Nodal Analysis introduction to inflow and outflow performance - next

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Production Engineering for All

Analisis Nodal - Introduction to Inflow and Outflow Performance

2Copyright 2007, , All rights reserved

NODAL ANALYSIS CONCEPT

QQNODE

Pn

OUTFLOWINFLOW

Pu PdUPSTREAM COMPONENTS

DOWNSTREAMCOMPONENTS

Pnode = Pu – ∆Pupstream components (1) = f1(Q)

∆Pu∆Pd

∆P = f (Q)

Pnode = Pd + ∆Pdownstream components (2) = f2(Q)


GRAPHICAL SOLUTION OF THE PROBLEM

Outflow from node

Inflow to node

SYSTEM FLOW CAPACITY

NODE PRESSURE

(1)

(2)

NO

DE

PRES

SUR

E, P

node

FLOW RATE, Q


EXERCISE # 1ILUSTRATION OF NODAL ANALYSIS CONCEPT

Calculate:

1) Actual capacity of the system in BPD.2) 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.

2000 feet, Ø= 3” 1000 feet, Ø=2”

P1= 200 psi P3= 60 psi

Pnode

WATERSOURCE WATER

SINK

∆P1 ∆P2

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.



FLOW RATE, Q

NO

DE

PRES

SUR

E, P

node

Outflow performance

Inflowperformance

Actual system flow capacity

Pnode

(1)

(2)2” (1) Pnode = P1-∆P1

(2) Pnode = P3+∆P2

2000 feet, Ø= 3” 1000 feet, Ø=2”

P1= 200 PSI P3= 60 PSIPnode

WATERSOURCE

WATERSINK

∆P1 ∆P2



FLOW RATE, Q

NO

DE

PRES

SUR

E, P

node

Outflow performance

Inflowperformance

Actual system flow capacity

Pnode

(1)

(2)2”

3”

new system flow capacity

(1) Pnode = P1-∆P1

(2) Pnode = P3+∆P2

SOL

2000 feet, Ø= 3” 1000 feet, Ø=2”

P1= 200 PSI P3= 60 PSIPnode

WATERSOURCE

WATERSINK

∆P1 ∆P2


Why ‘Nodal’?

Reservoir

PrPwfs

Pwf

Psep

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

hole, Pwf

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?

Pwh


Pressure Losses in Well System

∆P1 = Pr - Pwfs = Loss in reservoir

∆P2 = Pwfs - Pwf = Loss across completion

∆P3 = Pwf - Pwh = Loss in tubing

∆P4 = Pwh - Psep = Loss in flowline

Pr PePwfsPwf

∆P1 = (Pr - Pwfs)∆P2 = (Pwfs - Pwf)

∆P3 = Pwf - Pwh

∆P4 = (Pwh - Psep)

Psep

Sales lineGas

LiquidStock tank

∆PT = Pr - Psep = Total pressure loss

Adapted from Mach et al, SPE 8025, 1979.

Pwh


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.

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Well Outflow Performance


RESERVOIR INFLOW PERFORMANCEPsep

QSeparator

Tubing

Pwf

FlowlinePwh

∆Ptubing

∆P flowline GAS

OIL+WATER

∆Pres

Pr, IPR, K

Reservoir

∆Pres = f(Q)

NODE (Pwf)

Pwf

Q

INFLOW


Types of Outflow Systems

Single / multipleselective / non-selectiveflowing / lifted– gas-lifted– pumped

• beam pump• ESP• PCP• Jet Pump• Hydraulic Pump


WELLBORE FLOW PERFORMANCE (OUTFLOW)Psep

QSeparator

Tubing

Pwf

FlowlinePwh

∆Ptubing

∆P flowline GAS

OIL+WATER

∆Pres

Pr, IPR, K

Reservoir

∆Ptbg = f(Q)

NODE (Pwf)

Pwf

Q

OUTFLOW


SINGLE PHASE FLOWBASIC 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 temperatureconditions of the pipe element

q A v

v = q / A

P,T


FUNDAMENTALS OF FLUID FLOW IN PIPES

ZZ

δP/δZ

θ

FLOW GEOMETRY

GENERAL ENERGY EQUATION

∆P ∆P ∆P ∆P( ) T = ( ) acceleration + ( ) elevation + ( ) friction∆L ∆L ∆L ∆L


FUNDAMENTALS OF FLUID FLOW IN PIPES

∆P( )elevation = ∆L 144

ρ

∆P ρ v 2

( )friction = f∆L 2 g d

∆P ρ ∆( v 2)( )acc = ∆L 2g ∆L


FRICTION LOSSES CALCULATION (single phase flow)

∆P ρ v 2( )f = f∆L 2 g d

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

µ is the viscosity in lbm/ft-sec1cps= 0.00067197 lbm/ft-sec

dvρNR =

µe


Friction Factor Calculation (single phase flow)

Depends on the flow regime:

For laminar flow NRe < 2000

For turbulent flow NRe > 2000.

64f =

NRe

ε 2.51√1/ f = - 2 log ( + )

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


Moody Diagram for Friction Factor Calculation


EXERCISE 10SINGLE PHASE FLOW

Calculate the friction pressure drop in a section of horizontal pipeline of3000 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 roughnessis 0.006 ft.

∆P ρ v 2( )f = f∆L 2 g d

q A v

1cps= 0.00067197 lbm/ft-sec 1 Bbl=5,615 Ft31 day=86400 secv = q / A

dvρNRe =

µ f from Moody

ε/D

sol


Oil Reservoir Phase Envelop

Temperature

Pres

sure

Gas

Dew P

oint

Lin

e

% Liquid

Single Phase Region(Liquid)

Bubble Point Line

Pb

Two Phase Region

CPres

Psep

10075

5025201510

50

Single Phase Region(Gas)


MULTIPHASE FLOW

PRESSURE GRADIENT EQUATION FOR TWO-PHASE FLOW:

∆P ∆P ∆P ∆P( ) T = ( ) acceleration + ( ) elevation + ( ) friction∆L ∆L ∆L ∆L


ρm

∆P ρm vm2


∆P ρm ∆( vm2)

( )acc = ∆L 2g ∆L


GRAVITYTERM


ρm

Correcting weight of fluidDominant termSingle phase simpleMultiphase complex


FRICTIONTERM

∆P ρm vm2


Increases with rateProportional to velocityProportional to relative roughnessLaminar vs turbulent flowEffect of viscosityEffect of mixture densitySensitive to gas volumes


ACCELERATIONTERM

∆P ρm ∆( vm2)

( )acc = ∆L 2g ∆L

Expansion of fluid as pressure decreasesSmallest termOften ignoredNeed to account in high rate


BASIC CONCEPTS

Mixture Velocity, V (Two-phase flow)

vL

qg AqL

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

v = (qL+qg) / A


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

qL

Apv

Ag

AL

L

qg

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

P,T

λ = AL /AP = qL / (qL + qg)


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

qL

Apv

Ag

AL

L

qg

RATIO OF THE VOLUME OF LIQUID IN A PIPE ELEMENT THAT WOULD EXISTIF 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)

P,T

However, the gas velocity is higher than the liquid velocity and as a consequence the volumeof liquid in the pipe element increases.

This phenomenon is known as “slippage between phases” , and the volumen fraction occuppiedby 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.


Superficial Gas Velocity, VSG

qL

Apv

Ag

AL

L

qg


vSG = qg / Ap

Is the velocity that the gas phase would exhibit if it flowed through the total crosssectional area of the pipe alone.


Superficial Liquid Velocity, VSL

qL

Apv

Ag

AL

L

qg


vSL = qL / Ap

Is the velocity that the liquid phase would exhibit if it flowed through the total crosssectional area of the pipe alone.

Vm= Vsl + Vsg


Vertical Flow Parameters

Temperature Pressure

Approximate linear

temperature profile

Dep

th

oil

Single-phase

oilp > pBP

bubbleflow

chumflow

slugflow


Two-Phase Vertical Flow

Analysis and Calculations are Complex

Dec

reas

ing

Pres

sure

Flow regime (gas distribution)1

Proportion gas vs liquid changes2

Gas tends to rise faster than liquid (slippage)

3

Factors affecting ∆Pvert.Mass flow rate:Oil Rate

1Gas Rate (GLR)Water Rate (CUT)Physical properties PVT2ViscositySurface tension

Conduit Configuration Size3RoughnessConcentric?Pressure4

5

Single PhaseLiquid Flow

Bubble Flow

Plug ORSlug Flow

Churn Flow

AnnularFlow

Mist Flow

Temperature


Vertical Flow Paterns

BUBBLYFLOW

SLUGFLOW

CHURNFLOW

ANNULARFLOW


Horizontal Flow Paterns

Annular Dispersed

Stratified Wavy

Slug (Intermitent)

Dispersed Bubble


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.


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.


Flow Regime (Ros)

0.1 0.2 0.3 0.5 0.7 1 2 3 5 7 10 100 1000

RN = Dimensionless Gas Velocity NumberFN = Dimensionless Liquid Velocity Number

0.01

0.02

0.05

0.1

0.2

0.5

1

10

100

BUBBLE FLOW

FROTH FLOW

SLUG FLOWPLUG FLOW HEADING

MIST FLOW

RN

FN

As µ, Increases, heading regime may range up to

TRAN

SITI

ON

SLUG

/ M

IST

RNTRAN

RN

MIS

TRNBUB

RNSL

UG*

RNSLUG*

TRANSITION

BUBBLE /

SLUG


CORRELATIONSBabson (1934)Gilbert (1939 / 1952)Poettmann & Carpenter (1952)Duns & RosHagedorn & BrownOrkiszewskiAziz, Govier and FogarasiChierici et alFancher & BrownBeggs &BrillDuckler FlanniganGrayH.MONA, AsheimHasan and Kabir


PROCEDURE FOR PRESSURE TRAVERSE CALCULATION(incrementing pressure drop)

1. Starting with the known pressure value, P1, at location L1, select a lengthincrement ∆L.

2. Estimate a pressure drop, ∆P, corresponding to the length increment, ∆L.3. Calculate the average pressure and temperature in the selected pipe

element.4. Calculate the the fluids PVT properties at the average conditions of P and T.5. Calculate fluids densities and flow rates at the average conditions.6. Calculate the input liquid content, λ and the superficial velocities vsl and

vsg.7. Determine the flow regime pattern.8. Calculate the hold-up factor, HL, corresponding to the stablished flow

regime pattern.9. Calculate the mixture properties for the calculated hold-up factor.10. Calculate the two-phase friction factor.11. Calculate the total pressure gradient in the increment of pipe at the average

conditions of P and T.12. Calculate the pressure drop corresponding to the selected length increment.13. Compare the estimated and calculated pressure drop. If they are not

sufficiently close, estimate a new pressure drop an repeat the procedurefrom steps 3 through 13.

14. Repeat steps 3 through 13 until the estimated and calculated values are sufficiently close.

15. Calculate a new position L2 = L1 + ∆L and the corresponding pressure P2 = P1 + ∆P.

16. Repeat steps 1 through 15 until the total pipe length is completely covered.

P2

∆L

L1

L2

∆P

P1


Outflow Calculation (node at the bottomhole)

Q1

PressurePwh

Dep

th E

quv.

. To

Pwh

Tubi

ng D

epth

Pwf1 Q Q1 Q2 Q3Pwf Pwf1

Q2

Pwf2Pwf2

Q3

Pwf3

Pwf3

Pwf1Pwf3Pwf2

QPw

fq1 q2 q3

Outflow


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 performanceprograms have been developed for commercial or private use.


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

FLOWRATE, Q

BO

TTO

MH

OLE

FLO

WIN

G P

RES

SUR

E, P

wf

INFLOWIPR

0

OUTFLOW

d1

d2>d1

Pr

0


FINDING OPTIMUM TUBING SIZE

UNSTABLE REGION

DIAMETER FORMAXIMUM FLOW RATE

FLO

W R

ATE

, Q

TUBING DIAMETER, d


Tubing Size in Depleting Reservoir

Pinitial

Tubing Intake Pressure

Q

1 “

2 3/8 “3 1/2 “

5 “4 1/2 “

P5

P10

Pwf


Effect of Gas Injection Rate

P

Qmax

IPR250

200

150

100

50

0400

300


Gas Lift Performance Curve

∆x

∆x

∆x

∆x

∆x

∆x∆x

∆x∆x

∆x

LIFT-GAS INJECTION RATEOR PRODUCTION COSTS

NET

OIL

PR

OD

UC

TIO

NO

R R

EVEN

UE

2

13

4

SLOPE = 1.0Economic Limit

Technical Optimum

1 Kick-OffLift-Gas Requirement

2 Initial Oil Rate at Kick-off

3 Technical cut-off limit

4 Max. Oil Rate

∆x Incremental Lift-Gas Volume


Inflow Performance Curve

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Production rate, STB/D

Flow

ing

botto

mho

le p

ress

ure,

psi

Inflow (Reservoir) Curve

AOFP

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

Pr


Outflow Performance Curve

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500


Flow

ing

botto

mho

le p

ress

ure,

psi

Outflow (Tubing) Curve

Tubing Performance Curve


System Graph

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500


Flow

ing

botto

mho

le p

ress

ure,

psi

Inflow (Reservoir) CurveOutflow (Tubing) Curve

2111 STB/D

1957.1 psi


System Graph – Wellhead Node

0

200

400

600

800

1000

1200

1400

1600

0 500 1000 1500 2000 2500 3000


Flow

ing

wel

lhea

d pr

essu

re, p

si

Inflow CurveOutflow Curve

2050 STB/D

500 psi


Nodal Analysis: Uses

Estimation of Reservoir Parameters – Skin– Permeability– Reservoir Pressure– Note : Non unique solutions unless only one unknownEvaluation of Potential Stimulation Treatments – Primarily through reduction in skin– Parameter sensitivity studies are important


Nodal Analysis

Two Main ComponentsInflow 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


Nodal Analysis

Inflow Operating Point

OutflowPressure PWF

Operating Flowrate

Flowrate (stb/d)

Pres

sure

at N

ode

Reservoir Pressure


The Inflow Performance RelationshipDependent 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, DarcyWell Geometry i.e. Vertical or HorizontalFormation Properties– Reservoir Pressure – Permeability– Skin (Includes deviation, perforation, damage etc)– Net Pay Height


Effect of Skin in IPR

Outflow

Flowrate

Pres

sure

at N

ode

5 0 -1 -3

SKIN

Inflow(IPR)

Note : Log effect

10

⎟⎟⎠

⎞⎜⎜⎝

⎛+ s

rrln

1 αq

w

eO


Effect of Pressure Depletion in IPR

Outflow

Flowrate

Pres

sure

at N

ode

8 04

Oil Recovery (% STOIIP)

12

Reservoir with no pressure support

Inflow


The Outflow Performance RelationshipDependent 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 - GrayFrictionCompletion Properties

• Tubing Size • Tubing Restrictions• Tubing Roughness


Effect of Tubing Size in Outflow

Inflow(IPR)

Outflow

Flowrate (stb/d)

Pres

sure

at N

ode

For a Tubing Restricted Well

2 3/8”

2 7/8”4 1/2”3 1/2”

Nodal Analysis introduction to inflow and outflow performance - next

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Transcript of Nodal Analysis introduction to inflow and outflow performance - next