Two Phase Flow Research

Two-Phase Flow Models
Comparison and Analysis
Yun Zhe Liu
3/5/2013

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Introduction
Gas Liquid two-phase flow occurs ubiquitously in various major industrial fields, like petroleum, chemical,
refinery and nuclear. Two-phase pressure loss calculation parallels single phase pressure loss calculation and
comprise of important part of process work. The presence of the second phase (sometimes third liquid phase
like oil and water) greatly complicates pressure drop calculation. This is due to the fact that the existence of two
phase and the interactions of two phases make the regime of flow more complicated, and the mixture
properties must be used, therefore the gas and liquid in-situ volume fractions throughout the pipe need to be
determined.
Great effort and many studies have been made to understand two-phase flow behavior and many two-phase
and multiphase pressure drop prediction correlations has been proposed for accurate prediction of two-phase
flow pressure drop. Still, none of them are proven to give good results for all conditions that may occur in
industrial fields(1).
In order to check the validity and accuracy of the correlations, many studies have been performed in which the
correlation predictions have been compared with data available. Most of thess studies have used laboratory
data for comparison; some have utilized limited field data for analysis.
The important general conclusions of these studies can be summarized as follows:
Most correlations are experical and accuracy and good agreement with the data are only limited to the situation and range which they
were derived;
The conclusions of different studies are contradictory in determining the most accurate correalions
In some cases pressure drop field data have reasonably matched the predicted values from some correlations, but very large deviation
has been encountered more frequently.
No one correlation has a solution to all two phase flow problem. The general determination of pressure drop for plant process lines and
pipeline can only be approximated with most suitable correlation selected.
Selecting a suitable two-phase flow pressure drop calculation correlation is the basis and a key step to
appropriately size a pipeline (or flowline) or process line. Published two-phase flow pressure drop correlations
are applicable for specific situations. Blindly applying a correlation may result in orders of magnitude error(13).
The purpose of this study is to explore the applicability of different two-phase (multiphase) flow pressure drop
correlations and help to select most suitable correlation for different applications.
Fundamentalsof Two-Phase Flow
Important Two-Phase-Flow Vaiables
Liquid Holdup
The proportion of the pipe cross-section or volume that is occupied by the liquid phase is defined as the liquid
holdup (HL).
Gas Void Fraction
The gas void fraction is the fraction of the volume elment that is occupied by the gas phase (α).
Note: For two-phase flow, 0 < HL or α< 1, and 𝐻 𝐿 + 𝛼 = 1
Superficial Velocities vSL and vSG (m/s)
The superficial velocity of a phase is the volumetric flux of the phase, which represents the volumetric flow rate
per unit area. In other word, the superficial velocity of a phase is the velocity which would occur if that phase
alone flows in the pipe. Thus, the superficial velocities of the liquid and gas phases are, respectively,

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𝑣 𝑆𝐿 =
𝑞 𝐿
𝐴 𝑝
,and𝑣 𝑆𝐺 =
𝑞 𝐺
𝐴 𝑝
Where qL and qG are respectively liquid phase and gas phase volumetric flow rate (m3/s), and AP is the
cross-sectional area of the pipe (m2).
Actual Velocity vL and vG (m/s)
The actual velocities of liquid phase and gas phase are defined respectively as:
𝑣 𝐿 =
𝑞 𝐿
𝐴 𝐿
=
𝑣 𝑆𝐿
𝐻 𝐿
,and𝑣 𝑆𝐺 =
𝑞 𝐺
𝐴 𝐺
=
𝑣 𝑆𝐺
1−𝐻 𝐿
Slip Velocity, vSLIP (m/s)
The actual velocities of the liquid and gas phase are usually different. The slip velocity represents the relative
velocity between the two phases, as given by
𝑣 𝑆𝐿𝐼𝑃 = 𝑣 𝐺 − 𝑣 𝐿
Flow Patterns/Regimes of Two Phase Flow
In two-phase flow, interactions between liquid and vapor phases, as influenced by their physical properties and
flow rates and bythe line size, roughness and orientation of the pipe, cause the fluids to flow in various types of
patterns. The term flow pattern refers to the geometrical configuration of the gas and the liquid phases in the
pipe. The flow pattern is calledflow regime. Only one type of flow exists at a given point in a line at any given
time. However, as flow conditions change, theflow regime may change from one type to another.
The variables affecting flow patterns can be classified into three groups:
Operational parameters, namely, gas- and liquid-flow rates.
Geometrical variables, including pipe diameter and inclination angle.
The physical properties of two phases (i.e., gas and liquid densities, viscosities and surface tension)
Flow Regime in Horizontal or Slightly Inclined Pipes
Seven principal flow regimes have been defined to describe flow found in horizontal or slightly inclined pipes.
These flowregimes are described below, in order of increasing vapor velocity. In the accompanying sketches,
the direction of flow is fromleft to right.
Dispersed Bubble Flow or Bubble Flow - liquid occupies the bulk of the cross-section and vapor
flows in the form of bubbles along the top of the pipe. Vapor and liquid velocities are
approximately equal. If the bubbles become dispersed throughout the liquid, then this is
sometimes called froth flow. In uphill flow bubbles retain their identity over a wider range of
conditions. In downhill flow the behavior is displaced in the direction of plug flow.
Elongated Bubble Flow or Plug Flow - as the vapor rate increases, the bubbles coalesce, and
alternating plugs of vapor and liquid flow along the top of the pipe with liquid remaining the
continuous phase along the bottom. In an uphill orientation, the behavior is displaced in the
direction of bubble flow; in a downhill orientation, stratified flow is favored.
Stratified Smooth Flow or Stratified Flow - as the vapor rate continues to increase, the plugs
become a continuous phase. Vapor flows along the top of the pipe and liquid flows along the
bottom.The interface between phases is relatively smooth and the fraction occupied by each
phase remains constant. In uphill flow, stratified flow rarely occurs with wavy flow being favored.
Downhill, stratified flow is somewhat enhanced, as long as the inclination is not too steep.

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Wavy Flow - as the vapor rate increases still further, the vapor moves appreciably faster than the
liquid, and the resulting friction at the interface forms liquid waves. The wave amplitude increases
with increasing vapor rate. Wavy flow can occur uphill, but over anarrower range of conditions
than in a horizontal pipe. Downhill, the waves are milder for a given vapor rate and the transition
to slug flow, if it occurs at all, takes place at higher vapor rates than in horizontal pipes.
Slug Flow - when the vapor rate reaches a certain critical value, the crests of the liquid waves
touch the top of the pipe and form frothy slugs. The velocity of these slugs, and that of the
alternating vapor slugs, is greater than the average liquid velocity. In the body of a vapor slug the
liquid level is depressed so that vapor occupies a large part of the flow area at that point. Uphill,
slug flow is initiated at lower vapor rates than in horizontal pipe. Downhill, it takes higher vapor rates to establish slug flow than in
horizontal pipe, and the behavior is displaced in the direction of annular flow. Since slug flow may lead to pulsation and vibration in
bends, valves and other flow restrictions, it should be avoided where possible.
Annular Flow - the liquid flows as an annular film of varying thickness along the wall, while the
vapor flows as a high-speed core down the middle. There is a great deal of slip between phases.
Part of the liquid is sheared off from the film by the vapor and is carried along in the core as
entrained droplets. At the same time, turbulent eddies in the vapor deposit droplets on the liquid
film. The annular film on the wall is thicker at the bottom of the pipe than at the top, the difference
decreasing with distance from slug flow conditions. Downstream of bends, most of the liquid will be at the outer wall. In annular flow, the
effects of friction pressure drop and momentum outweigh the effect of gravity, so that pipe orientation and direction of flow have less
influence than in the previous flow regimes. Annular flow is a very stable flow regime. For this reason and because vapor-liquid mass
transfer is favored, this flow regime is advantageous for some chemical reactions.
Spray Flow (also known as Mist Flow or Dispersed Flow) - when the vapor velocity in annular flow
becomes high enough, all of the liquid film is torn away from the wall and is carried by the vapor as
entrained droplets. This flow regime is almost completely independent of pipe orientation or
direction of flow.
More updated,the following four flow patterns are classified as below:
Stratified Flow (ST), including stratified smooth flow and wavy flow;
Intermittent flow (I), including slug flow and elongated bubble flow;
Annular Flow (A)
Dispersed-Bubble Flow (DB)
Under Dispersed-Bubble Flow conditions, as a result of high liquid flow rates, the two phases move at the
same velocity, and the flow is considered as homogeneous no-slip.
Flow Regimes in Vertical Pipes
Conditions under which certain flow regimes exist depend largely on the orientation of the pipe and the
direction of flow. In a situation where stratified or wavy flow would exist in a horizontal pipe, tilting the pipe
downward increases the relative velocity of the liquid, making a larger part of the flow area available for the
vapor. On the other hand, tilting the pipe upward causes the liquid to drain back downhill until enough has
accumulated to block off the entire cross-section. The vapor can then no longer get past the liquid, and
therefore pushes a slug of liquid through the inclined section of the line.
Five principal flow regimes have been defined to describe vertical flow. These flow regimes are described
below, in order of increasing vapor velocity. In the accompanying sketches, the direction of flow is upward.

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Bubble Flow - upward flowing liquid is the
continuous phase, with dispersed bubbles of
vapor rising through it. The velocity of the
bubbles exceeds that of the liquid, because
of buoyancy. As vapor flow rate is increased,
the sizes, number and velocity of the
bubbles increase. The bubbles retain their
identity, without coalescing into slugs, at
higher vapor rates than in a horizontal pipe.
Slug Flow - as the vapor rate increases,
bubbles coalesce into slugs which occupy
the bulk of the cross-sectional area.
Alternating slugs of vapor and liquid move
up the pipe with some bubbles of vapor
entrained in the liquid slugs. Surrounding
each vapor slug is a laminar film of liquid
which flows toward the bottom of the slug.
As the vapor rate is increased, the lengths
and velocity of the vapor slugs increase.
Slug flow can occur in the downward
direction, but is usually not initiated in that orientation.
However, if slug flow is well established in an upward leg of
a coil, it will persist in a following downward leg, provided
that other conditions remain the same.
In designing for two-phase flow, it is normal practice to try to
avoid slug flow, since this regime can lead to serious
pressure fluctuations and vibration, especially at vessel
inlets and in bends, valves and other flow restrictions. This
could lead to serious equipment deterioration or operating
problems. When slug flow cannot be avoided (for instance,
in thermo syphon reboilers), one should avoid flow
restrictions and use long-radius bends to make turns as
smooth as possible.
Churk Flow - as the vapor rate increases further, the laminar
liquid film is destroyed by vapor turbulence and the vapor
slugs become more irregular. Mixing of vapor bubbles with
the liquid increases and a turbulent, disordered pattern is
formed with ever shortening liquid slugs
separating successive vapor slugs. The
transition to annular flow is the point at
which liquid separation between vapor
slugs disappears and the vapor slugs
coalesce into a continuous, central core of
vapor. Since froth flow has much in
common with slug flow, the two regimes are
often lumped together and called slug flow.
In the downward direction, froth flow
behaves much the same as slug flow does, except that the
former is more easily initiated in this orientation, particularly
if conditions are bordering on those for annular flow.
Annular Flow - this flow regime is similar to annular flow in
horizontal pipe, except that the slip between
phases is affected by gravity. In upflow, the
annular liquid film is slowed down by
gravity, which increases the difference in
velocities between vapor and liquid. In
downflow, the reverse is true, with gravity
speeding up the liquid and reducing the
difference in velocities between vapor and
liquid. On the other hand, the liquid film
thickness is more uniform around the
circumference of the pipe than in horizontal
flow. Annular flow tends to be the dominant
regime in vertical downflow.
Mist Flow - this flow regime is essentially
the same as spray flow in horizontal pipe.
The very high vapor rates required to
completely disperse the liquid essentially
eliminate the effects of orientation and
direction of flow. In identification of vertical
two-phase flow regimes, annular and mist
flow are often considered together (and
called annular-mist).
Flow Pattern & Pressure Drop
The flow patterns differ from each other in the spatial distribution of the interface, resulting in different flow
characteristics, such as velocity and holdup distribution. Any attempt to have a general and unique solution for
two-phase problems for all flow patterns is quite challenging due to its flow characteristics change. However,
as for each existing flow pattern the flow behavior is rather similar, two-phase flow becomes somewhat easier,
as it is possible to analyze each flow pattern separately. Thus, the general approach is to first predict the flow
pattern in the pipe. Once the flow pattern is determined, a separate model for each flow pattern can be used to

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predict the flow characteristics, such as the pressure gradient, liquid holdup and the phase heat transfer
coefficients. So, determination of flow patterns is a central problem in two-phase flow calculation.
Two-Phase Flow Pressure Gradient
In gas-liquid two phase flow, the pressure gradient through a pipe consists of three components: hydrostatic,
momentum (acceleration) and friction. The overall pressure gradient is written as:
−
𝑑𝑃
𝑑𝐿
= −
𝑑𝑃𝑔
𝑑𝐿
−
𝑑𝑃𝑎
𝑑𝐿
−
𝑑𝑃𝑓
𝑑𝐿
The static pressure gradient can be expressed in following equation:
(
𝑑𝑃
𝑑𝐿
)
𝑔
= 𝜌𝑡𝑝 𝑔 ∙ 𝑠𝑖𝑛𝛼
Where g is gravity constant, α is the angle with respect to the horizontal. Ρtp is two-phase flow mixture density
and a strong function of void fraction or the fractional volume occupied by the gas phase within the tube which
itself is a function of the flow conditions.
The acceleration component depends both on the quantity of vapour and liquid flowing through the pipe as well
as the radial profiles of the velocity of the phases.
The frictional component arises due to viscous friction at the walls and is a strong function of the flow velocities
and the characteristic flow patterns or flow regimes that the gas-liquid flow assumes within the tube.
In general, all the three components are influenced by a range of geometric and flow parameters as well as the
thermo-physical properties of the fluid flowing through the line.
Two-Phase Flow Pressure Drop Calculation Approach
For estimation purpose, it is possible to calculate line pressure drop with simplified model by taking the whole
length of pipe as one segment and ignore the acceleration item. That is the basis of in-house spreadsheet in
many companies.It should be mentioned that the calculation with spreadsheet could be unreliable for even the
most simple flow configuration – dispered bubble flow.
For accurate calculation of the pressure drop, particularly in long pipe, due to the change of pressure and the
fraction of vapor as well as physical properties of fluid, the length is divided into many small increments. The
segements should be small enough so that the pressure gradient can be considered constant within the
segement. An iterative calculation for each pipe segment is performed starting from the end of the pipe with the
known pressure and temperature. The total pressure drop over a pipeline may be calculated by integrating the
pressure gradient over the whole length.
∆𝑃 = ∫ (
𝑑𝑃
𝑑𝐿
) 𝑑𝐿
𝐿
0
The challenge lies in the fact that the pressure gradient is dependent on operational parameters (i.e., pressure,
temperature and rate of each phase), geometrical variables and fluids properties, inversely, the operational
parameters and fluid properties of next segement are dependent the pressure gradient. Therefore the
complication of two-phase flow makes it impossible to complete such an inteative calculation with a
spreadsheet, even the tools like KORF. The softwares with an appropriate thermodynamic method and
complete component library support, like HYSYS PIPE SEGEMENT & PIPESYS, or SimSci PIPEPHASE have
to be used for more accurate pressure drop calculation
Pressure is calculated stepwise. With the known operational conditions at the inlet of segement, the fluid
properties and flow pattern can be determined and pressure gradient can be calculated. Multiplied by the

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length of the segement, the outlet pressure can be getten. The outlet pressure for the segment i will be used as
the inlet pressure for segement i+1. The flow rates, fluid propertiesand flow pattern information are updated for
each segement along the pipe then. This way the total pressure drop for line can be calculated.
Analysis of Two-Phase Flow Model
Classification of Two-Phase Flow Model
Based on modeling approach, the two-phase flow pressure drop prediction model can be classified into two
types: empirical correlation and mechanistic model. The empirical correlations are black-box models and they
were developed wholly based on empirical information without any physical basis while the mechanistic
models are built based on fundamental mass and momentum conservation equation, then these equations are
solved numerically with other kinematic and constitutive conditions to arrive at an overall flow models.
There is a vast amount of literature on the prediction of pressure drop in gas-liquid flow in the pipe. Nearly all
prediction methods require experimental information to a varying degree. Since the first correlation was
developed by A, which is a pure empirical correlation, many empirical correlations have been used
successfully for solving two-phase problem for decades with an updated performance of ±30% error.(3). It has
been found that rigorous mechanistic model is not available yet due to the complication of two-phase flow
system. Most of models is between pure empirical model and rigorous mechanistic.
More detailedly, it can be found all of the two-phase flow models fall into following four classes:
Homogenous No-Slip Model, the two-phase mixture is treated as a pseudosingle-phase fluid with average velocity and fluid properties.
(i.e., no slippage). No consideration is given to the flow regime, pure empirical model
Separated Models, assuming that the gas and liquid phases flow separatele from each other. Thus, each of the phases can be
analyzed on the basis of single phase flow methods using the hydraulic-diameter concept. Slip is taken into account, but no attention is
paid to the flow regime. Empirical model based on drift flux analysis.
Flow Regime Empirical Models. Appling the same principles as separated models, however, the flow pattern is taken into account (i.e.,
a different separated model for each flow regime)
Mechanistic Models, based on simplified mechanistic (physical) considerations like momentum,
Homogenous No-Slip Model, Separated Models and Flow Regime Empirical Model are all empirical
correlations. They were developed by establishing mathematical relations based on experimental data.
Dimensional analysis is often used to select correlating variables. The dimensionless groups for the data
correlations were guessed without any physical basis. It is important to notice that application of empirical
correaltions is limited to the range of data used when it was developed.
The mechanistic Models are based on a phenomenological approach and they take into account basic
principles, like conservation of mass and energy. In mechanistic models, flow regime determination is
important. Normally, a mechanistic transport equation is written for each of the phases in the multiphase flow.
Separate models for predicting pressure drop, liquid holdup and temperature profile have been developed by
flow regime determination and separating the phases.
It is difficult to discriminate between empirical and mechanistic models. Often, a combination is used to
develop two-phase flow correlations.
Similar equations for pressure drop are proposed for all correlations. The main difference between the
correaltions is how liquid holdup, mixture density and frictional factor are estimated. Desicription of common
used correlations are found in the flowing sections.
An Introduction toTwo-Phase Flow Models
Many correlations have been developed for predicting the pressure drop and some of them have very limited

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application. The correlations listed above are mostly accepted for two-phase flow simaultion application based
on its better performance in application. The content below regarding the function, data source, appliabiltyis
summarized from application guide for diffenrt simulation model and review and comparison essay.
Ansari
The Ansari model was developed as part of the Tulsa University Fluid Flow Projects (TUFFP) research
program. The comprehensive mechanistic model is composed of a model for flow pattern prediction and a set
of independent models for predicting holdup and pressure drop in bubble, slug, and annular flows. The model
was evaluated by using the TUFFP well databank that is composed of 1775 well cases, with 371 of them from
Prudhoe Bay data.
Fuction: Flow pattern predictionDP calculation
Model Classfication: Mechanistic Model.
Year Developed: 1990
Data Source: TUFFP databank
Application: Vertical well
Baker Jardine Revised
Baker Jardine& Associates (now is part of Schlumberger) have developed a correlation for two phase flow in
gas-condensate pipelines with a no-slip liquid volume fraction of lower than 0.1. This model represents no
major advance in theory, but rather a consolidation of various existing mechanistic models, combined with a
modest amount of theoretical development and field data testing. The model uses the TaitelDukler flow regime
map and a modified set of the TaitelDukler momentum balance to predict liquid holdup. The pressure loss
calculation procedure is similar in approach to that proposed by Oliemans, but accounts for the increased
interfacial shear resulting from the liquid surface roughness. The BJA correlation is used for pressure loss and
holdup with flow regime determined by the TaitelDukler correlation.
Function: DP calculation and Holdup prediction
Model Classfication:
Year Developed:
Data Source: Field testing data
Flow regime correlation required: TaitelDukler correlation
Application:Pipelines(horizontal, inclined and vertical), specifically for applications involving low liquid/gas ratios, e.g. gas/condensate
pipelines. Not recommended for systems having a non-slip liquid volume fraction greater than 0.1.
Beggs & Brill Original
The Beggs& Brill correlation is developed for tubing strings in inclined wells and pipelines for hilly terrain. This
correlation resulted from experiments using air and water as test fluids over a wide range of parameters. The
performance of the correlation is outlined below:
Line orientation: Horizontal, inclined and vertical line.
Model Classfication:Regime Empirical Model
Year Developed: 1973.
Line size: For the range in which the experimental investigation was conducted (i.e., line sizes between 1 and 1.5 inches), the pressure
losses are accurately estimated. Any further increase in line size tends to result in an over prediction in pressure loss.
Data Source: experimental data from lab.
Flow regime correlation required: Beggs& Brill or TaitelDukler correlation
Application: Oil/gas flowline and vertical wells.

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 Oil gravity: A reasonably good performance is obtained over a broad spectrum of oil gravities
 Gas-liquid Ratio: In general, an over predicted pressure drop is obtained with increasing gas-liquid ratio. The errors become
especially large for gas-liquid ratio greater than 5000.
 Water-cut: The accuracy of the pressure profile predictions is generally good up to about 10% water-cut.
Beggs & Brill Revised
As above except that the revised version of the Beggs& Brill correlation is used, with rough pipe friction factors,
holdup limiters and corrective constants as proposed by Palmer and Payne. The following enhancements to
the original method are used; (1) an extra flow regime of froth flow is considered which assumes a no-slip
holdup, (2) the friction factor is changed from the standard smooth pipe model, to utilize a single phase friction
factor based on the average fluid velocity.
Duns & Ros Correlation
The Duns &Ros correlation is developed for vertical flow of gas and liquid mixtures in wells. This correlation is
valid for a wide range of oil and gas mixtures and flow regimes. Although the correlation is intended for use
with “dry” oil/gas mixtures, it can also be applicable to wet mixtures with a suitable correction. For water
contents less than 10%, the Duns-Ros correlation (with a correction factor) has been reported to work well in
the bubble, slug (plug) and froth regions. The pressure profile prediction performance of the Duns &Ros
method is outlined below in relation to the several flow variables considered:
Fuction: Flow patternprediction, DP and holdup calculation
Model Classfication: Regime Empirical Model
Line orientation: Vertical line
Data Source: experimental data from lab.
Flow regime correlation required: Duns &Ros or TaitelDukler correlation
Line size: In general, the pressure drop is seen to be over predicted with a relative error (between the measured and predicted values of
pressure drop) less than or equal to 20% for a range of tubing diameters between 1 and 3 inches.
Application: Oil well
 Oil gravity: good predictions of the pressure profile are obtained for a broad range of oil gravities (13 -56°API)
 Gas-liquid Ratio: the pressure drop is over predicted with a relative error less than or equal to 20% for a wide range of gas-liquid
ratio. The errors become especially large (>20%) for gas-liquid ratio greater than 5000.
 Water-cut: The correlation is not applicable for multiphase flow mixtures of oil, water and gas. However, the correlation can be
used with a suitable correction factor with mentioned above.
Govier & Aziz
The Govier, Aziz &Fogarasi correlation was developed following a study of pressure drop in wells producing
gas and condensate. Actual field pressure drop v. flowrate data from 102 wells with gas-liquid ratios ranging
from 3,900 to 1,170,000 scf/bbl were analyzed in detail. The phase conditions in the well bore were determined
by standard flash calculations. Pressure-gradient data for flow under single-phase conditions were compared
with conventional predictions, and found generally to confirm them. For the test in which two-phase conditions
were predicted throughout the well bore, the field data were compared with several wholly empirical prediction
methods, with a previously proposed method, and with a new prediction method partly based on the
mechanics of flow. The new prediction method incorporates an empirical estimate of the distribution of the
liquid phase between that flowing as a film on the wall and that entrained in the gas core. It employs separate
momentum equations for the gas-liquid mixture in the core and for the total contents of the pipe.

9
Fuction: Flow regime prediction, DP and holdup calculation
Data Source: Field data
Application: Gas or Oil well
Gray
This correlation was developed by H. E Gray of Shell Oil Company for vertical flow in gas and condensate
systems which are predominantly gas phase. Flow is treated as single phase, and dropped out water or
condensate is assumed to adhere to the pipe wall.
Fuction: DP and holdup calculation
Model Classfication: Separated Model.
Reference software: Pipesim
Application: Gas well with the gas velocity below 50 ft/s, the tube size is below 3½-in, the condensate ratio is below 50 bbl/mmscf, and
the water ratio is below 5 bbl/mmscf.
Hagedorn& Brown
This correlation is developed using data obtained from 1500 ft vertical well. Tubing diameters ranging from 1 –
1 ½ inches were considered in the experimental analysis along with 5 different fluid types, namely: water and
four types of oil with viscosities ranging between 10 and 110 cp at 80°F. The correlation developed is
independent of flow patterns and its performance is briefly outlined below:
Fuction: DP and holdup calculation
Model Classfication: Separated Model
Data Source: field data
Flow regime correlation required: No flow pattern involved
Line size: The pressure drops are accurately predicted for line sizes between 1 and 1 ½ inches, the range in which the experimental
investigation was conducted. A further increase in line size causes the pressure drop to be over predicted.
Application: Oil well
 Oil gravity: The correlation is seen to over predicted the pressure drop for heavier oils (13 -25°API) and under predict the
pressure drop for lighter oils (40 -56°API)
 Gas-liquid Ratio: The pressure drop is over predicted for gas-liquid ratio greater than 5000.
 Water-cut: The accuracy of the pressure profile predictions is generally good for a wide range of water-cuts
Mukherjee & Brill:
The Mukherjee & Brill correlation was developed following a study of pressure drop behavior in two-phase
inclined flow. For bubble and slug flow a no-slip friction factor, calculated from the Moody diagram, was found
adequate for friction head loss calculations. In downhill stratified flow, the friction pressure gradient is
calculated based on a momentum balance equation for either phase assuming a smooth gas-liquid interface.
For annular-mist flow, a friction factor correlation was presented that is a function of holdup ratio and no-slip
Moody friction factor. Results agreed well with the experimental data and correlations were further verified with

10
Prudhoe Bay and North Sea data.
Year Developed:1985
Line orientation: Horizontal, inclined and vertical line
Flow regime correlation required: Mukherjee and Brill.Selection of alternative flow maps and/or holdups will cause unpredictable results.
Application: flowline and oil well
OLGAS
OLGAS is based in larger part on data from the SINTEF two-phase flow laboratory near Trondheim, Norway.
The test facilities were designed to operate at conditions that approximated field conditions. The test loop was
800 m long and 8 inches in diameter. Operating pressures between 20 and 90 barg were studied. Gas
superficial velocities of up to 13 m/s, and liquid superficial velocities of up to 4 m/s were obtained. In order to
simulate the range of viscosities and surface tensions experienced in field applications, different hydrocarbon
liquids were used (naptha, diesel, and lube oil). Nitrogen was used as the gas. Pipeline inclination angles
between 1° were studied in addition to flow up or down a hill section ahead of a 50m high vertical riser. Over
10,000 experiments were run on this test loop during an eight year period. The facility was run in both steady
state and transient modes. OLGAS considers four flow regimes, stratified, annular, slug and dispersed bubble
flow and uses a unique minimum slip criterion to predict flow regime transitions. This correlation is available to
all members of the SINTEF syndicate, and to non-members on payment of the appropriate royalty fees.
Model Classfication: Mechanistic Model
Line orientation: Horizontal, Inclined and vertical line
Data Source: experimental data from field
Flow regime correlation required: OLGA-S 2000
Application: flowline and oil well
Oliemans
The Oliemans correlation was developed following the study of large diameter condensate pipelines. The flow
regime is predicted using the TaitelDukler flow regime map, and a simple model, which obeyed the correct
single phase flow limits were introduced to predict the pressure drop. The model was based on a limited
amount of data from a 30-in, 100-km pipeline operating at pressures of 100 barg or higher. The Oliemans
pressure loss correlation can be used with the Eaton, BJA, BRIMINholdup correlations.
Fuction: DP
Line orientation: Horizontal and Inclined
Data Source: Experimental data from field
Flow regime correlation required: Taitel&Dukler
Application: flowline
Orkiszewski
The Orkiszewski correlation was developed for the prediction of two phase pressure drops in vertical pipe.

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Four flow regimes were considered, bubble, slug, annular-slug transition, and annular mist. The method can
accurately predict, to within 10%, the two phase pressure drops in naturally flowing and gas lifted production
wells over a wide range of well conditions. The precision of the method was verified when its predicted values
were compared against 148 measured pressure drops. Unlike most other methods, liquid holdup is derived
from observed physical phenomena, and is adjusted for angle of deviation.
Line orientation: vertical line
Line size: The correlation performs well between 1 and 2 inches line sizes. The pressure loss is over predicted for line sizes greater
than 2 inches.
Flow regime correlation required: Orkiszewski
Application: oil or gas well
 Oil gravity: For heavier oils (13 -30°API), the correlation over predicts the pressure profile. However, predictions are seen to
improve as oil API gravity increases.
 Gas-liquid Ratio: The accuracy of correlation is very good for gas-liquid ratio up to 5000. The errors become large (>20%) for
gas-liquid ratio greater than 5000.
 Water-cut: The correlation predicts the pressure drop with good accuracy for a wide range of water-cuts.
Xiao
The Xiao comprehensive mechanistic model was developed as part of the TUFFP research program. It was
developed for gas-liquid two-phase flow in horizontal and near horizontal pipelines. The model is able first to
detect the existing flow pattern, and then to predict the flow characteristics, primarily liquid holdup and pressure
drop, for the stratified, intermittent, annular, or dispersed bubble flow patterns. The model was tested against a
pipeline data bank. The data bank included large diameter field data culled from the AGA multiphase pipeline
data bank, and laboratory data published in literature. Data included both black oil and compositional fluid
systems. A new correlation was proposed which predicts the internal friction factor under stratified flow.
Model Classfication:Mechanictic Model
Line orientation: Horizontal and Inclined
Data Source: Data from databank or literature
Flow regime correlation required: Xiao or Taitel&Dukler
Application: flowline
Analysis of Applicability of Two-Phase Flow Models
As indicated in the induction section, no one correlation has a solution to all two phase flow problem. The range
of applicability of the pressure drop calculation correlation is dependent on several factors such as line size or
diameter, pipe orientation, fluid properties, gas-liquid ratio and two phase flow with or without water-cut.
Two-Phase Flow Pattern Prediction
Before 1970, the common approach for two-phase flow-pattern determination has been through visal
observation of the flow in a transparent pipe. The coordinates of the 2D map are dimensional. A flow-regime
map with such coordinates is not expected to apply under conditions different from the actual experimental
conditions used for the data acquisition. Though several corection factors for physical properties have been

12
suggested by Baker (1954), but it didn’t improve its overall applicability.
Mandhane et al. correlation (1974) for horizontal pipe is much worthy to mention because it was ever widely
used as a reference map for horizontal flow. It was developed based on the 1178 data points from American
Gas Association and American Petroleum Institute (AGA/API) and represents “an average” of all the other
earlier maps. The weakness of the Mandhan et al. map is that no physical basis was given for the choice of the
superficial velocities of the two phases as the mapping coordinates. Study shows it has very good agreement
withTaitel and Dukler (1976) model and experimental data from later reseach regarding the stratified to
nonstratified transition boundary, but for other transition prediction, it obviously differs from the experimental
data. Also, most of the data were based on experiments conducted in pipes with diameters of ½ inch to 2
inches, therefore, extension of the map to larger pipes should be cautiously considered.
Beggs and Brill (1973) horizontal-flow-pattern map adoped dimensionless factor as the coordinates and is
general correlation for all most system and all sizes of line. With the correlations for liquid holdup and pressure
drop calculation, Beggs and Brill Model is applicable to the entire range of inclination angles, namely, from
vertical upward through horizontal to vertical downward conditions. However, it is not recommended for vertical
upward flow because it underpredicts the pressure loss for this case.
Taitel and Dukler (1976) Model is mostly widely used and succeful correlation up to now. This model is
applicable for steady-state, fully developed, Newtonian flow in horizontal and slightly inclined pipeline. The
model was tested successfully against data mainly collected in small-diameter pipe.
Pressure Drop Calculation Correlations for Two-Phase Flow in Horizotal and Inclined Pipe
For correlations used for pipeline two-phase flow pressure drop calculation, Behnia(2) compared 7 correlations
selected from over 20 models against data from American Gas Assciation (AGA) databank and found that
Beggs and Brill correlation has a deviation mostly in the -50% to 50% range to data from AGA databank and
have the lowest average error (14%) followed by Aziz (20%). Dukler correlation has the highest positive
(overprediction) value of average error (51%). Behnia concluded that the set of actual, measured data is best
represented by Begges and Brill correlation.
In a study to develop a Comprehensive Pipeline Model, Xiao(9) (1990) evaluated his comprehensive model and
other models against the data from Pipeline Databank.Xiao conluded that the comprehensive model
exhibitsthe smallest average percentage error and absolute average error as well as the best performance.
The overall and separated regime prediction performance is very close to his model, Mukherjee and Brill
(1985), Dukler Original (1964) and Dukler-Eaton-Flanigan Model also has very good overall performance.
More recently, Munkejord(7) found the Beggs and Brill correlation and OLGAS Model exhibits the smallest
deviations between experimental data from the TILDA two-phase flow database at the SINTEF multiphase flow
laboratory and calculated pressure drop compared to other models.
Pressure Drop Calculation Correlations for Two-Phase Flow in Vertival Pipe
In a report called “Mlutiphase Flow Models Range of Applicablity”, Rao(12) recommend that Orkiszewski
correlation and Hagedorn& Brown correlation are found to perform satisfactorily for vertical wells with or
without watercut, and andshoud therefore be considered equally as the first choice in such wells. Begges and
Brill method is applicable for inclined wells with or without water cut and is cuurently the best choice available
for deviated wells.
In a study to develop a Comprehensive Wellbore Model, Ansari(10)(1994) evaluated his comprehensive model
and other models against the data from Wellbore Databank. Ansariconludes that Hagedorn and Brown

13
correlation has best overall performance against all data from wellbore databank among the models evaluated:
Ansari, Hagedorn and Brown correlation, Aziz et al correlation, Dunrs and Ros correlation, Hasan and Kabir
mechanistic Model, Beggs and Brill correlation, Orkiszewski correlation and Mukherjee and Brill correlation.
Recommendation Based on Study
1. No one correlation has a solution to all two phase flow problem. It is suggested that the designer compare results from
several correlations and interpret which best encompasses the design problem under consideration.
2. Two phase flow pressure drop calculation is not very accurate. Errors as high as ±50 % in pressure drop calculations are not
uncommon.
3. For flow regime determination, Taitel and Dukler is generally recommended, but if Beggs and Brill correlation is selected,
Beggs and Brill correlation for regime prediction should be used, especillay for horizontal pipe.
4. For two-phase pressure drop calculation, Brigges and Brill is recommended for horizontal and inclined pipe and Orkiszewski
correlation and Hagedorn& Brown correlation is recommended for vertical pipe. But if the problem is in the situation close to
that some correlation was studied, the correlation can be used instead recommended one for best result.
5. To obtain the most accurate pressure drop estimation, the piping system should be evaluated in small segments. In addition,
because the methods presented are flow regime and pipe orientation dependent, each segment should only have one pipe
diameter, one pipe orientation and flow direction and one flow regime. Pipe fittings should be treated as their segments.
6. The pressure drop for each segment should be limited to less than 10% of either the upstream or downstream pressure. This
reduces the compressibility induced errors to less than 1%. Significant changes in the gas/liquid ratio due to flashing may
necessitate further subdivision to update the phase volumes and physical properties. Caution must be used to ensure that a
flow regime transition has not occurred due to flashing.
7. If possible, slug flow should be avoided. This regime can lead to serious pressure fluctuations and vibration, especially at
vessel inlets, pipe bends, valves and other flow restrictions. This can lead to equipment deterioration and operating
problems.
Reference
(1).Duckler, A. E., Wicks, III, Moye, and Cleveland, R. G., Frictional Pressure Drop in Two-Phase Flow, AICHE Journal, January 1964.
(2). MasudBehnia, Most Accurate Two-Phase Pressure Drop Correlation Identified, Oil & Gas Journal, September, 1991.
(3). Brill, J. P., and Beggs, H. D, Two-Phase Flow in Pipes, 5th Edition, December 1986.
(4). Shoham, O.,Mechanistic Modeling of Gas-Liquid Two-Phase Flow in Pipe.2006.
(5). SimSci-Esscor, PIPEPHASE 9.4 Keyword Manual, January 2010
(6). Schlumberger, PIPESIM Suite User Guide, 2005
(7). SvendTollakMunkejord, Mona J. Mølnvik, Jens A. Melheim, Inge R. Gran, Robert Olsen, “Prediction of Two-Phase Pipe Flows
UsingSimple Closure Relations in 2D Two-Fluid Model, Fourth International Conference on CFD in the Oil and Gas (conference), June
2005
(8). Taitel, Y., Flow Pattern Transition in Two-Phase Flow, Heat Transfer 1990, Vol. 1
(9). Xiao, J. J., Shoham, O., and Brill, J. P., A Comprehensive Mechanistic Model for Two-Phase Flow in Pipelines, 1990 SPE Annual
Technical Conference and Exhibition, New Orleans, September 1990.
(10). Ansari, A. M., Sylvester N. D., Sarica, C., Shoham, O., and Brill, J. P., A Comprehensive Mechanistic Model for Upward Two-Phase
Flow in Wellbores, 1990 SPE Annual Technical Conference and Exhibition, New Orleans, September 1990.
(11). Fossmark, M. G., Multiphase-Flow Correlations’ Ability to Model Vertical Lift Performance. MS Thesis, U. of Stavanger, 2011.

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(12). Rao, B., Multiphase Flow Models Range of Applicability, CTES, L. C May 1998

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