Page 305 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

260 Fundamentals of Water Treatment Unit Processes: Physical, Chemical, and Biological

P=V are common. The dilemma is that similitude for all of the 10.3.4.1 Disparity of Flows
dimensionless parameters cannot occur simultaneously. Cer- As noted, the problem in mixing of a coagulant flow with
tain ones may be selected for scale-up, i.e., remain constant; the raw-water flow is that a large disparity exists between the
all or most of the others will change. This incongruity may be two flows. For example, suppose Q(raw water) ¼ 3785
seen by substituting algebraic expressions for one parameter m =day (1.0 mgd) ¼ 0.044 m =s ¼ 44,000 mL=s; let alum
3
3
into another, as illustrated for the power number in the fol- concentration, C(alum) ¼ 10 mg=L, and from Appendix F,
lowing paragraph. C(neat alum) ¼ 647,000 mg=L. Then, by mass balance as
illustrated by Example 10.3, Q(alum, neat) ¼ 0.68 mL=s. As
10.3.3.5.1 Inherent Incongruity seen by calculation, the ratio of the two flows is Q(raw water)=
of Scale-Up—Illustration Q(alum, neat) ¼ 44,000 mL=s=0.68 mL=s ¼ 65,000=1.
Scale-up from model to prototype requires geometric, kin- Kawamura (2000, p. 307) gives 50,000 as a nominal value
ematic, and dynamic similarity. Geometric similarity may be and mentions that many design engineers are not cognizant of
obtained by setting u m ¼ u p , i.e., with V m =Q m ¼ V p =Q p . Kin- this high ratio. That these two flows must be mixed is the
ematic similarity is based on setting R m ¼ R p , and dynamic major challenge.
similarity is obtained by setting P m ¼ P p . respectively. The
rule is, however, that two parameters may be maintained 10.3.4.2 Advection of Neat Alum
constant between model and prototype, but not three. To
The approach in dispersing one milliliter neat alum solution
illustrate, if L m =L p and R are to be maintained constant, in 65,000 mL of raw water is twofold: (1) the entire flow of
2
substitute n ¼ Rm=(rD ) for the ‘‘n’’ in the power number,
raw water must enter turbulence zones created for mixing,
P, which gives
and (2) the flow of alum must be distributed uniformly by
advection into the same zones of turbulence to comingle with
2
3

P p r m m p D m the raw water. The methods of creating turbulence zones
(10:62)
¼
P m r p m D p within a pipe were reviewed in Section 10.3.1.2, and
m
involved submerged jets or disturbances such as an orifice
In other words, if r m ¼ r p and if m p ¼ m m , then it is evident or a pipe constriction (wake turbulence). To disperse a
that for the power ratio, P p =P m 6¼ D m =D p . The only means to neat alum solution by advection, a ring manifold within the
achieve dynamic similarity is for fluid properties, i.e., r and m, raw-water pipe discharging the alum under high pressure,
to vary; thus, the scale-up of a model using water is not through six orifices, was used by Vrale and Jorden (1972).
feasible. In other words, the selection of parameters for Another method is to feed the alum just before the nozzle
scale-up and how to scale up remains an art (see, for example, of an orifice that creates one or more high-velocity sub-
Oldshue, 1983, p. 197). merged jets.
10.3.3.5.2 Further Notes on Scale-Up—From Oldshue 10.3.4.2.1 Injection of Neat Alum around an Impeller
(1983, p. 197) The velocity gradients are steepest at the outflow (i.e., at the
The most common guideline for scale-up is to maintain tip) from a radial-flow impeller, and are less steep for the
geometric similarity. A major point is that trying to maintain axial-flow impeller. Therefore, the radial-flow impeller (i.e.,
constant selected parameters may add false confidence to a as opposed to a marine impeller) is favored for blending,
scale-up and could lead to a failure of the mixer to achieve a which is the case for rapid mix in coagulation, or for disper-
required process result. Some may avoid scale-up as being too sing a polymer emulsion. A side stream of neat alum solution
risky and the process result too uncertain; a more useful role will mix most rapidly by injection within this high-shear zone,
of models, as opposed to direct scale-up is to study, in an i.e., at the tip of the impeller, as illustrated in Figure 10.3c.
empirical fashion, the effect of each of the parameters on the Injection of alum just upstream of the shear zones of two or
process being considered. more ‘‘in-line’’ impellers would be more effective than a
single injection point using one impeller. In other words, the
idea is to try to distribute the alum over the raw-water flow to
10.3.4 INJECTION OF COAGULANT CHEMICALS the extent feasible.
Dispersing a coagulant solution, e.g., a neat solution of liquid
alum, into a raw-water flow is a major task in mixing for water
treatment, often overlooked. The two issues are (1) the disparity Example 10.3 Mass Flow of Neat Alum
of flows, and (2) the reaction time for Al 3þ (or Fe ) hydrolysis
3þ
to occur. To utilize alum (or ferric) for charge neutralization, Given
the dispersion of coagulants throughout the raw-water flow must Assume that the concentration of alum required
occur within <1sandideally <0.1 s (Clear Corp., 2001). Jet for coagulation is 10 mg Al 2 (SO 4 ) 3 14H 2 O=L raw water.
3
mixers, in-line mixers, or static mixers are the technologies of Let Q(raw water) ¼ 3785 m =day (1.0 mgd). Also, let
choice to approach resolving these two issues. d(pipe) ¼ 500 mm; therefore, v(pipe) ¼ 5.1 m=s. The alum