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Introduction to Nodal Analysis

Advanced Artificial Lift for Production Solutions and

Optimization Engineers

Presented by Jeff Kain

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Objectives

• Understand the components of Inflow performance

• Understand the components of vertical lift performance

• Understand combining inflow and vertical lift performance

• Describe the Pressure versus depth relationship for different lift methods

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Pressure Losses

Pe

_

PrPwfsPwf

Pdr

Pur

Pusv

Pdsv

Pwh

Pdsc Psep

DP1 = Pr - Pwfs = Loss in Porous MediumDP2 = Pwfs - Pwf = Loss across CompletionDP3 = Pur - Pdr = Loss across RestrictionDP4 = Pusv - Pdsv = Loss across Safety ValveDP5 = Pwh - Pdsc = Loss across Surface ChokeDP6 = Pdsc - Psep = Loss in Flowline

DP7 = Pwf - Pwh = Total Loss in TubingDP8 = Pwh - Psep = Total Loss in Flowline

Possible Pressure Losses in Complete Production System

Bottom

HoleRestriction

SafetyValve

Surface

Choke

Separator

Pe

_

PrPwfsPwf

Pdr

Pur

Pusv

Pdsv

Pwh

Pdsc Psep

DP1 = Pr - Pwfs = Loss in Porous MediumDP2 = Pwfs - Pwf = Loss across CompletionDP3 = Pur - Pdr = Loss across RestrictionDP4 = Pusv - Pdsv = Loss across Safety ValveDP5 = Pwh - Pdsc = Loss across Surface ChokeDP6 = Pdsc - Psep = Loss in Flowline

DP7 = Pwf - Pwh = Total Loss in TubingDP8 = Pwh - Psep = Total Loss in Flowline

Possible Pressure Losses in Complete Production System

Bottom

HoleRestriction

SafetyValve

Surface

Choke

Separator

Pe

_

PrPwfsPwf

Pdr

Pur

Pusv

Pdsv

Pwh

Pdsc Psep

DP1 = Pr - Pwfs = Loss in Porous MediumDP2 = Pwfs - Pwf = Loss across CompletionDP3 = Pur - Pdr = Loss across RestrictionDP4 = Pusv - Pdsv = Loss across Safety ValveDP5 = Pwh - Pdsc = Loss across Surface ChokeDP6 = Pdsc - Psep = Loss in Flowline

DP7 = Pwf - Pwh = Total Loss in TubingDP8 = Pwh - Psep = Total Loss in Flowline

Possible Pressure Losses in Complete Production System

Bottom

HoleRestriction

SafetyValve

Surface

Choke

Separator

Pe

_

PrPwfsPwf

Pdr

Pur

Pusv

Pdsv

Pwh

Pdsc Psep

DP1 = Pr - Pwfs = Loss in Porous MediumDP2 = Pwfs - Pwf = Loss across CompletionDP3 = Pur - Pdr = Loss across RestrictionDP4 = Pusv - Pdsv = Loss across Safety ValveDP5 = Pwh - Pdsc = Loss across Surface ChokeDP6 = Pdsc - Psep = Loss in Flowline

DP7 = Pwf - Pwh = Total Loss in TubingDP8 = Pwh - Psep = Total Loss in Flowline

Possible Pressure Losses in Complete Production System

Bottom

HoleRestriction

SafetyValve

Surface

Choke

Separator

Pe

_

PrPwfsPwf

Pdr

Pur

Pusv

Pdsv

Pwh

Pdsc Psep

DP1 = Pr - Pwfs = Loss in Porous MediumDP2 = Pwfs - Pwf = Loss across CompletionDP3 = Pur - Pdr = Loss across RestrictionDP4 = Pusv - Pdsv = Loss across Safety ValveDP5 = Pwh - Pdsc = Loss across Surface ChokeDP6 = Pdsc - Psep = Loss in Flowline

DP7 = Pwf - Pwh = Total Loss in TubingDP8 = Pwh - Psep = Total Loss in Flowline

Possible Pressure Losses in Complete Production System

Bottom

HoleRestriction

SafetyValve

Surface

Choke

Separator

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INJECTION GAS

PRODUCED FLUID

WELL

INFLOW (IPR)

WELL OUTFLOW

RELATIONSHIP

(VLP) or (TPC)

SURFACE PRESSURE

SANDFACE PRESSURE

BHFP

RESERVOIR PRESSURE

BOTTOM HOLE PRESSURE AS A FUNCTION OF FLOWRATEBOTTOM HOLE PRESSURE AS A FUNCTION OF FLOWRATE

PRODUCTION POTENTIAL AS A FUNCTION OF PRODUCTION RATEPRODUCTION POTENTIAL AS A FUNCTION OF PRODUCTION RATE

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Pe

_

PrPwfsPwf

Pdr

Pur

Pusv

Pdsv

Pwh

Pdsc Psep

DP1 = Pr - Pwfs = Loss in Porous MediumDP2 = Pwfs - Pwf = Loss across CompletionDP3 = Pur - Pdr = Loss across RestrictionDP4 = Pusv - Pdsv = Loss across Safety ValveDP5 = Pwh - Pdsc = Loss across Surface ChokeDP6 = Pdsc - Psep = Loss in Flowline

DP7 = Pwf - Pwh = Total Loss in TubingDP8 = Pwh - Psep = Total Loss in Flowline

Possible Pressure Losses in Complete Production System

Bottom

Hole

Restriction

SafetyValve

SurfaceChoke

Separator

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Inflow Performance Curve

0

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0 500 1000 1500 2000 2500 3000 3500 4000 4500

Production rate, STB/D

Flo

win

g b

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Inflow (Reservoir) Curve

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Tubing Curve

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Production rate, STB/D

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Tubing Curve

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0

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Production rate, STB/D

Flo

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Inflow (Reservoir) Curve

Tubing Curve

System Graph

2111 STB/D

1957.1 psi

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INFLOW PERFORMANCE

RADIAL FLOW

Pwf

Pe

dr

rre

Pr

Pe = boundary pressurePwf = well flowing pressure

Pr = pressure at r

re = drainage radius

rw = wellbore radius

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INFLOW PERFORMANCE

SEMI (PSEUDO) STEADY STATE INFLOW (using average reservoir pressure)

kh(Pav - Pwf)qo = -----------------------------------

141.2 µµµµ oBo.[ln(re/rw) - 3/4]

where:P = pressure (psi)k = permeability (md)

h = height (ft)

re = drainage radius (ft)

rw = wellbore radius (ft)

µµµµO = fluid viscosity (cP)Bo = formation volume factor (bbls/stb)

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IDEAL FLOW ASSUMPTIONSIDEAL FLOW ASSUMPTIONS• Ideal well

• Purely radial flow

• Infinite reservoir

• Uniform thickness

• Stabilized flow

• Single phase

• Above bubble point

• Homogeneous & isotropic reservoir

• Perforations penetrate throughout reservoir

• Reservoir shape

• Proximity of wellbore

• Wellbore clean / uncased

• No skin

• Darcy’s law

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NON IDEAL FLOW

• Departures from Darcy’s law

• Effects at boundaries

• Position of well

• Non homogeneous reservoir

• Perforation positions

• High velocities

• Fluid type / high GOR

• Transient behavior

• Relative permeability effects - oil/water/gas near the wellbore

• Depletion if reservoir

• Flow restrictions (skin)

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INFLOW PERFORMANCE

SKIN

• Ideal flow conditions rarely exist

• Restricted flow into the wellbore

• The total skin factor may be calculated from well test

data

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INFLOW PERFORMANCE

PRINCIPLE ORIGINS OF SKIN

• Formation damage (+ve)

• Perforations (+ve)

• Partial completions/limited entry (+ve)• Gravel packs (+ve)

• Non-Darcy flow (+ve)• Multiphase flow (+ve)

• Natural fractures (-ve)

• Hydraulic fractures (-ve)• Deviated/horizontal wells (-ve)

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INFLOW PERFORMANCE

PRODUCTIVITY INDEX

The relationship between well inflow rate and pressuredrawdown can be expressed in the form of a Productivity Index, denoted ‘PI’ or ‘J’, where:

qq = J(Pws - Pwf) or J = ------------------

Pws - Pwf

kh(Pav - Pwf)

qo = -----------------------------------

141.2 µµµµ oBo.[ln(re/rw) - 3/4]

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WELL & RESERVOIR INFLOW PERFORMANCE( Successful design depends upon prediction of flow rate)

FACTORS AFFECTING PI

1. Phase behaviour•Bubble point pressure•Dew point pressure

2. Relative permeability behaviour•Ratio of effective permeability to a particular fluid (oil, gas or water) to the absolute permeability of the rock

3. Oil viscosity•Viscosity decreases with pressure decrease to Pb•Viscosity increases as gas comes out of solution

4. Oil formation volume factor (bo)

•As pressure is decreased the liquid will expand•As gas comes out of solution oil will shrink

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AS RATE INCREASES IS NO LONGER STRAIGHT LINE• Increased gas sat. Near wellbore - rel. Perm. Effects• Laminar > turbulent flow• Exceeds critical flow of sandface

WELL & RESERVOIR INFLOW PERFORMANCE( Successful design depends upon prediction of flow rate)

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WELL & RESERVOIR INFLOW PERFORMANCE( Successful design depends upon prediction of flow rate)

INFLOW PERFORMANCE RELATIONSHIP

• Vogel• Back pressure/Fetkovich• Lit (Jones, Blount and Glaze)• Normalized pseudo pressure

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WELL & RESERVOIR INFLOW PERFORMANCE( Successful design depends upon prediction of flow rate)

VOGEL

Dimensionless reference curve based on the following equation:

Q/Qmax = 1 - 0.2(Pwf/Pws) - 0.8(Pwf/Pws)2

where: Q = the liquid production rate, stb/dQmax = the maximum liquid rate for 100% drawdownPwf = bottom hole flowing pressure, psiPws = the reservoir pressure, psi

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WELL & RESERVOIR INFLOW PERFORMANCE( Successful design depends upon prediction of flow rate)

SUMMARY OF FACTORS AFFECTING PREDICTIONOF WELL PRODUCTION

• Presence of three phase flow

• Nature of drive mechanisms

• Physical nature of reservoir (non homogeneous)

• Availability of stabilized flow

• Changes over time & drawdown

• Increased gas solution near wellbore

• Stabilised flow near wellbore

• Flow regime near wellbore

• Critical flow at wellbore

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MULTIPHASE FLOWOUTFLOW PERFORMANCE

MOVEMENT OF A MIXTURE OF FREE GASES AND LIQUIDS

Vertical flowing gradients

Horizontal flowing gradients

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FACTORS EFFECTING VLP

� VLP is a function of physical properties not inflow• Tubing ID

• Wall roughness• Inclination• Liquid / gas density• Liquid / gas viscosity• Liquid / gas velocity• Well depth / line lengths• Surface pressure• Water cut• GOR• Liquid surface tension• Flowrate

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PRESSURE LOSS IN WELLBORE

‘Complicated expression’

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• System described by a energy balance expression• Mass energy per unit mass in = energy out • (+ - exchange with surroundings)• For wellbore- pressure Calc. for length of pipe• Integrated each section• Pressure can be divided into three terms

ZZ

δδδδP/δδδδZ

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PRESSURE LOSS IN WELLBORE

δδδδP/δδδδZtotal = g/gcρρρρcosθθθθ + fρρρρv2/2gcd + ρρρρv/gc[δδδδP/δδδδZ]

TOTAL

PRESSURE

DIFFERENCE

GRAVITY

TERM

ACCELERATION

TERM

FRICTION

TERM

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• Correcting weight of fluid

• Dominant term

• Single phase simple

• Multiphase complex

g/gcρρρρcosθθθθ

GRAVITY

TERM

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Pressure loss due to gravity

• Based on fluid densities at element for

conditions Pelement, Telement

• Phase volumes = % of pipe occupied by

fluid * density of fluid

• Assumes liquid and gas phases at same

velocity

• This is the no slip case that will produce

minimum delta P due to gravity

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SLIP• The gas phase moves at a faster velocity than

the liquid phase due to buoyancy forces

• Consequence is a change in the areas of each phase in an element

• The slip corrected liquid area is termed LIQUID HOLDUP

• Correction from phase volumes to holdup volumes through multi-phase correlations

• Complex determination characterised in flow regime maps

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Liquid Holdup

• Consider an element for Pelement , Telement

LIQUIDLIQUID GASGAS

LIQUIDLIQUID GASGAS

% Liquid% Liquid % Gas % Gas

Liquid Liquid HoldupHoldup 1 1 -- Liquid Liquid HoldupHoldup

Slip correctedSlip corrected

Mixture density = L Mixture density = L densitydensity * % L + G * % L + G densitydensity * %G* %G

Mixture density = L Mixture density = L densitydensity * H* HLL + G + G densitydensity * (1* (1--HHLL))

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FLOW REGIMES

• Based on observations

• Different flow patterns

– Proportion of phases

– Flow velocity

– Viscosities

– Interfacial tension

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FLOW REGIMESFLOW REGIMES

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• Increases with rate

• Proportional to velocity

• Proportional to relative roughness

• Laminar vs turbulent flow

• Effective viscosity

• Effective mixture density

• Sensitive to gas volumes

fρρρρv2/2gcd

FRICTION

TERM

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• Expansion of fluid as pressure decreases

• Smallest term

• Often ignored

• Need to account in high rate

ρρρρv/gc[δδδδP/δδδδZ]

ACCELERATION

TERM

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Proportion of terms in oil well close to

sandface (no significant GLR)

GRAVITY

FRICTION

ACCELERATION

Proportion of terms in oil well significant

GLR close to surface

GRAVITY

FRICTION

ACCELERATION

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• Fluid density in every term• Errors would be cumulative• PVT important

PRESSURE LOSS IN WELLBORE

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CORRELATIONS• Babson (1934)

• Gilbert (1939 / 1952)

• Poettmann & Carpenter (1952)

• Duns & Ros

• Hagedorn & Brown

• Orkiszewski

• Fancher & Brown

• Beggs &Brill

• Duckler Flannigan

• Gray

• Mechanistic

• Proprietary

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0 1000 2000 3000 4000 5000

Pressure, psig

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t

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5200

0 1000 2000 3000

Rate, bbls/d

FB

HP

, p

sig

INFLOW AND OUTFLOW

PERFORMANCE

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Effect of Skin on IPR

Outflow

Flowrate

Pre

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5 0 -1 -3

SKIN

Inflow(IPR)

qo

αααα 1/ ln re +S

rw

Note : Log effect

10

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Effect of Pressure Depletion on IPR

Outflow

Flowrate

Pre

ssu

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t N

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eReservoir with no pressure support

Inflow

Decreasing reservoir pressureDecreasing reservoir pressure

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Effect of Tubing Size on Outflow

Inflow(IPR)

Outflow

Flowrate (stb/d)

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2 3/8”

2 7/8”4 1/2”

3 1/2”

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Pressure versus Depth for

various Artificial Lift Methods

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Natural Flow Pressure vs Depth

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Gas Lift Pressure vs Depth

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Pump Pressure vs Depth