Performance of Flowing Wells

8/12/2019 Performance of Flowing Wells

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January 04 Performance of Flowing Wells 11

Production Technology

Performance of Flowing Wells

Professor Bahman TohidiInstitute of Petroleum EngineeringHeriot-Watt UniversityEdinburgh EH14 4ASScotlandTel: +44 (0)131 451 3672Fax: +44 (0)131 451 3127Email: [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 various

concepts 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 export

pipeline to storageJanuary 04 Performance of Flowing Wells 44

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 maximise

oil and gas recovery.


Production Performance Production performance involves

matching up the following threeaspects: Inflow performance of formation fluid flow

from formation to the wellbore. Vertical lift performance as the fluids flow

up the tubing to surface. Choke or bean performance as the fluids

flow through the restriction at surface.


Fluid Flow Through Porous Media The nature of the fluid flow Time taken for the pressure change in the

reservoir 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 Darcys 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 FlowPatterns

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 zone4. Difference in production rate from well to

well5. Many wells do not fully pene trate the pay

zone, or not fully perforated.


Well Inflow Performance

Q

L

A

P 1 P 2

AL

PPQ 21

=

AL

PPKQ 21

Darcys Law

LPK

LPPK

AQ

U 21

=

==


Darcys LawDefinitionOne Darcy is defined as the permeability which willpermit a fluid of one centipoise viscosity to flow at alinear velocity of one centimeter per second for apressure gradient of one atmosphere per centimeter.

Assumptions Fo r Use of Darcy s LawSteady flowLaminar flowRock 100% saturated with one fluidFluid does not react with the rockRock is homogeneous and isotropicFluid is incompressible


Radial Flow for Incompressible Fluids Reservoir is horizontal and of

constant thickness h. Constant rock properties 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 . The well is vertical and completed

open hole


Characteristics of the Flow Regimes Steady-State; the pressure and the rate distribution in

the 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 st eady st at e: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 anIncompressible Fluid

r dr

Kh2q

dP

dr dPK

rh2q

Aq

U

rh2 A

r

r r

=

=

==

=

Can be integrated between the limits of:inner boundary i.e. the wellbore sand face: r = r w P = P wouter boundary i.e. the drainage radius: r = r e P = P e



[ ] )r r

ln(Kh2

qPP

r dr

Kh2q

r dr

Kh2q

dP

w

er we

r

r

r r

r

r P

P

e

w

e

w

e

w

=

=

=

[P e - P w ] is the total pressure drop across the reservoir andis denoted the drawdown .q r is the fluid flowrate at reservoir conditions.If the production rate measured at standard conditions atsurface i.e. q s then q s .B = q r

[ ] )r r

ln(Kh2Bq

PPw

eswe

=



If the production rate measured at standard conditions atsurface i.e. q s then q s .B = q r

[ ] )r r

ln(Kh2Bq

PPw

eswe

=

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

[ ] )r r

ln(Kh

Bq10x082.7

1PPw

es3we

=



Highly supportive reservoir pressure maintenancewith water injection or gas reinjection.Reservoir production associated with a substantialexpanding gas cap. [ ] )

r r

ln(Kh

Bq10x082.7

1PP

w

es3we

=


4/18


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Steady State Radial Flow for a Gas Approximate solution - average pressure or P 2

approach.

2wf Pwf P

FlowOpen AbsoluteQ AOF =


Semi-Steady State Flow for a Gas System

Using the bounded reservoir assumption and thedefinition of isothermal compressibility:


Multiphase Flow within the Reservoir

Only single phase flow, so far. Most oil reservoirs will produce at a bottom hole

pressure below the bubble point, either:- Initially where the reservoir is saturated Or after production where the pressure in the pore space

declines below the bubble point, resulting in 2-phase flow

Saturations in pore space S o+S w+S g=1.0

Critical saturation S c Connate water S wc Residual saturation S or Absolute permeability K Relative permeability k ro=ko/K


Multiphase Flow within the Reservoir


2-Phase Flow, Vogels Equation

2

r

wf

r

wf

maxo

o )PP

(8.0)PP

(2.01q

q =

A simplified solution was offered by Vogel. He simulated the PVTproperties and cumulative production from different wells oncomputer to produce many IPR curves. These were then normalisedfor pressure and producing rate. The curves produced representmany different depletion drive reservoir. A single curve can be fittedto the data with the following equation.

This equation has been found to be a good representation of manyreservoirs 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%.


Vogels Equation, Example-1

b/d 211)2400800

(8.0)2400800

(2.01250)(8.0)(2.01

psi800PFor

b/d 250)

24001800

(8.0)24001800

(2.01

100

)(8.0)(2.01

psi1800P

b/d 100q

psi2400P

:datafollowinggiven the psi,800Pforq and q Find

22max

22max

wf

o

wf oomax

===

=

=

=

=

===

=

r

wf

r

wf oo

r

wf

r

wf

oo

r

P

P

P

Pqq

P

P

P

Pq

q


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Vogels Equation, Example, Cont.

If other values of P wf are chosen, sufficientqos can be generatedto plot the curve, e.g.:

P wf qo800 2111200 1751600 1282000 69

IPR

0

500

1000

1500

2000

2500

3000

0 100 200 300q o

P w

f


Vogels Equation, Combined Single Phase Liquid and 2-Phase

In this case there is a singlephase liquid which exists

above the bubble point. Belowthe bubble point the systembecomes 2-phase.

The figure opposite shows theIPR, which is a combinedlinear-Vogel plot (i.e., straightline above Pb and Vogelbelow Pb with Pb substitutedfor Pr).

P b

P r

qb qmaxq

P wf

Straight line above P b

Vogel below P b


Vogels Equation, Example-2

psia1000 b. psia2500 a. :of Pforq iii)

P belowIPR Vogelassuming,q )

q i):Find

)43

(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 oo

o

r

=

=========


Example-2, Solution

=

=+

=

=

2max

b

3

3

)(8.0)(2.01

P beyond Vogelusing ii)

b/d 2010)0

4

3

4.0

2000(ln2.168.0

)20003000(60301008.7

)43

(ln

)(1008.7

:used isequationinflowradialfore there

point, bubbletheabovePIgivennoisThere i)

r

wf

r

wf oo

w

eoo

wfsr oo

P

P

P

Pqq

r r

B

PPhk q


Example-2, Solution

b/d/psi01.220003000

2010PatPItherefore

8.1PPI)Vogel(q

P8.1q

PP6.1

P2.0q

dPqd-PI PPatand

P

P6.1P

2.0q

dPqd-

P

P6.1P

2.0q

dPqd

PI.thegivesitateddifferentiis equationsVogel'if IPR,theof slopetheisPIthethatmemberingRe

b

bmaxo

bmaxo2

b

b

bmaxo

wf

obwf

2r

wf

r maxo

wf

o2r

wf

r maxo

wf

o

=

=

=

=+===

+==


Example-2, Solution

b/d357315632010qqq

b/d1563)20001000

0.8()20001000

(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

8.1P

PIq

o(Vogel)bo(total)

2)Vogelmax(o(Vogel)

bwf

wf r

bwf

)vogelmax(b)totalmax(

b)vogelmax(o

=+=+=

==

=

=+=+=

===


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Vogels Equation, Problems-1&2

IPRthePlotb/d/psi2PI

psi3000Ppsi4200P

psi.2500Pfor qand,q,qfinddata,followingtheUsing2-Problem

_________ __________ __________ __________psig1000P b/d150qpsig1600P psig1600P

:datafollowingthefor IPRplotandqFind1-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 pressuredrop 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 of

production to the pressure draw down at themid-point of the production interval

rateflowoilQ presure

presurereservoiraverage

o ==

=

=

flowingP

PPP

QPI

wf

Rwf 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 (P R) 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 intothe well

The flowing bottom hole pressure (P wf ) 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 rates2- decrease in relative permeability due to thepresence of free gas caused by the drop inpressure at the well bore3- 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 P 2

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

Parameters, assuming nochange in the fluid andreservoir properties, shouldremain constant. Hence, Jshould 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.flowpointstabilisedonefromcalculatedisCflow).(turbulent0.5andflow)state-steady(laminar 1betweenvariesn

paper.log-logaonQvs)P(Pof plottheof slopetheisn1

C)Qlog(n1

)Clog(n1

)Qlog(n1

)Plog(P

)Pnlog(Plog(C)log(Q)

constantsare n"" andC"" pressurefacesandflowingP pressurereservoir in-shutP rateflowvolumetricQ

)PC(PQ

2wf

2wi

'2wf

2wi

2wf

2wi

wf

wi

n2wf

2wi

+==

+=

=== =


Gas Wells: Potential CurvePotential Curve

1

10

100

1000

10000

1 10 100 1000 10000q

P

w i ^ 2 - P w

f ^ 2

Slope=1/n

Zero sand face pressure

AbsoluteOpenFlow (AOF)

C


Potential Curve: PracticalDetermination

The potential curve is obtained either through a backpressure test or an isochornal flow test.

A back pressure test consists of succession of fourincreasing flow rates. The pressures are measured atthe end of a flow period at a given rate, after which therate is changed immediately to a new value withoutclosing the well.

Back pressure tests are used for formations with goodpermeability, where the measured pressure at the end ofeach flow period reaches a stabilised value.


Potential Curve: Back Pressure Test

q1

q2q3

q4q

t

t

P wf P wf1

P wf2P wf3

P wf4


Potential Curve: PracticalDetermination

In low permeability formations where stabilised flowconditions would be attained in a prohibitive time,isochronal tests give better results.

An isochronal test consists of flowing the well at fourflow rates for period of equal duration. After each periodthe well is shut-in for sufficiently long time in order toreach static conditions with a satisfactory approximation.

An additional point is used from a run with an extendedflow period approximating stabilised conditions. A linedrawn through this point, with correct n represents thetrue stabilised potential curve.


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Potential Curve: Isochronal Test

q1q2

q3q

t

t

P wf

q4


Example 1 From a well test, it has been determined that

the performance constant, C of the well is0.0037 (for q sc in MMSCF/D) and n=0.93.Determine the flow rate when P r =3000 psiaand P wf =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

2r 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 22006 1782 3.4 22006 1647 4.8 22006 1511 5.4 2200

Analyse the following isochronal well test data

Afterwards, the well continued to produced at 6 mmscf/d andreached a stabilised flowing sandface pressure of 1180 psia.

Plot the deliverability curve and determine flow index and theperformance constant. Determine AOF


Example 2: Isochronal Test-Solution

P wf(psia)

q sc (MMSCF/D)

P wf 2 (psia) 2

Pr 2-Pwf 2 (psia) 2

2200 0 4.84 x 10 6 01892 2.8 3.58 x 10 6 1.26 x 10 6 1782 3.4 3.18 x 10 6 1.66 x 10 6 1647 4.8 2.71 x 10 6 2.13 x 10 6 1511 5.4 2.28 x 10 6 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 (P r 2-P wf 2) v q sc on log-log paper.


Example 2: Isochronal Test- Solution

0.1n0.1)102.2log()108.8log()100.1log()100.4log(

n1

66

66

===

MMSCF/4.8 AOF1084.4

0)2200(PP6

22wf

2r

==

=

6

0.16

n2wf

2r

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 forSingle Phase Flow

IPR were derived on theassumption that radialflow occurred

The formation wasassumed to be isotropicand homogeneous.

However the basicprocess of drilling andcompleting a well willcause changes in thecondition of the physicalflow process.


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These perturbations to radial flow may comprise thefollowing:

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

A large number of wells are cased off and thenperforated.

Often, only a small section of the reservoir is to beperforated (fluid convergence and verticalpermeability).



Perturbations from radial flow theory will generate anextra pressure drop component which will affect thethe actual bottomhole flowing pressure, P wf .

where P wf actual is the actual bottom hole flowingpressure and P wf ideal is the idealised bottomholeflowing pressure which assumes true radial flow.

And P SKIN is the additional pressure loss associatedwith the perturbation(s). It should be noted that mostof the perturbations will cause the P SKIN to bepositive and accordingly



It should be noted that most of the perturbations willcause the P SKIN to be positive and accordingly

The pressure drop associated with these nearwellbore phenomena is termed a SKIN and is definedas a dimensionless skin factor, S:

For fractures, acid stimulations and for deepperforations, there will be less resistance to flow andhence


Skin Factor Pressure drop associated with these near wellbore

phenomena is termed a SKIN and is generallydefined as a dimensionless skin factor, S:


Skin Factor The actual drawdown across the reservoir when a

skin exists, P actual , can be related to the idealdrawdown predicted from radial flow theory P idealand the skin pressure drop P SKIN by:

In field units


Skin Factor We can simply add the P SKIN to the radial flow

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

For compressible fluids


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

proportion of the total pressure loss. However itscalculation is complicated by the number of phaseswhich may exist in the tubing.

It is possible to derive a mathematical expressionwhich describes fluid flow in a pipe by applying theprinciple of conservation of energy.

The principle of the conservation of energy equatesthe 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 casefor laminar flow, but the proportionality will be morecomplex and a function of the relative roughness.

It can be seen thatthe pressuregradient dP/dL is afunction 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 FlowEffect 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


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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 oilwith an API gravity of, say, 35 would be morecompressible than a heavier crude oil with an APIgravity of 20 API. A typical oil compressibility (C o )would be 8 - 12 x 10 -6 vol/vol/ psi.

Water is even less compressible and is frequentlyconsidered to be incompressible (C w = 6 - 8x10 -6vol/vol/psi).



For the flow up tubing of a single phaseliquid, the following will occur: As the liquid flows upwards, the density will

decline by the order of 0.5 - 1.0% for every 1000psi drop in pressure. The effect on hydrostaticpressure gradient is minimal.

As pressure declines, the viscosity will decreaseslightly. Hence, for oil or water, the impact of f lowon the physical properties of the fluid will benegligible and hence the increase in frictionalgradient 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 markedlydifferent. The flow of a gas-liquid mixture would bemore complex than for single phase flow.

Each of the phases, have individual properties suchas density and viscosity which is a function of P&Tand 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 ispreferable to maintainthe flowing bottom holepressure above thebubble point so thatsingle phase oil flowsthrough the reservoirpore space.


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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 PlugFlow

AnnularFlow

MistFlow



A stage is reached where these large bubblesextend across almost the entire diameter of t hetubing. As a result, slugs of oil containing smallbubbles 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 PlugFlow

AnnularFlow

MistFlow



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 PhaseLiquid Flow

Slug or Plug

FlowBubbleFlow

AnnularFlow

MistFlow



These flow patterns have been observed by anumber of investigators who have conductedexperiments with air-water mixtures in visual flowcolumns.The conventional manner of depicting theexperimental data from these observations is tocorrelate the liquid and gas velocity parameters

against the physical description of the flow patternobserved.Such presentations of data are referred to as flowpattern maps. The map is a log-log plot of thesuperficial velocities of the gas and liquid phases.


Flow pattern mapfor a gas/watermixture


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.


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Flow Characteristics for HydrocarbonReservoir 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 aslug 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 ifP wf >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 Patternsin 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, V s , 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 promote

segregated flow particularly in the low velocitybubble flow regime.


Fluid Parameters in Multiphase Flow:Holdup

Holdup is a term used to define the volumetric ratiobetween two phases which occupy a specifiedvolume or length of pipe.

The liquid holdup for a gas-liquid mixture flowing in apipe is referred to as H L:

HL therefore has a value between zero and one. Similarly, the gas holdup H g is defined as:


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15


Fluid Parameters in Multiphase Flow:Fluid Velocity

A difficulty arises as to how to define thevelocity of a specific phase. There are twooptions: 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 superficial

velocity.

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 )dLdP

()dLdP

()dLdP

()dLdP

( ++=

melev)dLdP

( =

dg2vf )

dLdP(

c

mmmfrict

=

dL)v(

g2)

dLdP

(2m

c

maccel

=


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 tocollect all the curves for aconstant tubing size andflowrate on one graph,resulting in a series ofgradient curves whichwould accommodate avariety of GLRs.

He then prepared a seriesof gradient curves atconstant liquid productionrate and tubing size.


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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 orificecapability or "bean" isinstalled.

A "bean" which consistsof a short length 1-6", ofthick walled tube with asmooth, machined boreof 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


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Choke Flow Characteristics Chokes normally operate in multiphase

systems. Single phase can occur in dry gas

wells.


Critical Flow through Chokes

R=P 2/P 1The value of R at the

point where theplateau productionrate is achieved istermed thecritical pressure ratioR c.


Critical Flow through Chokes Critical flow behaviour is only exhibited by highly

compressible fluid such as gases and gas/liquidmixtures.

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

this means that a disturbance in pressure or flowdownstream of the choke must t ravel at greaterthan the speed of sound to influence upstream flowconditions.

In general, critical flow conditions will exist whenR c=


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Documents

Performance of Flowing Wells