Mohammed E. Osman, Mahmoud E. DoklaUniversity of United Arab Emirates

Abu Dhabi, U.A.E.

Empirical correlations have been developed to describe the behavior of gas-condensate flow through surface chokes. The field data were obtained from a Middle East gas-condensate reservoir and cover a wide range of flow rates and choke sizes.

Correlations for gas-condensate systems have not been previously available. These new correlations will help the production engineer to size chokes for controlling production of gas-condensate wells and predicting the performance of flowing wells under various conditions.

Four forms of the correlation were developed and checked against data. One form correlates choke upstream pressure with liquid production rate, gas/liquid ratio, and choke size.

The second form uses gas production rate instead of the liquid rate. The other two forms use the pressure drop across the choke instead of upstream pressure.

All four of the correlations are presented here as nomograms. Accuracy of the different forms was checked with five error parameters: root-mean-square error, mean-absolute error, simple-mean error, mean-percentage-absolute error, and mean-percentage error.

The correlation was found to be the most accurate when pressure-drop data are used instead of choke upstream pressure.

### CHOKE CORRELATIONS

The main reason that flowing wells use chokes is to produce reservoirs at the most efficient rate.

This rate will prevent water or gas coning and sand problems.

The other reason is that in the critical-flow region, mass flow rate becomes independent of pressure drop across the choke. Therefore, chokes isolate the reservoir from pressure disturbances of surface production facilities.

The problem of multiphase flow through chokes has not been satisfactorily solved for all cases. Most solutions are offered only for the case of critical flow

Surbey, et al., discussed this application of multiple-orifice valve chokes in critical flow conditions. 1 Wallis developed a correlation to predict the sonic velocity in a two-phase homogeneous system. 2

A different correlation was developed by Fortunati under no-slip conditions between different phases. 3 Fortunati also proposed a correlation for flow rates under critical flow conditions.

Ashford and Pierce developed an equation to predict the flow rates. 4 They stated that uncertainty is introduced in their model because of the difficulty of precisely measuring downstream pressure. Their work was extended by Sachdeva, et al., to develop a correlation to predict the critical pressure ratio. 5

Surbey, et al., developed a new correlation to predict performance of multiple-orifice valve chokes under critical flow conditions. 6 Experimental data collected for a high-pressure, air-water system were used.

Many investigators have offered empirical correlations based on field and laboratory data. One of the early choke correlations was developed by Gilbert using production data from the Ten Section field in California. 7 This was followed by the theoretical correlation, developed by Ros. 8

Poettmann and Beck converted the Ros correlation to oil field units and reduced it to a graphical form. 9

Omana obtained data from the Tigre Lagon field in Louisiana to check the existing correlations and to develop a new one. 10 The data were gathered from a natural gas-water system using 4/64 to 14/64-in. choke sizes, up to 800 b/d flow rates, and 400-1,000 psi upstream pressure. The limited range of data is the main reason that this correlation is not widely used.

Achong derived a choke correlation similar to that of Gilbert. 11 This correlation was for the Lake Maracaibo field in Venezuela and was presented in nomogram form. Similar correlations were developed by Boxendell 12 and Pilehrari. 13

Several empirical equations have been developed using field data. But none of these correlations are based on data from gas-condensate systems.

The production engineer should be careful in using such correlations. He should only apply them within the appropriate ranges of fluid properties, flow rates, upstream pressures, gas/liquid ratios, and choke sizes.

This study uses 87 data points of gas-condensate flow through chokes of eight different wells. The gas-condensate field is in the Middle East. The data cover wide ranges of choke sizes, flow rates, and fluid properties.

### EQUATIONS

The general form of multiphase flow through chokes can be written as Equation 1 (See Equation box), The variables are defined in the Nomenclature box. Note that the choke size S is in sixty-fourths of an inch.

In this equation, c is a constant and a and b are exponents to be determined from field data. The equation can take four forms, Equations 1a-1d.

A least-square method, Equations 2-7, is applied to Equations 1a-1d to evaluate Constant c and Exponents a and b. E is the error parameter.

As the right-hand side of Equation 5 is minimum, the differentials of the left-hand side with respect to c, a, and b are equal to zeros, thus Equation 6 can be written.

The four forms of the choke flow equation, Equations la-Id, were evaluated using field data from eight wells.

Table 1 lists a sample of field data gathered from one of the wells. Table 2 shows the composition of both gas and condensate. The water production is added to the oil production to obtain the liquid production rate from the well.

The total number of data points in this study is 87. In Equations 8-9, these points were used to determine the different constants and exponents of Equation 7a-7c for each of the four forms of Equation 1.

To eliminate confusion over which equation to use, a further study was carried out to evaluate the accuracy of each form of Equation 9 using five different error parameters (Equations 10a-10b).

Equations 9a-9d are evaluated using these error parameters represented by Equations 10a-10e. The final results are in Table 3.

One can conclude that Equation 9c best fits the field data while Equation 9d is the second best. Thus Equation 9c is recommended for predicting the pressure drop across the choke. Both Equations 9a and 9b are expected to give the same results in predicting well head pressures.

Figs. 1a and 1b cross plot the measured upstream pressure-vs.-estimated values using Equations 9a and 9b. Most of the plotted points fall very close to the perfect correlation on the 45 line.

Similar cross plots for pressure drop across the choke are found in Figs. 1c and 1d. Again, most of the plotted points fall very close to the perfect correlation of the 45 line.

### NOMOGRAMS

The four forms of Equation 9 can be solved with the nomograms shown in Fig. 2. These figures should help the production engineer to monitor gas-condensate production from gas-condensate reservoirs. The procedure for using these charts is as follows:

- Connect choke size to the flow rate (liquid or gas rate) and extend the line to intersect with the reference line J.
- From the intersection with reference one J, connect to the value of liquid/gas ratio (LGR) or gas/liquid ratio (GLR). On the pressure axis, read the upstream pressure or pressure drop across the choke.

Knowing any three of the four parameters (flow rate, choke size, GLR or LGR, and well head or pressure drop) the fourth parameter can be obtained from the nomograms.

Equations 9a-9d and Fig. 2 should be used only within the range of data (Table 4) of this study.

### REFERENCES

- Surbey, D.W., Kelkar, B.G., and Brill, J.P. "Study of Subcritical Flow Through Multiple-Orifice Valves," SPEPE, February 1988, pp. 103-08.
- Wallis, G.B., One-Dimensional Two-Phase Flow, McGraw-Hill Book Co. Inc., New York City, 1969.
- Fortunati, F., "Two Phase Flow Through Wellhead Chokes," Paper No. SPE 3742, SPE European Meeting, Amsterdam, MaN, 1718, 1972.
- Ashford, F.E., and Pierce, P.E., "Determining Multiphase Pressure Drops and Flow Capacities in Downhole Safety Valves," JPT, September 1975, pp. 1145-52.
- Sachdeva, R., et al., "Two-Phase Flow Through Chokes," Paper No. SPE 15657, SPE Annual Technical Conference and Exhibition, New Orleans, Oct. 5-8, 1986.
- Surbey, D.W., Kelkar, B.G., and Brill, J.P., "Study of Multiphase Critical Flow Through Wellhead Chokes," SPEPE, May 1989, pp. 142-46.
- Gilbert, W., "Flowing and Gas-Lift Performance," API Drilling and Production Practices, 1954, p. 126.
- Ros, N., "Simultaneous Flow of Gas and Liquid as Encountered in Well Tubing," JPT, October 1961.
- Poettmann, F., and Beck, R., "New Charts Developed to Predict Gas-Liquid Flow Through Chokes," World Oil, March 1963.
- Omana, R., Multiphase Flow Through Chokes," Tulsa, 1968.
- Achong, L.B., "Revised Bean and Performance Formula for Lake Maracaibo Wells," Shell internal report, 1961.
- Baxendell, P.B., "Bean Performance-Lake Wells," Shell internal report, October 1957.
- Pilhvari, A., "Experimental Study of Critical Two-Phase Flow Through Wellhead Chokes," University of Tulsa Fluid Flow Projects Report, Tulsa, June 1981.

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