Page 248 - Water and wastewater engineering

COAGULATION AND FLOCCULATION 6-25

The velocity gradient may be thought of as the amount of shear taking place; that is, the
higher the G value, the more violent the mixing. The velocity gradient is a function of the power
input into a unit volume of water. The RMS velocity gradient may be estimated as

/
⎛ P ⎞ 12
G ⎜ ⎝ ⎟ ⎠ (6-12)

V
1

where G global RMS velocity gradient, s
P power of mixing input to vessel, W

dynamic viscosity of water, Pa · s
3
,
V volume of liquid m
Different velocity gradients are appropriate for different processes. Coagulation requires very
high velocity gradients. Flocculation requires a velocity gradient high enough to cause particle
contact and to keep the flocs from settling but low enough to prevent the flocs from tearing apart.
In addition, different chemicals require different velocity gradients.

Mixing Time
Experimental work has revealed that coagulant reactions are very fast. Alum hydrolyzes to
5
2
Al(OH) within 10 s (Base and Mesmer, 1976). Hahn and Stumm (1968) found the time
3
to form mono- and polynuclear hydroxide species was on the order of 10 s, and the time of
2
formation of polymer species was on the order of 10 s.
This work along with field observations implies that nearly instantaneous and intense mixing
of metal salts is of critical importance. This is especially true when the metal salts are being used
to lower the surface charge of the particles (adsorption and destabilization in Figure 6-9 ). Mixing
times of less than 1 s are recommended in this case. The formation of the aluminum-hydroxide-
precipitate is slower and occurs in the range of 1 to 7 s. Thus, in sweep coagulation ( Figure 6-9 )
the extremely short mixing times are not as critical (Amirtharajah and Mills, 1982).
The time requirements for flocculation are more dependent on the requirements of down-
stream processes. For conventional treatment where settling follows flocculation the flocculation
time ranges from 20 to 30 minutes. If direct filtration is to follow flocculation, shorter times on
the order of 10 to 20 minutes are often selected (MWH, 2005).
For these time-dependent reactions, the time that a fluid particle remains in the reactor
affects the degree to which the reaction goes to completion. In ideal reactors the average time
in the reactor (the theoretical detention time also known as hydraulic detention time, hydraulic
residence time, or detention time) is defined as
t = V (6-13)
Q

where t theoretical detention time, s
V volume of fluid in reactor m 3
,
3
Q flow rate into reactor, m /s
Theoretically, given the desired detention time and the design flow rate, the liquid volume of
the vessel to achieve the design detention time may be calculated. However, real reactors do not
behave as ideal reactors because of density differences due to temperature or other causes, short