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Distinguished uthor Series
Nodal Systems nalysis of
il
and
Gas Wells
By Kermit E. Brown, SPE and James F Lea,
SPE
Kermit E. rown is F.M. Stevenson Professor of Petroleum Engineering at the U of
Tulsa. Since
1966
Brown has served as head of the Petroleum Engineering Dept., vice
president of research, and chairman of the Resources Engineering
Div.
He has conducted
many courses on gas lift, multiphase flow, and inflow performance and served as a
Distinguished Lecturer during 1969-70. Brown holds
a
BS degree in mechanical and
petroleum engineering from Texas A M U and MS and PhD degrees from the
u
of
Texas
both in petroleum engineering. Brown served as the
SPE
faculty advisor for the U
of
Tulsa
student chapter during
1982-83.
He also served on the SPE board during
1969-72, the Education and Professionalism Committee during 1966 67, and the
Education and Accreditation Committee during
1964 66
and was Ba/cones Section
chairman during
1964-65. He is
currently on the Public Service Award Committee.
James F ea is a research associate in the Production Mechanics Group of Amoco
Production Co. in Tulsa . He works on computer implementation of existing design and
analysis methods for artificial lift
and
improved application techniques. Previously,
he
worked with Pratt Whitney Aircraft and Sun Oil Co. and taught engineering science at
the university level. Lea holds BS and MS degrees in mechanical engineering and
a
PhD
degree in thermal/fluid science from Southern Methodist u , Dallas.
Summary
Nodal
l
analysis , defined as a systems approach to the
optimization
of
oil and gas wells, is used to evaluate
thoroughly a complete producing system. Every
component in a producing well
or
all wells in a
producing system can be optimized to achieve the
objective flow rate most economically. All present
components-beginning with the static reservoir
pressure, ending with the separator, and including
inflow performance, as well as flow across the
completion, up the tubing string (including any
downhole restrictions and safety valves), across the
surface choke (if applicable), through horizontal flow
lines, and into the separation facilities are analyzed.
ntroduction
The objectives
of
nodal analysis are as follows.
1 To determine the flow rate at which an existing
oil
or
gas well will produce considering well bore
geometry and completion limitations (first by natural
flow).
2. To determine under what flow conditions (which
may be related to time) a well will load
or
die .
3. To select the most economical time for the
installation of artificial lift and to assist in the selection
of
the optimum lift method .
4. To optimize the system to produce the objective
flow rate most economically.
Copyright t 985 Society of Petroleum Engineers
OCTOBER 1985
5. To check each component in the well system to
determine whether it is restricting the flow rate
unnecessarily.
6. To permit quick recognition by the operator s
management and engineering staff
of
ways to increase
production rates.
There are numerous 11 and gas wells around the
world that have not been optimized to achieve an
objective rate efficiently. In fact, many may have been
completed in such a manner that their maximum
potential rate cannot be achieved. Also, many wells
placed on artificial lift do not achieve the efficiency
they should.
The production optimization
of
oil and gas wells by
nodal systems analysis has contributed to improved
completion techniques, production, and efficiency for
many wells.
l t h o u ~ h
this type
of
analysis was
proposed by Gilbert in 1954, it has been used
extensively in the V S only in the last few years. One
principal reason for this was the changing
of
allowable
producing rates, and another has been the development
of computer technology that allows rapid calculation of
complex algorithms and provides easily understood
data.
Past conservation practices in the
V
S. more
or
less
restricted operators to
2 -
and
2 1 2
-in. [5.08- and
6.35-cm] tubing and 4 shots/ft [13.1 shots/m] for
perforating. The use
of
larger tubing (4 /2 and 5 12 in.
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llPI
P
r
Pwfs
LOSS
IN POROUS
MEDIUM
llP
2
Pwfs Pwf
LOSS
ACROSS COMPLETION
LlP
3
PUR P
R
RESTRICTION
llP4
P
USy
POSy
=
SAFETY
VALVE
llP
5
Pwh Pose =
SURFACE CHOKE
llP
6
Pose Psep
IN FLOWLINE
llP
7
Pwf Pwh
TOTAL LOSS TUBING
llP
s
Pwh
P
sep
FLOWLINE
Fig. 1 Possible pressure losses in
complete
system.
[11.43 and 13.97 cm)) and 16 shots/ft [52.5 shots/mJ
is common today.
Although the increase in flow rates in high
productivity wells has popularized nodal analysis, it is,
nevertheless, an excellent tool for low-rate wells (both
oil and gas) as well as for all artificial lift wells. Some
of
the greatest percentage increases in production rates
have occurred
in
low-rate oil wells (from 10 to 30
ID
[1.59 to 4.77 m
3
/d and low-rate gas wells (from 50
up to 100 to 200
MscflD
[1416 up to 2832 to 5663 std
m
3
/d . Numerous gas wells have needed adjustments
in tubing sizes, surface pressures, etc., to prolong the
onset
of
liquid loading problems. Nodal analysis can
be used to estimate the benefits
of
such changes before
they are made.
One
of
the most important aspects of nodal analysis
is to recognize wells that should be producing at rates
higher than their current rate. Therefore, it can serve
as an excellent tool to verify that a problem exists and
that additional testing is necessary. For example,
assume that a well is producing 320
BID [51
m
3
Id] of
oil. Applying nodal analysis to this well shows that it
is capable
of
producing 510
ID
[81 m
3
I
d]. This
difference may be attributed to several factors, but
nodal analysis can determine which component is
restricting the rate or can determine that incorrect data
are the cause
of
the higher predicted rate. A basic
requirement for well analysis
is
the ability to define
the current inflow performance relationship (IPR)
of
the well. Accurate well test data must be obtained and
the proper IPR applied for successful analysis. Then
1752
models
of
other well components can be used to
complete the predicted well performance.
Fig. 1 shows components that make up a detailed
flowing well system. Beginning with the reservoir and
proceeding to the separator, the components are (1)
reservoir pressure, 2) well productivity, (3) wellbore
completion, (4) tubing string, (5) possible downhole
restrictive device, (6) tubing, (7) safety valve, (8)
tubing, (9) surface choke, (10) flowline, and (11)
separator.
To optimize the system effectively, each component
must be evaluated separately and then as a group to
evaluate the entire well producing system. The effect
of
the change
of anyone
component on the entire
system is very important and can be displayed
graphically with well analysis. Some aspects
of
the
IPR component are covered in Appendix A; discussion
of
multiphase-flow pressure-drop correlations for
pipelines is found in Appendix
B.
The most common positions for nodal analysis
graphical solutions are listed below.
1. At the center
of
the producing interval, at the
bottom
of
the well. This isolates the well s inflow
performance.
2. At the top
of
the well (wellhead). This isolates
the flowline or the effects
of
surface pressure on
production.
3.
Differential pressure solutions t..p) across the
completion interval to evaluate the effect
of
the
number
of
perforations on production in gravel-packed
or standard completion wells.
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t
BHP
or
~
RATE
Fig.
2 Constructed
IPR curve.
4. Solutions at the sepamtor, especially with gas-lift
wells. This isolates the effect
of
sepamtor pressure on
production.
5. Other solution positions for gmphical solution are
at surface chokes, safety valves, tapered string
connection points, and downhole restrictions.
The user must understand how pressure-flow
components of the well are grouped to form a
gmphical solution at a node point. For example, if the
solution
is
plotted at the bottom
of
the well (center
of
completed interval), then the reservoir and the
completion effects can be isolated completely from the
entire piping and production system.
Caution should be taken in neglecting even 200 to
300 ft
[61
to
91
m]
of
casing flow from the center of
the completed interval to the bottom of the tubing.
Because
of
lower velocities, the larger pipe may not be
flushed out with produced fluids. This large section of
pipe still can be nearly full of completion fluids (water
and mud), even though the well may be producing
100 oil. Numerous flowing-pressure surveys have
verified this occurrence. A major company recently
surveyed a well producing 1,600 ID [254 m
3
d] of
oil up
2Ys in.
[7.3-cm] tubing. Because
of
a dogleg,
tubing was set 1,000
ft
[305 m] off bottom in the
1l,000-ft [3353-m] well. Both water and mud were
found in the 7-in. [17.8-cm] casing below the tubing,
even though the well produced 100 oil. Cleaning
this well resulted in an increase of the mte to more
than 2,000
ID
[318 m
3
d] of oil. This points out one
type
of
pmctical limitation
of
nodal analysis when
tubing-pres sure-drop calculations are used to calculate
accumtely a bottornhole flowing pressure (BHFP).
Here, the analysis showed that the mte should be
higher and, hence, served
as
a diagnostic tool that
prompted the running of a pressure tmverse. In many
cases, the analysis predicts what should be expected,
and the opemtor is advised to look for problems if the
well is producing below that prediction.
OCTOBER 1985
t
BHP
or
~
RATE
Fig. 3 Constructed tubing
intake
curve.
Specific Examples
A limited number of examples are presented here;
numerous examples, however, appear in the
litemture.
I
-
5
Two specific subjects have been selected for
example solutions.
1. The effect of the downhole completion on flow
mte is illustmted. An example solution for both a
gmvel-packed well and a standard perfomted well is
presented. Procedures to optimize the completions are
outlined.
2. Quick recognition of those wells with a greater
predicted potential than the present production mte is
covered. These situations may be caused by a
restriction in one
of
the components in the system.
Gravel-Packed Oil and as Wells
A paper presented by Jones t
at 4
seemed to be the
catalyst that started opemtors looking more closely at
their completions. This paper also suggests procedures
for determining whether a well's inflow capability
is
restricted by lack of area open to flow, by skin caused
by
mud infiltmtion, etc.
Ledlow and Gmnger3 have prepared an excellent
summary of background material on gmvel packing,
including details on mechanical running procedures
and selection
of
gmvel size.
The nodal analysis procedure for a gmvel-packed
well, illustmted with a sequence of figures, is
presented here. The appropriate details, additional
references, and equations can be found in Ref. 3.
The following procedure
is
valid for either an oil or
gas well with the solution node at bottornhole.
1.
Prepare the node IPR curve (Fig. 2). (This step
assumes no t p across the completion.)
2. Prepare the node outflow curve (tubing intake
curve in Fig. 3), which is the surface pressure plus the
tubing pressure drop plotted as a function of mte.
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t
HP
or
~
RATE
+
Fig. Transfer Ap.
3. Transfer the differential pressure available
between the node inflow and node outflow curve on
the same plot Fig. 4 to a /lp curve.
4. Using the appropriate equations,3,4 calculate the
pressure drop across the completion for various rates.
Numerous variables have to be considered here,
including shots per foot, gravel permeability, viscosity
and density
of
the fluid, and length
of
the perforation
tunnel for linear flow. Add this /lp curve on Fig. 4,
as
noted in Fig. 5.
5. Evaluate this completion Fig. 5) to determine
whether the objective rate can be achieved with an
accepted differential across the gravel pack. Company
philosophies on accepted /lp values differ. A
reasonable maximum allowable
/lp
that has given
good results ranges from 200 to 300 psi [1379 to 2068
kPa] for single-phase gas or liquid flow. Most
operators will design for smaller
/lp s
for multiphase
flow across the pack.
t
HP
or
~
1754
RATE
+
Fig. 6 Evaluation of
various shot
densities.
t
HP
or
~
RATE +
Fig.
5 Construct
Ap across gravel pack.
6. Evaluate other shot densities or perhaps other
hole sizes until the appropriate
/lp is
obtained at the
objective rate Fig. 6). Perforation efficiency should
be considered at this time. A good review on
perforating techniques, which points out such factors
as
the number of effective holes expected and the
effect of the number of holes and hole sizes on casing
strength, was presented by Bell.
6
7. The
/lp
across the pack can be included in the
IPR curve, as noted in Fig. 7.
Example Problem-Typical Gulf Coast Well With
Gravel Pack. Below
is
a list of given data.
r
= 4 000
psi
[27.6
MPa],
= 11,000 ft [3352 m] center
of
perforations),
k
=
100 md permeability to gas),
h = 30
ft
[9.1
m]
pay interval),
p
= 20
ft
[6.1
m]
perforated interval),
t
HP
or
~
RATE
+
Fig. 7 Gravel pack
solution
by
including
Ap
completion in
IPR curve.
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f)
0..
M
0
)
0..
I
III
3
2
P
r
= 4000 PSI
DEPTH = 11,000
K = 100 MD
20 40
RATE, MMCFD
Fig. 8-IPR
curve for
gas
well-gravel-pack analysis.
40/60-mesh gravel-packed sand,
640-acre [259-ha] spacing,
8 -in. [2l.9-cm] casing;
l O ~ i n .
[27.3-cm]
drilled hole,
Y = 0.65,
screen size
=
5-in. [12.7-cm] OD,
gas-sales-line pressure = 1,200 psi [8273 kPa],
short flowline.
This well is to be gravel packed. The tubing size
and the number
of
shots per foot are to be evaluated
with an underbalanced tubing-conveyed gun. It is
assumed that there is no computable zone restriction
4
u
3
< \ 1 > - t - ~ 0
0..
~ \ ~
M
0 ~ \ ~ v
b. \\'2-
)
0..
2
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4
3
(j5
0..
-
0
>
2
0..
x
CD
DEPTH =
11,000
41/2 TUBING
Pwh
= 1200 PSI
00
10
30
40
50 60 70
RATE
MMCFD
Fig. 12-Completion effects included
with
IPR-gravel
packed well.
conditions permitted, much higher rates could be
projected with adequate sand control.
3. The
Ap
is transferred, as noted in Fig. 10. This is
the Ap available across the gravel pack.
4. The p across the pack for 0.75-in. [1.905-cm]
-diameter holes with 4, 8, 12, and 16 effective shots/ft
[13.12, 26.2, 39.4, and 52.5 effective shots/m] (Fig.
11) should be calculated with Jones
et al
s equations
or with modifications of these equations adjusted to fit
field data.
5. Figs.
11
and
12
show the final two plots
indicating that 16 shots/ft [52.5 shots/m] are necessary
to obtain a Ap
of
about 300 psi [2068 kPa] at a rate o f
58.5 MMscfID [1.7XI0
6
std m
3
/d]. Additional
perforations could bring this Ap below 200 psi
[1379 kPa].
6. To bring this well on production properly, one
more plot (such as Fig. 13) should be made with
several wellhead pressures so that p across the pack
can be watched through the observation
of
rate and
wellhead pressure. This procedure is described by
Crouch and Pack
5
and Brown
et al
3
Nodal Analysis To Evaluate a Standard
Perforated Well
In 1983 McLeod
7
published a paper that prompted
operators to examine completion practices on normally
perforated wells. Although numerous prior
publications8-10 discussed this topic and companies
had evaluated the problem, this paper sparked new
interest. A modification of this procedure is presented
in Ref. 3.
The procedure is similar to that offered for gravel
packed wells, except that the equations used for the
calculation of pressure drop across the completion
have been altered to model flow through a perforation
1756
4
Ci5
3
0..
-
0
>
0..
2
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ii5
c..
x
c..
I
CO
3.0
< .V
'0\'0
2.5
~ - - \ '
t>-v
vt>-
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TABLE 1 SAMPLE COMPLETIONS FOR PERFORATED OIL WELLS
Feet
Number
Shots/Ft Perforated
4
20
2
8
20
3
4
20
4
8
20
parallel line instead of replacing the current line with a
larger size.
Restriction Caused by Incorrect Tubing Size. The
tubing may be either too large (causing unstable flow)
or
too small (reducing flow rate). This can be
recognized immediately on a nodal plot and is as
important in high-rate gas lift wells as in low-rate gas
wells.
A weak gas well is chosen to show how to
determine when the tubing is too large and to predict
when loading will occur. The Gray 11 correlation
is
recommended for use in the calculation of tubing
pressure drops in gas wells that produce some liquids.
Example
Problem Weak
Gas Well with
Liquid Production.
u;
0...
M
0
x
0...
300
j)
Pwh
60
PSI
j)
w Pr
=
2100
PSI
a
0...
0
200
w
I
...J
...J
w
RATE,
BID
Fig. 17 Wellhead
nodal
plot flowline size effects.
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Well Inflow
and
Completion Restrictions.
It
is very
important for operators, engineers, and managers to
recognize inflow restrictions immediately. Some
companies have arranged their computerized well
records to do such things as call up a group
of
wells in
one field in descending-kh-value order. In addition, all
other available pertinent information, including the
latest test data, can also be printed out.
Example Problem. Compare predicted performance to
actual oil well performance.
k = 50
md (cores),
h = 30 ft [9.14 m] (logs),
35
API
[0.85-g/cm
3
]
oil,
casing = 7 in. [17.78 cm],
tubing
= 2
in.
[6.1
cm],
D = 7,000
ft
[2134 m],
Y g = 0.65,
T = 170
0
P [71C]
Pr =
estimated
2,400
psi
[16.5
MPa], and
Pwh = 250 psi [1723 kPa].
The latest well test shows this well producing 600
BID [95 m
3
Id]
oil (no water) with a GOR
of 400
scf/bbl [71.2 std m
3
/m
3
] (natural flow).
Determine whether this well is producing near its
capacity.
It
is the engineer s responsibility to recognize
this well s potential quickly and to recommend
additional testing, a workover, a change in tubing, or
other action.
A very quick estimate
of
the productivity index can
be estimated from the product kh in darcy-feet.
50 30) BID
k h = = =
1.5 .
2.5
2.0
n
[L
1.5
x
[L
i 1.0
.5
o
1,000 psi
DEPTH = 10,000
Pwh = 100 PSI
Pr = 3200 PSI
30 B/MMCFD
CONDo
5 B/MMCFD
WATER
50
100 150 200
RATE MCFD
Fig.
18
Tubing-diameter
effects-weak
gas well.
OCTOBER 1985
250
TABLE 2-AOFP S FOR HIGHER
VALUES OF
n
n
0.7
0.8
0.85
0.9
1.0
(MMscflD)
7
38
90
211
1,157
AOFP
[m
3
/d x 10 -51
2
11
92
60
328
A closer estimate can be made from
50) 30) BID
= ==1.56 -
kh
(1,000)(0.8)(1.2)
psi
but it requires that P o and Bo are known. One can
recognize that a
35
API
[0.85-g/cm
3
]
crude at
170
0
P
[7 0c] with 400 scf/bbl [71 std m
3
m
3] in solution
will have a viscosity less than 1 and that the product
P oB 0
will be close to
1.
Heavy crudes,
of
course, will
have high viscosities, and a larger value must be used
in estimating the productivity index.
Also, a reasonable estimate at lower pressures
is
that
about 500 psi [3447 kPa] is required to place 100
scf/bbl
[17.8
std
m
3
/m
3
]
in solution giving a
bubblepoint pressure, Pb
of
2,000 psi [13.8 MPa].
Standing s 14 correlation shows the
P
b to be very close
to 2,000 psi [13.8 MPa] for these conditions. This
permits a quick calculation of the maximum flow rate.
n
[L
S
x
[L
I
co
JPb
qmax q
b
+
1.8
30
25
20
15
10
5
00
1.5 (2,000)
=1.5
2 , 400 - 2 , 0 00 + - - --
1.8
=600 1,667
=2 267
BID.
I
I
I
0
0
w
r
w
)
>
0
:
w
w
( f )
a:
co
[L
0
I
I
I
500 1000
1500
RATE
MCFD
2000
2500
Fig.
19-Predicted
vs. observed oilwell performance.
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3.0
2.5
U
2.0
a
M
0
1.5
x
a
I
D
1.0
.5
o
DEPTH
=
7000'
TUBING 1.0.
=
1.995
500 1000
1500
RATE ID
2000
2500
Fig. 20 Wellhead pressure effects
on
rate nodal
plot.
The IPR curve can be drawn quickly and the tubing
curve imposed on the sample plot (Fig. 19). The
intersection shows a rate
of
760 BID [ 2 m
3
/d]
of
oil.
The question
of
whether this well is worth spending
sufficient money to determine why the rate is less than
the predicted rate now arises. The source
of
error
could be with two bits
of
information. Is the
permeability
of
50 md (obtained from cores) correct?
Is there a completion problem? For this well, the
possibility
of
additional production justifies the
expenditure to run a buildup test to verify kh/ J.I .oB 0
and to check for skin. A high skin may indicate that
further testing is needed to determine whether a rate
sensitive skin exists to decide whether stimulation or
reperforating is required.
Restricted Gas Well
Many operators fail to recognize the significance
of
the exponent n for gas-well IPR equations obtained
from four-point tests. It is common to see exponents
of
0.7 to 0.8 or less in gas wells. For example, the
following equation was obtained from a U.S. gulf
coast well after data were plotted on log-log paper.
q
gsc
=0.0463[(5,000)2
p
w/]
0.7
Mcf/d.
The operator
of
this well had a market
of
5
MMscf/D [424
x
10-
3
std m
3
/d]. Note that this well
has an absolute 0j en-flow potential (AOFP) of 6,984
Mcf/D
[198xlO
m
3
/d]. See Table 2 for AOFP s for
higher values
of n
Obviously, this well has a serious completion
restriction. Sufficient data are already available to plot
in
the form suggested by Jones et at
4
They suggested
plotting Pr
2
-Pw/)/qgsc
on the ordinate vs. qgsc on
the abscissa to evaluate the need for opening more
1760
U
a
500
ui
400
a:
=>
en
[B 300
a:
a
o 200
I
l 100
w
:
---
-
TUBING 1.0.
=
1.995
DEPTH = 7000'
200 400
600
RATE ID
800 1000 1200
Fig. 21 Production vs. wellhead pressure.
area to flow than to stimulation. Refs. 3 and 4 provide
more details on this procedure.
Effects of Wellhead And Separator Pressure
Specific cases
of
gas wells and gas-lift oil wells may
be influenced significantly by changes
in
separator
pressure and/or wellhead pressure.
A good plot for both oil and gas wells
is
a
deliverability plot
of
wellhead pressure vs. rate and, in
tum, separator pressure vs. rate. This plot also can
show the loading or critical rate and offers immediate
selection
of
rates based on wellhead pressures. The
sample data used to construct Fig.
9
are used to
construct Fig. 20 at various wellhead pressures. From
this graph, data are used to construct Fig. 21, which
demonstrates the well response as a function of surface
pressure.
Summary
and
Conclusions
Nodal analysis
is
an excellent tool for optimizing the
objective flow rate on both oil and gas wells. A
common misconception is that often there are
insufficient data to use this analysis. This is true
in
some cases, but many amazing improvements have
been made with very
few
data. The use
of
nodal
analysis has also prompted the obtaining
of
additional
data
by
proper testing
of
numerous wells.
Another common statement is that there
is
too much
error involved
in
the various multiphase-flow tubing
or
flowline correlations, completion formulas, etc., to
obtain meaningful results. Because
of
these possible
errors, it is sometimes difficult to get a predictive
nodal plot to intersect at exactly the same production
rate
of
the actual well. Even if current conditions
cannot be matched exactly, however, the analysis can
show a percentage increase in production with a
change, for instance, in wellhead pressure. These
JOURNAL OF PETROLEUM TECHNOLOGY
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predicted possible increases often are fairly accurate
even without an exact match to existing flow rates.
Two detailed illustrations are given
in
this paper to
show the effect
of
perforation shot density in both
gravel-packed and standard perforated wells on
production.
Nodal analysis has completely altered perforation
philosophy in the U.S. and has encouraged higher
density perforating and use
of
open-hole completions
when practical. One of the most important aspects
of
nodal analysis is that it offers engineers and managers
a tool to recognize quickly those components that are
restricting production rates.
Although not discussed in this paper, nodal analysis
is used to optimize all artificial lift methods.
3
Rate
predictions, along with horsepower requirements for
all lift methods, can be predicted, thereby permitting
easier selection
of
lift methods.
Finally, some very complex network systems, such
as ocean-floor gas-lift fields (including gas allocation
to maximize rates) and most economical gas rates, can
be predicted with this procedure.
Nodal analysis, however, should not be used
indiscriminately without the recognition
of
the
significance
of
all plots and the meaning
of
each
relationship. Engineers should be trained to understand
the assumptions that were used in developing the
various mathematical models to describe well
components. Also, recognizing obvious error and
using practical judgment are necessary. Experience in
different operating areas can indicate the accuracy to
be expected from various correlations used
in
nodal
analysis well models.
omenclature
Bo
FVF, bbllstb [m
3
/stock-tank m
3
]
C
1
numerical coefficient
d
p
perforation-tunnel diameter, in. [cm]
D
depth,
ft
[m]
e
c
crushed-cone thickness, in. [cm]
h height of pay interval,
ft
[m]
hp
height
of
interval perforated,
ft [m]
J = productivity index, BID/psi [m
3
/d/kPa]
k = permeability
kc
= permeability
of
crushed zone around
perforation, md
k
f
= formation permeability, md
Lp
= length
of
perforation tunnel, in. [cm]
P
= pressure, psi [kPa]
Pb = bubblepoint pressure, psi [kPa]
P r
= reservoir pressure, psi [kPa]
Pwf = BHFP, psi [kPa]
Pwh
= wellhead pressure, psi [kPa]
f:J p
pressure difference, psi [kPa]
qb flow rate at the bubblepoint, MscflD [10
3
std m
3
/d]
qrnax
maximum flow rate, B/D [m
3
/d]
q liquid flow rate,
BID
[m
3
/d]
OCTOBER 1985
T
= temperature,
OF [0C]
Y g
= gas gravity
(air=
1.0)
Y
w = water gravity
/ to
= oil viscosity, cp
[Pa' s]
References
1
Mach, J., Proano, E., and Brown, K.E.:
A
Nodal Approach for
Applying Systems Analysis to the Flowing and Artificial Lift Oil
or Gas Well, paper SPE 8025 available at SPE, Richardson, TX.
2. Gilbert, W.E.: Flowi ng and Gas-Lift Well Performance, Drill.
and Prod. Prac. API (1954) 126-43.
3. Brown, K.E.
et al.:
Production Optimization of Oil and Gas
Wells by Nodal Systems Analysis, Technology ofArtificial Lift
Methods
PennWeli Publishing Co., Tulsa (1984) 4.
4. Jones, L.G. Blount, E.M., and Glaze, C.E.: Use of Short Term
Multiple Rate Flow Tests to Predict Performance of Wells Having
Turbulence, paper SPE 6133 presented at the 1976 SPE Annual
Technical Conference and Exhibition, New Orleans, Oct. 3-6.
5. Crouch, E.C. and Pack, K.J.: Systems Analysis Use for the
Design and Evaluation of High-Rate Gas Wells, paper SPE 9424
presented at the 1980 SPE Annual Technical Conference and Ex
hibition, Dallas, Sept. 21-24.
6. Bell, W.T.: Perforating Underbalanced-Evolving Tech
niques,
J
Pet. Tech. (Oct. 1984) 1653-62.
7. McLeod, H. O. Jr.: The Effect of Perforating Conditions on Well
Performance, J
Pet. Tech.
(Jan. 1983) 31-39.
8
Locke, S.: An Advanced Method for Predicting the Productivity
Ratio of a Perforated
Well,
J Pet. Tech. (Dec. 1981) 2481-88.
9. Hong, K.C.: Productivity
of
Perforated Completions in Forma
tions With or Without Damage,
J
Pet. Tech. (Aug. 1975)
1027-38; Trans. AIME, 259.
10 Klotz, J.A., Krueger, R.F., and Pye, D.S.: Effect
of
Perforation
Damage on Well Productivity,
J
Pet. Tech. (Nov. 1974)
1303-14; Trans. AIME, 257.
11 Gray, H.E.: Vertical Flow Correlation
in
Gas Wells, User
Manual
for PI 14B
Subsuiface Controlled Safety Valve Sizing
Computer Program App. B, API, Dallas (June 1974).
12. Vogel, J. V.: Inf low Performance Relationships for Solution-Gas
Drive Wells, J Pet. Tech. (Jan. 1968) 83-92; Trans. AIME,
243.
13 Fetkovich, M.J.:
The
Isochronal Testing of Oil Wells, paper
SPE 4529 presented at the 1973 SPE Annual Meeting, Las Vegas,
Sept. 30-0ct. 3.
14 Standing, M.B.: Inf low Performance Relationships for Damaged
Wells Producing by Solution-Gas Drive, J. Pet. Tech. (Nov.
1970) 1399-1400.
15 Eickmeier, J.R.:
How
to Accurately Predict Future Well Pro
ductivities, World Oil (May 1968) 99.
16 Dias-Couto, L.E. and Golan, M.: Genera l Inflow Performance
Relationship for Solution-Gas Reservoir Wells,
J
Pet. Tech.
(Feb. 1982) 285-88.
17. Uhri, D.C. and Blount, E.M.: Pivot Point Method Quickly
Predicts Well Performance, World Oil (May 1982) 153-64.
18 Agarwal, R.G., AI-Hussainy, F., and Ramey, H.J. Jf.: An In
vestigation of Wellbore Storage and Skin Effect
in
Unsteady Liq
uid Flow: 1 Analytical Treatment, Soc. Pet. Eng.
J
(Sept.
1970) 279-90;
Trans.
AIME, 249.
19. Agarwal, R.G., Carter,
R.D.,
and Pollock, c B : Evaluation
and Performance Prediction of Low-Permeability Gas Wells
Stimulated by Massive Hydraulic Fracture,
J.
Pet. Tech. (March
1979) 362-72; Trans. AIME, 267.
20. Lea, J.F.: Avoid Premature Liquid Loading in Tight Gas Wells
by Using Prefrac and Postfrac Test
Data,
Oil and Gas
J
(Sept.
20, 1982) 123.
21. Meng, H.
et al.:
Production Systems Analysis of Vertically
Fractured Wells, paper SPE/DOE 10842 presented at the 1982
SPEIDOE Unconventional Gas Recovery Symposium, Pittsburgh,
May 16-18.
22. Greene, W.R.: Analyzing the Performance of Gas Wells,
Proc. 1978 Southwestern Petroleum Short Course, Lubbock, TX
(April 20-21) 129-35.
1761
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23. Hagedorn, A.R. and Brown, K.E.: Experimental Study of
Pressure Gradients Occuning During Continuous Two-Phase
Flow in Small-Diameter Vertical Conduits,
J Pet Tech
(April
1965) 475-84;
Trans
AIME, 234.
24. Duns, H. Jr. and Ros, N.C.J.: Vertical Flow
of
Gas and Liquid
Mixtures in
Wells,
Proc. Sixth World Pet. Congo (1963) 451.
25. Orkiszewski, J.: Predicting Two-Phase Pressure Drops in Ver
tical
Pipes, J
Pet Tech (June 1967) 829-38; Trans. AIME,
240.
26. Beggs, H.D. and Brill, J.P.:
A
Study
of
Two-Phase Flow in In
clined Pipes,
J
Pet
Tech
(May 1973) 607-14; Trans. AIME,
255.
27. Aziz, K., Govier,
G.W., and Fogararasi, M.: Pressure Drop in
Wells Producing Oil and Gas,
J Cdn
Pet Tech (July-Sept.
1972), 38-48
28. Dukler, A.E. et al.: Gas-Liquid Flow in Pipelines, 1. Research
Result s, AGA-API Project NX-28 (May 1969).
29. Dukler, A.E. and Hubbard, M.G.:
A
Model for Gas-Liquid Slug
Flow in Horizontal and Near Horizontal Tubes,
Ind
and Eng
Chern (1975) 14, No.4, 337-47.
30. Eaton, B.A.
et al.: The
Prediction
of
Flow Patterns, Liquid
Holdup and Pressure Losses Occuning During Continuous Two
Phase Flow In Horizontal Pipelines,
J Pet Tech
(June 1967)
815-28; Trans.
AIME, 240.
31. Cullender, M.H. and Smith, R.V.: Practical Solution
of
Gas
Flow Equations for Wells and Pipelines with Large Temperature
Gradients,
J Pet Tech
(Dec. 1956) 281-87;
Trans.
AIME,
207.
32. Poettmann, F.H. and Carpenter, P.G.:
The
Multiphase Flow
of
Gas, Oil and Water Through Vertical Flow String with Applica
tion to the Design of Gas-Lift Installations, Drill. and Prod
Prac. API (1952) 257-317.
APPENDIX A
Inflow
Performance
Inflow perfonnance is the ability of a well to give up
fluids to the wellbore per unit drawdown. For flowing
and gas-lift wells, it
is
plotted nonnally
as
stock-tank
barrels of liquid per day (abscissa) vs. bottomhole
pressure (BHP) opposite the center
of
the completed
interval (ordinate). The total volumetric flow rate,
including free gas, can also be found with production
values and PVT data to calculate, for instance, a total
volume into a pump.
Brown et al. has given detailed example problems
for most methods
of
constructing IPR curves. Nothing,
however, replaces good test data, and many
procedures, in fact, do require from one to four
different test points-that is, a stabilized rate and
corresponding BHFP, as well as the static BHP, are
usually a minimum requirement for establishing a
good IPR.
IPR Methods for Oil Wells
For flowing pressure above the bubblepoint, test to
find the productivity index, or calculate the
productivity index from Darcy's law.
For t w o ~ h a s e flow in a reservoir, apply Vogel's
procedure 1 or Darcy's law using relative
penneability data.
For reservoir pressure greater than bubblepoint
Pr
>Pb) and BHFP above or below the bubblepoint,
use a combination
of
a straight-line productivity index
above Pb and Vogel's
2
procedure below.
1762
The Fetkovich procedure
13
requires a three- or four
flow-rate test plotted on log-log paper to detennine an
equation in the fonn
of
a gas-well backpressure
equation with a coefficient and exponent detennined
from plotted data. This is equivalent to analysis
of
an
oil well with gas well relationships.
Standing's
4
extension of Vogel's work accounts for
flow-efficiency values other than 1.00. Jones
et al.
's4
procedure will detennine whether sufficient area is
open
to
flow.
Future IPR Curves
The prediction of future IPR curves is critical in
detennining when a well will die or will load up or
when it should be placed on artificial lift. The
following procedures can be used: (1) Fetkovich
13
procedure,
(2)
combination of Fetkovich and Vogel's
equation,13 (3) Couto's 6 procedure, and the (4) pivot
point method. 17
Transient IPR
Curves
Oil
or
Gas
Wells. A time element allowing the
construction of IPR curves for transient conditions can
be brought into Darcy's law. This is important in
some wells because of the long stabilization time. (See
Ref. 3 for discussions by several authors.)
Fractured Oil and Gas Wells. The construction of
IPR curves for fractured oil or gas wells has been
treated in the literature by Agarwal et
ai.
18 19 Lea, 20
and Meng.
2
Fractured wells can show flush
production initially but drop off considerably in rate at
future times.
IPR
Methods
For
Gas
Wells. Generally, a three-
or
four-flow-rate test is required for a gas well from
which a plot
is
made on log-log paper and the
appropriate equation derived.
where q
is
the rate of flow, C 1 is a numerical
coefficient, characteristic
of
the particular well, r is
the shut-in reservoir pressure, wf is the BHFP, and n
is a numerical exponent that is characteristic
of
the
particular well. (See Ref.
22
for a discussion on gas
well perfonnance). Also, Darcy's law can be used,
and the turbulence tenns should always be included
6
for all but the lowest rates.
Fractured and transient wells have also been treated
in the literature.
APPENDIX B
Multiphase Flow Correlations
The use of multiphase-flow-pipeline pressure-drop
correlations
is
very important in applying nodal
analysis.
The correlations that are most widely used at the
present time for vertical multiphase flow were
JOURNAL OF PETROLEUM TECHNOLOGY
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developed by Hagedorn and Brown,23 Duns and
Ros,24 Ros modification (Shell Oil Co., unpublished),
Orkizewski,25 Beggs and Brill,26 and Aziz.27 These
correlations calculate pressure drop very well in certain
wells and fields. However, one may be much better
than the other under certain conditions, and field
pressure surveys are the only way to find out. Without
knowledge
of
a particular field, we would recommend
beginning work with the correlations listed in the
above order.
Horizontal MultiJ>hase-Flow Pipeline Correlations.
Beggs and Brill,2 Dukler et al. 28 Dukler and
Hubbard,29 Eaton
et aI.
3 and Dukler using Eaton s
hold
up
28 30
are the best horizontal-flow correlations.
Again, we recommend to begin work using them
in
the order given.
OCTOBER
1985
Vertical Gas Flow. The procedures by Cullender and
Smith 31 and Poettmann and Carpenter
32
are
recommended for gas-flow calculations in wells.
Wet Gas Wells.
We recommend the Gray
correlation for wet gas wells.
SI Metric Conversion Factors
bbl
x
1.589 873
E Ol
cu
t
x
2.831 685
E 02
t
x
3.048*
E Ol
in.
x
2.54* E+OO
psi x
6.895757
E+OO
Conversion fac tor is exact.
m
3
m
3
m
cm
kPa
JPT
Original manuscript SPE 14714) received in the Society of Petroleum Engineers of-
fice Aug.
19. 1985.
1763