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 𝐻𝐿 + 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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𝑣𝑆𝐿 =𝑞𝐿

𝐴𝑝,and𝑣𝑆𝐺 =

𝑞𝐺

𝐴𝑝

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:

𝑣𝐿 =𝑞𝐿

𝐴𝐿=

𝑣𝑆𝐿

𝐻𝐿,and𝑣𝑆𝐺 =

𝑞𝐺

𝐴𝐺=

𝑣𝑆𝐺

1−𝐻𝐿

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

𝑣𝑆𝐿𝐼𝑃 = 𝑣𝐺 − 𝑣𝐿

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−𝑑𝑃𝑎𝑑𝐿

−𝑑𝑃𝑓

𝑑𝐿

The static pressure gradient can be expressed in following equation:

(𝑑𝑃

𝑑𝐿)𝑔= 𝜌𝑡𝑝𝑔 ∙ 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.

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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

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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

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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

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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

two phase flow research

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