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liquid holdup. They found that two-phase pressure drop may actually

be less than the single-phase liquid pressure drop with shear thinning

liquids in laminar flow.

Pressure drop data for a 1-in feed tee with the liquid entering the

run and gas entering the branch are given by Alves (Chem. Eng.

Progr., 50, 449–456 [1954]). Pressure drop and division of two-phase

annular flow in a tee are discussed by Fouda and Rhodes (Trans.

Inst. Chem. Eng. [London], 52, 354–360 [1974]). Flow through tees

can result in unexpected flow splitting. Further reading on gas/liquid

flow through tees may be found in Mudde, Groen, and van den Akker

(Int. J. Multiphase Flow, 19, 563–573 [1993]); Issa and Oliveira (Com￾puters and Fluids, 23, 347–372 [1993]) and Azzopardi and Smith (Int.

J. Multiphase Flow, 18, 861–875 [1992]).

Results by Chenoweth and Martin (Pet. Refiner, 34[10], 151–155

[1955]) indicate that single-phase data for fittings and valves can be

used in their correlation for two-phase pressure drop. Smith, Mur￾dock, and Applebaum (J. Eng. Power, 99, 343–347 [1977]) evaluated

existing correlations for two-phase flow of steam/water and other

gas/liquid mixtures through sharp-edged orifices meeting ASTM

standards for flow measurement. The correlation of Murdock

(J. Basic Eng., 84, 419–433 [1962]) may be used for these orifices. See

also Collins and Gacesa (J. Basic Eng., 93, 11–21 [1971]), for mea￾surements with steam and water beyond the limits of this correlation.

For pressure drop and holdup in inclined pipe with upward or

downward flow, see Beggs and Brill (J. Pet. Technol., 25, 607–617

[1973]); the mechanistic model methods referenced above may also

be applied to inclined pipes. Up to 10° from horizontal, upward pipe

inclination has little effect on holdup (Gregory, Can. J. Chem. Eng.,

53, 384–388 [1975]).

For fully developed incompressible cocurrent upflow of gases

and liquids in vertical pipes, a variety of flow pattern terminologies

and descriptions have appeared in the literature; some of these have

been summarized and compared by Govier, Radford, and Dunn (Can.

J. Chem. Eng., 35, 58–70 [1957]). One reasonable classification of pat￾terns is illustrated in Fig. 6-28.

In bubble flow, gas is dispersed as bubbles throughout the liquid,

but with some tendency to concentrate toward the center of the pipe.

In slug flow, the gas forms large Taylor bubbles of diameter nearly

equal to the pipe diameter. A thin film of liquid surrounds the Taylor

bubble. Between the Taylor bubbles are liquid slugs containing some

bubbles. Froth or churn flow is characterized by strong intermit￾tency and intense mixing, with neither phase easily described as con￾tinuous or dispersed. There remains disagreement in the literature as

to whether churn flow is a real fully developed flow pattern or is an

indication of large entry length for developing slug flow (Zao and

Dukler, Int. J. Multiphase Flow, 19, 377–383 [1993]; Hewitt and

Jayanti, Int. J. Multiphase Flow, 19, 527–529 [1993]).

Ripple flow has an upward-moving wavy layer of liquid on the pipe

wall; it may be thought of as a transition region to annular, annular

mist, or film flow, in which gas flows in the core of the pipe while an

annulus of liquid flows up the pipe wall. Some of the liquid is

entrained as droplets in the gas core. Mist flow occurs when all the

liquid is carried as fine drops in the gas phase; this pattern occurs at

high gas velocities, typically 20 to 30 m/s (66 to 98 ft/s).

The correlation by Govier, et al. (Can. J. Chem. Eng., 35, 58–70

[1957]), Fig. 6-29, may be used for quick estimate of flow pattern.

Slip, or relative velocity between phases, occurs for vertical flow

as well as for horizontal. No completely satisfactory, flow regime–

independent correlation for volume fraction or holdup exists for verti￾cal flow. Two frequently used flow regime–independent methods are

those by Hughmark and Pressburg (AIChE J., 7, 677 [1961]) and

Hughmark (Chem. Eng. Prog., 58[4], 62 [April 1962]). Pressure

drop in upflow may be calculated by the procedure described in

Hughmark (Ind. Eng. Chem. Fundam., 2, 315–321 [1963]). The

mechanistic, flow regime–based methods are advisable for critical

applications.

For upflow in helically coiled tubes, the flow pattern, pressure

drop, and holdup can be predicted by the correlations of Banerjee,

Rhodes, and Scott (Can. J. Chem. Eng., 47, 445–453 [1969]) and

6-28 FLUID AND PARTICLE DYNAMICS

FIG. 6-27 Liquid volume fraction in liquid/gas flow through horizontal pipes.

(From Lockhart and Martinelli, Eng. Prog., 45, 39 [1949].)

FIG. 6-28 Flow patterns in cocurrent upward vertical gas/liquid flow. (From

Taitel, Barnea, and Dukler, AIChE J., 26, 345–354 [1980]. Reproduced by per￾mission of the American Institute of Chemical Engineers © 1980 AIChE. All

rights reserved.)

FIG. 6-29 Flow-pattern regions in cocurrent liquid/gas flow in upflow through

vertical pipes. To convert ft/s to m/s, multiply by 0.3048. (From Govier, Radford,

and Dunn, Can. J. Chem. Eng., 35, 58–70 [1957].)