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A New Correlation for Calculating Wellhead

Production Considering Influences of

Temperature, GOR, and Water-Cut for

Artificially Lifted Wells

Article · January 2007

DOI: 10.2523/11101-MS

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IPTC 11101

A New Correlation for Calculating Wellhead Production Considering Influences of Temperature, GOR, and Water-Cut for Artificially Lifted Wells

Mohamed Ghareeb, Lufkin-Industries, Maadi, Cairo, Egypt.

Shedid A. Shedid, Teaxs A & M University, Doha P. O. Box 23874, Qatar.

Copyright 2007, International Petroleum Technology Conference

This paper was prepared for presentation at the International Petroleum Technology Conference held in Dubai, U.A.E., 4–6 December 2007.

This paper was selected for presentation by an IPTC Programme Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the International Petroleum Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the International Petroleum Technology Conference, its officers, or members. Papers presented at IPTC are subject to publication review by Sponsor Society Committees of IPTC. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the International Petroleum Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, IPTC, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract

Several classical wellhead production correlations have been

developed and widely used all over the world for naturally

flowing wells. For artificially flowing wells, many important

well and fluid parameters are ignored in these correlations.

This results in erroneous results and inaccurate predictions

when these correlations are applied. These current correlations

are mainly function of tubing head pressure, bean size (which

has almost no effect for artificially flowing wells), and gas-

liquid ratio only.

The man objective of this study is to ovecome the limitations

of these correlations for artificially flowing wells by

development a new correlation capable to predict accurately

the wellhead flow production. The new correlation was

developed using a set of 1,750 data points from 352 producing

wells in Egypt. The newly-developed correlation includes

several parameters of tubing size, wellhead and bottom-hole

temperatures, producing gas-oil ratio, pay zone depth, and

water cut. A sensitivity analysis using the newly-developed

correlation about the influences of involved well and reservoir

parameters, is carried out.

The results indicated that the newly-developed correlation is

capable to predict the wellhead production rate accurately.

Noteworthy, the variation of producing depth, tubing size and

wellhead temperature has real impact on production rate while

variation in bottom-hole temperature, water-cut and gas-oil

ratio has relatively smaller effect on well production rate.

The enhanced prediction of production rate using the new

correlation is attributed to its consideration to many other

parameters, which were ignored before in Gilbert and other’s

correlations; such as tubing size, wellhead temperatures, and

pay zone depth.

1. Introduction and Literature Review

The separator and multiphase meters have been considered

and used to determine the oil well production. This has been

considered as the most accurate method for calculating the oil

and gas flow rates. However, these current methods are rather

expensive and time consuming to be achieved. Therefore, it is

usually desired to have quick and accurate evaluation of well

performance considering wellhead parameters, especially

pressure and temperature. Good utilization of pressure and

temperatures parameters of producing wells reveals excellent

and reliable information about well behavior and can help to

make required remedial action(s) in required suitable time.

For naturally flowing wells, bean performance correlation is

the most widely used to monitor well performance. Most

current correlations (Gilbert, 1954; Ros, 1960; Ashong, 1961;

Asford, 1973; Secen, 1976; Abdul-Majeed, 1986) for two-

phase flow across chocks are valid only for critical flow across

the choke. The literature presented good correlations for single

phase flow of either liquid or gas. However, reliable

correlations for two-phase are limited and for multiphase are

rare and scarce. This is especially true for flow in the sub-

sonic flow region (i.e., flow velocities smaller than that of

sound.

The majority of current correlations for multiphase flow are

valid only for critical flow condition. The most popular

correlation was developed by Gilbert (1954) but it is valid for

critical flow occurring when the upstream pressure of the

choke is at least 70 % higher than the downstream pressure or

when the ratio of down stream pressure to upstream pressure is

equal to 0.588. In general, the literature (Abdul-Majeed, 1986;

Al-Attar and Abdul-Majeed, 1988) reveals that keeping the

ratio of downstream pressure to upstream pressure in the range

from 0.50 to 0.60 secures the critical flow condition of the

choke.

2 A New Correlation for Calculating Wellhead Production IPTC 11101

2

T a

In naturally-flowing wells, the production rate is controlled by

means of surface choke (or bean). Economides et al (1993)

indicated that the two-phase flow through actual wells has not

been described theoretically yet. Therefore, many empirical

correlations have been developed for this purpose of the

determination of two-phase flow through a choke. These

correlations are usually applied for critical flow condition.

This is the condition when gas-liquid mixture flows through

choke at velocity sufficient enough to reach sonic velocity.

When this condition occurs, the flow is called “critical flow”

and changes in pressure downstream of the choke do not affect

the flow rate.

Accordingly, Gilbert (1954) developed his correlation to

calculate the production rate as follows:

10 R 0 .546 Q

Pwh S 1 .89 (1)

Re-arranging equation (1) yields,

P S 1 . 89

of multiphase flow performance through a wellhead choke

using a statistical analysis based upon production data from

155 well tests from Iraqi wells. They concluded that Ashford

correlation provided overpredicted production rates, and

Poettmann correlation produced underpredicted production

rates. The study also concluded that Gilbert, Poettmann, and

Ashford correlations for oils in the range of 38 to 45 API

gravity resulted in underpredicted production rates.

2. Development of a New Correlation Although the tubing-head pressure is a factor considered for

calculating production rate in several bean performance

equations, it is not a factor at all for predicting the production

rate in an artificial lift system. This is mainly attributed to the

absence of critical flow conditions in the case of artificial lift

system in which the choke is either disconnected or kept fully

opened.

For the goal of the development the new correlation for

artificially flowing wells, the wellhead temperature is

considered a function of some producing well and reservoir

Q wh (2) parameters. The proposed function of these parameters can be

10 R 0 . 546 presented in the following mathematical form:

Where Q is gross liquid rate (bbl/d), Pwh is well (or tubing) a b c d e f head pressure (psig), S is bean size (1/64 inch), and R is gas- Tth f Tbh , Q ,WC , H , A , GOR liquid ratio (MSCF/BBL).

Following the same approach of Gilbert (1954), Ros (1960)

developed a very similar correlation but with different

correlating exponents as follows:

………………………………………. (5)

Consideration of direct and reverse proportionality of these

parameters with wellhead temperature and insertion of a

constant of proportion (K), based on actual measured data,

results in: 17 R 0 . 65 Q

P wh

(3) a b C

S 1 . 88

Tth

K Tbh Q

H d A e

WC GOR f

(6)

Achong (1961), Ashford (1973), Secen (1976) developed similar correlations with different constant and exponents in

the same form of Gilbert correlation. Tantway et al (1995)

Re-arranging equation (6) yields:

developed a computer program to calculate these exponents T H d

A e

GOR f b th

for different local oil fields in Egypt. All of the previously-

mentioned studies used Gilbert’s form, which can be written in

a general form as follows;

Q K bh WC C

(7)

C Pwh

R a Q b

S d

(4)

Actual data from 352 producing wells of flow rate (Q), wellhead temperature (Tth), tubing cross-sectional area (A),

gas-oil ratio (GOR), bottom-hole temperature (Tbh) are used as

A list of most popular correlations used to predict wellhead

production rate for naturally-flowing wells is presented in

Appendix A. This list includes Gilbert, Achong, Poettmann,

Omana, and Ashford correlations.

Abdul-Majeed (1986) performed a sensitivity study about

correlations predicting two-phase flow through wellhead

choke using data from 210 Iraqi well tests. The data included

production rate, choke size, upstream pressure, gas-liquid

ratio, and API gravity of oil. He concluded that Gilbert’s

correlation yielded relatively accurate results but Omana’s

correlation is poor in accurate prediction of production rate.

Al-Attar and Abdul-Majeed (1988) compared the correlations

shown in Fig. 1 and Fig 2. Figures 1-a to 1-d present the systematic approach used to develop the direct proportionality

of actual production rate and wellhead temperature for

different gas-oil ratios and water-cut equals zero. Figures 2.a

and 2.b show the variation of actual rate with wellhead

temperature for different water-cuts. The same approach is

applied for other considered well and reservoir parameters

involved in the new correlation. Then, the least square method

was applied using all data points together and the resultant

equation was solved using Gaussian elimination method. A

FORTRAN computer program was developed to calculate the

constant K and coefficients a, b, c, d, e, and f. The final form

of the developed correlation is given by:

IPTC 11101 M. GHAREEB and S. A. SHEDID 3

3

T

9.2 x10 4 T 3.27 H 1.2

A0.81

GOR 0.041

lighter mixture of liquid and gas resulting in higher liquid

production. It also indicates that the increase of GOR by 40

Q th times (from 25 to 1,000 scf/stb) has a minor effect on the 1.2

bh WC 0.046 increase of wellhead production rate.

………………………………………. (8)

Where, Tth is wellhead temperature (oF), Tbh is bottom hole

temperature (oF), A is tubing cross-sectional area (in

2), GOR is

producing gas/oil ratio (scf/stb), and WC is producing water-

cut (%).

In order to test the accuracy of developed correlation versus actual measured production rates, Figure 3 is developed and shows very good accuracy of predicted production rates with

correlation factor (R2) of 0.973.

The newly-developed correlation of equation (8) considered

many well and reservoir parameters which were not included

in the previous correlations, such as; water-cut, wellhead and

bottom-hole temperatures, and producing depth. This is in

addition to other parameters appeared in Gilbert and other

correlations, such as; GOR and wellhead pressure.

3. Results and Discussion

All measured actual wellhead production rates from 352

producing well are plotted versus predicted ones using the

newly-developed correlation, equation 8, and graphically

depicted in Figure 3. This Figure reveals accurate prediction

results with an excellent correlating coefficient of 0.97. The

accurate prediction of wellhead production rate is mainly

attributed to the consideration of more well and reservoir

parameters; such as water-cut, wellhead and bottom-hole

temperatures, producing depth, and tubing size. The

importance of each single parameters involved in this new

correlation is also investigated by performing a sensitivity

analysis. The results of this analysis are presented in Figures 4

to 8.

Figure 4 presents the predicted wellhead production versus

wellhead temperature for different pay zone depths. It

provides a general conclusion that the increase of wellhead

temperature increases wellhead production. This can be

attributed to the reduction of oil viscosity because of the

increase of wellhead temperature. This means for oil fields in

hot areas, the wellhead production will be higher than that

ones in cold areas. This Figure, Figure 4, also reveals that pay

zone of higher producing depth is expected to have higher

wellhead production rate for the same wellhead surface

temperature.

Figure 5 shows the predicted wellhead production rate versus

wellhead temperature for different gas-oil ratios (GORs). It

confirms the same conclusion, drawn-above for the effect of

pay zone depth, that the increase of surface temperature

increases the wellhead production rate but for different GORs.

This may be attributed to that the increase in GOR will cause

Figure 6 depicts graphically the predicted wellhead production

versus wellhead temperature for different tubing areas (or

sizes). It reveals that the increase of tubing size increases the

production rate. This is because of the increase of area open to

flow, as proven by continuity equation (Q = velocity x area). It

also proves that the increase of tubing area has a major effect

of increment of wellhead production. This also confirms the

conclusions attained before by Abdel-Majjed (1986).

Figure 7 indicates the calculated wellhead production versus

wellhead temperature for different bottom-hole temperatures.

This is based actual field data used to develop the newly-

developed correlation, equation 8. It may be explained that the

increase of wellhead temperature decreases the oil viscosity

and then increases the production rate. This is confirmed using

field data from different oil wells and at different bottom-hole

temperatures.

Figure 8 presents the calculated wellhead production versus

wellhead temperature for different water-cuts. It shows that

the increase in water-cut decreases the oil wellhead

production. It also proves that the influence of water-cut on oil

production increment is minor for water-cuts below 50 %.

In general, some conclusions can be drawn based upon the

results using the newly-developed correlation sensitivity of the

importance and deep impact of producing depth, tubing size

and wellhead temperature on oil production and also minor

influence of GOR, bottom temperature and water-cut.

4. Conclusions

This study was undertaken to review current correlations for

wellhead performance and to develop a new correlation

considering new important parameters affecting wellhead

production rate. The following conclusions are drawn:

1. Current bean performance correlations for naturally and

artificially flowing wells are limited in application to the

fields they were developed for and new correlating

coefficients should be developed for other wells/fields.

2. Current correlations predicting wellhead production rate are

very sensitive to choke size change and limited I application

to naturally-flowing wells.

3. A new correlation was developed for quick and accurate

prediction of wellhead production considering several well

and formation parameters, ignored before in classical

correlations.

4. Sensitivity analysis of factors affecting wellhead production

rate indicated that producing depth, tubing size, and bottom-

hole temperatures have a real impact while gas-oil ratio,

wellhead temperature, and water-cut have a minor effect on

predicted values of wellhead production rate.

4 A New Correlation for Calculating Wellhead Production IPTC 11101

4

Nomencltaure

A Tubing cross-sectional area, in2.

C Proportionality constant (C = 10 for Gilbert,

C =17 for Ros, and C = 1.03

for Poettmann-Beck)

D Bean size, 1/64 inch

F water-oil ratio

G Gas-liquid ratio, scf/bbl

GOR Gas-oil ratio, scf/bbl

K Correlating constant H Well producing depth, 1000 ft

Q Gross liquid rate, bb/d

P Tubing head pressure, psig R Gas-liquid ratio, MSCF/bbl

N Dimensionless Number

P Pressure, psia S Bean size, 1/64 inch

T Temperature, oF

WC Water-cut, ratio

Sub/Superscripts

b bottom

PB Poettmann-Beck

h head g gas

L Liquid viscosity

Q flow rate

o oil

th tubinghead w well

w water

References

1. Economides, M. J., Hill, A. D., Ehlig-Economides.,

Petroleum Production Systems, Prentice Hall PTR,

New Jersey, p. 229, 1993.

2. Gilbert, W. E, “Flowing and gas-lift well

performance” API Drilling and Production Practice,

p. 143, 1954.

3. Ros, N. C. J. “An analysis of critical simultaneous

gas/liquid flow through a restriction and its

application to flow metering” Applied Sci Res., 9,

Sec. A, p. 374, 1960.

4. Achong, I. B. “Revised bean and performance

formula for Lake Maracaibo wells” published by the

University of Zulia, Maracaibo, Venezula, 1961.

5. Secen, J. A., “Surface choke measurement equation

improved by field testing analysis” Oil and Gas

Journal, pp. 65-68, August 1976.

6. Tantawy, M., Elayouty, E. D., and Elgibaly, A.

“Comparative investigation of bean performance

correlation for flowing oil wells,” Journal of

Engineering and Applied Science, vol. 42, No. 4, pp.

861-875, 1995.

7. Poettmann, F. H., and Beck, R. L. “New charts

developed to predict gas-liquid flow through chokes”

World Oil, March 1963).

8. Omana, R., Houssiere, C. Jr., Brown, K. E., Brill, J.

B., Thompson, R. E., “Multiphase flow through

chokes” paper SPE 2682, 1969.

9. Ashford, F. E. “An evaluation of critical multiphase

performance through wellhead chokes” Journal of

Petroleum Technology (JPT), August 1973.

10. Abdul-Majeed, G. H. “Correlations developed to

predict two-phase flow through wellhead chokes”

paper SPE 15839, 1986.

11. Al-Attar, H. H., and Abdul-Majeed, G. H. “Revised

bean performance formula for East Baghdad oil

wells” Journal of SPE Production Engineering,

February 1988, pp. 127-131.

IPTC 11101 M. GHAREEB and S. A. SHEDID 5

5

L

l

L

Appendix A: List of correlations for wellhead performance

Gilbert (1954)

10

GLR 0.546 Q Omana correlation is restricted to critical flow, requiring that

q1/q2 > 1.0 and P1/P2 < 0.546. It is best suited for to low P l viscosity liquids and bean sizes of 14/64 or less.

wh

Achong (1961)

17

D1.89

GLR 0.65 Q

(A-1)

Ashford (1973)

1.53C D

2 P

Q x Pwh (A-2) B F

D1.88 o wo

(A-5)

Poettmann and Beck (1963) M m T Z (G RS ) (A-5-a)

Q 86 ,400

Ao

C PB x

m

WW

FWO

O FWO W

water / oil ratio

(A-5-b)

(A-5-c)

x R 0.5663

(A-3)

m 350.4 o 0.0765 g G

Vsg 0.00504T Z (G R ) R s

(A-3-a)

(A-3-b)

Vsl

V M L ,

L

and

P Bo

M L

1

g

(A-3-c)

1R

L

Omana (1969)

N 0.263 N 3.49 N 3.19 0.657 N 1.8 (A-4) qL

g

N

Pl l D

(A-4-a) L

NPl 1.74 x102

P 1

L L

(A-4-b)

1

, where l

1 R

Vsg

R VsL

(A-4-c)

ND 0.1574 D64

1.25

(A-4-d)

N qL 1.84 ql

(A-4-e)

L

L

L

9273 .6 P

V L 1.0 0.5 M L

0.4513 R 0.766

(Mm 151P)(0.000217g Rs Ww)

(Mm 111P)(0.000217 gGWw)

6 A New Correlation for Calculating Wellhead Production IPTC 11101

6

1200 1200

1000

1000

800

800

600

600

400

400

200

200

0

60 80 100 120 140 160

Well- head temperature,0F

0

60 110 160

Well-head temperature, oF

(a) Q vs Tth for WC = zero, (b) Q vs Tth for WC = zero, GOR = GOR = zero up to 100 scf/stb. 100 up to 200 scf/stb.

1200

1400

1000

800

1200

1000

800

600

600

400

400

200 200

0

60 80 100 120 140 160

Well-head temperature, oF

0

60 80 100 120 140 160

Well-head temperature, oF

(C) Q vs Tth for WC = zero, GOR =

200 up to 300 scf/stb.

(d) Q vs Tth for WC = zero, GOR =

zero up to 400 scf/stb.

Fig. 1. Variation of actual Q with Tth for different GOR.

Q = 0.0001 T3.2227

R2 = 0.9708

Q = 9E-05*Ts3.2277

R2 = 0.9705

GOR from zero up to 100

scf/stb

GOR from 100 up to 200

scf/stb

GOR from 200 up to 300

scf/stb

GOR from 300 up to 400

scf/stb

Q = 0.0002 T3.0955

R2 = 0.8152

Pro

du

ctio

n r

ate

, b

pd

Pro

du

ctio

n r

ate

, b

pd

Pro

du

ctio

n r

ate

, b

pd

Pro

du

cti

on

rate

, b

pd

IPTC 11101 M. GHAREEB and S. A. SHEDID 7

7

1200

1000

1200

1000

800 800

600 600

400 400

200 200

0

60 110 160

Well- head temperature,0F

0

60 110 160

Well- head temperature, oF

(a) Q vs Tth for WC = 20 to 50 % and (b) Q vs Tth for WC = 50 to 90 % and

GOR = 0 to 100 scf/stb. GOR = 0 to 100 scf/stb.

Fig. 2. Variation of actual Q with Tth for different values of WC and GOR.

1400

1200

1000

800

600

400

200

0

0 200 400 600 800 1000 1200 1400

Q actual, BFPD

Fig. 3. Calculated Q versus actual measured Q.

Q = 5E-05 T3.2897

R2 = 0.9592

Q = 0.001 TTh^(2.6695)

R2 = 0.9688

y = 0.9602x + 7.1308

R2

= 0.97

Pro

du

cti

on

ra

te,

bp

d

Q c

alc

ula

ted

, B

FP

D

Pro

du

ctio

n r

ate

, b

pd

8 A New Correlation for Calculating Wellhead Production IPTC 11101

8

2500

2000

1500

1000

500

0

60 80 100 120 140 160 180

Wellhead temperature. oF

Fig. 4. Effect of producing depth on flow rate using new correlation.

1600

1400

1200

1000

800

600

400

200

0

40 60 80 100 120 140 160 180

Wellhead temperature, oF

Fig. 5. Effect of GOR on production using new correlation.

GOR = 100 scf/bbl A = 7.027 sq in

WC = 1 % Tbh = 190 F

depth =4000 ft

depth =6000 ft

depth =8000 ft

Depth = 5 (1000) ft A = 7.027 sq in

Tbh = 190 F WC = 1 %

GOR =25 SCF/STB

GOR =100 SCF/STB

GOR =250 SCF/STB

GOR =500 SCF/STB

GOR =1000 SCF/STB

Pro

du

ctio

n R

ate

, B

PD

P

rod

uct

ion

Rate

, B

PD

IPTC 11101 M. GHAREEB and S. A. SHEDID 9

9

IPTC 11101 M. GHAREEB and S. A. SHEDID 9

1400

1200

1000

800

600

400

200

0

60 80 100 120 140 160 180

Wellhead Temperature, oF

Fig. 6. Effect of tubing size on production using new correlation.

1600

1400

1200

1000

800

600

400

200

0

60 80 100 120 140 160 180

Wellhead temperature, oF

Fig. 7. Effect of wellhead temperature on production using new correlation.

9

Depth = 5 (1000) ft GOR = 100 scf/bbl

Tbh = 190 F WC = 1 %

tubing, 3 1/2"

tubing, 2 7/8"

tubing, 2 3/8"

Depth = 5 (1000) ft GOR = 100 scf/bbl

WC = 1 %

Tb=170 oF

Tb=185 oF

Tb=200 oF

pro

du

ctio

n r

ate

, B

PD

p

rod

uct

ion

rate

, B

PD

10 A New Correlation for Calculating Wellhead Production IPTC 11101

10

1400

1200

1000

800

600

400

200

0

60 80 100 120 140 160 180

Wellhead Temperature, oF

Fig. 8. Effect of water-cut on production using new correlation.

WC= 1% WC= 25%

WC= 50% WC=75%

Depth = 5 (1000) ft

GOR = 100 scf/bbl

A = 7.027 sq in

Tbh = 190 F

Pro

du

ctio

n R

ate

, B

PD