PRESSURE GRADIENT AND LIQUID HOLDUP

IN

IRRIGATED PACKED TOWERS

Thesis for the Degree of

Doctor of Philosophy

by

John Buchanan

May 1968

iii

SUMMARY

In the existing treatments of pressure gradient in irrigated

packed towers operating below the loading point it is assumed that, for

a given packing and gas flow,the gradient is a function only of actual

bed voidage or, in terms more appropriate to the situation, of liquid

holdup. Experiments are described in which simultaneous measurements

of pressure gradient and liquid holdup were made; the results indicate

that the assumption needs some qualification. They show that a small

initial portion of the holdup seems to have little if any influence on the

pressure loss; when the holdup is large other important effects come

into play.

Within the limits imposed by these qualifications, however,

it is possible to correlate the data on the basis of the assumption. But

-3the experimental results show further that the voidage functions £

and £ 3(l - c) derived from theoretical considerations by previous workers

as pressure multiplying factors to describe the influence of holdup,both

lead to unsatisfactory predictions.

A new theoretical approach is therefore developed.

It leads to a factor Cl A which, being more flexible than

those mentioned can give a good correlation of the results.

For such an equation to have practical utility it must

iv

be possible to calculate liquid holdup directly from the liquid flow

variables and packing characteristics. Again the existing equations

are shown to be inadequate and new correlations are developed and

tested using a wide range of published holdup data.

The complete final set of pressure gradient equations

takes the form :

d AP Sc /P& UCr2 = f ( 1 ~ k Ht )

where jif Rej — F C 1 + C /Re )

and is evaluated from single phase experiments

Ht — Ho Hs by definition

Ho - S ( F L )^3 +- S ( F

and tentatively,

H s = B {?/f>L g d)

The coefficients of all of these equations are evaluated

for ceramic Raschig rings from the experimental data and their values

are shown to be in satisfactory agreement with the theoretical models.

Finally, the predictions of the equations are tested

against an extensive set of published data and satisfactory agreement

is found in this independent check. It is noted, however, that the

effect of varying initial voidage is not dealt with.

V

CONTENTS

Summary iii

Declaration vi

Acknowledgement vii

Chapter 1 INTRODUCTION 1

2 EXPERIMENTAL

Apparatus 17

Materials 38

Procedure 41

3 RESULTS AND DISCUSSION

Static Holdup 47

Single Phase Pressure Gradient 49

Two Phase Pressure Gradient 52

4 THE PRESSURE GRADIENT EQUATION 75

5 PREDICTION OF HOLDUP

Operating Holdup 91

Static Holdup 113

6 FINAL EQUATIONS AND CONCLUSIONS 12 0

Nomenclature 130

Literature Cited 133

Appendix 1 Calculations 136

2 Computer Programmes 149

3 Tabulated Results 16 0

vi

DECLARATION

This is to certify that this work is the original

work of the candidate and has not been submitted, for

an award, to any other university or institution.

J. Buchanan.

vii

ACKNOWLEDGMENT

It is a pleasure to record my appreciation

of the assistance and interest of the staff of the

School of Chemical Engineering and in particular of

Associate Professor J. R. Norman, the supervisor

of the work.

Chapter 1

Introduction

In the design and operation of irrigated packed towers in

gas - liquid mass transfer operations the pressure loss in the vapour

phase passing through the tower is a most important variable. In vacuum

distillation, for instance, low pressure loss is a necessary condition for

the operation to be a success and an accurate knowledge of the pressure

gradient is essential for sound design. In gas absorption - desorption

processes, when the gas is supplied under pressure by artificial means,

the economically best design is established by setting off the capital cost

of the tower and packing against the capital and operating costs of the

blower required. Only in moderate to high pressure distillation or when

the gas phase is supplied under pressure at negligible cost is the pressure

loss of little moment.

It is surprising, therefore, to find, on searching the

literature, that there is available no satisfactory general equation for

the calculation of pressure gradient directly from the fluid flowrates and

properties and from the properties of the packing.

The earliest proposed set of equations were those of

Mach (1935). Mach carried out extensive experiments on a variety of

packing shapes and sizes using principally air and water as the fluids

but also studying the effect of changes in fluid properties using glycerine

2

solutions for his liquids and carbon dioxide and coal gas for alternative

gases. He described the results using equations of the empirical form :

Ap = (X. ( l + 0-005 0C°'S UL )U/

where :

Oc = j&pG0Si ( 1 0-0IZ5jjl )

— Ap for dry packing with lm./sec., p^ 1 Kg/m.

^ = an exponent, a function of j3 having values

ranging from 1.8 to 1.9 5

(Here and below OC and ]f represent arbitrary coefficients to be

determined by experiment. In a few cases, as above, they are dimensional

quantities but in most instances they are dimensionless shape factors).

More typical of the empirical equations which have been

suggested is that of Leva (1954), one which has gained wide currency and

acceptance. Using the experimental results of Lubin (1949) he produced

the equation :

Ap = cco:'u/ * 10 M

Further examples of the empirical forms are those of

Schrader (1958),

Ap ocGrLp. f

3

and of Teutsch (1962),

UL(l += A pQ OC

where A p° — the pressure gradient for the same gas flow

through dry packing.

The practical inadequacy of the Leva equation was

illustrated recently in a comparison made by Clay et al. (19 66) of calcu­

lated predictions with experimental data from a variety of operating

columns. In common with the others cited it may be rejected immediately

and without apology on simple dimensional grounds and because obviously

important variables are ignored.

The same objection may be raised against the members of

a group of graphical representations due to Leva (1954), Eckert (19 61)

and Eduljee (1960). All of these are primarily flooding correlations and

have their origin in the well known correlation of Sherwood, Shipley and

Holloway (1938). It was observed by Leva that in the reported experi­

mental results flooding always occurs at about the same pressure gradient,

some 2 to 3 inches water gauge per foot. Since the flooding line was

evidently a line of constant pressure gradient it seemed that other such

lines could be interpolated onto their flooding graphs . The later workers

added some modifications to this original idea. There are, however,

serious dimensional flaws in the implied equations and they may be freely

rejected on that ground alone. The equations are :

4

- Leva

(The relevance of Pw - the density of water - has never been explained)

data used in producing the empirical correlations have usually been for

air as the gas and for water or for liquids of similar density and viscosity

as the irrigating liquid. For systems with properties corresponding

closely to these any of the empirical forms can probably give reasonably

accurate predictions. But in more unusual applications the fluid properties

may be very different from those of air and water. In such cases the

dimensional equations will be quite unreliable.

least dimensionless in form though still empirical in origin. Thus the

equation of Barth (1951) is:

- Eckert

and, worst of all,

- Eduljee

In partial justification it should be noted that the experimental

More acceptable formally are the equations which are at

5

where /\ A, - the pressure gradient for the same gas flow through

dry packing.

But, as has been pointed out by Teutsch (1962), this equation ignores

liquid density and viscosity and is unacceptable for that reason.

Teutsch further shows that the implication that pressure drop increases

linearly with liquid rate is at variance with experimental facts.

Teutsch himself ( 1962, 1964 ), recognising that flow

resistance depends basically upon liquid holdup proposes, besides the

dimensional equation cited above, a semi-empirical graphical correlation

which implies

Ap/dp0 Re^ °'8), (1 +a Res V0.8

- where the term Fr . Re^ is said to take account of the reduction in

voidage caused by the irrigating liquid; that is of the liquid holdup. It

derives from the Otaka and Okada holdup relations which will be discussed

below.

This equation does include the important variables in

dimensionless form and gave a good correlation of Teutsch's experimental

results for the air-water system. But since he studied only this system

and on a limited range of packings only two of the three dimensionless

groups were varied independently over wide ranges. The correlation

requires further testing with Fr and ReL more positively separated

6

as could be done, for instance, by studying a more extensive range of

liquid viscosities. The correlation is graphical in form and empirical

in origin; it does not satisfy the need for a theoretically based analytical

equation.

Probably the best of the semi - empirical equations is also

one of the earliest, the equation proposed by Uchida and Fujita ( 1936 )

and later improved by them ( 1938) to give, finally :

Af>/pe = a ^aVZ3cf)0(*e^)r e ,S€ + Ap^o /pG

This equation gave a good description of the very large

body of experimental data they produced and it remains the only equation

to take account of the fact that at large irrigation rate Ap may be finite

at zero gas velocity. If the dimensional error is discounted - <JC should replace J and jS then must equal unity as, in fact, they found

experimentally - the expression is sound in form. But in using the

equation the voidage £ must be evaluated from graphical correlations

showing €/£ as a function of UQ/UL and d J^

The authors found it necessary to give different graphs for water and for

the hydrocarbon oils which were the other experimental liquids. No

general graphical or analytic correlation was found.

Finally, in the discussion of semi - empirical forms,

mention should be made of the graphical correlation proposed by

Mersmann (1965). Like the group cited earlier it derives, essentially,

7

from a flooding correlation but in this case the correlations are dimension­

less in form. The implied pressure drop equation is :

APlAPo = J[< M. Ul Id 7 = J ( FrV- below the loading point. The independent variable is meant to

describe the holdup on the packing and derives from a holdup correlation

given by Brauer (1956) and Feind (1960) for liquid flow in vertical circular

tubes. Because the relation is given only in graphical form, because

it is not supported by experimental evidence and because the holdup

function is known to be unsatisfactory for packed towers under all

conditions, the correlation is not further considered.

The theoretical treatments of the subject agree that the flow

resistance is a function of the actual voidage in the packed bed; that

is, the initial voidage less the total liquid holdup. The pressure

gradient equation is assumed to take the form:

dAP%lp6U6 ■ P'(e) ......................................... (1)

It is further agreed that the Reynolds number function can

be evaluated from experiments with single phase flow. Because it has

been associated with the much more general problem of flow through porous

media of arbitrary shape, a very wide variety of correlating expressions

has been suggested for this function. (See, for instance, the very complete

critical review by Schwidegger (1957) dealing with the equations proposed

8

up till that time).

Because, in the present case, only a single shape is

considered,the simple equation of Forchheimer (1901) will be used :

( Re ) — ot + f3/ Re

This equation has been shown to give a good empirical fit to experimental

results and is the basis of the general equation adopted and very

successfully developed by Ergun and Orning (1949, 1952).

Study of the voidage function 4>C^-) resolves itself

immediately into two more or less independent aspects : the effect of

varying holdup on pressure gradient and the prediction of holdup variations

Considering first the influence of voidage on pressure loss

it appears that several approaches have been followed. Uchida and

Fujita (1938), in their pioneering work derived the empirical rule given

above, that, for a fixed gas flow, pressure gradient should be proportional

-is €to e . Later workers have adopted equations based on theoretical

considerations and originally developed to deal with single phase flow

through general porous media. Thus Morton et al. (1964) favour a form

of equation attributed to Carman (1937) which requires pressure gradient

”3to be proportional to £ . Brauer (1960) and Mersmann (19 65) use the

form proposed by Leva (1947) which implies a factor €. 3 (1 - &]

Each of these latter equations involves also a further correction term

important only at low Reynolds numbers and, in fact, negligible in

9

practical packed tower calculations.

For beds of the popular commercial packings these rules

give significantly different pressure drop predictions. Indeed it has not

been clearly shown that the basic assumptions of Equation (1) are

universally true. The primary aims of the present work in these respects

are : to establish experimentally whether, for a given gas flow, pressure

gradient is a function of holdup only; if so, to test whether any of the

above-mentioned relations correctly describes the function; and finally,

if they do not, to develop a form of equation based on theory which can

do so. The experimental data required for this purpose are values of

pressure gradient and holdup measured simultaneously over a wide range

of fluid flowrates and flow properties - in particular of liquid viscosity.

No such data are available in the literature. The experimental programme

to be described was designed to supply them.

To avoid dealing, at this time, with the effects of variable

packing shape, arrangement and initial voidage , only a single packing

has been studied. Because it was believed that there exists at least

one large collection of useful pressure drop data for this form of packing

the Raschig ring type was chosen. This form is also peculiarly suitable

because of its simple, regular and well defined shape. Except perhaps

for the relative wall thickness all sizes of Raschig ring have the same

shape. In equations containing shape factors established by experiment

10

it can be expected that these will be constant for all ring sizes and that

the ring size can be characterised simply by the nominal size; the ring

diameter or height.

But the general conclusions established here should be

applicable to any packing of the film type. Only the empirical coefficients

in the describing equations - which are indeed only shape factors -

should need to be evaluated anew to extend the equations to deal with

packings of different shapes.

Also, for reasons which are fully explained in Chapter 4,

the work covers only the range of gas flows below the loading point.

Since towers are always designed to work in this operating region to

avoid the danger of flooding and the expense of high pressure drop, this

limitation is no serious restriction.

If an equation which successfully predicts the influence

of changing holdup on pressure drop can be found, the second part of

the problem still remains. For such an equation to have practical utility

it is also necessary to be able to predict accurately the liquid holdup on

the packing, a question introducing further complexity.

Three modes of liquid holdup were distinguished by Fenske

et al. (1939) and have been discussed by many later workers:

Total Holdup, Ht - the total amount of liquid

on the packing under some stated conditions.

11

Static Holdup, H - the amount of liquid

remaining on the packing after it has been

thoroughly wetted and drained for a long time.

Operating Holdup, H - the difference between

total and static holdups; that portion of the

holdup which varies with liquid rate.

Static holdup is clearly a function only of the static

properties of the liquid and of the packing. In a similar way the dynamic

variables are taken to affect directly only the operating holdup. The total

holdup is affected indirectly as being the sum of the other two terms.

This approach implies that the liquid comprising the static

holdup remains stagnant and in place under all operating conditions.

A partial justification for this view will be suggested below and in practice

the assumption has been found successful; but in general it must be

considered as only an approximation.

Largely the total holdup has been divided in this way for

convenience in the derivation of correlations . The form of the describing

equations is much simpler if the holdup approaches zero when liquid rate

approaches zero. This is true of operating holdup but not of total holdup.

There has been very little study of static holdup. Some

experimental data have been reported by Shulman and his coworkers (1955)

for ceramic Raschig rings and Berl saddles and for carbon Raschig rings.

12

Empirical, dimensional equations were presented to describe these

results but no general conclusions were reached.

It is significant that, in these experiments, the static

holdup on the carbon rings was found to be more than twice that on

ceramic rings of the same size and general shape which suggests that

material or surface finish effects may be of prime importance. Fortunately

for practical packings, static holdup makes a comparatively small contri­

bution to the total; quite crude approximations are adequate for the

present purpose.

Operating holdup, on the other hand, has been the subject

of numerous investigations. The pioneering work of Uchida and Fujita

(1936, 193 7, 1938) has already been quoted. These workers carried out

an extensive experimental programme using liquids and packings having

a wide range of properties. Their holdup correlations, however, are

graphical in form; no general correlation was found, the results for water

lay on a different curve from that describing the data for hydrocarbon oils.

Elgin and Weiss (1939) and Jesser and Elgin (19 43) from more restricted

experimental work deduced only dimensional empirical equations. The

equations of Shulman et al. (1955) are similarly dimensional and empirical

but they derive from data for a complete range of liquid properties.

The most important study is that of Otake and Okada (19 53)

who, using all of the earlier data as well as the results of their own

13

experiments, produced the following dimensionless equations.

H = 21.1 Fr 0,44 Re "°*37 (ad) ”°*6° 0.01 < Re < 10 o

Hq = 15. 1 Fr 0,44 Re "°*2° (ad) ”°*6° 10 < Re <2000

As will be seen below, these equations do fit the experi­

mental data very well.

Mention should also be made of the work of Mohunta and

Laddha (196 5) . These workers also considered some published data

with their own experimental results and produced a general dimensionless

equation and several separate equations for specific packing types.

That for Raschig rings is:

- i oH = 16.95 Fr 2 Re 4 (Nd ) o

There is a clear similarity between this equation and those

of Otake and Okada but, as will be seen later, it is much less successful

as a correlating expression over the whole range of liquid flows and

properties.

The available theoretical treatments of the problem derive

essentially from the description by Nusselt (1916) of flow of a liquid film

down an inclined plane. By equating gravitational driving force to

viscous resistance they arrive at equations of the form

H = Constant ( Fr/ Re ) ^ o

14

It is enough to compare this expression with the prag­

matically successful Otake and Okada equations to see that it will not

satisfactorily correlate the experimental data.

Thus it may be seen that there is required an equation with

a more sound theoretical basis; a single equation to cover the full range

of Reynolds numbers continuously. This problem is treated at greater

length in Chapter 5 below.

If successful correlations for these two parts of the problem

can be established it should then be possible to test the combined

equations against published experimental results. One large collection

of such data is to be found in the work of Lubin (1949). This series

includes data for a variety of ring sizes in a large diameter column and

for a wide range of liquid flowrates and viscosities. Extensive details

of packing geometry are described but, unfortunately, static holdup was

not measured. So that the final equations can be checked against this

data it will be necessary to make some estimate of static holdup from

equations to be developed also in Chapter 5.

The whole of the discussion so far has been concerned

only with the pressure gradient due to fluid friction. Also to be con­

sidered, of course, is the static component, the contribution caused by

gravitational force. When gas flows countercurrent to the liquid the

static component is added to the frictional gradient; in the case of

15

cocurrent flow it is subtracted. Its magnitude P 3/3 *s a^ways

small at moderate pressures and, in comparison with the frictional

part is usually negligible in importance in the calculation of pumping

power.

Fig. 1. Apparatus

17

Chapter 2

Experimental Work

i) Apparatus

A photograph of the assembled apparatus is given as

Figure 1 opposite. Figure 2 is a diagrammatic representation of the

system.

The column assembly comprised the packed column and

liquid distributor mounted above the gas feed section and the liquid

stock tank. Irrigating liquid was drawn from this tank and recirculated

by a pump through the liquid meter and up to the distributor. From here

it flowed down over the packing and back to the stock tank in a closed

circuit. Air, supplied from a water-ring type of compressor was metered

through rotameters and delivered below the packing. It flowed, counter-

current to the liquid, up the tower and was discharged to atmosphere

through a top vent.

Pressure differences were measured between two tappings

within the packed section. Holdup was assessed by noting the fall in

level in the stock tank when liquid was circulated. Due to the closed

circuit for liquid flow, holdup on the packing necessarily caused a

deficit in the tank's contents.

The weight of the column assembly was carried by a three-

legged stool support bolted to the lowest flanged joint of the assembly.

i1

PUMP

M E 7 E R

Fig. 2. Flow Diagram

19

Its legs were adjustable in length so that the column could be properly

levelled. A stanchion of 4 x 2 inch steel channel was erected and fixed

vertically between the floor and ceiling to act as a spine for the assembly.

It gave lateral support and rigidity to the column and carried the minor

appurtenances of the system.

Details of the principal parts of the system are given

below :

(a) Column - Mechanical details of the column assembly are shown in

the drawing Figure 3. The column was made from a 5 foot length of tube,

6 inches O.D., 5 % inches I.D., of acrylic plastic material. Joints with

the adjacent parts were made with lap-joint flanged connections. These

were formed by cementing hubs, also of acrylic plastic, to the ends of the

tube and fitting steel backing flanges behind them. By this means the

column was securely joined with the distributor assembly above and the

gas feed section below. The joints were sealed with -4? inch thick

black rubber gaskets.

Drillings for the pressure tappings were located at levels

6 inches and 42 inches above the face of the lower flange giving a 3 foot

high pressure drop gauging section.

The air feed section was merely a standard 6 inch glass

pipeline unequal tee piece with a li inch flanged connection on the branch.

It occupied a space 4 inches deep and was held, by long bolts, between

Vent

LIQUID IN

AIR OUT

3 - 0"GAUGE LENGTH

AIR IN

LI QU I D OUT

Dro in

1 COLUMN2 PAC KING SUPPORT3 DISTRIBUTOR4 TANK5 UPPER TANK6 GAUGE TUBE

Fig. 3. Column Details

21

the flanges of the column and the liquid tank.

Clamped between this gas feed tee and the column flange

was the packing support grid, a small brass fabrication. This was composed

of a 1 inch length of tube 6 inches O.D. fixed to a narrow flange by which

it was held in position; two pieces of 1 inch x inch flat set on edge

bridged the tube. The parts were assembled by brazing. This main

supporting piece carried a disc of brass wire screen 3 mesh x 16 gauge

which fitted neatly inside the column, its upper face flush with the lower

flange.

(b) Liquid Stock Tank - Below the packed column and the air supply

tee was the liquid tank, a 30 inch long section of six inch glass pipeline

closed at the bottom with a glass end section carrying the liquid outlets.

A 1 inch branch at the bottom was fitted with a 1 inch hosecock and was

used for a drain; a 1^ inch side-entering branch provided the outlet to

the circulating pump.

The tank was fitted with an internal gauge glass, a vertical

glass tube running the full depth of the tank and fixed in position at the

wall with epoxy cement. The bottom was extended down into the

stationary liquid in the drain outlet and a return bend was fitted at the top

to prevent the entry of falling liquid. Thus the liquid level in this tube

showed the true content of the tank undisturbed by falling liquid and taking

no account of air in suspension. The level in the tube could be easily

22

observed through the glass wall of the tank. A reference scale was pasted

to the tank wall adjacent to the gauge glass and the tank was calibrated

with reference to this scale by the addition of known volumes of water.

It was found that the tank had a very nearly constant cross section giving

a capacity of 0.0177 cubic feet per inch. A thermometer was hung beside

the gauge tube so that the liquid temperature could be directly observed.

(c) Liquid Distributor - Irrigating liquid was distributed uniformly

over the packing at the top of the column by a multi-tubular distributor

comprising 29 copper tubes i inch O.D. by 18 S.W.G., and inches

long fixed by soldering on a 25/32 inch square pitch pattern in a brass

disc i inch thick and 9 inches in diameter. The lower ends of the tubes

were all cut off at the same level which was about \ inch above the top

level of the packing. The tube plate was clamped between the top flange

of the column and the flange of the distributor tank.

This distributor design had an important function in holdup

measurements. Because the lower tube openings were small and all at the

same level the upper tank, once it was filled with liquid, was kept full

even at zero flow by reason of surface tension effects at the ends of the

tubes. Thus the system could be kept full of liquid for long periods while

the packing was drained and the zero operating holdup point established.

At the top of the distributor tank a small vent line was fitted

which ran to a valve at floor level. At the beginning of a run all the air

23

in the top tank was vented to atmosphere so that the liquid-circulating

system was completely filled with liquid. A zero level of operating

holdup was established by allowing the liquid to drain from the packing

for a long time. Subsequently liquid holdup was found simply by measuring

the drop of level in the liquid stock tank.

At high liquid flowrates the equal pressure drops in the

identical tubes assured uniform liquid distribution. At low rates drops

could be observed to fall from all the tubes in synchronism. This

behaviour due again, no doubt, to surface tension effects produced good

distribution at even the lowest rates.

(d) Packing - The packing pieces used were Raschig rings of unglazed

porcelain purchased from Hydronyl Limited ( U.K.). Only the % inch

ring size was used and only a single filling of the column.

In accordance with the manufacturers' recommendations

(1963) the rings were packed into the column wet and redistributed on a

rising cone. That is, the column was first filled with water and a 4 inch

filter funnel, hung in an inverted position on a long wire, was placed at

the bottom of the column. Then the rings were gradually added and the

funnel lifted until the column was filled to the required depth. The

presence of water effectively prevents ring breakage in falling into the

tower; the use of the cone is claimed to produce the least biased packing

arrangement.

24

During the trial runs made in the first few days after the

column was packed it was found that there was considerable settlement

of the packing. Further pieces were added to bring the filling up to the

desired level and no further settling was subsequently observed.

The dimensions of the rings were established by measure­

ments made on a sample of 100 rings and the mean ring weight with a

sample of 200. The density of the ring material was measured by weighing

some 40 lb. of the rings first dry and then immersed in water. A known

weight of the rings was put into the tower. Physical details were as

follows:

Table 1 - Properties of the Packing

Material Density 154 lb/cub. ft.

Bulk Density 46 lb/cub. ft.

Packing Weight 38.60 lb.

Packed Height 55.3 inches

Packed Volume 0.837 cub. ft.

Number per fubic foot (N) 5200/cub. ft.3

Dimensionless packing density (Nd ) 0.766

Mean ring height 0.639 inches

Mean ring diameter 0.629 inches

Mean wall thickness (calculated) 0.091 inches

Mean ring weight 0.0089 lb.

Voidage 0.701

25

The packing characteristic size cl used in calculations

was taken to be 0.634 inches - the mean of ring height and diameter.

(e) Pressure Tappings - It has been observed by Mach (1935) and by

Lubin (1949) that when pressure differences are measured over the full

depth of packing there occur inevitable errors arising from column end

effects. The packing support grid and screen at the bottom of the column

and the region at the top where liquid splashes as it is initially dis­

tributed both exhibit special pressure drop effects. It is desirable

therefore to locate the pressure tappings within the packed section and

well away from the ends.

Because of the known tendency for liquid to concentrate

at the walls it is also desirable that the tappings be away from the walls

to avoid both the possible pressure gradient anomalies and the flow of

liquid into the tappings - an effect which is likely to be particularly

troublesome if the tapping is simply a hole in the side of the column.

In this apparatus the tappings were placed 3 feet apart,

being at levels 6 inches above the packing support and 18 inches below

the top flange of the column, that is about 13 inches below the top of

the packing. To shield the tapping from the direct impingement of

high velocity air, to place it in the body of the packing and to minimise

liquid inflow a special tapping design was developed. It is shown at

about actual size in Figure 4.

Fig. 4. Pressure Tapping

27

1Except that the piece nearer the wall had only 4 inch

internal diameter, that part of the fitting which was inside the column

corresponded in shape to two Raschig rings. The fitting was placed

with both ring axes horizontal to reduce liquid flow into the tapping and

air flow through it.

The assembly was fixed to the wall of the column by

tightening the 4- inch B.S. P. backnut and a seal was made with a cured -

in - place silicone rubber washer. Externally a liquid catchpot was

fitted, a standard J inch B.S.P. brass tee piece into which were

screwed the connections for a liquid drain line and a line to the pressure

gauges. Any liquid getting into the pressure tapping flowed out of the

lower connection. It flowed into a short length of vinyl tube closed at

the lower end with a small rubber stopper. Thus the quantity of liquid

collecting could easily be seen and quickly drained away.

In spite of the precautions taken it was found that at the

very highest liquid rates there was considerable flow of liquid into the

tappings causing false readings on the sensitive pressure gauges. An

attempt was made to alleviate this difficulty by supplying a small counter­

flow of air to prevent liquid invasion. A short glass tube with the upper

end drawn out to a jet was inserted in the vinyl tube coming down from

each catchpot. The tube was supplied through a needle valve with

compressed air from the main, and, after a small amount of liquid was

28

allowed to collect over the jet the rate of flow was adjusted to a slow

bubbling.

Reverse air flow did stop the liquid from running out of

the pressure tapping into the catchpot. But the pressure difference

readings were little less erratic than before. Evidently the overpressure

required to form bubbles within the tapping was significantly high. Little

real benefit was gained from the provision of the air purge.

Tappings were located in vertical lines, two at each level

in diametrically opposed positions. Measurements made in trial runs

showed that there was negligible difference between the pressures at the

two tappings at either level.

(f) Pumps - For the circulation of water and the low viscosity solutions

a Day "Delta" size 1 DC centrifugal pump was used. This pump had a

cast iron body and impeller with stainless steel trim and was driven at

1410 r. p.m. by a close-coupled l| h.p. electric motor. It was fitted

with a "Crane" mechanical shaft seal and it was found that there was

negligible liquid leakage. Liquid flowrate was regulated by valves in

the discharge line.

High viscosity solutions were circulated by a 1 inch "HPM"

bronze gear pump driven through a 4 : 1 speed reducing vee-belt drive

from a Kopp "Variator" variable speed unit close - coupled to a 960 r. p.m.

1 h.p. electric motor. By this arrangement pump speeds from 80 to

720 r. p.m. could be produced giving liquid flows from 2 to 18 g.p.m.

Fig . 5 . Liquid Flow M eter

30

Lower flowrates were produced by allowing some of the liquid to flow

through a bypass around the pump.

(g) Liquid Flow Meter - Because of the unusually wide ranges of liquid

flowrate and viscosity being dealt with .special consideration had to be

given to the means for measurement of liquid flow. To minimise the

influence of liquid viscosity a positive displacement meter was chosen.

Then measurement of flowrate involved only observation of the rate of

motion of the metering element with a minor correction for liquid viscosity.

The basic metering unit selected was a Parkinson-Cowan

1 inch type S3G meter. This unit was a rotary piston type meter having

a bronze body and a carbon piston. It was rated to measure flows down

to 2% and - for short times - up to 150% of the nominal maximum flow of

6 00 g.p.m. with + 2% accuracy.

In place of the usual mechanical integrating revolution

counter the meter was fitted with an electro-mechanical timer-revolution

counter specially developed for this purpose.

Figure 5 is a photograph of the components of the metering

system: the meter with pulse generator fitted, the pulse generator control

box and the timer - counter unit. A more detailed view of the pulse

generator is given in Figure 6 and electrical circuits of the sensor and

counter are given in Figures 7 and 8.

A meter of this size makes about 40 revolutions per gallon

of liquid. The meter body originally contained an internal triple-reduction

Fig. 6. Pulse Generator & Control Box

32

gear train having an overall 125 : 1 speed reduction ratio and driving the

sealed output shaft. This gear train was removed and replaced by the

sensor unit shown in Figure 6.

The sensor comprised basically a toothed copper disc,

driven by the rotating piston, and two sets of pickup coils arranged as

shown in Figure 7. The coils were the feedback coupling elements in an

oscillator circuit and the system was adjusted with shading plates so that

oscillation occurred only while the coils had no part of the moving disc

between them. When a part of the disc passed between the coils the

inductive coupling was reduced and oscillation ceased. The output of

the oscillator was amplified, rectified and smoothed so that as the wheel

turned a train of pulses was produced. This part of the system is essen­

tially the same as a vane switched pulse generator described by Barclay

(1964) and Longfoot (1965) but the pickup coil assembly had to be minia­

turised to fit the very limited space inside the meter body ..

The pickup coils were mounted in blocks of acrylic plastic

and were sealed against water penetration with a cold - curing silicone

rubber potting compound. Electrical leads were brought out of the meter

body through a short nipple piece replacing the counter drive shaft. The

six wires were sealed in the same silicone rubber compound.

Depending on the set of coils switched into the oscillator

circuit either two or twenty pulses were produced per revolution of the

-24 V.9

-12 V.

9

.22/JF.

12 K>OUTPUT

DC 2 10AC 125

COILS : 400 turns 30 DCS on Ferrite core

Hull or d VINKOa LA2901 Former DT216S

VANE-SWiIC HEO PULSE 6ENERATOR

ARRGT. COILS a INTERRUPTER DISC( Actual Size)

Figure 7

34

piston - that is about eighty or eight hundred pulses per gallon. The

switching arrangement is not shown on the circuit diagram.

Pulses were sent on to an all transistor control unit and

power amplifier driving a "Hengstler" Model F048 electromechanical

counter. Pulses were gated by the action of a relay controlled by a

"Trumeter" Model EP1P self-run predetermining timer. This timer

operated a switch at the end of a preset period of up to 899 seconds.

It was driven by a stepping motor counting the 100 c./s. of the rectified

5 0 cycle A. C. supply, and its accuracy was limited only by the short

term accuracy of the mains frequency. There was, however, a lag in

the mechanical cutoff linkage leading to an overall error of + 0. 03,

-0. 00 seconds in the gate time.

The electrical circuit of the Timer - Counter is given in

Figure 8. The required sampling time was set on the timer and counting

and timing began simultaneously when the pushbutton switch was closed.

At the end of the timing period a signal was passed to the NOR gate unit

blocking the passage of further pulses and the timer was stopped. After

the counter reading was noted both timer and counter were reset manually

for a new cycle of counting.

The counter used had a maximum counting rate of 25 counts

per second. Thus the equipment was inherently capable of very high

accuracy in quite short counting times.

50 V.

START

I TIMER

L_____ 4.7 K

240 V

-24 V.

COUNTER I

Yl 6000

NOR YL60G2PULSEINPUT

TIMER-

COUNTER

-50 V.

2 0 0/UF

2.2 K24 0 V. SO-12 V.

BZZ 23

OA 605

POWER SUPPLY

Figure 8

36

As a result of internal leakage there was a small variation

with liquid viscosity of the meter displacement per revolution. For this

reason the meter was separately calibrated for each liquid by counting

the revolutions registered in taking a known volume from the stock tank.

(h) Rotameters - Air flow to the tower was metered by one of a bank of

rotameters. There were five of these in all; "Metric" rotameters manu­

factured by Rotameters Limited (U.K.), sizes 7,10,18 and 35 with

duralumin floats and size 47 with a float of korannite - a ceramic material.

These meters between them covered a range of maximum flowrates from

0.4 to 65 s.c.f.m. of air. They had overlapping ranges of use so that

it was possible to read the meter scale to an accuracy of + 2% at the

worst.

The guaranteed accuracy of the two largest meters was well

within that required for these experiments. The smaller meters were

calibrated against a dry gas meter over their full range and the second

largest over part of its range. The dry meter was checked, in turn,

against a wet test meter.

Rotameter readings were corrected for variable gas density

by the usual rotameter characteristic formulas.

(j) Pressure Gauges - When air was passing through the tower

pressure drop was measured with one of two slack - diaphragm type

draught gauges; a Dwyer "Magnehelic" 0 to 0.5 inch W. G. meter for

37

the lower pressures and a Negretti and Zambra 0 to 9 inch W.G. meter for

the higher. Each of these instruments was separately calibrated against

a Casella Micromanometer.

For the single phase runs where the flowing liquid filled

the column pressure drop was measured with an inverted U - tube mano­

meter having air over the flowing fluid.

Air pressure was also measured at the rotameters and at

the column using mercury U-tube manometers.

(k) Static Holdup Bucket and Balance - For the measurements of

static holdup a 12 inch length of the same tube used for the column was

fitted with a screen bottom and a bridle by which it hung from an "Ohaus"

Model 1122 solution balance. This container hung inside a copper tank

which was covered to minimise liquid evaporation and disturbance by

draughts.

38

ii) Materials

The irrigating liquids used in this investigation were water,

a light distillate fuel oil (Dieseline) and a series of concentrated sucrose

solutions. Compositions of the liquids used in pressure drop runs are

shown in Table 2 below with the approximate physical properties at the

operating temperatures.

Table 2 - Irrigating Liquids

Solution Density (gm./ml.)

Viscosity(centipoise)

SurfaceTension

(dynes/cm)

Water 1. 000 1.0 71

45% Sucrose 1. 204 5. 5 65

6 0% 1.283 45 69

6 7.5% " 1. 331 200 69

Dieseline 0. 810 2 27

Densities were measured by hydrometers and viscosities

with Ostwald type viscometers. Using measured densities the viscos­

ities of the sucrose solutions were checked against the N.B.S. standard

values reported by Bates (1942) and gave good agreement in every case.

Surface tensions were measured with a Cambridge - Du Noiiy platinum

ring surface tensiometer.

39

For the single phase pressure drop runs the fluids were

water and a 48.5% sucrose solution having density 1.221 gm/ml and

viscosity 10.9 centipoise.

A further set of solutions, of approximately the same

concentrations shown in the table above, were used for the series of

static holdup measurements. These experiments were carried out

some time after the pressure drop runs. For one static holdup test some

of the left-over sucrose solution was used and it was found, no doubt

due to biological degradation, to have a much lower surface tension

than the other solutions. The relevant properties are given in Table 3

below.

Table 3 - Static Holdup Solutions

Liquid Density (gm./ml .)

SurfaceTension

(dynes/cm)

Water 1.00 69. 8

Sucrose 45% 1.204 71. 7

" 45% 1.204 46. 5

" 6 0% 1.283 63.6

" 6 7.5% 1.331 74. 7

Dieseline 0.815 28. 4

40

When flowing over packing in the tower the light oil

showed a marked foaming tendency. Regardless of whether gas was

flowing or not, when the oil flow exceeded a critical value the column

would quickly fill with a mass of large bubbles. The foam subsided

rapidly if the oil flow was stopped but unless this was done the column

would soon flood.

Attempts were made to alleviate this problem by adding

a silicone antifoaming agent to the liquid but they proved completely

unsuccessful. This behaviour therefore provided the limit to possible

oil flows in the tower.

41

iii) Procedure

(a) Operating Holdup and Two Phase Pressure Drop

Experimental work with a new irrigating liquid was begun by

filling the stock tank and pumping the liquid over the packing at a fast

rate and for a long time so that the packing was thoroughly soaked and

the liquid well mixed. Any inhomogeneity in the solution could easily

be detected visually since the refractive index changes rapidly with

sucrose concentration.

When the packing was judged to be fully wetted the liquid

flow was stopped and, with the distributor kept full the liquid was allowed

to drain from the packing until drainage ceased. The level of liquid in

the stock tank was then adjusted to a convenient level and this level

was recorded as the zero point for operating holdup measurements.

The packing was then once more thoroughly wetted and allowed

to drain, this time for only a short time - twenty minutes or half an hour.

The liquid level in the tank was recorded again. In this way a subsidiary

standard liquid holdup was established, a level having a known relation

to the zero. The amount of liquid leakage or evaporation could thus be

checked without the necessity for a very long draining period.

A set of measurements were then made of operating holdup with

free air flow. The air inlet and outlet were left open and air was allowed

to flow freely through the packing. Liquid flow was set at a fixed rate

42

and readings of flowrate and holdup were made continually until both came

to equilibrium. These values and the liquid temperature were then

recorded and the liquid rate changed for the next reading. In the calcu­

lations measured holdups were adjusted by a small correction to take

account of the quantity of liquid in free fall from the packing. It was

found in these experiments that the tower came to equilibrium very quickly.

The time required for the level in the stock tank to settle down after a

change in flowrate was little more than the time taken for liquid to flow

from the top of the tower to the bottom.

Next the two phase flow runs were begun. The liquid flow

was set at a value which gave the required holdup and an air flow sufficient

to give a pressure gradient about 0.01 inches W.G. per foot was

established. Readings of liquid flow, air flow, pressure drop, liquid

level, liquid temperature, and air pressure in the column and at the rota­

meter were recorded when they came to equilibrium. The air flow was

then increased and the same procedure was repeated. Air flow increments

were chosen so that (aincreased in equal steps of about 0.1 (inches_i

W.G./ft.)2 . As the air flow was increased it was necessary to shift

the flow measurement to larger and larger rotameters. In every case the

smallest rotameter which could accommodate the flow was used.

Air flow was increased and readings were recorded usually

until flooding began in the tower. This was easily detected by visual

inspection and finally by splashing of liquid from the air discharge pipe

43

adjacent to the operating station. In a few runs with very high air

flowrates evaporation became excessive and the run was concluded before

flooding occurred. Liquid evaporation produced a continuous fall in

liquid level in the stock tank and led to uncertainty in the holdup measure­

ments at the highest air rates.

At the end of such a run the packing was allowed to drain for

the short period drain time to reestablish the holdup zero and measure

the amount of leakage and evaporation, if any. During this time a liquid

sample was taken for a density measurement and readings were taken of the

air supply wet and dry bulb temperatures for calculation of humidity and

specific volume.

After this draining time the liquid losses were made up, if

necessary, and the next run begun. Pressure drop runs were continued

up to the highest practical holdups. The limit occurred at the maximum

tank capacity - equivalent to a holdup about 0.2 - or when the pressure

drop readings became erratic as a result of liquid flow into the tappings or,

finally, when air entrainment in the circulating liquid was observed.

At either the beginning or the end of such a series of runs with

one particular liquid the flowmeter was calibrated for this liquid. A minor

modification was made in the circuit of the timer-counter so that the timer

and counter could be started and stopped simultaneously by the action of

an external push-button switch. The liquid flow circuit was also

modified so that liquid was discharged from the pump and meter into an

44

external drum rather than into the column.

Then a series of readings of the meter constant were taken

over the full operating range of liquid flows. In each test the tank was

filled and the pump started. The timer-counter was started as the liquid

level passed an upper index mark and was stopped as it passed a lower one.

The elapsed time and the number of revolutions of the meter for the known

volume were both recorded so that the flowrate and the meter calibration

could be calculated.

At the end of these twro phase flow runs the tower was

thoroughly flushed out with water and dried by passing a large air flow

through it for several hours and a series of pressure drop measurements

was made with air flow in the dry tower. While strictly, of course, this

was a single phase flow the results are discussed with those of the two-

phase runs where they more properly belong.

It is worthy of note that at very high irrigation rate in the

two-phase runs there was some visual evidence of channelling of the

liquid and preferential flow at the wall of the column. There was no means

for measuring the extent of this phenomenon provided in the apparatus nor

any way to control it.

(b) Static Holdup

The bucket was weighed dry and after being thoroughly wetted

internally with the test liquid and drained. It was then filled with dry

45

packing and weighed again before the packing was saturated by pouring

irrigating liquid over it at a rapid rate. At this point samples of the liquid

were taken for the measurements of density and surface tension.

The saturated packing was allowed to drain until it showed no

further weight change, but in no case for less than 24 hours. The static

holdup was then taken to be the difference between the weight of the bucket

filled with packing wetted and drained and the weight of the bucket itself

after draining.

On the assumption that static holdup would be proportional to

the number of packing pieces the reported static holdup was calculated

by dividing the weight specified above by the liquid density and multiply­

ing by the ratio of the weight of dry packing per cubic foot in the column

to the weight of dry packing added to the test bucket.

(c) Pressure Drop in Single Phase Flow

To evaluate the function of Equation (1) measurements

of single phase pressure drop were required over a wide range of Reynolds

numbers. It was found most convenient to do this using liquids as the

flowing phase. By using water and a 48.5% sucrose solution having

viscosities of 1 and 11 centipoise respectively a range of Reynolds numbers

from 4 to 1500 was easily covered with satisfactory accuracy by the

apparatus described.

The liquid tank and the column were filled with the liquid to

46

a point well above the upper pressure tapping and the liquid was cir­

culated at a high rate for a short time to assure good mixing. Some

liquid was then run out into the leads of the inverted U - tube manometer

until the levels were brought to the height required.

A small liquid flow was then established, sufficient to give an

accurately readable pressure drop at the manometer, and readings were

taken of flowrate, liquid temperature and pressure drop. The flow was

then increased and further readings taken until the pressure drop reached

the maximum for the manometer or flowrate reached the maximum capacity

of the flowmeter.

At the end of the series of measurements on the sucrose

solution samples were taken for the measurement of density and viscosity

Also for this run a separate flowmeter calibration was determined.

47

Chapter 3

Experimental Results and Discussion

i) Static Holdup

A dimensional analysis of the variables influencing static

holdup gives an equation of the form :

Hs -ff Shape, Cf/f>qd\ lt/d ,lz/d,--------------)------ (2)

where the terms lL/d are a series of shape factors, the dimensions l being significant - but so far unidentified - linear dimensions defining

important details of the packing shape. Thus, for instance, they might

describe the distribution and size of roughness elements.

For this present case the general shape and these undefined

dimensions are constant and the equation reduces to :

// - J- ( (f/pCfd J........................................................................ (2(a))

Experimental results with values of the function (cf/p d Z)

are given in Table 4 below. The experimental points are plotted

according to the equation in Figure 9 with the best straight line fitted

through the points .

It should be emphasized that these results were required

for, and apply only to the packing used in these experiments.

Fig. 9. Static I-Ioldup - Experimental Results

49

Table 4 - Static Holdup Results

Solution Density(gm/ml)

Surface Tension

(dynes/cm)

H

xlO2

cr/p gd 2

x 10

Water 1.00 70 2.74 2.75

45% Sucrose 1.20 72 2.07 2.34

45% 1.20 47 1.83 1.52

60% 1.28 64 2.24 1.95

67.5% " 1.33 75 2.13 2.21

Dieseline 0.81 28 1. 77 1. 37

Values of static holdup assumed for calculations of

pressure drop runs were established by interpolation from the straight

line of Figure 9.

As is suggested on the plot of Figure 9, the claimed

accuracy of static holdups is not high,mainly because of doubts about

the amount of evaporation which may have occurred during draining.

An accuracy of - 0.002 is estimated. This is quite adequate for the

present purpose.

ii) Pressure Gradient

(a) Single Phase Flow - Tabulated results of these experiments are

given in Appendix 3; the methods of calculation are shown in Appendix 1.

But the results are summed up in the simplest way in the graph of

100

CD

O

o

oin

cnLO

CD(T

cnco0cc

\i{

F ig . 10. S ingle P hase P re ssu re Drop - E xperim ental

51

Figure 10, opposite, where experimental values of the friction factor

(d Ap /p U Z) are plotted against the Reynolds Number (d Up/jj )

These results were correlated by an empirical expression

first proposed by Reynolds (19 00) for flow in pipes and for flow in

porous media by Forchheimer (19 01); it takes the form :

f = F (1 + C/Re)....................................... ( 3 )

and has been found to be very successful in dealing with experimental

data. The best values of the constants were calculated by a linear

regression of the experimental values of f and 1 /Re . The

calculated values led to the equation finally adopted ;

f = 8.6 (l + 52/Re )................................... ( 4 )

The curve of this equation is shown on Figure 10. It should be noted

that the friction factor f is the same quantity as the function <f> ( Re)

of Equation (1).

In regard to the consistency of the experimental results

the graph of Figure 10 speaks for itself. The accuracy of the final

equation depends upon the absolute accuracy of the flow measurements

and the goodness of fit of the chosen form of equation to the experimental

results. Considering these matters it is estimated that within the range

of investigation Equation (4) should describe the function (Re) with

an accuracy of - 5%.

52

(b) Two Phase Flow - The results of the two phase flow experiments

are analysed using the assumptions stated earlier that the pressure

gradient equation takes the general form :

d Ap /f> UGZ = 4>(€)....................................................(1)

and that the Reynolds Number function can be evaluated from experiments

with single phase flow such as those which have been described.

Substituting from Equations (3) and (4) the relation can

be expressed in the more explicit form :

P =[dAp^c/^&(l-l-S2/'Re.)]2-^mUei........................... (5)

where m = [F <p' (£ ) ] 2 ................................................................ (6)

(As will be shown later it is undesirable to introduce at this point the

value of F from the single phase experiments).

Below the loading point the liquid holdup and hence the

voidage are substantially independent of gas rate and j> (e) is a

constant. Therefore, if the experimental values of P are plotted against

corresponding values of the gas velocity UG , below the loading

region the points should lie on straight lines of slope m passing

through the origin.

Figures 11 to 15 are plots of the experimental data treated

in this way. The methods of calculation, complete tables of results and

plots for the individual runs may be found in the Appendices.

53

For the experimental run with air flow through dry packing

(Run 3) and for those runs in which the packing was wet but there was no

liquid flow (Runs 6 , 15,80) a straight line through the origin gave an

excellent fit to the experimental points. In the other runs, with some

exceptions noted below, after several points were set aside as being in

a transition region the remainder clearly defined two straight lines; one

passing through the origin and covering the range of flows below the

loading point; the second describing performance in the loaded region.

The gas velocity at the intersection of these lines is reported in the

tables as the loading velocity. This method of data selection is partly

subjective and may be criticised on that score; but the implied loading

points do show reasonably consistent trends on the graphs of P and of

holdup against gas velocity. In any case the procedure entails the

rejection of high velocity points only and has little effect on the value

finally calculated for the preload slope.

In a few cases the gas velocity was not taken to a level

sufficiently high for the loaded range to be clearly defined. For these

runs it was assumed that points for which A jp> was less than 0.7

inches W.G. per foot were definitely in the preload range and only

these points were used for correlation. Of course no loading point was

reported for these runs. The experimental results for the two highest

water flows (Runs 35 and 37) were exceptional in that no straight line

through the origin was clearly defined. They were anomalous also in

14

13

12

1 1

10

9

8

7

6

5

4

3

2

1

0

54

Water

55

o.oss

0. 062

0.04 2

0.022

0.012 S

0.004-5

(J = 0. 0012 it./sec.Run 2 9

Sec,

Fig. 11 (a) Experimental Results - Viscosity = 1 cp.Water

1 4

13

1 2

1 1

10

9

8

7

6

5

4

3

2

1

0

56

Run 37• -

35 ’

P(ft./sec.)

34-

Cft. / sec.)

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 .1 .2

Fig. lib Experimental Results - High Water Rates

57

0.088Run 37

0.042

(ft./Sec.)

9 1.0

Fig. 1 1 (c) Experimental Results - High Water Rates

1 4

13

1 2

1 1

10

9

8

7

6

5

4

3

2

1

0

58

sec.

Run 43

Fig. 12 Experimental Results - Viscosity - 6 cp.

Sucrose

59

.4

.3

.2

. 1

.08

.06

.05

.04

.03

.02

•

49.6.4 xfO'2 •

••

*

42 . . . • *'4.3 */0~ 2 ♦

H* 41▼ T T T ♦ T2 S»/0~5

. * ♦ +T

♦+ T

M*•V •*

+ ♦ +

. * *1.43*1 o'*+ + ▼ ▼

♦ •

52•8.7 r/o;3 . .

• •• #• * •

•

55 5~xlO~\. ' ‘ ♦. + ▼. A T

+ + ‘ +

. ♦ .3 * /0“3♦ ♦ ♦

♦ ♦

♦M* ♦

♦ ♦

Run 55T T T T

*r ♦

Uc - 3.5 * /0~4 ft./sec.

Oft./ sec.)

0 1 2 3

Fig. 12 (a) Experimental Results - Viscosity = 6 cp.Sucrose

14

13

1 2

1 1

10

9

8

7

5

4

3

2

1

0

60

Run 1G

Cft. /Sec.)

Fig. 13 Experimental Results - Viscosity = 45 cp.Sucrose

61

* 3.7 */0~

6.1 * 10

0-0 ft./Run 80

Fig. 13 (a) Experimental Results - Viscosity = 45 cp.Sucrose

14

13

12

1 1

10

9

8

7

6

5

4

3

2

1

0

62

Fig. 14 Experimental Results - Viscosity = 200 cp. Sucrose

0

63

3.4 */0

(ft./sec.)

Fig. 14 (a) Experimental Results - Viscosity = 200 cp.Sucrose

14

13

12

1 1

10

9

8

7

6

5

4

3

2

1

0

64

Fig. 15 Experimental Results - Viscosity = 2 cp. - Oil

4

3

2

1

08

06

05

04

03

02

65

' 3 - (J = 0-010 ft./sec. , *** •• •• • • • »

T

\^ 0.0065"+ ’’’ T

■r T T ▼ T ▼ .

»

II 0.0033 . • •• • • •• • •

Run 15 - 0-0A 4, A A A Jk A A A X X X X

t ■ T . ■ 1 t T t f 1 ■ » I f I 1 ■ > » 1 » » f » , > » f f i i ■ ■ ■ » t t » i J I 1 > I ■ . T ■ U 1 I l J . . IIJ.

0 12 3

U (fft./sec.)Or

Fig. 15 (a) Experimental Results - Viscosity = 2 cp. - Oil

66

other ways and are treated at greater length below.

Holdups measured at the same time as the pressure drops

are shown in Figures 11 (a) to 15 (a) complementary to the P graphs.

The plotted values are total holdups each being the sum of a measured

operating holdup and a static holdup estimated from the correlating line

of Figure 9. No correction for liquid evaporation has been applied;

the amount of evaporation was small in every case and certainly

negligible in the preloading range. Methods of calculation and complete

tables of holdups are given in the Appendices.

Holdup was found to follow the course described

previously by many workers. It was substantially constant over the

preloading range and began to rise quite sharply just before the estimated

loading point. Again the runs for the two highest water flows were

exceptional. In these cases no region of constant holdup was discern­

ible; the holdup increased continuously at an accelerating rate as the gas

rate increased.

Since £ - C.Q - Ht , where £0 is the voidage of

dry packing, Equation (6) predicts that, for a given packing,m , the slope

of the P versus UQ line in the preload region should be a function of

Ht alone. The experimental result is shown in the graph of Figure 16

where experimental values of m~z are plotted against Ht .

The values of m used in plotting this graph are the

slopes of the straight lines fitted to the experimental points by a linear

o

1 5

05 -

h Sy m(cp.)

Water 1 o6 A

Sucrose- 45 □O 200 V

AOil 2 X

G

K*

□* v

□ v

▲

.1

Ht (exptl.)

.2

Fig. 16 Experimental Results, m vs. H

regression using the proviso that the line must pass through the origin.

The form m~ is chosen to avoid giving undue emphasis to the high

holdup region and because, since Ap is proportional to the reciprocal

of rn~2‘ , the accuracy of prediction is the same for both,though in

opposite senses. High values of tn imply low Ap and conversely.

As may be seen from the graphs the internal consistency of the pressure

drop data is very good. Individual values of the statistically estimated

_2tolerance on m are given in the tabulated results . An average value

would be about - 0.002. This is apart from any possible systematic

errors in the initial determination of absolute values of P . Considering

the accuracy of the rotameters in particular it appears that the absolute

“I"

values of m would be subject to errors of the order of - 5%.

Just as the values of m are determined in the region well

below loading so also the holdup figures used on the graph are values for

gas velocity extrapolated to zero. As explained above the experimental total

holdups are the sums of experimental operating holdups and interpolated

static holdups . The accuracy of the operating holdups is estimated to

be - 0.002 or - 5% whichever is the greater. Combined with the

+ 0.003 accuracy estimated for static holdup this implies possible errors

in total holdup ranging from - 0.005 at low values of Hto - 0.014

at the highest experimental flowrates. This tolerance is of the same

order as, but rather larger than the size of the plotted symbols on the

68

graph.

69

Considered in the light of these tolerances the results

summed up on the graph of Figure 16 suggest a number of points of some

interest. They suggest first that the primary assumption - that m

should be a function of alone - is not entirely true. In the region

of low to moderate holdups the experimental points are well grouped;

but for holdups greater than about 0.1 the points begin to diverge

^ 2markedly. There is a clearly visible and significant tendency for m

to be less (Ap greater) for low viscosity liquids than for high. This

result need not be surprising. There is no a priori reason to suppose

that the liquid holdup should be distributed in just the same way

irrespective of liquid properties; and if the shape of the gas flow conduit

varies the pressure drops may be expected to differ also. Again this

effect may well be a consequence of rippling in the liquid film, an

effect which will be more important when the liquid film is thick and

when viscous damping is least.

It can also be seen in Figure 16 that the extrapolation

to zero holdup of the trend of the results for wet packing does not pass

through the experimental point for zero holdup. As there is no holdup

error for this point the deviation seems to be definitely significant.

It appears that the first increment of holdup has little effect on pressure

gradient. Again such a result might have been expected. Since it is

held in place by surface tension forces the first portion of the liquid

holdup occupies surface pits and, more particularly the narrow crevices

70

at the points of contact of packing pieces. In neither case is the volume

concerned of much significance for gas flow. It should be noted that the

-2value 0. 12 8 for m at zero holdup is just 10% greater than the value

for 1/p found in the liquid flow experiments. This difference evidently

arises from errors in the several flowmeter calibrations but although the

calibration figures have been checked it has not been possible to reconcile

the results. This difference is just within the estimated + 5% errors of

-2each set of experiments; the measured values of /77 are probably

high and by about 5%.

The most marked divergences of experimental points

from the general trend are seen in the results for the runs with the two

highest water rates - Runs 35 and 3 7 which have been remarked upon

earlier. In Figure 16 the points representing the results of these runs

are shown as open circles. The data for these runs are plotted in

Figures 11(c) and 11(d) with those for Run 34 which followed the normal

course. Several types of anomalous behaviour occurred in these runs.

In both cases there was a finite pressure gradient at zero gas flow, the

sign of a phenomenon called "sucking" to be more extensively discussed

in the next chapter. Large distinct bubbles or slugs of air could be

seen to form at certain points in the packing and to move down the

column with the flowing liquid. As the air flow was increased the liquid

holdup curve rose continuously; no region of constant holdup was discern­

ible. The P curve was also abnormal as can be seen in Figure 11(c).

71

The pressure drops rose rapidly at first and then more slowly and, although

the pressure drops were carried up to the levels where loading might be

expected, no obvious change of slope was seen. The runs had to be

abandoned well before the flooding point because of an excessive flow

of water into the pressure tappings which made the pressure readings

extremely erratic. The slopes reported and used in the graphs are slopes

of the best fitted straight lines - not forced through the origin - for

pressure gradients less than 0.7 inches W.G. per foot. The behaviour

observed in these runs is considered to be beyond the scope of the present

discussion and the results are not used in the correlations.

Summing up then, it appears that the initial assumptions

can be accepted only with some reservations. They are subject to

considerable inaccuracy at large holdups connected with an ill-defined

limit of validity when liquid viscosity is low. Also there is a small

initial portion of the holdup which seems to have little if any effect on

the pressure gradient.

But, accepting the limitations it is still desirable and

at least partly possible to derive a useful correlation based on the

assumptions.

Using the experimental data described it is possible now

to test whether any of the equations previously proposed gives a

satisfactory correlation. Equation (6) may be rearranged to give :

Water

Sucrose

Fig. 17 Experimental Data Compared with Predictions

73

m'z = l /f p'(e )......................................................................................................... (7)

where 4> (6) — 1 for £ =

and the proposed correlating curves are:

Uchida and Fujita (1938)

,// i -15 6.<p (e) - oc e

-2 -IS6 / —IS £ 0m = e / e

m~z = e~^Ht/F............................................. (8)

■Morton et al. (1964)

(j> (6 ) — OC €

m-2 ^(e/£0f/F

m~z = f 1 - Ht/Ga ) /p........................................................... (9)

Brauer (1960)

(t ) - ot(l~(z)/ C3

m-z = £3(l-£0)/F ea(l-G)

m-2 = (1 - Ht /Vj*/f [l+ Ht/(l - ej]........ do)

The curves of these equations, calculated using the

value 0.128 for l/F, are shown in Figure 17 superimposed upon the

74

experimental points .

It is apparent that neither of the theoretically based

equations describes the data satisfactorily. The empirical equation of

Uchida and Fujita comes nearest to giving a good fit to the data and by

suitable adjustment of the empirical exponent an even better correlation

could be produced. The theoretical equations have no such flexibility

and allow no scope for adjustment. Instead of relying upon the purely

empirical form it is preferable to use an expression with some theoretical

justification. As neither Equation (9) nor Equation (10) meets the need

a new approach is wanted; this subject is taken up in the next chapter.

75

Chapter 4

The Pressure Gradient Equation

The independent variables influencing the gas phase

pressure gradient are:-

Column Diameter

Packing Size

Shape

Gas Flowrate

Density-

Viscosity

Liquid Flowrate

Density

Viscosity

Surface Tension O'

Local Gravitational Field J

- and a simple application of the methods of dimensional analysis

suggests that at least seven independent dimensionless variables are

required to describe the state of the system. This is a far cry from the

two independent variables, Rp. and € , in Equation (1). Therefore,

before dealing specifically with the theoretical model it is desirable

to anticipate some difficulties which will appear later by showing,

more clearly than has been done previously, how it is that pressure

D

d

p*/LUL

AA-

76

drop results can be predicted by the comparatively simple form of

Equation (1), what assumptions are used and, more particularly, what

are the limits of validity of the equation. But first there are two items

on the list of variables which call for special comment. These are

packing shape and size.

Shape, when applied to a packed bed has two aspects :

the shape of the individual packing piece and that of the assembly.

The present treatment is intended to be applicable to all packings of the

film type; but it is applied only to Raschig rings. All sizes of Raschig

rings have the same general shape, a hollow cylinder of length equal to

the diameter. Small rings, however, tend for mechanical reasons to

have relatively thicker walls than large ones and geometric similarity

may not be exactly maintained over the full range of sizes. It will be

assumed here that all rings do have effectively the same shape.

This treatment is limited again in considering only

random dumped packings. While it is doubtful that such packings can

be considered random in the strict statistical sense - that is in the sense

that all orientations are equally probable - yet, so long as the column

diameter is much greater than the packing size and the voidages are

about the same, all dumped beds may be taken to have virtually the same

shape. It is commonly suggested that for this to be true D/d should be

greater than about 8. In the experiments described above the ratio had

a value just over 9 and it is assumed that D was not an effective

77

variable. Similarly the equations to be derived will apply only to beds

meeting this requirement.

In this work the scale specification or relevant linear

dimension is taken to be the ring diameter or height, d. Frequently

in discussions of packed beds the chosen relevant dimension is taken

to be the diameter of a sphere having the same surface area or some other

such equivalent diameter. It is tacitly assumed that by the use of such

a dimension in company with a voidage function and, perhaps, a

sphericity all the influences of shape are included and results for very

different particle shapes can be made to agree. But why should they ?

It has been convincingly demonstrated by Fan (1960) that even in the

studies of pressure gradient in single phase flow for which the concepts

were developed the assumptions are of limited value. Where, as in this

case, shape is virtually constant there is no need for such an elaboration;

any relevant linear dimension will serve to define the scale of the system.

The dimension chosen is the simplest available.

The equations to be developed will contain dimensionless

constants whose value must be established by experiment. The constants

are, in fact, shape factors. Their values will certainly change for other

packing shapes.

As a result of the assumption mentioned above column

size may be eliminated from the list of effective independent variables

and the number of dimensionless variables required is likewise reduced.

78

The six remaining dimensionless variables still make a formidable total.

Fortunately, well known and verified experimental results show how the

total can be further curtailed and the system simplified.

In discussing the influence of irrigation on gas phase

pressure gradient it is necessary to consider the interactions between

the gas stream and the liquid film on the packing. These may be studied

under three main headings, the different, though not necessarily

independent ways in which the streams affect each other.

(a) Geometric Interaction. The first and most obvious connection

between the two streams is that they compete for flow space in their

conduit; together they fill the packing void space. As liquid flow and

hence liquid holdup increases there is less room for flow of gas and a

higher pressure gradient necessarily results.

(b) Buoyant Interaction. The simple presence of a flowing gas phase in

the same conduit produces a change - usually a decrease - in the

available head loss in the liquid stream. Effectively it acts against the

gravitational force and it is most easily taken into account by applying

to the term cj wherever it appears a correction factor

(i ~~ ft*/pu ~ 9° Pl ) * *n usua^ case the effect of

this phenomenon is very small. It is described at greater length in a

later chapter.

(c) Interfacial Traction - Surface Drag. With two fluids moving in

79

opposite directions through the same space there must be some drag of

each upon the other at the separating surface. Whether this drag is

significant in a given situation depends upon the other flow resistances

present. In this regard the effects on the two streams may be considered

separately.

Liquid: When no gas is flowing the liquid film is supported

entirely by the solid packing. The only flow resistances acting

upon it are due to liquid viscosity and the tortuous flow path

imposed by the shape of the packing. Apart from the small

buoyant interaction mentioned above this is still true when a

small countercurrent gas flow is established as is shown by the

fact, amply demonstrated by Elgin and Weiss (1939), Shulman

et al. (1955) and many others, as well as in the present experi­

ments, that with moderate gas flows the liquid holdup is sub­

stantially independent of gas rate. If the natural effect of drag

is absent it may safely be assumed that there is no significant

drag operating. Evidently, within this range of gas flows, the

drag imposed by the gas on the liquid surface is small compared

with the flow losses within the liquid film itself.

But as gas flow is further increased the drag increases and there

comes a point where the holdup does begin to increase. This is

the point known as the loading point. It appears to represent

80

the boundary of the region in which the drag of the gas on the

liquid surface is negligible; the point at which the interaction

becomes important.

Gas. The flow situation in a packed tower is such that, as a

result of the continuous changes in flow direction, cross-

sectional area and shape of the gas flow path, form drag is

greatly predominant over skin drag as a mode of pressure loss.

Large rates of pressure loss do not necessarily entail corres­

pondingly large values of shear stress at the boundary. As a

corollary, experiment shows that variations in skin drag have

little influence on the total pressure loss.

By varying liquid viscosity it is easy to produce a wide range

of liquid surface velocities for a given liquid holdup. But, as

will be seen, for such cases the gas phase pressure loss at

a given gas flow is found to be constant.

Again, at least at the accuracy of pressure measurement used

in the experiments to be described, there is usually zero pressure

gradient at zero gas flow, confirming that there is negligible

traction by the liquid film on the gas. With very high flows of

low viscosity liquid this is no longer quite true. Under these

conditions there does develop a finite pressure gradient at zero

flow or, what is equivalent, a measurable gas flow with no

81

pressure gradient. This is the phenomenon described by

Uchida and Fujita (1938) which they called "sucking". But

even in this case in the present experiments the behaviour

seems not to be caused by simple traction. Rather it occurs

by the formation of bubbles or cells of gas which are then

carried down with the liquid. The mode of action corresponds

closely to the pore closure model described by Lerner and

Grove (19 51); more closely indeed than does the performance

near the flooding point which their account was meant to portray.

It represents the onset of "slug" flow familiar in studies of two

phase flow in pipes.

But a very wide range of operating conditions is available

between the loading and sucking limits. Most commercial towers are

designed to work within this range as a matter of practical convenience

and economy. If the limits are exceeded pressure loss begins to increase

very rapidly with little corresponding improvement in mass transfer

efficiency; it is only a short step further to complete failure by tower

flooding. Within the practical range there is negligible dynamic

interaction between the streams. It should be noted that, since high

liquid rate necessarily entails low gas rate at loading, it is possible for

the operating limits of loading on the one hand and sucking on the other,

to merge. At very high liquid rates there may not exist any gas rate

82

for which the interaction between the streams is negligible.

For these reasons the present study deals only with the

flow regime between the stated limits. It is the absence of dynamic

interactions which allows the equation to be drastically simplified.

Within the specified operating limits the liquid flow variables act quite

independently of the gas flow variables. The two may be considered

separately and the pressure gradient equation may be written in a general

way as :

Ap = S[d,Ue,f>0,^a,Sha^,(d,S,a,UL,pL,jiL,Sha?e)].... (11)

or, using the conventional dimensionless forms :

f - f[tea , Shapef (HeL , Fr, (f/p^ g Shape)].................... (12)

including now only four independent dimensionless variables.

The only significant interaction between the streams in

this flow regime is a purely geometrical one. The irrigating liquid

occupies some of the void space in which gas would otherwise flow. In

conjunction with the solid packing, the liquid merely establishes the

boundary of the gas flow conduit, the initial packed assembly modified

by the presence of a liquid film on the packing surfaces. Now all the

details of this film are defined by the liquid flow variables given and

within the preload range Equation ( 12 ) is exactly true.

83

That the required function of the liquid flow variables is

the bed voidage is the natural and simple next assumption. But it is

only an assumption and although it has proved useful in this and in

associated fields it must be tested experimentally. It would seem that

the distribution of the liquid film should be as important as the total

quantity and that this distribution might show wide variation in different

flow conditions. But accepting the assumption, the voidage is certainly

a function of the fluid flow variables listed.

£ - £, - Ht -/ (*SL , FrL >cr/pL9 d\ Shape )........... (13)

and Equation (12 ) becomes :

f - j e, shaPe)......................................... a4)or, what is really the same :

/ Shape; ...................................................... (15)

The final step, the complete separation of these two

remaining variables, requires several further minor assumptions or

reasonable approximations. In the range of gas Reynolds number

(Uq po d/jj J involved, the friction factor for a dry tower is only

a weak function of Reynolds number. With fluid interactions ignored

the situation is just that of a dry tower with slightly changed dimensions

and shape. The assumption that these slight changes cause no

significant change in the Reynolds number function is one that seems

84

reasonable and one which allows further useful simplification.

Equation (12 ) is now brought to the required form :

f = ^ (*£$) ■ 4>' (&).............................................................. (1)

Clearly, following the discussion given above, the further

treatment is confined to flows within the preloading range. This is no

serious restriction since, in practice, it is desirable to operate towers

in this regime to avoid both the danger of flooding and the relatively

high pressure drops with attendant pumping expense incurred at higher

flow rates.

It is appropriate now to examine how holdup influences

the pressure gradient or, more exactly, how it affects the various terms

in the pressure drop equation. The quantities primarily affected are the

effective pore size & and the mean gas velocity in the pores '^r

Neither of them is measurable, nor, indeed, clearly definable so they

are represented in the flow equations by the packing size d and the

superficial gas velocity both quantities being exactly defined and

accurately measurable. In a packed assembly of specified shape any

definable linear dimension or any velocity will be simply related to

these quantities, thus :

S * d ................................................................................... (i6)

•v = /3 UG .......................................................................... (17)

85

When liquid is applied to the packing the effective pore

size is reduced. If a film of mean thickness A is spread over the

packing surface 8 will be reduced to a value about (8 2 A )

The term d representing it in the equation is replaced by d where

d ' ~ (S2 A)/oc = d - ZA/ol.....................(is)

With the flow passages thus restricted the pore velocity

is naturally increased. The flow area is reduced by a factor about

(d/d ) and the pore velocity increased in the same ratio. The

term U representing it in the equation becomes d d / d J

Now the pressure gradient in a dry tower is given by :

9caP» ‘ pa Ud/d ■ / , Shape).............. (19)

and if it can be assumed that the Reynolds number function is the same

in both cases, that is that the shape is virtually unchanged, the pressure

gradient in the irrigated tower will be given by ;

dp = Ap0 (d/d') (2 0)

Pc 4°

86

Noting that d = d at A - 0 Equation (18 ) may be put in the form :

d'/d

where

- i ~ *b/d

f = Z/oc

Also A mean

(22)

(23)

where Ht is the total holdup and Q the packing interfacial area.

For a given shape of packing the product Q d is a dimensionless

constant. (For Raschig rings ad-~5)

Substituting in Equation (22)

<*'/<! - 1 - k. H± ..............................................................(24)

where ft is a constant given by :

H ~ P'/ad or A. ~ ^ /oc ad . . . . . . . . . . . . . . . . . <25>

Substituting now in Equation (21)

Sc Ap - (l - k H€ ) . (fe V(*/d)-J:C^ - Shape J . (26)

or, where Apo is the pressure gradient for the same gas flow in a

dry tower,

APo/Ap = ( 1 - P Ht )5................................................. (27)

that is, for this model

m = ( 1 ~ ft di£ ) //p .............................................(28)

1 5

1 0

05

0

Symbolh(cp.)

Water 1 6

Suero se x 45 200

2

Eq. 29

o▲□y

.1 .2

Ht (expt L.)

Fig. 18 Data Correlated by Equation 28.

88

In Figure 18 a curve of this form is shown superimposed

upon the experimental points. The parameters of the curve were

established by a linear regression of m ^ on . Since it was

doubted whether the points for and for Ht greater than about

0. 1 were properly a homogeneous part of the data, only those points for

0 Ht <0.1 were used in the correlation. As expected, the fitted

curve has an intercept at Ht - 0 greater than the experimental value

0. 12 8. This agrees with the conclusion that the first part of the holdup

has little effect on pressure gradient.

The equation of the fitted curve is:

m~2 = o.l38 (t -2.1 Ht)S ......................... (29)

and it can be seen to give a good correlation of the data.

Clearly the important operational difference between

Equation 2 8 and the theoretically based equations cited earlier is the

appearance of the coefficient k . Suitable adjustment of this parameter

allows the curve to be closely fitted to the experimental points.

That its value is not completely arbitrary can be seen from Equation 2 5.

If the product ad is given the value - typical for Raschig

rings - then /c should have a value about where 06 is

the ratio of effective pore size to packing size. The result fc m 2..1

suggests that the effective pore size is about one fifth of the packing

89

size - a value rather smaller than might be expected but in good order

of magnitude agreement with the model.

holdup is to be calculated from the liquid properties and flowrate as

it must be if the equations derived here are to have any practical utility.

This subject is taken up in the next chapter.

Effect of Initial Voidage

of constant shape, that is, by implication of constant initial voidage.

Real packings, however, exhibit varying initial voidages and this factor

has a strong influence on the pressure gradient both in dry and in

irrigated packings. Since initial voidage was not an experimental

variable this study casts no new light on the question. It would seem

reasonable to adopt the well known rule due to Leva (19 47) that, in

packed beds differing only in voidage the pressure gradient should be

proportional to But Brauer (19 5 7), Whitt (196 0), Sonntag (196 0),

Fan (1960) and Teutsch (1962) aver that, at least for hollow packings,

The term (1~ k ) appearing in Equation (26) is

evidently the function of voidage <f> of Equation (1) and the function

of the liquid flow variables referred to in a general way as

The discussion so far has dealt only with packed assemblies

such a rule is insufficient. It appears that the space within the rings

90

is less useful for gas flow than the space between them and that the

total voidage should be split up into these two parts to then be given

different weightings. This topic is not further pursued in the present

work whose prime object is to account for the modifying effect of

irrigation with liquid.

91

Chapter 5

Prediction of Holdup

i) General

As was suggested in the introduction holdup on irrigated

packing is commonly divided into two parts corresponding to two modes of

occurrence : Static holdup, depending on static properties and operating

holdup resulting from liquid flow. The sum of these is the total holdup,

the quantity assumed to be the primary determinant of variation in flow

resistance. It has been shown by Shulman et al. (1955) that the distinc­

tion is a sound one and that, for purposes of prediction, the two modes

may be considered separately. This course is followed in the following

discussion.

ii) Operating Holdup

(a) Sources of Experimental Data - The theoretical treatment offered

here is tested against a wide range of published experimental data.

Several large collections of experimental results for liquid holdup on

Raschig rings are available. Two very extensive investigations are those

of Uchida and Fujita (1936, -37, -38) and of Shulman and his co-workers

(1955). A shorter series and one more restricted in scope is that reported

by Otake and Okada (1953). The ranges of the experimental variables

studied by the three groups, with some properties of their packings are

set out in Table 5.

92

o-QaCO■

◄

X

0

o 0

M—

t

0CO

60

oo \

--H co

^

0

0

0h !■

M 73

-XCONCOCOICOCO

*COIN

*COnoCO

*COIN.IoCO

*COINIoCO

oCOCMI

oCOI

LO0I--10H

XSO

O

IN

CM

r-tIO

IN

CDCD

CMCM

COCO

ININ

COCO

CO00

XS.

1.

.1

ii

1S

OO

oO

oo

rHCO

CMCM

COCO

COCD

CDIN

INN

LOCD

ININ

ININ

•.

..

..

•.

••

Oo

oO

oo

Oo

OO

xs0

00

06

aa

a6

aa

-i—i-r-t

-rH-rH

oo

ou

oo

o.

CMo

LO0

LOo

LOO

OCD

LOLO

CDCD

LO-r-t

••

••

••

•.

•.

•Q

o1—1

I—l1--t

r-H1-1

CSIr-H

r-HCM

CO

0Sh0S~<o£

0+->0d0S' ■ I 0 x: co

0+->0Ph

C<30X3-i-i

XoID* A ssum ed . The liq u id w as w a te r .

93

It can be seen that the experimental variables cover very

wide ranges. In most cases the ratio ^ is sufficiently large for the

column diameter to be ignored as an effective variable. For packings of

uniform shape the dry voidage €q and the dimensionless packing density

Nd ought to be constant and it can be seen that in this regard the data

leave something to be desired. This fact, no doubt, accounts for some

of the scatter found in the final results.

The operating holdup used for correlation was the value at

zero gas flow or, where a range of gas flows was studied, the value for

gas flow rate extrapolated to zero. The other condition applied in the

selection of data was that the flows should be definitely below loading and

that sucking, if present, should be unrestricted. For some of the Uchida

and Fujita runs for very large flows no definite preloading range could be

detected and the data were rejected for that reason.

(b) Theoretical Considerations

Limiting Flow Regimes - Forces acting on fluid particles are:

Gravity

Viscous Drag

Inertia

While gravity is always the driving force either viscous or inertial forces

may predominate as the resistance. Thus, two limiting flow regimes

may be distinguished, namely, the gravity-viscosity and gravity-

94

inertia regimes. In general it can be stated that these will occur at low

and high values of Reynolds' Number, respectively. That is, at low

velocity or high viscosity losses will be mainly due to viscous drag in

an essentially laminar flow. In the converse case the losses will be

caused mainly by turbulence arising at sudden changes of flow path.

Gravity-Viscosity Control

Behaviour in this regime has been described by several workers,

notably Nusselt (1916) and Davidson (1959). The basic assumption is

that the liquid is everywhere at its terminal velocity, no accelerations

need be considered.

The model used is an assembly of flat surfaces inclined at

angle, 0 , to the horizontal and having a liquid film of uniform thickness,

2 3A / flowing down the surface of total area, Q ft /ft . The liquid

2loading is L lb/(sec.) (ft. ) of horizontal cross section.

At any cross section of the assembly the width of the surface

will be a sin Q and the liquid loading may be expressed in another way

as q — l/ lb./(sec.) (ft. width of surface). Then by the well known

derivation of Nusselt ,

= a AH mean (31)

9

8

7

6

5

4

3

2

1

0

X ■ MA

-. N■ •

\ *«4

A •

*4v* i4*.x “*•V.

• ▲•a

A •

• X *AX A * A ^

v* #* *2 *

_j________________ ■ ■________________ i i

-10 12 3

Log (Re )

Fig. 19. Holdup Data Plotted according to Eq. 34.

96

H Lp cj sin 9

(32)

For standard packings the packing size, d , is a more

convenient quantity than the area, O . For packings of constant shape

the product Old is a dimensionless constant.

Noting also that LAtj* £/ the superficial liquid velocity,

we may write:

The first term is a coefficient depending on the inclination

of the surfaces. The second is equal to the quotient of the Froude and

Reynolds numbers and will be referred to as the Film Number, Fi. The

third term may be combined with the first as a shape factor for a given

packing. The equation may be written briefly as:

H = S ( (34)

For dumped Raschig rings ad~5; and for G taken to be

from 60° to 80°, 5 is calculated to be in the range 4.2 to 4.5.

Figure 19 is a plot of s. Re. It can be seen that

at low Reynolds numbers approaches a constant value in the

range 5 =2 to 3. At high Re the holdup is greater than Equation (3 4) would

predict.

Fig. 20 Gravity - Inertia Model.

98

Gravity-Inertia Control

The assumption made here is that energy losses resulting

from viscous drag are negligible. The only losses occur when the natural

liquid flow path is impeded from time to time and energy is dissipated in

turbulence. This dissipation is an effect of liquid viscosity but the

amount of energy dissipated is not strongly dependent on the magnitude of

the viscosity.

except that the flow is interrupted, at intervals 1 by steps, as shown in

Figure 20, at each interruption the liquid loses a fraction, R , of its kinetic

energy before proceeding down the next slope. Other losses are negligible.

The model for this situation is similar to the previous one

If the initial velocity is we may write:

n VL 2 = 2 cj l sin 9 (35)

where (36)

At distance p down the plate

(37)

(39)

(38)

now A r

99

^mean = 1A J ^ r dro

VJ L___________p a sin 6 (J l sun d) ^

(n + l)z - 1n %■ ........(42)

But

and as before, H = a A mean (31)

Froude number. The others may be combined to form a single coefficient,

a shape factor. The value of J , in a packing must be related to the

packing size and might be expected to be of about the same magnitude.

Thus, assuming Z to be equal to d and R and 9 to be independent of

liquid rate the equation reduces to :

H = S ' ( Fr J ^ (44)

-2-10123Lo g (Re)

Fig. 21 Holdup Data Plotted according to Eq. 44.

101

where :

s sen &)h. (n + 1 ) 2 ~ /

h.(45)

For values of R ranging from 0.5 to 0.9 and 0 from

60° to 80° calculated values of 5 are in the range 0.61 to 1.26.

(Note that holdup in falling drops or streams would follow

a similar law, 9 now being 90°).

Figure 21 is a plot of ///Fr^vs. Re. In this case it may

be seen that at high Reynolds number approaches a constant value

of about 3. At low Re the holdup is greater than can be accounted for by

Equation 22.

(c) The Correlation

From Figures 19 and 21 it is evident that, except for some

of the points at very low Reynolds numbers, the experimental results

cannot be described by either Equation (34) or Equation (44) but appear to

be in a transition region. An interpolating expression is required to cover

the transition. A simple expression is the sum of the terms for the

limiting conditions.

H S ( Fi)^ +■ 5 Y FrJ (46)

For convenience in developing a correlation this equation

is transformed to the straight line expression

1.6 1.8 2.0

S'Fig. 22 95% Joint-confidence Ellipse for 5 and S*.

103

H0/Fl^ “ ^ 5 ' Fr1/F/.................... (47>

The experimental data have been examined using this

equation and coefficients S and S found to give the line of best fit.

A joint 95% confidence ellipse (see Acton (1959)) for S

and <5 is shown in Figure 22. The indicated best values of 2.2 and

1.8 compare well with the order of magnitude estimates of 4 and 1 given

above.

The experimental points are shown in Figure 23 plotted

according to Equation (47) the line of best fit is the final proposed

equation:

Ho = 2-2 Fu ^ + /• 8 Fr ^ ...................... (48)

As may be seen from Figure 24 this equation, with two

arbitrary coefficients, satisfactorily correlated all the data over a

range of almost five orders of magnitude in Reynolds number.

For comparison the Otake and Okada relationship is shown

in the same way in Figure 25.

The equations are:0 44 —0.37 /

H0 =2.1 Fr Re O.O] < Re <f/0

H = 6.3 Fr Re 10 Re,(Z00o

and it may be seen that the agreement is only slightly better. Note,

104

Fig. 23 Holdup Data Plotted according to Eq. 47.

105

( d*i»H /

oid

oh ) 6on

/'■

/

Log (R e )F ig . 24 E quation 48 C om pared w ith d a ta .

106

COCNOCNl

( dxaH /o

ido

h ) 6 on /

Lo g ( R e)F ig . 25 O take and O kada E quation C om pared w ith D a ta .

Log (

HCal

c/ ^e

xp

0.3

0.2 f

0.1

0

0.1

■0.2

0.3

-0.4

A **■ A A

+ 20%

-A-

-20%

a iA - »i#

*4

A * ** J\A \/ I v B

A *><*

• XA . • •

*» . * * .I —-----

xJTa■ ^ i

H = 16.1 Fr ** Re"V<

-2 -1 0 1

Log {Re )

Fig. 25(a) Mohunta and Laddha Equation Compared with Data.

108

however, that the range of Reynolds numbers had to be separated into two

parts, leading to a total of six empirical constants in the two equations.

Finally the same experimental data are compared with the

prediction by Mohunta and Laddha (1965). Using a value of 0. 8 for3

the dimensionless packing density Nd (measured values are in the

range 0.62 to 0.83) the correlating equation becomes:

H = 16.1Fr*Re~*o

The comparison is illustrated in Figure 25 (a) and it can be

seen that in the low Reynolds Number range this equation gives a most

unsatisfactory fit to the data. It could be useful for Re greater than

about 2 with, perhaps, a downward adjustment of the coefficient.

(d) Effect of Surface Tension

This general correlation has been developed without taking

any account of surface tension. It is desirable to re-examine the data

to see whether any surface tension effect can be found.

For this purpose the data of Shulman, et al. (19 55) are

relevant. In these experiments a wide range of surface tensions was

examined using both low surface tension organic liquids and aqueous

solutions of widely varied surface tensions.

The relevant data are shown in Figure 26 plotted according

to Equation (48). The points cover quite a wide range but in an

+ 20%

1 2 3Log(Re)

Liquid

•

Surface Tension, Dynes/Cm.

Symbol

Water 73 •Calcium chloride solution 86 ■Petrowet solution 58 ♦Petrowet solution 43 ▲Petrowet solution 38 ▼Methanol 23 XBenzene 29 •¥

Fig. 26 Operating Holdup - The Effect of Surface Tension

no

apparently random fashion. No residual surface tension effect is dis­

cernible.

described independently of the ambient gas. It has been tacitly assumed

that the gas flow has little influence on the film; that the gas density

and viscosity are negligible. In the usual cases the assumptions are

nearly true and the effect is indeed small but it is useful to investigate

how the small effect occurs.

as it affects the head available to drive the liquid stream down the tower.

Where no gas phase is present the frictional head loss in the liquid must

be 1 foot of liquid per foot height of the tower. But in real cases,

because the two streams flow in parallel, the pressures in each phase at

a given level must be equal, which fact causes a change - usually a

decrease - in the available head.

flow situation each of them causes a pressure increasing downwards

through the packing. As a result the available head loss in the liquid

(e) Effect of the Gas Stream

Up to this point the behaviour of the liquid film has been

The presence of the gas phase is significant mainly insofar

term

The pressure gradient in the gas phase is the sum of a static

and the frictional term An . In the usual countercurrent

film becomes ft. of liquid

Ill

per foot of packed height.

The effects may most easily be incorporated into the

predicting equations as modifying the influence of gravity on the liquid

film. Thus, wherever it appears, the term CJ should be replaced by

thought of as a buoyancy effect.

It is important that the final term in the correcting factor

should not be taken as describing the traction of the flowing gas on the

liquid film. Where it occurs this phenomenon produces an additional

increase in holdup. It appears in fact, that, at least in the Reynolds

number range commonly observed experimentally for the gas flow, the

skin friction effect is small below the loading point and it seems probable

that it is the appearance of significant traction which produces loading

behaviour. The gas phase pressure loss occurs principally by an

expansion-contraction mechanism and involves little significant traction

on the liquid surface. The observed increases in liquid holdup with

increasing gas rate seem to be sufficiently accounted for by the "buoyancy"

mechanism described above but the available data are not sufficiently

accurate to verify the point.

and the combination may be

Thus, since operating holdup is roughly proportional to g-0. 44

the correcting factor may be approximated by

112

when the gas density and the pressure gradient are small. It is generally

found that in experiments using air as the gas phase loading takes place

at a gas pressure gradient of about 1 inch of fluid per foot depth of

packing, i.e. gc Ajo/J pL ~ 0.083

The result that operating holdup should increase by about

4% between zero gas flow and the loading point is in reasonably good

agreement with the results reported by Prost and Le Goff (1964), Shulman

et al. (19 55) and many others.

(f) Scope of the Correlation

The experimental data used in developing the correlation

were taken from experiments with ceramic Raschig rings only and the

resulting equation applies strictly only to such packings.

An equation of the same form should be applicable, however,

to any packing of the film type, but the shape factors S and «S must

be expected to take on different values when the packing shape is changed.

113

iii) Static Holdup

In order that the proposed correlations can be tested against

available experimental data an estimate of static holdup is required. In

view of the paucity of static holdup data it is fortunate indeed that the

static holdup usually makes only a minor contribution to the total. The

results of Shulman (1955) for static holdup on stoneware rings have been

examined to find some approximate general relation for such packings

which should be adequate for the present purpose.

On the reasonable assumption that static holdup is

influenced by gravity and surface tension forces only, the basic general

relation is that given in Chapter 3 above:

= j- [^/oyc/2 > Shape y................................................. (2)

- where the term "shape" includes, besides the gross form

of the packing piece (ring, saddle, etc.) such fine details as porosity and

surface roughness.

That these details of shape must be considered is shown by

the graph of Figure 2 7 where values of and from Shulman's

experiments are plotted for the various packings and irrigating liquids

studied, just as was done in Figure 9 for the experimental results of this

present investigation. It can be seen from the graph that the experimental

points for various liquids on 1 inch rings are well grouped and clearly

4

Hs

X 10*

3 ■

G

• /

0 l_________ ._________ ._________ .---------------0 1 2 3 4

_2_ x102pgd

Liquid Surface Tension (dynes/cm.)

Density Ring Size (Inches)

Symbol

Water 73.0 1.00 1.5 O» « » 0.5 G■ " 1.0 O

CaCl, Solution 86. 3 1.32 o« 2 80. 3 1.23 o" 77.4 1.17 G

Petrowet M 57.S 1.00 □N " 43.0 " a" * 38. 0 " B

Sorbitol " 73.0 1.30 A" " ■ 1.27 V

« 1.22 ABenzene 28.9 0.88 +Methanol 22.6 0.80 X

Fig. 2 7 Data of Shulman et al.

5

115

define a straight line correlation with good precision. This is as might

be expected when all details of shape are held constant. The few points

for the single liquid, water, on several sizes of rings, also seem to show

a clear trend, but a trend quite different from the first. Thus it appears

that an equation of the simple form:

= ......................................................... (2a)

will not give a satisfactory general description.

On closer examination of the data it was noticed that the

results for water on the three different sizes of rings implied a mean film

thickness hj /0 almost constant at 0. 003 inches. This fact suggests

that ring size as such is not the significant variable but that it influences

liquid static holdup only insofar as small rings have a greater specific

surface area than do large ones. As was noted earlier, for a given shape

of packing piece the interfacial area is given by:

Q = Constant//^/ (49)

With such a small film thickness it is reasonable to suppose

that, in the absence of significant solid porosity, the static holdup

would depend critically upon surface details.

Now the rings used in Shulman's studies were all from the

same manufacturer and, presumably, were made from the same materials

—5— X 103 (ft.) pg d

Liquid Surface Tension (dynes/cm.)

Density (gm./ml.)

Ring Size (Inches)

Symbol

Water 73.0 1.00 1.5 9" " 0. 5 O" M " 1.0 ©

CaCL Solution 86.3 1.32 " o„ L „ 80. 3 1.23 " o" " 77. 4 1.17 " ❖

Petrowet " 57.5 1.00 " □.. « 43.0 " " a.. 38.0 " " D

Sorbitol " 73.0 1.30 " A» " 1.27 .w v.. •• 1.22 " A

Benzene 28.9 0.88 " +Methanol 22.6 0.80 XSucrose Solns. (This woric) See Table 3 0.63 •Dieseline " " ” M

Fig. 28 Shulman's Data according to Eq.52.i

117

and by the same processes. The surfaces could be expected to be of the

same shape and the scale of roughness could be characterised by a single

linear dimension constant for all ring sizes.

These considerations suggest an equation of the form:

H*/a8 - / ( ^/pgS2).............. (so)- where 8 is the dimension describing the scale of roughness, a real

enough quantity though very difficult to measure or to define unequivocally.

The simplest form of the functional relation is the linear type:

Hs = oc (acr/pgS)..................................................................... (51)

Noting again that the product qd is a dimensionless constant

and that, for this case, 8 is constant, the equation becomes:

Hs - B ( er/ pjd) .............................................................. (52)

- where B^OCOd/^ and is a dimensional constant proportional to the

scale of roughness.

The experimental points are plotted according to this

equation in Figure 2 8 and it can be seen to give a good correlation. Also

shown is the best fitted straight line. Its slope B is 16 ft ^ or 0.53 cm ^

where the other terms are expressed in consistent absolute units. This

value of B will be used with Equation 52 for the prediction later on of

static holdup on ceramic rings.

118

Also shown on the graph of Figure 2 8 are the experimental

results for the static holdup measurements in the present work. These

data were not used in the correlation but they do show fair agreement

with it, although, considering what was said above concerning the

critical importance of the superficial roughness, there is no compelling

reason why they should do so.

15

10

05

0

XP

fJL Symbol

Wq t e r(cp.)

1 •' 6 ▲

Sucrose - 45 ■200 ▼

Oil 2 X

A

.1 -2

Ht (calc.)Fig. 29 m~L vs. Calculated Holdup.

120

Chapter 6

Final Equations and Conclusions

It is possible now to combine the results established in

earlier chapters into a complete set of equations by which pressure

gradients can be predicted from a knowledge of ring size, fluid

properties and fluid flowrates only. The equations will be developed

from the experimental results of the present work and their validity will

be tested against a set of published data.

First the experimental pressure drops are correlated with

calculated, rather than experimental, holdups - calculated as the sum

of static holdup interpolated from the experimental line of Figure 9

and of operating holdup calculated from Equation (48).

The data are illustrated in the plot of Figure 29. It is a

-2curiosity of the method that this plot of m against calculated holdup

gives a rather better grouping of the points than does that against the

experimental values. But clearly there is still obvious divergence in

the points for holdups greater than about 0.1.

At this point, therefore, it is necessary, before attempting

a correlation to decide what is to be the scope of the equations - to

choose whether all the data points are to be used or whether, in the

area where the deviations appear, some or all of the results should be

passed over.

.15

Ht ( CO Ic.)

Fig. 3 0 Data Correlated by Eq. 53

"1

122

Now in fact, the form of the proposed pressure drop equation

gives the best fit if the low viscosity, high holdup points are excluded.

While it would be unwise to build an argument on this fact, it does lend

support to the view expressed earlier that new phenomena and more complex

interactions come into play under just these conditions. But equations

applying only to irrigating liquids of high viscosity will be of limited

value since the use of such liquids in packed towers is certainly

exceptional. For these reasons it appears safest to attempt a correlation

only for holdups less than the critical value of 0. 1 and to leave the

higher holdup region for further investigation. The range covered

includes the majority of practical cases.

On this basis the equation of the best fitted line is

m~z = 0.14-0 (1 - 1.33 Ht) ...................... (53)

which curve is included on the graph of Figure 30, opposite.

On the assumption that there is a threshold value of the

holdup below which the pressure drop is substantially that of the dry

tower the results can be reconciled with those of the single phase

-2experiment by applying the limitation that /77 can never be greater

than 0. 128, the dry tower value. This rule implies that for values of

the total holdup up to 0. 009 the pressure gradient is unchanged.

To take account of this possibility the form of the equation

123

is modified to:7 5"

m '2 = 0.128 fl - 2.0 (- 0.01}/'L ..................................... (54)

w'2 > 0-128-2

The value 0. 12 8 for m in single phase flow corresponds

to a value of 7. 8 ( = 1/0. 128) for F . It leads to:

<f> He) = J. 8 (l +- S2/z_e ) ........................................(55)

Also shown in Figure 3 0 is the extrapolation of the curve

of Equation 53 into the high holdup range. It can be seen to give a

good fit for the data for high viscosity fluids but to give low prediction

of pressure gradient for the low viscosity fluids at high flowrates.

Using Equation 54 as the final predicting expression the

equations may now be brought together into an almost complete set

which should give useful predictions for values of total holdup up to

about 0.1.

f - d&P3/p0U* - f> (Ke) ■ 4>‘(&)............................. (r)

0 fee.) = 7‘% (l + 52/Re ) ............................................ (55)

f(e) = [1 -l.o (Ht-0.0i)] ..............................(56)

K 1

124

Ht H0 + H' by definition

H = Z-Z Fi. % + Fr ^ .................................................................. (48)

The only doubtful quantity is the static holdup Hs .

No general equation is available; it should be evaluated experimentally

for each packing and liquid. In the absence of such data the static

holdup may be ignored with usually only minor error in the prediction of

pressure gradient or, for stoneware rings, it may be estimated by:

As an independent test of the validity of this set of

equations a comparison has been made with the experimental results of

Lubin (1949). In this work water and dextrose solutions of viscosities

up to about 15 cp. were used to irrigate rings of nominal size from

3/4 inch to 2 inches in a tower 24 inches in diameter packed to a depth

of about 8 ft. The gas phase was air. Measured properties of the

packings are shown in Table 6 below, with those for the packing used

in the present work given for comparison.

LEGENDRing size (in.)Dry packing

(approx.) (cj)J_____

Ht (calc.)

Fig. 31 Final Equations & Data of Lubini

126

Table 6

Ring Size Voidage Number/ft N dd

(inches)o

N

LUBIN

34 0. 742 2530 0.618

1 0. 685 1207 0.695

0. 711 381 0. 744

2 0. 734 169 0. 783

This Work

0. 63 0. 701 5197 0. 766

The results are displayed on the graph of Figure 31. Values of

the ordinates (m 2J for points on the graph were calculated by treating

the data in the same way as has already been described for the experi­

mental results of this present work. Total holdup values were calculated

using Equations (48) and (52). The curve of Equation (54) is drawn

onto the plot of experimental points.

It can be seen from the graph that these experimental data are in

fair accord both among themselves and with the curve of the proposed

equation. That the points fall below the predicting curve at high

holdups is as might be expected for irrigating liquids of these compara­

tively low viscosities, but the divergence begins at rather lower holdups

127

than the value of 0. 1 observed for the experimental results of the present

-2work. The scatter in the absolute values of m is about the same at

all holdup levels but the percentage deviations are obviously more serious

in the high holdup range.

Some of the scatter in the data can certainly be ascribed to

the variations in shape of the packed assemblies both within Lubin's

work and in comparison with the present work. The variations are evident

in the values of 60 and N d^ in Table 6. Again, the differences in

tower/diameter packing size ratios ( 9 : 1 in this work vs. 12 : 1 to

32 : 1 in Lubin's ) or in tower height/tower diameter ratio (8.5 : 1 vs.

4:1) may well be of some importance. As was noted earlier visual

observation of the tower operation indicated possible channelling and

wall flow at high liquid rates. It has been observed by Baker et al. (19 35)

and many later workers that these phenomena are more pronounced as

tower height is increased or diameter decreased and it may be they are

responsible for part of the observed differences.

It should be remarked here that the trend of Lubin's data

further than Equation 53 away from the previously proposed theoretical

relations and towards the empirical equation of Uchida and Fujita. In

terms of the form of equation developed in this work, the combination of

-2positive deviations of the m data from the curve at zero holdup and

negative at high holdups suggests that perhaps a value of the coefficient

128

/c less than the 2.0 of Equation 56 should be adopted. But the Lubin

data are neither so accurate, so homogeneous nor so consistent among

themselves as to make them preferable to those of the present work.

They cannot be considered decisive either as confirmation or disproof

but do seem in general to give support to the principles stated.

In view of this and since no investigation has been made

of the influence of variable initial voidage it would seem premature to

offer the equations which have been developed as the final correlation

for pressure gradient in ring-packed towers. But the proposed theoretical

approach does supply a methodology for the final solution. In the

absence of better information the equations have been shown to give

reasonably accurate predictions if their use is confined to the moderate

holdup region.

129

Suggested Future Work

The results achieved in this investigation suggest that

further work could be profitably pursued in the following areas -

i) Measurements of the effects of changes in the initial

packing density and voidage on both one and two phase flow.

ii) Holdup and Pressure drop measurements in towers

of a size more closely representing commercial practice

taking particular notice of the phenomenon of channelling.

iii) Measurements on commercial packing pieces of other

shapes. The Intalox saddle and the Pall ring in particular

seem to have become more important than the traditional Raschig

rings and reliable data for these packings is needed.

iv) Further study of the flow limiting phenomena in the

high holdup region.

v) A thorough investigation of the factors influencing

static holdup.

130

NOMENCLATURE

FLFr

Re

Film number, Fr/Re, dimensionless

Froude number, U /gd, dimensionless

Reynolds number, , dimensionless

aBCd

DfF

d%G

H

Hc

"sH.

-I 2. 3interfacial area of packing, L , ft./ft.

constant in Eq. (26), L'1, ft.1

constant, dimensionless

packing size, ring diameter or height, L, ft.

column internal diameter, L, ft.

friction factor (d Appc/p(J*) • dimensionless

constant in Eq. (3), dimensionless

local gravitational acceleration, LT~2 , ft./sec }

conversion factor = * ^orce / \ poundal, dimensionless

superficial mass velocity of gas, ML 2 T-1 , lb./ft.2, sec.

holdup, operating holdup, ft?/ft^ , dimensionless

operating holdup " "

static holdup " "

total holdup " "

constant, dimensionless

constant, dimensionless

131

a length, L, ft._ 2 _ i r

superficial mass flow rate of liquid, ML T lb./ft.

mass flow rate of liquid in film, ML ^ lb./sec. ,f

d P/d £/. , dimensionless

constant = R/(l - R), dimensionless

-3 -3number of packing pieces percubic foot, L , ft.

k+ 52/%e)Lix 1, ft./sec.

-2-2 2pressure gradient, ML T , lb /ft. , ft.

distance, L, ft.

fractional loss of kinetic energy, dimensionless

constants, shape factors, - dimensionless

superficial fluid velocity, LT \ ft./sec.

mean fluid velocity in pores, LT \ ft./sec.

velocity of liquid in film, LT ^, ft./sec.

Greek Letters

a,/3/= S = S' =

A =

constants

scale of surface roughness, L, ft.

effective pore size, L, ft.

liquid film thickness, L, ft.

, sec.

:. width

132

£ voidage, fractional free space, dimensionless

Co = voidage of dry packing

9 = angle of inclination to horizontal

M - dynamic viscosity, ML ^ T ^ , lb./ft. sec.

v =

P -

2 -1kinematic viscosity, L T , ft./sec.

density, ML ^, lb./ft.^

& =-2

surface tension, MT , lb./sec.

Subscripts

L Liquid Phase

G Gas or Vapour Phase

133

Literature Cited

Acton, F.S., "Analysis of Straight-Line Data", Wiley, New York, (1959)

Baker, T., Chilton, T.H., and Vernon, H.C., Trans. Am. Inst. Chem. Engrs. 31, 296 (1935)

Barclay, G.R., Miniwatt Digest 3, 71 (1964)

Barth, W., Chem. Ing. Tech., 23, 289 (1951)

Bates, F.J., "Polarimetry, Saccharimetry and the Sugars", N.B.S.Circular No. C 440, U.S. Govt. Printing Office, Washington, (1942)

Brauer, H., V.D.I. Forschungsheft No. 457 (1956)

idem. Chem. Ing. Tech. 29, 785 (1957)

idem ibid. 32, 585 (1960)

Carman, P.C., Trans. Inst. Chem. Engrs. 15, 150 (1937)

Clay, H.A., Clark, J.W. and Munro, B.L., Chem. Eng. Progr. 62,No. 1, 51 (1966)

Davidson, J.F., Trans. Inst. Chem. Engrs. 37, 131 (1959)

Eckert, J.S., Chem.Eng.Progr. 57, No. 9, 54 (1961)

Eduljee, H.E., Brit. Chem. Eng. 5, 330 (1960)

Elgin, J.C. and Weiss, F.B., Ind. Eng. Chem. 31, 435 (1939)

Ergun, S., and Orning, A.A., ibid. 41, 1179 (1949)

Ergun, S., Chem.Eng.Prog. 48, No. 2, 89 (1952)

Fan, Liang-Tseng, Can. J. Chem. Eng. 38, 138 (1960)

Feind, K., V.D.I. Forschungsheft No. 481 (1960)

Fenske, M.R., Tongberg, C.O. and Quiggle, D., Ind.Eng.Chem. 31, 435 (1939)

134

Forchheimer, P. , Z. Ver. deuts. Ing. 45, 1782 (1901)(quoted by Scheidegger (195 7)

Hydronyl Limited, London, "Tower Packings", Bulletin TP 33 (1963)

Jesser, B.W. and Elgin, J.C., Trans. Am. Inst. Chem. Engrs. 39, 277 (1943)

Kestin, J. and Whitelaw, J.H. , Intemat. Joum. Heat & Mass Transf. 7, 1425 (1964)

Lemer, B. J. , and Grove, C.S., Jr., Ind. Eng. Chem. 43, 216 (1951)

Leva, M. , Chem. Eng. Progr. 43, 549 (1947)

idem, Chem. Eng. Progr. Symp. Ser. 50, No. 10, 51 (1954)

Longfoot, J.E. , Miniwatt Digest 4, 103 (1965)

Lubin, B. , Ph.D. Thesis, University of Missouri (1949)

Mach, E. , V.D.I. Forschungsheft No. 375, 9 (1935)

Mersmann, A., Chem. Ing. Tech. 37, 218 (1965)

Mohunta, D.M. andLaddha, G.S., Chem. Eng. Sci. 20, 1069 (1965)

Morton, F. , King, P.J. and Atkinson, B. , Trans. Inst. Chem. Engrs. 42, 35 (1964)

Nusselt, W. , Z. Ver. deuts. Ing. 60, 541 (1916)

Otake, T. and Okada, K. , Kagaku Kogaku 17, 176 (19 53)

Perry, J.E. (Ed.), "Chemical Engineers' Handbook" 4th Edition-, McGraw - Hill, New York (1963)

Prost, C. and Le Goff, P. , Genie Chim 91, 6 (1964)

Reynolds, O. , "Papers on Mechanical and Physical Subjects", Cambridge University Press (19 00)(quoted by Ergun and Orning (19 49))

135

Scheidegger, A.E. , "The Physics of Flow through Porous Media",Univ. of Toronto Press, Toronto (1957)

Schrader, H. , Kaltetechnik 10, 290 (1958)(Quoted by Teutsch (1962))

Sherwood, T.K. , Shipley, G.H. and Holloway, F.A.L., Ind. Eng. Chem. 30, 765 (1938)

Shulman, H.L. , Ullrich, C. F. and Wells , N. , A. I. Ch. E. J. ,1, 247 (1955)

Shulman, H.L. , Ullrich, C.F. , Wells, N. and Proulx, A.Z. , ibid. 1, 259 (1955)

Sonntag, G. , Chem. Ing. Tech. 32, 317 (1960)

Teutsch, T. , Doctoral Dissertation, Technische Hochschule Munchen (1962)

idem. Chem. Ing. Tech. 36, 496 (1964)

Uchida, S. , and Fujita, S. , J.Soc. Chem. Ind. (Japan) 39, 876,432B (1936)

idem, ibid. 40, 538, 238 B (1937)

idem, ibid. 41, 563, 275 B (1938)

Whitt, F.R. , Brit. Chem. Eng. , 5, 179 (1960)

136

Appendix 1

Calculations

Most of the calculations were carried out by computer;

either the University's IBM 360 Model 50 or the IBM 1620 of the Faculty

of Applied Science. This section is therefore devoted mainly to describ­

ing the arithmetical basis of the computer programmes shown in

Appendix 2.

Common to many of the calculations are the data given

below :

Column Diameter D

Column Area

5.75 inches

0. 1803 ft.2

0.634 inches

0.479 ft.

Packing Size d = 0.634 inches = 0.0528 ft.

Packed Height = 55 inches = 4.604 ft.

3Packed Volume = 0.830 ft.

2Gravitational Acceleration g = 32.142 ft ./sec .

(a) Air

i) Rotameter Calibrations - Calibration charts for the larger rotameters

were supplied by the manufacturers and ± 2% precision guaranteed. The

smaller meters were separately calibrated against a wet test meter.

This was done for meters Size 7A, 10A and 18A. A check was also made

137

over the lower part of the range of meter 35A. Where their ranges over­

lapped meters 35A and 47K were checked and found to be consistent.

Meters were calibrated by placing them in series with

the standard meter and timing with a stopwatch an integral number of

meter revolutions .

For uniformity and for comparison with the manufacturers'

data all calibrations were brought to a common basis of gas specific

volume, 13.06 ft.'Vlb. - the specific volume of dry air at 15°C and

760 m.m. Hg. absolute pressure. For meters of the sizes used the

volumetric flow for a given rotameter reading is inversely proportional to

gas density. Thus Q the volumetric rate at standard density for a

given reading was calculated from Q , the measured rate and the actual

specific volume Vm by:

4s - 4m Sl3.°(,/Vm'

The actual specific volume was estimated from measured

absolute pressures and wet and dry bulb temperatures. The complete

form of expression used for the calculation of air flows in calibration

runs was

Q — Measured Volume (ft.^) x 60 x y/ 13.06s ,-------

(c.f.m.) Time (seconds) x y

ii) Gas Velocity - In calculating gas velocity in the column it was

necessary to take account also of the difference in gas density between

the rotameter and the column, caused by differences in pressure,

138

temperature and moisture content.

The pressures above atmospheric at the rotameter entrance

and in the column were measured by mercury U - tube manometers.

Added to the barometric pressure these gave the absolute pressures at

each location. The humidity of the inlet air was estimated from measure­

ments of wet and dry temperatures made after each run. Air in the column

was assumed to be in equilibrium with the irrigating liquid. The absolute

humidity H (lb. of water per lb. of dry air) and specific volume at 1 atm.

pressure (ft.3 per lb. of dry air) were taken from the graphs given by

Perry (1963). Actual specific volumes in the rotameter, |/ft , and in

the column, V were calculated by:

(both in cm. Hg .)

The difference between the actual mass rates of gas flow

in the rotameter and in the column was taken into account by the factor:

Thus the gas rate in the rotameter was calculated from the

calibration chart figure by:

1/ 54 Humidity Correction * Pressure Corrn.

Humidity Corrn. = 1 / ( 1 + H )

Pressure Corrn. = 76 /(Barometer + Manometer Rdg.)

139

then

<?, 4 v.ROT

COL i H.

14ROT / l~lROT

finally the superficial gas velocity 64 (ft./sec.) is

given by:

64 = /Column Area K 6 0

= gs * Krw. * (l +■ IjcoL ) X _____________ 1____________

*(l+H«0r) 60 * 0.1203 x/Tyoi

UG = 0- 02.55 J * K:oi. ~( l + ^COL )

* a - wfoj

140

iii) Pressure Gradient - The pressure difference was measured in

inches water gauge over a 3 foot measuring length using gauges calibrated

against a water column. The measured difference was modified by a very2

small gravity correction and converted to the desired units (lb.^/ft. , ft.)

by:

Ap Measured Diff. x 5.198 3 x 1.001

n

Ap(lb.^/ft. ,ft.)= 1.731 x Measured Diff. (in.W.G.)

iv) Viscosity - Air viscosity was calculated as a function of tempera­

ture by an equation adapted from the work of Kestin and Whitelaw (1964)

Jd (micropoise) = 174.5 + 0.44 T

- where T is measured in degrees Celsius. These workers showed that,

in the experimental range, humidity and pressure effects are negligible.

141

(b) Liquid

i) Flowrate - Using the liquid flowmeter described in Chapter 2 Liquid

rates were calculated from recorded counting time in seconds and meter

revolutions x 20. A small correction was applied for liquids other than

water.

In calibration runs with water it was found that a displaced

volume of 10 litres gave 1152 counts on the meter. This is equivalent to

3262 counts per cubic foot. As a result of reduced internal leakage

it was found that the liquids of viscosity greater than water gave slightly

higher count rates as shown in the table below.

Solution Approx. Viscosity Factor(cp.)

Water 1 1

45% Sucrose 6 1.004

48.5 12 1.007

60 45 1.014

67.5 250 1.024

Dieseline 2 1.007

It was found convenient to use counting times of 100 seconds,

or some simple multiple or fraction of that time and hence to apply the

correction factor to that time. In such a timing period the observed

error of 0.03 seconds was quite negligible.

142

Thus the flowrate was calculated by:

Volumetric Rate (ft. /sec.) CountTime (seconds) Factor x 3262

and finally,

U, Vol. Rate / Column Area

Vol. Rate / 0.1803 ft.2

1.7003 x 10"3 x CountsTime (seconds) x Factor

It is believed that U was measured with an accuracy ofi-i

± 1% over most of the flow range.

ii) Holdup - The stock tank was calibrated by adding known volumes

of water and noting the change in level as indicated on the level scale.3

The tank had a surprisingly uniform calibration of 0.01766 ft. / inch

depth. Now,

Holdup = Liguid Volume Packed Volume

0.01766 x Drop in level (inches) 0.8301 ft.3

= 0.02127 x Drop in level (inches)

iii) Holdup Correction - Some of the liquid missing from the stock

tank is not held up on the packing but is in free fall from the packing to

the level of liquid in the tank. It is desirable that a correction be made

to the measured holdup to take account of this fact.

Now if the actual liquid velocity of fall is U the fraction of

tower cross section occupied by liquid is XJ / U. If liquid starts its fallJ-j

143

at velocity U the velocity after distance r is:

Ur = U.2 + 2 g r

and the total volume of liquid in free fall, per unit cross sectional area,

for a total distance of fall 5 is given by:s

Volume U, (ft.Vft.2)

uL/g [(US* Zgs)^ -

To avoid an absurdity UL must have a finite value. It was assumed

equal to the mean liquid velocity downwards in the packing - U / H.JLa

The holdup before correction was used for this estimation.

The quantity , the liquid drop, is the sum of the

distance from the packing support to the zero of the level scale

(9.4 inches), the scale reading at zero operating holdup ( HZ inches -

usually =0) and the fall to the actual operating level (HI inches).

The final holdup correction is given by:

Correction = Vol.x Column Area / Packed Volume

UT x 0.1803-i—i________________________________

0.8301 x 32. 14

2 x 32.14 12 (HZ + HI + 9.4)

0.006706 UJj

+ 5.36 (HZ + HI + 9.

where U: = UT / H (uncorrected)u L

144

and :

Actual Holdup = Measured - Correction

The holdup correction was calculated only for the operating

holdup at zero gas flowrate. Only a very small error would be involved

in the higher holdups observed at larger flowrates.

single run by evaporation. This factor also was of negligible importance

within the preloading range except perhaps for the lowest liquid flows.

iv) Pressure Gradient - The calculation was as for the gas flow

case except that the pressure difference was measured in centimeters

of the flowing liquid. This led to :

Reported holdups take no account of liquid loss during a

Ap = Differential Head x Liquid Density x 5.19 8 2.54 x 3 x 1. 001

0.6815 x Diff. Head (cm.) x Density (gm. /ml.)

145

(c) Dimensionless Groups

i) Reynolds Numbers

Re = Superficial Velocity x Packing Size x DensityViscosity

Re_ = Ur (ft./sec.) x 0.0528 (ft.)

Specific Vol. (ft.'Vlb.) x Viscosity (cp.) x 6.7 2 x 10

= 78.6 x U&3

Specific Vol. (ft. /lb.) x Viscosity (cp.)

and similarly

Re^ = 78.6 x UL x Density (lb ./ft.2)

Viscosity (cp.)

ii) Froude Number (Liquid)

Fr -g x Packing Size

20.5893 UL - (uL in ft ./second

iii) Friction Factor ol

fu

Packing Size x Pressure Gradient x c/c—

Fluid Density x (Superficial Velocity)

f(Liquid) 0.0528 (ft.) x 32.174 Ap (lb.f / ft.2, ft.)

2 3U , x Density (lb. / ft. )

1.686 A p2 x Density ( lb./ft.^)L.

146

and

f = 1.686 Ap x Specific Volume (ft.'Vlb.)(Gas) 2

U G

147

(d) Loading Point, etc.

From the basic quantities whose calculation has been

described the important derived quantity is the function P where •

- as was derived in Ch. 3. It was from a plot of this quantity vs. U^.

that the Loading Point was defined and the slope m found.

This was done in two steps. First the simple plot of P vs

was produced. On this plot the approximate location of the Load

point was found by eye as the point of intersection of the two straight

lines which in most cases could be clearly discerned in the plotted

points. Points near the Loading Point which defined the transition region

and all points for higher values of UQ were then rejected and the

preload line established by linear regression as the best straight line

through the remaining points and, in almost every case, through the

coordinate origin. These lines are shown on the plots of experimental

results - Figures 33 to 68.

In a similar way the line defining the Loading region was

established and a calculated Loading Point found. The location

p

of this at loading are given

in the complete tables of results.

148

The quantity m is the slope of the correlating line fitted

to the preload points. Its 9 5% confidence limits were calculated from

the standard formula:

5SD

where is the 9 5% value of Student's t distribution for a sample

size one less than the number of points correlated, and S££) is the sum

of squared deviations in P from the fitted line.

From m were calculated F, the equivalent value of

the friction factor coefficient, being m , and the correlated quantity

m . The confidence limit for m , quoted as TOL in the tables

-2of results was calculated by applying to m a fractional error twice

± tn-t

the value for m .

149

Appendix 2

Computer Programmes

150

C J BUCHANAN LIQUID FRICTION FACTOR

DIMENSION X(400),Y(400),NR(400),RE(40)COMMON NG,N,LX,LY,X,Y,NR EQUIVALENCE (Y (350) , RE( 1 ))EQUIVALENCE (Y(300),A)EQUIVALENCE (Y(301),B)GO TO (21,22),NG

21 N=0PRINT 106

106 FORMAT (1H4)PRINT 102

1 READ 2,NP,M2 FORMAT (213)

IF (NP)99,97,3C READ RUN HEADINGS3 READ 101,NRUM,RATL,TIHE,V ISCL,DENM.HZ101 FORMAT ( I 3.5F6.0)

VISK=VISCL/DENM DENL=62.43*DENM

C CALCULATE PRESSURE CONVERSION FACTOR - CM. LIQUIDTO LB/SQ.FT/FT

PCON=.6815*DENM J~1 +N N=N+NP DO 11 I — J , N

C READ LIQUID RATE,PRESSURE DROPREAD 104,RATL,DP

104 FORMAT (2F6.0)C CALCULATE LIQUID VELOCITY,REYNOLDS NO.,FRICTION FACTOR

UL*=RATL/(TIME*588.1)DP=PCON*DPFL=1.699*DP/(DENL*UL*UL)REL= 78.6*UL*DENL/VISCL RE(I)=RELCALCULATE TRANSFORMED VARIABLES FOR REGRESSION

C X(I)=1./RELV / | )PRINT 103,VISK,UL,REL,DP,FL,X(I)

103 FORMAT (F27.2,4X,E9.2,F10.1,F12.2,FI4.2,3X,E9.2)11 NR(I)=M

GO TO 1C LINEAR REGRESSION FOR ERGUN TYPE EQUATION97 SUMX=0.

SUMY=0.SUMXY=0.SUMX2=0.SUMY2=0.AN=NDO 31 1=1,N

151SUMX=SUMX+X(I)SUMY=SUMY+Y(I)SUMXY=SUMXY+X(I)*Y(I)SUMX2=SUMX2+X(I)*X(I)

31 SUMY2=SUMY 2+Y(I)*Y(I)PRINT 41

41 FORMAT (1H1)XMEAN=SUMX/AN YMEAN=SUMY/AN SXX=SUMX 2-SUMX* SUMX/A N SYY=SUMY 2—SUMY*SUMY/AN SXY=SUMXY-SUMX*SUMY/AH B=SXY/SXX A =Y M EAN-8* XMEA N SSD=SYY-B*SXY Q=B/A

C PRINT REGRESSION PARAMETERS AND FINAL EQUATIONPRINT 43,NPR INT44,XMEAN,YMEAN,SXX,SYY,SXY,SUMX2,SUM !Z,SUMXYPRINT 45,4,8,550PRINT 109,A,QLX=0LY=0

C PRINT GRAPH OF FRICTION FACTOR VS. 1/RE CALL LINK (GRAPH!.)

C CALCULATE AND PRINT GRAPH OF LOG(F) VS. LOG(RE)22 E=2.5

DO 12 I=1,9 J=N+I E=2.*E RE(J)=EY(J)=A+B/RE(J)

12 NR(J)=-60N=9+NDO 23 I=1,NX(I)=.4343*L0G(RE(I))

23 Y(I)=.4343*L0G(Y(I))LX=1I V —1NG=99CALL LINK (GRAPHL)

99 CALL EXIT43 FORMAT (4H0N =,I4)

152

44 FORMAT (8HOXMEAN =, E15.7,15H /'MEAN -,E15.7/3HO SXX = ,E15.7

1,15H SYY «, E15.7,15H SXY -,E15.7/8HOSUMX2 «,E15.

27,15H SUMY2 «,E15.7,15H SUMXY «>El 5.7)

45 FORMAT (4HOY =,E15.7,3H + ,E15.7,2H X/21HO SUM SQ. DEVIATIONS =,E15

2.7)102 FORMAT (20X,49HKINEMATIC LIQUID REYNOLDS

PRF^SURE 116HFRICTI ON 1/RE/20X,49HVISCOSITY VELOCITY

NUMBER GRAD I2ENT ,7H FACT0R/20X,20H(C.STOKES) (FT/SEC),14X,

1 3)1 (LB/SQ. FT/F3T)/)

109 FORMAT (18H4FRICTI ON FACTOR =,F8.4,1H(,F7.2.8H/RE + 1)) END

153

c imiESS“S"x(4oorrff4sssf,®JS' irrig4i6° t“ersDATA NSTAR, NPLUS/(5>0(T),(3))(3)/COMMON X, Y, N RLX=0LY=0

10 READ (1,102)NRUN,NPTS,BAR,TEMP,VSUP,VSAT,HSUP,HSAT102 FORMAT (2I3.6F6.0)

N=NPTSC CALCULATE AIR VISCOSITY AND DENSITY

AVISC=.01745+44.E-6* TEMP GDEN=(1.+HSAT)/VSAT

C READ LIOUID FLOW VALUESREAD (1.101)NRUN,RATL,TI ME,VISCL,DENM,UZ,HI,HS,SL

101 FORMAT (I3.BF6.0)DENL=62.43*DENM

C CALCULATE LIQUID VELOCITY AND HOLDUPUL=RATL/(TI ME*538.1)

C CALCULATE LIOUID REYNOLDS AND FROUDE NOS. AMD PREDICTED HOLDUP

IF (UL)99,11 ,1211 HCALC=0.

HD=0.H=0.REL-O.FR=0.GO TO 13

12 FR=.5S93*UL*ULREL= 78.6*UL*DENL/VISCLHCALC=2.2*(FR/REL)**.3333+1.8*SQRT(FR)

C CALCULATING LIQUID IN FLIGHT AND CORRECTING HOLDUPH=. 02127*111 UA=UL/H HD=HZ+HIHD=.0067 06*UL*(SQRT(UA*UA+5.36*(9.4+HD))-UA)| i s=H —H D

C CALCULATE TOTAL HOLDUPS13 HT=H+HS

HTC=HCALC+HSC OUTPUT RUN HEADINGS-LIQUID

WRITE (3,61)WRITE (3,62)UL WRITE (3,63)NRUN,DENM,HS WRITE ( 3,64) V I SCL ,11 WRITE (3,65)SL,HCALC WRITE ( 3,66)REL,HT WRITE (3,67)FR,HTC WRITE (3,68)GDEN WRITE (3,69)AVI SC

154

WRITE (3,70)WRITE (3,71)WRITE (2,301) NRUN, UL, DENM, VI SCI, SI., REL, FR WRITE (2,301)NRUN.HS,H,HCALC.HT.HTC,GDEN.AVISC

301 FORMAT (I 3,7E11.4)HD=HD-HS DO 1=1,N

C READ AIR FLOWRATES AND PRESSURE DROPS2 READ (1.111)QSTD,DP,PROT,PCOL,HI111 FORMAT (2F6.0,2F5.0,F6.0)C CALCULATE PRESSURE CONVERSION AND AIR

FLOW CORRECTIONS3 DP=1.731*DP

VR0T=76.*VSUP/((1.+HSUP)*(BAR+PROT))VC0L=7 6.*VSAT/((1.+H SAT)*(BAR+P COL))FADW=( 1 . +HSAT) / (1 ,+HSUP)UG=.02557*FADW*VCOL*QSTD/SQRT(VROT)REG=78.57*UG/(VCOL*AVISC)Y(I)=SQRT(1.686*DP*VCOL/(52./REG+1.))X(I)=UGIF (HI)99,201,202

201 H T=H SGO TO 112

202 H=.02127*HI HT=H-HD

C OUTPUT GAS FLOW AND PRESSURE DROP VARIABLES112 WRITE (2,113)UG,DP,REG,Y(I),HT113 FORMAT (5F14.4)

NR(I)=NSTAR1 WRITE (3,76)UG,DP,REG,Y(I),HTC CALCULATE PARAMETERS OF PRELOAD AND LOAD LINES

AND LOAD POINT DIMENSION A(2),B(2),S(2)READ (1,121) NRUN.NPTS.N1,N2,N3,N

121 FORMAT ( 12.41 3, 12)READ (1,60) T J = 1 K=N 1 AN=N1DO 29 1=1,2 SUMX=0.SUMY=0.SUMXY=0.SUMX2=0.SUMY 2=0.DO 19 M=J,K SUMX=SUMX+X(M)SUMY=SUMY+Y(M)SUMXY=SUMXY+X(M)*Y(M)

155

SUMX2=SUMX2+X(M)*X(M)19 SUMY 2=SUMY2+Y(M) * Y (M)

XMEAN=SUMX/AN YMEAN=SUMY/AN SXX=SUMX2-SUMX*SUMX/AN SYY=SUMY2-SUMY*SUMY/AN SXY-SUMXY-SUMX*SUMY/AN B( I) =SXY/SXX A(I)=YMEAN-3(I)*XMEAN S(I) =SUMXY/SUMX2 XI NT—A( I ) /B(I )SSD=SYY-B(I)*SXY GO TO (83,84),I

83 ERR=T*SQRT(SSD/( (AN-1 .)*SXX))IF (A(1)-.2)15,1 6,1 6

15 SL=S(1)GO TO 17

16 SL=B(1)17 F=SL*SL

ERR=2.*ERR*SL AM=1./F TOL=ERR*AM*AM

84 IF (N3)99,97,9696 J=1 +K+N2

AN=N329 K=J+N3-197 WRITE {3,72)N1,N3

WRITE (3,73)F,AM,TOLWRITE (2,302)NRUN,N1,N3,F,AM,TOL

302 FORMAT (3 I 3,3E11.4)IF (N3)99,93,95

95 R0ADX=A(2)/(S(1)-B(2))ROADY=ROADX*S(1)D S R=R 0 A D X / U L * S Q R T (G D E N / D E N L)WRITE (3,74)ROADX WRITE (3,75)OSRWRITE (2,301)NRUN,ROADX,ROADY,DSR L-NPTS DO 80 M=1,3 J =L+M X(J)™0,Y(J)=0

80 NR(J)=NPLUS X (L-M )=R0ADX Y(L+1)=ROADYIF (X I NT)82,82,81

81 X(L+2)=XI NT82 NPTS=3+L98 N=NPTS

156

C PLOT PRESSURE DROP FUNCTION VS. GAS VELOCITYCALL GRAPHS (N,LX,LY)GO TO 10

99 STOP60 FORMAT (F6.0)61 FORMAT (1H1.//////17X.15HRUN LIQUID)62 FORMAT (17X.3HNO.,9X,3HVEL0CITY,E9.2,6HFT/SEC

,3X,6HH0LDUP)63 FORMAT (17X,I3,9X,7HDENSITY,F11.2.5HGM/ML

,10X,6HSTATIC,F15.3)64 FORMAT (29X,9HVISCOSITY,F11.2,3HCP.

, 10X,l6H0PERATING(EXPTL),F5.3)65 FORMAT (29X,15HSURFACE TENS I ON,F4.0,7HDYNE/CM,

7X, 15H0:3ERATIMG(CALC1),F6.3)

66 FORMAT (29X,15HREYN0LDS NUMBER,El0.3,8X,13HT0TAL (EXPTL),F3.3)

67 FORMAT (29X,13HFR0UDE NUMBER,E10.3,10X,1 2HT0TAL ( CALC) , F9. 3)

68 FORMAT (1H ,25X,3HGAS/29X,7HDENSITY,F8.4,8HLB/CU.FT)69 FORMAT (29X.9HVISC0SITY.F6.4,3HCP.)70 FORMAT (1H0,17X.32HGAS VELOCITY PRESSURE GRAD.

,36HREYNOLDS1 PRESSURE FUNCTION TOTAL)

71 FORMAT (21X,6HFT/SEC,7X,11HLB/S0.FT/FT,6X,6HNUMBER,9X,6HFT/SEC.9X,

1 6HH0LDUP/)72 FORMAT (1H0,26X,20HP01 NTS BELOW LOAD ING,14,9H

ABOVE, 14)73 FORMAT (27X,22HFRICTI ON FACTOR COEFF.,F7.2,3X, 11H

RECIPROCAL ,F6.4,13H TOL. ,F6.4)

74 FORMAT (27X,16HL0ADING VELOCITY,F9.3,6HFT/SEC)75 FORMAT (27X.39HSQRT DYNAMIC STRESS RATIO

AT LOADING ,E10.3)76 FORMAT (F27.3,F16.3,F14.1,F14.2,F15.3)77 FORMAT (3HRUN,8X,2HRE,16X,2HFR,10X,6HSTATIC,6X,25H

TOTAL HOLDUP1 FRICTION/42X.36HHOLDUP (EXP) (CALC)

COEFF.)END

157

C

10334567891011

15

16

17

1811819

20

21

2223

111

11 2 113

GENERAL SCALING AMD PLOTTING PROGRAM SUBROUTINE GRAPHS(N.LX LY)DIMENSION X(400),Y(400),|Y(400),NR(400),IA(101)COMMON X, Y,NR YHI =-1.E49YLO-1.E49 XHI»-1.E49 XL0=1.E49DO 11 1=1,N I F (Y (I ) -YH I ) 5,5,4 YHI=Y( I )IF(YLO-Y(I))7,7,6YLO=Y(I)IF(X(I)-XHI)9,9,8 XHI=X(I)IF(XLO-X(I))11,1 1,10 XLO=X(I)CONTINUE V/RI TE( 3,96)WRI TE(3,95)XH I , XLO, YH I ,YLO DO 55 NC-1 ,2 GO TO (15,16),NC CHI=XH!CLO=XLOL=LXGO TO 17 CHI=YH I CLO=YLO L=LYj _ 1IF(L—1)181,23,99 I F( CLO)18,23,21 IF(CH1)19,20,23 R=CLO/CHI IF(R-2.>23,20,20 CH I =-CLO

G02T0 22 R=CHI/CLO IF(R-2.)23,22,22 CLO=0.D=CHI-CLO L=0GO TO 112 D=10.*D L”1 +LIF(D—1.005)111,120,114D=.1*D U—L—1

158

114 IF(D—10.05)120,113,113120 AULT=10.**L 211 SL0=CL0*AULT

IF(SLO)24,27,1 21 24 SL0=SL0-1.121 I CLO=SLO

SLO=lCLOD=CHI*AULT-SLO GO TO (106.27),NC

106 IF(D-10.05)27,1 25,1 25125 AULT=.1*AULT

GO TO 211 27 L=-L

CLO=SLOWRITE(3,97)L,LI B=96*( J-1 )*8**8M— 1

31 IF(D-10.05)32,40,4032 IF(D-5.025)133,40,40133 GO TO (130,33) NC130 IF(D—3.35)140,41,41140 IF(D—2.01)42,42,4933 IF(D-2.01)42,41,4142 M=2+M49 M=1 +M41 M=1+M40 FACT=10*m

GO TO (52,50),NC50 WRITE(3,91)SL0,IB,IB

DO 53 1=1,N53 I Y( I )=FACT*(Y( I )*AIJLT-CLO) + . 5

I NC=1 00. /FACTGO TO (109,108),J

108 YHI=YL0109 IYHI=FACT*(YHl*AULT-CLO)+.5

GO TO 5552 WRITE(3,90)SLO,IB,IB

DO 54 1=1 ,N54 X(I)=FACT*(X(I)*AULT-CL0)+1.5

K=M55 CONTINUE61 GO TO (44,46,149,99,48),K44 WRITE(3,92)

GO TO 5146 WRITE(3,93)

GO TO 51149 WRI TE(3,190)

GO TO 51

159

48 WRITE(3,94)51 IF(J)99,62,6363 L=5*(IYHI/5+1)

IABS=INC*L81 DO 82 1=1,10182 IA(I)=0

DO 85 I =1 . N IF(L-lY(I)>85,83,85

83 IX=X(I)IA{IX)=NR(I)

85 CONTINUEWRITE(3,89)IABS,IA,IABS

89 FORMAT (112.50A1,51A1,I4)IABS=I ABS-I NCL=L-1IF(L+1>99,88,81

88 J=0GO TO 61

62 RETURN99 STOP90 FORMAT (11X21HABCI SSA )X-AXIS* 0(3, F8. 2,2H *,1A1,

2 On 10 SCAI.IE UNIT®), 1A1,21110/)

91 FORMAT (11X21H0RDI NATE )Y-AXIS* 0(3,F8.2,211 *,1A1,2OH 1 0 100 ON

I SCALE®), 1A1.2H10/)92 FORMAT (12X40110___ *____ 1____ *____2____ *____3____ .

40H 4 *1! '.S___ _________________ 7____ *____ , 21H8____ *____9____*....0)

93 F0RMAT(12X40H0 1 .,40112 ....

1*....3....*.... , 21H4 . 5)

94 FORMAT( 1 2X401(0___ *____ *____*____*____ V____ *____ *. ...,40H*....*...II it it k it \J 21H* * * it

:.:i)...............................190 FORMAT(12X40H0 1 . .

., 40H . * .1 . . . 2 . . . . * . ,21H . . . 3 . .

. )95 FORMAT (4(4XE11.4)/)96 FORMAT (1111 ,5X, 4HXMAX 11X,4HXMI N, 11 X.4HYMAX, 11X.4HYMIN)97 FORMAT (44X,I 3,18X,I 3)

END

160

Appendix 3

Tabulated Results

RESSURE GRADIENT - SINGLE PHASE FLOW

161

—i

(M N

M M

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162

RUN NO. 3 L iUUID

VELOCITY 0.00E-99FT/SEC HOLDUPDENSITY l.OOGM/ML STAT IC 0.000VISCOSITY 1.OOCP. OPERATING(EXPTL)O.OOOSURFACE TENSION 73.DYNE/CM OPERATING(CALC) 0.000REYNOLDS NUMBER O.OOOE- 99 TOTAL (EXPTL) 0.000FROUDE NUMBER 0.000E-99 TOTAL (CALC) 0.000

GASDENSITY •0743LB/CU.FT

VISCOSITY .0I84CP.

G A S PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCTION HOLDUP

F T/SEC LB/SQ.FT/FT FT/SECD

. 300 .050 96.1r.85 0.000

.4 88 .117 155.2 1.40 0.000

.672 .211 214.9 1.95 0.000

.860 .313 271.6 2.43 0.0001.065 .474 340.2 3.04 0.0001.238 .63 7 395. 5 3.56 0.0001.429 .804 456.7 4.03 0.0001.691 1.125 540.2 4.80 0.0001.822 1.315 582.0 5.21 0.0002.074 1.627 662.6 5.82 0.0002.261 1.904 722.3 6.32 0.0002.625 2.49 2 838.7 7.26 0.0003.083 3.392 985.0 8.51 0.0003.391 4.085 1083.5 9.36 0.000

POINTS ON PRELOAD LINE 14 ON LOADED LINE 0 FRICTION FACTOR COEFF. 7.80 RECIPROCAL CuEFF./tT2. 1281 TO L. .uuo

14

13

12

1 1

10

9

8

7

6

5

4

3

2

1

0

163

I1tttittit

iI

(ft./sec.)

Fig. 32 Run No. 3.

164

RUN NO* 6LiGUID

VELOCITY 0.00E-99FT/SEC HO L DU PDENSITY 1.OOGM/ML STaT ic .026VISCOSITY l.OOCP. 0PERATING(EXPTL)0 .000SURFACE TENSION 73.DYNE/CM OPERATING(CALC) 0 .000REYNOLDS NUMBER 0.000 E- 99 TOTAL (EXPTL) .026FROUDE NUMBER U.OOOE-99 TOTAL (CALC) .026

GASDENSITY •0730LB/CU.FT

VISCOSITY .0186CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUivJCT ION HOLDUP

F T/SEC LB/SQ.FT/FT FT/SECp

. 284 .057 8 7.6i.91 .026

.440 .103 135.4 1.31 .026

.596 . 186 183.4 1.83 .026

.7 90 .311 243.1 2.43 .026. 984 .453 302.8 2.99 .026

I. 140 .595 350.9 3.46 .0261.343 .808 413.5 4.07 .0261.552 1.055 477.6 4.68 .0261.713 1.332 527.1 5.29 .0261.902 1.644 585.3 5.90 .0262.082 1.921 640.7 6.40 .0262.432 2.579 748.4 7.46 .0262.848 3.392 8 76.6 8.60 .0263. 161 4.189 972.7 9.58 .0263.265 4.466 1004.7 9.90 .026

POINTS ON PRELOAD LINE 15 ON LOADED LINE 0FRICTION FACTOR COEFF. 9.28 RECIPROCAL COEFF.m'2 . 10 77 TOL. .0017

14

13

1 2

1 1

10

9

8

7

6

5

4

3

2

1

0

165

Fig. 33. Run No. 6.

166

RUN NO. 2 7LIUU ID

VELOCITY 4.54E-03FT/SEC HOLDUPDENSITY .99GN/ML STATIC .026VISCOSITY 1.01CP. OPERATING* EXPTL) .021SURFACE TENSION 70.DYNE/CM OPERATING(CALC) .024REYNOLDS NUMBER 2.201E+01 TOTAL (EXPTL) .047FROUDE NUMBER 1.215E-05 TOTaL (CALC) .050

GASDENSITY .0745LB/CU.FTVISCOSITY .0183CP .

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRaDI ENT NUMBER FUNCTION HOLDUPFT/SEC LB/SQ.FT/FT FT/SEC

p

.240 .050 76.8r.82 .047

. 368 . 100 117.6 1.25 .047

.537 .199 171.8 1.85 .0 47

.585 .299 187.0 2.30 .047

.821 .439 262.5 2.88 .048

.990 . 614 316.9 3.4 5 .0491. 161 .801 371.5 3.98 .0491.284 1.038 411.0 4.56 .0491.4 64 1.298 468.8 5. 13 .0501.643 1.644 526.6 5.80 .0501.772 1.921 568.2 6.29 .0511.943 2.267 623.6 6.86 .0522.079 2.613 66 7 • 1 7.39 .0532.202 2.942 707.6 7.8 5 .0542.327 3.306 747.7 8.33 .0562.473 3.808 794.5 8.96 .0582.568 4.154 82 6. 1 9.37 .0602.7 20 4. 708 876.2 9.98 .0612.836 5.141 913.5 10.44 .0632.942 5.608 947.8 10.92 .0653.051 6.145 982.8 11.44 .0663. 146 6.733 1014.8 11.97 .0723.245 7.581 1048.2 12.71 .076

POINTS ON PRELOAD LINE 15 ON LOADED LINE 6 FRICTION FACTOR COEFF. 12.58 RECIPROCAL COEFF .m"2.0794 TOL. .002 4 LOADING VELOCITY 2.577FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 1.964E+01

1 4

13

1 2

1 1

10

9

8

7

6

5

4

3

2

1

0

167

Fig. No. 34 Run No. 27.

168

RUN NO. 29 LIQU ID

VELOCITY 1•24E-03FT/SEC HOLDUPDENSITY •99GM/ML STAT IC .026VISCOSITY 1.01CP. OPERATING(EXPTL) .013SURFACE TENSION 70 .DYNE/CM OPERAT ING(CALC) .013REYNOLDS NUMBER 6.019E-00 TOTAL (EXPTL) .039FROUDE NUMBER 9.080E-07 TOTAL (CALC) .039

GaSDENSITY •0745LB/CU.FTVISCOSITY .0 183CP•GAS PRESSURE REYNOLDS PRESSURE TOTAL

VELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF T/SEC LB/SQ.FT/FT FT/SEC

P.83.255 . 0 50 81.6 .039

.373 .091 119.4 1.20 .039

.567 . 199 181.3 1.87 .039

.7 33 .315 234.4 2.41 .039

.870 . 432 278.5 2.86 .0391.031 .600 330.1 3.42 .0391.210 .798 387.9 3.98 .0401.381 1.038 442.5 4.57 .0401.562 1.280 500.8 5.11 .0 401.758 1.62 7 563.7 5.79 .0411.911 1.904 613.2 6.28 .0412.094 2.267 672.0 6.88 .0 422.229 2.596 715.7 7.3 8 .0 422.421 3.011 777.9 7.96 .0422.5 75 3.392 82 7.9 8.47 .0432.701 3.825 868.9 9.00 .0 442.865 4.189 921.7 9.43 .0 452.983 4.70 8 960.4 10.01 .0 453. 109 5.175 1001.7 10.50 .0473.286 5.868 1059.2 11.19 .0493.479 6.612 1123.0 11.89 .0493.658 7.477 1181.7 12.66 .0503.821 8.360 1236.7 13.38 .0524.016 9.208 1302.1 14.04 .0554.131 9.693 13 41.1 14.41 .058POINTS ON PRELOAD LINE 15 ON LOADED LINE 9 FRICTION FACTOR COEFF. 10.85 RECIPROCAL COEFF jtTz .0921 TOL. • UUU6 LOADING VELOCITY 2.742FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 7.642E+01

1 4

13

12

1 1

10

9

8

7

6

5

4

3

2

1

0

169

. 4

.3 ■ ■

• 2 "■

0 2 3

Fig. 35 Run No. 29.

170

RUN NO. 30L IUU ID

VELOCITY 8.58E-03FT/SEC HOLDUPDENSITY .99GIV ML STATIC .026VISCOSITY 1 .U1CP. OPERaTING(EXPTL) .033SURFACE TENSION 70.DYNE/CM OPERATING(CALC) .034REYNOLDS NUMBER 4.164E+01 TOTAL (EXPTL) .059FROUDE NUMBER 4.345E-05 TOTAL (CALC) .060

G A SDENSITY .0745LB/CU.FTVISCOSITY .0183CP .GAS PRESSURE REYNOLDS PRESSURE TOTAL

VtLOCITY GRADIENT NUMBER FUNCTION HOLDUPFT/SEC LB/SQ.FT/FT FT/SEC

P.231 .050 74. 0 .81 .059. 374 .116 119.5 1.35 .059.5 11 .199 163.3 1.84 .059.634 .299 202.7 2.32 .059.776 .432 248.2 2.84 .060.928 . 614 296.8 3.43 .060

1.079 .798 345. 5 3.95 .0601.241 1.038 3 97.2 4.55 .0611.402 1.315 449. 2 5. 15 .0611.574 1.609 504.3 5.73 .0611.688 1 .904 541.3 6.25 .0621.784 2.215 572.5 6.76 .0631.950 2.596 626.7 7.34 .0642.096 3.011 6 73.4 7.93 .0652.191 3.358 704.4 8.38 .0662.296 3.8 42 739.3 8.97 .0672.382 4.206 767.4 9.40 .0682.497 4. 708 805.0 9.95 .0692.604 5.348 839.9 10.62 .0712.699 5.868 871.8 11.13 .0742.813 6.456 909.9 11.68 .076POINTS ON PRELOAD LINE 15 ON LOADED LINE 5 FRICTION FACTOR COEFF. 14.00 RECI > l. C0EFF.nf2.0714 TOL. .U02uLOADING VELOCITY 2.093FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 8.432E-00

1 4

13

1 2

1 1

10

9

8

7

6

5

4

3

2

1

0

171

Fig. 36 Run No. 30.

172

RUN NO. 31LiUUID

VELOCITY 1 •25 E-02 FT/SEC HO L DU PDENSITY .99GM/ML STAT IC .026VISCOSITY 1.01CP. OPERATING(EXPTL) .042SURFACE TENSION 70.DYNE/CM OPERATING(CALC) .042REYNOLDS NUMBER 6.101E+01 TOTAL (EXPTL) .068FROUDE NUMBER 9.330E-05 TOTAL (CALC) .068

GaSDENSITY •0745LB/CU.FTVISCOSITY .0 183CP.GAS PRESSURE REYNOLDS PRESSURE TOTAL

VELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF T/SEC LB/SQ.FT/FT FT/SEC

P.79. 204 .050 65.3 .068

.369 .124 118.0 1.39 .068

.478 . 199 152.8 1.83 .068

.620 .31 5 198.2 2.37 .068

.75 7 . 448 2 42.0 2.88 .068

.881 . 598 281.6 3.38 .0681.023 . 798 3 2 7.2 3.94 .0681.184 1.038 37 8.9 4.54 .0691.326 I . 280 424.8 5.0 7 .07 01.4 97 1.644 479.9 5.78 .0701.592 1.904 510.7 6.24 .0701.718 2.250 551.2 6.80 .0711.817 2.596 583.6 7.32 .0731.961 3.081 630.2 8.00 .0742.058 3.444 6 61. ( 8.47 .0/62. 143 3.946 689.7 9.07 .0772.239 4.483 721.5 9.68 .0792.345 4.968 756.0 10.20 .0822.394 5.504 772.3 10.74 .0862.482 5.781 801.0 11.02 .090POINTS ON PRELOAD LINE 12 ON LOADED LINE 5 FRICTION FACTOR COEFF. 15.05 RECIPROCAL COEFF .m'2.06 64- TOL. .0010 LOADING VELOCITY 1.761FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 4.841E-00

1 4

13

1 2

1 1

10

9

8

7

6

5

4

3

2

1

0

173

.4

.3

Fig. 37 Run No. 31.

174

RUN NO• 32LIQUID

VELOCITY 1 • 85E-02FT/SEC FIO L DU PDENSITY .99GM/ML STAT IC .026VISCOSITY 1.01CP. OPERATING (EXPTL) .054SURFACE TENSION 70.DYNE/CM OPERATING(CaLC) .054REYNOLDS NUMBER 8.987 E + 01 TOTAL ( EXPTL) .080FROUDE NUMBER 2.024E-04 TOTAL (CALC) .080

GaSDENSITY •0745LB/CU.FTVISCOSITY .0183CP.GAS PRESSURE REYNOLDS PRESSURE TOTAL

VELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF T/SEC LB/SQ.FT/FT FT/SEC

P.77. 186 .050 59.5 .080

.336 .126 107.3 1.38 .080

.435 . 197 139.1 1.80 .07 9

.549 .299 175.5 2.28 .080

.66 7 . 441 213.4 2.83 .080

.800 . 598 255.8 3.35 .080

.928 . 798 296.8 3.91 .0801.056 1.038 338.0 4.50 .0801 . 184 1.280 379.1 5.04 .0801.346 1.644 431.1 5.75 .0811.431 1.921 458.7 6.23 .0821.541 2.284 494. 1 6 .,82 .0851.618 2.596 519.3 7.29 .0851.7 36 3.098 557.7 7.98 .088I .914 4. 189 615.9 9.31 .0932.009 4.517 647.2 9.68 .096POINTS ON PRELOAD LINE 10 ON LOADED LINE 5 FRICTION FACTOR COEFF. 17.99 RECIPROCAL C0EFF jv1 *0555 TOL. .0009LOADING VELOCITY 1.409FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 2.630E-00

14

13

12

1 1

10

9

8

7

6

5

4

3

2

1

0

175

Fig. 38 Run No. 32.0 2

176

RUN NO. 33 LIUUIQ

VELOCITY 2.82E-02FT/SEC HOLDUPDENSITY .99GM/ML STAT IC .026VISCOSITY .9 8C P • OPERATING(EXPTL) .071SURFACE TENSION 70.DYNE/CM OPERAT ING(CALC) .071REYNOLDS NUMBER 1.411E+02 TOTAL (EXPTL) .097FROUDE NUMBER 4.695E-04 TOTAL (CALC) .097

G A SDENSITY .0743LB/CU.FTVISCOSITY .0183CP.GAS PRESSURE REYNOLDS PRESSURE TOTAL

VELOCITY GRADI ENT NUMBER FUNCT ION HOLDUPF T/SEC LB/SO.FT/FT FT/SEC

P. 147 .050 46.7 .73 .097.263 .116 83.6 1.27 .097.366 .199 116.3 1.76 .098.470 .318 149.5 2.31 .098.556 .432 176.7 2.75 .098.680 .623 216. 1 3.37 .098. 780 . 796 247.9 3.86 .098.895 1.038 284.4 4.46 .099.989 1.298 314.8 5.02 . 100

1.094 1.62 7 348.4 5.66 . 1011. 180 1.921 3 75.9 6.18 . 1021.257 2.371 400.6 6.89 . 1031.353 2.804 431.6 7.52 . 1061 .486 3.548 474.7 8.49 .1111.557 4.067 498.2 9.11 . 118POINTS ON PRELOAD LINE 10 ON LOADED LINE 5FRICTION FACTOR COEFF. 25 .33RECIPROCAL COEFF .m'2.0394 TOL. 0016LOADING VELOCITY 1.067FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 1.305E-00

14

13

12

1 1

10

9

8

7

6

5

4

3

2

1

0

177

. 4

.3

.2

sec.

Fig. 39 Run No. 33.

178

RUN NO. 34 LIQU ID

VELOCITY 4.21 E-02 FT/S EC HOLDUPDENSITY . 99GPi/ML STATIC .026VISCOSITY .97CP. OPERATING(EXPTL) .094SURFACE TENSION 70.DYNE/CM OPERATING(CALC) .095REYNOLDS NUMBER 2•129E+02 TOTAL (EXPTL) . 120FROUDE NUMBER 1.048E-03 TOTAL (CALC) .121

ASDENSITY .0740 Lb/CO.FT

VISCOSITY .0184CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALELOCITY GRADIENT NU MBER FUNCTION HOLDUPFT/SEC lb/sq.ft/ft FT/SEC

D.091 .050 28.9

r.63 .120

. 167 . 107 53.0 1.11 .120

.24 7 . 199 78.4 1.65 .120

. 330 .315 104.4 2.18 . 121

.403 . 502 128.3 2.85 .121

.472 .623 149.5 3.24 .121

.544 .813 172.2 3.77 .121

.659 1.073 208.6 4.42 .123

.7 35 1.280 232.9 4.87 .123

.826 1.627 261.9 5.55 .125

.887 1.852 281.6 5.95 .125

.992 2.371 315.3 6.7 9 .1291.098 3.115 349. 1 7.83 .1331 . 184 3.635 3 77.1 8.49 . 1471.222 3.981 389.8 8.90 .153

POINTS ON PRELOAD LINE 12 ON LOADED LINE 3 FRICTION FACTOR COEFF. 43.76 RECIPROCAL COEFF jrfz .u, TOL. .0007LOADING VELOCITY .865FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 7.078E-01

1 4

13

1 2

1 1

10

9

8

7

6

5

4

3

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1

0

179

.4

.3

.2

Fig. 40 Run No. 34.

180

RUN NO. 35LIuUID

VELOCITY 6.15E-02FT/SEC HOLDUPDENSITY • 9 9 Gii / PiL STAT IC .026VISCOSITY .82C P. OPERATING (EXPTL) .120SURFACE TENSION 70.DYNE/CM OPERATING(CALC) . 125REYNOLDS NUMBER 3.669E+02 TOTAL (EXPTL) . 146FROUDE NUMBER 2.233E-03 TOTAL (CALC) . 151

G A SDENSITY •0719LB/CU.FT

VISCOSITY .0187CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCT ION HOLDUP

FT/SEC Lb/SQ.FT/FT FT/SECP

.013 .050 3.9 .28 . 151

.034 . 109 10.3 .65 . 151

.046 . 207 14.0 1.01 . 151

.066 .277 20.0 1.34 .152

.092 .450 2 7.8 1.91 . 153

.139 .709 42.2 2.72 . 154

. 170 .865 51.5 3.17 . 154

.215 1.384 65.0 4.24 . 154

.253 1.557 76.8 4.66 . 156

.292 1.731 88.5 5.04 . 156

. 339 1.990 102.7 5.55 . 157

.404 2.42 3 122.3 6.30 . 158

.44 6 2.596 135.2 6.61 . 159

.541 3.115 163.9 7.43 . 162

.645 3.808 1 95.7 8.37 . 164

.710 4.500 215.7 9.19 . 168

. 795 5.019 2 41.5 9.80 . 173

.853 5.539 260.1 10.34 . 183

.913 5.885 278.7 10.72 . 194

POINTS ON PRELOAD LINE 14 ON LOADED LINE 0 FRICTION FACTOR COEFF. 196.40 RECIPROCAL COEFF .m’2 .D0 3u .. .u,

1 4

13

12

1 1

10

9

8

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6

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181

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Fig. 41 Run No. 35.

182

RUN NO. 37L IQU ID

VELOCITY 8.79E~02 FT/SEC HOLDUPDENSITY .99GM/RL STATIC .026VISCOSITY .77CP. OPERATING(EXPTL) . 164SURFACE TENSION 70.DYNE/CM OPERATING(CALC) . 165REYNOLDS NUMBER 5.574E + 02 TOTAL (EXPTL) . 190FROUDE NUMBER 4.554E-03 TOTAL (CALC) . 191

GaSDENSITY . 0708 LB/CO.FT

VISCOSITY •0188CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADI ENT NUMBER FUNCTION HOLDUP

FT/SEC LB/SQ.FT/FT FT/SECp

.05 7 2.250 16.91

3.62 . 190.085 2.423 25.1 4.33 . 190. 146 3.115 43.1 5.79 . 192.214 3.462 63.2 6.72 . 195.283 4.154 83.7 7.80 . 199. 363 4.8 46 107.6 6.80 . 203.413 5.366 122.4 9.44 .205.456 5.885 135.4 10.03 .209.517 6.577 153.7 10.77 . 224.572 7.097 171.0 11.31 .243

POINTS ON PRELOAD LINE 4 ON LOADED LINE 0 FRICTION FACTOR COEFF. 395.30 RECIPROCAL COEFF./na.OO; . .01

14

13

12

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10

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8

7

6

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183

Fig. 42 Run No. 37.

184

RUN NO. 47 L IQUID

VELOCITY 2.51E-02FT/SEC HOLDUPDENSITY 1. 19GM/ML STATIC .022VISCOSITY 5.90CP. OPERATING{EXPTL) .079SURFACE TENSION 64.DYNE/CM OPERATING (CALC ) .088REYNOLDS NUMBER 2.507E+01 TOTAL (EXPTL) . 101FROUDE NUMBER 3.732E-04 TOTAL (CALC) .110

G A SDENSITY .0719LB/CU.FT

VISCOSITY • 0188CP .

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADI ENT NU MB ER FUNCTION HOLDUP

FT/SEC LB/SQ.FT/FT FT/SECP

.76.169 .050 50.6 . 101.28 7 .116 85.9 1.30 . 101.393 .199 117.8 1.80 . 101.491 . 308 147.1 2.31 . 101.590 .432 176.7 2.80 . 101. 706 . 611 211.5 3.39 . 101.813 .806 243.5 3.95 . 101.915 1.038 274.1 4.52 . 102

1.021 1.280 306. 1 5.07 . 1031. 147 1.644 3 44.2 5.7 9 . 1041.200 1.904 360.4 6.24 . 1061.287 2.250 386.8 6.81 . 1071.332 2.544 400.4 7.26 . 1101.448 3.063 43 5.7 8.00 . 1121.501 3.340 452.0 8.37 .1141.590 3.981 478.9 9.16 . 1181.6 87 4.812 508.7 10.09 .1221.747 5.902 528.0 11.18 . 1241.7 95 5.902 542.6 11.20 .1291.890 6.993 571.9 12.2 1 . 137

POINTS ON PRELOAD LINE 11 ON LOADED LINE 7FRICTION FACTOR COEFF. 24 .72RECIPROCAL EFF . u 40 4 TOL. . 0022LOADING VELOCITY 1.305FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 1.609E-0U

14

13

12

1 1

10

9

8

7

6

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4

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2

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185

Fig. 43 Run No. 47.

186

RUN NO* 46LIGUID

VELOCITY 4.33E-02FT/SEC HOLDUPDENSITY 1.19GM/ML STATIC .022VISCOSITY 5.40CP. OP ERATING(EXPTL) . 113SURFACE TENSION 64.DYNE/CM OPERATING(CALC) .122REYNOLDS NUMBER 4.716E+01 TOTAL (EXPTL) . 135FROUDE NUMBER 1.108E-03 TOTAL (CALC) . 144

GaSDENSITY .0711 LB/CU.FTVISCOSITY .0189CP.GAS PRESSURE REYNOLDS PRESSURE TOTAL

VELOCITY GRADIENT NUMBER FUNCTION HOLDUPFT/SEC LB/SQ.FT/FT FT/SEC

P.119 .050 35.0 .69 .134. 221 .124 65.0 1.28 . 135.302 .207 88.9 1.76 .134. 372 . 304 109.4 2.21 .135.466 .457 137.0 2.80 .135.531 . 598 156.1 3.26 . 135.618 .813 181.5 3.87 .136.696 1.055 204.6 4.47 .136.775 1.40 2 227.9 5.20 .136. 794 1.557 2 33.7 5.49 .138.863 1.938 254. 1 6.18 . 140.917 2.250 2 70.1 6.69 . 142.966 2.683 284. 8 7.33 . 145

1.050 3.063 3 09.8 7.88 . 1481.060 3.323 312.6 8.21 .150I . 109 3.808 32 7.5 8.81 . 1531. 149 4.154 339.4 9.22 . 1561 . 198 4.673 354.2 9.81 . 1591.266 5.539 375.3 10.70 . 1681.324 6.577 393.4 11.68 . 1761.3 73 6.40 4 408.7 11.54 . 186POINTS ON PRELOAD LINE 10 ON LOADED LINE 11 FRICTION FACTOR COEFF. 41.74 RECIPROCAL COEFF«m"2 *0239 .. .0LOADING VELOCITY . 763 FT/SECCURT DYNAMIC STRESS RATIO AT LOADING 5.432E-01

14

13

12

1 1

10

9

8

7

6

5

4

3

2

1

0

187

.4

.3

.2

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

Fig. 44 Run No. 48.

.1 .2

188

RUN NO. 49LIQUID

VELOCITY 6.42E-02FT/SEC HO L DU PDENSITY 1.19GM/ML STAT IC .022VISCOSITY 5.40CP. OPERATING(EXPTL) . 148SURFACE TENSION 64.DYNE/CM OPERATING(CALC) .160REYNOLDS NUMBER 6.997 E+01 TOTAL (EXPTL) .170FROUDE NUMBER 2.435E-03 TOTAL (CALC) .182

GASDENSITY .0711LB/CU.FT

VISCOSITY .0189CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCT ION HOLDUP

F T/SEC LB/SQ.FT/FT FT/SECp

.084 .050 24.8L

.62 . 170. 157 .116 46. 1 1.13 . 170.220 . 199 64.6 1.62 . 170.280 .308 82.3 2.12 . 170.330 . 439 96.8 2.60 . 170.380 .60 5 111.6 3.13 . 169.423 .778 124.4 3.61 . 170.443 1.177 130.3 4.47 . 170.477 1.384 140.4 4.89 . 171.5 11 1.644 150.6 5.38 . 172.541 1.938 159.4 5.89 . 172.585 2.250 172.5 6.40 . 174.630 2.561 185.6 6.88 .176.709 3.288 209. 1 7.89 . 182.739 3.981 218.3 8.71 . 188.7 89 5.539 233.4 10.34 . 195.818 5. 539 2 42.2 10.37 .203.847 5.712 251.3 10.55 .215

POINTS ON PRELOAD LINE 7 ON LOADED LINE 6FRICTION FACTOR COEFF. 64. 82RECIPROCAL COEFF.m"2 .0154 TOL. 0023LOADING VELOCITY .471 FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 2.262E-01

14

13

12

1 1

10

9

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7

6

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189

Fig. 45 Run No. 49.

190

RUN NO. 51LIQUID

VELOCITY 1.43 E-02FT/SEC HOLDUPDENSITY 1.20 Gn/ML STAT IC .022VISCOSITY 7.40CP. OPERATING(EXPTL) .061SURFACE TENSION 64.DYNE/CM OP ERATING(CALC) .068REYNOLDS NUMBER 1.143E+01 TOTAL (EXPTL) .083FROUDE NUMBER 1.211E-04 TOTAL (CALC) .090

GaS

DENSITY •0727LB/CU.FTVISCOSITY .0186CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCT ION HOLDUP

F T/SEC LB/SQ.FT/FT FT/SECP

. 199 .050 61.1 .79 .083

.3 36 .116 103.2 1.33 .083

.451 . 199 138.3 1.83 .083

.562 .299 172.2 2.31 .084

.687 .432 210.6 2.83 .084

.831 .614 254.9 3.44 .084

.962 .813 2 94.8 4.00 .0841.091 1.055 334. 8 4.60 .0841.241 1.367 380.9 5.28 .0841.328 1.575 407.6 5.69 .0851.463 1.938 449.4 6.34 .0861.559 2.250 479.2 6.85 .0871 • 665 2.613 512.1 7.40 .0871.7 38 2.960 535.0 7.89 .0891.85 7 3.548 571.7 8.6 7 .0911.924 3.998 592.9 ' 9.21 .0921.983 4.362 611.2 9.63 .0942.071 4.846 63 8.8 10.17 .0952. 130 5.331 657.2 10.67 .0982.208 5.920 681.9 11.25 . 1022.297 6.906 709.7 12.17 . 106

POINTS ON PRELOAD LINE 12 ON LOADED LINE 7FRICTION FACTOR COEFF. 18.23 RECIPROCAL COEFF jvz• Q 5 4 8 TOL. .0018LOADING VELOCITY 1.652FT/SEC SORT DYNAMIC STRESS RATIO AT LOADING 3•5 BYE-00

14

13

12

1 1

10

9

8

7

6

5

4

3

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191

Fig. 46 Run No. 51.

192

RUiM NO. 5 2LIOUID

VELOCITY 8.65E—03FT/SEC HULDUPDENSITY 1.20GM/ML STATIC .022VISCOSITY 7.50CP. OPERATING!EXPTL) .044SURFACE TENSION 64.DYNE/CN OPERATING(CALC) .052REYNOLDS NUMBER 6.829E- 00 TOTAL (EXPTL) .066FROUDE NUMBER 4.414E-05 TOTAL (CALC) .074

GaSDENSITY .0727 LB/CU.FT

VISCOSITY .0186CP .

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADI ENT NUMB ER FUNCTION HOLDUP

FT/SEC LB/SQ.FT/FT FT/SECP

.236 .050 72.2 .82 .066

.456 . 107 139.3 1.34 .066

.488 .192 149.3 1.81 .0 66

.628 . 308 191.8 2.3 7 .06 7

.75 7 .432 231.3 2.86 .067

.891 . 581 2 72.5 3.36 .0671.065 .822 32 5.5 4.05 .0681.208 1.038 369.7 4.59 .0681.344 1.263 411.1 5.09 .0681.537 1.644 470.2 5.85 .0691.643 1.921 503.1 6.35 .0701.750 2.250 536.1 6.89 .0711.883 2.613 576.7 7.45 .07 22.029 3.115 621.8 8.15 .0732. 145 3.617 658.2 8.80 .0742.240 3.998 688.5 9.26 .0762.318 4 • 448 712.9 9.77 .077a.405 4.881 740.1 10.25 .0802.463 5.383 758.5 10.77 .0812.544 5.885 783.2 11.27 .0842.621 6.370 80 t . 6 11.73 .0862.721 6.958 839.0 12.27 .0872.76 8 7.651 854.4 12.87 .09 32.820 8.395 870.5 13.49 .0972.907 9.139 898.5 14.07 . 1012.996 10.299 927.2 14.94 . 1063.065 10.905 950.0 15.38 .116

POINTS ON PRELOAD LINE 14 ON LOADED LINE 8 FRICTION FACTOR COEFF. 15.06 RECIPROCAL Cut FF.ro'2.0663 TOL. .u0^2 LOADING VELOCITY 2.263FT/SECSORT DYNAMIC STRESS RATIO aT LOADING 8.127E-00

14

1 3

1 2

1 1

10

9

3

7

6

5

4

3

2

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193

Fig. 47 Run No. 52.

194

RUN NO* 5 3LIQUID

VELOCITY 5•0 3 E-0 3 FT/S EC HOLDUPDENSITY 1.20 Gi'i/ ML STAT IC .022VISCOSITY 6.80CP. OPERATING(EXPTL) .031SURFACE TENSION 64.DYNE/CM OPERATING(CALC) .040REYNOLDS NUMBER 4.373E- 00 TOTAL (EXPTL) .053FROUDE NUMBER 1.493E-05 TOTAL (CALC) .062

GASDENSITY .0723 LB/CO.FT

VISCOSITY .0187CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALvelocity GRADIENT NUMBER FUNCT ION HOLDUP

F T/SEC Lb/SO.FT/FT FT/SECP

. 242 .050 73.2 .82 .053

.384 . 107 116. 1 1.31 .052

.535 .207 162.0 1.91 .053• 6 66 .308 201.5 2.39 .053.811 . 439 245.3 2.90 .053.946 . 590 286.3 3.41 .053

1.111 .789 336.2 3.99 .0541.285 1.055 389.3 4.65 .0541.444 1.332 43 7.7 5.26 .0551.59 5 1.575 483.7 5.75 .0551.75 0 1.956 531.3 6.43 .0561.892 2.250 574.6 6.92 .0572.039 . 2.631 619.6 7.50 .0582.225 3.081 6/6.6 8.14 .0592.353 3.531 715.9 8.7 3 .0602.480 3.981 755.3 9.29 .0612.558 4. 310 7 79.5 9.6 7 .0632.657 4.708 810.2 10.12 .0642.764 5.141 843.4 10.58 .0662.914 6.058 889.6 11.50 .0693.013 6.820 921.1 12.20 .0713.122 7.443 955. 1 12.76 .0753.222 8.204 986.2 13.40 .07 83.321 9.053 1018.0 14.08 .0833.426 10.593 1052.9 15.22 .0893.557 11.511 1094.6 15.87 .096

POINTS ON PRELOAD LINE 14 ON LOADED LINE 11 FRICTION FACTOR COEFF* 13.30 RECIPROCAL Cue FF jv~z *0152 TUL. .0009 LOADING VELOCITY 2.491FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 1.535E+01

1 4

13

1 2

1 1

10

9

8

7

6

5

4

3

2

1

0

195

sec.

196

RUN NO. 54 LIQUID

VELOCITY 2•97E-03FT/SEC HOLDUPDENSITY 1.20GM/ML STATIC .022VISCOSITY 7.50CP. OPERATING(EXPTL) .025SURFACE TENSION 64.DYNE/CM OPERATING(CALC) .032REYNOLDS NUMBER 2.346E-00 TOTAL (EXPTL) .047FROUDE NUMBER 5.216E-06 TOTAL (CALC) .054

GaSDENSITY •0727LB/CU•FT

VISCOSITY .0186CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVtLOCITY GRADIENT NUMBER FUNCT ION HOLDUP

F T/SEC Lb/SQ.FT/FT FT/SECP

.239 .0 50 73.1 .82 .047

.368 . 100 112.7 1.26 .047

.551 .207 16 8.3 1.91 .047

.685 .308 209.4 2.39 .047

. 843 .439 257.8 2.91 .0471.007 .623 307.8 3.51 .0471. 175 .813 359.3 4.06 .0471.325 1.038 405.2 4.61 .0 481.566 1.402 479.2 5.41 .0491.710 1.661 523.8 5.91 .0491.881 1.956 5 76.4 6.44 .0512.044 2.336 627.3 7.06 .0522.198 2.683 6 75.3 7.5 8 .0522.336 3.046 717.7 8.09 .0532.500 3.479 769.1 8.66 .0552.637 3.981 811.7 9.28 .0562.774 4.379 854.4 9.74 .0572.899 4. /60 893.7 10.17 .0582.999 5.331 925.2 10.77 .0603.195 6.248 986.8 11.67 .0623.383 7.529 1046.2 12.82 .0673.591 8.914 1111.9 13.96 .0713.818 10.472 1185.5 15.13 .0774.066 12.203 1265.6 16.34 .085

POINTS ON PRELOAD LIimE 16 ON LOADED LINE 7 FRICTION FACTOR CUEFF. 12.03 RECIPROCAL C0EFF./rT2 .0831 .. .0012LOADING VELOCITY 2.823FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 2.950E+01

1 4

1 3

1 2

1 1

10

9

8

7

6

5

4

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197

.4

.3

Fig. 49 Run No. 54.

198

RUN NO. 5 5LIUUID

VELOCITY 9.52E-04FT/SEC HO L DU PDENSITY 1.20CM/ML STATIC .022VISCOSITY 7.50CP. OPERATING(EXPTL) .011SURFACE TENSION 64.DYNE/CM OPERATING(CALC) .020REYNOLDS NUMBER 7.507E-01 TOTAL (EXPTL) .033FROUDE NUMBER 5.343E-07 TOTAL (CALC) .042

G A SDENSITY .0723LB/CU•FTVISCOSITY .018 TCP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF T/SEC Lb/SO.FT/FT FT/SEC

P. 265 .050 80.1 .84 .033.414 . 107 125.3 1.33 .033.646 .20 7 195.4 1.95 .033.7 38 .308 223.2 2.41 .033.897 . 439 271.6 2.93 .034

1.076 .60 5 325.7 3.49 .0351.274 .822 386.0 4.10 .0351.4 35 1.038 43 4. 6 4.64 .0361.584 1.246 480.2 5.11 .0371.769 1.540 536.7 5.71 .0 371.932 1.817 586.1 6.23 .0392. 186 2.267 663.5 6.99 .0 402.320 2.579 705.7 7.4 6 .0 402.4 77 2.925 753.4 7.96 .0412.654 3.392 80/»6 8.59 .0422.821 3.808 859.0 9.12 .0422.980 4.2 40 907.6 9.64 .0433. 119 4.742 950.9 10.20 .0 443.298 5.210 1006.3 10.70 .0 443.493 6.058 1067.8 11.54 .0463.717 7.045 1137.0 12.46 .0483.925 8.153 1202.9 13.41 .0504.115 9.312 1263.0 14.34 .0524.245 10.178 1304.5 14.99 .0544.407 11.372 1356.0 15.85 .0574.550 12.290 1401.7 16.47 .0604.719 13.501 1455.8 17.27 .0634.823 14.453 1489.8 17.86 .0674.943 15.492 1530.9 18.47 .071

POINTS ON PRELOAD LINE 19 ON LOADED LINE 8 FRICTION FACTOR COEFF. 10.46 RECIPROCAL COEFF.m‘z .09 55 TOL. .0011 LOADING VELOCITY 3.506FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 1.142E+02

1 4

13

1 2

1 1

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9

8

7

6

5

4

3

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199

(ft. /sec.)08

06 -k

03 ..

Fig. 50 Run No. 55

200

RUN NO. 61LIUU ID

VELOCITY 3.37E-03 FT/SEC HOLDUPDENSITY 1 • 33 GM/ M L STATIC .021VISCOSITY 240 .OOCP. OPERATING(EXPTL) . 114SURFACE TENSION 69.DYNE/CM OPERATING(CALC) .096REYNOLDS NUMBER 9.173E- 02 TOTAL (EXPTL) . 135FROUDE NUMBER 6.696E-06 TOTAL (CALC) .117

GASDENSITY • 07 49 LB/ C U. FTVISCOSITY .0183CP .

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADI ENT NU MBER FUNCTION HOLDUPFT/SEC LB/SQ.FT/FT FT/SEC

P. 167 .050 53.9 .75 .135. 262 . 107 84.4 1.22 .135.368 .192 118.3 1.73 .135.470 . 315 151.3 2.29 .135.564 .439 181.3 2.77 .135.652 . 598 209.8 3.28 . 135.774 .820 248.9 3.90 .135.85 7 1.038 2 76.1 4.42 .135.9 37 1.350 301.8 5.08 .137

1.063 1.592 3 42.6 5.56 .1391. 156 1.990 373.0 6.25 . 1411.212 2.388 391.3 6.8 7 . 1421.260 2.752 406.7 7.39 . 1461.288 3.063 416.0 7.8 0 . 1481.344 3.565 434. 5 8.43 . 1501.411 4. 119 456.1 9.09 . 1521.481 4.742 479.4 9.77 .154

POINTS ON PRELOAD LINE 11 ON LOADED LINE 6 FRICTION FACTOR COEFF. 27.11 RECIPROCAL COEFF jrf1 .0 3 TOL. .0022LOADING VELOCITY 1.104FT/SECSORT DYNAMIC STRESS RATIO aT LOADING 9.840E-00

14

13

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8

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6

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201

0

Fig. 51 Run No. 61.

202

RUN NO. 62 LIQUID

VELOCITY 6•59E-03FT/SEC DENSITY 1.33GM/HLVISCOSITY 225.00CP.SURFACE TENSION 69.DYNE/CP1 REYNOLDS NUMBER 1.914E-01 FROUDE NUMBER 2.561E-05

NO L DU PSTATIC .021 OPERATING(EXPTL) .161 OPERATING(CALC) .121 TOTAL (EXPTL) .182 TOTAL (CALC) .142

GaSDENSITY .0747LB/CU•FTVISCOSITY .0 183CP.GAS PRESSURE REYNOLDS PRESSURE TOTAL

VELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF1/SEC LB/SQ.FT/FT FT/SEC

P. 130 .0 50 41.5 .70 . 182.217 .116 69.6 1.22 . 182. 294 .199 94.1 1.70 . 182.371 .308 118.7 2.19 . 182.44 8 . 439 143.6 2.69 . 182.523 .607 167.6 3.23 . 182.598 .803 191.6 3.77 . 183.673 1.10 7 215.6 4.48 . 184. 734 1.384 235.4 5.05 . 188.772 1.540 247.5 5.35 . 188.852 2.129 2 73.2 6.34 . 191.899 2.527 288.6 6.93 . 192.941 3.202 3 02.4 7.83 . 197.992 4.500 319.3 9.31 .203

POINTS ON PRELOAD LINE 7 ON LOADED LINE 4 FRICTION FACTOR COEFF. 37.06

PROCAL C 01 F F jii2 • u TOL. .u016LOADING VELOCITY . 789FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 3.591E-00

1 4

1 3

1 2

1 1

10

9

8

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6

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203

.4

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+ T .2+ + + T+ ♦ + + + + + ▼

Fig. 52 Run No. 62.

204

RUN NO. 63LIQUID

VELOCITY 9•69E-03FT/S EC HOLDUPDENSITY 1•33GM/ML STAT IC .021VISCOSITY 215.00CP. OPERATING(EXPTL) . 190SURFACE TENSION 69.DYNE/CM OPERATING(CALC) . 139REYNOLDS NUMBER 2.946E-01 TQTaL (EXPTL) .211FROUDE NUMBER 5.542E-05 TOTAL (CALC) . 160

GASDENSITY •0744LB/CU.FTVISCOSITY •0184CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF T/SEC LB/SQ.FT/FT FT/SEC

P. 103 .050 32.8 .66 .210. 163 . 107 51.9 1 . 10 .211. 239 .207 76.1 1.67 .211.291 .306 92.5 2.10 .211. 358 . 448 113.8 2.63 .211.413 .621 131.4 3.17 .211.465 .606 147.9 3.6 7 .212.530 1.090 169.0 4.34 .213.5 72 1.315 182.7 4.80 .217.6 18 1.938 197.7 5.88 .220.670 3.098 214.7 7.49 . 229.718 3.860 230.0 8.41 .236. 76 0 4.673 2 43.8 9.3 0 .238.807 6.145 259. 1 10.71 .2 44. 846 7.616 2 71.7 11.97 . 256.884 10.039 284. 5 13.78 .268.921 10.732 2 97.0 14.28 . 273.956 11.078 309.9 14.52 .268

POINTS ON PRELOAD LINE 7 ON LOADED LINE 9 FRICTION FACTOR COEFF. 36.65 RECIPROCAL COEFF^n2.0176 TOL. .0016 LUADING VELOCITY * 558FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 1.723E-00

205

(ft. /sec.)

.9 1.0

Fig. 53 Run No. 63

206

RUN IMG. 6 4LIUUID

VELOCITY 2.49E-03FT/SEC HOLDUPDENSITY 1.33GM/ML STAT IC .021VISCOSITY 210.00CP. OPERATING(EXPTL) .088SURFACE TENSION 69.DYNE/CM OPERATING(CALC) .082REYNOLDS NUMBER 7.747E-02 TOTAL (EXPTL) . 109FROUDE NUMBER 3.656E-06 TOTAL (CALC) . 104

GASDENSITY •0744LB/CU.FT

VISCOSITY .018 4CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCT ION HOLDUP

F IV SEC Lb/SO.FT/FT FT/SECP

. 187 .050 5 9.7 .77 . 109

.307 .116 98.3 1.30 . 109

.416 . 207 133.1 1.83 . 109

.5 15 .31 5 164. 6 2.32 . 109

.622 . 439 199.1 2.80 . 109

.7 35 .605 235. 1 3.34 . 109

.84 7 .806 271.1 3.90 . 110

.950 1.038 304.2 4 • 46 . 1101.063 1.280 340.4 4.99 .1111.209 1.713 387.2 5.82 .1141.294 2.042 414.7 6.38 . 1151.393 2.42 3 446.7 6.97 . 1181.454 2.890 4 66. ( 7.6 3 . 1211.483 3.046 476. 1 7.84 .1221.572 3.669 505.0 8.63 .1251.629 4.275 523.8 9.33 .1281.680 5.054 540.8 10.15 .1321.75 7 5.93 7 566.0 11.02 .1371.908 6.750 614.1 11.79 .1371.944 8.412 627.9 13.15 . 1432.077 10.247 6 72.2 14.54 . 1582.185 12.601 708.5 16.14 . 1722.282 15.319 741.0 17.81 . 189

POINTS GiM PRELOAD LINE 12 ON LOADED LINE 9 FRICTION FACTOR COEFF. 22.86 RECIPROCAL COEFFjtP.0437 TGL. .UU24 LOADING VELOCITY 1.437FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 1.727E+01

14

13

12

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8

7

6

5

4

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207

0 2

208

RUN NO. 6 5LiUU ID

VELOCITY 1.51E-03FT/SEC HOLDUPDENSITY 1.33GM/ML STATIC .021VISCOSITY 240.OOCP. OPERATING(EXPTL ) .067SURFACE TENSION 69.DYNE/CM OPERATING(CALC ) .072REYNOLDS NUMBER 4.141E- 02 TOTAL (EXPTL) .088FROUDE NUMBER 1.360E-06 TOTAL (CALC) .093

GaSDENSITY • 0747LB/ CU. FT

VISCOSITY .0183CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCTION HOLDUP

FT/SEC LB/SQ.FT/FT FT/SECP

.197 .050 63.4 .78 .089

. 312 . 107 100.2 1.25 .089

.4 38 .20 7 140.8 1.84 .089

.540 . 308 173.7 2.30 .089

.666 .448 214.3 2.84 .089

. 76 9 . 605 247.3 3.34 .089

.900 .813 289.5 3.93 .0891.007 1.038 324.1 4.47 .0891.120 1.298 360.3 5.04 .0891.260 1.592 405.6 5.62 .0911.369 1.938 440.8 6.23 .0911.448 2.250 4 66.6 6.72 .0931.561 2.613 503.4 7.27 .0951.664 3.115 536.9 7.96 .0971.740 3.617 561.8 8.59 .0991.75 6 3.964 567.0 9.00 . 1011.803 4.327 582.5 9.41 . 1031.897 4.864 613.6 9.99 . 1061.937 6.266 62 6.9 11 .35 . 114

POINTS ON PRELOAD LINE ID ON LOADED LINE 6 FRICTION FACTOR COEFF. 10.40 RECIPROCAL COtFF.m2 .0515 TOL. .0014 LOADING VELOCITY 1.586FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 3.127E+01

14

13

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sec.

0Fig. 55 Run No. 65.

210

RUN NO. 66LIQUID

VELOCITY 6.64E-04FT/SEC HOLDUPDENSITY 1.33GM/ML STAT IC .021VISCOSITY 260.00CP. OPERATING(EXPTL) .042SURFACE TENSION 69.DYNE/CM OPERATING(CALC) .055REYNOLDS NUMBER 1.674E-02 TOTAL (EXPTL) .063FROUDE NUMBER 2.600E-07 TOTAL (CALC) .076

G A SDENSITY .0 747 LB/CU.FTVISCOSITY .0183CP .GAS PRESSURE REYNOLDS PRESSURE TOTAL

Velocity GRADIENT NUMBER FUNCT IUN HOLDUPF T/SEC LB/SQ.FT/FT FT/SEC

P. 222 .050 71.4 .80 .062.354 .107 113.9 1.28 .062.498 .207 160.0 1.87 .062.610 .308 196.0 2.33 • 064. 745 . 439 239.4 2.84 .064.880 .60 5 282.9 3.38 .064

1.020 .806 328.0 3.95 .0641.146 1.038 368.7 4.51 .0651.305 1.315 420.0 5.12 .0651.44 6 1.609 465.4 5.69 .0651.558 1.886 502.0 6.18 .0661.7 00 2.267 547.8 6.80 .06 71.800 2.596 580.1 7.3 0 .0691.930 3.011 622.8 7.88 .0742.025 3.462 653.8 8.4 6 .0772.111 4.033 682.0 9.14 .0792.232 4.673 722.3 9.8 5 .0812.318 5.43 5 750.5 10.63 .0852.445 6.577 791.5 11.72 .0902.616 8.135 848.5 13.05 .0942.741 9.607 890.4 14.19 .0982.8 39 11 .805 92 3.8 15.73 . 1072.973 13.2 42 968.6 16.67 .1153. 118 14.886 1017.2 17.68 .1223.163 16.271 1034.5 18.47 . 134POINTS ON PRELOAD LINE 14 ON LOADED LINE 9 FRICTION FACTOR COEFF. 15.82 RECIPROCAL C0EFF«m~2 . 1 L. .0016LOADING VELOCITY 2.060FT/S ECSORT DYNAMIC STRESS RATIO AT LOADING 9.286E+01

14

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sec.

sec.

Fig. 56 Run No. 66.0 2

212

RUN NO. 73LIQU ID

VELOCITY 8.50E-03FT/SEC HOLDUPDENSITY 1.28GM/ML STATIC .022VISCOSITY 47.00CP. OPERaTING(EXPTL) .083SURFACE TENSION 69.DYNE/CM OPERATING(CALC) .085REYNOLDS NUMBER 1.138E- 00 TOTAL (EXPTL) . 105FROUDE NUMBER 4.260E-05 TOTAL (CALC) . 107

GASDENSITY • 07 40L6/CU. FTVISCOSITY .0184CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCTION HOLDUPFT/SEC Lb/SQ.FT/FT FT/SEC

P. 191 .050 60.8 .78 . 105. 294 . 107 93.7 1.24 . 105.421 .207 134.3 1.83 . 105.515 . 308 164.2 2.29 . 106.628 .43 9 200.2 2.80 . 106.741 .614 236.0 3.36 . 106.854 .798 272.0 3.88 . 107.976 1.055 311.0 4.51 . 108

1.089 1.315 347.3 5.07 . 1081.210 1.627 386.3 5.68 . 1081.324 2.025 422.8 6.36 .1101.410 2.267 450.2 6.7 6 .1101.504 2.735 480.5 7.44 .111i .565 3.029 500.5 7.85 .1121.636 3.548 52 3.6 8.51 .1141.703 3.964 545.2 9.00 . 1151.731 4.414 554.6 9.51 .1161.768 4.8 29 567.2 9.95 . 1171.840 5.539 590.7 10.67 .1191.983 6.647 637.4 11.71 . 1212.088 8.083 672.0 12.93 .1252.212 9.572 713.3 14.09 .1302.2 97 11.251 743.0 15.27 .136

POINTS ON PRELOAD LINE 10 ON LOADED LINE 11 FRICTION FACTOR COEFF. 21.13 RECIPROCAL COEFFV772 ,u473 TOL. ,0010 LOADING VELOCITY 1.436FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 5.139E-00

1 4

13

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U (ft,/sec.)

Fig. 57 Run No. 73.0 2

214

RUN NO. 74- LIQUID

VELOCITY I•59 E-02FT/SEC HOLDUPDENSITY 1•28GM/ML STAT IC .022VISCOSITY 45.00CP. OPERATING(EXPTL) .118SURFACE TENSION 69.DYNE/CM OPERAT ING(CALC) .111REYNOLDS NUMBER 2.231E-00 TOTAL (EXPTL) . 140FROUDE NUMBER 1.499E-04 TOTAL (CALC) . 133

ASDENSITY •0740LB/CU.FTVISCOSITY .0184CP.GAS PRESSURE REYNOLDS PRESSURE TOTAL

ELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF T/SEC LB/SQ.FT/FT FT/SEC

P. 161 .050 48.2 .73 .139.244 .107 77.7 1.20 .139. 34 8 .199 110.8 1.74 .139.440 .315 140.0 2.27 .138.520 . 429 165.4 2.71 .138.619 .602 196.8 3.27 .139.712 . 791 226.7 3.80 . 140• 844 1.125 268.7 4.60 .140.918 1.384 292.7 5.14 . 141

1.003 1.713 319.9 5.75 . 1441.073 2.319 3 42.6 6.72 . 1461. 149 2.942 367.0 7.60 . 1481.201 3.427 384.0 8.22 . 1521.271 4.154 406.9 9.08 .1541.361 5.366 436.1 10.35 . 1611.431 6.508 459.4 11.42 . 1691.502 7.789 483.2 12.51 .17 81.569 8.481 505.6 13.07 . 199POINTS ON PRELOAD LINE 9 ON LOADED LINE 9 FRICTION FACTOR COEFF. 29.01 RECIPROCAL C0EFF ,nfz « 03 44 TOL. .0018LOADING VELOCITY .965FT/SECSORT DYNAMIC STRESS RATIO aT LOADING 1.842E-00

14

13

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.4

Fig. 58 Run No. 740 2

216

RUN NO. (5LIQUID

VELOCITY 2.44E-02FT/SEC HOLDUPDENSITY 1.28GM/ML STAT IC .022VISCOSITY 44.00CP. OPERATING(EXPTL) . 149SURFACE TENSION 69.DYNE/CM OP ERATING(CALC) . 136REYNOLDS NUMBER 3.496E—00 TOTAL (EXPTL) . 17 1FROUDE NUMBER 3.518E-04 TOTAL (CALC) . 158

A SDENSITY . 0738LB/CU.FTVISCOSITY .0185CP.GAS PRESSURE REYNOLDS PRESSURE TOTAL

ELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF T/SEC LB/SQ.FT/FT FT/SEC

P. 131 .050 41.5 .71 . 171.202 . 103 64. 1 1 . 13 . 171. 295 .199 93.4 1.70 . 171.380 .313 120.3 2.22 . 171.460 .457 145.6 2.76 . 171.521 .604 164.9 3.22 . 171.601 .806 190.2 3.7 8 .17 3.6 76 1 .073 214.2 4.41 . 175. 70 4 1.246 223.2 4.7 7 . 177.765 1.731 242.8 5.67 . 179.816 2.163 259.4 6.3 7 . 182.873 2.977 277.7 7.51 . 186.925 3.756 294.6 8.47 . 191.953 4.154 303.9 8.92 . 195

1.013 5.539 323.7 10.34 .2041. 104 6.750 353.0 11 .47 .219POINTS ON PRELOAD LINE 8 ON LOADED LINE 6 FRICTION FACTOR CUEFF. 38.53 RECIPROCAL COE«02 TO L . .0022LOADING VELOCITY . 698FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 8.677E-01

1 4

1 3

1 2

1 1

10

9

8

7

6

5

4

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217

Fig. 59 Run No. 75

218

RUN NO. (6LIQUID

VELOCITY 3.74E-02FT/S EC HOLDUP' DENSITY 1.28GM/ML STATIC .022VISCOSITY 43.00CP. OPERATING(EXPTL) . 190SURFACE TENSION 69.DYNE/CM OPERATING(CALC) . 168REYNOLDS NUMBER 5.475E-00 TOTAL (EXPTL) .212FROUDE NUMBER 8.241E-04 TOTAL (CALC) . 190

GASDENSITY .073 5LB/CU.FTVISCOSITY .0185CP.GAS PRESSURE REYNOLDS PRESSURE TOTAL

VELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF T/SEC LB/SQ.FT/FT FT/SEC

P.094 .050 29.5 .64 .212. 157 .107 49.4 1.09 .212. 228 .206 71.6 1.64 .212.286 .308 90.0 2. 10 .212. 34 7 . 444 109.4 2.61 .212.391 .571 123.1 3.02 .215• 4 2 4 .778 133.6 3.56 .215.485 1.073 152.9 4.26 .218.522 1.384 1 64.8 4.88 .219.574 1.696 181.4 5.46 .224

POINTS UN PRLLOAD LINE 5 ON LOADED LINE 5 FRICTION FACTOR CUEFF. 54.07 RECIPROCAL COEFFvn2 .0184 TOL. .0011 LOADING VELOCITY .358FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 2.909E-01

14

13

12

1 1

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8

7

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2

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219

.4

.3

• 2

H0LDUP . 1

.08

Fig. 60 Run No. 76

220

RUN NO. 77L 1UU ID

VELOCITY 6.12E-04FT/SEC HO L DU PDENSITY 1.28GM/ML STAT IC .022VISCOSITY 48.00CP. OPERATING(EXPTL) .025SURFACE TENSION 69.DYNE/CM OPERATING(CALC) .031REYNOLDS NUMBER 8.034E-02 TOTAL (EXPTL) .047FROUDE NUMBER 2.208E-07 TOTAL (CALC) .053

GASDENSITY .0740LB/CU.FTVISCOSITY .0184CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCT ION HOLDUPF T/SEC LB/SQ.FT/FT FT/SEC

P.83.253 .050 80.3 .047

.403 .107 128.0 1.31 .047

.56 7 . 204 180.2 1.89 .048

.703 .309 223.4 2.38 .047

. 849 .432 269.7 2.86 .0471.018 .605 32 3.6 3.43 .0 481. 187 .806 3 77.5 3.99 .0481.352 1.038 430.0 4.57 .0491.522 1.315 484.2 5.17 .0491.692 1.609 53 8.6 5.75 .0491.841 1.921 586.1 6.30 .0502.023 2.284 644.0 6.90 .0512.127 2.596 6 77.6 7.37 .0522.298 2.977 732.9 7.90 .0532.431 3.306 775.9 8.34 .0532.632 3.929 840.4 9.11 .0542.77 7 4. 448 887.4 9.71 .0552.879 4.846 921.3 10.14 .0553.034 5.556 971.3 10.87 .056

POINTS ON PRELOAD LINE 15 ON LOADED LINE 0 FRICTION FACTOR COEFF. 11.69 RECIPROCAL COEFFjv2 *08 TUL. .0010

1 4

13

1 2

1 1

10

9

8

5

4

3

2

1

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221

(ft ./sec)

(ft./sec.)

Fig. 61 Run No. 77.

222

RUN NO* /8LiOU ID

VELOCITY 1.87 E-03 FT/S EC HOLDUPDENSITY 1.28GM/ML STATIC .022VISCOSITY 47.00CP. OPERATING(EXPTL) .036SURFACE TENSION 69•DYNE/CM OPERATING(CALC) .047REYNOLDS NUMBER 2.520E- 01 TOTAL (EXPTL) .058FROUDE NUMBER 2.079E-U6 TOTAL (CALC) .069

G aSDENSITY . 07 40 LB/ C U. FTVISCOSITY .0184CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCTION HOLDUPFT/SEC LB/SO.FT/FT FT/SEC

P.224 .050 71.2 .81 .058. 364 . 103 115.5 1.27 .058.533 .207 169.4 1.89 .059.650 .299 2 06.6 2.32 .058.814 • 446 258.7 2.89 .058. 964 .619 306.4 3.45 .059

i. 115 .806 354.2 3.98 .0591.255 1.055 399.1 4.58 .0601.378 1.280 438.0 5.08 .0611.5 86 1.661 5 04.4 5.82 .0611.691 1.938 537.7 6.31 .0621.838 2.302 585.0 6.90 .0631.980 2.613 630.6 7.37 .0642. 124 3.133 6 76.7 8.09 .0652.210 3.392 704.2 8.43 .0672.401 4.119 765.6 9.31 .0682.553 4.846 815.1 10.11 .0692.6^6 5.521 855.4 10.80 .071

POINTS ON PRELOAD LINE 15 ON LOADED LINE 0 FRICTION FACTOR COEFF. 13.88 RECIPROCAL COEFF jtT2 *0720 TOL. 0021

14

13

1 2

1 1

10

9

8

7

6

5

4

3

2

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223

S&c.

Fig. 62 Run No. 78.0 2 3

224

RUN NO. 7 9 LIQU ID

VELOCITY 4.64E-03FT/SEC HOLDUPDENSITY 1.28GM/ML STATIC .022VISCOSITY 48•OOCP• OPERATING(EXPTL) .061SURFACE TENSION 69.DYNE/CM OPERATING(CALC) .066REYNOLDS NUMBER 6.107E-01 TOTAL (EXPTL) .083FROUDE NUMBER 1.272E-05 TOTAL (CALC) .088

GASDENSITY .0738 LB/CU.FTVISCOSITY • 0 18 5C P .GAS PRESSURE REYNOLDS PRESSURE TOTAL

VELOCITY GRADIENT NUMBER FUNCTION HOLDUPFT/SEC LB/SQ.FT/FT FT/SEC

P. 206 .050 65.2 .79 .083. 323 . 107 102.6 1.2 7 .083.470 .206 148.5 1.85 .083.378 .311 182.6 2.3 4 .083.710 .453 224.3 2.88 .083.827 . 604 261.5 3.37 .084.959 .806 303.3 3.94 .084

1.082 1.038 3 42.1 4.51 .0841. 195 1.263 378.0 5.01 .0851.356 1.627 428.9 5.73 .0861.461 1.921 462.2 6.25 .0861.556 2.233 492.5 6.76 .0871.669 2.561 52 8.7 7.26 .0891.775 2.994 562.7 7.87 .0901.846 3.340 585.7 8.32 .0921.942 3.808 616.3 8.90 .0942.046 4.379 650.0 9.56 .0952.162 4.8 98 687.0 10.13 .0972.295 5.989 730.3 11.21 . 1012.381 7.477 759.1 12.53 . 1072.517 9.001 803.5 13.77 .1172.674 11.770 855.2 15.76 . 1302.846 14.194 912.8 17.31 .1442.954 15.492 949.3 18.09 . 149POINTS ON PRELOAD LINE 13 ON LOADED LINE 9FRICTION FACTOR COEFF. 17 .97RECIPROCAL »m~2 . 3 6 TOL. 0018LOADING VELOCITY 1.913FT/SECCURT DYNAMIC STRESS RATIO AT LOADING 1.249E+01

14

13

12

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8

7

6

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225

Fig. 63 Run No. 79 .

226

RUN NO. 80L iUU ID

VELOCITY 0.00 E-99 FT/SEC HOLDUPDENSITY 1.28GM/ML STATIC .022VISCOSITY 45.00CP. OPERAT ING(EXPTL)Q .000SURFACE TENSION 69•DYNE/CM OPERATING (CALC ) 0 .000REYNOLDS NUMBER 0.000E- 99 TOTAL (EXPTL) .022FRUUDE NUMBER 0.000E-99 TOTAL (CALC) .022

GasDENSITY .0744LB/CU.FTVISCOSITY .0184CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADI ENT NUMBER FUNCTION HOLDUPFT/SEC LB/SQ.FT/FT FT/SEC

P.84.2 77 .050 88.1 .022

.431 . 107 137.0 1.32 .022

.623 .207 198.1 1.92 .022

.787 . 315 250.3 2.42 .022

.952 .439 302.6 2.91 .0221. 125 . 605 358.0 3.45 .0221.323 .813 42 0.9 4.04 .0221.503 1.055 478.1 4.63 .0221.692 1.350 538.5 5.26 .0221.898 1.644 604.1 5.8 4 .0222.078 1.921 661.6 6.33 .0222.290 2.2 67 729.2 6.90 .0222.430 2.544 774.9 7.32 .0222.678 3.011 854.9 7.98 .0222.841 3.375 907.7 8.46 .0223.032 3.808 9 6 9.5 9.00 .0223. 164 4.206 1012.8 9.47 .0223.339 4. 708 1069.4 10.02 .0223.512 5.106 1125.5 10.45 .0223.782 5.781 1213.7 11.13 .0223.998 6.439 1284.0 11.75 .0224.213 7.201 1355.5 12.43 .0224.4 18 7.945 1 42 3.4 13.06 .0224.684 8.845 1511.0 13.79 .0224.963 9.901 1603.2 14.59 .0225.183 10.888 1676.3 15.30 .0225.380 11.770 1744.7 15.90 .0225.553 12.688 1803.0 16.50 .0225.803 14.107 1888.9 17.39 .0225.973 14.800 1946.9 17.81 .0226.086 15.405 1986.1 18.16 .022

POINTS ON PRELOAD LINE 31 ON LOADED LINE 0 FRICTION FACTOR COEFF. 8.84 RECIPROCAL COEFF.m~2 •1130 TOL. .0011

1 4

13

12

1 1

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9

8

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6

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227

0 1

Fig. 64 Run No. 80.

2 3

228

RUN NO, 11LIQUID

VELOCITY 3.29E-03FT/S EC HOLDUPDENSITY .81GM/ML STATIC .017VISCOSITY 2.24CP. OPERATING(EXPTL) .022SURFACE TENSION 26.DYNE/CM OPERATING!CALC) .027REYNOLDS NUMBER 5.857 E-00 TOTAL (EXPTL) .039FROUDE NUMBER 6.413E-06

GASDENSITY .0718LB/CU.FT

VISCOSITY .0188CP.

TOTAL (CALC) .044

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITYFT/SEC

GRADIENTLB/SQ.FT/FT

NUMBER FUNCTIONFT/SEC

P.83

HOLDUP

.25 3 .050 75.4 .038

.401 .109 119.6 1.33 .038

.569 .206 169.4 1.92 .038

.693 .299 206. 5 2.37 .039

.860 .439 256.3 2.93 .0391.023 .598 304.7 3.47 .0391 . 194 .806 356.2 4.07 .0391.381 1.073 411.8 4.73 .0401 .552 1.384 463.3 5.41 .0411.733 1.731 517.6 6.08 .0411.929 2. 181 576.1 6.85 .0422.100 2.596 627.6 7.50 .0422.376 3.462 710.6 8.70 .0442.5 09 4.154 750.8 9.55 .0472.74 7 5. 106 822.5 10.61 .0532.954 6.231 886.2 11.73 .059

POINTS ON PRELOAD LINE 10 FRICTION FACTOR COEFF. 11

ON LOADED LINE 5 .92

RECIPROCAL COE FF.m2.0839 TOL. . 0022LOADING VELOCITY 1.970FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 2.250E+01

14

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Cft. / ^ec )

Fig. 65 Run No. 11

230

RUN NO. 12 LIQUIDVELOCITY 6.53E-03FT/SEC HOLDUPDENSITY .80GM/ML STATIC .017VISCOSITY 2.18CP. OPERATING(EXPTL) .031SURFACE TENSION 26.DYNE/CM OPERATING(CALC) .037REYNOLDS NUMBER 1.191E+01 TOTAL (EXPTL) .048FROUDE NUMBER 2.517E-05 TOTAL (CALC) .054

GASDENSITY .0713LB/CU.F TVISCOSITY •0189CP.GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCTION HOLDUP

FT/SEC LB/SQ.FT/FT FT/SECn.240 .050 70.9 .82 .048.385 .105 113.5 1.31 .048.529 . 193 156.1 1.85 .048.659 .294 194. 5 2.34 .048.832 .446 245.6 2.95 .0481.001 .62 3 295.3 3.54 .0481.155 . 798 340.8 4.05 .048

1.313 1.073 387.8 4.73 .0491 .481 1.367 437.5 5.38 .0501 • 644 1.713 486.0 6.05 .0501.765 2.077 521.5 6.68 .0511.875 2.735 554.4 7.69 .0552.172 3.462 642.7 8.70 .0562.258 4.102 668. 5 9.48 .0582.411 4.985 714.3 10.47 .062POINTS ON PRELOAD LINE 10 ON LOADED LINE 3 FRICTION FACTOR COEFF. 12.97 RECIPROCAL COEFF .077 1 TOL. .0028LOADING VELOCITY 1.919FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 1.103E+01

14

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Fig. 66 Run No. 12

232

RUN NO. 13 LIQU ID

VELOCITY 1.03E-02FT/SEC HOLDUPDENSITY • 80GM/ ML STATIC .017VISCOSITY 2.12CP. OPERATING(EXPTL) .0 44SURFACE TENSION 26.DYNE/CM OPERAT ING (CALC ) .046REYNOLDS NUMBER 1.932E + 01 TOTAL (EXPTL) .061FROUDE NUMBER 6.273E-05 TOTAL (CALC) .063

GASDENSITY • 0713 LB/CU.FT

VISCOSITY .0189CP•

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCTION HOLDUP

FT/SEC LB/SQ.FT/FT FT/SECP

.213 .050 62.8 .80 .061

.341 . 103 100.6 1.27 .061

.505 .207 148.8 1.91 .061

.625 .304 184.2 2.37 .061

.760 .436 223.9 2.89 .061

.919 .628 270.8 3.53 .0621.053 .806 310.5 4.04 .0621.217 1.073 358.7 4.71 .0631.381 1.402 406.9 5.43 .0651.452 1 • 644 428.3 5.89 .0651.626 2.111 479.4 6.72 .0671.76 9 2.665 522.1 7.57 .0691.980 3.929 584.7 9.24 .0732.075 4.673 613.5 10.09 .0782.142 5.158 633.4 10.61 .082

POINTS ON PRELOAD LINE 10 ON LOADED LINE 4 FRICTION FACTOR COEFF. 15.29 RECIPROCAL COEFF ,m~2 .0653 TOL. .0034 LOADING VELOCITY 1.619FT/SECSORT DYNAMIC STRESS RATIO AT LOADING 5.898E-00

1 4

1 3

1 2

1 1

1 0

9

8

7

6

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233

P(ft./sec.)

♦ +T T T ▼ ▼

U (ft./sec.)G-

.4

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H0LDUP . 1

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.06

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. 04

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Fig. 6 7 Run No. 13

234

RUN NO. 15LIQUID

VELOCITY 0.00 E-99FT/SEC HOLDUPDENSITY • 81GM/ML STATIC .017VISCOSITY 2.64CP. 0PERATING(EXPTL)0 .000SURFACE TENSION 26.DYNE/CM OPERAT ING(CALC) 0 .000REYNOLDS NUMBER O.OOOE-99 TOTAL (EXPTL) .017FROUDE NUMBER 0.000E-99 TOTAL (CALC) .017

GASDENSITY .0732LB/CU.FT

VISCOSITY .0185CP.

GAS PRESSURE REYNOLDS PRESSURE TOTALVELOCITY GRADIENT NUMBER FUNCT ION HOLDUPFT/SEC LB/SQ.FT/FT FT/SEC

P.276 .050 85.3 .84 .017.425 .100 131.5 1.28 .017.614 . 193 190.0 1.87 .017.789 .304 244. 1 2.40 .017.979 .444 302.6 2.96 .017

1.154 .598 356.7 3.47 .0171.36 7 .806 422.4 4.07 .0171.603 1 .090 495.7 4.77 .0171.796 1.367 555.7 5.37 .0171.966 1.644 608.5 5.90 .0172.221 2.059 687.5 6.64 .0172.4 76 2.561 766.7 7.43 .0172.85 3 3.323 884.1 8.50 .0173.211 4.154 995.7 9.53 .0173.474 4.846 1078.0 10.30 .017

POINTS ON PRELOAD LINE 15 ON LOADED LINE 0 FRICTION FACTOR COEFF.* 8.89 RECIPROCAL CO E F F •m1.112 4 TOL. .0008

14

13

12

1 1

10

9

8

7

6

5

4

3

2

1

0

235

.4

.3

P(ft./sec.)

Fig. 68 Run No. 15

Reprinted from l&EC FUNDAMENTALS, Vol. 6, Page 400, August 1967 Copyright 1 967 by the American Chemical Society and reprinted by permission of the copyright owner

HOLDUP IN IRRIGATED RING-PACKED TOWERS BELOW THE LOADING POINT

J. E. BUCHANANUniversity of New South Wales, Kensington, N.S.W., Australia

Iiquid holdup may well be considered as the basic liquid- side dependent variable in packed tower operation.

Holdup has been shown to have a direct influence on liquid- phase mass transfer (2), on loading behavior (72), on gas- phase pressure gradient (72), and on mass transfer (9). In itself it is important only in the consideration of unsteady- state behavior of a tower—e.g., in batch distillation (8).

Many workers (3, 4, 7, 10-12) have measured holdup, with or without gas flow, and have produced empirical de­scriptions of their results. Only the correlation of Otake and Okada (7) is in dimensionless form and can claim any gen­erality. This correlation fits the available experimental data very well but it is derived by essentially empirical methods. It is desirable therefore to justify this form of relation theo-

400 l&EC FUNDAMENTALS

Two limiting dynamic regimes for liquid flow on an irrigated packing may be distinguished: the gravity-viscosity regime at low Reynolds numbers and the gravity-inertia regime at high values. Examination of simple models of the two modes suggests the form of the holdup relation for each case and gives order of magnitude estimates of the coefficients. Experimental results lie between the limits but are satisfac­torily correlated by an interpolation formula.

retically or to find an expression with a firmer theoretical basis.

Modes of Holdup

Three modes of liquid holdup have been discussed in the literature (/7), all expressed as cubic feet of liquid per cubic foot of packed volume, a dimensionless unit.

Total Holdup, the total amount of liquid on the packing at a given operating condition.

Static Holdup, the amount of liquid remaining on the packing after it has been fully wet\ed and drained for a long time.

Operating Holdup, the difference between total and static holdups.

The static holdup is clearly a function of static properties only. In a similar way it is usually taken that flow rates and dynamic properties affect only the operating holdup. This assumption implies that the static holdup remains stagnant and in place under all operating conditions. A partial justification for this view can be suggested, but in general it must be taken as only an approximation. At high liquid rates the static holdup makes only a small contribution to the total and little error is occasioned by accepting the assump­tion.

Largely, of course, the holdup is divided into two types as a matter of convenience in producting correlations. The

form of expression used is considerably simpler if the holdup approaches zero when liquid rate approaches zero. This is the case for operating holdup but not for total holdup.

Loading

Because most towers are operated below the loading point and because the problem is considerably simplified thereby, this treatment deals only with operating holdup in the pre- loading range of flow rates. To show the significance of this specification and to justify the methods of data selection it is necessary to discuss briefly the meaning of loading and the relation between holdup and loading.

Following White (13), the loading point is usually defined in terms of the gas-phase pressure gradient by reference to a plot of log (pressure gradient) vs. log (gas flow rate) at con­stant liquid rate, such as Figure 1 a. When experimental data are plotted in this way, most of the points usually fall convincingly on three straight lines, the points not on the straight lines showing smooth transitions between them. The lowest line has a slope 1.8 to 2 and the next about 4; the last line is practically vertical. The point of intersection of extrapolations of the two lower lines defines the loading point.

Visual observation of a tower shows that as gas velocity in­creases from zero the liquid flow pattern is unchanged until the loading region is approached. Then the pattern begins

cJ T

Xjd

i.o

•o'-

Superficial Gas Velocity (ft./sec.)

Figure 1. Holdup and pressure gradient

VOL. 6 NO 3 AUGUST 1967 401

to change and a buildup of liquid on the packing may be observed. This phenomenon was the origin of the name “loading point” and was one early way of defining it.

Measurements of holdup and pressure gradient over the same range confirm the close connection, implied above, between holdup and pressure gradient near the loading point. This also is shown in Figure 1, using some experimental data of Elgin and Weiss (3). At low gas rates the holdup increases very slowly, if at all, about linearly with gas rate. Near the loading velocity the holdup increases sharply and at an in­creasing rate. The region in which holdup begins to increase corresponds closely to that in which the slope of the pressure gradient line increases. The loading point could well be defined in this way. At high liquid rates holdup is indeed a more sensitive indicator of loading than is pressure gradient.

In such cases the pressure gradient curves change their form. The experimental points now clearly define a con­tinuous curve, the slope in the lower part being considerably less than the usual value of about 1.9. The position of the loading point is effectively obscured. This is the natural result of plotting on log-log coordinates a line that has nonzero intercepts. The holdup curves, however, follow their usual course, loading naturally, occurring at lower gas rates (Figure U).

At the highest liquid rate there is a change in the holdup behavior, as indicated in Figure 2. It is evident that at the highest rates used in this series of experiments (72) the loading point occurs at gas rates velocities near zero or negative. This fact too is concealed by the usual log-log plot. Use of a logarithmic plot implies some absolute significance of a zero value of the quantity plotted and no significance of negative values. When, as in the two cases cited, this assumption is unsound, the resulting picture is likely to be misleading.

Independent Variables

Holdup is almost independent of gas rate below the loading point. With little. loss of precision it can be taken to be completely independent, and may be treated as a function of the liquid flow variables only:

Liquid flow rateLiquid flow properties

Density Viscosity Surface tension

Local gravitational accelerationShape of the bedScale

Three items of the list—surface tension, shape, and scale— require further discussion.

It is assumed that all of the packing surface is wet, though not necessarily active; thus the only relevant surface tension is that between gas and liquid phases. As is established at greater length below, the experiments of Shulman et al. (71), in which surface tension was an experimental variable, show that its effect is small; it is neglected in the following dis­cussion.

When applied to a packed bed, “shape” has two aspects: the shape of the individual packing pieces and that of the assembly. The following treatment, while general in its application to all packing shapes of the film type, is applied only to Raschig rings. For these the height and diameter are equal for all sizes of rings. For mechanical reasons, however, small rings tend to have relatively thicker walls than large ones and so geometric similarity may not be exactly main­tained through the full range of sizes.

All of the data used are for dumped, random packings. It is not certain that such packings can be considered fully random in the statistical sense. Indeed, some recent work suggests that they are definitely not. Yet, so long as the bed diameter is sufficiently greater than the ring diameter and if the voidages are about the same, all beds may be taken to be equivalent and to have virtually the same shape. The usual requirement that D 8d has been met by almost all of the data which I have used.

In this work the relevant linear dimension is taken to be the ring diameter, d. Commonly, in treatments of packed beds the dimension is taken to be the diameter of a sphere of the same surface area or some other such equivalent diameter, which, with the voidage, is considered a sufficient description

Wa t e r- A i r

35mm.Raschig Rings

„ -

^ 0.23

/0?17 • /

"1

0.091•

0 044

-------- . 0.02 8--------*“

UL = 0.015 ft. sec.

0 12 3Superficial Gas Velocity (ft./sec.)

Figure 2. Holdup at high liquid flows

402 l&EC FUNDAMENTALS

of scale and shape. But even in the pressure drop studies for which it was derived this assumption has proved to be of limited value (5). Where shape is virtually constant, as in the case being considered, there is no need for such an elaboration and any relevant linear dimension will do.

Exact geometric similarity requires that all the packing pieces have the same shape and that beds be formed by stack­ing these pieces in the same way. For such assemblies the voidage, e, and dimensionless packing density, Nd3, should be the same. Where these quantities are available they are listed in the summary of data used (Table I). The data are not perfectly homogeneous, which no doubt accounts for some of the scatter in the results.

Data Selection and Methods of Measurement

Holdup data have been taken from several sources, dis­cussed separately below.

The best experimental methods were those of Shulman, Ullrich, and Wells (70), who used a tower mounted on a weighing scale so that water holdups could be measured directly by weight. For each liquid rate, measurements were taken over a range of gas flow rates, so that it can be established that operation was definitely below the loading point. These data have been accepted unreservedly.

Uchida and Fujita (72) used an arrangement where both the liquid inlet and the outlet to the tower could be cut off simultaneously. After stable operation had been established, the valves were closed and the volume of liquid which drained from the packing was measured. This was essentially a measurement of operating holdup. Again the holdup was measured over a range of positive gas flow rates for each liquid rate. Some of the results for very high liquid rates have been rejected because no region where holdup was independent of gas flow could be found in the results. In these cases the loading point was evidently near zero or in the negative gas flow region, as in cocurrent flow.

Shulman, Ullrich, Wells, and Proulx (77) used the ap­paratus described by Shulman, Ullrich, and Wells (70) with a large variety of liquids. All measurements were taken at zero gas rate, but the absence of loading could be checked from the Uchida and Fujita data and all of their results were accepted. Otake and Okada (7) used a method similar to that of Uchida and Fujita but in this case air flowed freely through the tower, the flow being restricted only partly at a measuring orifice. It is here assumed that this arrangement would avoid loading and that the measured holdup would be the value independent of gas velocity.

In all of the other cases the holdup value used was either that at zero gas flow (77) or extrapolated to zero gas flow (70, 72).

Operating Holdup

Limiting Flow Regimes. Forces acting on fluid particles are gravity, viscous drag, and inertia.

While gravity is always the driving force, either viscous or inertial forces may predominate as the resistance. Thus, two limiting flow regimes may be distinguished—the gravity- viscosity and gravity-inertia regimes. In general, these will occur at low and high values of Reynolds number, respec­tively—that is, at low velocity or high viscosity losses will be mainly due to viscous drag in an essentially laminar flow. In the converse case the losses will be caused mainly by turbu­lence arising at sudden changes of flow path.

Gravity-Viscosity Control. Behavior of this regime has been described by several workers, notably Nusselt (6) and Davidson (2). The basic assumption is that the liquid is everywhere at its terminal velocity; no accelerations need be considered.

The model used is an assembly of flat surfaces inclined at angle, 9, to the horizontal and having a liquid film of uniform thickness, A, flowing down the surface of total area, a, sq. feet per cu. foot. The liquid loading is L lb./(sec.) (sq. ft.) of horizontal cross section.

At any cross section of the assembly the width of the surface will be a sin 6 and the liquid loading may be expressed in

Lanother way as —7— = L' lb./(sec.) (ft. width of surface)

a sin 9Then by the well known derivation of Nusselt (6)

A

Now H = aA and

7>pL' 113

_p2g sin 9

H =3 p.a~L 1/3

_p2g sin2 9

For standard packings the packing size, d, is a more convenient quantity than the area, a. For packings of constant shape ad = k, a dimensionless constant.

Noting also that L/p = U, the superficial liquid velocity, we may write:

3 " 1/3 ~mu: 1/3 .H =

sin2 9 _d‘2Pg_• [ad]z/3

Table I. Summary of DataSurface

v, Tension,Workers Ref. Diameter, d e Nd3 D/d Centistokes Dynes/Cm. Symbol

Shulman et al. (10) 0.5 in. 0.61 0.79 20 1 73“1.0 in. 0.73 0.79 10 1 73“ ■1.5 in. 0.72 0.84 7 1 73“

Shulman et al. (17) 1.0 in. 0.72 10 0.74-125 38-86 A

Otake and Okada (7) 1.02 cm. 0.59 0.82 10 1 73“1.60 cm. 0.82 16 1 73“ X2.55 cm. 0.64 0.83 10 1 73“

Uchida and Fujita (12) 1.5 cm. 0.74 17 1 73“1.6 cm. 0.73 16 20-330 302.6 cm. 0.73 10-14 1-280 30-73“ •3.5 cm. 0.76 7 1-310 30-73“

“ Assumed. The liquid was water.

VOL. 6 NO. 3 AUGUST 1967 403

9

8

7

H 6

5

4

3

2

1

0-2-10123

Log ( Re )Figure 3. Data plotted according to Equation 1

The first term is a coefficient depending on the inclination of the surfaces. The second is equal to the quotient of the Froude and Reynolds numbers, referred to as the film number,Fi. The third term may be combined with the first as a factor shape for a given packing. The equation may be written briefly as

H = .SXFi)1'3 (1)

For dumped Raschig rings ad ^ 5; and for 6 taken to be from 60° to 80°, S is calculated to be in the range 4.2 to 4.5.

Figure 3 is a plot of H/Fi1/3 vs. Re. At low Reynolds num­bers H/Fi1/3 approaches a constant value in the range S = 2 to 3. At high Re the holdup is higher than Equation 1 would predict.

Gravity-Inertia Control. The assumption made here is that energy losses owing to continuous viscous drag are negligible. The only losses occur when the natural liquid flow path is impeded from time to time and energy is dissi­pated in turbulence. This dissipation is an effect of liquid viscosity, but the amount of energy dissipated is not strongly dependent on the magnitude of the viscosity.

The model for this situation is similar to the previous one, except that the flow is interrupted, at intervals l by steps, as shown in Figure 4; at each interruption the liquid loses a fraction, F, of its kinetic energy before proceeding down the next slope. Other losses are negligible.

If the initial velocity is Ff, we may write

nVi = 2gl sin 6

where

n = F/(l ~ F)

Figure 4.Gravity-inertiamodel

At distance r down the plate

V2 = v? + 2 gr sin 6

= 2g sin 0 [(//n) + r]

VT = (2g sin ey12 • [(//«) + r]1/2

Now A (r) = L'/(pVr)

and Amean = 1// Mr) dr

Vpl(2g si

V

— rn 0)1'2 Jo W/n) + r]1/2

{n + 1)1/2 - 12/1/2 •

pl(2g sin 0)1/2

y/2Lp a sin 6 (gl sin 8)112

(n + 1)1/2 - 1

* yn;-

K*

X V.A •*k*

X- A**& *X X

▲

A

•a 4.a % :*

404 l&EC FUNDAMENTALS

HFr

Lo g ( Re)Figure 5. Data plotted according to Equation 2

~u2' 1/2 2

_gl _ sin3 6

L/p = U

H rrAmean

{n + 1 )112 - 1

But

and, as before,

If it is assumed that /, F, and 6 are independent of liquid flow rate, the equation reduces to:

H = S' (Fr)1/2 (2)

Now the value of /, in a packing must be related to the packing size and may be expected to be of about the same magnitude. Taking /, to be equal to d.

s' = (2/sin3 ey2 •(n + 1)1/2 - 1

nF2

For values of F ranging from 0.5 to 0.9 and 6 from 60° to 80° calculated values of S' are in the range 0.61 to 1.26. Holdup in falling drops or streams would follow a similar law, 6 now being 90°.

Figure 4 is a plot of H/Fr1/2 vs. Re. In this case it may be seen that at high Reynolds number H/Fr1/2 approaches a constant value of about 3. At low Re the holdup is greater than can be accounted for by Equation 2.

Correlation

Figure 6. 95% joint-confidence ellipse forcoefficients S and S'

H = S Fi1/3 + S' Ft1'2 (3)

For convenience in developing a correlation this equation is transformed to the straight-line expression

H/Fi1/3 = S + S’ Fr1/2/Fi1/3 (4)

From Figures 3 and 5 it is evident that except for some of the points at very low Reynolds numbers the experimental results cannot be described by either Equation 1 or 2 but appear to be in a transition region. An interpolating expression is required to cover this transition. A simple expression is the sum of the terms for the limiting conditions.

The experimental data have been examined using this equa­tion and coefficients S and S' found to give the line of best fit. A joint 95% confidence ellipse (7) for S and S' is shown in Figure 6. The indicated best values of 2.2 and 1.8 compare well with the order of magnitude estimates of 4 and 1 given above.

VOL. 6 NO 3 AUGUST 1967 405

The experimental points are shown in Figure 7 plotted according to Equation 4; the line of best fit is the final pro­posed equation,

H= 2.2 Fi1/3 + 1.8 Fr1/2 (5)

As may be seen from Figure 8, this equation, with two arbi­trary coefficients, satisfactorily correlates all the data over a range of almost five orders of magnitude in Reynolds number.

For comparison the Otake and Okada relationship is shown in the same way in Figure 9.

The equations are:

H = 8.1 Fr°-44Re_0-:i7 for 0.01 < Re < 10

and

H = 6.3 Fr°-44 Re-0-20 for 10 < Re < 200

2.2Fi»+1.8Fr

FrVFI*Figure 7. Data plotted according to Equation 4

■ +20%

Log (Re)Figure 8. This correlation compared with experiment

406 l&EC FUNDAMENTALS

H= 8.1 Fr Re 6.28 Fr Re

-2 0%

-J -0.2

Lo g ( Re)Figure 9. Otake and Okada correlation compared with experiment

and the agreement is only slightly better. However, the range of Reynolds numbers had to be separated into two parts, leading to a total of six empirical constants in the two equations.

Effect of Surface Tension. This general correlation has been developed without taking any account of surface tension. It is desirable to re-examine the data to see whether any sur­face tension effect can be found.

For this purpose the data of Shulman et al. (7 7) are relevant. In these experiments a wide range of surface tensions was examined, using both low surface tension organic liquids and aqueous solutions of a surface-active agent.

The relevant data are shown in Figure 10 plotted according to Equation 5. The points cover a wide range but in an ap­parently random fashion. No residual surface tension effect is discernible.

Scope of Correlation. The experimental data used in developing the correlation were taken from experiments with ceramic Raschig rings only and the resulting equation applies strictly only to such packings.

^exp

) o

+2 0%■

jj

S 0X

o>o_J

-0.1

■ ** ■* ■ +« +1 ♦ +* •- xl t *# • : t

-2 0%

•

1 2 3

Log (Re)Figure 10. Effect of variable surface tension

Liquid Surface Tension, Symbol

Dynes/Cm.

Water 73 •Calcium chloride solution 86 ■Petrowet solution 58 ♦Petrowet solution 43 APetrowet solution 38 T

Methanol 23 XBenzene 29 +

An equation of the same form should be applicable,' how­ever, to any packing of the film type, but the shape factors, S and S', must be expected to take on different values when the packing shape is changed.

NomenclatureFi Fr Re a D dgH L L’NS. S'uV

film number = Fr/Re, dimensionlessFroude number, U2/gd, dimensionlessReynolds number Ud/v, dimensionlessinterfacial area of packing, sq. ft./cu. ft.tower diameter, ft.packing size(ring diameter), ft.local gravitational acceleration, ft./sec.2operating holdup, cu. ft./cu. ft., dimensionless.liquid rate, lb./hr., sq. ft.liquid rate, lb./hr. ft. width of surfacenumber of packing pieces per cubic foot, ft.-3shape factors, dimensionless.superficial liquid velocity, ft./sec.liquid velocity, ft./sec.dimensionless constantsn, F, k

Greek Letters A = film thickness, ft.e = void fraction, dimensionless0 = angle of inclination of surface to horizontalp = liquid dynamic viscosity, lb./(ft.) (sec.) v — liquid kinematic viscosity, sq. ft./see.p = liquid density, lb./cu. ft.

Literature Cited(1) Acton, F. S., “Analysis of Straight-Line Data,” Wiley, New

York, 1959.(2) Davidson, J. F., Trans. Inst. Chem. Engrs. 37, 131 (1959).(3) Elgin, J. C., Weiss, F. B., Ind. Eng. Chem. 31, 435 (1939).(4) Jesser, B. W., Elgin, J. C., Trans. Am. Inst. Chem. Engrs. 39,

277 (1943).(5) Liang-Tseng Fan, Can. J. Chem. Eng. 38, 138 (1960).(6) Nusselt, W., Z. Ver. Deut. Ing. 60, 541 (1916).(7) Otake, T., Okada, K., Kagaku Kogaku 17, 176 (1953).(8) Rose, A., Welshans, L. M., Ind. Eng. Chem. 32, 673 (1940).(9) Shulman, H. L., Savini, C. G., Edwin, R. V., A.I.Ch.E. J.

9, 479 (1963).(10) Shulman, H. L., Ullrich, C. F., Wells, N., Ibid., 1, 247

(1955).(11) Shulman, H. L., Ullrich, C. F., Wells, N., Proulx, A. Z., Ibid.,

1, 259 (1955).(12) Uchida, S., Fujita, S., J. Soc. Chem. Ind. {Japan) 39, 876,

432B (1936); 40, 538, 238B (1937); 41, 563, 275B (1938).(13) White, A. M., Trans. Am. Inst. Chem. Engrs. 31, 390 (1935).

Received for review October 10, 1966 Accepted March 27, 1967

VOL. 6 NO. 3 AUGUST 1 9 67 407

Printed in U. S. A.