Page 325 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

b. Effect of #elements. Now examine the effect dif- Regarding technologies, the three categories are (1)
ferent numbers of elements. A four-element static impellers, (2) jets, and (3) static. Within each category a
mixer has only 0.508 m of headloss with 3.468 number of specific technologies are listed. The ‘‘back-mix’’
kW (4.6 hp) and Gu 2850 (u ¼ 2.1 s). reactor, a traditional technology within the first category,
c. Effect of flow variation. The third scenario set is to has inherent limitations in that each parcel of fluid entering
explore effect of Q on h L , P, and G. The G value
3
is on the low side at 0.348 m =s (10 mgd), i.e., the reactor has a different residence time (evident from a
1
3
G 471 s . For Q ¼ 1.044 m =s (30 mgd), simple reactor analysis). The submerged jet (i.e., a high-
P ¼ 11,705 kW (15.6 hp) which would probably velocity flow from a nozzle that disperses throughout the
require a booster pump (unless the raw-water raw-water flow) within the second category has been
source has sufficient head). favored since the 1990s in coagulation. Submerged jets
have been used also in anaerobic reactors. The proprietary
Discussion ‘‘static mixer’’ has found increasing use in various applica-
As seen by the spreadsheet exploration, there is no single tions. Both of these have, to some extent, displaced the
definitive design (in terms of d(pipe) and #elements). The back-mix reactor. Some of the jet-mixer technologies, e.g.,
R-values are seen to be in the turbulent range, i.e., weirs and baffles, are ‘‘passive’’ in nature and may have
R 2000. The design is for illustrative purposes only. A appeal in places where mechanical systems may be ‘‘not
manufacturer’s catalog should be consulted to obtain appropriate’’ (such as in small systems). The ‘‘bottom-line’’
L(mixer) and to confirm the value of f.
is that design of any mixing system remains an ‘‘art,’’ i.e.,
there is not an ‘‘algorithm,’’ or protocol, that leads to an
unequivocal design.
10.5 SUMMARY
Mixing has evolved from its first uses, c. 1900, toward being
recognized as important, c. 1950, toward having both empir- PROBLEMS
ical and science foundations, c. 2000 (i.e., with CFD maturing
as a science). There is a general awareness of its importance in 10.1 Examples of G and u Parameters in Practice
numerous applications, e.g., coagulation, polymer mixing, Given
dissolution of solid chemicals, gas dissolution, disinfection, Locate a nearby water treatment plant that has a rapid-
aerobic bacterial reactions, and anaerobic bacterial reactions. mix basin, i.e., with an impeller. If it is not feasible to
Mixing may be the rate-limiting factor in most of these use data from an operating plant, make assumptions
applications, i.e., the more intense the mixing, the more com- about the system. Assume the plant capacity is 0.876
3 3
plete the reaction, up to the point that diffusion is rate con- m =s (20 mgd) and has two trains of 0.438 m =s
trolling. (10 mgd) capacity each and that the system is a
On understanding, the three transport mechanisms, linked ‘‘Rushton’’ type (see glossary).
as a sequence of steps, are (1) advection, (2) turbulence, and Required
(3) diffusion. The first two mechanisms must be developed in For the foregoing rapid mix, calculate (a) G, (b) u, and
any design to either promote direct contacts between reactants (c), Gu. Do this for a full range of flow conditions, and
or to bring a given substance into the diffusion proximity of a summarize in tabular form, and compare with values for
surface, i.e., a ‘‘sink.’’ comparable plants (using data from the literature). What
With an improved understanding of turbulence, as com- range in operator control is possible for G?
prising perhaps a tangle of vortex tubes, and of the role of 10.2 Turbidity
eddy size and particle size in particle transport, more sophis-
Given=Required
ticated notions of the role of turbulence have evolved since
What is the turbidity of the input water and of the output
the 1950s. While these ideas help to understand how turbu-
water for a rapid-mix unit in a water treatment plant in
lence affects particle transport and mixing, they have not been
your vicinity?
reduced to the format of design guidelines.
10.3 Chemical Feed
For design, the old standby of Camp and Stein, G, has not
been discarded. Alternatively, P=V, of which G is a derivative, Given=Required
has been used by tradition. A limitation of either of these Describe the chemical feed methods into the rapid mix.
parameters is that there are not unequivocal criteria. Recom- Is the chemical injection a point source to the rapid mix?
mendations have vacillated for some 40 years. Is it a ring of point sources? Is the coagulant fed neat or
While model studies are invaluable, the main value is to diluted? If diluted, what is the pH of the feed solution?
better understand the role of independent variables in the What should be the pH?
process being considered. Scale-up remains an art. This is 10.4 Thermal Energy
evident from the number of parameters that may be operative, Given=Required
e.g., geometric scale and detention time, tip speed, Reynolds What is the order of magnitude of thermal energy,
number, Froude number, and Power number. There is not in kcal=mol, associated with diffusion (perikinetic)
compatibility in scale-up for more than two. mixing?