mc kee - thermosiphon reboileres a review

8/9/2019 Mc Kee - Thermosiphon Reboileres a Review

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HUGH

R. McKEE

latest holdup correlation proposed is the model of Levy

55) with additional empirical relationships between

variables established from actual data applicable to

thermosiphons. Pressure-drop calculations follow the

recommendations of Collier and He witt

14)

who found

agreement with the Lockhart-Martinelli correlation

below a liquid Reynolds number of 2100, and Cheno-

weth-Martin ( 73) above 2100.

Nucleation effects are

considered as a function of liquid film thickness in the

calculation of a maximum flux, thus relating these two

design features to experimental d ata.

A

recent study by Tripathy

(73)

compared the pres-

sure-drop calculation methods of Fair, Hughmark, and

a shortcut method based on an overall average two-

phase density, using data obtained on a 5/8 in., 1 6

gauge, 4.5-ft tube, with w ater as the process fluid.

Agreement was found best using Fair's method, ac-

ceptable for Hughmark's method, a nd rather poor for

the shortcut method. It was recommended tha t the

designer follow the more sophisticated methods for

other than very approximate work.

Design Data Sources

Overall design data, including both local heat-transfer

coefficients and pressure-drop values, started appearing in

the mid-fifties. Piret and Isbin (67) investigated six fluids :

water, carbon tetrachloride, normal butyl alcohol,

isopropyl alcohol, 35 wt

%

KzCOa, and 50 wt %

KzCOa

at atmospheric pressure in a 1-in. nominal copper tube

with a heated length of 46.5 in. Th ey correlated th e

inside heat-transfer coefficient by using a modified

Dittus-Boelter equation

where ha, is the inside average boiling coefficient,

Urn is a log mean velocity assuming homogeneous

flow equals (U mixture outlet

-

U liquid inlet)/ln

erties (surface tension, viscosity, thermal conductivity,

hea t capacity, a nd density, respectively), ur s the surface

tension of water, and D is the characteristic length.

Th e authors also correlated their dat a using t he superpo-

sition technique of convection and pool boiling.

Guerrieri and Talty

(36)

employed a light oil as a

heating medium around a 0.75 in. i.d. by 6-ft long tube

an d a 1.0 in. i.d. by 6.5-ft long tube. Inside wall an d

boiling stream temperatures were measured at 6-in.

intervals along the tubes. Film coefficients ar e pre-

sented for methanol, cyclohexane, benzene, pentane,

an d heptane atmospheric pressure as a function of the

Lockhart-Martinelli parameter X t t . Wall tempera-

tures were found generally to decrease from the bottom

to the top of the tube. Stream- tempera ture distribu-

tions displayed the expected maximum at some inter-

media te point. Th e boiling film coefficient is also pre-

sented in terms of a nucleate boiling correction factor.

Dengler and Addoms

18)

used a

1

in. i.d. by 20-ft

long copper tube in a forced convection study on water,

using radioactive tracers to measure liquid fractions

along the tube. The y present the ratio of the local co-

efficient to the liquid-phase coefficient as a function of

the reciprocal of the Lockhart-Martinelli parameter.

The y observe an d discuss the suppression of nucleate

boiling by forced convection either externally induced

or

vapor induced.

Beaver and Hughniark (8) used an electrically heated

3 4

in. by 8-ft long carbon steel tube to investigate the

reliability of using developed correlations in vacuum

operations. Th e authors decided tha t for wall minus

saturation temperature differences less than 15°F single

phase coefficients dominate and can be predicted by a

modified Dittus-Boelter equation (Sieder-Tate modifica-

tion)

[ u o u t / u i n l ,

UL PL kz , Cz, PL are liquid phase prop-

Nu

=

0.023

(Re)'J.*

(Pr)0.4

[ . 1 4

Steam

Thermosiphon

Reboi ler

Tubes

Figure

7. Vertical thermosiphon

reboiler

VO L 6 2

NO.

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D E C E M B E R

1 9 7 0 77


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Nucleation occurs for temperature differences greater

than 15°F and local inside coefficients can be predicted

by existing two-phase correlations. Investigations

covered a total of twelve fluids, and the observed liquid

circulation rates are presented ; this allows the designer

to compare calculated an d experimental liquid rates.

Lee et

al. 53)

sed a reboiler consisting of se\wi tubes

in a bundle. Th e tubes \ve x 1 in. o.d., 14 gauge, 10-ft

long Admiralty metal. Dat a for a total of s e ~ e niquids

are presented for pressure ranges of approxiniatcly 2

to

120 psia. T h e authors present overall coefficients

as

functions of overall temperature differences. The aver-

age inside-film coefficient and tlie niaxiriiuiii flux are

presented in terms of dimensionless groups. The niaxi-

mu m flux

vas

found for each fluid and system pressure.

Above the niaximuni flux, vapor lock occurred; it \vas

the departure from smooth cocurrent

f low

of the two

phases through tlie equipment. Recoininendations

include a inaximurii overall coefficient of 500 Btu jh r

s q f t O F , an d the need for giving particular atrention to

reboiler entrance an d exit piping.

Johnson (46) measured circulation rates and overall

temperature driving forces for a 15-in. shell reboiler

con-

taining 96

1

in., 1 2 gauge, 8-ft long tubes. One tube was

equipped with a temperature probe

to

obtain local boil-

iiig stream temperatu res. Circulation rates wer e pre-

dicted by Kern's method. This method assumes a linear

variation of specific volume Tvith leng th in

the

vapor-

ization zone, and that heat transfer proceeds from

the

wall

to

the liquid and then

to

the vapor ca\.ities. T he

Lockhart-h,lartinelli parame ter is used in t h e calculation

of friction and expansion losses for the two-phase zonc.

Overall coefficients, driving forces, fluxes, flow, and

vaporization rates are tabulated for water and a hydro-

carbon having a normal boiling point of

80. 8 C.

Typ-

ical temperature profiles are show711 for six runs on the

hydrocarbon. Overall temperature differcncc predic-

tions are compared to the work of Piret and Isbin (67).

Data on 44 runs are included.

Shelleiie et

al. (69)

also used an industrial-size reboiler

having a 14-in. shell, containing 70 3/4 in., 13 gauge, and

3 7/ 8 in., 12 gauge, 8-ft long tubes, providing 110 s q

f t

of area . The reboiler was connected to

an

existing dis-

tillation column and, except for instrunlentation, was

identical to a typical coriiniercial unit. The hcat sourcc

was steam, and the process fluids \vex benzene, water,

isopropyl alcohol, methyl ethyl ketone, glycerine, and

various aqueous solutions of the alcohol, ketone, and

glycerine. Of parti cular interest in the work was the

exploration

of

the onset of unstable operation. Th e

authors found t ha t rhe addit ion of flow resistance

to

the

inlet line extended the srable operating range and: as

might be expected, the allowable pressure drop across

the tubes decreases as the heat flux increases. Resis-

tances were also added to the vapor return line, which

resulted in a decrease in the niaxirnuni flux as the resis-

AUTHOR Hugh R. McKee

is with

Born Engineering Co mp an y,

P.0 ox 102, Tu l sa , Okla . 74101.

tance increased. The resulting rccoiiiiiiciidation o

keeping

t h e

return line flow area cqual

to

the tubc fl o

area was consistent with t ha t of Giliiiorc

(L31) .

Max

imum lieat fluxes are tabulated for the various fluids with

accoiiipanying ie inper ature differences and

c;/c

17aporiza

tion. Other data are prescntcd as

flux

us. log nieai

temperature differciic,e and mass x-clocity us. pressur

drop. This work will be invaluable for design and

coin

parison purposes, an d it

shows

that an opportunily cxist

for a n experi inen talist to iiivestiga tc the contribution o

the various componcnis in the flow loop to stablc opcra

rion. Emphasis to da te has

been

placed on

the

hcat.cd

elenient of the loop, ivhicli

is

certainly justified. Th e

designer also needs to be sure that his filial proposal wil

meet both heat transfer

arid

stable operation rcquirc

men s.

Research into boiling heat-transfer cocf-licients ha

been rather recent, and a s

y e t

no coiiiplctcly reliable

correlation h a s evolved, a s it has for single p h a s e flow fo

various geometries.

Table I is a brief suiiiiiiary

of

typical boiling data in

tcrnis of the more coiniiionly investigated fluids. W h e n

lack of a siinilar fluid-surface coiiibination

is

encountered

particular attention should be givcn in riiatchiny sur

faces when using a generalized correlation. Fluid prop-

erty variations are adequately described in inost cor

relations, the surface characteristic remaining inde

pendent. Unfortunately, the best one can do is

rc i i ic i i i

ber that the type

of

surface is iiiiportant i n boiling hea

transfer, and remain alert to clcvelopinents in this arca.

Schrock aiid Grossman (68) correlated local hcat

Lransfer cocfficients for the

lorccd

f l ow of water in the

wettcd-wall rcgion---i.e., between subcoolcd boiling and

the traiisition to dry wall conditions-in tcrnis of the

Lockhart-hlartin elli parameter and the boiling nuliibcr

The boiling num ber is the hcat flux cli\rided by the prod

uct of

the

m a s s flux aiid rhc latent heat of vaporization

Local pressure gradients are presented

as

functions of a

niodified Lockhart-hlartinclli parameter

where p is the viscosity. 17 is the specific volume. x is the

fraction vapor. and F efers to saturatcd liquid.

Experiinents \ \ere perforiiied on tubes 0.116 2 to

0.4317 in. i.d

,

15-

to 40-111.

long, Tlith hcat fluxcs of

6 X

l o 4 to 1 . 4 5

X

l o GBtu/lir

f t 2 .

inav fluxes

of

49 to

911

lb/sec f t L , and system pressures from 42 to

505

psia

The authors rccornrriend their correlation for cxit qual-

ities up to

50%

A niax imuni coefficient was observed by Groothius an d

Hendal (35) a t the suspected transition from slug to

niist-annular flow. Th e authors were in\-estigating two-

phase heat transfer in air-water and air-gas oil mixtures.

Th e conditions for the riiaxirnurn coefficient arc related

to a dimensionless group deri\-ed from the IVeber nuiii-

ber . Local coefficients are presented in terms of

S u ,

Re

Pr, and viscosity rati o.

The concept of superposition of heat-transfer inecha-

78 I N D U S T R I A L A N D E N G I N E E R I N G C H EM IS T RY


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TABLE I NUCLEATE B OIL ING CORRELATIONS

Surface

Stainless steel

Comments

low

pattern

Inside horizontal, vertical

Fluid

Aniline

Aniline

Generalized correlation

independent of flow pat-

tern

Brass

Chromium

304 Stainless

Stainless steel

Copper

Annular

Pool boiling

Pool boiling

Inside horizontal, vertical

Benzene

13.5 to 48.8 psia

Data from 14 runs

-Butyl alcohol

Alcohol, n butyl

Data from 15 runs

arbon tetrachloride

Cyclohexane

Diphenyl

Copper

Brass

304 Stainless

Annular

Pool boiling

Pool boiling

Pool boiling, axial, and

twisted tape swirl flow

Alcohol, ethyl ethanol

Ethylene glycol

Copper

347 Stainless

A-nickel

Copper and stainless steel

Atmospheric pressure

Burnout data included

Freon 11, 113

Heptane

Inside horizontal

Annular

Pool boiling

Pressure drop da ta included

Polished chromium

Hydrogen

Isopropyl alcohol

Alcohol, isopropyl

Methyl alcohol

Alcohol, methy l

Mercury

11 correlations

Data from

1 4

runs

opper

Annular

Inside tubes, across flat

plate

Annular

1 and

3

atm

30"-78"K temperature

range

30'-78 OK tempe rature

range

Neon

Copper, nickel, cadmium

Copper, nickel, cadmium

Pool boiling

Annular

Pool boiling

Annular

Inside horizontal and

vertical

Nitrogen

Pentane

Potassium carbonate,

35% and 50%

Stainless steel

Nickel

Data from 15 runs length-

wise temperature profile

included

65-400 mm Hg abs

1200°-15000F

Sodium Horizontal disk

Pool boiling

Pool boilingeta-terphenyl, ortho-

terphenyl, 4.35y0 pura-

terphenyl in meta-ter-

phenyl (Santowax-

Monsan o)

Water

Inside vertical tubesopper

Oth er correlations Boiling

Two-phases (gas-liquid)

Review

22,

23,

24,

71)

69)

66)

nisms was modified by Chen (72) to account for the sup-

pression effect of the moving fluid on the boiling rate.

The conditions of convective heat transfer are met at the

limits of 0% and

1 0 0 %

quality, and in the boiling, two-

phase region the interaction between the mechanisms

is accounted for. I t

is

at this point that empiricism

enters the model, that is, in the determination of the

interaction effect. Chen's appr oac h provides the de-

signer with a method of obtaining a forced con-

vection boiling coefficient with a min imum of model

detail considerations.

Other generalized boiling correlations have been pre-

sented by Levy 54, Gilmore (31), and Forster and

Greif

(25).

Boiling curves and correlations are also to

be found in the general review

of

boiling by Westwater

(79,

80).

Pressure effects on boiling curves have been

studied by Mendler

e t

al . (63).

For those

who

insist on climbing the nucleate boiling

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79


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curve as far

as

possible, a grea t deal of attention has been

given to the critical flux, first boiling crisis or burnout

point. This riiaxiiiiuiii nucleate boiling flux is slightly

above the DNB (departure from nucleate boiliiig) point.

The area

is

unreliable in ternis of stability and repro-

ducibility. On e easily slips over into either the transi-

tion region or the film-boiling region, with a resultant

decrease in the flux. Thi s critical flux

is a

point the

designer should respect enough

to

check a nd avoid.

Bergles et a l . ( 9 ) investigated the critical hcat flux for

water at low pressures (below 100 psia ). They iiivesti-

gated the effects of tube lengt h, inler temperature , tube

diameter, and pressure on the critical heat flux. Th c

authors relate their results

to

the instabilities of th e slug-

flow regime. Critical heat fluxes for water a re normally

considered to start around 0 . 4

X

l o 6

Btulhr ft’;

ho\v-

ever, the authors have shown values of half this amount

und er low pressure conditions.

Gaiiibill

(28)

has kept abreast of the critical flux liter-

ature in ternis of general rcvie\vs (27) , aiid in the prc-

sentation of a corrclation. Th e latter correlation

is

based

on

two

ternis,

a

forced convection term and

a

boil-

ing term. Gaiiibill has also demonstra ted the uncer-

tainty i n predicting the critical flux ( 2 9 ) . If one needs

to be impressed xvith the magnitude of the problem, the

latte r reference is suggested.

Boiliiig curves and critical fluxes for some binary

liquids have been presented by

van

tVijk

t al.

75) or

benzene, toluene, and acetone for both pool boiliiig, aiid

for forced convection lengthwisc outsidc tubes by Carne

I ). Pressure effects on the critical flux have been in-

\-cstigated by Hoxvell and Bell

(37) .

Th e designer then

h a s

the usual problem of selecling

which approach to utilize, empirical or theoretical.

Fair

(22)

describes these approaches as the statistical

approach of Iliighniark, arid his o i vn riiechanistic ap-

proach. Th e former presents sccurity to the, dcsigner,

if

siiiiilar coiidir ioiis can be found betwxen his prob lem

and the contributing data . T he advaiitage of the rnech-

anistic approach lies

in

extrapolation into the unknown.

Th e soft spot in Fair’s nierhod is in

the

selection of a boil-

TABLE

I I .

VERTICAL FLOW TWO-PHASE

CORRELATIONS

jsteni

Comments Rejerence

Introductory survcy ( 7 7 )

Survcy advocating

Dukler’s

Energy equation discussion

Film thickncss, film

f low

rate

Air-lvat er Pressure drop and holdup

study comparison with ex-

Pressure drop in slug flow, ex-

Elevated pressure effects, cx-

(20, 21)

approach (76)

(theory) (76, 74)

.lir-Water

study 30.1

perimcntal dat a 1 7

perimciital study (33)

perimeiital study 1631

.\ir-\Vater

Boiling water

-

ing coefficient, which places one in the wonderland o

boiling da ta . The most benevolent advice to the d

signer in selecting a boiling coefficient is to adopt Hug

mark’s attitude and search for an appropriate boilin

curve that represents identical fluid propcrties

and

su

face characterisLics.

Pressu re Drop

Calcu la t i ons

First, it should be mentioned that several valuab

works are available for reference purposes in tkvo-pha

flow. Kepple an d Tun g

(47)

have absrracted the lite

ature for the period 1950- 1962. Grouse (34) has als

classified a large amo unt of the tLvo-phase lit era ture.

Anderson and Russell (2, 3,

4 )

present

a

thrce-pa

survey of nvo-phase floxv. Parr I deals with

f l ow

pattern

encountered in two-phase flo\v, an d how to predict thes

floiv pat terns for horizontal and \,ertical

f l ow

For ve

tical

f l o ~ ,

he slug-flow regime envelope (between bubb

and annular mist), is presented as thc voluiiietric g

fraction of

the

entering fuel streaiii ZJS. a gas-liqu

Froude nuniber. 4 econd correlation is also presente

a s

the liquid superficial velocity

us.

the gas-liquid vol

iiictric ratio at input, which

is

divided into the bubbl

slug, fro th, ripple, an d film-flow regimes.

Part I1 considers the prediction of pressure drop

two-phase f l ow. The authors recommend Dukler’s (2

27) method as a general approach

and

they also fin

favor in Hughmark’s 43) ethod

as

applied to eith

horizontal o r vertical f l ow.

Part

I11

coiicerns itself with a review of the status

inass transfer, heat transfer, and clieinical reaction

tlvo-phase f l ow (Other pertinent references arc pre

scntcd in Table 11.)

Hsu and Graham (38) forced water through

13-

an

1~-11111i ubes Lvith boiling in an effort to gain soiiie insig

into the niechaiiisiri of boiling inside tubes. Th e force

floiv produces a scarcity of nucleation sites and a co

responding small bubbly f l ow region. Coiivcciioii slu

f l o ~ v a large hot layer forining vapor instead of bubb

coalescence

to

form slugs) occurs rapidly, forming a lon

Tay lor bubble. Bubble trajectories into the stream ar

compared

to

jet rrajectories, aiid an actual trajector

from high-spced motion picture studies

is

shown. T h

change from bubble to slug aiid ann ula r flow is compare

to the adiabatic map : ( r7,j

(

JTL+ V , )

ZJS.

Fr, whe

Fr

=

( V ~ + V J 2 / ( D g ) ,V is velocity, D is characteristi

leng th, an dg is acceleration of gravity), not too favorabl

Th e slug to annular

f l ow

transition occurred ax

a

dinien

sionless vapor velocity Ut*

=

0.417 M-hich, according

Wallis (78) should take place at

G,*

= 0.525, (U,*

U / d G where

U

equals superficial vapor velocity).

The calculation of the void fraction is dependent up01

the relative velocity ratio between the phases (velocit

slip rat io) , which is unknown. Von Glahn (77) corrc

lated all xhe available steam-water data froin th e literatur

in the form of an empirical equation that needs

to

b

tested on other s>-stems. Hughmark (47, 42) also h

been busy in the holdup correlation area. Xicklin e t a

(65) investigated the rise velocity of bubbles in a one-in

8 0 I N D U S T R I A L A N D E N G I N E E R I N G

C H E M I S T R Y


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tube . Equa tions are presented for the velocities in slug

flow as approximations below Re

=

8000, and accurate

above Re

=

8000.

Th e dimensionless group approach as employed by the

petroleum industry in two-phase flow problems has been

discussed by Baker

(5).

Th e work of Lockhart and Martinelli (56) has been

modified innumerable times, which only seems to attest

to its utility. Chenoweth and Marti n

(73)

extended the

Lockhart-Martinelli work to larger straight pipes and

included flow through some fittings.

Dukler et a l . (20, 27) have presented a review of two-

phase pressure drop. The conclusion of (20)was that the

Lockhart-Martinelli correlation showed the best agree-

men t with reality of t he pressure-drop correlations tested,

and the holdup correlation of Hughmark (42) or holdup

calculations was best. Hughmark's correlation

is

a

modifica tion of one proposed by Bankoff 6),which as-

sumes a high bubble concentration at the center of the

stream, decreasing to zero at the wall for bubble flow.

The slippage between the phases also is assumed zero,

which is the single fluid model assumption. Th e model

is applied to stream qualities for zero

to

60%.

Following the work of Bankoff, we have the salvation

of two-phase flow by Zuber and Findlay (87). They

considered both the velocity and concentration profiles

across the duct, along with the relative velocity between

the phases in arriving at a holdup correlation.

The

result

is

a correlation that

is

independent of flow regime;

however, it is limited to two-phase systems in which no

phase change occurs by evaporation, condensaiion, boil-

ing, or chemical reaction.

Davis

( 7 5 )

modified the Lockhart-Martinelli param-

eter using the Froude number to accommodate the hori-

zontal to vertical flow geometry change. Lockhart-

Martinelli :

Revised Lockhart-Martinelli parameter by Davis :

where V, is the mean velocity of the liquid-vapor mix-

ture, D s the diameter, and g c is the gravitational con-

stant.

The Davis correlation for pressure drop ( 0%)

is

applicable to the same pressure range as the Lockhart-

Martinelli correlation : for the turbulent-turbulent flow

regime with liquid Reynolds numbers above 8000, and

the vapor Reynolds numbers above 2100 ; for liquid Reyn-

olds numbers between 6000 and 8000, providing the

vapor flow rate is great enough to obtain a Froude num-

ber above 100.

The inclusion of interfacial roughness considerations

into the Lockhart-Martinelli correlation improved the

pressure-drop prediction, as shown by McMillan et

al .

(62). Among the fluids used in horizontal systems was

trichloromonofluoromethane.

Baroczy (7) modified the Lockhart-Martinelli two-

phase pressure drop gradient ratio,

r li2,by

considering

the ratio of the two-phase gradient

to

the total liquid

gradient

In terms of the mass fraction (quality) vapor or gas

This two-phase friction multiplier has been correlated

for substances of a wide range of properties, in terms of

a property index

p

and p are viscosity and density,

respectively)

with quality as the correlating parame ter. Th e autho r

also presents a method for finding the two-phase pressure

drop for changes in flow geometry, such as contraction-

expansion, sharp-edged orifices, and other velocity-head

related elements.

Entrance effects and flow-transition effects for the slug-

flow regime were considered by Moissis and Griffith 64

in their description of the density distribution. Th e

pressure drop is calculated

to

a first approximation for

the final 20 pipe diameters.

For work in which the critical pressure or above is

liable to be encountered for homogeneous, two-phase

flow, for appreciable AP, Paige

(66)

has presented three

methods of calculating the pressure drop with a flashing

liquid. Based on the use of average mixture densities

and starting with the mechanical energy equation, the

prediction of the pressure profile along the line is possible.

The amount

of

effort being expended on two-phase

flow is of an order of magnitude that allows

us

only to

indulge in a selected bibliography. Th e game of com-

parison quickly gets to be an infini tum of cornbinat ions.

For example, Hughmark (43) has shown the similarity

of form between the work of Lamb a nd White (57) and

Hughmark and Pressburg (47). Pressure-drop expres-

sions derived from a momentum balance result in a drag

coefficient form. Energy balance derived expressions

take on the lost work form.

Hughma rk applies the latter

to data for horizontal,

vertical upward, and vertical

downward flow for isothermal systems.

Gill

e t

al . (30

compare favorably with Lockhart-Martinelli for vertical

upward flow of air-water.

Conclus ions

Th e standard of comparison seems to have been estab-

lished by Lockhart -Martinelli. There must be some

satisfaction in having produced the most often quoted,

compared, an d modified work in the field. Th e Lock-

hart-Martinelli standard appears not only in pressure-

drop correlations, but also in two-phase coefficient cor-

relations.

There are several design methods currently available

the classic local coefficient approach utilizing average

conditions and properties in the two-phase region, the

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statistical or empirical approach, and the more sophis-

ticated method of Fai r. T he first

is

dangerous for the

serious designer. Realistically a nd traditionally, the

designer has functioned in the realm of experience and

expedience. He, therefore, tends toward the second or

empirical approach, which is highly useful for repeat

rout ine work, b ut suffers from the limitation

of

producing

questionable results when extrapolated beyond the con-

ditions of the original da ta . Sufficient mater ial is now

available to produce a satisfactory iriethod of design, if

one remembers that investigations into areas such as f low

control are still incomplete.

The

more theoretical ap-

proach overcoines the extrapolation limitation, but

d e -

mands more effort to successfully set up the calculating

procedure. The ubiquitous piper seems

to

be demand-

ing his due for the pleasure of flexibility.

REF

E

R ENCES

1 j

Anderson, G. H.

and hl antzourdni s,

B. G.. "T>\o-Ph;isc (G'is-Liquid)

I'low

( 2 )

hndcrson:

R.

J . and Russcll, T . IV. F., "Dcsigning for Tso-Phab c Floi*," Pa rt

ind

Russcl l ,

T .

IV. F..

"Dcsigning

l or

Tuo-I'hdsc

Florc,

I'.iri

(4)

Anderson,

R .

J . and

Russcll, T.

I V . F., "Designing for 'Two-l'htiic Flow," P x t

(5)

Bakcr.

O. ,

Design of Pipclincs for Simultaneous Flow

of

Oil

and

Gas," 011 Gas

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82 I N D U S T R I A L A N D E N G I N E E R I N G C H EM I ST R Y

mc kee - thermosiphon reboileres a review

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