Nodal Systems Analysis of Oil and Gas Wells

8/10/2019 Nodal Systems Analysis of Oil and Gas Wells

1/13

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.

1751


2/13

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.

JOURN L OF PETROLEUM TECHNOLOGY


3/13

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.

1753


4/13

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.

JOURNAL OF PETROLEUM TECHNOLOGY


5/13

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


6/13

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


7/13

ii5

c..

x

c..

I

CO

3.0

< .V

'0\'0

2.5

~ - - \ '

t>-v

vt>-


8/13

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.



9/13

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.

1759


10/13

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



11/13

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


12/13

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



13/13

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

Nodal Systems Analysis of Oil and Gas Wells

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