally, they are made in standard
pipe diameters.
T h e se mixers have two advantages: (1) there are no moving parts and (2) no external energy
source is required. They have the disadvantage that the d egree of mixing and mixing time is a
fu
nction of flow rate.
Although it applies to all mixers, a m easure of the uniformity of the blend of the chemical
and the water has been found to be particularly useful in selecting static mixers. The measure
used is the coefficient of variation with time (COV) of the blended mixture. It is defined as
COV
C
%
⎛
⎝
⎞
⎠
()100
(6-14)
where COV coefficient of variation with time
standard deviation of concentration, mg/L
C average concentration over time, mg/L
The standard deviation is defined as
()CC
n
t
2
1
(6-15)
where C
t
concentration of sample, mg/L
n number of samples
The following design criteria that may be used in selection are: (1) COV of 1 to 10 percent
with an average of 5 percent, (2) Gt in the range 350–1700, (3) a mixing time of 1 to 3 s, and (4) a
maximum headloss of 0.6 to 0.9 m. The design should spec
ify that the mixing elements be remov-
able so they may be cleared and/or cleaned (Bayer et al., 2003; Kawamura, 2000; MWH, 2005).
The selection process is highly dependent on the approach suggested by the manufacturer for
their mixer. The following method is representative:
• Select the number of mix
ing elements to achieve the desired COV. Bayer et al. (2003) sug-
gest that three elements will yield a COV of about 10 percent and that six elements will
yield a COV of about 1 percent for mixers designed for turbulent flow (Reynolds number
greater than 5,000). Turbulent flow may be assumed for water entering water treatment
plants from p
umped sources.
COAGULATION AND FLOCCULATION 6-31
• Using either an equation or a graph, suc h as that shown in Figure 6-16 provided by the
manufacturer, determine the pressure drop per element.
• With the pressure drop per element and the number of elements, estimate the detention
time, water power, and velocity gradient, and check these against the design criteria.
The detention time is
calculated with Equation 6-13 . The power imparted by static mixing devices
may be computed using Equation 6-16 . The velocity gradient is calculated with Equation 6-12 .
P
QH
(6-16)
where P water power, kW
specific weight of fluid, kN/m
3
9.807 kN/m
3
for water at 5 C
Q flow rate, m
3
/ s
H total dynamic head, m
efficiency
0.01
0.1
1
10
100
1000
1 10 100 1000 10000
Flow rate, m
3
/h
Pressure drop per element, kPa
150 mm
250 mm
300 mm
350 mm
400 mm
600 mm
700 mm
200 mm
FIGURE 6-16
Typical static mixer pressure drop selection graph for pipe diameters from 150 mm to
700 mm.
6-32 WATER AND WASTEWATER ENGINEERING
Example 6-6. Design a static mixer for the following conditions:
D e sign flow rate 150 m
3
/h
Minimum water temperature 5 C
M i xer aspect ratio 1.5
D e sign COV is 1%
Solution. This problem is solved by iteration; that is, a set of reasonable assumptions is made
and then the calculations are performed to verify or correct the assumptions.
a . Select a pipe diameter of 400 mm for the d
esign flow rate.
b. Select the number of elements to achieve a COV of 1%, that is, six elements.
c. From Figure 6-16 determine the headloss per element is 0.16 kPa per element. The total
headloss through the mixer is then
()( )6016 096elements kPa/element kPa..
d. With six elements that have an aspect ratio of 1.5, the length of the mixer is
Lnoofelements aspect ratio pipe diame ()()(.tter
m) 3 6 m
)
()( )(615 040.. .
e. The volume of the mixer is
()( )
()
040
4
3 6045
2
3
.
..
m
mm
V
f. The detention time is
t
045
150
3 010 10
3
3
3
.
..9
m
m /h
hor s
g. The water power imparted by the mixer is estimated using Equation 6-16 with
1.00:
PQH
()()
(
9 807 15 0
3 600
096
33
.
,
.
kN/mm/h
s/h
kPa m/kPa kW)( )0 102 0 0400..
where (0.102 m/kPa) is a conversion factor.
h. Estimate the velocity gradient using Equation 6-12. Using the water temperature of 5 C
and Appendix A, 1.519 10
3
Pa · s
G
0 5
33
1 519 10 0 45
.
40.0
..
W
Pa sm()()
⎛
⎝
⎜
⎞
⎠⎠
⎟
s241 9
1
.
COAGULATION AND FLOCCULATION 6-33
i. Estimate Gt.
Gt
(. )( ) .241 9 10 2 636 7 2 600
1
ss or.9 , ,
Comments:
1 . The detention time and Gt criteria were not met. At this point in the design calculation,
another trial would be attempted. The variables that can be explored are the diameter of
the pipe and the number of elements (by assuming a less stringent COV). Alternatively,
another manufacturer’s mixer may be suitable under the assumptions given.
2. When the final design is selected, two mixers of this size would be provided for
redundancy.
3. The failure of this design to meet the design criteria will be exacerbated when the flow
rate is at the average and minimum flow rates. For this reason alone, static mixers have
limited application in
mixing coagulant.
4. Because this is an iterative problem, it is well suited to a spreadsheet solution.
Mechanical Mixing in Stirred Tanks. When the predominant coagulation mechanism is sweep
coagulation, extremely short mixing times are not as important, as in adsorption-destabilization.
A typical completely mixed flow reactor (CMFR) or continuous-flow stirred tank reactor (CSTR)
as shown in Figure 6-17 will perform well for sweep coagu lation. Detention times of 1 to 7 s
and G valu es in the range of 600 to 1,000 s
1
are recommended (Letterman et al., 1973, and
Amirtharajah, 1978).
The volume of a rapid-mix tank seldom exceeds 8 m
3
because of mixing equipment and
geometry constraints. The mixing equipment consists of an electric motor, gear-type speed
reducer, and either a radial-flow or axial-flow impeller as shown in Figure 6-18 . The radial-flow
impeller provides more turbulence and is preferred for rapid
mixing. The tanks should be hori-
zontally baffled into at least two and preferably three com partments in order to minimize short
circuiting and thus provide sufficient residence time. They are also baffled vertically to minimize
vortexing. Chemicals should be added below the impeller. Some geo
metric ratios for rapid mix-
ing are shown in Table 6-5 . These values can be used to select the proper basin depth and surface
area and the impeller diameter. For rapid mixing, in order to construct a reasonably sized basin,
often more depth is required than allowed by the ratios in Table 6-
5 . In this case the tank is made
Chemical addition
Chemical addition
Chemical addition
FIGURE 6-17
Completely mixed flow reactor (CMFR) or continuous-flow stirred tank
reactor (CSTR). (Source: Davis and Cornwell, 2008.)
6-34 WATER AND WASTEWATER ENGINEERING
deeper by using two impellers on the shaft. When dual impellers are used, the top impeller is
axial flow, while the bottom impeller is radial flow. When dual impellers are employed on gear-
driven mixers, they are spaced approximately two impeller diameters apart. We normally assume
an efficiency of transfer of motor power to water power of 0.8 for a single i
mpeller.
The power imparted to the liquid in a baffled tank by an impeller may be described by the
following equation for fully turbulent flow developed by Rushton (1952).
PNnD
p i
()( )
35
(6-17)
where P power, W
N
p
impeller constant (also called power number)
TABLE 6-5
Tank and impeller geometries for mixing
Geometric ratio Range
D/T (radial)
0.14–0.5
D/T (axial)
0.17–0.4
H/D (either)
2–4
H/T (axial)
0.34–1.6
H/T (radial)
0.28–2
B/D (either)
0.7–1.6
D impeller diameter
T
A
equivalent tank diameter
4
0 5
⎛
⎝
⎞
⎠
.
A the plan area
H water depth
B water depth below the impeller
(a) Radial-flow turbine impeller
(b) Axial-flow impeller
FIGURE 6-18
Basic impeller styles. (Source: SPX Process Equipment.)
COAGULATION AND FLOCCULATION 6-35
n rotational speed, revolutions/s
D
i
impeller diameter, m
r density of liquid, kg/m
3
The impeller constant of a specific impeller can be obtained from the manufacturer. For the radial-
flow impeller of Figure 6-18 , the impeller constant is 5.7, and for the axial-flow impeller it is 0.31.
Example 6-7. Design a cylindrical flash mixing basin by determ ining the basin volume, tank
diameter, dimension
s, required input power, impeller diameter from manufacturer’s data pro-
vided below, and its rotational speed using the following parameters:
D e sign flow rate 11.5 10
3
m
3
/ d
Rapid mix t 5 s
Rapid mix G 600 s
1
Water temperature 5 C
Place impeller at one-third the water depth
From manufacturer’s data, the following impellers are available:
Impeller type Impeller diameters (m)
Power number (N
p
)
Radial 0.3 0.4 0.6 5.7
Axial 0.8 1.4 2.0 0.31
Solution:
a . Convert 11.5 10
3
m
3
/ d to m
3
/ s.
11 5 10
86 400
0133
33
3
.
,
.
m /d
s/d
m /s
()
b. Using Equation 6-13 , determine the volume of the rapid mix basin.
Q
t
()()
0133 5 0665
33
..m /ss mV
c. Using the radial impeller gu idance from Table 6-5 , assume H / T 2.0, that is H 2 T.
For a round mixing tank
()
()
T
T
2
4
2
V
and
T
1 3
3
40665
2
0751075
/
m
or
()( ).
..
⎧
⎨
⎩
⎪
⎫
⎬
⎪
⎭
mm
and
H 2(0.75m)1.5m
and because the impeller is at 1/3 water depth
B ()()0 333 1 5 0 5.. .mm