RN Day 1- Part 3 Nodal Analysis Theory(Rev3)

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Day 1 Page 3.1

Weatherford WellFlo 2011 User Training Course

Nodal Analysis Theory Review

© 2012 Weatherford. All rights reserved.

ay

March 12, 2012

Course Contents

• PVT Basics

• Inflow Performance Relationship (IPR)

• Outflow or VLP curves

• Temperature Model

• Nodal Analysis Basics:

– What is Nodal Analysis?

– Why Nodal Analysis?

– What is optimization?

– Optimization approaches

– The production system


– ys ems anays s concep

– Factors affecting system performance

– Predicting cession of natural flow

– Liquid loading in gas wells

1



Day 1 Page 3.2


Petroleum Fluid Properties


Module Contents

– Why is PVT important?

– Key PVT Properties

– PVT Correlations

–


3



Day 1 Page 3.3


Introduction to PVT

• What is PVT?

– Pressure – Volume – Temperature

– Pressure and temperature are imposed on thesystem and determine the phase or phases whichexist. The phases which exist are identified by theirspecific volume or densities.

• Why is PVT important?


–

• pressure losses in the production system• Sizing of equipment

4

Petroleum Fluid Types

• Black Oil – Initial producing GOR < 2000 scf/STB

– Oil gravity below 45° API

• Volatile Oil – Contains fewer heavy molecules than black oil, and higher shrinkage

– Initial producing GOR between 2000 – 3300 scf/STB

– Oil gravity 40° API and higher

• Gas Condensate: (Retrograde and Wet Gas) – Initially the fluid is totally gas in the reservoir. With decreasing pressure, liquid

condenses from the gas at surface conditions


– Initial producing GOR is 3300 scf/STB or higher. Or condensate-Gas ratio CGR is5 – 500 STB/MMscf.

– Condensate gravities between 40° and 60° API

• Dry Gas – Fluid is totally gas in the reservoir and no (hydrocarbon) liquid is formed at the

surface conditions either.

5



Day 1 Page 3.4


Example Phase Diagram for MulticomponentHydrocarbon System

© 2012 Weatherford. All rights reserved.6

Key PVT Properties

• Specific gravity or density: How heavy it is?

• Bubble Point Pressure: When does first gas bubble come

- Applicable for oil and volatile oil systems

- At pressures above bubble point pressure, oil iscalled undersaturated as it can dissolve more gas

• Dew Point Pressure: When does first liquid droplet form?


– Applicable for condensate and dry gas systems• Solution Gas-Oil Ratio (R s ): How much gas has gone into

solution?

– The quantity of gas dissolved in an oil at reservoirconditions.

7



Day 1 Page 3.5


Key PVT Properties

• Formation Volume Factor (B): How much has it shrunkbetween reservoir and surface?

– o – o ume o reservo r o requ re o pro uce one arre o oin the stock tank.

– Bw – Volume of reservoir water required to produce one barrel ofwater in the stock tank.

– Bg – Volume of reservoir gas required to produce one scf of gasin the stock tank.


• Viscosity ( μ): How much resistance does it offer to flow?

• Surface Tension ( σ ): Helpful in flow regime and holdupdetermination. Though effect is small.

• Compressibility (Z): Factor used to determine Gas Bg8

PVT in WellFlo

• Reservoir fluid PVT data must be entered. There is achoice of:

1. Black Oil (with Water-Cut (WCT) and Gas/Oil Ratio (GOR))

2. Volatile Oil (with WCT and GOR).

3. Gas Condensate (with Water/Gas Ratio (WGR) andCondensate/Gas Ratio (CGR))

4. Dry Gas (with Water/Gas Ratio (WGR))

5. Compositional Fluid (C-Components, Plus fraction with pseudocomponents)


• PVT Correlations are used for the first two fluid types,while Gas Condensate, Volatile Oil and Compositionalsystems are handled by an Equation of State (EoS).

• Computed fluid properties can be tuned to measureddata, if such data is available.

9



Day 1 Page 3.6


WellFlo: Black oil and dry gas PVT

• Oil: industry standard black oil correlations:

– Pb, Rs: Lasater, Standing, Vazquez-Beggs, Glaso, Petrosky-Farshad, Macar

– Bo: Standing, Vazquez-Beggs, Glaso, Petrosky-Farshad,Macary

– µo: Beal, Chew & Connally, Beggs & Robinson, option for ASTMmethod for dead oil viscosity

– Can be tuned to CCE (Constant Composition Experiment) data


•

– z-factor: Standing & Katz (Dranchuk, Purvis & Robinson) – µg: Carr, Kobayashi & Burrows, Lee, Gonzalez & Eakin

– Can be tuned to measured data

10

PVT Correlations Range




Day 1 Page 3.7


WellFlo: Condensate PVT and Volatile Oil

• Use of Equation-of-State

– Peng Robinson (PR)

– Soave-Redlich-Kwong (SRK)

• Models condensate with dew point or volatile oil withbubble point

• Tuneable against CCE (Constant CompositionExpansion) data at different P and CGR/GOR:


- dew point/bubble point - liquid dropout

- relative volume - z-factor

- vapour and liquid viscosities - surface tension

12

Use of PVT Correlations for Predictions

The published correlations are mostly based on regional data:

Standing's California crudes,

etros y an ars a s u o ex co cru es, an

Glaso's North Sea crudes.

Use of these regional correlations is more appropriate for crudes fromthe same basins for which the correlation was derived.

The Vas uez and Be s correlations are based on a ver lar e number


of samples coming from multiple regions.

Even though one is tempted to use these universal correlations, therange of error for their predictions is, however, typically large due to thescatter involved in using a large number of data sets to generate thesecorrelations.

13



Day 1 Page 3.8


Use of PVT Correlations for Predictions

• Better approach would be to use field measured data,and tune the most appropriate correlation using the fielddata.

• Tuning PVT properties with field Data will be coveredlater on Day 3 exercise of training course.


Constant Composition Expansion (CCE)

• A series of isothermal flash expansions at constant temperature(normally T res ).No fluid is removed from the cell

Sin le

Vapour

Vapour

olume


SinglePhase

Phase Liquid

@ Psat

P > Psat P = Psat P < Psat P << Psat



Day 1 Page 3.9


Constant Volume Depletion (CVD)

• A series of flash expansions at T

• ,cell volume at P sat

a our

Vapour Vapour


Vapour Vapour Vapour

Liquid Liquid Liquid Liquid

P sat P1 P1 P2 P2

WellFlo PVT Data Tips

• The Bubble-Point Pressure is calculated at the CheckTemperature for the specified Produced GOR. To checka ainst laborator PVT data the measured GOR of thereservoir oil would normally be entered here.

• Calculations will be performed for 0 ≤ GOR ≤ 200,000scf/STB, although these correlations were rarely


- .calculated at the Check Pressure and CheckTemperature. If the Check Pressure is below thecalculated Bubble-Point Pressure, the Solution GOR willbe less than the specified Produced GOR.

17



Day 1 Page 3.10


End Section.

Petroleum Fluid Properties


Inflow Performance




Day 1 Page 3.11


Module Contents

• Reservoir Drive Mechanisms

• What is Inflow Performance?

• Inflow Performance Relationships

– Straight Line

– Vogel

• Non-Ideal Conditions


• Well Testing

• Inflow Performance Tuning based on Well Test Data

20

Simple Single-Well System




Day 1 Page 3.12


Well System Pressure Losses

• Reservoir Inflow (kh)IPR

• omp e on er ormance s n

• Tubing Performance

• Surface Equipment Performance

Tubing Performance consists of determining theressure dro enerated b trans ortin a fluid


through a pipe or annulus. The pressure vs.depth (or length) profile is called a “pressuretraverse”.

Well Performance

Outflow performance =flowing bottom holepressure as a function offlow rate


Inflow performance = flowrate as a function offlowing bottom holepressureQ

P r

P bp

AOF



Day 1 Page 3.13


Well & Reservoir Inflow Performance

• Types of Reservoir Drive Mechanisms

–

– Gas cap drive

– Water expansion drive


– v

– Combination drive

24

Solution Gas Drive

• Gas dissolved in oil

provides “expansion”

energy

• Constant volume

• No water encroachment

• Two phase flowingreservoir below bubble


point• No gas cap

25

OilOil



Day 1 Page 3.14


Solution Gas Drive

• PI not linear

• PI declines with de letion

• Formation GOR increaseswith depletion

• Least efficient with ~ 15%recovery


Gas Cap Drive

• Gas from solution will formgas cap

• With production gas capincreases providing drive

• Excessive drawdown cancause coning




Day 1 Page 3.15


Gas Cap Drive

• PI usually not linear

• GOR constant exce t near depletion

• ~ 25% recovery


Water Drive

• Not constant volume

• Reservoir ressure more constant - expansion ofwater 1 in 2500 per 100 psi

OilOil


Water Water



Day 1 Page 3.16


Water Drive

• PI more constant

• GOR more constant

• Combination of water drive& gas cap expansion

• Often supplemented bywater injection


• ost e c ent w t up to

50% recovery

30

Compaction Drive

• Energy provided bycollapse of porous medium,expans on o u s

• Common in highly-compressible,unconsolidated reservoirs

• Examples: Heavy oil


,Venezuela, WesternCanada

31



Day 1 Page 3.17


Combination Drive

• Combination of two or moreof the following:

– Solution gas drive

– Gas cap drive

– Water drive

– Compaction drive

Example showing combinationof natural water influx and gascap expansion


Reservoir Performance Trends

*GOR a strong


mechanism



Day 1 Page 3.18


Ideal Flow Assumptions

• Ideal well• Purely radial flow• Infinite reservoir

• Stabilized flow• Single phase• Above bubble point• Homogeneous & isotropic reservoir • Perforations penetrate throughout reservoir • Reservoir shape•


• Wellbore clean / uncased

• No skin• Darcy’s law

34

Reservoir Performance

• Darcy LawP 1 P 2

∆P = P 1 – P 2

L

q A

PkAq


Where

q = volumetric flow rate k = permeability of the porous medium

A= area open to flow ∆P = pressure drop

µ = viscosity L = length

35

L



Day 1 Page 3.19


Steady State Radial Flow

• Oil reservoir (In oilfield units)

Oil flow rate r e

Productivity Index

r w

hpR

4306.10

ln21

)(00708.0

2w A

oo

wf Roo

r C A

B

p phk q

00708.0 o hk J


where, C A is the shape factor which depends on the shape of the reservoir and the well position

36

4306.10

ln21

2w A

oo r C A

B

Non-ideal Flow

• Departures from Darcy’s law• Effects at boundaries• • Non homogeneous reservoir • Perforation positions• High velocities• Fluid type / high GOR• Transient behavior


• Relative permeability effects - oil/water/gas near thewellbore

• Depletion of reservoir • Flow restrictions (skin)

37



Day 1 Page 3.20


Inflow Performance

• The Inflow Performance Relationship (IPR) describes the abilityof the reservoir to deliver fluid (i.e. rate) for a prescribed pressuredro between reservoir and wellbore drawdown .

• The IPR is a function of the reservoir and the interface(completion) between the reservoir and the tubulars (i.e. skin).The IPR is independent of the tubulars.


• The IPR is defined as Q vs. P. A number of differently shaped

curves may describe a well’s IPR, depending on the actualphases produced .

38

Inflow Performance Relationship

• IPR is a plot of flow rate vs flowing pressure at the node in consideration. Commonlythe bottom of the well against perforation is considered as the solution node

• IPR for single phase flow

wf R p p J q Inverse of Slope= PI




Day 1 Page 3.21


Straight-Line IPR

Static Reservoir Pressure (Q = 0)

Constant PI (Linear Behavior)

PI = Inverse Slope


Maximum Flow Rate, AOF (Pwf = 0)

Inflow Performance Relationship (IPR)

• Relationship between flow rate Q into the wellbore andwellbore flowing pressure P wf

Methods:

– Straight Line Undersaturated oil

–


–

– Back Pressure/Fetkovich/C&n Saturated oil/Dry gas

– Linear Inertial Turbulent (LIT) Dry gas

– Normalised Pseudo Pressure Oil/Gas/Condensate

41



Day 1 Page 3.22


Origin of PI Single Phase Incompressible Flow

• For a single phase, incompressible fluid, therelationship between well inflow rate and pressuredrawdown can be expressed in the form of Darcy’sequation for radial flow:

PPkh

units field oilin


w

eoo

weo

r r BQ

ln.2.141

Productivity Index Concept

• The relationship between the flow rate and the pressuredrawdown, in its most simple form, reduces to a straightline defined as follows:

• The Productivity Index isdefined as PI = -1/J, and

S

r r

B

khQ J

w

e

43ln2.141

P

P res

slope = J


yields the deliverability of the well in terms of volume/dayper unit of drawdown,bbl/d/psi

43

w

QAOF



Day 1 Page 3.23


Straight-Line IPR

• Productivity Index (or PI)

wf r q

wf r PPq

PI


q = Total Liquid Flow Rate, STB/d

PI = Productivity Index, STB/d/psi

P r = Average Reservoir Pressure, psig

P wf = Flowing Bottomhole Pressure, psig

Example

For a well producing 424 STB/day with an averagereservoir pressure of 2,000 psig, and a flowingbottomhole pressure of 1460 psig, calculate:

1. The productivity index,

2. The producing rate if Pwf is decreased to 1400 psig,

3. The bottomhole pressure that should be obtained inorder to get a flow rate of 500 STB/day, and


.

45



Day 1 Page 3.24


Factors Affecting PI

1. Phase Behaviour

2. Relative permeability behaviour

3. Oil Viscosity

4. Oil Formation Volume Factor


1. Phase Behaviour

dew point line

bubble point line

2-Phase Regions




Day 1 Page 3.25


2. Relative Permeability

• Defined as the ratio of effective permeability to aparticular fluid (oil,gas or water) to the absolute

ermeabilit of the rock, e. . for oil k ro=ko/k

0.60

0.80

1.00

1.20Kro

Krw


0.00

0.20

0.40

0.00 0.24 0.37 0.49 0.61 0.74 1.00

Oil Rel perm Water Rel Perm

3. Oil Viscosity

O i l V i s c o s

i t y


P b P i



Day 1 Page 3.26


4. Oil formation Volume Factor

Bo


P b

P i

Inflow Performance Relationship

• IPR for two phase flow

– Vogel IPR

2Single phase

– Fetkovich IPR

max,

8.02.01 R

wf

R

wf

o

o

p

p

p

p

qq

n

wf Ro p pC q 22

ow Two phase flow

InverseSlope= PI




Day 1 Page 3.27


Vogel IPR

Bubble Point Pressure, P b


Variable PI (Vogel Behavior)



Vogel IPR

• For cases where well is producing below bubble pointpressure, IPR can be approximated using Vogel’smethod:

2

max

8.02.01

r

wf

r

wf

P

P

P

P

qq

Where:


q = Total Liquid Flow Rate, STB/dq max = Maximum Liquid Rate, STB/d

P r = Average Reservoir Pressure, psig

P wf = Flowing Bottomhole Pressure, psig



Day 1 Page 3.28


Vogel IPR for Undersaturated Reservoir


Constant PI (Linear Behavior)

Bubble Point Pressure, P b

Variable PI (Vogel Behavior)



bwf wf r PPwhenPPPI q

bwf b

wf

b

wf b B PPwhen

P

P

P

Pqqqq

2

max 8.02.01 or

bwf b

wf

b

wf B PPwhen

P

P

P

PPIxPbqq

2

8.02.018.1

Example

Given Data:

– Pr=3500 psi

– Pb=1800 psi

– S=0

– Test data: Q= 320 stbd at Pwf=2900 psi

Generate an IPR




Day 1 Page 3.29


Solution


Skin Effects

Skin effects modelling:• damage,• perforations,• partial penetration,• gravel packs,• fractured wells, and• deviation.




Day 1 Page 3.30


Partial Completion Effects

• Deviation from Pure Radial Flow

• Modelled in the WellFlo as ‘LimitedEntr Skin’

• Partial Completion Effects


Negative Skin Effect – Due to Near Wellbore Permeability Improvement

Reasons for Negative Skin

•Deliberate Stimulation

•Acidizing


•Fracturing•High Shot Density Perforations

•Well Deviation



Day 1 Page 3.31


Transient Pressure Testing of Wells

• The pressure analysis of wells essentially concerns thedynamic relation between the producing rate, the BHPand the reservoir ressure in the vicinit of the well under consideration. Knowledge of this relation from field tests,combined with a realistic model for fluid flow in thereservoir rock surrounding the well, allows parameters of the flow system such as permeability to be established byinference.


• Field tests involve pressure build up followed by pressuredrawdown testing at one or more (stabilised) flow rates.

60

Multi-point Well Testing

• The basic methods used in the multipoint well testing are the‘isochronal’ and ‘flow after flow’ tests.

• The isochronal test involves flowing a well at several rates,interspersed with periods in which the well is shut-in. During the shut-in periods the well is allowed to return to the average pressurecondition. This procedure is repeated for several flow rates.

• The "flow after flow" method consists of flowing a well at a selected


.process is repeated. Usually tests are run for four different flow ratesand then the well is shut-in.

61



Day 1 Page 3.32


Well Testing


Pressure Build up test Pressure Drawdown test

Pressure buildup is followed by pressure drawdown testsat two or more stabilized rates.

End Section.

Inflow Performance




Day 1 Page 3.33


Outflow Performance


Module Contents

• What is Outflow Performance?

• Multiphase Flow in Tubulars

• Multiphase Flow in Flowlines

• Multiphase Flow in Chokes


• Tuning a well model

65



Day 1 Page 3.34


Outflow Performance

• Total Pressure Losses in System:

p p p pPP


Pressure Drop over a pipe segment

Δ Zvout

S stem described b an ener balance ex ressionS stem described b an ener balance ex ression

z p

v in


Mass energy per unit mass in = energy outMass energy per unit mass in = energy out(+(+ -- exchange with surroundings)exchange with surroundings)

Pressure drop conveniently divided into three terms:Pressure drop conveniently divided into three terms:Gravitational or Hydraulic due to gravity effectsGravitational or Hydraulic due to gravity effectsFrictional, andFrictional, andAccelerationalAccelerational due to change in velocity over segmentdue to change in velocity over segment

67



Day 1 Page 3.35


Energy Balance Equation

• The three components of the total pressure loss are given by the following equation:

Dv

f dz

vdvgdzdP

2sin=

2

– hydrostatic: gravitational component

– acceleration: expansion/kinetic component

– friction: irreversible heat loss due to work

– vertical: sin horizontal: sin

whilst hydrostatic and acceleration can be determined analytically, friction has to bedetermined from correlations

r caccc yco a


Pressure Drop over a pipe segment

dzdP

dzdP

dzdP

dzdP

=

accc fricelectotal

onacce era iric ione eva iono a

dzgvdv

Dgv

f gg

dzdP

2

sin=2

= =


, , ,

D = pipe diameter, v = velocity,

f = friction factor, g = gravitational acceleration

gc = gravitational constant.



Day 1 Page 3.36


For multiphase flow, the pressure loss is given bya similar expression, where “m” represents the

ro erties of the mixture determined b an

Multiphase Flow

averaging technique:

To know the quantities of gas and liquid anywhere

accc

mmm

fric

mmm

ele

mctotal dzg

dvv Dg

v f

gg

dzdP

2

sin=2


in the production system, it is necessary to

establish the correct PVT behaviour of the fluid.

70

Relative Contribution of three pressure drop components

• In wells and risers:

– Mostly vertical or inclined flow prevails, the elevation

pressure loss.

– Friction component contributes 10 to 20% of totalloss.

– Acceleration is usually negligible. Ignored in most ofthe calculations, unless velocity differential is


substantial.• In flowlines, friction component contributes most of the

losses.

71



Day 1 Page 3.37


Relative Contribution of three pressure drop components

NEAR SURFACE

NEAR SANDFACE

GRAVITY

FRICTION

ACCELERATION


GRAVITY

FRICTION

ACCELERATION

Mixture Properties

accc

mmm

fric

mmm

ele

mctotal dzg

dvv Dg

v f

gg

dzdP

2

sin=2

• Mixture properties – like density and velocity – in a segment aredetermined by adding liquid and gas properties proportionately to their

)1(

)1(

lgllm

lgllm

H v H vv

H H


re a ve con en w c s ca e o up eno e y .

• Holdup: fraction of a particular fluid present in an interval of pipe.

73



Day 1 Page 3.38


Determination of Friction Factors

• Single phase fluid: f = f( /D, N Re ) – two flow regimes: laminar & turbulent

– NRe accounts for density and viscosity

– Moody chart or single phase correlations

• Multiphase fluids

– averaging of phase properties (accurate PVT)

– multiphase flow correlations

• empirical/mechanistic

• complex flow regimes (bubble/slug/froth/mist/annular…)

• need to be tuned/calibrated to observed data


Friction Component

• Multi-phasefriction factor iscorre a e w atwo-phaseReynolds numberusing Moodydiagram.




Day 1 Page 3.39


Flow Regimes


Vertical Flow: Common Flow Regimes

• Gravity Forces and surface tension cause different physical flow patterns in the pipe.

• Determined experimentally

– Bubble liquid fall back

– ug u e coa esce, e c en p s on sp acemen

– Churn very turbulent, large slugs move up and down

– Annular gas coalesces, liquid up pipe wall

– Mist high gas and liquid rates

• Flow Regime Map can be generated

– gas and liquid superficial velocities

– different regimes in the map will have different equations to calculate friction loss and overallpressure gradient




Day 1 Page 3.40


Multiphase Flow Regimes


Flow Maps

• Dictate flow regime

• Varies between authors

• Required for appropriatecalculation


After Beggs and Brill



Day 1 Page 3.41


Why should we care about flow patterns?

• Class Discussion

– Flow Assurance ???

• Implications on well design

• Flow line design (Flow assurance)

– Artificial Lift design

– Operational considerations


Multiphase Flow Models

• Correlations – Type I – No Flow Pattern, No Slip

• Poettmann & Carpenter (1952)• Baxendell and Thomas 1961• Fancher & Brown (1963)

– Type II – No Flow Pattern; Slip is considered• Hagedorn & Brown (1965)

– Type III – Flow Pattern and Slip considered• Duns & Ros (1963)• Orkiszewski (1967)• Govier and Aziz (1972)• Be s & Brill 1973


• Gray (1978) – Primarily for wet gas well• Mechanistic Models

– Mechanistic (i.e. EPS Mechanistic, Ansari, others) – Proprietary (i.e. Shell, OLGAS, others)

81



Day 1 Page 3.42


Methods for Calculating Pressure Drop

• Empirical formulae (analytical) – e.g. Hazen Williams, single phase (Moody)

– very large length increments

– cannot handle multiphase

• Pressure drop charts

– Gilbert, Brown…ad nauseam

– initially standard methodology for multiphase

– not comprehensive enough and time consuming

• Computational software packages

– ri orous calculation of ressure radients from multi hase flow correlations


– comprehensive: equipment, reservoir and fluid properties

– speed

Flowing Pressure Gradients




Day 1 Page 3.43


• Select fixed variables (fluid and completion geometry) – wellhead pressure

– flow rate

–

Pressure Traverse Calculation

–

– WOR

– GLR

• Select Temperature model

• Select interval (h) for calculation

• Estimate P for selected interval

• Based on PVT, calculate fluid (oil, gas, water) properties, averaged over the


interval

• Determine Pressure Gradient – friction: flow correlations/maps-> slip & holdup

– hydrostatic: from averaged densities/holdups

– acceleration: analytical calculations

Pressure Traverse Calculation

• Calculate “h” from gradient

– compare calculated “h” with actual/initial (h)

– if not equal, select new P and iterate again

• If calculated “h” = actual (h), the P is correct

– add P to P1 at top of interval (e.g. wellhead)

– this yields correct pressure at bottom of interval

– this is then starting pressure P2 at top of next interval

• Restart process from top of the next interval using P2 and a new guess forthe next P

• “ ”


. .





Day 1 Page 3.45


Effect of Increasing GOR on Tubing Pressure Losses


Effect of Increasing Water Cut






Day 1 Page 3.47


Surface and Subsurface Chokes

• Chokes are used

– to maintain a fixed flow rate,

– to protect surface equipment,

– to prevent formation damage, and

– to stabilize the flow.


• In the field, one usually knows the flow through a choke

and one of the pressures of the choke (i.e., thedownstream or upstream pressure).

92

Multiphase Flow through Chokes

• Most flowing wells have some sort of surface choke to:

– Maintain stable pressure downstream for processingequipment

– Maintain sufficient backpressure to prevent sandentry

– Prevent gas and/or water coning

–


– Produce the well/reservoir at the most efficientpossible rate.

93



Day 1 Page 3.48


Chokes: Flow Process

Fluid entersthe choke

P 1, T 1, H 1, S 1Fluid acceleratesthrough the choke


Fluid leaves the chokeP 2(<P 1), T 2, H 2, S 2

Critical Flow Choke Correlations

• Achong , Aussens , Baxendall , Gilbert and Ros ,arecorrelations that are valid only for critical flow

scf/stb.

Subcritical

Critical

F l o w

r a t e


Pressure

A ruleA rule- -of of--thumb for critical flow is that thethumb for critical flow is that thePP UpstreamUpstream / /PP DnStreamDnStream is greater than 2.is greater than 2.



Day 1 Page 3.49


Critical Flow Choke Correlations

• Correlations are based on the general equation:C GLRQ

1

where:

P up is the pressure upstream of the choke

Q 1 is the flow rate of the fluid

Dchoke is the choke inner diameter

Achoke

up D


, , -

96

Correlation A B C

Gilbert 1.89 10.00 0.546

Baxendall 1.93 9.56 0.546

Achong 1.88 3.82 0.65

Ros 2.00 17.40 0.5

Aussens 1.97 3.89 0.68

Choke Models

• Sachdeva ’s choke correlation is used for Multi-phasefluids and is suitable for both critical and non-criticalflow.

• In the limit of single-phase gas, the Sachdeva modeland gas choke model are identical.




Day 1 Page 3.50


End Section.

Outflow Performance


Temperature Modeling




Day 1 Page 3.51


Module Contents

• Why temperature modeling is important?

• Temperature modeling

• Tuning calculated temperature model with measured data


Why Temperature Modeling Is Important?

• Temperature affects in-situ fluid properties that in turnimpacts pressure loss calculations and dependentequ pmen s z ng cons era ons.

– Effect on in-situ fluid properties

• Oil density decreases w/ temperature

• Solution GOR decreases w/ temperature, … … etc.

– Gas lift valve(s) do not pass design/expected gas quantity or


.

– ESPs experience higher gas quantity, insufficient cooling formotor may lead to higher failures

101



Day 1 Page 3.52


Pressure and Temperature profile


Well bore temperature prediction

• Profile based on geothermal temperature gradient

– Useful for well start-up consideration. Considerable underestimation

– ,heats up the tubing, casing and well bore.

where TL = Temperature at (measured) depth L

BHT = Bottom hole temperature

gG = Geothermal gradient

θ = deviation angle

sin Lg BHT T G L


• Linear profile based on (measured) surface and bottomholetemperature

– Rarely well bore temperatures follow this profile. Underestimates.

103

sin L Depth

WHT BHT BHT T L





Day 1 Page 3.54


Wellbore Two-phase Fluid Energy Balance

J pm

f

dLdp

C dLdH

C dL

dT 1Temperature Gradient as a Function of Enthalpy and Pressure gradients

Zero: assumption no flow-work

cem

cowbto

cas

cicoto

anr cins

to

ins

toinsto

t

titoto

f ti

to

wb

wb f m

t ti

f

cc

k r r r

k r r r

hhr r

k r r r

k r r r

hr r

U

T T q

U r dL

dQ

JdL JdLgvdv

J gg

dLdQ

dLdH

/ln/ln/ln/ln1

2

sin

Enthalpy gradient equation

Heat Transfer gradient

Wellbore Heat Transfer Coefficient:


=Temperature of Fluid (tubing) = Depth

= Enthalpy = Mean Heat Capacity of Wellbore fluid= Pressure = Joule-Thompson Coefficient= Heat Transfer = Gravity acceleration= Gravity conversion factor = Mechanical equivalent of heat 778 ft-lb force/BTU= Velocity = Fluid Flow-Work= Inclination Angle from horizontal = radius of (tubing in/out, insulation, casing in/out, wellbore)

= Temperature at Wellbore = Over-all Heat Transfer Coefficient (outside tubing)= Thermal Conductivity (tubing, insulation, casing, cement, formation) = convective Heat transfer coeff. annulus fluid= Convection Heat Transfer Coeff . tubing f luid = radiat ive Heat Transfer Coefficient for annulus

f T pmC H J C

L

pQ g

cg J v f W

r wbT k

tiU

ch

r h f h

Earth

CementAnnulus

Tubing

Radial heat transfer Model

29.02

ln)(

)(

2

sin)(

D

wbti De

wbet

t ti

pmm

pmc J

pmc

e f f

t t f

U r t f k

U k U

U r

C q Awhere

JC gvdv

dLdp

C JC g

g A

T T

dL

dT


wb

Tf …Fluid Temperature – function of Depth and time v….Velocity

A … Relaxation distance ….Thermal Diffusivity

Ut … Over-all Heat Transfer Coefficient t….Time producing/Injecting

Uwb … Heat Transfer Coefficient outside casing T e…Earth or Reservoir Temperature

f D(t)… Dimensionless Transient Heat Conduction time function r wb . Wellbore radius

Cpm … Specific heat of fluid mixture q m ..Mass flowrate

C J … Joule-Thompson coefficient k e…Formation (earth) Thermal conductivity

r ti..Radius Inside Tubing J…Mechanical equivalent of heat 778 ft-lb/BTU

g…Gravity acceleration g c..Gravity conversion factor



Day 1 Page 3.55


Radial heat transfer Model

Once “A” Relaxation distance is calculated,then fluid temperature “T f ” can be

)()1(sin)sin(

'//

),( A Lebh

A LGGet L f eT T e Ag LgT T

Injectionliquid phaseSingles Ramey

e erm ne rom equa ons e ow.

Note: The EQ’s are consideringinjection or production wells.The difference is whenproducing T bh is equal to T r or


)1(.)()1)((sin)sin(

'

///),( A L

J A L

ebh A L

G pmc

Get L f edLdp

C AeT T eg JC g

g A LgT T

injectiongas phaseSingles Ramey

Note: For Gas wells the Joule-Thompson effect is consideredin C J term

Te , then one term drops out.

L….Depthg G..Geothermal GradientTbh .Bottom hole temp.

Temperature models in WellFlo

• WellFlo offers four temperature models:

– Manual model

• . .

• No changes with flow conditions

– Calculated model

– Pressure effects are not included

– Rigorous approach based on Ramey and Willhite’s heat losscorrelations


– Calibrated model -- Recommended

– Same as Calculated model except the relaxation distance is calibratedagainst measured temperature data at a flow rate

– Coupled model

– The most rigorous as takes into account pressure effects

– Joule-Thompson effect is considered109



Day 1 Page 3.56


End Section.

Temperature Modeling


Nodal Analysis




Day 1 Page 3.57


Defining Production Optimization

op· ti· mi· za· tion (Ŏ p ΄tə-m ĭ-zā′ sh ən)

n. The procedure or procedures used to make a system or design as effective orfunctional as possible

• Optimization is not maximization of production always!?


Solutions for High and Low Producers

HighIdentify infill candidatesMaximize productionMinimize intervention expenseFacilities Constraints

ModerateMaximize productionIdentify infill candidatesMinimize cost per barrelManpower constraints


Minimize cost per barrelOPEX/BOEExtend reservoir lifeManpower constraints

Production Rates



Day 1 Page 3.58


Defining Production Optimization

op· ti· mi· za· tion (Ŏ p ΄tə-m ĭ-zā′ sh ən)

n. The procedure or procedures used to make a system or design as effective orfunctional as possible

• Increase Production

– Increase flow rate

– Maximize reservoir production

– Lower mean failure rate


• Lower Costs

– Reduce down times

– Maximize human resource potential

– Doing more with less

114




Day 1 Page 3.59



Optimization Levels

• First level: Individual well performance optimization

– More a question of "maximising" productivity, and notstrictl s eakin an exercise in resource distribution

– Completion, stimulation, artificial lift designs,troubleshooting

• Second Level: Allocation of resources to maximizeproduction from a "group" of wells


– can take into consideration costs as well as revenuein deciding where to allocate resources.

– lift gas allocation, ESP power distribution

117



Day 1 Page 3.60


Optimization Levels

• Third Level: Optimizing overall performance of aproduction system

– u u v upossibilities for revenue generation and differentconstraints present in the production system

– System automation through dynamic modelling linkedto SCADA


I’ve completed my well. Now what?

• How do I know when I’ll need artificial lift?

• Is my artificial lift system optimized?

• Is my completion optimized?

• Is there room to improve my inflow performance?

• When can I expect my gas well to load up?

• When should I abandon this interval and plug back to a


different zone?

119



Day 1 Page 3.61


Harder Questions

• Is the well’s poor performance due to high skin ordecline in local reservoir pressure?

• Will a reduction in Qgi result in a productionincrease?

• If the delivery of one well is enhanced will thiscause a reduction in the delivery of nearby wells?


Oil and Gas system analysis

• Basic principles

– Inflow to any node

res - = node

– Outflow to any node

P sep + ∆ P (Downstream components) = P node

• Conditions

Flow into a node equals flow out of a node


Only one temperature can exist at a node

121



Day 1 Page 3.62


Simple Single-Well System


The Systems Analysis Concept*


* Often called NODAL™ Analysis. Mark of Macco-Schlumberger



Day 1 Page 3.63


The Systems Analysis Concept

1. Select a division point or aNode, and divide productionsystem at this point.

2. Components upstream of anode make Inflow section anddownstream of a node makeOutflow section.

3. Flow into the node equals flowout of the node.

4. Only one pressure can exist at a


NodeComponents DownstreamSep

NodeComponentsUpstream R

PPPOutflow

PPP Inflow

:

:

124

no e.

Systems Analysis On a Graph




Day 1 Page 3.64


0

1000

2000

Pres sure, psig

Inflow and Outflow Performance

3000

4000

5000

6000

7000

8000

9000

D e p

t h ,

f e e

t

4200

4400

4600

4800

5000

5200

F B H P

, p s i g


10000

11000

12000

13000

14000

0 1000 2000 3000 4000 5000

0 1000 2000 3000

Rate, bbls/d

126

“NODAL” Analysis

• Perform pressure drop calculation for a number of different flow rates = generate family of pressure

• Calculate Vertical Lift Performance (VLP) = wellboreflowing pressures for different flow rates against aconstant WHP

• Solve simultaneous equations defined by VLP and


IPR, giving unique solution at selected “solution”node.

• The intersection of the VLP and IPR curves denotesthe “operating” point of the system.



Day 1 Page 3.65


Application of Nodal Analysis

• Sizing

– Tubing

– Flowline

– Surface choke or Subsurface safety valve

– Artificial lift equipment

• Completion design (Gravel pack, perforations)


• Stimulation evaluation

• Surface choke sizing

128

What can Nodal Analysis do for me?

• Predict when well will need artificial lift.

• Predict when gas wells will load up.

• Design artificial lift systems.

• Determine if stimulation will help.

• Determine if completion is optimized.


• Evaluate impact of facilities upgrades/enhancements.

• Predict abandonment pressure.

129



Day 1 Page 3.66


What data will I need?

• Completion data

• Deviation data

• PVT data

• Well test data (Q o, Q w, Q g)

• Wellhead pressure

• Wellhead temperature


• Bottomhole pressure (static and flowing)

• Bottomhole temperature

• IPR data (derived from PTA, openhole logs, etc.)

130

Inflow performance curve




Day 1 Page 3.67


Outflow performance curve


System Plot ( Bottomhole node)

Inflow Curve

Outflow Curve

Operating point




Day 1 Page 3.68


Operating Point

for a given flowrate, drawdown yieldsBHFP much less than required by tubing tolift against WHP: not enough energy

Operating point =stable equilibrium


,BHFP much greater than required bytubing to lift against WHP: too much energy

134

Do I need artificial lift?




Day 1 Page 3.69


Sensitivity Analysis


Performance Curve




Day 1 Page 3.70


Factors affecting production system

Influx Group

• Reservoir pressure

• Productivity index

Efflux Group• Tubing diameter

– Casing diameter

• Fluid properties

• Formation GOR

• Water cut

• Completion parameters

– Perforation size

• Flow line diameter

• Wellhead pressure

• Separator pressure

• Surface, Sub-surface Chokesize


– Perforation density

– Stimulation

•

– Lift gas

• Injection pressure/depth

• Injection gas rate

– ESP Pump size

138

Reservoir Pressure Effect

• Reservoir pressure declines with increased recoverydepending on pressure support mechanism.




Day 1 Page 3.71


Productivity Index Effect

PI = 2.1 STB/d/psi


PI = 1.5 = . 5

Formation GOR Effect




Day 1 Page 3.72


Effect of Water Cut


Effect of Perforation Density




Day 1 Page 3.73


Effect of Tubing Diameter


Effect of wellhead pressure






Day 1 Page 3.75


Completion Data: A01

• vertical well

• 9 5/8” casin shoe

4 1/2”

9000 ft.

• 4.5” (12.75#) tubing shoe@ 9900 ft.

• 7” liner (29#) mid pointerforations ”


10,000 ft

148

7”

Operating Point Sensitivities: Production History

• changes in reservoir pressure

– Drops from 4600 psi to 2400 psi

• changes in water cut

– Increases from 50% to 80%

• skin evolution

• changes in GOR




Day 1 Page 3.76


Reservoir Depletion: Pres = 3600 psig

• no intersection• no operating point


• w• candidate for artificial

lift

Combined Water Cut and Layer Pressure Analysis




Day 1 Page 3.77


Combined Water Cut and Layer Pressure Analysis


Gas Well and Liquid Loading




Day 1 Page 3.78


Liquid Loading Common Symptoms

• Sharp drop in decline curve

• Onset of liquid slugs at the surface

• Increasing difference between flowing tubing and casingpressures

• Sharp gradient changes in the flowing pressure survey


–

154

Sensitivity – Gas Well Unloading

Inflow – Outflow doesnot complete the

picture




Day 1 Page 3.79


Liquid Loading – Turner Velocity

• Drag from the flowing gas tends to lift water droplet, whilegravitational pull tends to push the droplet downwards.


Liquid Loading – Turner Velocity

• Terminal velocity of droplet is given by followingexpression:

11

• When as su erficial velocit is less then the terminal

leman1.593...Co

rner 1.912...Tuwhere

)( 21

k

Cosk v

g

glgc


velocity of droplet, droplets fall and accumulate at thebottom causing the liquid loading.

• Inclination Angle Correction (V’):

157

HorizontalVertical 900



Day 1 Page 3.80


Gas Well Unloading – When does it begin?


Sizing tubing to eliminate loading




End Section.

Nodal Analysis


Documents

RN Day 1- Part 3 Nodal Analysis Theory(Rev3)