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Description  |
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BACKGROUND OF THE INVENTION
Flocculation is a process utilized in water and waste-water treatment, as
well as the chemical process industry, to form aggregates of particles by
effecting contact between the particles by means of velocity gradients
established in the fluid to be treated. These velocity gradients can be
brought about either mechanically or hydraulically.
Mechanical flocculation is widely known and practiced. A stirring paddle in
a large tank filled with liquid to be flocculated is moved through the
liquid at a very slow speed, in the neighborhood of one to three feet per
second, thereby setting up velocity gradients in the liquid and bringing
about collisions of particles, one with another, so as to effect
aggregation of the particles. Paddle speed is held at a value which
assures minimal turbulence levels so that excessive breakup of the
particle aggregates does not occur. Overall detention time in a staged
mechanical flocculation system in a typical water treatment plant
generally ranges from thirty to sixty minutes.
Hydraulic flocculation has generally been restricted to water treatment
plants, not being widely practiced either in chemical processing or in
waste water treatment. Various baffle arrangements provide a labyrinthine
path for the flow of the water being treated, the induced velocity
gradients causing particle collision and resultant aggregation. Overall
hydraulic head losses in such installations are preferably limited to less
than one foot of liquid so as to minimize the breakup of particle
aggregation. Residence, or dwell, time is correspondingly lengthy.
For additional background information, reference is had to applicant's
Dissertation entitled INITIAL MIXING AND TURBULENT FLOCCULATION submitted
in partial satisfaction of the requirements for the degree of Doctor of
Philosophy in Engineering in the Graduate Division of The University of
California, Berkeley, California.
SUMMARY OF THE INVENTION
The invention relates to a flocculation apparatus which can conveniently be
used either in new construction or integrated in an existing fluid
treatment installation with advantageous results.
It is an object of the invention to provide a flocculator in which the
residence time is substantially less than that encountered in the
mechanical and hydraulic installations heretofore known.
It is another object of the invention to provide a flocculation system
which is capable of operating efficiently even in a waste water treatment
plant in which there are wide variations in flow rate over a 24 - hour
period.
It is a further object of the invention to provide a flocculation apparatus
which is relatively compact in size and economical both with respect to
initial installation costs and maintenance expense.
It is yet a further object of the invention to provide a flocculation
apparatus and process which is versatile in that the system readily lends
itself to use in a number of different environments.
It is still another object of the invention to provide a flocculation
system which provides a continuous decayed hydraulic gradient capable of
yielding a narrow size distribution of a large average particle aggregate
size in a minimum time.
It is an additional object of the invention to provide a generally improved
flocculation apparatus.
Other objects, together with the foregoing, are attained in the embodiment
described in the following description and illustrated in the accompanying
drawings in which:
FIG. 1 is a developed view of a flocculator pipe constructed pursuant to
the invention, portions of the pipe being broken away to reduce the extent
of the figure;
FIG. 2 is a top plan view of the straight pipe flocculation apparatus of
FIG. 1 wound in a coil and installed in a typical installation;
FIG. 3 is a median vertical sectional view of the installation shown in
FIG. 2, the plane of the section being indicated by the line 3 -- 3 in
FIG. 2;
FIG. 4 is a top plan view of a modified form of apparatus;
FIG. 5 is a front elevational view of the FIG. 4 form of apparatus; and,
FIG. 6 is a diagrammatic view of another form of flocculator.
While the flocculation apparatus of the invention can be embodied and
practiced in a variety of ways, depending upon the environment and
requirements of use, a preferred embodiment is shown most clearly in FIGS.
1-3, and described in the following description.
Since a pipe flow type of installation affords several advantages over the
basin arrangements heretofore widely used, there is provided, as appears
in FIG. 1, in developed form, a pipe generally designated by the reference
numeral 12, extending from an upstream end 13 to a downstream end 14 with
an over-all length L.
Assuming that the flocculation system is to be utilized in connection with
the treatment of a liquid, such as water, and, more particularly, the
reduction of turbidity caused by extremely small particles of clay, or
other colloidal material, suspended therein, the liquid to be treated is
first mixed with a predetermined quantity of coagulant such as alum. This
preliminary treatment forms no part of the present invention, has long
been known and used, and is therefore not described in detail.
The coagulated liquid is introduced into the pipe inlet at the upstream end
13 and flows downstream, emerging in due course from the outlet end 14
from which location the liquid and the accompanying large particle
aggregations are conducted to a separating station, as will subsequently
be described.
In traveling through the pipe 12, the fluid has induced in it a myriad of
velocity gradients effective to cause collisions between the colloidal
particles and thereby creat particle aggregations of substantial
magnitude.
A careful balance must be maintained as the liquid progresses from the
inlet end toward the outlet end. That is to say, it is desirable to
maintain a maximum velocity gradient in order to yield a particular
particle aggregation size, and distribution, in minimum time, but without
breakup of formed particles. This optimum velocity gradient is termed the
maximum sub-breakable velocity gradient.
In order to maintain this desirable balanced condition, the extremely high
velocity gradient at the inlet part 13 must be continuously reduced to
lower relative velocity gradients. An effective way to achieve this result
is to diverge the pipe in a downstream direction.
Although a smoothly continuous divergent pipe construction would provide
good results, practical considerations point to a series of discrete pipe
sections each of predetermined increasing diameter and length joined by
diverging transition members also of predetermined size.
Thus, as appears most clearly in FIG. 1, the first section B1 having
diameter D1 is connected to transition member T2 which merges into a
section of larger diameter D2, followed by transition member T3 connected
to the next section of still larger diameter D3, then by transition member
T4 and the next section of yet larger diameter D4 succeeded by transition
member T5 and the last section of largest diameter D5.
For convenience, a transition member T and the immediately succeeding pipe
section is designated by the reference letter B. Thus, as shown in FIG. 1,
the first pipe section is B1 (there being no transition member T in this
first section; B2 consists of transition member T2 and the succeeding pipe
section; B3 consists of transition member T3 and the succeeding pipe
section, etc.
It is again emphasized that in order to maintain the desired balance in the
flow conditions, the pipe dimensions must carefully be predetermined.
For straight pipe Decayed Gradient Flocculation, the optimum pipe diameter,
D, is related to travel distance, x, as follows:
##EQU1##
where, D = pipe internal diameter (cm)
f = pipe Darcy friction factor (l)
Q = flow rate (cm.sup.3 /sec)
x = fluid travel distance (cm)
B = floc particle breakup rate coefficient (sec.sup.2 /cm.sup.2) = k.sub.2
/e.sub.T
where,
k.sub.2 = floc breakup rate constant (sec.sup. .sup.-1) ascertained by the
procedure described in Wilson, "Initial Mixing and Turbulent
Flocculation", Ph.D. Thesis, University of California, Berkeley,
California, 1972
e.sub.T = total specific energy dissipation rate (cm.sup.2 /sec.sup.3)
For coiled pipe Decayed Gradient Flocculation, wherein the coil has a
radius of r, measured to the center of the coiled pipe of diameter
D.sub.c, the Darcy friction factor, f.sub.c, will be larger than the
straight pipe fraction factor, f, specified above. To achieve a given
degree of flocculation in a minimum of time, the coiled pipe diameter,
D.sub.c, will be related to the straight pipe diameter, D, above, as
follows:
##EQU2##
and the length of coiled pipe, x.sub.c, will be related to the length of
straight pipe, x, above, as follows:
##EQU3##
The critical Reynolds number for turbulence in coiled pipe flow is reported
as follows in Perry's Chemical Engineers Handbook, 4th Edition,
##EQU4##
Based upon the foregoing, installation dimensions can be ascertained for
any desired capacity.
Thus, for a relatively small installation, termed Model 150 (capable of
treating 150 gallons per minute), in which the over-all pipe length L is
450 feet, the first section B1 is 5 feet in length and has a diameter D1
of 2.0 inches; the second section B2 is also 5 feet in length including
transition member T2, which is nominally equal to 6 inches, and D2 is 3
inches; T3 is nominally 7 inches, B3 is 10 feet and D3 is 4 inches; T4 is
nominally 9 inches, B4 is 95 feet and D4 is 6 inches; lastly, T5 is
nominally 11 inches, B5 is 335 feet and D5 is 8 inches.
For a somewhat larger installation, termed Model 400 (capable of treating
400 gallons per minute), the over-all pipe length L is 562 feet and the
respective dimensions are as follows: B1, 6.5 feet, D1 2.5 inches; T2,
about 24 inches, B2, 16.5 feet, D2, 6 inches; T3, about 11 inches, B3, 53
feet, D3, 8 inches; T4 about 12 inches, B4, 106 feet, D4, 10 inches; and,
T5, about 14 inches, B5, 308 feet, D5, 12 inches.
In addition to maintaining the maximum sub-breakable velocity gradient, it
is also necessary to maintain a nearly laminar flow condition throughout
the pipe length in order to minimize the potential for particle aggregate
breakup resulting from turbulent velocity fluctuations. In other words,
random swings from steady state flow conditions could be of such magnitude
as to cause undesirable particle disruptions and consequent degradation of
the aggregate buildup pattern.
Accordingly, I have subjected the continuous pipe flow arrangement
heretofore described to the influence of centrifugal forces, such forces
being capable of stabilizing flow conditions and maintaining laminar flow
conditions even at relatively high Reynolds numbers.
These stabilizing forces are introduced by coiling the pipe into a spiral,
or helix, bearing in mind that the critical Reynolds number is a function
both of pipe diameter and coil diameter. Pipe diameter, in other words, is
a parameter affecting not only the establishment of the maximum
sub-breakable velocity gradient, along with pipe section length, but must
also be considered in conjunction with coil diameter to maintain laminar
flow conditions.
It is also to be noted that by superimposing these centrifugal forces on
the customary pipe wall forces found in linear flow, much greater head
loss per unit volume of liquid is encountered; i.e. the equivalent
"hydraulic length" of a coiled pipe may be much greater than that found in
linear flow. Here again, the amount depends upon the ratio of pipe to coil
diameter.
Thus, by adjusting the various dimensions of the system components, the
desired flow properties and attendant beneficial flocculation results can
most advantageously be achieved.
An installation incorporating the foregoing principles so as to maintain
the maximum sub-breakable velocity gradient throughout the length of the
pipe and under laminar flow conditions is most clearly shown in FIGS. 2
and 3.
In FIGS. 2 and 3, the pipe illustrated in linear, or developed, form in
FIG. 1 is curved into a coil 21 having an internal diameter C which in the
case of the Models 150 and 400 is 10 feet and 16 feet, respectively.
The coiled pipe 21 is disposed within a holding tank 22, having an upper
portion 23 which is preferably cylindrical in shape and supported on a
plurality of columns 24 extending upwardly from ground level 25. The lower
end of the cylindrical tank is closed by an inverted conical bottom 26
terminating at the apex in a drain 27 controlled by a valve 28 to be used
periodically when the relatively heavy particle aggregations 30 which have
accumulated at the bottom of the tank are to be removed.
An annular ledge 31 around the bottom of the cylindrical tank serves to
support the pipe coil 21 as shown, with the upstream end 13 of the pipe
coil at the bottom so as to receive liquid from the adjacent inlet nipple
32 in the direction indicated by the arrow 33. Suitable support blocks 34
and spacers 35 transfer the weight of the pipe coil to the annular ledge
31.
As the liquid from the inlet nipple 32 passes through the initial curved
pipe section B1, then enters the divergent portion T2 and into the
expanded chamber created by the larger diameter of the section B2, the
relatively high initial velocity gradients begin to decay, this process
continuing as the flow proceeds onwardly through successively more
capacious conduits. At the same time aided by centrifugal force and the
additional "hydraulic length" afforded by the coiled pipe configuration,
nearly laminar flow is maintained. Optimum conditions are thereby created
for the aggregation of the floc bodies, with the result that as the liquid
emerges from the outlet end 14 of the pipe, a very large number of
particle aggregates of a desirable size range is present, and
substantially all the suspended particles have been captured.
Upon emerging from the outlet end 14 of the pipe section B5, the liquid and
entrained floc aggregates enter the body of liquid 40 in the annular space
41 between the cylindrical tank 23 and a cylindrical divider wall 43, or
baffle, which is coextensive in height with the cylindrical tank 23. The
divider wall 43 is suitably attached to and depends from a horizontal
X-shaped framework 44 supported on the upper rim 46 of the tank 23.
The body of liquid 40 in the annular passageway 41 is substantially greater
in extent than the stream emerging from the pipe outlet 14 and serves
still further to reduce any residual velocity gradients. Thus, the
relatively large and heavy aggregate particles begin to descend in the
direction indicated by the arrows 47 in FIG. 3. At the same time the
liquid itself flows slowly downwardly in the same direction 47.
Upon reaching the lower end 48 of the divider wall, the liquid flows
inwardly and upwardly as indicated by the arrows 49 whereas the relatively
heavy floc groupings continue to descend, by inertia, toward the inverted
conical bottom 26 as shown by the arrows 50, and are deflected laterally
and downwardly by the conical walls to collect in the bottom of the cone
from which location the accumulation is drained, or flushed, at suitable
intervals.
The clear fluid, devoid of aggregate particles, continues to ascend, as
indicated by the arrows 53, through the body of fluid in the large central
chamber 54 defined by the divider walls 43. Upon reaching the top 56, or
lip, of the ring 57 spaced inwardly from the cylindrical divider wall 43,
the clear fluid spills over the lip 56 into the annular trough 58 defined
by the ring 57, the encompassing wall 43 and the annular bottom 59, the
bottom 59 being suitably mounted on the divider wall 43, as by welding.
Entry of the fluid into the very large body of fluid in the chamber 54
marks the last and largest cross-sectional areal expansion of the
conductor carrying the fluid, beginning with the relatively small pipe
section B1. The specific energy and velocity gradients have
correspondingly been substantially dissipated at the optimum rate.
After rising through the large body of fluid in the central chamber 54 and
spilling over the weir-like lip 56 into the annular trough 58, the clear
fluid descends through an opening 61 in the trough 58 thence through a
radial pipe 62 extending through the wall 23 of the cylindrical tank 22,
down a downspout 63 and into a pipe 64. From the pipe 64 the clear fluid
is conducted away in the direction of the arrow 66 to storage and ultimate
distribution, as desired.
A variant form 70 of the flocculator is disclosed in FIGS. 4 and 5. In this
modification, a pipe 71 is again used, but in this instance the pipe is of
uniform diameter and the desired nearly laminar flow conditions and
maximum sub-breakable velocity gradients are controlled by appropriately
adjusting pipe diameter 72, pipe length 73 and continuously varying the
radii of curvature 74, 75, 76, etc. It will be noted, for example, that
the initial radius of curvature 74, near the inlet 77, is relatively
"tight", thereby affording a substantial "hydraulic length" so as to
effect prompt decay or degradation of the velocity gradients existing at
the inlet 77 and, at the same time, maintaining control over flow
conditions owing to the considerable centrifugal force imposed upon the
stream flow by tightly winding the coil.
As the liquid proceeds on its way, continuous decay of the velocity
gradients occurs so that when the liquid and the attendant floc
congregations emerge from the outlet end 79 in the direction of the arrow
81, the extent of the velocity gradients is minimal and separation by any
suitable, conventional system is readily taken care of.
FIG. 6 shows another modified form of flocculator involving a plurality of
staged compartments 84a - 84f at progressively lower "heads" corresponding
to the progressively reduced velocity gradients of the previously
described flocculation systems.
In the FIG. 6 form of device, the liquid to be treated, descends in steps,
or stages. As before, the energy dissipation rate is carefully
predetermined so as to achieve optimum flocculation with a minimum of time
and a minimum of aggregate particle breakup. Thus, the first compartment
84a, or stage, of the flocculation reactor, or system, generally
designated by the reference numeral 88, is filled with liquid to a height
h1, descending to a height h2 in the second compartment 84b, through a
differential head .DELTA.h2, then to height h3 in the third compartment
84c, through a differential head .DELTA.h3, etc.
It will be noted that the differential head drop is exponential in nature,
with the differential head drop .DELTA.h6 closely approaching an
insignificant amount.
With Ai the surface area of the ith compartment; Vi, the entrance velocity
to the ith compartment; Qi, the amount of flow to the ith compartment; hi,
the liquid height in the ith compartment; the maximum specific energy
dissipation rate to the ith compartment, ei, is given by the formula:
##EQU5##
where
.rho. = density (gm/cm.sup.3)
and
Ti = Average residence time in ith compartment (sec)
For a submerged orifice
Vi.sup.2 /2 = g[h(i-l)-hi] = g.DELTA. hi
Therefore
##EQU6##
Further, compartment residence times are related to the maximum
sub-breakable energy dissipation rate, ei, as follows:
##EQU7##
where,
ei = specific energy dissipation rate in the ith compartment (cm.sup.2
/sec.sup.3)
B = breakup rate coefficient (sec.sup.2 /cm.sup.2) (see above); and,
ti = T1 = T2 + . . . Ti (sec)
Thus, by selecting suitable values so that the Decayed Gradient
Flocculation equations are satisfied, systems having specific dimensions
and configurations can be arrived at.
* * * * *
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