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: B.Tohidi@hw.ac.uk
January 04 Performance of Flowing Wells 22
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
January 04 Performance of Flowing Wells 33
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
January 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 maximiseoil and gas recovery.
January 04 Performance of Flowing Wells 55
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.
January 04 Performance of Flowing Wells 77
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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January 04 Performance of Flowing Wells 88
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.
January 04 Performance of Flowing Wells 99
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.
January 04 Performance of Flowing Wells 1010
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
==
January 04 Performance of Flowing Wells 1212
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
January 04 Performance of Flowing Wells 1313
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
January 04 Performance of Flowing Wells 1414
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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January 04 Performance of Flowing Wells 1515
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.
January 04 Performance of Flowing Wells 1616
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.
January 04 Performance of Flowing Wells 1818
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
January 04 Performance of Flowing Wells 1919
Steady State - Radial Flow of an
Incompressible Fluid
[ ] )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=−
January 04 Performance of Flowing Wells 2020
Steady State - Radial Flow of an
Incompressible Fluid
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=− −
January 04 Performance of Flowing Wells 2121
Steady State - Radial Flow of an
Incompressible Fluid
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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January 04 Performance of Flowing Wells 2222
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.
January 04 Performance of Flowing Wells 2323
Semi Steady State Radial Flow of a
Slightly Compressible Fluid
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
∂∂
−=
January 04 Performance of Flowing Wells 2525
Semi Steady State Radial Flow of a
Slightly Compressible Fluid
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 :
January 04 Performance of Flowing Wells 2626
Semi Steady State Radial Flow of a
Slightly Compressible Fluid
•Pe has no physical significance.
• Volumetrically averaged reservoir pressure should be
used.q=constant
Pe
Pwf
r w r er
P
h Pave
January 04 Performance of Flowing Wells 2727
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
January 04 Performance of Flowing Wells 3030
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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January 04 Performance of Flowing Wells 3131
Steady State Radial Flow for a Gas
• Approximate solution - average pressure or P2
approach.
2
wf Pwf P
FlowOpen AbsoluteQ AOF =
January 04 Performance of Flowing Wells 3333
Semi-Steady State Flow for a Gas System
• Using the bounded reservoir assumption and the
definition of isothermal compressibility:
January 04 Performance of Flowing Wells 3434
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
January 04 Performance of Flowing Wells 3535
Multiphase Flow within the Reservoir
January 04 Performance of Flowing Wells 3636
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%.
January 04 Performance of Flowing Wells 3737
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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January 04 Performance of Flowing Wells 3838
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
January 04 Performance of Flowing Wells 3939
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
January 04 Performance of Flowing Wells 4040
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
January 04 Performance of Flowing Wells 4141
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
January 04 Performance of Flowing Wells 4242
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
=−
=
×=
⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡+===
⎥⎦
⎤⎢⎣
⎡+=⇒⎥
⎦
⎤⎢⎣
⎡−
−=
January 04 Performance of Flowing Wells 4343
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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January 04 Performance of Flowing Wells 4444
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
=
=
=
=
====
January 04 Performance of Flowing Wells 4545
Two Phase Flow: Effect of GOR
January 04 Performance of Flowing Wells 4747
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:
January 04 Performance of Flowing Wells 4949
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.
January 04 Performance of Flowing Wells 5050
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
January 04 Performance of Flowing Wells 5151
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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January 04 Performance of Flowing Wells 5353
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
January 04 Performance of Flowing Wells 5454
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
−
+=−=−
−+=
=
==−=
January 04 Performance of Flowing Wells 5555
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
January 04 Performance of Flowing Wells 5656
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.
January 04 Performance of Flowing Wells 5757
Potential Curve: Back Pressure Test
q1
q2
q3
q4
q
t
t
Pwf Pwf1
Pwf2
Pwf3
Pwf4
January 04 Performance of Flowing Wells 5858
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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January 04 Performance of Flowing Wells 5959
Potential Curve: Isochronal Test
q1
q2
q3q
t
t
Pwf
q4
January 04 Performance of Flowing Wells 6060
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
=−=
=−=−=
January 04 Performance of Flowing Wells 6161
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
January 04 Performance of Flowing Wells 6262
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.
January 04 Performance of Flowing Wells 6363
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
)
January 04 Performance of Flowing Wells 6464
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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January 04 Performance of Flowing Wells 6565
Perturbations from Radial Flow Theory for
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).
January 04 Performance of Flowing Wells 6767
Perturbations from Radial Flow Theory for
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
January 04 Performance of Flowing Wells 6868
Perturbations from Radial Flow Theory for
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
January 04 Performance of Flowing Wells 6969
Skin Factor • Pressure drop associated with these near wellbore
phenomena is termed a SKIN and is generally
defined as a dimensionless skin factor, S:
January 04 Performance of Flowing Wells 7070
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
January 04 Performance of Flowing Wells 7272
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
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January 04 Performance of Flowing Wells 7373
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.
January 04 Performance of Flowing Wells 8686
January 04 Performance of Flowing Wells 8787
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:
January 04 Performance of Flowing Wells 8888
Single Phase Turbulent Flow
• In flowing to surface,the fluid will:
• lose pressure
• Expansion for highcompressibility fluids
• lose heat to the
surroundingformations
January 04 Performance of Flowing Wells 8989
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
January 04 Performance of Flowing Wells 9090
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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January 04 Performance of Flowing Wells 9292
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).
January 04 Performance of Flowing Wells 9393
Single Phase Liquid Flow - Oil or Water
• 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.
January 04 Performance of Flowing Wells 9494
Single Phase Liquid Flow - Oil or Water
January 04 Performance of Flowing Wells 9696
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.
January 04 Performance of Flowing Wells 9797
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
January 04 Performance of Flowing Wells 9898
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.
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January 04 Performance of Flowing Wells 101101
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
January 04 Performance of Flowing Wells 102102
Flow Regimes in Vertical 2-Phase Flow, Cont.
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
January 04 Performance of Flowing Wells 103103
Flow Regimes in Vertical 2-Phase Flow, Cont.
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
January 04 Performance of Flowing Wells 104104
Flow Regimes in Vertical 2-Phase Flow, Cont.
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.
January 04 Performance of Flowing Wells 105105
Flow pattern map
for a gas/water
mixture
January 04 Performance of Flowing Wells 106106
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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January 04 Performance of Flowing Wells 109109
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.
January 04 Performance of Flowing Wells 110110
Flow Characteristics for Hydrocarbon
Reservoir Fluids Systems
• 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.
January 04 Performance of Flowing Wells 111111
Flow Characteristics for Hydrocarbon
Reservoir Fluids Systems
• 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.
January 04 Performance of Flowing Wells 115115
Flow Patterns
in a Horizontal
Pipe
January 04 Performance of Flowing Wells 118118
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.
January 04 Performance of Flowing Wells 119119
Fluid Parameters in Multiphase Flow:
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:
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January 04 Performance of Flowing Wells 120120
Fluid Parameters in Multiphase Flow:
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.
January 04 Performance of Flowing Wells 123123
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.
January 04 Performance of Flowing Wells 125125
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=
January 04 Performance of Flowing Wells 126126
Pressure Transverse or Gradient Curves
A, B, C=DifferentTubing HeadPressures
January 04 Performance of Flowing Wells 127127
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
January 04 Performance of Flowing Wells 128128
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.
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January 04 Performance of Flowing Wells 129129
Gradient Curves
January 04 Performance of Flowing Wells 130130
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.
January 04 Performance of Flowing Wells 133133
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.
January 04 Performance of Flowing Wells 134134
Rotating Disc Choke
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January 04 Performance of Flowing Wells 135135
Choke Flow Characteristics
• Chokes normally operate in multiphase
systems. Single phase can occur in dry gas
wells.
January 04 Performance of Flowing Wells 136136
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.
January 04 Performance of Flowing Wells 137137
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=
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January 04 Performance of Flowing Wells 141141
10
20
64
January 04 Performance of Flowing Wells 142142
Matching the Inflow and Tubing Performance
Method 1 - Reservoir
and tubing pressure
loss convergence inpredicting bottomhole
flowing pressure
January 04 Performance of Flowing Wells 143143
Matching the Inflow and Tubing Performance
January 04 Performance of Flowing Wells 144144
Matching the Inflow and Tubing Performance
Method 2 -
cumulative pressure
loss from reservoirto separator
January 04 Performance of Flowing Wells 145145
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