Multiphase Flow in Pipes, 2006, Critical Velocity, Presentacion

8/20/2019 Multiphase Flow in Pipes, 2006, Critical Velocity, Presentacion

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Multiphase Flow in Pipes

© Copyright 2006 iPoint LLC. Prepared for iPoint Clients only. All rights reserved. This work contains proprietary presentation of iPoint LLC and may not be copied or stored in an informational

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Outline

1. Components of pressure loss for

multiphase flow in pipes.

2. Liquid holdup.

3. Shape of the tubing curve.

4. Correlation for oil and gas wells

5. Critical rate to unload a well


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Single-phase Flow

q L

q L


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Pressure Loss Components

dL

dv

g

v

d g

v f

g

g

dL

dP

ccctot

ρ ρ θ ρ ++=

2

sin

2

Elevation

Friction

Acceleration


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Single Phase Flow

Fluid occupies 100% cross section of the pipe:

q = Phase rate in bpd, cubic meters per day

A = Area of cross section of pipe, ft2 or m2

v = q/A, Velocity in ft/sec or m/sec

f = Friction Factor = f (NRe)

ρ = Density of fluid (lbm/ft3)

µ = Viscosity of fluid, cp

σ = Surface Tension, dynes/cm


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Moody Friction Factor Diagram

Laminar Critical Zone Transition Zone

Complete Turbulence, Rough Pipes

Pipe Rel.

Roughness

Smooth Pipe

FrictionFactor

Reynolds Number


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Reynolds Number

Where,

v = q/A, Velocity in ft/sec

d = Pipe diameter, ft

ρ = Density of fluid (lbm/ft3)µ = Viscosity of fluid, cp

µ ρ vd N 488,1Re =


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Friction Factor

For Laminar Flow, NRe

< 2000 and

f = 64/NRe

For Turbulent Flow , 3000


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Pipe Roughness

Normally inside wall of a pipe is not smooth In non corrosive environment oil or gas wells tubing may

behave like smooth pipe

Absolute Roughness ε, is the mean protruding height of piperoughness

• Measured with mean protruding height of uniformly distributed, sized,tightly packed sand grains giving same pressure gradient behavior as theactual pipe.

Absolute Roughness = ε in.

Relative Roughness = ε / d Diameter of pipe = d in.


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Friction Factor Rough Pipe:

“ In turbulent flow the effect of wall roughness on pressureloss in pipes depends on both the relative roughness andthe Reynolds number”

If a thick laminar sublayer of l iquid exists in the boudary layeradhering to the pipe wall, the pipe behaves as a Smooth

pipe.

−=

d f ε 2log274.11

Based on his Sand Grain Experiments, Nikuradse Suggested,


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Friction Factor in Transition Region

Transition Region, where friction factor varies

both with relative roughness and Reynolds

number

Colebrook (1938) proposed (Iterative),

+−=

f N d f Re

7.182log274.1

1 ε


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Friction Factor in Transition Region

A simpler equation explicit in friction factor‘f’ was

proposed by Jain (1976) - reproduces Colebrook

equation over the entire range of relative

roughness and Reynolds Number and is

presented as follows:

+−=

9.0

Re

25.21log214.11 N d f

ε


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Single Phase Pressure

Loss

dL

dv

g

v

d g

v f

g

g

dL

dP

ccctot

ρ ρ θ ρ ++=

2

sin

2

Elevation

Friction

Acceleration


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Single Phase Calculations

Calculate Velocity from rate

Calculate friction factor from Reynolds

Number

Calculate pressure losses in smallsegments assuming average fluid physical

properties in case of compressible flow

Use single phase pressure loss equations


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Single Phase Gas

pT TZ p B Bqq

ZRT pM Where

Sc

ScggSc === ;;, ρ

d

v f g

dL

dP gggg

gas 2sin

2 ρ θ ρ +=

dpC g

ZT

p

ZT

p

dL R

M wf

tf

p

p

L

+

= ∫∫ θ sin2

0


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Single-Phase gas Flow

dp

F

ZT

p

ZT

p

I where

+

=

2

2

sin001.

,

θ

,75.18 dp I L

wf

tf

p

p

g ∫=γ

ft andLind MMscfDq RT psia p

d

fq

F and

sc

o

sc

======.;;;;

,

667.0

, 5

22


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Cullender and Smith Ex.

Calculate the flowing bottom hole pressure

in a gas well (γg=0.75),Well Depth,L = 10,000 ft

BH Temp.,T = 245 oF

Wellhead Pressure, ptf = 2,000 psia

Wellhead Temp., Ts = 110oF

ε = 0.00007 ft

d = 2.441 in.

q sc = 4.915 MMscfd

Assume f =0.015 and the first pressure estimate,

p(est) = p(known)(1+2.5x10-5xL/2 Sinθ)


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Multiphase Flow


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Pressure Loss Components

dL

dv

g

v

d g

v f

g

g

dL

dP m

c

mm

c

mmmm

ctot

ρ ρ θ ρ ++=

2sin

2

Elevation

Friction

Acceleration


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Multiphase Flow

q L ,q g

q L ,q g


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Multi phase Flow

Characteristic

More than one phases flow through every-cross section of the pipe

Cross section occupied by a fluid phase

continuously change in the direction offlow due to slippage between phases

Ratio of this cross section for any phase,

over the whole pipe cross section isdefined as the Holdup (HL) for the liquidphase


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Holdup??

q L ,q g

q L ,q g

G

LHL = 0.5

HL = 0.25

HG = 1 - HL


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Definition of Variables

In multi-phase flow calculations,

Single-phase flow equations are modified• To account for the presence of second or third phase

• Involves mixture expressions for velocity, fluid properties

with weighting factors» Based on in-situ volume or mass fraction - holdup

• Weighting factors are flow pattern dependent

• Example: For Liquid-Gas flow, if HL is the weighting factor

for liquid,

( ) LG L Lm H H −+= 1 ρ ρ ρ


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No-Slip Holdup

In oil-water flow,

watercut f w is defined

as,

Where, f 0

= 1- f w

Under no-slip

condition, volume

fraction of liquid, λL Where, λL = 1- λG G L

L

L qq

q

+=λ

ow

ww

qq

q f

+=


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Note!!

For Holdup: HL + Hg = 1

No-slip Holdup: λL + λg = 1Watercut: f O + f w = 1


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Velocities

Superficial Velocity (vSL): Assumes a given phaseoccupies the entire pipe area, Ap

Mixture Velocity (vm): Sum of phase superficial

velocities

p

g

Sg A

qv =

p

LSL

A

qv =

SgSL p

g L

m

vv A

qqv +=

+=


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Actual Phase Velocity

No-Slip flow: Gas and liquid flows at the mixture velocity

Because of the slippage between phases, liquid velocity

will slow down compared to gas in uphill flow and the vice

versa in downhill flow.

Actual velocities vL,vg and slip velocity vs are,,

L

SL L

H

vv =

g

Sg

L

Sg

g H

v

H

vv =

−=

1

Lgs vvv −=


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wwoo L f f ρ ρ ρ +=

wwoo L f f σ σ σ +=

wwoo L f f µ µ µ +=

Mixture Properties

Oil/water mixture flow No Slip condition


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Mixture Properties

Gas/Liquid mixture flow Slip or No-Slip condition

Numerous weighting rules used by different

authors, eg. For mixture viscosity,

)1( Lg L Ls H H −+= µ µ µ

)1(

, L L H

g

H

Lsor

−

×= µ µ µ

)1(, Lg L Lnor λ µ λ µ µ −+=


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Mixture Properties

Gas/Liquid mixture flow

Slip or No-Slip condition

Numerous weighting rules used by different

authors, eg. For mixture density,)1( Lg L Ls H H −+= ρ ρ ρ

)1(, Lg L Ln

or λ ρ λ ρ ρ −+=


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Multiphase Flow

Mixture Properties:

• Holdup Weighting or Dependence

•

Flow Regime Actual phase velocities Affected

by Slippage between phases


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Flow RegimesDuns and Ros (Vertical Uphill)

BubbleBubble Slug Annular Mist MistTaylor BubblePlug


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Stratified Flow - Downhill

q l , q gq l , q g


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Flow Regimes in Two Phase Flow

Bubble flow: (can be present in both upflow or

downflow)

• Slug flow: (can be present in both upflow ordownflow)

• Annular/mist flow: (can be present in both

upflow or downflow)• Stratified flow: (only possible in downflow or

Horizontal well)


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Pressure Traverse- Segmentation

Pressure drops arecalculated for each

calculation increments

(i=1,-----,m) in each

segments (j=1,----,n).

Uses pressure

gradient equation for

each increments and

segments.

Iterative calculation

Segments

1

2

3

4

Calc.increments


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Computing Algorithm

Marching Algorithm

Known Wellhead

pressure, pi

Calculate pi+1 in thecalculation increment

iteratively

A complete traverse is

calculated bysequentially marching

through the traverse.

dLdL

dp p

L

∫

=∆

0

ji

ji

m

i

n

j

L

dL

pd p ,

,11

∆

=∆ ∑∑

==


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Marching Algorithm

1. Assume a rate and calculate the pwf from IPR2. Start from the bottom segment L(more accurate ?) – Why?? And

estimate the end of segment pressure

3. Estimate avg. p and T in the segment

4. Calculate Fluid props in the segment at this avg. p & T

5. Calculate the end of segment pressure, if i t is not the same as theassumed one in step 2

1. Continue the iteration using standard methods such as Newton-

Raphson or Wagstein’s till it converges w ithin acceptable

tollerance

6. Now assume the second segment end pressure and repeat steps 2-5

7. When the surface terminal segment is reached, the calculated

pressure must match this given terminal pressure.

8. If not, either fol low the steps 1-7 till a match is obtained or

graphically solve like in the with systems approach


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Tubing Curve

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Production rate, STB/D

F l o w

i n g b o t t o m h o l e

p r e s s u r e , p s i

Tubing Curve


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Dimensionless Numbers

4Lv N Number,VelocityLiquid

L

LSL

gv

σ

ρ =

4gv N Number,VelocityGas

L

LSg

gv

σ ρ =

L

Lgd σ

ρ = N Number,DiameterPipe d

43L

N Number,ViscosityLiquid L L

L

g

σ ρ µ =

T Ph Fl R i M


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Two-Phase Flow Regime Map

- Duns and Ros

.

1 10 102 103

1

10

102

10-1

BUBBLE FLOW

PLUG FLOWSLUG FLOW

MIST FLOW

REGION IIIREGION II

REGION I

GAS VELOCITY Number, Ngv

L I Q U I

D V E L O C I T Y N u m b

e r , N L v

Vertical upflow


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Multiphase Flow

Determine Flow Regime• Phase Velocities

• Phase physical properties

• Pipe inclination• Production and injection

Determine Holdup - Dependence on

• Pipe inclination

• Flow Regime


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Multiphase Flow Calculation

Superficial Velocities

Flow Regime Maps

Holdup Slippage Velocity

Two Phase Flow pressure gradients


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Pressure Gradient Prediction

Vertical Upflow• Duns and Ros (1963)

• Hagedorn and Brown (1965)

• Orkiszewski (1967)

• Mechanistic Models: Ansari et al. (1994) Inclined Flow

• Beggs and Brill (1973)

• Mukherjee and Brill (1980)

Horizontal Flow• Dukler (1964)

Important Dimensionless


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Important Dimensionless

Variables

In multiphase flow calculations differentempirical equations for flow regimes and

liquid holdup are correlated with

dimensionless variables first proposed byDuns and Ros.

Knowing Phase rates and pipe inclination,

calculate Flow regime and liquid Holdup

Calculate pressure gradient (Ref. Note)


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Two-Phase Friction Gradient

Two phase friction factoris defined differently by

different authors as it is

no more analytically

predictable as in singlephase flow.

d g

v f

dL

dP

c

SL L L

Bubbleflow 2

2 ρ =

d g

v f

dL

dP

c

Sggg

mistflow 2

2 ρ =

;2

2

d g

v f

dL

dP

c

m f tp

twophase

ρ

=


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Two-Phase Hydrostatic Gradient

Two phase hydrostatic gradient is defined as,

θ ρ sinscc Hydrostati g

g

dL

dP

=


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Tubing gradients

9,810 ft at top perf.

0

2000

4000

6000

8000

10000

12000

0 500 1000 1500 2000 2500 3000 3500

Press ure (psig)

< - - - - -

D e p t h

( f t )

Ansari

Aziz

BB

HB

Muk BR

ORK


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Gradient Curves

0 1000 2000 3000 40000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Pressure, psig

D e

p t h ,

f t

Gradient (A) Case 2 (B)

Case 3 (C) Case 4 (D)

Case 5 (E) Not Used

ABCDE

Inflow

Outflow

Inflow Outflow

Gas/Liq Ratio, scf/bbl

Gas/Liq Ratio, scf/bbl

(1) 100.0 (A) 100.0(2) 200.0 (B) 200.0(3) 400.0 (C) 400.0(4) 1500.0 (D) 1500.0(5) 3000.0 (E) 3000.0

Reg: Authorized User - Dowell Schlumberger

WHP= 200 psi

Rate = 2000 bpd 27/8”;350 API; 2000 F


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Hagedorn and Brown

Published in 1963

Widely accepted throughout industry

Based on data from 1500’ test “well”

Tubing size: 1”, 1 1/4”, and 1 1/2” nominal

Different liquids: water, oil: 10 - 110 cp


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Beggs and Brill

Published in 1973

Based on experimental data from inclined

90’ long acrylic pipe

Pipe size: 1” and 1 1/2”

Gas flow rate: 0-300 Mscf/D

Liquid flow rate: 30-1000 bbl/D

Inclination: ±90, 85, 75, 55, 35, 20, 15, 10,5, 0°


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Mukherjee and Brill

Published in 1983

Based on data from 1 1/2” ID inclined pipe

Developed three separate correlations

• Uphill and horizontal flow

• Downhill stratified flow

• Other downhill flow regimes

Wellbore Correlations


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High GLR Gas Wells

Cullender and Smith (1956)• Dry gas only. GLR > 100,000 scf/bbl

Fundamental Flow

• Dry gas only. GLR > 50,000 scf/bbl. Shallow depth,low pressure

Fundamental Flow adj

• Adjusts gas density for GLR > 50,000



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Low GLR Gas Wells

Gray (1974)• Wet gases, gas condensates

Ros and Gray (1961)

Oil well correlations may also be useful• Duns and Ros (1963)

• Hagedorn and Brown (1963)


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Pressure Balance

)()()()()()( q pq pq pq pq p pq p acc f cht flhsepwf ∆+∆+∆+∆+∆+=


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Liquid Holdup

Vg

VL

g L

L L

V V

V H

+≡

( ) g L L Lm H H ρ ρ ρ −+= 1

Determination Of Liquid


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Determination Of Liquid

Holdup

Oil/Water Flow

Gradiomanometer


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ρtool

Water

Holdup

ρwater ρoil

0%

100%100%

water

point

In this example

Hw = 40%

100%

oil

point Gradio

DensityError In

Measurement

Error In Expected

Downhole Oil Density

Uncertainty in

Water Origin and

Salinity

ρ= ρo Ho + ρw Hw

1 = Ho + Hw

ow

o H

w

ρ ρ

ρ ρ

−

−=

ow

w

o H ρ ρ ρ ρ

−−=

Hold-Up Determination

C f


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Critical Rate To Lift Liquid

Most gas wells produce some liquids

Liquids may be

• Vaporized in reservoir gas

• Free liquid in reservoir

Liquids will accumulate if not lifted to surface

Accumulated liquids will reduce productivity

For a given set of conditions, there is a minimumflow rate to lift liquids


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Models for Liquid Transport

Continuous film model Entrained drop model


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Critical Velocity

( )

−

=21

4141

912.1

g

g Lt v

ρ

ρ ρ σ

vt = terminal velocity of liquid droplet, ft/sec

ρL = liquid density, lbm/ft3

ρg = gas density, lbm/ft3

σ = interfacial tension, dynes/cm


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Critical Rate

Tz

A pvq t c

3060=

A = area open to flow, ft2

p = flowing pressure, psia

qc = critical rate, Mscf/DT = flowing temperature, ºR

vt = terminal velocity of liquid droplet, ft/sec

z = real gas deviation factor, dimensionless


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Examples : Perform

Documents

Multiphase Flow in Pipes, 2006, Critical Velocity, Presentacion