Thermosiphon Reboilers-A Review Literature pertaining to the design o f thermosiphon reboilers is reciewed in terms of available meth‘ods and appropriate data sources
he practice of boiling inside vertical tubes has been
Tin existence for almost a century in the forin of evaporators. T h e use of a steam chest inside the process \,esse1 was not always practical, and a separate unit evolved (Figure 1). The thermosiphon reboiler contains the two endearing qualities of the evaporator, namely, mechanical simplicity, and operation in the nucleate boiling regime with its attractively high fluxes. I t is unfortunate thar the design of a thermosiphon reboiler does not follow along the lines of simplicity, although all that is required is the prediction of the f l o ~ 7 and heat-transfer rates. T h e successrd design of a therinosiphon reboiler then is dependent upon the prediction of a tubeside coefficient, which in turn is beset by complications owing to the presence of two phases. T h e designer is quickly involved in considering pressure drop, flow regime prediction, realistic boiling curves, flolv instabilities, and scale-up reliability from single tube data to tube bundles. Since available head to a reboiler is usually fixed by existing equipment, the allowable pressure drop is considered a dependent variable for design purposes. T h e tubeside pressure drop then becomes a function of the physical properties of the fluid, the fraction vaporized, and the flow geometry. Design Procedures
A general design procedure for thermosiphon reboilers was presented in 1960 by Fair (22). This method is flexible enough to allow inclusion of newer and more reliable correlations as they evolve. Pertinent areas of research concentration in the past ten years have included two-phase flow friction losses, boiling coefficients, and two-phase heat-transfer coefficients. Fair’s method involves a nestled series of trial and crror calculations, starting with a rough estimate as a pre76
INDUSTRIAL A N D ENGINEERING CHEMISTRY
liminary design. T h e outermost loop is thc cornparison of the flow performance of the preliminary design with the available head. A secondary inner loop consists of assuming a total fraction vaporized, and estimating the circulation rate. This may require correction of the preliminary design a t this point, or, if not, then the heat-transfer raie is calculated by proceeding to another trial and error loop that converges on the assumed fraction vaporized. Additional calculation loops could be incorporated to include the effect of variation of liquid phase friction factor and lengthwise inside tube temperature profile effects. Fair’s method requires selection of a boiling coefficient in the deterrnination of the two-phase coefficient. Fair (24) also presented a reviey of the state-of-the-art for reboilers in general, including kettle-type units. Fair (23) lists references for holdup correlations. T h e essentials of a computer program were later discussed by Fair (24) based on earlier work (22). T h e problems involved in estimating circulation and heat-transfer rates were discussed by Hughmark (40) with the utilization of a lengthwise temperature profile. T h e overall design approach is essentially the same as Fair’s method, with a simplification in the form of a correlation for predicting the inside coefficient. Prediction of the circulation rate was considered by Hughinark in a later report (44) in which the two-phase pressure drop was calculated by means of a polynomial in terms of the Froude number and volume fraction liquid. Pressure drop calculated values are point values and the total pressure drop is obtained by integration over the tube length. Hughmark (45) has summarized his efforts (40, 42, 44) with therniosiphon design. Inside coefficient relationships are presented for the liquidsensible heat region, nucleate boiling region, and the two-phase region (slug, annular, and mist flow). T h e
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 Hewitt (14) who found agreement with the Lockhart-Martinelli correlation below a liquid Reynolds number of 2100, and Chenoweth-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 data. A recent study by Tripathy (73) compared the pressure-drop calculation methods of Fair, Hughmark, and a shortcut method based on an overall average twophase density, using data obtained on a 5/8 in., 16 gauge, 4.5-ft tube, with water as the process fluid. Agreement was found best using Fair's method, acceptable for Hughmark's method, and rather poor for the shortcut method. I t was recommended that the designer follow the more sophisticated methods for other than very approximate work.
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 UL, PL, kz, Cz, PL are liquid phase prop[uout/uinl, erties (surface tension, viscosity, thermal conductivity, heat capacity, and density, respectively), urnis the surface tension of water, and D is the characteristic length. T h e authors also correlated their data using the superposition 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 and a 1.0 in. i.d. by 6.5-ft long tube. Inside wall and boiling stream temperatures were measured a t 6-in. intervals along the tubes. Film coefficients are presented for methanol, cyclohexane, benzene, pentane, and heptane atmospheric pressure as a function of the Lockhart-Martinelli parameter X t t . Wall temperatures were found generally to decrease from the bottom to the top of the tube. Stream-temperature distributions displayed the expected maximum at some intermediate point. T h e boiling film coefficient is also presented 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. They present the ratio of the local coefficient to the liquid-phase coefficient as a function of the reciprocal of the Lockhart-Martinelli parameter. They observe and 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. T h e authors decided that 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 modification) Nu = 0.023 (Re)'J.* (Pr)0.4
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 a t atmospheric pressure in a 1-in. nominal copper tube with a heated length of 46.5 in. They correlated the inside heat-transfer coefficient by using a modified Dittus-Boelter equation
[
5
.
1
4
Steam
Thermosiphon Reboiler Tubes
Figure 7.
Vertical thermosiphon reboiler
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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 and experimental liquid rates. Lee et al. (53)used a reboiler consisting of se\wi tubes in a bundle. T h e tubes \vex 1 in. o.d., 14 gauge, 10-ft long Admiralty metal. Data for a total of s e ~ e nliquids are presented for pressure ranges of approxiniatcly 2 to 120 psia. T h e authors present overall coefficients as functions of overall temperature differences. T h e average inside-film coefficient and tlie niaxiriiuiii flux are presented in terms of dimensionless groups. T h e niaximum flux !vas found for each fluid and system pressure. Above the niaximuni flux, vapor lock occurred; it \vas the departure from smooth cocurrent flow of the two phases through tlie equipment. Recoininendations include a inaximurii overall coefficient of 500 Btujhr sq ft O F , and the need for giving particular atrention to reboiler entrance and exit piping. Johnson (46) measured circulation rates and overall temperature driving forces for a 15-in. shell reboiler containing 96 1 in., 1 2 gauge, 8-ft long tubes. One tube was equipped with a temperature probe to obtain local boiliiig stream temperatures. Circulation rates were predicted by Kern's method. This method assumes a linear variation of specific volume Tvith length in the vaporization zone, and that heat transfer proceeds from the wall to the liquid and then to the vapor ca\.ities. T h e Lockhart-h,lartinelli parameter 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 hydrocarbon having a normal boiling point of 80.8"C. Typical temperature profiles are show711 for six runs on the hydrocarbon. Overall temperature differcncc predictions 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 sq f t of area. T h e reboiler was connected to an existing distillation column and, except for instrunlentation, was identical to a typical coriiniercial unit. T h e 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 particular interest in the work was the exploration of the onset of unstable operation. The authors found that rhe addition 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. Resistances 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 Company,
P. 0.Box 102, Tulsa, Okla. 74101. 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 CHEMISTRY
tance increased. The resulting rccoiiiiiiciidation of keeping t h e return line flow area cqual to the tubc flow area was consistent with that of Giliiiorc (L31). Maximum lieat fluxes are tabulated for the various fluids with accoiiipanying ieinperature differences and c;/c 17aporization. Other data are prescntcd as flux us. log nieaii temperature differciic,e and mass x-clocity us. pressure drop. This work will be invaluable for design and coinparison purposes, and it shows that an opportunily cxists for a n experiinen talist to iiivestiga tc the contribution of the various componcnis in the flow loop to stablc opcrarion. Emphasis to date has been placed on the hcat.cd elenient of the loop, ivhicli is certainly justified. The designer also needs to be sure that his filial proposal will meet both heat transfer arid stable operation rcquircmen t s . Research into boiling heat-transfer cocf-licients has been rather recent, and as yet no coiiiplctcly reliable correlation has evolved, as it has for single phase flow for 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 surfaces when using a generalized correlation. Fluid property variations are adequately described in inost correlations, the surface characteristic remaining independent. Unfortunately, the best one can do is rciiiciiiber that the type of surface is iiiiportant i n boiling heat transfer, and remain alert to clcvelopinents in this arca. Schrock aiid Grossman (68) correlated local hcatLransfer cocfficients for the lorccd flow of water in the wettcd-wall rcgion---i.e., between subcoolcd boiling and tcrnis of the the traiisition to dry wall conditions-in Lockhart-hlartinelli parameter and the boiling nuliibcr. The boiling number is the hcat flux cli\rided by the product of the mass 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 refers to saturatcd liquid. Experiinents \\ere perforiiied on tubes 0.11 62 to 0.4317 in. i.d , 15- to 40-111. long, Tlith hcat fluxcs of 6 X l o 4 to 1.45 X l o G Btu/lir ft2. i n a v fluxes of 49 to 911 lb/sec ftL, and system pressures from 42 to 505 psia. The authors rccornrriend their correlation for cxit qualities up to 50%. A niaximuni coefficient was observed by Groothius and Hendal (35) a t the suspected transition from slug to niist-annular flow. The authors were in\-estigating twophase heat transfer in air-water and air-gas oil mixtures. The conditions for the riiaxirnurn coefficient arc related to a dimensionless group deri\-ed from the IVeber nuiiiber. Local coefficients are presented in terms of S u , Re, Pr, and viscosity ratio. T h e concept of superposition of heat-transfer inecha-
TABLE I. Surface
Fluid Aniline Aniline
Stainless steel
Benzene
Brass Chromium 304 Stainless Stainless steel
n-Butyl alcohol Alcohol, n butyl Carbon tetrachloride Cyclohexane Diphenyl Alcohol, ethyl ethanol Ethylene glycol
Freon 11, 113 Heptane
NUCLEATE BOILING CORRELATIONS
Generalized correlation independent of flow pattern Annular Pool boiling Pool boiling Inside horizontal, vertical
Copper Brass 304 Stainless
Copper 347 Stainless A-nickel Copper and stainless steel
Data from 15 runs Annular Pool boiling Pool boiling Pool boiling, axial, and twisted tape swirl flow Inside horizontal Annular Pool boiling
Atmospheric pressure Burnout data included Pressure drop data included
11 correlations Data from 14 runs
Copper Annular Inside tubes, across flat plate Annular
Neon
Copper, nickel, cadmium
Nitrogen
Copper, nickel, cadmium
Pentane Potassium carbonate, 35% and 50%
Stainless steel
Sodium
Nickel
Meta-terphenyl, orthoterphenyl, 4.35y0 puraterphenyl in meta-terphenyl (SantowaxMonsan to) Water
Horizontal disk Pool boiling Pool boiling
Copper
Inside vertical tubes
Other correlations
13.5 to 48.8 psia Data from 14 runs
Copper
Polished chromium Hydrogen Isopropyl alcohol Alcohol, isopropyl Methyl alcohol Alcohol, methyl Mercury
Comments
Flow pattern Inside horizontal, vertical
Pool boiling Annular Pool boiling Annular Inside horizontal vertical
1 and 3 atm 30"-78"K temperature range 30'-78 OK temperature range
and
Data from 15 runs lengthwise temperature profile included 65-400 mmHg abs 1200°-15000F
Boiling Two-phases (gas-liquid) Review
nisms was modified by Chen (72) to account for the suppression effect of the moving fluid on the boiling rate. T h e conditions of convective heat transfer are met at the limits of 0% and 100% quality, and in the boiling, twophase region the interaction between the mechanisms is accounted for. I t is a t this point that empiricism enters the model, that is, in the determination of the interaction effect. Chen's approach provides the designer with a method of obtaining a forced con-
(22, 23, 24, 71) (69) (66)
vection boiling coefficient with a minimum of model detail considerations. Other generalized boiling correlations have been presented 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 et al. (63). For those who insist on climbing the nucleate boiling VOL. 6 2
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curve as far as possible, a great 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 reproducibility. One easily slips over into either the transition region or the film-boiling region, with a resultant decrease in the flux. This critical flux is a point the designer should respect enough to check and avoid. Bergles et al. ( 9 ) investigated the critical hcat flux for water at low pressures (below 100 psia). They iiivestigated the effects of tube length, inler temperature, tube diameter, and pressure on the critical heat flux. T h c authors relate their results to the instabilities of the slugflow regime. Critical heat fluxes for water are normally considered to start around 0.4 X l o 6 Btulhr ft’; ho\vever, the authors have shown values of half this amount under low pressure conditions. Gaiiibill (28) has kept abreast of the critical flux literature in ternis of general rcvie\vs (27), aiid in the prcsentation of a corrclation. The latter correlation is based on two ternis, a forced convection term and a boiling term. Gaiiibill has also demonstrated the uncertainty in predicting the critical flux ( 2 9 ) . If one needs to be impressed xvith the magnitude of the problem, the latter reference is suggested. Boiliiig curves and critical fluxes for some binary liquids have been presented by van tVijk e t al. (75)for benzene, toluene, and acetone for both pool boiliiig, aiid for forced convection lengthwisc outsidc tubes by Carne ( I I). Pressure effects on the critical flux have been in\-cstigated by Hoxvell and Bell (37). T h 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 oivn riiechanistic approach. The former presents sccurity to the, dcsigner, if siiiiilar coiidir ioiis can be found betwxen his problem and the contributing data. T h e advaiitage of the rnechanistic approach lies in extrapolation into the unknown. T h e soft spot in Fair’s nierhod is in the selection of a boil-
TABLE I I . Sjsteni
.lir-Water Air-lvater
.\ir-\Vater
Boiling water
V E R T I C A L FLOW TWO-PHASE CORRELATIONS Comments
Rejerence
Introductory survcy Survcy advocating Dukler’s (20, 2 1 ) approach Energy equation discussion (theory) Film thickncss, film flow rate study Pressure drop and holdup study comparison with experimcntal data Pressure drop in slug flow, experimciital study Elevated pressure effects, cxperimeiital study
(77) (76)
(76, 74)
(30.1
17) (33)
1631
80
I N D U S T R I A L AND ENGINEERING C H E M I S T R Y
ing coefficient, which places one in the wonderland of boiling data. T h e most benevolent advice to the designer in selecting a boiling coefficient is to adopt Hughmark’s attitude and search for an appropriate boiling curve that represents identical fluid propcrties and surface characterisLics. Pressure Drop Calculations
First, it should be mentioned that several valuable works are available for reference purposes in tkvo-phase flow. Kepple and Tung (47) have absrracted the literature for the period 1950-1962. Grouse (34) has also classified a large amount of the tLvo-phase literature. Anderson and Russell (2, 3, 4 ) present a thrce-part survey of nvo-phase floxv. Parr I deals with flow patterns encountered in two-phase flo\v, and how to predict these floiv patterns for horizontal and \,ertical flow. For vertical f l o ~the , slug-flow regime envelope (between bubble and annular mist), is presented as thc voluiiietric gas fraction of the entering fuel streaiii ZJS. a gas-liquid Froude nuniber. ,4second correlation is also presented as the liquid superficial velocity us. the gas-liquid voluiiictric ratio at input, which is divided into the bubble, slug, froth, ripple, and film-flow regimes. Part I1 considers the prediction of pressure drop in two-phase flow. T h e authors recommend Dukler’s (20, 27) method as a general approach and they also find favor in Hughmark’s (43)method as applied to either horizontal or vertical flow. Part I11 coiicerns itself with a review of the status of inass transfer, heat transfer, and clieinical reaction in tlvo-phase flow. (Other pertinent references arc prescntcd in Table 11.) Hsu and Graham (38) forced water through 13- and 1~-11111itubes Lvith boiling in an effort to gain soiiie insight into the niechaiiisiri of boiling inside tubes. The forced floiv produces a scarcity of nucleation sites and a corresponding small bubbly flow region. Coiivcciioii slugf l o ~ v(a large hot layer forining vapor instead of bubble coalescence to form slugs) occurs rapidly, forming a long Taylor bubble. Bubble trajectories into the stream arc compared to jet rrajectories, aiid an actual trajectory from high-spced motion picture studies is shown. T h c change from bubble to slug aiid annular flow is compared to the adiabatic map : ( r7,j ( JTL+ V,) ZJS. Fr, where Fr = ( V ~ + V J 2 / ( D g )( ,V is velocity, D is characteristic length, a n d g is acceleration of gravity), not too favorably. T h e slug to annular flow transition occurred ax a diniensionless vapor velocity Ut* = 0.417 M-hich, according to Wallis (78) should take place a t G,* = 0.525, (U,* = U / d G where U equals superficial vapor velocity). T h e calculation of the void fraction is dependent up011 the relative velocity ratio between the phases (velocity slip ratio), which is unknown. Von Glahn (77) corrclated all xhe available steam-water data froin the literature in the form of an empirical equation that needs to be tested on other s>-stems. Hughmark (47, 42) also has been busy in the holdup correlation area. Xicklin et al. (65) investigated the rise velocity of bubbles in a one-in.
tube. Equations are presented for the velocities in slug flow as approximations below R e = 8000, and accurate above R e = 8000. The dimensionless group approach as employed by the petroleum industry in two-phase flow problems has been discussed by Baker (5). The work of Lockhart and Martinelli (56) has been modified innumerable times, which only seems to attest to its utility. Chenoweth and Martin (73) extended the Lockhart-Martinelli work to larger straight pipes and included flow through some fittings. Dukler et al. (20, 27) have presented a review of twophase pressure drop. The conclusion of (20)was that the Lockhart-Martinelli correlation showed the best agreement with reality of the pressure-drop correlations tested, and the holdup correlation of Hughmark (42)for holdup calculations was best. Hughmark's correlation is a modification of one proposed by Bankoff (6),which assumes 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. The 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, boiling, or chemical reaction. Davis ( 7 5 ) modified the Lockhart-Martinelli parameter using the Froude number to accommodate the horizontal to vertical flow geometry change. LockhartMartinelli :
Revised Lockhart-Martinelli parameter by Davis :
where V , is the mean velocity of the liquid-vapor mixture, D is the diameter, and gc is the gravitational constant. The Davis correlation for pressure drop ( f20%) is applicable to the same pressure range as the LockhartMartinelli correlation : for the turbulent-turbulent flow regime with liquid Reynolds numbers above 8000, and the vapor Reynolds numbers above 21 00 ; for liquid Reynolds numbers between 6000 and 8000, providing the vapor flow rate is great enough to obtain a Froude number 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 twophase pressure drop gradient ratio, r$li2, by considering the ratio of the two-phase gradient to the total liquid gradient
I n 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 parameter. T h e author also presents a method for finding the two-phase pressure drop for changes in flow geometry, such as contractionexpansion, sharp-edged orifices, and other velocity-head related elements. Entrance effects and flow-transition effects for the slugflow regime were considered by Moissis and Griffith (64) in their description of the density distribution. The 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. T h e 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. The game of comparison quickly gets to be an infinitum of cornbinations. For example, Hughmark (43) has shown the similarity of form between the work of Lamb and White (57) and Hughmark and Pressburg (47). Pressure-drop expressions derived from a momentum balance result in a drag coefficient form. Energy balance derived expressions take on the lost work form. Hughmark applies the latter to data for horizontal, vertical upward, and vertical downward flow for isothermal systems. Gill et al. (30) compare favorably with Lockhart-Martinelli for vertical upward flow of air-water. Conclusions
The standard of comparison seems to have been established by Lockhart-Martinelli. There must be some satisfaction in having produced the most often quoted, compared, and modified work in the field. The Lockhart-Martinelli standard appears not only in pressuredrop correlations, but also in two-phase coefficient correlations. There are several design methods currently available : the classic local coefficient approach utilizing average conditions and properties in the two-phase region, the VOL. 6 2
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statistical or empirical approach, and the more sophisticated method of Fair. T h e first is dangerous for the serious designer. Realistically and 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 routine work, but suffers from the limitation of producing questionable results when extrapolated beyond the conditions of the original data. Sufficient material is now available to produce a satisfactory iriethod of design, if one remembers that investigations into areas such as flow control are still incomplete. The more theoretical approach overcoines the extrapolation limitation, but demands more effort to successfully set up the calculating procedure. The ubiquitous piper seems to be demanding his due for the pleasure of flexibility.
REF E R ENC ES (1 j Anderson, G . H . and hlantzourdnis, B. G.. "T>\o-Ph;isc (G'is-Liquid) I'low Phenomena," Chem. Eng. S - L ~12 . , (Z),109-126 (1960). (2) h n d c r s o n : R . J. a n d Russcll, T . 'IV. F., "Dcsigning for T s o - P h a b c Floi*," P a r t Yorh), 139-44 ( D e i . 6,1965). ind Russcll,T. 'IV. F.. "Dcsigning lor Tuo-I'hdsc Florc," I'.iri 11, zbid., 99-104 (Dcc. 20,1965). (4) Anderson, R . J. a n d Russcll, T. I V . F., "Designing for 'Two-l'htiic Flow," P x t 111, i h d . . 87-90 (Jan. 3,1966). (5) Bakcr. O., "Design of Pipclincs for Simultaneous Flow of Oil a n d Gas," 011 Gas J . , 53 ( 1 2 ) , 185-195 (JuI) 1954). (6) Bankoff. S. G . : "\!ari,rble Density Single Fluid h l o d r l for T\r.o-l'h,tic Flov with Particular licicrcncc to Stedm-TVatcr Tlo\v," 7'rans. AS'.ifL', 265-272 (1960,. ( 7 ) Barocrv C. J., "A Syatem,itic Corrcl.ition for Two-Ph.ise I'ressurc Drop," AICIiE P & r . 37, Hc'it Transfer Conference. 1.0s Angclcs, 1965. (8) Bcaver, P. R . .ind Hughm,irk. G . )I,, .lIC/ii: J . >14 (j),746-749 (Scpt. 1968). (9) Berglcs. :\. E . , LopinSi: I., .IIChIY J . , (52) L.ipin, A , , T o t i c n , H . C.. .rnd XVcnzel, L OS Boiling h i t r o g c n ;and Neon i n Narrow 11 1965). (53) LCC,D.C., Dorsc\ J . \ V , , hlonrc, G . %., Thcrmosiphon Rcbckicra," Chem. P 5 q Progr.
ir IYow with Liquid I?ntr,iinmcnt,"
:LO) M'irtinclli, I"Forced C .\ucl. Sci. Eng., 12, 474 1~1962). (69) Shcllcnc, K.R., Stcrnlinz. C. V.. C h u r c h . D . hi.,and Sn)-dci, K . H., Chcm. h n g . Progr., Sjmp. S'er. 82,64:'102-113 :1963).' (70) Stahcl, E. P.a n d Ferrcll, J. K., "He,it Transfer," I A D .L N G .C111:hr,, 60 ( I ) , 75-83 (Jdn. 1968). (71) T o n g , L . S.,"Boilins H c a t Transfer a n i Two-I'haw Ilow," J o h n T V i l c y :ind Sons, I n c . , 1st ed., 1965. ( 7 2 ) T r i p a t h v C . S. D., "Litcraturc Survey ,ind Cvaluntion of the \',irioua Possiblc Methods ok'ferforming Two-I'h,ise Flow Pressurc Drop Calcul;itions," ?V S. I. T h e s i a , Dcpt. of Chem. Cng., T h e Univcrsity of T u l s . ~ ,I'ulsa, Okl.i., 1967. (73) Tripathv. C . S. "Hvdr.iulic Pcrformancc cf Thermosiphon Rcboilcr," M.S. Thesis, T h b Univeksity bf Tulsa, Tuls'i, Okla., 1968. (74) Van Deemter, J. J. a n d V a n Der V a a n , E. T.: "hlomcntum :and Energy Balance for Dispersed Two-Phase F l o ~ , ",lp,bi. Sci. R e s . , A10 (Z), 102-108 (1961). (75) v a n 'Ifijk, \V. R., Vor, A . S.: Boiling Bin,a.ry Liquid .Mixturcr:" (76) Vohr, J., " T h c Encrgy Equati 281 ( M a y 1962). v o n Glahn, U. € I . , "An Empirical Relation for Predictinm V r i r l rr'rctions with (7?'wo-Phase, Steam IVater Flow,'' .VAS.A 7 i c h . .Vote, D-l18$(Jan. 1962). (78) \Vallis, G.D . , "The Transition from Floodins to Upw;irds Cocurrent :\nnular Flow in a Vertical Pipe,'' C.1:. '41. Encrqy . A d z , , Reiic!or Group, R e / > . R-742 (Fcb. 1962). (79) \Veitwatcr, J. I$',, "Boiling of Liquids," in h d v a n c c r in Chcmicd I,nginecring, Vol. I , Academic Prcss l n c . , Kew York, 1956. (80) \Vest\\.atcr: J. W., ibid., Vol. 11, 1958. "A\-cragc Volumetric Conccntration i n Two(81) Zubcr, N. and Findlay, J Phase Flow Systems," .J. Hea nsjcr, 87C (4), 453-468 (Nov. 1965).
