Distinguished Author Series

Multiphase Flow in Pipes by Peter Griffith, Massachusetts Inst. of Technology

Peter Griffith has been on the faculty of the Massachusetts Inst. of Technology (MIT) since 1956. His primary research interests have been in two-phase flow, boiling, condensation, supercritical heat transfer, and various applications of nuclear reactor safety. He holds degrees in mechanical engineering from New York u. , the u. of Michigan, and MIT.

Introduction Multiphase flow is found in many places. In the petroleum industry it occurs in oil and gas wells , gathering systems, many piping systems, and key pieces of equipment needed in refineries and petrochemical industries, including boilers, condensers, distillation towers, separators, and associated piping. This article focuses on two-phase flow in pipes. Though a lot has been learned about two-phase flow in the past 25 years , much of that knowledge has not been collected in a convenient place . In particular, much work done for the nuclear industry remains unknown to the petroleum industry. The primary goal of this article is to describe the kinds of problems we are now able to solve and to point out where answers to these problems can be obtained.

When piping in which two phases are flowing is designed , a number of questions can arise, depending on the application:

I. What is the void fraction? 2. What is the pressure drop? 3 . What is the liquid level? 4. What is the flow at a break? 5. How can one separate the phases? 6. Where will corrosion occur? 7 . What is the wear rate caused by droplet

impingement? 8. What is the vibration of the pipes as a result of

two-phase flow? I shall begin by listing available books, then

recommend flow-regime maps and correlations for void, pressure drop, and critical flow, and finally touch on the problems of separation, corrosion, wear, and vibration. 01492136/84/00312895$00 .25

MARCH 1984

Books on Two-Phase Flow Various books on two-phase flow contain answers for many of the problems that arise. Almost all of the following books describe homogeneous and separated flow models for calculating void fraction and pressure drop, so I shall mention only those features unique to each book.

Wallis I contains the most complete mechanistic descriptions of void and pressure drop for the different flow regimes.

Hestroni 2 has a unique section on flow instability and also the best section on flow regimes.

Collier3 is primarily a mUltiphase heat-transfer book but has a unique section on two-phase pressure drop in fittings .

Hewitt and Hall-Taylor4 collect and rep0l1 more experimental observations on annular flow than any other source.

Lahey and Moody 5 have a unique section on choked flow. Their description of the drift-flux model is excellent.

Govier and Aziz 6 consider both slurries and non-Newtonian fluid plus a wide variety of solid, liquid , and gas systems.

Moore and Sieverding 7 have design data on screen and chevron separators that are not reported elsewhere.

Hsu and Graham 8 consider cryogens. Szilas 9 has a design section on both pool and

cyclone separators.

Flow Regimes The unique feature of two-phase flow is the presence of flow regimes- descriptions of how the two phases are distributed in the pipe. Flow regimes and flow-regime maps for horizontal, vertical, and inclined

361

E~_--~~~-:~~~ ~-~--~~ ~~~~o~:o9

~o~~~d c:~. -__ -=:;;-;J l~~"~ 0 ?~;~~~~~

Stratified smooth flow

Stratified wavy flow

Plug flow

Slug flow

Annular flow

Dispersed bubble flow

Fig.1-Flow regimes for a horizontal pipe (adapted from Refs. 2 and 10).

pipes are illustrated in Figs. I through 4.2.10.11 For quantities like void fraction or pressure drop. it

has not proved convenient to use these maps as part of the calculation scheme. The quantities of interest are continuous, while steps would occur at flow-regime boundaries if separate correlations were used for void or pressure drop for each regime. Rather, the utility of the flow-regime maps lies in their ability to help solve unconventional problems. such as:

Is there a liquid level? Is there carryover? Is there entrainment? Is the flow steady? Will the top of the pipe be wet? They are also of great interest when one runs

"thought experiments." It is hard to imagine how a two-phase flow will behave in an untested system without also imagining how the phases are arranged. The arrangement of the phases is the flow regime and can be predicted with the maps. Often one can guess how a flow regime will change as it passes through a fitting. for example.

There are also regime maps for inclined pipes. One of the most extensive sources of these is Ref. 12. All angles are included, from vertical uptlow to vertical downtlow.

The tlow-regime maps recommended have a consistent designation for the flow regimes, a broad data base. and a semitheoretical basis for determining flow-regime boundaries. The approach taken in these works reflects just about the right compromise between precision and simplicity.

A recent work U extends the data base for flow regimes and recommends changing the location of the

362

50

DISPERSED

10 BUBBLE (DB)

:( ELONGATED;3 SLUG BUBBLE

'-' INTERMITTENT (I) DISPERSED Q) If)

(AD) ..... LIQUID -.5.... ///,

.1 ::J STRATIFIED

SMOOTH (SS)

.01

.1 10 100 500

U6 (m/sec) Fig. 2-Flow-regime map plotted in terms of superficial

velocities of each phase for air and water in a 1-in. [2.54-cm]-ID pipe at room temperature and pressure. Crosshatched bands represent the data of Mandhane. 2,5,10

wavy stratified annular dispersed boundary farther to the right. Our experiments indicate that these recommendations improve the map,

Void Correlations One of the most basic quantities in two-phase flow is void fraction or its complement, liquid fraction, Various methods exists for calculating this quantity; each has its advantages and faults.

The simplest is the homogeneous model, which assumes that both phases move at the same velocity. However, they rarely do. Void is usually overestimated in horizontal and upflow and underestimated in downflow when this model is used. If pressure drop, rather than void, is the primary concern and the gravity contribution to the pressure drop is small (say 20% of the total), this model is often satisfactory,

The next most complicated expression for void assumes that the liquid moves more slowly than the vapor. These are called "slip correlations." The well-known Martinelli, Thom, or Baroczy correlations mentioned in all the handbooks on two-phase flow 1-3,8 fit into this category, Where pressure drop as such is the issue. these methods can be satisfactory. Martinelli and Baroczy have a data base that includes a wide variety of fluid properties in the correlations, At low velocity, however, they can give poor answers because the gravity contribution to the vapor velocity is practically ignored in both of these correlations,

The most precise method for calculating the void fraction relies on the drift-flux model. The most convenient description of this model is provided in Refs. 1 through 3, A recent compilation of the drift-

JOURNAL OF PETROLEUM TECHNOLOGY

t t--. IV 0 0 0 '0 0 O~ : :". ~ ~ ... 00 00 Q ~ : . " " Do 0 a o 0 0

o 0 0 0 . , -,0;0 0

10 ""':: :":"

00 0 0 0

00 0 0'0 : \ o 0 0

0 " .-000 ~ 0 00& \ \ 0 .. ' .,' o 0 0 0 00 0 00 ~o DO 0 00

o g V 000 o () 0 00 00 000 000 0 ~o 00000 f:2 00 000 7 00 00 0 " ,', a oGGa 00 , . o o~c ~ \ J _ " . C'oD 0

' .

000 0 .. -

000 0 00 . ',. 00 . ...-c:::::: t t t

Bubbl. Slug Churn Annular flow tlow flow rtow

Fig. 3-Flow regimes distinguished by Taitel and Dukler for a vertical upflow pipe. 2,11

flux model constants for various flow regimes 14 has a huge data base. Properly used, the drift-flux model generally gives the best predictions of void fraction because it explicitly recognizes the two most important factors that cause slip: combined velocity-density distributions in the channel and the direction of the gravity vector. This model also is unique because it properly predicts a liquid level for sufficiently small velocity levels. Thus, it can be used to help size devices such as separators or to tell whether some heated tubes will be wet when there is only a limited amount of liquid present. It also is unique because it can predict void in counterflow and gives an indeterminate form during a downflow when the void is sometimes indeterminate.

Whenever one has several methods of calculating a given quantity, guidance is needed in choosing which method to use. In general, homogeneous void can be used only when the contribution of gravity to the total pressure drop is unimportant. Slip models are most convenient for engineering calculations but give poor answers when the system operates outside of annular, dispersed, or bubbly flow regimes. In any regime where gravity is a dominant force, a slip model will fail to represent an important part of the physics, so a drift-flux model should be used.

Pressure-Drop Correlations Pressure drop is probably the quantity that one deals with most often in two-phase flow. In spite of this, our ability to predict it in truly new situations is not very good. Differences are primarily a result of the variety of flow regimes that one tries to bridge with a single correlation scheme. Another problem is the large number of dimensionless variables that are

MARCH 1984

100

A

10 BUBBLE

ANNULAR

-1

u II

'" ---- A "' ... ::l

,1

B

.01 .1 10 100 1000

U~ (ft /sec) Fig. 4-Flow-regime map for air and water in a vertical upflow

at 75F and 1 atm [24C and 101.3 MPa] (adapted from Refs. 2 and 11). The coordinates are the super-ficial velocity of each phase.

demonstrably important, at least at some conditions. For example, for a single-phase, fully developed

flow in a pipe, the friction factor is a function of a single dimensionless group, the Reynolds number. However, for a two-phase flow, the pressure drop (which can be calculated with a friction factor) is a function of at least six variables. For exampk, one such set of variables identifies the friction factor as a function of a Froude number, the Weber number, the Reynolds number, the density ratio, the viscosity ratio, and the flow-rate ratio. If we try to correlate data and leave out some dimensionless groups, we cannot expect a good result.

The same three alternatives exist for computing the pressure drop as exist for the void fraction: the homogeneous model, the slip model, and the drift-flux model. A number of comparisons between these models have been made in the literature. For example, Ref. 2 makes recommendations for calculating pressure drop in both horizontal and vertical pipes. When one looks at a large amount of two-phase pressure-drop data, the important differences tum out to be caused by the different data bases underlying the correlations. When the application for a correlation is known, the best general advice is to use a correlation with a data base similar to the application. If there are a number of differences between the data base and the proposed application, one has a problem deciding what constitutes the most similar. I would rank order the similarities from most to least important: (1) quality and velocity level, (2) density ratio, (3) geometry (up, down, or inclined), (4) diameter, and (5) other properties such as viscosity and surface tension.

Turning now to specific models, the homogeneous model is the simplest to use. Only one parameter is

363

needed to predict pressure drop: the friction factor. I recommend that the friction factor be chosen by use of the well-known Moody curves, assuming that only liquid is flowing at the mixture mass velocity. Use the liquid density and viscosity to calculate the Reynolds number and the Moody curves to determine the friction factor. This procedure gives a smooth transition to the two-phase pressure drop in the low-quality region and a step at 100% quality.

Surprisingly, the step at high quality has some experimental justification. In any case, the homogeneous methods that rely on a weighted viscosity have practically no experimental justification and make no physical sense. At best they provide a smooth transition from a single- to a two-phase flow of both ends of the quality range.

The slip models generally have a larger data base than the homogeneous models. Thom, Martinelli, and Baroczy all are included in this category. The empirical friction pressure-drop multipliers they propose are easy to use and give sensible answers to overall pressure drop. Average errors with these techniques are small, but errors possible for a single calculation sometimes are huge-as much as 60 %. In a complex system where heat addition may cause a quality change, and where there are fittings and perhaps several sources for the flow, the overall errors are much less because they tend to average out.

There is no suitable friction pressure-drop calculation procedure, which is needed to accompany the drift-flux model (used for density). Generally if the drift-flux model is appropriate, the friction contribution to the pressure drop is very small. Under the circumstances, I recommend that the homogeneous model be used to calculate the friction pressure drop.

Several pressure-drop models for vertical upflow, including those mentioned in this section, are compared and evaluated in Refs. 32 and 33. Recommendations for calculation are included.

Fittings often are important components in piping systems, though little information exists that can be used to calculate two-phase pressure drop in fittings. Ref. 3, in any case, has a section on pressure drop in fittings.

Inclined pipes are a special case. Naturally the data base for any particular angle inclination is skimpy, so more extrapolation is necessary. The important factor to keep in mind with inclined pipes is that there is often a flow-regime change as the pipe changes orientation from upflow to downflow. One often changes from slug flow in the upflowing portions to stratified or annular flow in the downflowing portions. There is little or no pressure recovery in downflow in stratified or annular flow, so the effect of replacing a section of horizontal pipe with an inclined pipe of the same overall length and net elevation changes is to increase the overall pressure drop substantially. To calculate this pressure drop properly, the void fraction in the upflowing portions must be calculated by use of the drift-flux model. For the stratified downflowing regions a theory presented in Ref. 12 is most appropriate. The most extensive study of inclined-pipe pressure drop is Ref. 15.

364

Critical Flow Two-phase critical flow is an important problem in several areas. Overpressure relief valves for devices such as boilers and cryogenic storage tanks need to be sized so the tank is protected from bursting against all transients. Subsurface safety valves contain choked flow and also must be sized. Break flows must be calculated for pipelines that contain two phases.

Over the past decade much work has been done on break flow since this is an important factor in how a nuclear reactor system behaves after a break occurs. This section explains the results of nuclear work to other parts of the technical community.

In this context, what we call a critical flow is defined by the following experiment. A pipe connecting a fluid reservoir close to saturation conditions is allowed to discharge into a reservoir at a lower pressure. As the pressure in the lower-pressure reservoir is dropped, the flow continues to increase to a certain point and then holds constant even though the discharge pressure is decreased. This asymptotic flow is the critical flow and its velocity is called the critical velocity. Unlike gases, there is no simple relationship between this velocity and the velocity of a pressure wave in the mixture. Both the frequency of the pressure wave and the flow regime change the measured pressure-wave velocity.

The homogeneous model and separated flow models both can be used to calculate choked flow for two-phase mixtures. At low quality and pressure the homogeneous-equilibrium model has been shown to underestimate the break flow greatly. Slip models for choked flow were developed to remedy some of these defects, but other factors, primarily the departure from thermal equilibrium, also apply. Because of these complications, the most successful critical flow models have an extensive data base and rely only minimally on theory.

The most convenient source of information on choked flow of steam/water mixtures is contained in Ref. 5. The results of calculations using the homogeneous equilibrium model and the best slip model are included in a form that is uncommonly convenient for calculation. Both models (as presented in this reference) are only for water, but the analytical details included allow calculations for fluids other than steam and water to be performed.

Recently several useful reviews have been published in this area. Ref. 16 discusses what goes out the break when there is a hole in a pipe with a stratified flow. This is important because proportions of the two phases that go out the break are not necessarily the same as those in the pipe or those flowing. The break quality and flow rate depend on the location of the break and its size, among other factors. Ref. 17 is a thoughtful review of the current theories on choked flow and compares data with a variety of theories. Ref. 18 examines data from a variety of sources and recommends calculations for the large pipes found in reactor systems.

Though break flow is still not entirely understood, we know enough to make serviceable estimates of the

JOURNAL OF PETROLEUM TECHNOLOGY

flow and the resulting set impact forces and critical pressure ratios. Other Topics The items touched on so far might be described as conventional two-phase flow topics. Many areas are affected by what we have learned about two-phase flow that are not usually regarded as two-phase flow concerns, even though two-phase flow is an important factor. It is worthwhile to spend some time on these topics because it is unlikely that the more conventional fields will be the real problems in the future. The first of these topics is gas/liquid separation. Separators. Most separators are built and tested by manufacturers with very little information provided to the purchasers about their operation or design. Scattered throughout the literature are papers and chapters in books that allow one to design separators and estimate their performance. This section attempts to draw this information together.

Both gravity and centrifugal separators are described in Ref. 9. Gravity separators, in essence, are tanks in which the velocity level is low enough to allow phase separation. They usually have demisters at the top to remove additional small drops that might be carried over. Ref. 9 gives a design procedure for separators of this kind. Properties like gas and liquid density are considered explicitly. Cyclone separators are also men-tioned, though less information is given about their design.

Ref. 7 describes demisters of various kinds such as screens, knitted wire mesh, and corrugated plate separators. Information on separator efficiency is presented for all these kinds of separators in a form that is useful for design. Flooding limits also are presented so that one can predict at what vapor velocity level the separated liquid will have difficulty flowing back against the wind.

Additional information on separators is provided in Ref. 2. A wider range of separators is considered, though some useful design information is lacking.

Perhaps the simplest separator is a vertical downflowing pipe in which the deposited liquid is allowed simply to run out. This kind of separator can be designed with the information contained in Ref. 19.

Stability. Two-phase systems often behave in an unstable manner. "Instability" in this context involves two separate manifestations: excursive instability (first described by Ledinegg) and oscillating instabilities. Both kinds of instabilities are found in two-phase piping systems. Ref. 2 is practically the only compilation of the information available for describing two-phase flow instabilities in general.

Unheated two-phase systems are prone to excursive instabilities if, for any reason, there are (1) parallel passages connecting common headers or plenums, or (2) a negative-sloping pressure-droplflow-rate curve in one or more of the passages connecting the two headers. The most common cause of a negative-sloping pressure-droplflow-rate curve is gravity. The slower the flow, the more liquid is held up and the greater the pressure drop. To determine whether a

MARCH 1984

system is prone to this kind of instability, it is necessary to calculate the pressure-droplflow-rate curve and see whether there is a negative-sloping region in the operating range.

In principle, all the information needed to do this is in the pressure-drop correlations mentioned earlier. In fact, how one should do this calculation is still somewhat in doubt. The calculation should be done where the proportion of the two phases distributed to the various parallel passages connecting the headers are allowed to vary as they will. One cannot assume, for example, constant quality or equal flow split unless the system is designed to ensure such a flow split. The root of the difficulty is that we don't have a method of calculating how two phases split when they come to a junction. This deficiency must be regarded as one of the outstanding, unsolved problems in two-phase flow.

Making a piping network predictable may well be a design requirement. If so, and if one has to distribute two phases, perhaps the best way is to design the system to ensure symmetry. There are at least two ways to do this. One can arrange any number of outlet pipes in a circle around a plenum. This practically guarantees that the flow out will have the same quality in each pipe. Another procedure is to split and resplit the flow in tee's in the horizontal plane. For equal pressures in both branches, the quality flowing in the two branches is the same.

The following are examples of specific excursive instabilities that have led to difficulties in various two-phase systems.

1. Small, highly heated tube. The friction term was found to be destabilizing when boiling began.

2. N-shaped three-pass vertical boiler tube. The gravity term has been found destabilizing. 20

3. Heated, inverted V-tubes (in a pendant super-heater). The gravity term was destabilizing. 21

4. Yankee dryer condensate drain (a "vertical" upt10w pipe sucking condensate from the inside surface of a rotating drum and is discharging it into a horizontal axle).22 The gravity term was destabilizing.

Many other examples in the literature duplicate the failures that already have been discovered. In general the following systems are particularly prone to two-phase flow pressure-droplflow-rate instabilities. All these instabilities appear when the pipe in question is part of a multiple-tube array connecting common headers.

I. Vpflowing two-phase pipes at low velocity (where gravity is dominant). Gravity destabilizes.

2. Downflowing heated tubes. Gravity destabilizes. 3. Vpflowing chilled tubes. Gravity and momentum

are both destabilizing. 4. Heated tubes of any orientation with vigorous

surface boiling. Friction is destabilizing. In general one stabilizes a system by putting

sufficient orificing in the lines to ensure a positive pressure-drop vs. flow-rate curve over the entire operating region.

These instabilities also can lead to oscillating flow rates. The most likely such instability, described in Ref. 23, is where a flow delivered to a heated pipe oscillates because of compressibility in the fluid

365

delivery system. Any soft delivery system can lead to an oscillating flow.

A more common cause of an oscillating flow is a density wave instability. Ref. 2 summarizes most of what is known about them. They are found in systems of any orientation in which heat addition causes a density change. When the oscillations occur, their period is about twice the transit time in the heated section.

For these oscillations to occur, a large proportion of the pressure drop must be concentrated in the exit section of the tube. If the flow is above the stable limit for the existing heat flux, a reduction in flow, for example, will cause a reduction in the exit pressure drop. This will tend to increase the flow. However, it takes time for the resulting increase in density to propagate to the exit section. When it gets there, the exit pressure drop increases (because of the increase in pV2, where p=density and V=velocity) and the inlet flow decreases. This causes the flow to decrease and the pV2 to decrease, but only after a delay. The cycle of increase and decrease occurs at a period equal to twice the transit time in the test section. In principle, the methods for calculating the pressure drop in heated sections mentioned earlier are adequate for predicting this instability. In fact. however, these correlations are generally too imprecise for this purpose. since pressure derivatives as well as pressure-drop values are important and the correlations are not that good. Again, these oscillations usually are eliminated by throttling at the inlet to the heated section. These oscillations can occur in any flow regime.

Corrosion-Erosion. One of the more peculiar two-phase flow problems concerns corrosion-erosion in wet steam-extraction lines. Carbon-steel pipes passing wet steam from extraction points on the turbine to the feed water heaters have suffered from wastage rates so large that pipes have to be replaced. 24-26 The location of the wastage is entirely a result of the peculiarities of the two-phase flow passing through these lines. The metal loss peaks at a temperature of 300F [149C] and typically is found in pipes and fittings with flowing steam of 80 to 95 % quality. The flow regime is annular-dispersed.

The most peculiar facet of this wear is that it is sometimes found on the outside of the pipe bend and sometimes on the inside. This is because two separate mechanisms are responsible for the removal of material. In any case, metal removal begins by the steel corroding to magnetite. Fe 3 0 4 , On the outside of the bend the secondary flow and centrifugal acceleration throw the drops out onto the magnetite, fatiguing it and causing it to erode away. This exposes new metal to the steam and accelerates the wastage.

On the inside, the shear stress caused by secondary flow in the bend draws the annular film from the bottom or sides of the pipe to the inside, where an inward-flowing stagnation point occurs. This stagnation point has a very high mass-transfer coefficient and the oxide is dissolved away as a result. To calculate the metal-removal rate, one needs to

366

know what the mass-transfer coefficient is around the bend.

Ref. 26 reports an ingenious experiment in which pure water and air are used to simulate the steam/water system of interest. The "pipe" is cast in two pieces of plaster of Paris. The system is run for a while using air and water and the erosion pattern is observed. This shows more clearly than any other method how the peculiar wear pattern observed in steam-extraction lines comes about.

Wear. Oil and gas pipelines and wellstrings, particularly in the vicinity of fittings, can exhibit wear from the impact of entrained sand. This has been studied in a recent work and an unpublished thesis. 27.28

The wear theory of Finnie 29 can be adapted to the case of sand entrained in a liquid rather than a solid. When this is done, reasonable wear rates are predicted. The secondary flows in the bends are important in determining how much of the sand hits the bend, while the effects of flow regime are much smaller than anticipated. For bubbly and slug flow, the sand is probably in the liquid but the velocities are low enough so that the resulting wear is not very important. In annular flow the film is apparently thin enough that the sand sticks out of the film and may be largely entrained. The wear pattern indicates that this is probably the case.

The homogeneous model appears adequate for predicting the sand velocity and distribution in the pipe.

Vibration Caused by Two-Phase Flow. Very little information is available that can be used to predict the vibration amplitudes caused by fluctuations in a two-phase flow. The mechanism of these fluctuations (as described in Ref. 30) follows.

In two-phase flow, especially slug flow, plugs of t1uid proceed down the pipe with the density fluctuating between that of almost pure liquid and that of almost pure gas. When these fluctuations hit a bend, for example, a fluctuating force resulting from the momentum change in the plug or bubble as it proceeds around the bend is exerted on the bend. This force can cause the pipe to vibrate if the fluctuations are near a natural frequency for the system. These vibrations are best described as random since there usually is not a single well-defined frequency that characterizes the flow. The maximum amplitude of the fluctuating force can be estimated conservatively from the maximum density difference between the phases and the mixture velocity. The frequencies can be estimated from the information presented in Ref. 30 or 31.

The exciting frequencies are typically from 1 to 20 cycles/sec [1 to 20 Hz] while the natural frequencies of the piping systems typically range from 5 to 40 cycles/sec [5 to 40 Hz]. This means that a pipe excited by a two-phase flow will vibrate at its natural frequency with a variable amplitude. The same kind of vibration would occur if a pipe were struck occasionally and allowed to vibrate between blows.

JOURNAL OF PETROLEUM TECHNOLOGY

Flow regime is of governing importance for this problem. The maximum amplitude of the exciting force occurs at the slug-annular boundary. Bubbly flow is very smooth, whereas annular flow becomes increasingly smooth as the velocity and quality increase. Slug flow, however, is very rough.

Conclusion Methods for calculating many of the quantities of interest in two-phase flows exist but are scattered in the literature. This article cites references where the information can be found, stressing the handbooks, which are the most generally available sources for this kind of information.

References 1. Wallis. G.B.: One-Dimensional Two-Phase Flow. McGraw-Hill

Book Co. Inc., New York City (1969). 2. Hestroni, G.: Handbook of Multiphase Systems. Hemisphere

Publishing Corp .. Washington, DC (1982). 3. Collier, 1 .G.: CO/J\'ectil'(! BoilinK and Condensation. McGraw-

Hill Book Co. Inc., New York City (1981). 4. Hewitt, G.F. and Hall-Taylor, N.S.: Annular Two-Phase Flow,

Pergamon Press, New York City (1970). 5. Lahey, R.T. and Moody, F.J.: The Thermal-Hvdraulics ofa Boil-

inK Water Nuclear Reactor. American Nuclear Soc., La Grange Park, IL (1977).

6. Govier, G.W. and Aziz, K.: The Flow of Complex Mixtures in Pipes, Van Nostrand Reinhold, New York City (1972).

7. Moore, M.J. and Sieverding, C.H.: Two-Phase Steam Flow in Turbines and Separators, Hemisphere Publishing Corp., Washington, DC (1976).

8. Hsu, Y.Y. and Graham, R.W.: Transport Process in BoilinK and Two-Phase Svstellls, Hemisphere Publishing Corp., Washington, DC (1976).

9. Szilas, A.P.: Production and Transport (~r Oil and Gas. Elsevier Scientific Publishing Co., New York City (1975).

10. Taitel, Y. and Dukler, A.E.: "A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas Liquid Flow," AIChE 1. 22 (Jan. 1976) 47-54.

11. TaiteL Y. and Dukler, A.E.: "Modeling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes," AIChE J. 26 (1980) 345-52.

12. Shohann, 0.: "Flow Pattern Transition and Characterization in Gas-Liquid Two Phase Flow in Inclined Pipes," PhD dissertation, Tel-Aviv U. (1982).

13. Weisman, 1. et al.: "Effects of Fluid Properties and Pipe Diameter in Two-Phase Flow Patterns in Horizontal Lines," 1111. 1. Multiphase Flo II' (1979) 5, 437-62.

14. Ishii, M. "One-Dimensional Drift-Flux Model and Constitutive Equations for Relative Motion Between Phases in Various Two-Phase Flow Regimes," ANL-77-47 (1977).

15. Beggs, H.D. and Brill, 1.P.: "A Study of Two-Phase Flow in In-clined Pipes," J. Pet. Tech. (May 1973) 607-17.

16. Zuber, N.: "Problems in Modeling of Small Break LOCA," NUREG-0724 (Oct. 1980).

17. Wallis, G.B.: "Critical Two-Phase Flow," Inti. J. Multiphase Flo\\' (Feb.! April 1980) 6, 97.

18. Abdollahiar. P. et al.: "Critical Flow Data Review and Analysis," EPRI NP-2192 (Jan. 1982).

MARCH 1984

19. Liu, Y.H. and Agarwal. 1.K.: "Experimental Observation of Aerosol Deposition in Turbulent Flow," Aerosol Science 5, (1974).

20. Donner, T.l. and Bergels, A.E.: "Pressure Drop with Surface Boiling in Small-Diameter Tubes," Report No. 8767-31, Dept. of Mechanical Engineering, Massachusetts Inst. of Technology, (Sept. 1964).

21. Krasykova, L. Y. and Glusker, B.N.: "Hydraulic Study of Three-Pass Panels with Bottom Inlet Headers for Once Through Boilers," Therlilal EnKineerinK (No.8, 1965).

22. Deane, R.A.: "A Experimental Study of Some Dryer Drainage Siphons," Technical Assn. of the Paper and Pulp Industry (March 1959) 42.

23. Maulbetsch, 1.S. and Griffith, P.: "A Study of Systems Induced Instabilities in Forced-Convection Flows with Sub-cooled Boil-ing," AIChE 3rd IntI. H.T. Conference, Chicago (1968).

24. Vu, H. V.: "Erosive-Corrosive Wear in Steam Extraction Lines of Power Plants," MS thesis, Massachusetts Inst. of Technology, Cambridge (1982).

25. Coulon, A. and Thauvin, G.: "Erosion and Erosion-Corrosion of Mctab," Pmc., 5th IntI. Conference on Erosion by Sol id and Liq-uid Impact (1979) 25, 1-11.

26. Sprague, P.J., Wilkin, S.K., and Coney, M.W.E: "Effects of Two-Phase Flow on Wall-to-Fluid Mass Transfer in Bends and Straight Pipes," Pmc., European Two-Phase Flow Group Meeting, Zurich (1963).

27. Bcnchaita, M.T., Griffith, P .. and Rabinowicz, E.: "Erosion of Metallic Plate by Solid Particles Entrained in a Liquid Set," Trans" ASME (1983) 105, 215-23.

28. Blanchard, D.: "Erosion of Metal Pipe by Solid Particles En-trained in Water." MS thesis, Massachusetts Inst. of Technology, Cambridge (1981).

29. Finnie, I.: "The Mechanism of Erosion of Ductile Metals," Pmc" 3rd U.S. Natl. Congress of Applied Mechanics (1958), 527-32.

30. Yih, T.S. and Griffith, P.: "Unsteady Momentum Fluxes in Two-Phase Flows and the Vibration of Nuclear System Components," ANL-7685 (May 1970).

31. Hubbard, M.G. and Duklcr, A.E.: "A Model for Slug Frequency During Gas-Liquid Flow in Horizontal and Near Horizontal Pipes," 11111. J. Multiphase Flo\\' (1977) 3, 585-96.

32. Idsinga, W., Todreas, N., and Bowering, R.: "An Assessment of Two-Phase Pressure Drop Correlations for Steam-Water Systems," 11111. J. Multiphasl' Flo\\' (1977) 3, 401-13.

33. Hernandez, F.: "Comparison of Friction Factor Correlations for Gas-Liquid Flow in Horizontal Pipes," MS thesis, U. of Tulsa (1973).

SI Metric Conversion Factors atm x 1.013 250* E+05 Pa

OF (OF-32)/l.8 C ft x 3.048* E-Ol m

m. X 2.540* E+OO cm

* Conversion factor is exact JPT

Distinguished Author Series articles are general, descriptive presentations that sum-marize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts In the areas, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: To Inform the general readership of recent advances in various areas of petroleum englneenng

367