1257705cs22 Introduction to NODAL Analysis 1

8/14/2019 1257705cs22 Introduction to NODAL Analysis 1

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1

Introduction to NODALanalysis





3

Introduction

Prouction !" natural flow #ee for !etter unerstaning of $arious concepts

which efine well performance% Pressure loss occurs in&

the reser$oir the !ottom hole completion the tu!ing or casing the wellhea the flowline the flowline choke pressure losses in the separator an e'port pipeline to

storage



4

Introduction Prouction is generall" limite !" the pressure in the reser$oir

an ifficult to o something a!out it% maor task is to optimise the esign to ma'imise oil an gas

reco$er"%



5

Production Performance

Prouction performance in$ol$es matchingup the following three aspects& Inflow performance of formation flui flow from

formation to the well!ore%

Vertical lift performance as the fluis flow up thetu!ing to surface%

Choke or !ean performance as the fluis flowthrough the restriction at surface%



6

Fluid Flow !roug! Porous "edia

The a!ilit" to etermine the proucti$it" of a reser$oiran the optimum strateg" to ma'imise the reco$er"relies on an unerstaning of the flow characteristicsof the reser$oir an the flui it contains%

The interaction !etween the flui (an its properties)

an the rock (an its properties) Comparison with flow through pipes%

Multiple fluis Surface tension

Capillar" forces



#

Fluid Flow !roug! Porous "edia

The nature of the flui flow Time taken for the pressure change in the reser$oir Flui to migrate from one location to another For an" pressure changes in the reser$oir* it might

take a"s* e$en "ears to manifest themsel$es inother parts of the reser$oir%

Therefore flow regime woul not !e stea" state +arc",s law coul not !e applie Time epenent $aria!les shoul !e e'amine



$

wo P!ase Flow% &ogel's ()uation

2

r

wf

r

wf

ma*o

o +P

P,$-.+

P

P,2-.1

)

)−−=

simplifie solution was offere !" Vogel% -e simulate the PVT

properties an cumulati$e prouction from ifferent wells on computer to

prouce man" IPR cur$es% These were then normalise for pressure an

proucing rate% The cur$es prouce represent man" ifferent epletion

ri$e reser$oir% single cur$e can !e fitte to the ata with the following

e.uation%

This e.uation has !een foun to !e a goo representation of man"

reser$oirs an is wiel" use in the preiction of IPR cur$es for /0phaseflow% lso* it appears to work for water cuts of up to 123%



/

&ogel's ()uation% (*am0le1

bd211+24..$..,$-.+

24..$..,2-.125.+

PP,$-.+

PP,2-.1))

0si$..PFor

bd25.

+24..

1$..,$-.+

24..

1$..,2-.1

1..

+P

P,$-.+

P

P,2-.1

))

0si1$..P

bd1..)

0si24..P

datafollwoingt!egiven0si%$..Pfor )and)Find

22

r

wf

r

wf ma*oo

22

r

wf

r

wf

oma*o

wf

o

r

wf ooma*

= −−×= −−=

=

=−−

=−−

=

=

=

=

=



1.

&ogel's ()uation% (*am0le% ont-

If ot!er values of Pwf

are c!osen% sufficient

)o's can be generated

to 0lot t!e curve% e-g-

Pwf )o

$.. 211

12.. 1#5

16.. 12$

2... 6/

IPR

.

5..

1...

15..

2...

25..

3...

. 1.. 2.. 3..qo

P w f



11

&ogel's ()uation% ombined ingle P!ase Li)uid

and 2P!ase

In t!is case t!ere is a single

0!ase li)uid w!ic! e*ists

above t!e bubble 0oint- elow

t!e bubble 0oint t!e s7stem

becomes 20!ase-

!e figure o00osite s!ows t!e

IP8% w!ic! is a combined

linear&ogel 0lot ,i-e-% straig!t

line above Pb and &ogel

below Pb wit! Pb substitutedfor Pr+-

Pb

Pr

)b )ma*

)

Pwf

traig!t line above Pb

&ogel below Pb



12

&ogel's ()uation% (*am0le2

psia4222 !% psia/122 a% &of Pfor. iii)

P !elowIPR Vogelassuming*. ). i)

&Fin

)5

6(ln

)(4227%8

cp2%97 /%4: 2S

ft2%5r ft/222r ft92h

m62k psia/222P psia6222P

&atafollwoing;i$en the

wf o

!ma'

!

6

o

we

!

ii

r

r B

P P hk q

w

eoo

wfsr o

o

o

r

−−×=

===

======

−

µ

µ



13

(*am0le2% olution

−−=

=+−××

−××××

=−

−×=

−

−

/

ma'

!

6

6

)(7%2)(/%24

P !e"onVogelusing ii)

!</242

)25

6

5%2

/222(ln/%497%2

)/2226222(92624227%8

)

5

6(ln

)(4227%8

&useise.uationinflowraialfore there

point* !u!!lethea!o$ePIgi$ennoisThere i)

r

wf

r

wf

oo

w

eoo

wfsr o

o

P

P

P

P qq

r

r B

P P hk q

µ



14

(*am0le2% olution

bd0si.1-22...3...

2.1.PatPIt!erefore

$-1

PPI+&ogel,)

P

$-1)

P

P6-1

P

2-.)

dP

)dPI PPatand

P

P6-1

P

2-.)

dP

)d

P

P6-1

P

2-.)

dP

)d

PI-t!egivesitateddifferentiis e)uations&ogel9if IP8%t!eof slo0et!eisPIt!et!atmembering8e

b

bma*o

b

ma*o2b

b

b

ma*o

wf

obwf

2

r

wf

r ma*o

wf

o2

r

wf

r ma*o

wf

o

=−

=

×=

=

+===

+=⇒

−

−=



15

(*am0le2% olution

bd35#315632.1.)))

bd1563+2...1....-$,+

2...1...,2-.1))

Pi-e-0si%1...P b-

bd1..5+25..3...,.1-2+PPPI,)

%Pi-e-0si%25..P a-iii+

bd424322332.1.)))

bd2233$-1

2....1-2$-1

PPI)

o,&ogel+bo,total+

2+&ogelma*,o,&ogel+

bwf

wf r

bwf

+vogelma*,b+totalma*,

b+vogelma*,o

=+=+=

= −−=

<=

=−×=−=>=

=+=+=

=×=×=



16

&ogel's ()uation% Problems1:2

IP8t!ePlot

bd0si2PI0si3...P

0si42..P

0si-25..Pfor )and%)%)finddata%followingt!e;sing

2Problem

<<<<<<<<< <<<<<<<<<< <<<<<<<<<< <<<<<<<<<<

0sig1...P bd15.)

0sig16..P 0sig16..P

datafollowingt!efor IP80lotand)Find

1Problem

b

r

wf ma*,total+b

wf o

br

oma*

==

=

=

==

==



1#

Two Phase Flow: Effect of GOR



1$

=on >arc7 Flow

+arc",s law onl" applies to laminar flow situations* a $ali

assumption for the maorit" of oil wells% For gas wells an some $er" high flowrate (light crue) oil

wells* the $olumetric e'pansion as flui approaches the

well!ore is $er" high an this can result in tur!ulent flow%

In such cases* a moifie form of the +arc" e.uation*

known as the Forchheimer e.uation* is use&

2;

?

;

dr

dPβρ+

µ=

The non0+arc" component ue to tur!ulent flow is

normall" hanle as an aitional pressure loss P #+



1/

Productivit7 Inde* ,PI+

Proucti$it" ine' is a measure of the capa!ilit" of a

reser$oir to eli$er fluis to the !ottom of a well!ore%

It relates the surface prouction rate an the pressure rop

across the reser$oir* known as the rawown%

To take into account the effect of the thickness of proucing

inter$al an comparison of $arious wells* the Specific

Proucti$it" Ine' is efine as&



2.

PI For Incom0ressible Flow

PI is constant if µ% and ? remain constant- Plot of Pw

versus )s s!ould be a straig!t line of slo0e @1A% wit!

an interce0t on t!e ordinate a*is of Pe-

PI for emitead7 tate Incom0ressible Flow

+r r ln,6

?!1..$2-#

PP

)

A+PI,

w

e

3

we

s

µ

×

=−==

−



21

Oil Bells Productivit7 Inde*

The Proucti$it" Ine' (PI) is the ratio of prouction to the pressure raw own at the mi0

point of the prouction inter$al

rateflowoilC 0resureflowingP

0resurestaticP PP

CPI

owf

wiwf wi

o

==

=−

=

!e 0roductivit7 inde* is a measure of t!e oil well 0otential or abilit7

to 0roduce and is a commonl7 measured well 0ro0ert7-

PI is e*0ressed eit!er in stocD tanD barrel 0er da7 0er 0si or in

stocD tanD cubic metres 0er da7 0er DPa-



22

Practical determination of PI

The static pressure (Pwi

) is measure !"&

prior to open a new well (after clean up)

after sufficient shut in perio (e'isting wells)

In !oth cases a su!surface pressure gauge is run into

the well

The flowing !ottom hole pressure (Pwf ) is recore

after the well has flowe at a sta!ilise rate for a

sufficient perio (new wells)

prior to shut in for the e'isting wells



23

>ecline of PI at Eig! Flow 8ates

In most wells the proucti$it" ine' remains

constant o$er a wie range of $ariation inflow rate% Therefore* the oil flow rate isirectl" proportional to !ottom hole

pressure raw own%

-owe$er* at high flow rate the linearit" failsan the proucti$it" ine' eclines* whichcoul !e ue to&

40 tur!ulence at high $olumetric flow rates

/0 ecrease in relati$e permea!ilit" ue tothe presence of free gas cause !" the ropin pressure at the well !ore

60 the increase in oil $iscosit" with pressure rop !elow !u!!le point

Flow rate

PI

>rawdown

Co PI



24

(*am0le 1

well !as a s!ut in bottom !ole 0ressure of 23.. 0sia and

0roduces oil at 215 barrelsda7 under a draw down of 5.. 0si-

!e well 0roduces from a formation of 36 feet net 0roductive

t!icDness- B!at is 0roductivit7 inde*% and s0ecific 0roductivit7

inde*G

0ecific 0roductivit7 inde*

Productivit7 Inde* is a function of 0roductive t!icDness ,in fact%t!e lengt! of 0erforation interval+- In order to com0are t!ewells wit! eac! ot!er% t!e s0ecific 0roductivit7 inde* ,PI+s isdefined as

ions+,0erformatHone0a7t!eof lengt!!

+PP,!

C!PI+PI,

wf wi

os

=

−==



25

ubing Performance

The pressure loss in the tu!ing can !e a significant

proportion of the total pressure loss% -owe$er its

calculation is complicate !" the num!er of

phases which ma" e'ist in the tu!ing%

It is possi!le to eri$e a mathematical e'pressionwhich escri!es flui flow in a pipe !" appl"ing

the principle of conser$ation of energ"%

The principle of the conser$ation of energ"e.uates the energ" of flui entering in an e'iting

from a control $olume%



26

Fundamental >erivation of Pi0e Flow ()uation

!e 0rinci0le of t!e conservation of energ7 e)uates

t!e energ7 of fluid entering and e*iting from a controlvolume-



2#

Flow 8egimes in &ertical 2P!ase Flow

s the pressure on a crue oil containing gas in solution is

steail" reuce* free gas is e$ol$e an as a conse.uence* the

li.ui $olume ecreases%

This phenomenon affects the relati$e $olumes of free gas anoil present at each point in the tu!ing of a flowing well%

If the !ottom hole pressure in a well is a!o$e the !u!!le point

of the crue oil* single phase li.ui is present in the lower part

of the tu!ing%



2$

Flow 8egimes in &ertical 2P!ase Flow% ont-

s t!e li)uid moves u0 t!e tubing% t!e0ressure dro0s and gas bubbles begin toform- !is flow regime w!ere gas bubblesare dis0ersed in a continuous li)uidmedium is Dnown as bubble flow-

s t!e fluid moves furt!er u0 t!e tubing%

t!e gas bubbles grow and become morenumerous- !e larger bubbles sli0 u0wardat a !ig!er velocit7 t!an t!e smaller ones%because of t!e buo7anc7 effect-

ingle P!ase

Li)uid Flow

ubble

Flow

lug or Plug

Flow

nnular

Flow

"ist

Flow



2/


stage is reac!ed w!ere t!ese large bubbles e*tendacross almost t!e entire diameter of t!e tubing- s aresult% slugs of oil containing small bubbles arese0arated from eac! ot!er b7 gas 0ocDets t!at occu07t!e entire tubing cross section e*ce0t for a film of oilmoving relativel7 slowl7 along t!e tubing wall- !is islug or Plug Flow-

till !ig!er in t!e tubing% t!e gas 0ocDets ma7 !avegrown and e*0anded to suc! as e*tent t!at t!e7 areable to breaD t!roug! t!e more viscous oil slug- Jasforms a continuous 0!ase near t!e centre of t!e tubing

carr7ing dro0lets of t!e oil u0 wit! it- long t!e walls oft!e tubing t!ere is an u0ward moving oil film- !is is nnular Flow-

ingle P!ase

Li)uid Flow

ubble

Flow

lug or Plug

Flow

nnular

Flow

"ist

Flow



3.


ontinued decrease in 0ressure wit! resultantincrease in gas volume results in a t!inner and t!inneroil film% until finall7 t!e film disa00ears and t!e flowregime becomes a continuous gas 0!ase in w!ic! oildro0lets are carried along wit! t!e gas% i-e-% "ist Flow-

=ot all t!ese flow regimes will occur simultaneousl7 ina single tubing string% but fre)uentl7 2 or 0ossibl7 3ma7 be 0resent-

In addition to flow regimes% t!e viscosit7 of oil and gasand t!eir variation wit! 0ressure and tem0erature%

P& c!aracteristics% flowing bottom !ole 0ressure,EP+% and tubing !ead 0ressure ,EP+ affect t!e0ressure gradient- ingle P!ase

Li)uid Flow

lug or Plug

Flowubble

Flow

nnular

Flow

"ist

Flow





32

Practical 00lication of "ulti0!ase Flow

"ulti0!ase flow correlations could be used for Predict tubing !ead 0ressure ,EP+ at various rates

Predict flowing bottom !ole 0ressure ,EP+ at various rates

>etermine t!e PI of wells

elect correct tubing siHes Predict ma*imum flow rates

Predict w!en a well will die and !ence time for artificial lift

>esign artificial lift a00lications

!e im0ortant variables are tubing diameter% flowrate% gas li)uid

ratio ,JL8+% viscosit7% etc-



33

Li)uidLi)uid Flow

The case of li.ui0li.ui flow in prouction wells ma"

occur in low ;=R wells which prouce water%

Since !oth phases are onl" slightl" compressi!le or

incompressi!le* it woul !e e'pecte that the ph"sical

nature of the flow of an oil0water mi'ture to surface

woul not !e as ramaticall" ifferent from single phaseli.ui flow as the oil0gas s"stem%

If oil an water enter the well!ore from the reser$oir an

flow up the tu!ing to surface* the ph"sical istri!ution of

the phases will epen upon their relati$e $olumetric properties* ie* one phase will !e continuous an the other

isperse%



34

Li)uidLi)uid Flow

>nlike the gas therewill !e little relati$e$olumetric e'pansion

!etween the two phases%

Thus* the ph"sicalistri!ution will !emore epenent onthe ?=R an the

flow $elocit"%



35

Pressure ransverse or Jradient urves

% % K>ifferentubing EeadPressures



36

Pressure ransverse or Jradient urves

7 s!ifting t!e curves

downwards% !e found t!at% fora constant JL8% flowrate andtubing siHe% t!e curvesoverla00ed

!en% a single curve could beutilised to re0resent flow in t!etubing under assumedconditions-

!e im0act was in effect toe*tend t!e de0t! of t!e well b7a lengt! w!ic!% would

dissi0ate t!e tubing !ead0ressure- % % K>ifferent

ubing EeadPressures



3#

Jradient urves

Jilbert was t!en able to

collect all t!e curves for aconstant tubing siHe and

flowrate on one gra0!%

resulting in a series of

gradient curves w!ic!would accommodate a

variet7 of JL8s-

Ee t!en 0re0ared a series

of gradient curves atconstant li)uid 0roduction

rate and tubing siHe-



3$

Jradient urves



3/

Positive or Fi*ed !oDe !is normall7 consists of two

0arts c!oDe w!ic! consists of

a mac!ined !ousing into

w!ic! t!e orifice ca0abilit7

or bean is installed-

bean w!ic! consists of

a s!ort lengt! 16% of t!icD

walled tube wit! a smoot!%

mac!ined bore of s0ecified

siHe-



4.

&alve eat wit! djustable &alve tem

In t!is design% t!e orifice

consists of a valve seatinto w!ic! a valve stemcan be inserted andretracted% t!us adjusting

t!e orifice siHe- !e movement of t!e valve

stem can eit!er be manualor automatic using an!7draulic orelectro!7draulic controller-





42

ritical Flow t!roug! !oDes

8KP2P1

!e value of 8 at t!e

0oint w!ere t!e

0lateau 0roduction

rate is ac!ieved istermed t!e

critical 0ressure ratio

8c-



43

ritical Flow t!roug! !oDes

Critical flow !eha$iour is onl" e'hi!ite !" highl"

compressi!le flui such as gases an gas<li.ui mi'tures% For gas* which is a highl" compressi!le flui* the critical

ownstream pressure Pc is achie$e when $elocit"

through the $ena contracta e.uals the sonic $elocit" this means that a istur!ance in pressure or flow

ownstream of the choke must tra$el at greater than thespee of soun to influence upstream flow conitions%

In general* critical flow conitions will e'ist whenR c@A2%1



44

"ulti0!ase Flow t!roug! a !oDe number of researc!ers !ave 0ublis!ed studies on

multi0!ase flow t!roug! c!oDes- ome of t!e studies relate to correlation of field

measurements-

PE K tubing !ead flowing 0ressure in 0sia

d K constant

8 Kgas li)uid ratio ,"Fbbl+C Koil flowrate ,d+

Kbean siHe in 164

Jilbert ,435 is correct+

c!ong ,8 in Fbbl+



45

"atc!ing t!e Inflow and ubing Performance

"et!od 1 8eservoirand tubing 0ressure loss

convergence in

0redicting bottom!ole

flowing 0ressure



46

Matching the Inflow and Tubing Performance



4#

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1257705cs22 Introduction to NODAL Analysis 1

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