Lecture 4 Holdup and Flow Maps

Multiphase flow in pipes

• simultaneous flow of gases, liquids and/or solids

• where?• where?• production wells: oil + gas + water (3-phase)

• why?• cheaper to have one pipeline instead of two• local separation/processing is costly

• challenges:

Flow Assurance - EG55F8/G8

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• challenges:• slug flow: one of the phases exits the pipeline as a large plug � overloads handling capacity of downstream plant• emulsions � reduced production• precipitation � blockage, erosion

Key design tasks

1. predict 1. predict

• flow configuration (“regime”)

• arrival schedule of the fluids at the flow-line exit to design separation facility

2. predict pressure drop[Fig. 1.2.1 Bratland 2010]


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2. predict pressure drop

•very sensitive to flow conditions

Key definitions

• input volumetric flow rates of gas Qg and liquid Ql

• input gas (liquid) volumetric flow fraction:Qg, Ag

Q , A • input gas (liquid) volumetric flow fraction:

• gas (liquid) area fraction αg (αl): fractional area of pipe cross-section occupied by gas (or liquid)

αg = Ag /A, αl = Al /A

Ql, Al

lg

ll

lg

gg QQ

Q

QQ

Q

+=

+= λλ ,


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g g l l

Key definitions - velocity

• superficial velocity

Qu

Qu lg == ,

volumetric flow rate of liquidQg, Ag

Q , A

• actual velocity

A

Qu

A

Qu l

slg

sg == ,

pipe cross-sectional area

===

l

sl

l

ll

g

gg

u

A

Qu

A

Qu

α,

Ql, Al


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• mixture velocity

liquid area fraction ≤1

( ) lgslsglg

m uuuuA

QQu +<+=

+=

Key definitions – liquid holdup

vol. segment pipe totalsegment pipe a in liquid of vol.=lHQg, Ag

Q , A

• [0, 1]

• gas holdup Hg = 1 – Hl

• local holdup

•total holdup

Ql, Al

Ql

QgVg Vl


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• Q: Isn’t this the same as the volumetric flow fraction of the liquid?


Q , A

In general, the (local) liquid vol. flow fraction λl is not equal to the (local) liquid holdup Hl.

Q: A horizontal pipeline with equal volumetric flow rate of gas and liquid. What is Hl?

• gas viscosity << liquid viscosity

•

• uAQuAQ == ,

Ql, Al

Ql

Qg

gl QQ =

gl uu <

gu

lu


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•

•lllggg uAQuAQ == ,

A

A

A

A

AA

gl

gl

>

>

liquid holdup

lg

l

lg

l

VV

V

QQ

Q

+≠

+liquid vol. flow fraction

liquid holdup


Q , A

In general, the (local) liquid vol. flow fraction λl is not equal to the (local) liquid holdup Hl.

• function of• pipe diameter

• liquid flow rate

• gas flow rate

• fluid properties (viscosity, density)

• pipeline slope (buoyancy)

Ql, Al

Ql

Qg

gl QQ =

gu

lu


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• pipeline slope (buoyancy)

• time / location

• Upward inclined sections• gravity contribution of

Flow upslope � larger liquid holdup;Flow downslope � smaller liquid holdup

gul

ll

g

gg A

Qu

A

Qu == ,

( )θ

ρρ gl −g

towards gas acceleration

� tendency for liquid accumulation

� larger Hl

g

lu

( )( ) θ

ρρρρ

singgl

gl

+−

θ

↓

↑

l

g

u

u


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gu

lu

↑

↓

l

g

u

u• Downward inclined sections

• liquid tends to run downward

� smaller Hl

Gravity controls flow at low gas production;Interfacial stress controls flow at high gas prod.

• Low gas production � gravity dominated flow1. high liquid holdup in upward inclined sections; 2. low liquid holdup in downward inclined sections.2. low liquid holdup in downward inclined sections.

• High gas production � friction (interfacial stress) dominated flow.1. Liquid flows with the gas (ul � ug).2. At increasingly high gas production rate, local liquid holdup fraction approaches the liquid vol. fraction.3. Low liquid holdup


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A proper understanding of the liquid holdup behaviour is a key element in the hydraulic design of pipeline systemsNB:• Holdup is an important parameter in estimating the pressure drop particularly in inclined or vertical flow where elevation losses are the major pressure loss component.

• It is also of prime importance in sizing downstream equipment, which must be able to operate properly when the liquid holdup in the line changes because of pigging operations or rate changes.

• It can take quite a long time before the pipeline is filled with sufficient liquid to reach the steady state especially at low production rates, where the total liquid holdup can become high.

• In hydraulic pipeline design, the optimum pipe diameter will be sufficiently large to allow


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• In hydraulic pipeline design, the optimum pipe diameter will be sufficiently large to allow production at high production rates (for the available reservoir pressure), and it will be sufficiently small to limit the liquid holdup such that the liquids produced at start-up, ramp up, pigging, and blow down can be handled by the facilities (e.g. slug catcher or separator).

Key definitions – two-phase density

n

jjj

HH

A

ρρρ

ρ +==∑

=1• Volume average.• Typically used to determine the

ggllj

m HHA

ρρρ +== =1 • Typically used to determine the pressure gradient due to elevation change.

ggllm, ρλρλρ +=−slipno Mixture density assuming no slip.� Assumes ul = ug

� liquid holdup Hl = liquid vol. flow frac. λllg

gg QQ

Q

+=λ


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Sometimes used in the friction loss term and Reynolds number.

lg

g

gg

l

llm HH

22 λρλρρ +=

Flow regimes – background

In multiphase flow, the gas and liquid within the pipe are distributed in several fundamentally different flow patterns or flow regimes, depending primarily on the gas and liquid velocities and the angle of inclination. Observers have labelled these flow and liquid velocities and the angle of inclination. Observers have labelled these flow regimes with a variety of names. Over 100 different names for the various regimes and sub-regimes have been used in the literature.

A number of workers have generated flow regime maps which can be used to determine which flow regimes are likely to occur within a particular pipeline (or parts of the pipeline) under various operating conditions. It is important to know this since the regimes will determine the pressure drop along the pipe, the liquid hold-up within it and the nature of the fluid mixture which will have to be treated on arrival. Research on two phase flow regimes goes back many decades (Baker 1954). Papers by Mandhane et al


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phase flow regimes goes back many decades (Baker 1954). Papers by Mandhane et al (1974), Taitel and Dukler (1976) are often quoted.

With the exception of Taitel and Dukler, these researchers have used an empirical approach to interpreting experimental results. Taitel and Dukler have produced a more theoretical or mechanistic approach and they compared this successfully with published results.

Horizontal flow regimes

Stratified smooth flow• Pipe acts as a separator: liquid along the bottom, gas along top.• Tends to occur in downhill or horizontal flow at small flow rates

Stratified wavy flow• waves form at higher gas velocity

Annular flow• high speed gas stream in middle• liquid film covers circumference of the pipe wall• turbulence rips the interface � liquid droplets suspended in gas.

Dispersed bubble flow• low gas volumetric flow fraction (but high liquid velocity)•


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• gas phase discontinuous � fine gas bubbles suspended in liquid

Elongated bubble / plug flow (intermittent)• slightly lower liquid velocity, low gas volumetric flow fraction• gas bubbles float towards top and cluster• bubbles separated by sections of continuous liquid

Slug flow (intermittent)• longer gas bubbles separating slugs of liquid

[Fig. 1.2.1 Bratland 2010]

Vertical flow regimes


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Flow regime maps

• Need to predict flow regimes for design purposes.

• Constitutive equations differ.

SU

PE

RF

ICIA

L L

IQU

ID V

EL

OC

ITY

, VS

L ,

FT

/SE

C

2 0 . 0

1 0 . 0

1 . 0

S L U G F L O W

A N N U L A R ,

B U B B L E ,E L O N G A T E D

B U B B L E F L O W

M a n d h a n e e t a l . H o r i z o n t a l F lo w P a t t e r n M a p

• Constitutive equations differ.

• Convenient to depict the dependence on system parameters as a 2-D map.

• Thresholds are verysensitive to pipe inclination.

• and to a lesser extent• fluid pressure

higher ρg


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S U P E R F I C I A L G A S V E L O C I T Y , V S G , F T / S E C

0 . 1 1 . 0 1 0 . 0 1 0 0 . 0 5 0 0 . 0

SU

PE

RF

ICIA

L L

IQU

ID V

EL

OC

ITY

, V 1 . 0

0 . 1

0 . 0 1

W A V EF L O W

A N N U L A R ,A N N U L A R M I S T

F L O W

S T R A T I F I E D F L O W

• fluid pressure• pipe diameter• viscosity• surface tension

larger D

higher IFT

Mandhane (1974) flow regime map

, F

T/S

EC

2 0 . 0

1 0 . 0

S L U G B U B B L E ,


S U P E R F I C I A L G A S V E L O C I T Y , V , F T / S E C

0 . 1 1 . 0 1 0 . 0 1 0 0 . 0 5 0 0 . 0

SU

PE

RF

ICIA

L L

IQU

ID V

EL

OC

ITY

, VS

L ,

FT

/SE

C

1 . 0

0 . 1

0 . 0 1

F L O W

W A V EF L O W


F L O W


B U B B L E F L O W



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• J.M. Mandhane, G.A. Gregory & K. Aziz 1974. Int. J. Multiphase Flow 1: 537-553.• horizontal flow • air/ water.• near-ambient pressure• purely empirical• scale up to field conditions uncertain.

Worked Example –Mandhane map

SU

PE

RF

ICIA

L L

IQU

ID V

EL

OC

ITY

, VS

L ,

FT

/SE

C

2 0 . 0

1 0 . 0

1 . 0

0 . 1

S L U G F L O W

W A V EF L O W


F L O W


B U B B L E F L O W


M a n d h a n e e t a l . H o r iz o n t a l F lo w P a t t e r n M a p


0 . 1 1 . 0 1 0 . 0 1 0 0 . 0 5 0 0 . 0

SU

PE

RF

ICIA

L L

IQU

ID V

EL

OC

ITY

, V

0 . 0 1


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24 ft/s

1.06 ft/s

Worked Example - Mandhane map

2 0 . 0

1 0 . 0


.

SU

PE

RF

ICIA

L L

IQU

ID V

EL

OC

ITY

, VS

L ,

FT

/SE

C

1 0 . 0

1 . 0

0 . 1

S L U G F L O W

W A V EF L O W


F L O W


B U B B L E F L O W


.


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0 . 1 1 . 0 1 0 . 0 1 0 0 . 0 5 0 0 . 0

SU

PE

RF

ICIA

L L

IQU

ID V

EL

OC

ITY

, V

0 . 0 1

, F

T/S

EC

2 0 . 0

1 0 . 0

S L U G


But we know from observation that flow regimes depend on other parameters as well.

• Thresholds are verysensitive to pipe inclination.

0 . 1 1 . 0 1 0 . 0 1 0 0 . 0 5 0 0 . 0

SU

PE

RF

ICIA

L L

IQU

ID V

EL

OC

ITY

, VS

L ,

FT

/SE

C

1 . 0

0 . 1

0 . 0 1

S L U G F L O W

W A V EF L O W


F L O W


B U B B L E F L O W


• and to a lesser extent• fluid pressure• pipe diameter• viscosity• surface tension

larger D

higher ρg

higher IFT


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0 . 1 1 . 0 1 0 . 0 1 0 0 . 0 5 0 0 . 0

• Baker, 1954. Simultaneous flow of oil and gas. Oil and Gas Journal 53.

Baker (1954) flow map for horizontal flows

• Plots GG / λB vs GL λB ψ B / GG

• GG , GL are mass flux of gas & liquid phases per unit area [lb/ s /ft2].

Gg = Qgρg/A = usgρg

• λB, ψ B are empirical parameters � crude attempt to account for thermophysical


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attempt to account for thermophysical properties.Reference properties are at 20°C (68°F) and

atmospheric pressure: • water density 1,000 kg/m3 (62.4 lbm/ft3)• air density 1.20 kg/m3 (0.075 lbm/ft3)• water viscosity 0.001 Pa.s (1.0 cp) • water/air surface tension 0.073 N/m

=

=

3/12

/

l

water

water

l

l

airwaterB

water

l

air

gB

ρρ

µµ

σσψ

ρρ

ρρ

λ

Worked Example –Baker map


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Worked Example –Baker map

=

= 0.8lg

B ρρ

ρρ

λ

=

=

=

=

0.20

0.8

3/12

/

l

water

water

l

l

airwaterB

waterairB

ρρ

µµ

σσψ

ρρλ


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B

B B

Reference properties for air & water: • water density 1000 kg/m3 (62.4 lbm/ft3)• air density 1.20 kg/m3 (0.075 lbm/ft3)• water viscosity 0.001 Pa.s (1.0 cp) • water/air surface tension 0.073 N/m

Worked Example – Baker map

.Baker map predicts dispersed bubble regime.

Recall that Mandhane map predicts slug flow.

What would you use?


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Pressure impact on flow regime(Horizontal flow)

BUBBLE

45 bar

90 bar

SLUG FLOW

BUBBLE


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20 bar

STRATIFIED

Pressure impact on flow regime(Vertical flow)

BUBBLE

SLUG FLOW

ANNULAR

BUBBLE


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ANNULAR

Inclination impact on flow regime

BUBBLE

Down

Horiz.

SLUG FLOW


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Horiz.

Up STRATIFIED

Viscosity impact on flow regime

BUBBLE

High

MediumLow

SLUG FLOW


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STRATIFIED

Taitel –Dukler (1976) flow regime

• Taitel, Y. & Dukler A. E. 1976. A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow. American Institute of Chemical Engineering Journal 22: 47-55.

• First attempt at understanding the underlying physics of flow transitions. The map uses the Martinelli parameter X, the gas Froude number, Fr and the parameters T and K.

• The map is composed of three graphs.


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Taitel –Dukler Flow Regime

kinematic viscosity


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jg = is the gas superficial velocity = G .x /ρgG = mass velocity kg/m2s x = mass vapour qualityθ = pipe angle



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Annular

Go to X-T 1

10

Stratified-Wavy

100


Go to X-K plot

Go to X-T plot

0.001

0.01

0.1

0.001 0.01 0.1 1 10 100 1000 10000

Fr G

X

Stratified-Wavy

Stratified

1

10

0.001 0.01 0.1 1 10 100 1000 10000

K

X

10


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Bubbly

Intermittent

0.01

0.1

1

10

0.001 0.01 0.1 1 10 100 1000 10000

T

X

Rapid approximate predictions of pressure drop for fully developed, incompressible horizontal gas/liquid flow may be made using

the method of Lockhart and Martinelli (Chem. Eng. Prog., 45, 39–48 [1949]). First, the pressure drops that would be expected for each of

the two phases as if flowing alone in single-phase flow are calculated. The Lockhart-Martinelli parameter X is defined in terms of the ratio

Horizontal Pressure Drop – Lockhart and Martinelli

the two phases as if flowing alone in single-phase flow are calculated. The Lockhart-Martinelli parameter X is defined in terms of the ratio

of these pressure drops:

The two-phase pressure drop may be then be estimated from either of the single-phase pressure drops, using


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where YL and YG are read from the accompanying figure as functions of X. The curve labels refer to the flow regime (laminar or turbulent)

found for each of the phases flowing alone. The common turbulent-turbulent case is approximated well by

Horizontal Pressure Drop – Lockhart and Martinelli

Lockhart and Martinelli

correlated pressure drop data

from pipes 25 mm (1 in) in

diameter or less within about

650 percent. In general, the

predictions are high for

stratified, wavy, and slug

flows and low for annular


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flows and low for annular

flow. The correlation can be

applied to pipe diameters up

to about 0.1 m (4 in) with

about the same accuracy.

Taitel –Dukler Flow Regime –Worked Example


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Annular

Go to X-T 1

10

Stratified-Wavy

100


Go to X-K plot

Go to X-T plot

0.001

0.01

0.1

0.001 0.01 0.1 1 10 100 1000 10000

Fr G

X

Stratified-Wavy

Stratified

1

10

0.001 0.01 0.1 1 10 100 1000 10000

K

X

10


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Bubbly

Intermittent

0.01

0.1

1

10

0.001 0.01 0.1 1 10 100 1000 10000

T

X

Intermittent or Slug Flow

Repeat with x = 0.5

Annular

Go to X-T 1

10

Stratified-Wavy

100

Go to X-K plot

Go to X-T plot

0.001

0.01

0.1

0.001 0.01 0.1 1 10 100 1000 10000

Fr G

X

Stratified-Wavy

Stratified

1

10

0.001 0.01 0.1 1 10 100 1000 10000

K

X

10


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Bubbly

Intermittent

0.01

0.1

1

10

0.001 0.01 0.1 1 10 100 1000 10000

T

X

Annular flow

Vertical Multi-Phase Govier Map

The correlation by Govier,

et al. (Can. J. Chem. Eng.,

35, 58–70 [1957]), may

be used for quick

estimate of flow pattern.


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Worked Example – Vertical Flow

.


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Worked Example – Vertical Flow

..


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The flow pattern map due to Hewitt and Roberts (1969) has been commonly used for vertical flows. The map was obtained from low pressure air-water and high pressure vapour-water in small diameter (1 – 3cm) tubes. The map

Vertical Multi-Phase Hewitt Map

vapour-water in small diameter (1 – 3cm) tubes. The map works reasonably well for air-water and steam-water systems. Whilst the transition between the neighbour flow regimes appears as lines, they will in practice occur over a range of given coordinates i.e there is not a discrete transition.Axes used in Hewitt and Roberts flow pattern map are the supercritical momentum fluxes for the respective phases:

j volumetric flux (superficial velocity) m/s (ft/s)G mass velocity kg/m2s (lb/ft2s)x mass vapour quality


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x mass vapour quality

Wet Gas Pipeline Pigging and Slug Catcher

Pipelines are pigged for several reasons. If liquid (hydrocarbons and/or water) is present in the line, it must be removed periodically in order to minimize corrosion. This water accumulates in dips in the pipeline, and these low spots are particularly susceptible to corrosion.

Pipelines are also pigged to improve pressure drop-flow rate performance. Water or hydrocarbon liquids that settle in the dips constitute constrained areas that increase pressure drop. Pigging or spering can remove these liquids and improve pipeline efficiency.

Pigging can also be used as a means of limiting the required slug catcher size. By pigging at frequent intervals, liquid inventory buildup in a pipeline can be reduced, and the maximum slug size can be limited. The required downstream slug catcher size must take into account pigging frequency. The amount of liquid in the pipeline is identified by calculating the liquid hold-up.


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Pipeline Sphering

Improve capacity by removing liquid.


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Wet Gas Pipeline Slug CatcherSlug Catchers — Slug catchers are devices at the downstream end or other intermediate points of a pipeline to absorb the fluctuating liquid inlet flow rates through liquid level fluctuation.Slug catchers may be either a vessel or constructed Slug catchers may be either a vessel or constructed of pipe. They provide residence time for vapor-liquid disengagement.Particularly for high pressure service, vessel separators may require very thick walls. In order to avoid thick wall vessels, slug catchers are frequently made of pipe. Lengths of line pipe tens or hundreds of feet long are used as long, slender horizontal separators. The pipe is generally inclined from one to ten degrees and banksof these slightly inclined pipes are frequently manifolded together.


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Hold up – Eaton Method

A correlation developed by Eaton is widely used for estimating hold-up in pipe lines flowing stratified. It is bettersuited for liquid holdup determination in liquid inventory calculations.The Eaton holdup correlation is shown in the opposite figure. InThe Eaton holdup correlation is shown in the opposite figure. Inthis figure, the holdup fraction is plotted directly as afunction of a dimensionless group. This dimensionlessgroup is of the form:


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Hold Up – Wide Variation in predicted amounts

4000

3000

2000

Minami-1

Minami-2

B.B.O

B.B.R

Tota

l Liq

uid

Ho

ldu

p (m

3)


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1000

05 10 15 20 25

Eaton

B.J.A-1MeasuredMuk & Br

B.J.A-2Dukler

No-Slip

Tota

l Liq

uid

Ho

ldu

p (m

Gas Flow Rate (mmsm3/d) 3

Key concepts

• hold-up• slip vs no-slip• implications for • implications for

• density estimation• velocity characterization

• flow regimes• horizontal• vertical

• use of flow maps• use of Eaton method for hold-up estimation


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• use of Eaton method for hold-up estimation• slug catchers and sphering operations

Documents

Lecture 4 Holdup and Flow Maps