Nodalanalysis Introductiontoinflowandoutflowperformance Next 161121154412

Production Engineering for All

Analisis Nodal - Introduction to Inflow and Outflow Performance

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NODAL ANALYSIS CONCEPT

Q

Q NODE

INFLOW

Pu

UPSTREAM COMPONENTS

Pn

OUTFLOW

DOWNSTREAM COMPONENTS

Pd

∆Pd

∆Pu ∆P = f (Q)

Pnode = Pu – ∆Pupstream components (1) = f1(Q) Pnode = Pd + ∆Pdownstream components (2) = f2(Q)

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NODE PRESSURE, Pnode

GRAPHICAL SOLUTION OF THE PROBLEM

(2) Outflow from node

NODE PRESSURE

(1) Inflow to node

SYSTEM FLOW CAPACITY FLOW RATE, Q

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EXERCISE # 1 ILUSTRATION OF NODAL ANALYSIS CONCEPT P1= 200 psi

P3= 60 psi ∆P1

Pnode

∆P2

WATER SOURCE 2000 feet, Ø= 3”

1000 feet, Ø=2”

WATER SINK

Calculate: 1) 2)

Actual capacity of the system in BPD. Capacity of the system when the diameter of the 2” pipe is increased to 3”.

Select the node at the point where the pipe diameter is reduced from 3” to 2”. Assume flow rates of 2500, 3000 y 3500, 5000, 5500, 6000 BPD. Use the following equation to calculate the pressure drop in a pipe L Q2 ∆P = 3.8 x 10 - 7 x

; D5

where, ∆P is the pressure drop in psi, L is the pipe length in feet, D is the pipe diameter in inches and Q the flow rate in BPD. Copyright 2007,

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NODE PRESSURE, Pnode

GRAPHICAL SOLUTION OF THE PROBLEM

(2)

2”

Pnode

Outflow performance

(1) Pnode = P1-∆P1 (2) Pnode = P3+∆P2 Inflow (1) performance

Actual system flow capacity

FLOW RATE, Q P1= 200 PSI ∆P1 WATER SOURCE Copyright 2007,

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Pnode

P3= 60 PSI ∆P2 WATER SINK

2000 feet, Ø= 3”

1000 feet, Ø=2”

5

NODE PRESSURE, Pnode

GRAPHICAL SOLUTION OF THE PROBLEM

(2)

2”

Pnode

Outflow performance

(1) Pnode = P1-∆P1 (2) Pnode = P3+∆P2

3” Inflow (1) performance

Actual system flow capacity

FLOW RATE, Q P1= 200 PSI ∆P1 WATER SOURCE Copyright 2007,

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new system flow capacity

Pnode

SOL

P3= 60 PSI ∆P2 WATER SINK

2000 feet, Ø= 3”

1000 feet, Ø=2”

6

Why ‘Nodal’? Pwh

Psep Fluid flows from the reservoir to the stock tank because of the pressure gradients within the system. The total pressure drop from the reservoir to the separator is the sum of the individual pressure drops through four different segments: in the reservoir, across the completion, up the wellbore, and through the flowline. But we do not know the flow rate - that is what we are trying to find. How do we calculate the flow rate, knowing the reservoir and separator pressures? This is the central question of Nodal Analysis. Given the reservoir pressure and the separator pressure, along with the physical properties of each segment, what is the flow rate at which the well will produce?

Reservoir Pwfs Pwf Copyright 2007,

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Pr

• As many ‘nodes’ as you want • The observer can be placed at any node • Normally, the well is observed from bottom hole, Pwf

7

Pressure Losses in Well System ∆P4 = (Pwh - Psep)

Gas

Pwh

Psep

Sales line

Liquid

Stock tank

∆P3 = Pwf - Pwh

Pwf

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∆P1 = Pr - Pwfs

= Loss in reservoir

∆P2 = Pwfs - Pwf

= Loss across completion

∆P3 = Pwf - Pwh

= Loss in tubing

∆P4 = Pwh - Psep

= Loss in flowline

∆PT = Pr - Psep

= Total pressure loss

Pwfs

∆P1 = (Pr - Pwfs) ∆P2 = (Pwfs - Pwf)

Pr

Pe

Adapted from Mach et al, SPE 8025, 1979.

8

Nodal Analysis How do we determine the right flow rate? We know the separator pressure and the average reservoir pressure. „ We start in the reservoir at the average reservoir pressure, Pr, and assume a flow rate. This lets us calculate the pressure just beyond the completion, Pwfs. We can then calculate the pressure drop across the completion, and the bottomhole pressure Pwf. This pressure is valid only for the assumed flow rate. „ Or, we may start at the separator at Psep, and calculate the pressure drop in the flowline to find the wellhead pressure, Pwh. Then we can calculate the bottomhole pressure Pwf. Again, this pressure is valid only for the assumed flow rate. „ The two calculated bottomhole pressures will probably not be the same. If not, then the assumed rate is wrong. „ “Nodal” analysis refers to the fact that we have to choose a point or “node” in the system at which we evaluate the pressure - in this case, the bottom of the wellbore. This point is referred to as the solution point or solution node. Copyright 2007, , All rights reserved „

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Well Outflow Performance

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RESERVOIR INFLOW PERFORMANCE Psep Pwf

∆P flowline

GAS

Pwh

Flowline

OIL +WATER

Q

Separator

Tubing

∆Pres = f(Q)

∆Ptubing

Reservoir

INFLOW Pwf

Pr, IPR, K

NODE, All(Pwf) rights reserved

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∆Pres

Q

11

Types of Outflow Systems „

Single / multiple

„

selective / non-selective

„

flowing / lifted – gas-lifted – pumped • • • • •

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beam pump ESP PCP Jet Pump Hydraulic Pump

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WELLBORE FLOW PERFORMANCE (OUTFLOW) Psep Pwf

∆P flowline

GAS

Pwh

Flowline

OIL +WATER

Q

Separator

Tubing

∆Ptbg = f(Q)

∆Ptubing

Reservoir

OUTFLOW Pwf

Pr, IPR, K

NODE, All(Pwf) rights reserved

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∆Pres

Q

13

SINGLE PHASE FLOW BASIC CONCEPTS FLUID VELOCITY Is the flow rate (q) divided by the pipe cross sectional area (A) through which the fluid flows at the pressure and temperature conditions of the pipe element

q

A

v P,T

v=q/A Copyright 2007,

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FUNDAMENTALS OF FLUID FLOW IN PIPES

FLOW GEOMETRY

Z δP/δZ

θ

GENERAL ENERGY EQUATION ∆P (

)T=( ∆L

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∆P

∆P ) acceleration + (

∆L

∆P ) elevation + (

∆L

) friction ∆L

15

FUNDAMENTALS OF FLUID FLOW IN PIPES

∆P ( ∆L

ρ )elevation =

∆P ( ∆L

ρ v )friction = f

∆P ( ∆L

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2

2gd

ρ ∆( v 2) )acc =

2g ∆L

16

FRICTION LOSSES CALCULATION (single phase flow) ∆P ( ∆L

ρv2 )f = f

2gd

where f, is the friction factor which is a function of the pipe roughness (ε) and theReynolds Number (NRe), which is calculated fromthe following equation:

dvρ

NRe =

µ µ is the viscosity in lbm/ft-sec 1cps= 0.00067197 lbm/ft-sec

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Friction Factor Calculation (single phase flow)

Depends on the flow regime: 64 For laminar flow

NRe < 2000

For turbulent flow NRe > 2000.

f= NRe ε √1/ f = - 2 log (

2.51 +

3.71d

) NRe√ f

The latest equation requires a trial and error process to calculate f An intial value to start the iterative process can be obtained from the following equation: f = 0.0056 + 0.5 NRe - 0.32

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Moody Diagram for Friction Factor Calculation

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EXERCISE 10 SINGLE PHASE FLOW

Calculate the friction pressure drop in a section of horizontal pipeline of 3000 ft length and 3.937 inches internal diameter, where 5000 STB/D of 0.9 sp. gr. oil with a viscosity of 5 cps oil are flowing. The absolute pipe wall roughness is 0.006 ft.

q

v

A

1cps= 0.00067197 lbm/ft-sec 1 Bbl=5,615 Ft3 1 day=86400 sec

v=q/A dvρ NRe =

µ

∆P

f

from Moody

( ∆L

ρv2 )f = f

2gd

ε/D sol Copyright 2007,

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Oil Reservoir Phase Envelop Single Phase Region (Liquid)

Pres

% Liquid

C

e

Psep

50 25 20 15 10 5 0

Gas

Temperature Copyright 2007,

Lin e

as h P

Re

on i g

Po int

o w T

Pb

De w

Pressure

ine L int o P e l bb u B 100 75

Single Phase Region (Gas)

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MULTIPHASE FLOW PRESSURE GRADIENT EQUATION FOR TWO-PHASE FLOW:

∆P (

∆P )T=(

∆L

) acceleration + ( ∆L

∆P ( ∆L

)elevation =

∆P ( ∆L

)friction = f

∆P ( ∆L

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∆P

)acc =

∆P ) elevation + (

∆L

) friction ∆L

ρm 144 ρm v m 2 2gd ρm ∆( vm 2) 2g ∆L

22

GRAVITY TERM

∆P ( ∆L

)elevation =

ρm 144

Correcting weight of fluid Dominant term Single phase simple Multiphase complex

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FRICTION TERM

∆P ( ∆L

)friction = f

ρm v m 2 2gd

Increases with rate Proportional to velocity Proportional to relative roughness Laminar vs turbulent flow Effect of viscosity Effect of mixture density Sensitive to gas volumes

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ACCELERATION TERM

∆P ( ∆L

)acc =

ρm ∆( vm 2) 2g ∆L

Expansion of fluid as pressure decreases Smallest term Often ignored Need to account in high rate

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BASIC CONCEPTS Mixture Velocity, V (Two-phase flow) L

qg

v

qL

A

Pipe element with liquid and gas travelling at the same velocity, V

v = (qL+qg) / A

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No-Slip Liquid Holdup (Input Liquid Content), λ

Ag

qg

L

v

qL

Ap

P,T

AL RATIO OF THE VOLUME OF LIQUID IN A PIPE ELEMENT THAT WOULD EXIST IF THE GAS AND THE LIQUID TRAVELED AT THE SAME VELOCITY (NO SLIPPAGE) DIVIDED BY THE VOLUME OF THE PIPE ELEMENT.

λ = AL /AP = qL / (qL + qg)

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No-Slip Liquid Holdup (Input Liquid Content), λ

Ag

qg

L

v

qL

Ap

P,T

AL

RATIO OF THE VOLUME OF LIQUID IN A PIPE ELEMENT THAT WOULD EXIST IF THE GAS AND THE LIQUID TRAVELED AT THE SAME VELOCITY (NO SLIPPAGE) DIVIDED BY THE VOLUME OF THE PIPE ELEMENT.

λ = AL /AP = qL / (qL + qg) However, the gas velocity is higher than the liquid velocity and as a consequence the volume of liquid in the pipe element increases. This phenomenon is known as “slippage between phases” , and the volumen fraction occuppied by the liquid in the pipe element under this conditions is known as“Hold-Up Factor” (HL), and is dependent on flow pattern, gas and liquid properties, pipe diameter and pipe inclination. Copyright 2007,

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Superficial Gas Velocity, VSG

Ag

qg

L

v

qL

Ap

AL Pipe element with liquid and gas travelling at the same velocity, V

vSG = qg / Ap Is the velocity that the gas phase would exhibit if it flowed through the total cross sectional area of the pipe alone.

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Superficial Liquid Velocity, VSL

Ag

qg

L

v

qL

Ap

AL Pipe element with liquid and gas travelling at the same velocity, V

vSL = qL / Ap Is the velocity that the liquid phase would exhibit if it flowed through the total cross sectional area of the pipe alone.

Vm= Vsl + Vsg Copyright 2007,

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Vertical Flow Parameters Temperature

Pressure

chum flow bubble flow

Depth

slug flow

Approximate linear temperature profile

Singlephase oil p > pBP oil Copyright 2007,

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Two-Phase Vertical Flow Analysis and Calculations are Complex 1 Flow regime (gas distribution) Mist Flow Decreasing Pressure

Annular Flow Churn Flow Plug OR Slug Flow Bubble Flow Single Phase Liquid Flow

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2 Proportion gas vs liquid changes 3 Gas tends to rise faster than liquid (slippage) Factors affecting ∆Pvert. 1 Mass flow rate: Oil Rate Gas Rate (GLR) Water Rate (CUT)

2 Physical properties PVT Viscosity Surface tension

3

Conduit Configuration Size Roughness Concentric?

4 Pressure 5 Temperature

32

Vertical Flow Paterns

BUBBLY Copyright 2007,FLOW , All rights reserved

SLUG FLOW

CHURN FLOW

ANNULAR FLOW

33

Horizontal Flow Paterns Annular Dispersed

Stratified Wavy

Slug (Intermitent)

Dispersed Bubble Copyright 2007,

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2-Phase –Gas-Liq) Flow Regimes „

Flow regime or Flow Pattern : is a qualitative description of the phase distribution in a pipe.

„

4 regimes are generally agreed upon: 1. BUBBLE FLOW: dispersed bubbles of gas in a continuous liquid phase 2. SLUG FLOW: at higher rates, the bubbles coalesce into larger bubbles, which eventually fill up the entire pipe section. Between the large gas bubbles are slugs of liquid that contain smaller bubbles of gas entrained in the liquid.

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2-Phase –Gas-Liq) Flow Regimes 3. CHURN FLOW: with further increase in gas rate, the larger gas bubbles become unstable and collapse, resulting in a highly turbulent pattern. Both phases are dispersed. Churn flow is characterized by oscillatory up-and-down motions of liquid. 4. ANNULAR FLOW: at higher rates, gas becomes the continuous phase, with liquid flowing in an annulus coating the surface of the pipe and with liquid droplets entrained in the gas phase.

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Flow Regime (Ros)

TR B AN U S B SL BL ITIO U E N G /

1 0.5 0.2 0.1

SLUG FLOW PLUG FLOW

TRA SLU NSITI O G/ MIS N T

SL UG

*

FROTH FLOW RN

BUBBLE FLOW

RN

R

10

R MI N ST

RN TR AN

N

B

SL UG

*

U

B

FN

100

As µ, Increases, heading regime may range up to

HEADING

MIST FLOW

0.05 0.02 0.01 0.1

0.2 0.3

0.5 0.7 1

2

3

5

7 10

RN RN = Dimensionless Gas Velocity Number Copyright 2007, All rights reserved FN = , Dimensionless Liquid Velocity Number

100

1000 37

CORRELATIONS Babson (1934) Gilbert (1939 / 1952) Poettmann & Carpenter (1952) Duns & Ros Hagedorn & Brown Orkiszewski Aziz, Govier and Fogarasi Chierici et al Fancher & Brown Beggs &Brill Duckler Flannigan Gray H.MONA, Asheim Hasan and Kabir Copyright 2007,

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PROCEDURE FOR PRESSURE TRAVERSE CALCULATION (incrementing pressure drop)

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Starting with the known pressure value, P1, at location L1, select a length increment ∆L. Estimate a pressure drop, ∆P, corresponding to the length increment, ∆L. Calculate the average pressure and temperature in the selected pipe element. Calculate the the fluids PVT properties at the average conditions of P and T. Calculate fluids densities and flow rates at the average conditions. Calculate the input liquid content, λ and the superficial velocities vsl and vsg. Determine the flow regime pattern. Calculate the hold-up factor, HL, corresponding to the stablished flow regime pattern. Calculate the mixture properties for the calculated hold-up factor. Calculate the two-phase friction factor. Calculate the total pressure gradient in the increment of pipe at the average conditions of P and T. Calculate the pressure drop corresponding to the selected length increment. Compare the estimated and calculated pressure drop. If they are not sufficiently close, estimate a new pressure drop an repeat the procedure from steps 3 through 13. Repeat steps 3 through 13 until the estimated and calculated values are sufficiently close. Calculate a new position L2 = L1 + ∆L and the corresponding pressure P2 = P1 + ∆P. Repeat steps 1 through 15 until the total pipe length is completely covered.

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L2

P2

∆L ∆P

L1

P1 39

Outflow Calculation (node at the bottomhole) Pressure

Pwf1

Depth Equv. . To Pwh

Pwh

Pwf2

Q

Q1

Q2

Pwf

Pwf1

Pwf2

Q3 Pwf3

Tubing Depth

Pwf3

Q1

Q2 Outflow Pwf

Q3 Pwf1 Pwf3 Pwf2

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q2

q3

Q 40

Well Performance Software The most noteworthy well performance programs on the market today are: „

Prosper

(Petroleum Experts)

„

WellFlo

(Edinburgh Petroleum Services)

„

Perform

(Dwight’s / IHS Energy Services)

„

PipeSim

(Schlumberger)

„

WEM

(P.E. Mosely & Associates)

In addition to these programs, numerous other well performance programs have been developed for commercial or private use. Copyright 2007,

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BOTTOMHOLE FLOWING PRESSURE, Pwf

EFFECT OF THE TUBING SIZE (NODE SELECTED AT THE BOTTOMHOLE)

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d1

Pr

d2>d1

INFLOW IPR

OUTFLOW

0

0

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FLOWRATE, Q

42

FLOW RATE, Q

FINDING OPTIMUM TUBING SIZE

UNSTABLE REGION DIAMETER FOR MAXIMUM FLOW RATE

TUBING DIAMETER, d Copyright 2007,

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Tubing Size in Depleting Reservoir 1“ Pinitial Tubing Intake Pressure

2 3/8 “ 3 1/2 “

P5 4 1/2 “

Pwf

5“

P10

Q Copyright 2007,

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Effect of Gas Injection Rate 0 400

50

300 100 150

P 200

IPR 250

Qmax Copyright 2007,

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Gas Lift Performance Curve Technical Optimum

SLOPE = 1.0 Economic Limit 4 ∆x Kick-Off Lift-Gas Requirement

2 Initial Oil Rate at Kick-off 3 Technical cut-off limit 4 Max. Oil Rate

∆x

Incremental Lift-Gas Volume

∆x ∆x

NET OIL PRODUCTION OR REVENUE

1

∆x

∆x

∆x ∆x ∆x ∆x

2 ∆x

3 1 Copyright 2007,

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LIFT-GAS INJECTION RATE OR PRODUCTION COSTS

46

Inflow Performance Curve 3500

Flowing bottomhole pressure, psi

Inflow (Reservoir) Curve

Pr

3000

Performance of an ideal OH well, no damage, no completion, no friction losses from reservoir to wellhead

2500

2000

1500

1000

AOFP

500

0 0

500

1000

1500

2000

2500

3000

3500

4000

4500

Production rate, STB/D Copyright 2007,

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Outflow Performance Curve

Flowing bottomhole pressure, psi

3500

Outflow (Tubing) Curve

3000

2500

2000

Tubing Performance Curve

1500

1000

500

0 0

500

1000

1500

2000

2500

3000

3500

4000

4500

Production rate, STB/D Copyright 2007,

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System Graph

Flowing bottomhole pressure, psi

3500

Inflow (Reservoir) Curve Outflow (Tubing) Curve

3000

2500

1957.1 psi 2000

1500

1000

500

2111 STB/D

0 0 Copyright 2007,

500

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1000

1500

2000

2500

3000

Production rate, STB/D

3500

4000

4500 49

System Graph – Wellhead Node 1600

Inflow Curve Outflow Curve

Flowing wellhead pressure, psi

1400 1200 1000 800

500 psi 600 400 200

2050 STB/D

0 0 Copyright 2007,

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500

1000

1500

2000

Production rate, STB/D

2500

3000 50

Nodal Analysis: Uses „

Estimation of Reservoir Parameters – – – –

„

Skin Permeability Reservoir Pressure Note : Non unique solutions unless only one unknown

Evaluation of Potential Stimulation Treatments – Primarily through reduction in skin – Parameter sensitivity studies are important

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Nodal Analysis Two Main Components Inflow Performance Curve/Relationship (IPR)

„

– Oil or Gas Flowrate vs Bottomhole Flowing Pressure – Ordinate Origin = Reservoir Pressure (∆P = 0 q = 0) – Abscissa Intercept = Absolute Open Flow Potential (∆P = Pr

q = Max)

Outflow Curve (Tubing Intake)

„

– Function of Hydrostatic, Friction & Acceleration Components – Curves Shifted by Wellhead Pressure & Artificial Lift

Intercept of Curves Gives FBHP (psi) & Flowrate

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Nodal Analysis Reservoir Pressure

Pressure at Node

Inflow

Operating Point

Pressure PWF

Outflow

Operating Flowrate

Flowrate (stb/d)

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The Inflow Performance Relationship Dependent On: „

Fluid Properties – Oil • •

Viscosity, Gas oil Ratio, Bubble Point Formation Volume Factor, Density

– Gas • • „ „ „

Viscosity, Z Factor, Compressibility Density

Inflow Correlation Used e.g. Oil - Darcy, Vogel, Gas - Jones, Darcy Well Geometry i.e. Vertical or Horizontal Formation Properties – – – –

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Reservoir Pressure Permeability Skin (Includes deviation, perforation, damage etc) Net Pay Height

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Effect of Skin in IPR

Pressure at Node

qO α

Inflow (IPR)

Outflow

5

0

Flowrate , All rights reserved

⎛r ⎞ ln⎜⎜ e + s ⎟⎟ ⎝ rw ⎠

SKIN 10

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1

-1

-3

Note : Log effect 55

Effect of Pressure Depletion in IPR

Pressure at Node

Reservoir with no pressure support

Inflow

Outflow

Oil Recovery (% STOIIP) 12

8

4

0

Flowrate Copyright 2007,

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The Outflow Performance Relationship Dependent On: Fluid Properties – Oil • •

Viscosity, Gas oil Ratio, Bubble Point Formation Volume Factor, Density

– Gas • • „ „ „

Viscosity, Z Factor, Compressibility Density

Outflow Correlation Used e.g. Oil - Duns & Ross, Gas - Gray Friction Completion Properties • • •

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Tubing Size Tubing Restrictions Tubing Roughness

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Effect of Tubing Size in Outflow For a Tubing Restricted Well

Pressure at Node

Inflow (IPR) Outflow 2 3/8” 2 7/8”

3 1/2”

4 1/2”

Flowrate (stb/d) Copyright 2007,

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