1257705cs22 introduction to nodal analysis 1
TRANSCRIPT
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 1/47
1
Introduction to NODALanalysis
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 2/47
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 3/47
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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 4/47
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"%
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 5/47
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%
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 6/47
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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 7/47
#
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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 8/47
$
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$es for /0phaseflow% lso* it appears to work for water cuts of up to 123%
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 9/47
/
&ogel's ()uation% (*am0le1
bd211+24..$..,$-.+
24..$..,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*
= −−×= −−=
=
=−−
=−−
=
=
=
=
=
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 10/47
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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 11/47
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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 12/47
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$en the
wf o
!ma'
!
6
o
we
!
ii
r
r B
P P hk q
w
eoo
wfsr o
o
o
r
−−×=
===
======
−
µ
µ
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 13/47
13
(*am0le2% olution
−−=
=+−××
−××××
=−
−×=
−
−
/
ma'
!
6
6
)(7%2)(/%24
P !e"onVogelusing ii)
!</242
)25
6
5%2
/222(ln/%497%2
)/2226222(92624227%8
)
5
6(ln
)(4227%8
&useise.uationinflowraialfore there
point* !u!!lethea!o$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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 14/47
14
(*am0le2% olution
bd0si.1-22...3...
2.1.PatPIt!erefore
$-1
PPI+&ogel,)
P
$-1)
P
P6-1
P
2-.)
dP
)dPI PPatand
P
P6-1
P
2-.)
dP
)d
P
P6-1
P
2-.)
dP
)d
PI-t!egivesitateddifferentiis e)uations&ogel9if IP8%t!eof slo0et!eisPIt!et!atmembering8e
b
bma*o
b
ma*o2b
b
b
ma*o
wf
obwf
2
r
wf
r ma*o
wf
o2
r
wf
r ma*o
wf
o
=−
=
×=
=
+===
+=⇒
−
−=
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 15/47
15
(*am0le2% olution
bd35#315632.1.)))
bd1563+2...1....-$,+
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
=+=+=
= −−=
<=
=−×=−=>=
=+=+=
=×=×=
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 16/47
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*
==
=
=
==
==
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 17/47
1#
Two Phase Flow: Effect of GOR
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 18/47
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 $er" high an this can result in tur!ulent flow%
In such cases* a moifie form of the +arc" e.uation*
known as the Forchheimer e.uation* is use&
2;
?
;
dr
dPβρ+
µ=
The non0+arc" component ue to tur!ulent flow is
normall" hanle as an aitional pressure loss P #+
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 19/47
1/
Productivit7 Inde* ,PI+
Proucti$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&
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 20/47
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..$2-#
PP
)
A+PI,
w
e
3
we
s
µ
×
=−==
−
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 21/47
21
Oil Bells Productivit7 Inde*
The Proucti$it" Ine' (PI) is the ratio of prouction to the pressure raw own at the mi0
point of the prouction inter$al
rateflowoilC 0resureflowingP
0resurestaticP PP
CPI
owf
wiwf wi
o
==
=−
=
!e 0roductivit7 inde* is a measure of t!e oil well 0otential or abilit7
to 0roduce and is a commonl7 measured well 0ro0ert7-
PI is e*0ressed eit!er in stocD tanD barrel 0er da7 0er 0si or in
stocD tanD cubic metres 0er da7 0er DPa-
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 22/47
22
Practical determination of PI
The static pressure (Pwi
) is measure !"&
prior to open a new well (after clean up)
after sufficient shut in perio (e'isting wells)
In !oth cases a su!surface pressure gauge is run into
the well
The flowing !ottom hole pressure (Pwf ) is recore
after the well has flowe at a sta!ilise rate for a
sufficient perio (new wells)
prior to shut in for the e'isting wells
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 23/47
23
>ecline of PI at Eig! Flow 8ates
In most wells the proucti$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 $iscosit" with pressure rop !elow !u!!le point
Flow rate
PI
>rawdown
Co PI
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 24/47
24
(*am0le 1
well !as a s!ut in bottom !ole 0ressure of 23.. 0sia and
0roduces oil at 215 barrelsda7 under a draw down of 5.. 0si-
!e well 0roduces from a formation of 36 feet net 0roductive
t!icDness- B!at is 0roductivit7 inde*% and s0ecific 0roductivit7
inde*G
0ecific 0roductivit7 inde*
Productivit7 Inde* is a function of 0roductive t!icDness ,in fact%t!e lengt! of 0erforation interval+- In order to com0are t!ewells wit! eac! ot!er% t!e s0ecific 0roductivit7 inde* ,PI+s isdefined as
ions+,0erformatHone0a7t!eof lengt!!
+PP,!
C!PI+PI,
wf wi
os
=
−==
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 25/47
25
ubing Performance
The pressure loss in the tu!ing can !e a significant
proportion of the total pressure loss% -owe$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 $olume%
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 26/47
26
Fundamental >erivation of Pi0e Flow ()uation
!e 0rinci0le of t!e conservation of energ7 e)uates
t!e energ7 of fluid entering and e*iting from a controlvolume-
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 27/47
2#
Flow 8egimes in &ertical 2P!ase Flow
s the pressure on a crue oil containing gas in solution is
steail" reuce* free gas is e$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%
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 28/47
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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 29/47
2/
Flow 8egimes in &ertical 2P!ase Flow% ont-
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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 30/47
3.
Flow 8egimes in &ertical 2P!ase Flow% ont-
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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 31/47
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 32/47
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-
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 33/47
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 $olumetric properties* ie* one phase will !e continuous an the other
isperse%
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 34/47
34
Li)uidLi)uid Flow
>nlike the gas therewill !e little relati$e$olumetric e'pansion
!etween the two phases%
Thus* the ph"sicalistri!ution will !emore epenent onthe ?=R an the
flow $elocit"%
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 35/47
35
Pressure ransverse or Jradient urves
% % K>ifferentubing EeadPressures
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 36/47
36
Pressure ransverse or Jradient urves
7 s!ifting t!e curves
downwards% !e found t!at% fora constant JL8% flowrate andtubing siHe% t!e curvesoverla00ed
!en% a single curve could beutilised to re0resent flow in t!etubing under assumedconditions-
!e im0act was in effect toe*tend t!e de0t! of t!e well b7a lengt! w!ic!% would
dissi0ate t!e tubing !ead0ressure- % % K>ifferent
ubing EeadPressures
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 37/47
3#
Jradient urves
Jilbert was t!en able to
collect all t!e curves for aconstant tubing siHe and
flowrate on one gra0!%
resulting in a series of
gradient curves w!ic!would accommodate a
variet7 of JL8s-
Ee t!en 0re0ared a series
of gradient curves atconstant li)uid 0roduction
rate and tubing siHe-
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 38/47
3$
Jradient urves
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 39/47
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-
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 40/47
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-
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 41/47
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 42/47
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-
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 43/47
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
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 44/47
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+
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 45/47
45
"atc!ing t!e Inflow and ubing Performance
"et!od 1 8eservoirand tubing 0ressure loss
convergence in
0redicting bottom!ole
flowing 0ressure
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 46/47
46
Matching the Inflow and Tubing Performance
8/14/2019 1257705cs22 Introduction to NODAL Analysis 1
http://slidepdf.com/reader/full/1257705cs22-introduction-to-nodal-analysis-1 47/47
4#