Flowing Wells

8/20/2019 Flowing Wells

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January 04 Performance of Flowing Wells 11

Production Technology

Performance of Flowing Wells

Professor Bahman Tohidi

Institute of Petroleum Engineering

Heriot-Watt UniversityEdinburgh EH14 4AS

Scotland

Tel: +44 (0)131 451 3672Fax: +44 (0)131 451 3127

Email: [email protected]


Learning Objectives

• Inflow Performance Relationship (IPR)

– Single phase

– Two phase

• Vertical Lift Performance

– Single phase

– Two phase

• Flow Through Chokes

• Matching Inflow and Tubing Performances


Introduction• Production by natural flow

• Need for better understanding of variousconcepts which define well performance.

• Pressure loss occurs in: – the reservoir

– the bottom hole completion

– the tubing or casing

– the wellhead

– the flowline

– the flowline choke

– pressure losses in the separator and exportpipeline to storage


Introduction• Production is generally limited by the pressure in

the reservoir and difficult to do something about it.

• A major task is to optimise the design to maximiseoil and gas recovery.


Production Performance• Production performance involves

matching up the following threeaspects:

– Inflow performance of formation fluid flowfrom formation to the wellbore.

– Vertical lift performance as the fluids flowup the tubing to surface.

– Choke or bean performance as the fluidsflow through the restriction at surface.


Fluid Flow Through Porous Media

– The nature of the fluid flow

– Time taken for the pressure change in thereservoir

– Fluid to migrate from one location to another

– For any pressure changes in the reservoir, it mighttake days, even years to manifest themselves inother parts of the reservoir.

– Therefore flow regime would not be steady state

– Darcy’s law could not be applied

– Time dependent variables should be examined


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Idealised Flow Pattern

• They are:

• Linear, Radial, Hemi-spherical, and Spherical

• The most important cases are linear andradial models, both used to describe thewater encroachment from an aquifer.

• Radial model is used to describe the flowaround the wellbore.


Characterisation and Modelling of Flow

Patterns

The actual flow patterns are usually complex,due to:

1. The shape of oil formations and aquifers arequite irregular

2. Permeability, porosity, saturations, etc arenot homogeneous

3. Irregular well pattern through the pay zone

4. Difference in production rate from well towell

5. Many wells do not fully penetrate the payzone, or not fully perforated.


Well Inflow Performance

Q

L

A

P1 P2

µ

−∝

A

L

PPQ 21 µ

−=

A

L

PPKQ 21

Darcy’s Law

L

PK

L

PPK

A

QU 21

∆∆

µ−=

−µ

==


Darcy’s Law

DefinitionOne Darcy is defined as the permeability which will

permit a fluid of one centipoise viscosity to flow at a

linear velocity of one centimeter per second for a

pressure gradient of one atmosphere per centimeter.

Assumptions For Use of Darcy’s Law

Steady flowLaminar flow

Rock 100% saturated with one fluid

Fluid does not react with the rock

Rock is homogeneous and isotropic

Fluid is incompressible


Radial Flow for Incompressible Fluids

• Reservoir is horizontal and ofconstant thickness h.

• Constant rock properties φ and K.• Single phase flow

• Reservoir is circular of radius r e• Well is located at the centre of the

reservoir and is of radius r w.

• Fluid is of constant viscosity µ.

• The well is vertical and completedopen hole


Characteristics of the Flow Regimes

• Steady-State; the pressure and the rate distribution inthe reservoir remain constant with time.

• Unsteady-State (Transient); the pressure and/or therate vary with time.

• Semi-Steady State (Pseudo Steady-State); is aspecial case of unsteady state which resemblessteady-state flow.

• It is always necessary to recognise whether a well ora reservoir is nearest to one of the above states, asthe working equations are generally different.


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Radial Flow for Incompressible Fluids

Two cases are of primary interest:

• Steady state: The reservoir conditions does not

change with time. – Flow at r=r e

• Semi steady state or pseudo steady state:

Reservoir conditions changes with time, but dP/dr isfairly constant and does not change with time.

– No flow occurs across the outer boundary

– Fluid production of fluids must be compensated for by the

expansion of residual fluids in the reservoir.


Coping with Complexities

• There are essentially two possibilities:

1. The drainage area of the well, reservoir or aquifer ismodelled fairly closely by subdividing the formationinto small blocks. This results in a complex series ofequations which are solved by numerical or semi-numerical methods.

2. The drained area is represented by a single block insuch a way that the global features are preserved.Inhomogeneities are averaged out or substituted by asimple pattern. Here the equations of flow can besolved analytically.


Steady State - Radial Flow of an

Incompressible Fluid

r

dr

Kh2

qdP

dr

dPK

rh2

q

A

qU

rh2 A

r

r r

πµ

=

µ=

π==

π=

Can be integrated between the limits of:

inner boundary i.e. the wellbore sand face: r = r w P = Pwouter boundary i.e. the drainage radius: r = r e P = Pe




[ ] )r

r ln(

Kh2

qPP

r

dr

Kh2

q

r

dr

Kh2

qdP

w

er we

r

r

r r

r

r P

P

e

w

e

w

e

w

πµ

=−

πµ

=πµ

= ∫∫∫

[Pe - Pw ] is the total pressure drop across the reservoir and

is denoted the drawdown.qr is the fluid flowrate at reservoir conditions.

If the production rate measured at standard conditions atsurface i.e. qs then qs.B = qr

[ ] )r

r ln(

Kh2

BqPP

w

eswe π

µ=−




If the production rate measured at standard conditions at

surface i.e. qs then qs.B = qr

[ ] )r

r ln(

Kh2

BqPP

w

eswe π

µ=−

In field units, i.e., P and qs in psi and STB/day

[ ] )r

r ln(

Kh

Bq

10x082.7

1PP

w

es

3we

µ=− −




Highly supportive reservoir pressure maintenancewith water injection or gas reinjection.

Reservoir production associated with a substantial

expanding gas cap. [ ] )r

r ln(

Kh

Bq

10x082.7

1PP

w

es

3we

µ=− −


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Semi Steady State Radial Flow of a

Slightly Compressible Fluid

If there is no flow across the outer boundary, flowoccurs solely as a result of the expansion of fluid

remaining within the reservoir. The reservoir isfrequently defined as being bounded.




C is the isothermal coefficient of compressibility.

)t(f P

ttancons)dr dP(

0)dr

dP(

e

e

r r

r r

=

≅

=

<

=

P

V.

V

1C

∂∂

−=




The application of Darcy’s law with the system

compressibility equation applied to cylindrical reservoir

volume, results in an equation which needs to be solved

analytically to give :




•Pe has no physical significance.

• Volumetrically averaged reservoir pressure should be

used.q=constant

Pe

Pwf

r w r er

P

h Pave


Radial Flow Theory for Single Phase

Compressible Fluids• Oil, in most cases, can be considered as only

slightly compressible.

• Gases, however, are highly compressible.

• The prediction of inflow performance for gas wells ismore complex due to: – Gas viscosity is dependent upon pressure.

– Gas compressibility is highly dependent upon pressure.

QR in bbls/day

Conversion to SCF/day


Steady State Radial Flow for a Gas• Approximate solution - average pressure or P2

approach.

Qs SCF/day

Qs’ MSCF/day

2


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Steady State Radial Flow for a Gas

• Approximate solution - average pressure or P2

approach.

2

wf Pwf P

FlowOpen AbsoluteQ AOF =


Semi-Steady State Flow for a Gas System

• Using the bounded reservoir assumption and the

definition of isothermal compressibility:


Multiphase Flow within the Reservoir

• Only single phase flow, so far.

• Most oil reservoirs will produce at a bottom holepressure below the bubble point, either:- – Initially where the reservoir is saturated

– Or after production where the pressure in the pore spacedeclines below the bubble point, resulting in 2-phase flow

• Saturations in pore space So+Sw+Sg=1.0

• Critical saturation Sc• Connate water Swc• Residual saturation Sor • Absolute permeability K

• Relative permeability kro=ko/K


Multiphase Flow within the Reservoir


2-Phase Flow, Vogel’s Equation

2

r

wf

r

wf

maxo

o )P

P(8.0)

P

P(2.01

q

q−−=

A simplified solution was offered by Vogel. He simulated the PVT

properties and cumulative production from different wells oncomputer to produce many IPR curves. These were then normalised

for pressure and producing rate. The curves produced representmany different depletion drive reservoir. A single curve can be fitted

to the data with the following equation.

This equation has been found to be a good representation of many

reservoirs and is widely used in the prediction of IPR curves for 2-phase flow. Also, it appears to work for water cuts of up to 50%.


Vogel’s Equation, Example-1

b/d 211)2400

800(8.0)

2400

800(2.01250)(8.0)(2.01

psi800PFor

b/d 250

)2400

1800(8.0)

2400

1800(2.01

100

)(8.0)(2.01

psi1800P

b/d 100q

psi2400P

:datafollowinggiven the psi,800Pforq and q Find

22

max

22max

wf

o

wf oomax

=⎥⎦

⎤⎢⎣

⎡ −−×=⎥⎦

⎤⎢⎣

⎡−−=

=

=−−

=−−

=

=

=

=

=

r

wf

r

wf

oo

r

wf

r

wf

oo

r

P

P

P

Pqq

P

P

P

P

qq


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Vogel’s Equation, Example, Cont.

If other values of Pwf are chosen, sufficientqo’s can be generated

to plot the curve, e.g.:

Pwf qo800 2111200 175

1600 128

2000 69

IPR

0

500

1000

1500

2000

2500

3000

0 100 200 300qo

P w f


Vogel’s Equation, Combined Single Phase Liquid and 2-

Phase

In this case there is a single

phase liquid which exists

above the bubble point. Belowthe bubble point the system

becomes 2-phase.

The figure opposite shows the

IPR, which is a combinedlinear-Vogel plot (i.e., straight

line above Pb and Vogelbelow Pb with Pb substituted

for Pr).

Pb

Pr

qb qmax

q

Pwf

Straight line above Pb

Vogel below Pb


Vogel’s Equation, Example-2

psia1000 b. psia2500 a. :of Pforq iii)

P belowIPR Vogelassuming,q )

q i)

:Find

)4

3(ln

)(1008.7

cp0.68 2.1B 0S

ft0.4r ft2000r ft60h

md 30k psia2000P psia3000P

:datafollowingGiven the

wf o

bmax

b

3

o

we

b

ii

r

r B

PPhk q

w

eoo

wfsr o

o

o

r

−

−×=

===

===

===

−

µ

µ


Example-2, Solution

⎥⎦

⎤⎢⎣

⎡−−=

=+−××

−××××

=−

−×=

−

−

2

max

b

3

3

)(8.0)(2.01

P beyond Vogelusing ii)

b/d 2010

)04

3

4.0

2000(ln2.168.0

)20003000(60301008.7

)4

3(ln

)(1008.7

:used isequationinflowradialfore there

point, bubbletheabovePIgivennoisThere i)

r

wf

r

wf

oo

w

eoo

wfsr o

o

P

P

P

Pqq

r

r B

PPhk q

µ


Example-2, Solution

b/d/psi01.220003000

2010PatPItherefore

8.1

PPI)Vogel(q

P

8.1q

P

P6.1

P

2.0q

dP

qd-PI PPatand

P

P6.1

P

2.0q

dP

qd-

P

P6.1

P

2.0q

dP

qd

PI.thegivesitateddifferentiis

equationsVogel'if IPR,theof slopetheisPIthethatmemberingRe

b

bmaxo

b

maxo2b

b

b

maxo

wf

obwf

2

r

wf

r maxo

wf

o2

r

wf

r maxo

wf

o

=−

=

×=

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡+===

⎥⎦

⎤⎢⎣

⎡+=⇒⎥

⎦

⎤⎢⎣

⎡−

−=


Example-2, Solution

b/d357315632010qqq

b/d1563)2000

10000.8()

2000

1000(2.01qq

Pi.e.psi,1000Pb.

b/d1005)25003000(01.2)PPPI(q

,Pi.e.psi,2500Pa.iii)

b/d424322332010qqq

b/d22338.1

200001.2

8.1

PPIq

o(Vogel)bo(total)

2

)Vogelmax(o(Vogel)

bwf

wf r

bwf

)vogelmax(b)totalmax(

b)vogelmax(o

=+=+=

=⎥⎦

⎤⎢⎣

⎡−−=

=

=+=+=

=×=×=


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Vogel’s Equation, Problems-1&2

IPRthePlot

b/d/psi2PI

psi3000P

psi4200P

psi.2500Pfor qand,q,qfinddata,followingtheUsing

2-Problem

_________ __________ __________ __________

psig1000P b/d150qpsig1600P psig1600P

:datafollowingthefor IPRplotandqFind

1-Problem

b

r

wf max(total)b

wf o

br

omax

=

=

=

=

====


Two Phase Flow: Effect of GOR


Productivity Index (PI)• Productivity index is a measure of the capability of a

reservoir to deliver fluids to the bottom of a wellbore.

• It relates the surface production rate and the pressure

drop across the reservoir, known as the drawdown.

• To take into account the effect of the thickness ofproducing interval and comparison of various wells,

the Specific Productivity Index is defined as:


Oil Wells Productivity Index

• The Productivity Index (PI) is the ratio ofproduction to the pressure draw down at the

mid-point of the production interval

rateflowoilQ presure

presurereservoiraverage

o ==

=−

=

flowingP

PPP

QPI

wf

R

wf R

o

The productivity index is a measure of the oil well potential or abilityto produce and is a commonly measured well property.

PI is expressed either in stock tank barrel per day per psi or in stocktank cubic metres per day per kPa.


Practical determination of PIThe static pressure (PR) is measured by:

- prior to open a new well (after clean up)

- after sufficient shut in period (existing wells)

In both cases a subsurface pressure gauge is run into

the well

The flowing bottom hole pressure (Pwf ) is recorded

- after the well has flowed at a stabilised rate for a

sufficient period (new wells)

- prior to shut in for the existing wells


Decline of PI at High Flow RatesIn most wells the productivity index remainsconstant over a wide range of variation inflow rate. Therefore, the oil flow rate isdirectly proportional to bottom holepressure draw down.

However, at high flow rate the linearity failsand the productivity index declines, whichcould be due to:

1- turbulence at high volumetric flow rates

2- decrease in relative permeability due to thepresence of free gas caused by the drop inpressure at the well bore

3- the increased in oil viscosity with pressuredrop below bubble point

Flow rate

PI

Drawdown

Qo PI


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PI for Gas Reservoir in SS Flow• For gas wells, the equations commonly involve a P2

term, hence the PI is redefined in terms of this.

Parameters, assuming nochange in the fluid and

reservoir properties, should

remain constant. Hence, J

should be a constant.

2


Gas Wells: Potential Curve• The productivity of a gas well is expressed by the

potential curve (or back pressure curve).

data.flowpointstabilisedonefromcalculatedisC

flow).(turbulent0.5andflow)state-steady(laminar 1betweenvariesn

paper.log-logaonQvs)P(Pof plottheof slopetheisn

1

C)Qlog(n

1)Clog(

n

1)Qlog(

n

1)Plog(P

)Pnlog(Plog(C)log(Q)

constantsare n"" andC"" pressurefacesandflowingP

pressurereservoir in-shutP rateflowvolumetricQ )PC(PQ

2

wf

2

wi

'2wf

2wi

2

wf

2

wi

wf

wi

n2

wf

2

wi

−

+=−=−

−+=

=

==−=


Gas Wells: Potential Curve

Potential Curve

1

10

100

1000

10000

1 10 100 1000 10000

q

P

w i ^ 2 - P w f ^ 2

Slope=1/n

Zero sand face pressure

Absolute

Open

Flow (AOF)

C


Potential Curve: Practical

Determination

The potential curve is obtained either through a back

pressure test or an isochornal flow test.

A back pressure test consists of succession of four

increasing flow rates. The pressures are measured at

the end of a flow period at a given rate, after which therate is changed immediately to a new value without

closing the well.

Back pressure tests are used for formations with good

permeability, where the measured pressure at the end of

each flow period reaches a stabilised value.


Potential Curve: Back Pressure Test

q1

q2

q3

q4

q

t

t

Pwf Pwf1

Pwf2

Pwf3

Pwf4


Potential Curve: Practical

DeterminationIn low permeability formations where stabilised flow

conditions would be attained in a prohibitive time,

isochronal tests give better results.

An isochronal test consists of flowing the well at four

flow rates for period of equal duration. After each periodthe well is shut-in for sufficiently long time in order to

reach static conditions with a satisfactory approximation.

An additional point is used from a run with an extended

flow period approximating stabilised conditions. A line

drawn through this point, with correct “n” represents the

true stabilised potential curve.


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Potential Curve: Isochronal Test

q1

q2

q3q

t

t

Pwf

q4


Example 1

• From a well test, it has been determined thatthe performance constant, C of the well is

0.0037 (for qsc in MMSCF/D) and n=0.93.Determine the flow rate when Pr =3000 psiaand Pwf =1850 psia. What is the AbsoluteOpen Flow (AOF) potential.

( ) ( )

( ) mmscf/d86.10)0()3000(0037.0 AOF

mmscf/d96.6)1850()3000(0037.0PPCq

93.022

93.022n

2wf

2

r qc

=−=

=−=−=


Example 2: Isochronal Test

Duration ofTest

(hours)

Sand-facePressure

(psia)

Flow Rate(MMSCF/D)

Shut-in bottomhole pressure

(psia)

Shut-in 2200 0 2200

6 1892 2.8 2200

6 1782 3.4 2200

6 1647 4.8 2200

6 1511 5.4 2200

Analyse the following isochronal well test data

Afterwards, the well continued to produced at 6 mmscf/d and

reached a stabilised flowing sandface pressure of 1180 psia.

• Plot the deliverability curve and determine flow index and the

performance constant.

• Determine AOF


Example 2: Isochronal Test-

Solution

Pwf(psia)

qsc (MMSCF/D)

Pwf 2

(psia)2

Pr 2-Pwf

2

(psia)2

2200 0 4.84 x 106 0

1892 2.8 3.58 x 106 1.26 x 10

6

1782 3.4 3.18 x 106 1.66 x 10

6

1647 4.8 2.71 x 106 2.13 x 10

6

1511 5.4 2.28 x 106 2.56 x 10

6

Stabilised point1180 6.0 1.39 x 10

6 3.45 x 10

6

The following table is prepared

Plot (Pr 2-Pwf

2) v qsc on log-log paper.


Example 2: Isochronal Test- Solution

0.1n0.1)102.2log()108.8log(

)100.1log()100.4log(

n

166

66

=⇒=×−×

×−×=

MMSCF/4.8 AOF

1084.4

0)2200(PP

6

22

wf

2

r

=

×=

−=−

6

0.16

n2

wf

2

r

sc

1074.1

)1045.3(

6

)PP(

qC

−×=

×=

−=

MMSCF/D42.8

)02200(

1074.1 AOF0.122

6

=−

××= −

1.00E+06

1.00E+07

1.E+06 1.E+07Q (SCF/D)

P r

2 - P w f 2 ( p s i a 2

)


Perturbations from Radial Flow Theory for

Single Phase Flow

• IPR were derived on the

assumption that radialflow occurred

• The formation was

assumed to be isotropic

and homogeneous.

• However the basicprocess of drilling and

completing a well will

cause changes in the

condition of the physical

flow process.


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10



Single Phase Flow

• These perturbations to radial flow may comprise the

following:

• A zone of permanent or temporary permeabilityimpairment around the borehole due to mud,completion fluid, and possibly cement filtrate

invasion.

• A large number of wells are cased off and then

perforated.

• Often, only a small section of the reservoir is to beperforated (fluid convergence and vertical

permeability).



Single Phase Flow

• Perturbations from radial flow theory will generate anextra pressure drop component which will affect the

the actual bottomhole flowing pressure, Pwf .

• where Pwf actual is the actual bottom hole flowing

pressure and Pwf ideal is the idealised bottomholeflowing pressure which assumes true radial flow.

• And ∆PSKIN is the additional pressure loss associatedwith the perturbation(s). It should be noted that most

of the perturbations will cause the ∆PSKIN to bepositive and accordingly



Single Phase Flow

• It should be noted that most of the perturbations will

cause the ∆PSKIN to be positive and accordingly

• The pressure drop associated with these near

wellbore phenomena is termed a SKIN and is defined

as a dimensionless skin factor, S:

• For fractures, acid stimulations and for deep

perforations, there will be less resistance to flow andhence


Skin Factor • Pressure drop associated with these near wellbore

phenomena is termed a SKIN and is generally

defined as a dimensionless skin factor, S:


Skin Factor • The actual drawdown across the reservoir when a

skin exists, ∆Pactual, can be related to the idealdrawdown predicted from radial flow theory ∆Pidealand the skin pressure drop ∆PSKIN by:

In field units


Skin Factor • We can simply add the ∆PSKIN to the radial flow

expressions developed earlier e.g. for steady stateflow of an incompressible fluid, by adding in the skin

pressure drop:

For compressible fluids


11/18

11


Tubing Performance• The pressure loss in the tubing can be a significant

proportion of the total pressure loss. However its

calculation is complicated by the number of phases

which may exist in the tubing.

• It is possible to derive a mathematical expression

which describes fluid flow in a pipe by applying the

principle of conservation of energy.

• The principle of the conservation of energy equates

the energy of fluid entering in and exiting from acontrol volume.



Single Phase Turbulent Flow• Frictional pressure loss for single phase turbulent

flow will still be a function of velocity as in the case

for laminar flow, but the proportionality will be more

complex and a function of the relative roughness.

• It can be seen thatthe pressure

gradient dP/dL is a

function of:


Single Phase Turbulent Flow

• In flowing to surface,the fluid will:

• lose pressure

• Expansion for highcompressibility fluids

• lose heat to the

surroundingformations


Dry Gas Flow

Effect of Pressure

• Gas is a low viscosity, low density fluid with a very

high coefficient of isothermal compressibility, e.g.,

Cg = 300 x 10-6 vol/vol /psi

• As the gas flows to surface, its pressure will declineand it will undergo the following changes:

– the density will dramatically decline

– the potential energy or hydrostatic pressure gradient will

decline proportionally.

– the gas will expand, resulting in an increase in velocity.

– the frictional pressure gradient will increase


Dry Gas Flow

• For most gas production wells, the flow regime in

the tubing will be transitional or turbulent.

The relativecontribution of boththe frictional andhydrostatic pressuregradients as afunction of gasflowrate


12/18

12


Single Phase Liquid Flow - Oil or Water

Effect of Pressure

• In general, crude oil can be classified as slightly

compressible, the degree of compressibility beingdependent on the crude oil gravity - a light crude oil

with an API gravity of, say, 35° would be more

compressible than a heavier crude oil with an API

gravity of 20° API. A typical oil compressibility (Co )would be 8 - 12 x 10-6 vol/vol/ psi.

• Water is even less compressible and is frequently

considered to be incompressible (Cw = 6 - 8x10-6

vol/vol/psi).



• For the flow up tubing of a single phase

liquid, the following will occur:

– As the liquid flows upwards, the density will

decline by the order of 0.5 - 1.0% for every 1000

psi drop in pressure. The effect on hydrostatic

pressure gradient is minimal.

– As pressure declines, the viscosity will decrease

slightly. Hence, for oil or water, the impact of f low

on the physical properties of the fluid will be

negligible and hence the increase in frictional

gradient will remain almost constant.




Procedure, Single Phase Flow

• The pressure drop equation must be integrated inorder to calculate the pressure drop as a function offlow rate (or velocity) and pipe diameter.

• It should be combined with a continuity equation andan equation of state to express velocity and density interms of pressure.

• The equation can be integrated numerically bydividing the pipe into small increments and evaluatingthe gas or fluid properties at average pressure andtemperature in the increments. Small increments willimprove the accuracy.


Multiphase Flow in Vertical and Inclined Wells

• The behaviour of gas in tubing strings is markedly

different. The flow of a gas-liquid mixture would bemore complex than for single phase flow.

• Each of the phases, have individual properties such

as density and viscosity which is a function of P&T

and hence position in the well.

• Some types of multiphase flow are:

– Gas-Liquid Mixtures

– Liquid-Liquid Flow

– Gas-Liquid-Liquid

– Gas-Liquid-Solid

– Gas-Liquid-Liquid-Solid


Gas-Liquid Mixtures

• In the production of a

reservoir containing oiland gas in solution, it is

preferable to maintain

the flowing bottom hole

pressure above thebubble point so that

single phase oil flows

through the reservoir

pore space.


13/18

13


Flow Regimes in Vertical 2-Phase Flow, Cont.

• As the liquid moves up the tubing, thepressure drops and gas bubbles

begin to form. This flow regime wheregas bubbles are dispersed in acontinuous liquid medium is knownas bubble flow.

• As the fluid moves further up thetubing, the gas bubbles grow andbecome more numerous. The largerbubbles slip upward at a highervelocity than the smaller ones,because of the buoyancy effect. Single Phase

Liquid Flow

BubbleFlow

Slug or Plug

Flow

Annular

Flow

Mist

Flow



A stage is reached where these large bubblesextend across almost the entire diameter of thetubing. As a result, slugs of oil containing small

bubbles are separated from each other by gaspockets that occupy the entire tubing cross sectionexcept for a film of oil moving relatively slowly alongthe tubing wall. This is Slug or Plug Flow.

Still higher in the tubing, the gas pockets may havegrown and expanded to such as extent that they areable to break through the more viscous oil slug. Gasforms a continuous phase near the centre of thetubing carrying droplets of the oil up with it. Alongthe walls of the tubing there is an upward moving oilfilm. This is Annular Flow. Single Phase

Liquid Flow

BubbleFlow

Slug or Plug

Flow

AnnularFlow

Mist

Flow



Continued decrease in pressure with resultantincrease in gas volume results in a thinner andthinner oil film, until finally the film disappears andthe flow regime becomes a continuous gas phase inwhich oil droplets are carried along with the gas,i.e., Mist Flow.

Not all these flow regimes will occur simultaneouslyin a single tubing string, but frequently 2 or possibly3 may be present.

In addition to flow regimes, the viscosity of oil andgas and their variation with pressure andtemperature, PVT characteristics, flowing bottomhole pressure (BHP), and tubing head pressure(THP) affect the pressure gradient.

Single Phase

Liquid Flow

Slug or Plug

FlowBubbleFlow

Annular

Flow

Mist

Flow



These flow patterns have been observed by anumber of investigators who have conducted

experiments with air-water mixtures in visual flowcolumns.

The conventional manner of depicting the

experimental data from these observations is to

correlate the liquid and gas velocity parameters

against the physical description of the flow patternobserved.

Such presentations of data are referred to as flow

pattern maps. The map is a log-log plot of the

superficial velocities of the gas and liquid phases.


Flow pattern map

for a gas/water

mixture


Practical Application of Multiphase Flow

• Multiphase flow correlations could be used for:

• 1. Predict tubing head pressure (THP) at various rates

• 2. Predict flowing bottom hole pressure (BHP) at various rates

• 3. Determine the PI of wells

• 4. Select correct tubing sizes

• 5. Predict maximum flow rates

• 6. Predict when a well will die and hence time for artificial lift

• 7. Design artificial lift applications

• The important variables are: tubing diameter, flowrate, gasliquid ratio (GLR), viscosity, etc.


14/18

14


Flow Characteristics for Hydrocarbon

Reservoir Fluids Systems

• Dry Gas – Since no liquid phase will be present under

any pressure conditions, the flow will bemonophasic.

• Wet Gas – A wet reservoir gas will have small quantities

of liquid associated with it. As the gas flows tosurface, the pressure will decline to the dewpoint, hence mist of particles in a continuousgas phase.

– Subsequent liquid deposition will emerge asmist.




• Gas Condensate – At low liquid concentration at the dew point,

the liquid phase could be present as a mistand as an “annular film” or subsequently a“slug” at higher concentrations.

– However, as flow continues up the tubing, thegas will expand dramatically and any liquid willtransfer from slug to annular film to mist.

– The above flow phenomena may beparticularly exacerbated if the fluid is aretrograde condensate where liquid dropout inthe tubing may revaporise as it flows up thetubing and the pressure declines.




• Volat ile Oil – A volatile oil is characterised by a high GOR and thus

as it flows to surface it may pass through all of the flowpatterns above, including the single phase regime ifPwf >P BPt .

– The range of patterns developed will depend on the flowvelocity and the GOR.

• Black Oil – A black oil has a very low GOR and accordingly is

unlikely to progress beyond the bubble and slug flowregimes into annular flow.

• Heavy Oil – Heavy oil normally has a very low (or nonexistent) GOR

and as such it will vary from single phase oil to thebubble flow regime.


Flow Patterns

in a Horizontal

Pipe


Fluid Parameters in Multiphase Flow:

Slippage

• If a gas-liquid mixture flows up a tubing string, theeffects of buoyancy on the phases will not be equal.

• The lighter of the phases will rise upwards at anincrementally higher rate compared to the oil.

• The slip velocity, Vs, is defined as the difference invelocities of the two phases, ie, for a gas-oil system.

Vs= Vg- Vo• Particularly in the flow slug regime, the impact of

slippage is to assist in lifting the heavier phase (oil).

• However if slippage is severe it can promotesegregated flow particularly in the low velocitybubble flow regime.



Holdup

• Holdup is a term used to define the volumetric ratio

between two phases which occupy a specifiedvolume or length of pipe.

• The liquid holdup for a gas-liquid mixture flowing in a

pipe is referred to as HL:

• HL therefore has a value between zero and one.

• Similarly, the gas holdup Hg is defined as:


15/18

15



Fluid Velocity

• A difficulty arises as to how to define thevelocity of a specific phase. There are two

options: – The first option is to define velocity based upon

the total cross-sectional area of the pipe.

– The velocity in this case is termed the superficialvelocity.

– A more accurate value for the velocity of eachphase is to correct for the holdup of each phase.


Practical Application of Multiphase Flow

• There are two choices in conducting twophase flow calculations in calculating verticallift performance of a well:

• 1. Computer - recommended if time andlocation permits

• 2. Working curves (pressure traverse orpressure gradient curves) - for initialestimation or when computer programme isnot available.


Multiphase Flow Models• Most of the multiphase flow correlations can

be used with the following general procedure:

• Use will be made of the general equation:

Hold up

Flow regime

accelfrictelevTot )dL

dP()

dL

dP()

dL

dP()

dL

dP( ++=

melev)dL

dP( ρ=

dg2

vf )

dL

dP(

c

mmmfrict

ρ=

dL

)v(

g2)

dL

dP(

2m

c

maccel

∆ρ=


Pressure Transverse or Gradient Curves

A, B, C=DifferentTubing HeadPressures


Pressure Transverse or Gradient Curves• By shifting the curves

downwards, he found that,for a constant GLR,flowrate and tubing size,the curves overlapped

• Then, a single curve couldbe utilised to representflow in the tubing underassumed conditions.

• The impact was in effect toextend the depth of thewell by a length which,would dissipate the tubinghead pressure.

A, B, C=DifferentTubing HeadPressures


Gradient CurvesGilbert was then able to

collect all the curves for aconstant tubing size and

flowrate on one graph,

resulting in a series of

gradient curves which

would accommodate a

variety of GLRs.

He then prepared a seriesof gradient curves at

constant liquid production

rate and tubing size.


16/18

16


Gradient Curves


January 04 Performance of Flowing Wells 131131 January 04 Performance of Flowing Wells 132132

Positive or Fixed Choke

• This normally consists

of two parts:

– A choke which consists

of a machined housinginto which the orifice

capability or "bean" is

installed.

– A "bean" which consistsof a short length 1-6", of

thick walled tube with asmooth, machined bore

of specified size.


Valve Seat with Adjustable Valve Stem• In this design, the orifice

consists of a valve seatinto which a valve stemcan be inserted andretracted, thus adjustingthe orifice size.

• The movement of thevalve stem can either bemanual or automaticusing an hydraulic orelectrohydrauliccontroller.


Rotating Disc Choke


17/18

17


Choke Flow Characteristics

• Chokes normally operate in multiphase

systems. Single phase can occur in dry gas

wells.


Critical Flow through Chokes

R=P2/P1The value of R at the

point where theplateau production

rate is achieved is

termed the

critical pressure ratio

Rc.


Critical Flow through Chokes

• Critical flow behaviour is only exhibited by highlycompressible fluid such as gases and gas/liquidmixtures.

• For gas, which is a highly compressible fluid, thecritical downstream pressure Pc is achieved whenvelocity through the vena contracta equals thesonic velocity

• this means that a disturbance in pressure or flowdownstream of the choke must travel at greater

than the speed of sound to influence upstream flowconditions.

• In general, critical flow conditions will exist whenRc=


18/18


10

20

64


Matching the Inflow and Tubing Performance

Method 1 - Reservoir

and tubing pressure

loss convergence inpredicting bottomhole

flowing pressure





Method 2 -

cumulative pressure

loss from reservoirto separator


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