Drag reduction caused by high ploymer solutions injected into water flowing around cylindrical bodies

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ARCHEF

I

DRAG REDUCTION CAUSED BY HIGH POLYMER SOLUTIONS INJECTED INTO WATER FLOWING

AROUND CYLINDRICAL BODIES

by

C. N. Baronet

and

W. H. Hoppmann II

Office of Naval Research

Contract No. Nonr-591(20)

DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED

Department of Mechanics

Rensselaer

Polytechnic

Institute

Troy, New York

July 1966

Lab. c.

ScheepshouwkufldQ

Tedrnische Hogeschool

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DRAG REDUC'rION CAUSED BY HIGH POLY)R

SOLUTIONS INJECTED INTO WATER FLOWING

AROUND CYLINDRICAL BODIES

by

C. N. Baronet

and

W. H. Hopptnann II

Contract No. Nonr-591(20)

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AB STRACI'

A study has been made Of the phenomenon, sometimes called the Toms

effect [l]l, of the reduction of drag on an obstacle in a stream caused by the

introduction

of high polymer solutions in the flow around the obstacle. For the purpose, models consisting of cylindrical bodies with

spherical ends were suspended coaxially within straight tubes in which

water was flowing. The drag on each model was measured with sufficiently

sensitive dynamometers designed and built for the purpose. Also, in

order to perform the experiments, a suitable recirculatory water

tunnel

of 450 liters per minute capacity was designed and built. Furthermore,

in order to study the drag reducing effects of the high polymer

solu-tions, a technique was developed fOr introducing these into the

main-stream of the flow. :

The models studied were of three lengths but of the same diameter

of cross-section. Their use provides an opportunity to see the influence

of length of the cylindrical portion between the spherical ends.

The long horizontal test section of tubing in the flow tunnel

with-out the models in place, was subjected to a series of experiments to

determine the nature of the water flow generated by the pump and

associ-ated system. It was determined that the flow within a sufficiently

large velocity range was uniformly turbulent and the measured velocity

profiles were of the turbulent type. Pressure drops measured along the

1

Numbers in brackets refer to References at end of report.

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tube checked very well with the standard Prandtl Universal Law Of

Friction for smooth pipes and the Blasius Equation [2].

In the drag reduction. study, two proprietary polymers were used;

Their molecular weights were checked by a standard viscometric method [3].

The aqueous solutions used were prepared by means of a mixer specially

designed fot the purpose. It is considered that uniform solutions were

obtained.

For comparison purposes, free field drag calculations for water

flow were made using the Nillikan method for frictional drag [4] and a

standard formula for the fotm drag effect [5]. Results are compared

with drag measurements obtained on the models in the flow tunnel.

in addition to drag measurements, pressure and velocity

distribu-tions were experimentally determined. All, of the experimental data are

shown in the form of curves and it is demonstrated that quite large

drag reductions are obtained with very dilute solutions of the high

polymers which were used.

The results are critically discussed and further extensions of the

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INT RODU cr ION

In recent years a great deal of interest has been aroused by the

discovery that there is a decrease in the pressure drop for flow in a

pipeline when very small amounts of high polymers _{are added to the liquid}

flowing. In addition to this knowledge about pressure loss reduction in pipes, experiments on rotating disks have shown torque reductions when

dilute solutions of high polymers are used [6]. The phenomenon was

apparently first observed by Toms [1] who described it in connection

with flow in pipes as a "hitherto unknown feature of the relation between.

polymer concentration and rate of flow at constant pressure."

Subse-quently, the existence of the reduction effect for flow in pipes was

verified by extensive experiments which were reported by Dodge and

Metzner [7], Shaver and Merrill [8], Savins [9] and Fabula [10]. In

similar experiments, HOyt and Soli [11] found that liquid cultures of

several fresh water and marine algae required less pressure to flow

through a pipe at a given flow rate than the pure liquid medium before

the growth of algae. It is interesting that in addition to laboratory

experiments on the power of certain macromolecular substances to reduce

resistance to flow, natural scientists have speculated on the possibility

that the mucus secretions from the sk-ins of fish enable them to move at

increased speed for a given expenditure of energy [12,13].

The mechanism responsible for the reduction of resistance to flow

caused by small amounts of macromolecular additives is not yet understood.

Some researchers such as Oldroyd [14,15] and Savins [9] have provided

speculations on the causes of the phenomenon but no fully acceptable

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theory is yet available. It is considered that in view of the obvious

importance of the physical results obtained so far in this field of

research, it is essential that a great deal more of theoretical and

experimental work be undertaken.

As far as is known, no work has yet been done on the experimental

determination of the effect of dilute solutions of high polymers on the

drag resistance on solid bodies immersed in flowing liquids. It was

the main purpose of the present study to thoroughly investigate this

aspect of the problem.

EXPERIMENTAL APPARATUS

In order to conduct the proposed research it was _{necessary to}

design and construct certain apparatus and measuring devices. _{A brief}

description of these will be presented in the following. _{The basic}

apparatus is a suitable water tunnel which will now be described.

A. Recirculatory System for Drag Experiments

A water tunnel having a capacity of 45O liters per minute _{was built}

in the Rheological Mechanics Laboratory of R.P.I. as shown in Figure 1.

It is equipped with a supply tank having a capacity of 1000 liters fed

by a 1.90 cm. diameter tap water pipe line. _{The inside of the steel}

tank was coated with "Quigley Triple-A No. 10 Black," a corrosion

pre-ventive for structural material. The standard openings in the tank

were modified appropriately with pipe fittings to accommodate the

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requirements of the system. A centrifugal pump having a capacity of

450 liters per minute and a. 10 meter head brings the water up to a 250

liter drum which is fitted with a 10 cm. diameter copper drainage pipe

overflow returning to the supply tank and ensuring a constant pressure

head over the test section. A cone attached to the supply pipe in the

drum changes the direction of the incoming water and prevents air bubbles

from being entrained in the bell shaped entrance [16] located at the

bottom of the tank. The water is fed into a 7.62 cm. diameter copper

pipe fitted with honeycombs, flows through a reducer, ands then

ad-mitted into the test section. The 3.20 meter long, 5.08 cm. diameter

test section is fitted with flanges bolting onto the reducers and can

easily be removed. A stan4ard orifice plate, 4.85 X 7.62 cm., is

located in the 7.62 cm. diameter return pipe. It is fitted with flange

taps and piezometer rings [17]. The pressure drop across the orifice

plate is recorded by a U tube, manometer filled with dyed carbon

tetra-chloride and water. By appropriate settings of gate valves, the flow

can either be returned to the supply tank for closed circuit operation

or else directed toward a drain. The drainage facilities for the

laboratory are too small to handle the large flow delivered in the

tunnel so an accumulating tank was incorporated into the system. It

is identical with the supply tank and was given a similar anticorrosion

treatment. The outlet of this tank was fitted with a valve so that by

graduat-ing a level gage alongside the tank and usiflg a stop watch,, it

gives 'a means of checking the orifice plate calibration curve for

water flow and also for dilute polymer solutions. In order to give

rigidity to the tunnel, stiff steel structural members were uàed

throughout for framing.

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B. Dynamometer for Measuring the Drag

It was necessary to design a special dynamorneter in order to

measure drag accurately. It is made up of four steel strips, 10.5 cm.

long, 1.2 cm. wide and 0.6 nun. thick, clamped to an outer rigid. support

and soldered to a 1.. 6 . diameter brass rod screwed into the model

undergoing tests as shown in Figure 2. The supports and strips are

en-closed by water sealing drums. This device allows the use of strips

long enough to produce measurable strafns picked up by four 350 ohms

SR-4 active strain gages. It was necessary to use a special procedure

to insUlate the gages from the water by using the f011owIng sequence

of layers: one coat of wax, five coats of Glyptal 1201 red enamel (G.E.),

one layer of thin rUbber sheet, a 1 . liquid rubber coating was sprayed

over and dried and finally tt!io coats of Glyptal sealed the whole

insula-tion. An Ohnuneter with a maximum readable scale of 20 megohms showed

no indication of leakage after iies.ion of the strips in water for

ex-tended periods of time. The bridge was activated with two HD-4D 12 volt

Willard batteries. A rheostat lowered the operating bridge voltage to

18 volts. A coarse and a fine potentiometer allowed zeroing of the

bridge which was done with a D.C. Leeds and Northrup Null Detector.

The e.m.f. output from the bridge was measured with a K-3 potentiometer.

Calibrations of the dynamometer were performed in situ, Figure 3a,

in order to insure greater reliability in the measurèments A thin

slot was machined in the pipe downstream from the model and using a

long thin screwdriver, a string was attached to the tail of the

experi-mental model to be studied by means of a machine screw. A thin pulley

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introduced into the pipe through the slot was held by a small shaft.

The string was placed over the pulley and a small bucket attached to

it. Precision ball bearings were used

_as

stand,ard weights to make the calibrations. In order to properly use the device tare drag

calibra-tions are fleeded and these were made as shown in Figure 3b.

C. Models Used in the Study of the Drag

In order to study the drag reduction three cylindrical models with

hemispherical ends, as shown in Figure 5, were studied. Their

respec-tive lengths were 43, 69 and 94 cm.; their cottunon diameter was l. 90 cm.

The material was brass. Struts 0.21 cm. in diameter were soldered to

the steel sttips of the transducer on one end and screwed into the model

on the other. These were used to hold the thodels. Dye injections near

the wall in the vicinity of the holes showed no appreciable disturbances.

The radial clearance between the models and the inner wall of the

plexi-glass

tube

is 1.59 cm. The drag could thus be readily measured with or

without polymer solutions in the water.

D. Polymer Solutions

The dilute solutions of polymer used in the investigation were made

up from proprietary products. weight solutions of Polyox

Coagulant and WSR-35 Polyox Resin manufactured by Union Carbide Corp.

were prepared. The coagulant was dissolved in four liter containers On

a reciprocating mixer. The necessary period of time for the solute to

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small quantities were later dumped into a large tank arid stirred in

order to insure a homogeneous solution. The WSR-35 Polyox Resin did.

not require any vigorous agitation and dissolved while standing still

for several days. _{Viscosity measurements showed no noticeable change}

in molecular weight for both polymers during the period in which the

experiments were performed.. _{Molecular weight determinations were made}

by a standard viscosity method.

E. Polymer Injection Device

In order to place the polymer solutions into the mainstream Of water, they were injected under presàure from plexiglass containers

shown in Figure 4. The pressurization device was built with a 240

liter drum in which a relative pressure of 150 cm. of water was built

by a pump and maintained.

A line, was connected from the drum to the supply container. The

level drop of the polymer solution in the tank for each measurement

was not sufficient to cause any significant change in the flow rate of

the polymer solution a4mitted into the system. Most of the tests were

carried out at relatively high velocity of the fluid, flow where a

relative pressure in the st-ream at the point of injection was 78 cm.

of water giving an overall pressure of 228 cm. of water applied on the

injected polymer solution. A millimeter scale was fixed on the s-ides

of the container and the flow rate of the solution was measured with a

stop watch. The containers used had cross-sectional areas of 19, 81.7

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were introduced in the stream by a. 0.8 cm. diameter slotted tube located.

transversely in the stream. The disturbance created in the stream was

observed to be minor and local.

EXPERINENTS AND RESULTS

A. Flow Characteristics of Water in the Test Section

and Without the Models in Place

The flow in the test section without models was studied in order to

determine whether fully developed turbulent flow was obtained.. it has

been found experimentally [2] that water entering a pipe from a large

container builds up a fully developed turbulent flow profile within 25

to 40 pipe diameters. In the present system more favorable condit-ions

prevail and fully developed turbulent flow was attained within 20

diaine-ters of pipe after the inlet of. the test section. A velocity profile

was determined with. a velocity impact traverse. It is in agreement with

the results obtained by Nikuradsee for the same Reynolds number [2].

Pressure drops along, the tube were measured at different. flow rates.

B. Flow Characteristics of Water in a Long Axnulus

The flow of water in a long arnulus with a. core having the same

diameter as the experimental models under study and an outer tube

identi-cal with the test section was studied. A velocity profile was determined

with an impact tube for the annulus. Pressure drop measurement.s were

also carried out on the atnulUs and these are in. agreement with published

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data [18]. The results show that the flow in the annulus is fully

turbulent.

C. Experiments with Cylindrical Models in Place in the TUbe

After the straight flow through tubes and annuli were thoroughly

studied for comparison with published data, thereby calibrating one

aspect of the system, drag experiments on the three models we±e begun.

The experiments were carried out with tap water which was at a

temperature of about 100 centigrade. The drag was measured for water flowing around the three models and was corrected by subtracting the

tare drag acting on the supports. The results are plotted On

loga-rithmic scale in Figure 6.

Polymer solutions were injected upstream from the models in

dif-ferent concentrations and the drag reduction was plotted as a function

of the average concentration in the stream in weight parts per million

(WPPM). As an example, the results are shown for model 3 in Figure 7.

Most of the runs were performed in the flow-through operations rather

than in the recirculatory arrangement in order to avoid contamination

of the water supply. The average velocity of the water flow, upstream

from the body, was from 225 to 250 cm. -sec. -1 during the experiments with the additives. it is assumed that the polymer solutions injected

tnixhomogeneously with the stream before coming in, contact with the

models. Injected dye solutions have revealed that the additives spread

evenly throughout the tube section and on this basis, an average

con-centration of the polymer in the stream is computed. The position of

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injection was located at 209 cm. upstream from the middle position of

the model. It is interesting to see that the concentration of the

solu-tion injected is an important parameter for the drag reducsolu-tion1 The

cause is probably the time required f or complete mixing of the polymer

with the water stream. Dyed polymer solutions have revealed a shorter

mixing distance from the point of injection when admitted in lower

con-centrations1 This is believed to be a crucial point in the application

of drag reduction technique to moving bodies and shows that some

advan-tages may be obtained by injecting lower concentration polymer solutions

into the boundary layer. It is shown that an average concentration of a

few parts per million by weight is sufficient to give substantial drag

reduction. The experiments have shown that an excess average

concentra-tion injected into the system can give rise to a drag higher than that

of pure water. The curves show that the drag is reduced more on the

longer models probably because of the larger proportion of skin friction

making up the total drag.

Polymer solutions with a concentration of 0.257 by weight were

in-jected in the tube and in the annulus. Pressure drop measurements were

recorded with standard equipment. The pressure loss reductions are

plotted in Figures 8 and 9. Velocity profiles were Obtained with an

impact tube for the pipe and the annulus. They are similar to those

for water with solution.

It is believed to be of value to compare the drag on the models for

a free stream condition for pure water with the corresponding drag on

the models in the tube. A potential flow function was used to obtain

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the velocity at the outer edge of the boundary layer and Millikan's

method of computation for a turbulent boundary layer was used to

calcu-late the frictional drag on the models. On account of the hemispherical

ends, the drag on a sphere was assumed to be a. good approximation to the

form drag on the models and added to the frictional part. Results of

the calculations are shown in Figure 6.

DISCUSSION AND CONCLUSION

It has been clearly demonstrated that high polymer solutions of a

few parts per million by weight substantially reduce the drag on

cylin-drical bodies, with spherical ends, which are suspended in water flowing

in a pipe. The finding is similar to that obtained by investigators for

the reduction of resistance tO flow Of liquids in pipes alone.

It is demonstrated that the water tunnel, the measuring equipment,

and the method of study are extremely convenient and effective for

study-ing the important phenomena associated with drag reduction caused by

dilute solutions Of high polymers.

It was encouraging that the measured pressure loss reduction as a

function of concentration of solute in the stream is in accord with that

previously reporte4 n the literature. Also, it is clearly shown that

the reduction factor decreases as the concentration increases beyond a

certain critical value.

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13

It is considered that an ithpor-tat piece of knowledge Is the

find-ing that the concentration of the injected substance upstream from the

models influences the drag reduction. The inference then is obvious

that the method of injection for flow around bodies suspended in a

stream is of practical concern in obtaining optimum performance in

engineering 'applications.

Opportunity was taken during the study to observe pressure drops

n the annulus provtded by the cylindrical models suspended in the test

section. For water the results'compare4 favorably with those previously

reported by droop and Rothfus [19]. In addition, the reduction in

pres-sure drop caused by inject-ions of' high polymers in the annulus was

clearly shown.

Finally, it is concluded that the method used in the present study can be fruitfully expanded to include microscopic observation of flow

structure in the boundary layer adjacent to the experimental models.

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REFERENCE S

1.. Toms, B. "Sprne Observations on the Flow of Liflear Polymer

Solutions Through Straight Tubes at Large Reynolds Numbers," Proceedings First .Internationai Congress of Rheology, p. 11-135

(1948);

Schlichting, H., Bouüdarv Layer Theory, McGraw-Hill Book Co., Inc., New York, 4th edition, pp. 502, 505 and 515 (1960).

Billmeyer, F. W., Textbook of Polymer Science, John Wiley and Sons, Inc., New York, p. 82 (1962).

Millikan, C. .B., "The Boundary Layer and Skin Friction for a Figure

of Revolution," Journal of Applied Mechanics, No 54, p 29 (1932)

Hunsaker, J. C. and Rightmire, B. G., Engineering Applications of

Fluid Mechanics, McGraw-Hill Book Co , Inc , New York, p 201 (1947).

Hoyt, J.. W. and Fabula, A. G., "The Effect of Additives on Fluid Friction," NAVWEPS REPORT 3636, NOTS TP 3670, Copy 185, U. S.

Naval Ordnance Test Station, China Lake, California, December 1964.

Dodge, D. W. and Metzner, A. B., "Turbulent Flow of Non-Newtonian

Systems," A.I.Ch.E. Journal, vol. 5, no. 2, p. 189 (1959).

Shaver, R. G. and Merrill, E. W., "Turbulent Flow of Pseudoplastic Polymer Solutions in Straight Cylindrical Tubes," A I Ch E Journal,

vol. 5, no. 2, p. 181 (1959).

Savins, J. C., "Drag Reduction Characteristics of Solutions of

Macromolecules in Turbulent Pipe Flow," Soc of Petroleum Engineers

Journal, p. 203, September 1964.

Fabula, A. G., "The Toms Phenomenon in the Turbulent Flow of Very

Dilute Polymer Solutions," Fourth International Congress on Rheology,, John Wiley and Sons, Inc., New York (1965).

Hoyt, J. W. and Soli, G., "Algae Cultures: Ability to Reduce Turbulent Friction in Flow," Science, vol. 149, no. 3691, p. 1509 (1965).

Jakowska, S. "Mucus Secretion in Fish," Note, Ann. N. Y. Acad. Sci., 106, P. 458 (1963).

Van Oosteen, J, The Skin and Scales Physiology of Fishes, edited by

M. E. BrOwn, Academic Press, Inc., New York, 212 (1957).

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Oldroyd, J. G., "A Suggested Method of Detecting Wall-Effects in Turbulent Flow Through Tubes," Proceedings First International

Congress of Rheology, p. II-l3O (1948).

Oldroyd, J. G., "The Interpretation of Observed Pressure Gradients in Laminar Flow of Non-Newtonian Liquids Through Tubes," Journal of CollOid Science, 4, p. 333 (1949).

Russe-1, G. E., Hydraulics, Holt, New York, p. 118 (1942).

Fluid Meters, Their Theory and Application, A.S.M.E., 5th edition, pp. 19 and 52 (1959).

Croop, E, J. and Rothfus, R. R., "Skin Friction Patterns for Transi-tional Flow in Axrnuli," A.I.Ch.E. Journal, vol. 8, no. 1, p. 26

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bleeding valve

I'

T

Material: transparent plexiglass

II

Test Section

5.08 cm. dia.. 3.20

3.82 cm. dia. supply

tap water supply

meters long

10.00 cm. dia. overflow

manometer

Orifice Plate 4.85x 7.62c,it.dia.

Figure 1.

Schematic Diagram of the Jater Tunnel

bell shaped entrance

(RL

splash cone iT 240 liter capacity working p1 at form honeycombs: drain to drain pump ,

'I 'F

capacity: water 500 liters rs supply tank. level meters accumulator tank head:

mm.

_{10 met}

1000 liters 1000 liters

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etol strip

SR-4 strain QOçe

wax

qlyptol

rubber sheet

iiq. rubber glypta I

brass rod

1.6 mm. dia.

electrical

connections

metal strip

dyn cm o m

_support

dater sealing

drum

Flq. 2

Drag Dynamom eter in the Test Section.

test

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Weights

Machined Slots

a.

Dynamorneter Calibration.

Weights

b.

Ta re Drag Ca Ii bra ton.

Fig. 3

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MMM'

A

Flow

High Polymer

Solution

Polymer Injection

R e gui a ti n g V Q I

ye

---Polymer Injector

,

Pressure Line.

,Trans parent

Piexigl a ss

Container.

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Test Section (508 cm. Dia.) of the Water Tunn.e

Model No.1

Models 190 cm. Dia.

Model No.2

Model No,3

C

)

Core D.ia. 1.90 cm., Outside Dia. 508 cm.

Fig. 5

Sketches of. Models, Tube and Annulu.s Used in the Experimeñfs.

43 cm. long

69 cm. long

94cm:. lor'g

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U)

E

30O

200

100

80

60 QAD Experimen1l results

obtained in the tube.

--Free field drag

40-IA

20-

_f

l0

I

10

20

40 60 80 100

200 300

vera.ge Velocity

(crn.-sec')

Fig.6

Drag on Model Suspended ifl Water

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100 The high polymer is Polyox

Coagulant (Mol. Weight:

6 l.74x,l0

)

Injected as

a:

80

70 o 1.00% by weight solution

90 _.50%il

_ii

_Ii

o

_{.25 % ii}

ii

A

_.

_{I 0}

/

Ii

ii

6

1 1 I I I _I I I

2

4

6

8

10

12

14

16 I\verage Concentration (WPPM)

Fig.7

_{Drag Reduction for Model No. 3 as}

a

Function of the Concentration of High

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100

70

60

50 5.08 cm

The high Polymer is

_Polyox

Coagulant (Mol. Weight:

174X

106)

_Injected

_{as a}

.25% by weight

solution.

a) U,

80 Average velocity

in the tube:

-I

100 cm-sec

135 cm-sec'

165 _crn-sec

220 cm-sec1

240 cm-sec

o

5 .10

15 Average Concentration (WPPM)

Fig.8

Pressure Drop Reduction

_{in the 508 Cm.}

Dia. Tube as a Function of the Concentration

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tOO'

0.

0 J90

080

70 5.08cm

The high polymer is Polyôx

Coagulant (Mol. Weight:

L74X

106)

_{Injected as a}

1.90 cm,

_{25% b}

_{weight solution.}

Average velocity

in the annulus;

110 cmsec

160 cm-sec4

60 195 cm-sec'

270 cm-sec'

5

10 IS

Average Concentration (WPPM)

Fig.9

Pressure

Drop Reduction

n

th,e

_Annulus

as a Function of the Concentration of High

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