Multiphase-flow choke correlation limits analyzed

Donald A. Lannom, D.G. Hatzignatiou
University of Alaska-Fairbanks

Equations [41439 bytes]

An evaluation shows the limitations of seven correlations for determining flow rate of multiphase fluids through restrictions.

No single correlation is best for all ranges of flow variables, but in this evaluation the best overall comparison was obtained with the Gilbert,¹ Ros,² and Poettmann and Beck³ correlations.

A number of published correlations, both analytical and empirical, are available to assess multiphase flow through restrictions. Besides the three previously mentioned, four other correlations in use today are those by Ashford,⁴ Omana,^{5 6} Achong,⁷ and Baxendell.⁸

This evaluation reviews these seven correlations using production data from 181 well tests. Statistical analysis is used to determine the strengths and weaknesses of each correlation and to develop practical guidelines that a production engineer can use to choose the proper correlation for a particular circumstance.

Also examined are the effects of several flow variables such as pressure ranges, producing gas/liquid ratios, restriction sizes, liquid flow rates, and flowing oil API gravity.

Multiphase flow

Multiphase flow occurs in almost all producing oil wells, and nearly every flowing well has some sort of choke to regulate the flowing rate for such reasons as to:

Maintain sufficient backpressure to prevent sand entry
Protect surface equipment from too much pressure
Prevent gas or water coning
Produce the reservoir at the most efficient possible rate.⁹

Engineers face the problem of selecting an appropriate correlation which best suits a particular set of circumstances, such as pressure, producing gas/liquid ratio, producing flow rate, and oil gravity.

Accurate correlations for predicting multiphase flow rates through restrictions are necessary for properly interpreting flowing well behavior. Without an accurate correlation, these interpretations are meaningless, and nodal analysis is highly questionable.

Inaccurate flow rate predictions could lead to gas/water coning, sand entry, excessively high inlet pressures at the separator, or killing the well.

Studies by Ajienka, et al.,⁹ and Ajienka and Ikoku¹⁰ analyzed several correlations, including those by Gilbert, Baxendell, Ros, Achong, and Ashford, as well as two models proposed in Ajienka, et al.⁹ These studies covered a very limited data range-only 26 test wells were included. They determined that the Gilbert correlation appears to perform better than the others because most analytical correlations are sensitive to many parameters.

Basic correlations

Correlations for calculating the pressure drop occurring when multiphase fluid flows through a restriction are either analytical or empirical.

The analytical correlations are those of Ashford, Poettmann and Beck, and Omana.

The Ashford correlation, Equation 1 in the equation box, is the only correlation for multiphase flow through chokes that accounts for the fractional flow of water and the effects of solution gas.

Poettmann and Beck generated a family of curves similar to the one in Fig. 1 [134,901 bytes]. These charts were based on the work by Ros on simultaneous flow of oil and gas through restrictions. The charts correlate gas/liquid ratio, tubing pressure, choke size, and flow rate.

Poettmann and Beck created three charts:

20 API chart for 25-34 API oil
30 API chart for 25-34API oil
40 API chart for 35API and higher oil.

None of these charts accounts for water flow.

The Omana correlation requires calculation of four dimensionless quantities (governing groups), N_r, N_p, Q_D, and N_D with Equations 2-5. These groups are then used in Equation 6 to calculate the dependent dimensionless flow number, N_qL, which is subsequently used in Equation 7 to estimate flow rate.

Table 1 lists the parameter ranges used for developing the three analytic correlations. Note that Ashford used two distinct data sets: one with higher pressures, gas/liquid ratios, and flow rates, and the other with lower pressure, gas/liquid ratios, and flow rates. Both data sets were based on a very limited range of API gravities.

On the other hand, Poettmann and Beck developed a correlation using a relatively global set of data.

Finally, Omana developed his correlation using extremely small chokes, low pressures, and water as the operating fluid. This is a limiting factor on using the Omana equations.

Empirical correlations make up the second set of correlations for multiphase flow through restrictions. These correlations include those of Gilbert, Ros, Baxendell, and Achong. All four correlations can be expressed using Equation 8, where A, B, and C are empirical coefficients given in Table 2 [10273 bytes].

Evaluation procedure

Evaluations of the seven correlations are based on the accuracy that each correlation predicts the flow rate compared to the actual flow rate data. The procedure used to meet the objectives, presented previously, consists of the following three steps.

Study each correlation in detail, including how the correlation was developed and the range of parameters used in developing the correlation.
Conduct a statistical analysis of how well each correlation performed within the data set in which it was developed.
Evaluate each correlation against an existing global data set obtained from literature.

Results

After each correlation was examined, the next step compared how each correlation performed within its own data set.

Fig. 2 [109,085 bytes] plots calculated-vs.-observed flow rates for each correlation within the data set used in its development.

The figure indicates that the Ashford correlation predicts well for actual flow rates less than 2,000 st-tk b/d. At higher flow rates, the Ashford correlation tends to underpredict flow.

Poettmann and Beck's correlations predict flow rates well when the actual rates are less than 400 st-tk b/d, but begin to scatter widely above that level (Fig. 3 [137,766 bytes]).

Finally, the Omana correlation performed well only for flow rates less than 180 st-tk b/d.

After analyzing how well the analytical correlations performed in their own set of data, all seven correlations were compared to a global data set. This data bank was obtained from literature surveys and includes the data used by Poettmann and Beck, Ashford, and Al-Attar and Abdul-Majeed.¹⁰Table 3 [12979 bytes] tabulates this comparison.

For analytical correlations, Table 3 [12979 bytes] shows that the average percent difference varies between 8.57% for the Poettmann and Beck correlation to 55.55% for the Omana correlation. The standard deviation varies between 40.23% for the Poettmann and Beck correlation to 113.34% for the Omana correlation.

Similarly, for empirical correlations, the average percent difference varies between 8.62% for the Gilbert correlation and 25.40% for the Baxendell correlation. The standard deviation for empirical correlations varies between 40.90% for the Gilbert correlation to 49.57% for the Achong correlation.

Note that over a very wide variety of data points only the Poettmann and Beck, Gilbert, and Ros correlations predict within acceptable limits.

Fig. 3 [137,766 bytes] shows the effects of API gravity, observed flow rates, tubing pressure, bean size, and gas/liquid ratio on each correlation's prediction and demonstrates several strengths and weaknesses of each correlation.

All of the correlations overpredict the flow rate of heavy oil. With heavy oil, the Poettmann and Beck correlation performs the best with a difference of 23%.

In the medium and lighter oils, the Gilbert, Ros, and Achong correlations are more accurate.

At very low flow rates, the Omana correlation is the most accurate, with the Poettmann and Beck, Gilbert, and Ros correlations predicting within acceptable ranges.

As flow rate increases, the Gilbert and Poettmann and Beck correlations are the only two correlations that accurately predict flow rate.

At very high flow rates, all correlations predict accurate flow rates except for the Omana correlation.

The Omana correlation also has a very wide scatter at different pressures, but all other correlations predict well at low pressures. As pressure increases, the Poettmann and Beck, Gilbert, and Ros correlations are the only ones that accurately predict flow rate.

For different bean sizes the Omana correlation predicts flow rates accurately for very small beans, but as bean size increases, the Poettmann and Beck, Gilbert, Ros, and Achong correlations become more accurate. For very large beans, the Gilbert and Achong correlations are the only two that predict flow rates with consistency.

All correlations work well with intermediate gas/liquid ratios. At the upper and lower ranges of gas/liquid ratio, the Poettmann and Beck, and Gilbert correlations are more accurate. At lower gas/liquid ratios, the Ros correlation also provides accurate flow rates and at higher gas/liquid ratios, the Achong correlation is also accurate.

Table 4 [34467 bytes]summarizes the results, listing most accurate correlations for each flow parameter range.

This table will allow the engineer to choose the proper correlation for an entire set of flow parameters. For example, with a 1,000-1,500 psi tubing head pressure, 26-35 API oil gravity, 8/64-16/64 in. bean size, and 2-3 Mscf/st-tk bbl gas/liquid ratio, Table 4 [34467 bytes]indicates that the Gilbert correlation should be used to predict flow rates.

For the same flow parameters but for a heavier oil (16-25 API) and a lower gas/liquid ratio, the Poettmann and Beck correlation becomes more appropriate.

Observations

Although individual flow parameters can affect the performance of each correlation, the parameters should not be the only method used for choosing a correlation.

The trends shown in the figures of this article may or may not be caused entirely by the single parameter that is plotted. All the flow parameters listed in these figures affect the accuracy of each correlation's prediction, and may not be the only cause of deviation.

If the flow parameters are not immediately available to the engineer, a correlation must still be selected to predict flow rates.

Although no one correlation performs best in all ranges of flow parameters, the Gilbert, Ros, and Poettmann and Beck correlations tend to predict flow rates more accurately over the widest range of various flow variables. If there is a lack of available information, time, or calculation capability, these three correlations, based on the author's experience, will provide immediate practical answers.

References

1. Gilbert, W.E., "Flowing and Gas-lift Well Performance," Drilling and Production Practice, API, Vol. 143, pp. 127-57, 1954.

2. Ros, N.C.J., "An Analysis of Critical Simultaneous Gas/Liquid Flow through a Restriction and its Application to Flow Metering," Applied Science Research, February 1961.

3. Poettmann, F.H., and Beck, R.L., "New Charts Developed to Predict Gas-Liquid Flow Through Chokes," World Oil, March 1963, pp. 95-101.

4. Ashford, F.E., "An Evaluation of Critical Multiphase Flow Performance Through Wellhead Chokes," JPT, August 1974, pp. 843-48.

5. Omana, R.A., "Multiphase Flow Through Chokes," Masters Thesis, University of Tulsa, 1968.

6. Omana, R.A., Houssiere, C.R., Brill, J.P., and Brown, K.E., "Multiphase Flow Through Chokes," Paper No. SPE 2682, 44th Annual Fall Meeting, Denver, September 1969.

7. Achong, I., "Revised Bean Performance Formula for Lake Maracaibo Wells," Internal Report, October 1961.

8. Baxendell, P.B., "Bean Performance-Lake Wells," Internal Report, October 1957.

9. Ajienka, J.A., Enaibe, O.E., and Owolabi, O., "Multiphase Flow Metering: An Evaluation of Discharge Coefficients," Journal of Canadian Petroleum Technology, Vol. 33, No. 8, October 1994, pp. 57-62.

10. Ajienka, J.A., and Ikoku, C.U., "An Evaluation of Critical Multiphase Orifice Flow Correlations," Nigerian Journal of Petroleum and Energy, 1991.

11. Al-Attar, H.H., and Abdul-Majeed, G.H., "Revised Bean Performance Equation for East Baghdad Oil Wells," SPE Production Engineering, February 1988, pp. 127-31.

Bibliography

Ashford, F.E., and Pierce, P.E., "Determining Multiphase Pressure Drops and Flow Capacities in Down-hole Safety Valves," JPT, September 1975, pp. 1145-52.

Beggs, H.D., and Brill, J.P., Two-Phase Flow in Pipes, Lecture Notes, University of Tulsa, 1994.

Brown, K.E., and Beggs, H.D., The Technology of Artificial Lift, Volume 1: Inflow Performance, Multiphase Flow In Pipes, and The Flowing Well, PennWell Publishing Co., Tulsa, 1977.

Fortunati, F., "Two-Phase Flow through Wellhead Chokes," Paper No. SPE 3742, SPE European Spring Meeting, Amsterdam, May 1972.

Geiger, G.E., and Rohrer, W.M., "Sudden Contraction Losses in Two-Phase Flow," Journal of Heat Transfer, February 1966.

Poettmann, F.H., and Carpenter, P.G., "The Multiphase Flow of Gas, Oil and Water Through Vertical Flow Strings with Application to the Design of Gas-Lift Installations," Drilling and Production Practice, 1952.

The Authors

Donald A. Lannom is a captain in the U.S. Army Quartermaster Corps, serving as a petroleum management specialist. He has a BS in petroleum engineering from the University of Missouri-Rolla and an MS.in engineering and science management from the University of Alaska-Fairbanks. Lannom is a member of the SPE.

Dimitrios G. Hatzignatiou is an associate professor at the University of Alaska-Fairbanks. Hatzignatiou holds a diploma in mining and metallurgical engineering from the National Technical University of Athens, Greece, an MS in petroleum engineering from the University of Alaska-Fairbanks, and a PhD in petroleum engineering from the University of Tulsa. He is a member of SPE.