1 - Introduction to Nodal Analysis

Advanced Artificial Lift for Production Solutions and Optimization Engineers Presented by Jeff Kain

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Introduction to Nodal Analysis

Objectives •

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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

Pressure Losses Pwh

Separator

Surface Choke

Psep

Pdsc Pdsv Pusv

Bottom Hole Restriction

Pdr Pur

Pwf

DP1 = Pr - Pwfs DP2 = Pwfs - Pwf DP3 = Pur - Pdr DP4 = Pusv - Pdsv DP5 = Pwh - Pdsc DP6 = Pdsc - Psep

= Loss in Porous Medium = Loss across Completion = Loss across Restriction = Loss across Safety Valve = Loss across Surface Choke = Loss in Flowline

DP7 = Pwf - Pwh = Total Loss in Tubing DP8 = Pwh - Psep = Total Loss in Flowline

Pwfs

_ Pr

Pe

Possible Pressure Losses in Complete Production System

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Safety Valve

SURFACE PRESSURE

PRODUCED FLUID

INJECTION GAS

BOTTOM HOLE PRESSURE AS A FUNCTION OF FLOWRATE

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WELL OUTFLOW RELATIONSHIP (VLP) or (TPC)

PRODUCTION POTENTIAL AS A FUNCTION OF PRODUCTION RATE

RESERVOIR PRESSURE

SANDFACE PRESSURE BHFP

WELL INFLOW (IPR)

Pwh

Separator

Surface Choke

Psep

Pdsc Pdsv Pusv

Bottom Hole Restriction

Pdr Pur

Pwf

DP1 = Pr - Pwfs DP2 = Pwfs - Pwf DP3 = Pur - Pdr DP4 = Pusv - Pdsv DP5 = Pwh - Pdsc DP6 = Pdsc - Psep

= Loss in Porous Medium = Loss across Completion = Loss across Restriction = Loss across Safety Valve = Loss across Surface Choke = Loss in Flowline

DP7 = Pwf - Pwh = Total Loss in Tubing DP8 = Pwh - Psep = Total Loss in Flowline

Pwfs

_ Pr

Pe

Possible Pressure Losses in Complete Production System

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Safety Valve

Inflow Performance Curve 3500

3000

2500

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Flowing bottomhole pressure, psi

Inflow (Reservoir) Curve

2000

1500

1000

500

0 0

500

1000

1500

2000

2500

3000

Production rate, STB/D

3500

4000

4500

Tubing Curve 3500

Tubing Curve

2500

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Flowing bottomhole pressure, psi

3000

2000

1500

1000

500

0 0

500

1000

1500

2000

2500

3000

Production rate, STB/D

3500

4000

4500

System Graph 3500

Inflow (Reservoir) Curve Tubing Curve

2500

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Flowing bottomhole pressure, psi

3000

1957.1 psi 2000

1500

1000

500

2111 STB/D

0 0

500

1000

1500

2000

2500

3000

Production rate, STB/D

3500

4000

4500

INFLOW PERFORMANCE RADIAL FLOW

r re Pwf Pr Pe

Pe = boundary pressure Pwf = well flowing pressure Pr = pressure at r re = drainage radius rw = wellbore radius

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dr

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

where: P = pressure (psi) k = permeability (md) h = height (ft) re = drainage radius (ft) rw = wellbore radius (ft) µO = fluid viscosity (cP) Bo = formation volume factor (bbls/stb)

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kh(Pav - Pwf) qo = ----------------------------------141.2 µ oBo.[ln(re/rw) - 3/4]

IDEAL 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

• Restricted flow into the wellbore

• The total skin factor may be calculated from well test data

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• Ideal flow conditions rarely exist

INFLOW PERFORMANCE PRINCIPLE ORIGINS OF SKIN Schlumberger Private

• 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)

INFLOW PERFORMANCE PRODUCTIVITY INDEX

q = J(Pws - Pwf) or

q J = -----------------Pws - Pwf

kh(Pav - Pwf) qo = ----------------------------------141.2 µ oBo.[ln(re/rw) - 3/4]

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

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

FACTORS AFFECTING PI

•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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1. Phase behaviour

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

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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)

INFLOW PERFORMANCE RELATIONSHIP Schlumberger Private

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

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

VOGEL

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

Q = the liquid production rate, stb/d Qmax = the maximum liquid rate for 100% drawdown Pwf = bottom hole flowing pressure, psi Pws = the reservoir pressure, psi

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Dimensionless reference curve based on the following equation:

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

SUMMARY OF FACTORS AFFECTING PREDICTION OF WELL PRODUCTION

• 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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• Presence of three phase flow

MULTIPHASE FLOW OUTFLOW PERFORMANCE MOVEMENT OF A MIXTURE OF FREE GASES AND LIQUIDS

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Vertical flowing gradients Horizontal flowing gradients

FACTORS EFFECTING VLP

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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

PRESSURE LOSS IN WELLBORE Schlumberger Private

‘Complicated expression’

Z

δP/δZ Schlumberger Private

• 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

PRESSURE LOSS IN WELLBORE GRAVITY TERM

FRICTION TERM

2

ACCELERATION TERM

δP/δZtotal = g/gcρcosθ + fρv /2gcd + ρv/gc[δP/δZ]

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TOTAL PRESSURE DIFFERENCE

GRAVITY TERM

g/gcρcosθ Correcting weight of fluid Dominant term Single phase simple Multiphase complex

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Pressure loss due to gravity Schlumberger Private

• 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

SLIP Schlumberger Private

• 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

Liquid Holdup • Consider an element for Pelement , Telement

% Liquid

LIQUID Liquid Holdup

GAS

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

% Gas

GAS 1 - Liquid Holdup

Slip corrected Mixture density = L density * HL + G density * (1(1-HL)

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LIQUID

FLOW REGIMES

– Proportion of phases – Flow velocity – Viscosities – Interfacial tension

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• Based on observations • Different flow patterns

FLOW REGIMES

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FRICTION TERM

2

fρv /2gcd Increases with rate Proportional to velocity Proportional to relative roughness Laminar vs turbulent flow Effective viscosity Effective mixture density Sensitive to gas volumes

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ACCELERATION TERM

ρv/gc[δP/δZ] Expansion of fluid as pressure decreases Smallest term Often ignored Need to account in high rate

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Proportion of terms in oil well close to sandface (no significant GLR)

GRAVITY FRICTION

Proportion of terms in oil well significant GLR close to surface

GRAVITY FRICTION ACCELERATION

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ACCELERATION

PRESSURE LOSS IN WELLBORE Schlumberger Private

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

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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INFLOW AND OUTFLOW PERFORMANCE Pressure, psig 0 1000

3000

5200

4000

5000 FBHP, psig

5000 Depth, feet

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2000

6000 7000

4800 4600

8000

4400

9000

4200

10000

0

1000

2000

Rate, bbls/d

11000 12000 13000 14000 0

1000

2000

3000

4000

5000

3000

Inflow (IPR)

Outflow

SKIN 10

5

0

-1

qo α 1/

Flowrate

-3

ln re +S rw Note : Log effect

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Pressure at Node

Effect of Skin on IPR

Decreasing reservoir pressure

Inflow

Outflow

Flowrate

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Pressure at Node

Effect of Pressure Depletion Reservoir with no pressure support on IPR

Inflow (IPR) Outflow 2 3/8” 2 7/8”

3 1/2”

Flowrate (stb/d)

4 1/2”

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Pressure at Node

Effect of Tubing Size on Outflow

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Pressure versus Depth for various Artificial Lift Methods

Natural Flow Pressure vs Depth

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Gas Lift Pressure vs Depth

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Pump Pressure vs Depth

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