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Gas Production and Handling Advances

REVIEW OF METHODS AND CORRELATIONS FOR THE ANALYSIS OF TRANSPORT LINES WITH MULTIPHASE FLOW

Authors: Ruth Anselmi, Alberto J. Baumeister, Katiuska C. Márquez

INELECTRA, S.A.C.A.

ASBTRACT

Multiphase flow transport lines sizing requires different or additional criteria to

those used for the design of single-phase flow lines or two-phase flow lines.

Unlike lines with a single phase, an oversized multiphase flow line can generate

serious operational problems.

Flow assurance is essential to the transportation of multiphase fluids, and

requires evaluations in steady state and dynamic simulations in order to analyze

the potential problems that could arise when changes occur in the flow regime

throughout the studied system.

Flow assurance consists of the analysis (hydraulic, thermal and thermodynamic)

required to maintain uninterrupted production from the reservoir up to the

reception facilities with minimum investment and operation costs.

During the last decades, several hydraulic models have been generated for

predicting and classifying flow patterns present in multiphase flow. In most cases,

these classifications have been developed for flow in horizontal and vertical

pipelines independently.

The limitations of these empirical correlations gave way to the mechanistic

models that originated during the mid-1970's. These models try to describe the

phenomenon of two-phase and multiphase flow using balance sheets and

XVIII Gas Convention, AVPG, Caracas, Venezuela, May 27 - 29 th, 2008


equations that describe the process, and therefore are not limited to specific

conditions such as type of fluid or pipe diameters.

Through this paper a comparison between these models is developed, and the

procedure and criteria currently used for sizing multiphase flow lines is described.

Advantages of the use of dynamic simulators which integrate new mechanistic

models for such evaluation are also discussed.

1. INTRODUCTION

The simultaneous flow of gas and liquid occurs frequently in the oil and chemical

industry, particularly in pipeline transportation, chemical reactors and heat

exchangers. For this reason, the study of the characteristics and mechanisms of

the two-phase flow, has attracted great interest since the decade of the 1940’s,

especially in the oil industry, where the possibility of using a single line for the gas

and oil transportation from the field to the processing plant, results in a substantial

reduction in costs. The design of these pipes requires an estimation of the

multiphase pressure drop as precisely as possible.

Figure 1 shows examples of multiphase flows in the production of hydrocarbons. The

combination of fluids can be present from the reservoir to the reception facilities. In

some cases, some of these phases can be originated during transport, mainly due to

the decrease in temperature, eg. the formation of hydrocarbon condensate, free

water, paraffin or hydrate [Azócar, 2007].



Multiphase Flow

Gas + Liquid Drops (Hydrocarbon o Water)

Hydrocarbon liquid + Bubble of gas and/or Water drops

Free water + Bubble of gas and/or Hydrocarbon drops

Hydrates + Another Phase

Paraffins(wax), Asphalthenes o Naphthene + Another

Sand+ another phase

Gas + Hydrocarbon liquid + Water

Figure 1. Multiphase flow during hydrocarbon production [Azócar, 2007].

Gas Phase Drop liquid within Gas Phase

Gas bubble within liquid phase

Liquid hydrocarbon phase

Liquid water Phase

sand Water Drop within hydrocarbon phase

Hidrocarbon drop within wather phase

Figure 2. Example of Multiphase flow present in transport lines [Azócar, 2007].

For the calculation of pressure drop in multiphase flow, it is customary to divide the

total pressure gradient in three components: friction, acceleration and elevation. Each

calculated separately and then combined. Due to the complexity of these calculations

for the two-phase flow, and the need to develop methods for easy application in

industry, the first approaches that were developed over 70 years ago to solve this

problem were the empirical type. The correlations that have been most commonly

used are those developed by Dukler et al. (1964) and Beggs and Brill (1973) for

horizontal and slightly slant flow in pipes, and the Hagedorn and Brown (1965), and

Duns and Ross (1963) for flow into wells (vertical pipes). These approaches were

very successful in solving two-phase flow problems, obtaining with them a maximum

error of ±30%. However, the empirical correlations have never explained why and



how the phenomenon of two-phase flow occurs [Gomez et al., 1999]. The other big

disadvantage of these correlations is that its use is limited to conditions similar to

those that were developed; outside them the deviations in the values predicted

increase significantly. Thus, when these correlations are used to predict the pressure

drop in larger diameter pipes, or fluids of different properties (more viscous, for

example), the values obtained vary appreciably from the experimental values [Badie

et al., 1999].

The empirical correlations proposed over the years to calculate pressure drop and

liquid holdup have been based on various approaches. The first of them were based

in so-called homogeneous models, which assumed that the liquid and gas phases

travel at the same speed (no slippage between phases), and make no consideration

of flow patterns. Subsequently, the separated flows models were developed, which

supposed that the liquid and gas phases have different speeds (slipping is taken into

account), but also paid attention to the flow regime. A substantial improvement of the

separated flows models occurred when the flow patterns were considered, and using

the same principles, different models were proposed for each flow regime present in

the system.

Due to limitations of the empirical correlations, a new approach emerged in the mid-

1970’s, called mechanistic models. This approach aims to clarify the physical

phenomenon. The mechanism that causes multiphase flow is determined and

modeled mathematically. The first objective of this approach is to predict the flow

regime in a given system. Then, a model is developed separately for each flow

pattern to predict its hydrodynamics and heat transfer [Gomez et al., 1999].

The mechanistic models developed in the last two decades have been formulated

separately for horizontal and vertical piping. The models for horizontal pipes can also

be used for slightly slant piping (±10 °). The first model, which has lasted the most for

the prediction of flow patterns, is the Taitel and Dukler (1976) model. A



comprehensive mechanistic model, is that which can predict flow patterns initially,

and then develop separate models for the prediction of the pressure drop for each of

these patterns. An example of this type was introduced by Xiao et al. (1990) for piping

design [Gomez et al., 1999].

The objective of this paper is to summarize the differences between the empirical

correlations more commonly employed in the industry vs. some of the most recent

mechanistic models that are integrated into some commercial simulators. These

simulators allow not only the prediction of pressure drop and liquid holdup in pipe

sections, but also the performance of transient state studies with the aim of analyzing

the behavior of systems under various disturbances during the same operation.

These analyses allow more appropriate and optimal designs to those made in

previous decades.

2. CONTENT 2.1. Basic Definition The calculation of the pressure gradient requires knowing the velocity and properties

of fluids such as density, viscosity and, in some cases, surface tension. When these

variables are calculated for two-phase flow, the use of certain rules and unique blend

definitions are required [Beggs and Brill, 1991]. The most important properties are the

following:

A) Liquid holdup:

The liquid holdup is defined as the ratio of the amount of liquid volume in a segment

of pipe and the total volume of this segment.

volume segment Pipesegment pipe in volume LiquidHL = (1)



The definition of HL varies between zero for gas phase only, and one for liquid phase

completely. The remaining volume of the pipe occupied by gas is called gas holdup or

vacuum fraction.

LG H1−=α (2)

B) No-slip holdup :

The liquid holdup without slippage is the ratio between the volume of the liquid in a

line segment divided by the total volume of this segment, considering that both

phases travel at the same speed. It can be calculated directly with the volume flow

rates.

GL

LL QQ

Q+

=λ (3)

The gas holdup without slippage is defined as:

LG 1 λλ −= (4)

The difference between the holdup with and without slip is a measure of the degree of

slippage between phases.

C) Superficial Velocity:

The superficial velocity of a fluid phase is the velocity that this phase would show if it

flowed alone through the cross section of the line. The superficial velocity is the

volumetric flow rate of one of the phases per unit area.



G

GSG A

Qv = (5)

L

LSL A

Qv = (6)

The speed of the mixture is the total volumetric flow rate per unit area and is given by:

SGSLT

GLM vv

AQQv +=

+= (7)

D) Actual (in situ) Velocity

The actual (or in situ) velocity is the volumetric flow rate divided by the area occupied

by that phase. Therefore, actual velocity of liquid or gas phase can be calculated

using the following expressions:

L

SL

LT

LL H

vHA

Qv =⋅

= (8)

L

SG

GT

GG H1

vA

Qv−

=⋅

=α

(9)

E) Slip Velocity

The slip velocity is the relative velocity between the two phases, and is defined as the

difference between the actual velocities of the gas and the liquid.

LGS vvv −= (10)



2.2. Flow Patterns

One of the most important factors in the study of multiphase flow are the flow

patterns, which are understood as the different configurations that phases acquire in

the pipeline, when both travel simultaneously. There are various classifications based

on visual observations carried out by different authors. The prediction of these

regimes is of great importance in determining the pressure drop and liquid holdup

because much of the empirical correlations and mechanistic models used in these

calculations depends on the flow pattern existing under different working conditions.

The flow patterns usually identified in the industry are defined below, in a general

manner.

Horizontal Flow

Segregated Flow: This flow is presented when liquid phase velocity is low, while the

velocity of the gas phase can go from low to moderate. Within the classification of

segregated flow are: stratified flow, wavy flow and annular flow.

Intermittent Flow: This flow occurs generally when the liquid phase has a moderate

velocity, while the gas phase is between moderate and high. Within the classification

of intermittent flow are: plug flow and slug flow.

Distributed Flow: Within this classification one of the two phases is dominant over

the other, because its flow rate, and thus its velocity, is much higher than the other’s.

In this category of distributed flow is included: bubble flow and mist flow.



Intermittent Distributed Segregated

Elongatea bubble flow

Slug Flow

Dispersed bubble flow

Mist

Stratified Smooth flow

Stratified Wavy Flow

Annular

Figure 4. Flow Patterns for gas-liquid systems in horizontal pipes, terminology

from Beggs and Brill, adapted from [Beggs and Brill, 1991].

Vertical Flow

Bubble Flow: The gas phase is distributed in the form of bubbles immersed in a

continuous liquid phase.

Bubble - Liquid Slug Flow: As the concentration of bubbles grows by the presence

of a higher quantity of gas, bubbles group or coalesce into one whose diameter

approaches the pipe diameter.

Transition flow, Liquid Slug -Annular: With greater flow rate, the bubbles formed in

the bubble flow collapse, resulting in a sparkling and disorderly flow of gas through

the liquid that is displaced to the wall of the channel.

Annular - Bubble Flow: The flow takes the form of a relatively thick liquid film on the

pipe wall, along with a substantial amount of liquid carried by the gas flowing in the

center of the channel.

Annular flow: The liquid film is formed on the wall of the tube with a central part

formed by gas.



Annular – Liquid Bubble

Bubble Bubble – Slug flow Annular Mist flow

Transition: Liquid Slug – Annular

Figure 5. Flow Patterns for gas-liquid system in vertical pipes, Beggs and Brill

terminology, adapted from [Beggs and Brill, 1991].

2.3. Flow-pattern map

The first approximation to predict flow patterns has been the empirical approach

based primarily on visual observation. Usually the data has been two-dimension

graphs and these figures identify the transition limits between different flow patterns.

These representations are called flow maps. In most cases, the coordinates are

chosen in an arbitrary manner, without a physical basis. For this reason, each map is

useful only at intervals of conditions similar to those in which the data was acquired,

and extending them to other conditions is uncertain. Figure 6 shows one of the first

flow maps developed and widely used in the industry as is the Beggs and Brill map.

Commonly, parameters such as surface and mixing velocities, among others, are

used as coordinates of these maps, because these parameters are the most

characteristic for multiphase flow and the most frequently used in the analysis of this

phenomenon. Other authors, in attempts to extend the validity of their maps have

chosen dimensionless coordinates or correction factors for the physical properties

[Shoham, 1998].




Figure 6. Flow Map, Beggs and Brill (1973) [Brill and Beggs, 1991].

2.4. Models and Correlations for Total Pressure Drop Calculation Like the single-phase case, the total pressure gradient is usually divided into three

components which are derived through an energy balance. An elevation component

(subscript e) which represents the change of potential energy or elevation on the line,

a frictional losses component (subscript f) and an acceleration component (subscript

a) which represents the change of kinetic energy.

afe dLdP

dLdP

dLdP

dLdP

⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛= (11)

Many correlations have been developed to predict pressure drop, which differed on

how to calculate these three components. The definitions of each term for single-

phase flow are usually adapted for two-phase flow assuming that the gas-liquid

mixture is homogeneous for a finite volume of the line.

Contents of liquid at the entrance, λL

Fr


Table 1. Summary of the effects of frictional, elevation and acceleration terms

according to flow type.

Flow Type Friction term Elevation term Acceleration term

Single Phase

Friction against the surface of pipe

Independent from flow Liquid: Dependent on elevation difference Gas: Negligible, except for very high-pressure systems

Generally negligible, but applies for high speed depressurizations

Multiphase flow

Friction of the phases against the surface of the line. Friction between the phases

Density of the phases. Angle of inclination. Liquid Amount (flow variations).

Generally negligible, but applies for high speed depressurizations

In general, the frictional component differs between one model and another mainly in

the way the friction factor is determined and the variety of flow patterns. Many

correlations try to relate the friction factor with different definitions of the Reynolds

number. On the other hand, the acceleration component is completely ignored by

some authors and ignored in some flow patterns by others.

Steady state process simulators have been traditionally used in the industry to

calculate and predict the behavior of two-phase mixtures; these have extensive

databases to estimate physical properties and use empirical correlations to predict

pressure drop and flow regime in each pipe section. Among these simulators is

PIPEPHASE®.



2.5. Flow Assurance

The objective of flow assurance is to guarantee or maintain uninterrupted production

from the reservoir up to the reception facilities with minimum investment and

operation costs.

Flow assurance is now one of the main topics for the design of a system for

hydrocarbons production and the specification of production processes.

The topics considered in flow assurance analysis are evaluated at steady and

transient state. The analysis includes the evaluation of risks and uncertainties

associated with the operational procedures, and contribute to a better economic

estimate of production facilities.

2.6. Simulation for non-stationary multiphase flow In recent years there has been diffused use of simulators that integrate mechanistic

models for the estimation of pressure drop. Using these simulators, it is possible to

size pipes considering flow assurance. Estimations made with these simulators

achieve a better reproduction of transportation systems behavior because they allow

transient-state simulation. Among these simulators are OLGA® from Scandpower

Petroleum Technology, and PIPEPHASE® with the TACITE® module from the

Institute Français du Petrole.

The mechanistic model called OLGA is based on separate balances for mass

conservation of the gas phase and the liquid phase, as well as the drag of liquid

droplets. The formulation of this model includes additional equations for momentum

balances for each phase, and combined mixture energy balance.



For this model, like any other mechanistic model, the implementation of conservation

equations is dependent on the flow pattern. In particular, friction factor and wet

perimeter terms are based on the prediction of the geometry of the flow distribution.

Therefore, the first step of the algorithm used in the model, is the determination of the

flow pattern based on the local distribution of the two-phase flow parameters.

OLGA has been compared with data from various experimental facilities, covering a

wide range of pipe diameters, fluids, angles of inclination and operating conditions.

Most of the information was obtained from experiments of SINTEF Two-Phase Flow

Laboratory in Norway. The model has also been tested successfully in a wide range

of oil production facilities.

Similarly, TACITE is a model that rigorously resolves mass balances for each

component of the mixture, as well as mass and energy balances for the multiphase

mixture. The mechanistic model depends on the flow pattern and has been

extensively validated with experimental field data. The model enables the tracking of

variations in the fluid composition and behavior of the phases along the pipeline for

changes in the inlet conditions and elevation during non-stationary state.

Table 2 shows a comparison between TACITE ® and OLGA ® simulators, which

have been used in recent projects developed by the company INELECTRA SACA.

The main advantage of the program OLGA ® from Scandpower Petroleum

Technology is that, according to project requirements, each module for flow

assurance can be purchased separately. However, the purpose of this comparison is

not to determine which of the models incorporated in these simulators is more

accurate for sizing multiphase pipes, but to show the versatility of each one. The

selection of the simulator to be used in each case depends on customer

requirements, study case characteristics, etc.



Table 2. Comparison between commercial simulators

Basic Evaluation TACITE® OLGA®

Mechanistic Model

Individual Pipes

Recollection Networks ---

Transient State Simulations

Slug Flow Formation Analysis

Control System for Slug Catcher Design.

Possibility to view different variables in profiles or time graphs. ---

Flow Assurance Modules

Three Phases considering separation of water and hydrocarbon, and velocity difference between liquid phases (slip)

---

Liquid Slugs tracking ---

MEG tracking as inhibitor of hydrates formation ---

Hydrates Formation ---

Paraffin Deposition ---

CO2 Corrosion ---

Bundled Lines ---

Heat transfer tridimensional for buried lines ---

For non stationary state simulations it is required first to conduct a sensitivity analysis

at steady state to define the preliminary limits of operation. With this analysis it is

possible to establish the diameter of the pipe and peak flow through it taking into

account the maximum permitted backpressure on the system and verifying that the

fluid velocities do not exceed the established design criteria. Similarly, it is possible to

establish the minimum system flow rate in order to avoid accumulations of liquid

beyond the capability of the reception facilities. This analysis can also be used to



study the temperature profile along the pipe to determine the flow ranges where

hydrates formation and / or deposition of paraffins could take place.

Subsequently, the development of the sensitivity analyses in non stationary state,

which are indispensable for flow assurance of multiphase flow lines, is required. The

presence of at least two phases causes changes as a function of time for variables

such as pressure, temperature, holdup and flow pattern.

The simulations in transient state allow establishing the minimum and maximum

values of the different studied variables (such as pressure drop, fluid, etc.) which

occur under changing operating conditions (eg Start/Stop conditions, increase or

decrease of load, changes in topography, etc.). The visualization of the system

behavior under these circumstances allows optimizing the design and establishment

of the operation ranges.

2.7. Results Comparison between Empirical Correlations vs. Mechanistic Models Following are the results of the evaluation of a section of pipeline that transports

natural gas and its condensates, using the Beggs - Brill - Moody (BBM) correlation,

and OLGAS (OLGAS is the steady-state version of OLGA from ScandPower AS, and

is an additional module that can integrate with PIPEPHASE®).

The purpose of this exercise was to demonstrate the difference in the values obtained

for pressure drop, friction factor, and liquid holdup at steady state for the same gas

flow (100 MMSCFD) and same operating conditions (Pressure defined at exit point:

500 psig, defined temperature at entry point: 150° F). In order to determine the

optimum diameter of the pipe, a sensitivity study was conducted in a range between

10" and 14" (considering carbon steel pipe, wall thickness: 0.5 in., buried pipe, soil

and coating properties known). One vertical branch (length: 1000 feet upstream, 1000

ft downstream) and one horizontal branch (length: 2000 ft) were considered.



In the case of a horizontal pipe, there is a significant difference between both models

for diameters of 10" and 12". The main reason for this difference is based on the

calculated values for the friction factor; in the case of OLGAS, the friction factor is

nearly constant for all diameters evaluated, while BBM presents a jump between 10"

and 12" (see Figure 7).

0

5

10

15

20

25

30

35

40

45

50

10 12 14 16

Pressure Drop [psi]

Internal D iam eter [ in]

B B M

O L G A S

Figure 7. Total pressure drop vs. internal diameter in horizontal pipe



0.00

0.05

0.10

0.15

0.20

0.25

0.30

10 12 14 16

Friction Factor

Internal Diameter [in]

BBM

OLGAS

Figure 8. Friction factor vs. internal diameter in horizontal pipe.

0.00

0.01

0.01

0.02

0.02

0.03

10 12 14 16

Liquid Holdoup


BBM

OLGAS

Figure 9. Liquid Holdup (slip) vs. internal diameter in horizontal pipe.



-0.03

-0.02

-0.02

-0.01

-0.01

0.00

10 12 14 16Frictional Pressure Drop [psi/ft]


BBM

OLGAS

Figure 10. Frictional Pressure Drop vs. internal diameter in horizontal pipe

In the case of vertical upward pipe model, BBM predicts large pressure drops from an

internal diameter of 14". Among the variables that could cause the results shown is

the slip liquid holdup and its effect on the pressure gradient per elevation. In the case

of BBM, the slip liquid holdup increase can be observed, as well as the elevation

gradient. Meanwhile, OLGAS predicts a behavior almost constant for these two

variables.

With respect to the discontinuance of the total pressure drop in BBM (Figure 11),

clearly visible on the 12" diameter, this is a compensation of the frictional and

elevation pressure drops, see Figure 15.



10

15

20

25

30

35

40

45

10 12 14 16 18 20 22

Pressure Drop [psi]


BBM

OLGAS

Figure 11. Total pressure drop vs. internal diameter in vertical pipe upward flow

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

10 12 14 16 18 20 22

Liquid Holdup

Internal Diameter[in]

BBM

OLGAS

Figure 12. Slip Liquid Holdup vs. internal diameter in vertical pipe upward flow



-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

10 12 14 16 18 20 22

Frictional Pressure Drop [psi/ft]


BBM

OLGAS

Figure 13. Frictional pressure drop vs. internal diameter in vertical pipe upward flow

-0.045

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

10 12 14 16 18 20 22

Elevation Pressure Drop[psi/ft]

Internal Daimeter [in]

BBM

OLGAS

Figure 14 Elevation pressure drop vs. internal diameter in vertical pipe upward flow



-0.045

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

10 12 14 16 18 20 22

Pressure Drop [psi/ft]


Frictional Pressure Drop

Elevation Pressure Drop

Total Pressure Drop

Figure 15. Total pressure drop according to BBM vs. internal diameter in vertical pipe upward flow

In the case of the vertical pipe for downward flow, the biggest difference in the result

of total pressure drop is presented in diameters of 10" and 12", but after 14" the

difference between the two models is lower. For the BBM model, a discontinuity in the

values of liquid holdup can be observed for diameters of 10" and 12", affecting the

elevation pressure drop as well.



-15

-10

-5

0

5

10

15

20

10 12 14 16 18 20 22

Pressure Drop [psi]


BBM

OLGAS

Figure 16. Total pressure drop vs. internal diameter in vertical pipe downward flow

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

10 12 14 16 18 20 22

Liquid Holdup


BBM

OLGAS

Figure 17. Slip Liquid Holdup vs. internal diameter in vertical pipe downward flow



-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

10 12 14 16 18 20 22

Fictional Pressure Drop [psi/ft]


BBM

OLGAS

Figure 18. Frictional pressure drop vs. internal diameter in vertical pipe downward flow

0.011

0.012

0.012

0.013

0.013

0.014

0.014

10 12 14 16 18 20 22

Elevation Pressure Drop [psi/ft]


BBM

OLGAS

Figure 19. Elevation pressure drop vs. internal diameter in vertical pipe downward flow



3. CONCLUSIONS

• A comparison of the results for the evaluated example shows that considerable

differences may occur in the pressure drop calculation using empirical

correlations and mechanistic models.

• Most of the curves obtained with BBM have “jumps” between one diameter and

another. The reasons for this may be:

a) Empirical correlations used for pressure drop estimation are limited to

the range of data to which they are based on. This fact reduces their

reliability for the fluid types and conditions that can be found in

production and transportation facilities.

b) Many models have discontinuities in determining the transitions

between the flow patterns.

• The mechanistic models are, according to the literature, more reliable in a wide

range of fluids, process variables, pipe inclinations, etc. Additionally, they

associate pressure drop calculations with liquid holdup and flow patterns,

which ensure continuity in optimal results.

4. REFERENCES

• Azócar, A. Dimensionamiento de Líneas de Transporte con Flujo

Multifásico. INELECTRA S.A.C.A. Process Department Work Instructions.

• Brill, J., and Beggs, H. Two-Phase Flow in Pipes. Sixth Edition (without

editorial name). 1991.

• Gómez, L.E., O. Shoham and Z. Schmidt. “A Unified Mechanistic Model for

Steady-State Two Phase-Flow in Wellbores and Pipelines”. SPE International.

October, 1999.



• Badie S., C.P. Hale, C.J. Lawrence and G.F. Hewitt. “Pressure Gradient And

Holdup In Horizontal Two-Phase Gas-Liquid Flows With Low Liquid Loading”.

International Journal of Multiphase Flow, vol. 26, 1999.


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