Distinguished Author Series
Nodal Systems Analysis of
Oil and Gas Wells
By Kermit E. Brown, SPE, and James F. Lea, SPE
Kermit E. Brown 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. Lea 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.
Introduction
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 011 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. Althou~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.
1751
llPI
Pr - Pwfs
LOSS IN POROUS MEDIUM
llP2
LlP3
Pwfs-Pwf
LOSS ACROSS COMPLETION
llP4
llP5
llP6
llP7
llPs
PUR - POR
PUSy -POSy
Pwh- Pose
Pose-Psep
Pwf-Pwh
Pwh - Psep
RESTRICTION
=
=
SAFETY VALVE
SURFACE CHOKE
IN
TOTAL LOSS
FLOWLINE
Ir~
TUBING
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 highproductivity 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 BID
[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 BID [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.
JOURNAL OF PETROLEUM TECHNOLOGY
t
t
BHP
BHP
or
or
~P
~P
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 BID [254 m 3Id] 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 BID [318 m 3I 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
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 Gas Wells
A paper presented by Jones et 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.
1753
t
t
BHP
BHP
or
or
~P
~P
RATE
+
RATE
Fig. 4-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.
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.
Pr
=
D
k
h
hp
=
t
t
BHP
BHP
or
or
~P
~P
RATE
+
Fig. 6-Evaluation of various shot densities.
1754
+
4,000 psi [27.6 MPa],
11,000 ft [3352 m] (center of perforations),
= 100 md (permeability to gas),
= 30 ft [9.1 m] (pay interval),
= 20 ft [6.1 m] (perforated interval),
RATE
+
Fig. 7-Gravel pack solution by including Ap completion in
IPR curve.
JOURNAL OF PETROLEUM TECHNOLOGY
:
.
8
DEPTH = 11,000'
Pwh= 1200 PSI
~
if
/.....::5
u;
<"\,
<V'
0..
0..
of
M
M
0
0
)(
2
)(
4
I
III
Pr = 4000 PSI
DEPTH = 11,000'
K = 100 MD
20
2
40
RATE, MMCFD
RATE, MMCFD
Fig. 9-Evaluation of tubing sizes.
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; lO~-in. [27.3-cm]
drilled hole,
'Y g = 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
around the perforation because of unconsolidated
formation-that is, sand flows immediately into all
perforated holes until properly prepacked.
Procedure.
l. The IPR curve is prepared with Darcy's law, and
the additional turbulence pressure drop4 is included
(Fig. 8).
2. Tubing sizes of 2,%, 3V2, and 41/2 in. [7.3, 8.89,
and 11.43 cm] are evaluated at a wellhead pressure of
1,200 psi [8272 kPa], which is needed to flow gas into
the sales line. From analysis of Fig. 9, 41/2-in.
[11.43-cm] tubing is selected. Note that, if market
4
4
3
<\1>-'t-~0
~P
0..
0\~ ~\~
'0~\~ """v
M
0
""
b. \\'2-
)(
0..
0
0..
(f)
0..
2
3
11,000'
DEPTH
Pwh= 1200 PSI
M
0
)(
0..
<l
<l
I
III
-f'
0..
0..
I
III
u;
,,~
6
3
(f)
2
0
0..
DEPTH = 11,000'
Pwh= 1200 PSI
I
III
~P
RATE, MMCFD
Fig. 10-Ap available from sandface to tubing intake.
OCTOBER 1985
RATE, MMCFD
Fig. 11-Ap across gravel pack at 4, 8, 12, and 16 shotslft.
1755
4
4
3
Ci5 3
.0..
(j5
0..
..-
0
0
><
>< 2
0..
<1
2
....
0..
:x:
0
0..
CD
:x:
CD
DEPTH = 11,000'
41/2" TUBING
Pwh = 1200 PSI
00
10
30
40
50
60
70
RATE, MMCFD
RATE, MMCFD
Fig. 12-Completion effects included with IPR-gravelpacked well.
Fig. 13-Effects of wellhead pressure-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 Ap 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 Ap 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
surrounded by a low-permeability zone. They still
incorporate basic concepts suggested by Jones et al. 4
for gravel-packed wells.
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
publications 8-10 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 gravelpacked 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
Example Problem and Procedure for
a Perforated Well
In this section, a sample oil well with a low GOR, a
low bubblepoint pressure, and assumed single-phase
liquid flow across the completion will be analyzed.
The reason for this selection is that current technology
has offered solutions only for single-phase flow (gas or
liquid) across such completions. When two-phase flow
occurs across either a gravel-packed or a standard
perforated well, relative permeability effects must be
considered. Additional turbulence then occurs in
gravel-packed wells and creates more energy losses.
McLeod 7 noted that most of the pressure drop can
occur across a compacted zone at the perforation wall
because of turbulence. He analyzed a gas-well
example and showed that 90% of the total Ap across
the completion, in fact, was caused by turbulence
across the approximately V2-in. [1.27-cm] -thick
compacted zone. (Refs. 3 and 7 provide more details).
To use this technique, the crushed-zone thickness,
e c, the permeability, k co the perforation-tunnel
diameter, d p' and the length, L p' must be known.
Obviously, because of the many input variables
required, the technique can only be approximate and
indicate trends. It is hoped that future research in this
area will lead to more accurate models of pressure
drop through perforations shot in both over- and
underbalanced conditions.
Example Problem.
fir = 3,500 psi [24.1 MPa],
D = 8,000 ft [2438 m],
JOURNAL OF PETROLEUM TECHNOLOGY
~~0
3.0
3.0
" -<,.V
~--\'"
2.5
vt>-<?
2.5
t>-v'
(j)
c..
ii5 2.0
,,' 2.0
c..
"0
x
0
~
x
c.. 1.5
1.5
<l
c..
0
I
CO
DEPTH = 8000'
Pr = 3500 PSI
TUBING 1.0. = 2.992"
'0\'0
c..
1.0
I
CO
DEPTH = 8000'
Pr = 3500'
Pwh = 140 PSI
.5
o
1000
2000
.5
3000
4000
5000
RATE, BID
Fig. 14-IPR and tubing curves for perforated oil well.
36° API [0.84-g/cm 3 ] oil,
Solution GOR = 180 scf/bbl [32 std m 3 1m 3],
80-acre [32.3-ha] spacing,
5V2-in. [13.97-cm] casing,
8 I/2-in. [21.59-cm] hole,
Lp = 4-in. [1O.16-cm] perforation tunnel (see
Table 6 of Ref. 7 for tabulated values),
e c around perforated tunnel = 0.5 in. [1.27 cm],
Pb = 800 psi [5515 kPa],
h = 30 ft [9. 1 m],
hp = 20 ft [6.1 m],
'Yg = 0.7,
T = 180°F [82°C], and
Pwh = 140 psig [965 kPa].
Procedure.
1. Prepare the IPR curve with Darcy's law,
assuming no /lp across the completion.
2. Plot the node outflow curve (tubing intake) for
2%- 2Ys-, and 3V2-in. [6.03-,7.3-, and 8.89-cm]
tubing. This determines the pressure required at the
bottom of tubing for flow through the tubing. Steps 1
(IPR) and 2 (tubing intake) are shown in Fig. 14.
Assume 3 I/2-in. [8.89-cm] tubing is selected.
3. Transfer the /lp curve, as shown in Fig. 15.
4. Using the appropriate equations from McLeod 7
(and as discussed by Brown et al. 3), determine the
/lp's across the completions listed in Table 1.
An analysis of Fig. 16 shows the importance of
perforating underbalanced. Of course, the best fluids
and techniques should be used.
Recognition of Components Causing Restricted
Flow Rates in a Well
Example Problem-Analysis of Flowline Capacity.
The following well is on gas lift.
OCTOBER 1985
1.0
o
1000
RATE, BID
Fig. 15-Transfer for Ap curve-perforated oil well.
D = 8,000 ft [2438 m],
2Ys-in. [7.3-cm] tubing,
Pr = 2,100 psi [14.5 MPa],
35° API [0.85-g/cm 3 ] oil,
50 % water [-y w = 1. 07],
solution GOR=300 scf/bbl [54 std m 3 /m 3 ],
separator pressure =60 psig [413 kPa],
flowline length=4,000 ft [1219 m],
well test: 500 BID [79.5 m 3 Id] at 1,740 psi [12 MPa],
Pb = 2,400 psi [16.6 MPa],
'Yg = 0.7, and
tubing size = 2V2-in. [6.35-cm] ID.
Sufficient gas pressure is available (2,000 psi [13.8
MPa]) to inject gas near the bottom, and a total
gas/liquid ratio of 800 scf/bbl [143 std m 3 /m 3 ] is
maintained for gas lift. The flowline might be
restricting the rate. With nodal analysis, a graphical
solution can be generated quickly at the wellhead
location.
Examination of the results in Fig. 17 indicates that
the flowline is a restriction because the pressure loss in
the flowline (2 I/2-in. [6.35-cm] ID) shows a significant
increase in pressure loss with rate and is angled
sharply upward at the intersection point between the
two curves shown. The intersection point of the
pressure required at the flowline intake and the IPR
pressure minus the pressure drop in the well from
sandface to the wellhead is the point of predicted flow
from the well.
A 3- and 4-in. [7.62- and 1O.16-cm] flowline is then
evaluated on the same plot. As soon as the slope of
the flowline intake pressure vs. rate becomes small
(showing very little increase of /lp with rate), then the
flowline diameter is sufficiently large. The diameter
should not be oversized because additional slugging
and heading may occur. Some operators just add a
1757
TABLE 1-SAMPLE COMPLETIONS FOR PERFORATED OIL WELLS
Shots/Ft
Feet
Perforated
Perforation
Condition
kc as % of
k f Formation
4
20
10
2
8
20
3
4
20
Overbalanced with
filtered salt water
Overbalanced with
salt water
Underbalanced
with
filtered salt water
Underbalanced
with
filtered salt water
Number
4
8
20
Example Problem-Weak Gas Well with
Liquid Production.
P r = 3,200 psi [22 MPa],
30 bbllMMcf [168 X 10 -6 m 3 /m 3 ] condensate,
5 bbllMMcf [28.1 x 10 -6 m 3 1m 3 ] water,
D = 10,000 ft [3048 m],
h = 15 ft [4.57 m],
u;
0...
30
Evaluate 3 1/2-, 2Ys-, 2%-, and Biz-in. [8.89-, 7.3-,
6.35-, and 3.81-cm] tubing (1.66-in. [4.21-cm] ID)
and I-in. [2.5-cm] tubing (1.049-in. [2.66-cm] ID) for
this well.
Note in Fig. 18 that all sizes of tubing are too large
for this particular case except the 1.049-in. [2.66-cm]
-ID tubing. Unstable flow is indicated by the tubing
curves crossing the IPR at a point to the left of the
minimum for the larger tubing. The J .O-in. [2.54-cm]
tubing shows stable flow.
The same type of analysis can be made for oil wells
for various tubing sizes.
500
3.0
2.5
30
320-acre [129-ha] spacing,
T = 200°F [93°C],
k = 0.12 md,
Pwh = 100 psig [689 kPa],
hp = 15 ft [4.57 m],
'Yg = 0.7,
hole size = 8 1/2 in. [21.6 cm], and
no skin effects.
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.
10
DEPTH = 8000'
TUBING I.D. = 2.992"
Pr = 3500 PSI
u;
400
0...
2.0
0
x
0...
Pwh "" 60 PSI
Pr = 2100 PSI
w
1.0
«w
8000'
0...
0
200
I
...J
...J
w
~
.5
RATE, BID
Fig. 16-Production vs. various perforated completions.
1758
(j)
a::
5
co
DEPTH
1.5
<l
0...
I
=
u.i
a::
TUBING I.D. = 2.441"
=>
(j) 300
M
RATE, BID
Fig. 17-Wellhead nodal plot-flowline size effects.
JOURNAL OF PETROLEUM TECHNOLOGY
TABLE 2-AOFP'S FOR HIGHER VALUES OF
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.
n
AOFP
n
(MMscflD)
0.7
0.8
0.85
0.9
1.0
7
38
90
211
1,157
[m 3 /d x 10 -51
2
11
92
60
328
Example Problem. Compare predicted performance to
actual oil well performance.
A closer estimate can be made from
k = 50 md (cores),
kh
(50)(30)
BID
--=------==1.56 - ,
(1,000)(0.8)(1.2)
psi
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 [71°C],
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)
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
[71 0c] with 400 scf/bbl [71 std m 3 1m 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.
JPb
qmax =q b + 1.8
1.5 (2,000)
=1.5 (2,400-2,000)+---1.8
=600+ 1,667
BID
kh=--== 1.5-.
1,000
psi
=2,267 BID.
2.5
30
DEPTH = 10,000'
Pwh = 100 PSI
Pr = 3200 PSI
30 B/MMCFD CONDo
5 B/MMCFD WATER
2.0
en
25
[L
en
~ 1.5
S
x
[L
ffi
20
[L
x
1.0
I
I
I
15
0
[L
I
co 10
w
w r()
>
a: 0w
w a:
0
(f)
.5
5
co
0
[L
I
I
I
o
50
100
150
RATE, MCFD
200
Fig. 18-Tubing-diameter effects-weak gas well.
OCTOBER 1985
250
00
500
1000
1500
2000
2500
RATE, MCFD
Fig. 19-Predicted vs. observed oilwell performance.
1759
3.0
2.5
500
U5 2.0
U5
a..
a..
M
ui 400
a:
=>
en
0
x
a..
I
CD
1.5
[B
--- -
300
a:
a..
1.0
DEPTH = 7000'
TUBING 1.0. = 1.995"
.5
o
~
200
:::l
100
w
= 1.995"
= 7000'
TUBING 1.0.
I
DEPTH
!:
o
500
1000
1500
2000
2500
RATE, BID
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 [121 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 ratesensitive 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 15
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
200
400
600
800
1000
1200
RATE, BID
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. 19 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
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 higherdensity 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.
Nomenclature
Bo
FVF, bbllstb [m 3 /stock-tank m 3 ]
C1
numerical coefficient
dp
perforation-tunnel diameter, in. [cm]
D
depth, ft [m]
ec
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
kf = 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]
qf
liquid flow rate, BID [m 3 /d]
OCTOBER 1985
T
'Y g
'Y w
/-to
=
=
=
=
temperature, OF [0C]
gas gravity (air= 1.0)
water gravity
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.: "Flowing 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 of Artificial 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 Exhibition, Dallas, Sept. 21-24.
6. Bell, W.T.: "Perforating Underbalanced-Evolving Techniques," 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 Formations 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 API 14B, Subsuiface Controlled Safety Valve Sizing
Computer Program, App. B, API, Dallas (June 1974).
12. Vogel, J. V.: "Inflow 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.: "Inflow 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 Productivities," World Oil (May 1968) 99.
16. Dias-Couto, L.E. and Golan, M.: "General 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 Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid 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
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 Vertical 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 Inclined 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
Results," 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 TwoPhase 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 GasFlow 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 Application 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 two-~hase 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 12 procedure below.
1762
The Fetkovich procedure 13 requires a three- or fourflow-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 14 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 16 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. 21 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, P r is
the shut-in reservoir pressure, Pwf 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
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., 30 and Dukler using Eaton's
holdup 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 II for wet gas wells.
SI Metric Conversion Factors
E-Ol
bbl x 1.589 873
E-02
cu ft x 2.831 685
E-Ol
ft x 3.048*
in. x 2.54*
E+OO
psi x 6.895757
E+OO
• Conversion factor is exact.
m3
m3
m
cm
kPa
JPT
Original manuscript (SPE 14714) received in the Society of Petroleum Engineers office Aug. 19. 1985.
1763