# CALCULATOR PROGRAM AUTOMATICALLY DETERMINES TWO-PHASE FLOW REGIMES AND PRESSURE DROPS

G.V. DevarajanKTA-Global Engineering Sdn Bhd

Miri, Sarawak, Malaysia

A calculator program to determine two-phase flow regimes and pressure drops was developed for the Hewlett Packard handheld calculator HP41CX used in conjunction with peripheral printer HP82143A.

The program (Fig. 1) can also determine the single-phase pressure drop (either vapor or liquid) in flow lines. Tables 1 and 2 lists the program operating instructions, labels used, and register contents. The program features are as follows:

- Calculates both single and two-phase pressure drop per 100 ft length of pipe.
- Identifies two-phase flow regimes automatically without the user having to use Baker's two-phase regime map. Overall execution time for two-phase calculations is about 30-40 sec.
- For vertical flow, the pressure drop does not include the hydraulic head required to lift the fluid.
- Values for Baker's parameters Bx 10,000 and By 100,000 are outside the two-phase flow regime map boundaries.
- The program assumes that the two-phase flow is isothermal, turbulent both in liquid and vapor phases, and that the pressure drop is no more than 10% of the absolute downstream pressure. Pipe roughness factor used in the program is 0.00015 ft.

The program uses the Lockart and Martinelli method coupled with Baker's two-phase correlations to determine two-phase pressure drop. All equations developed by Blackwell for single and two-phase flow pressure drop calculations are included.

Mathematical modeling has been performed for each of the two-phase flow regime curves represented in Baker's pattern map (Fig. 2).

Newton-Raphson's least squares method is used to generate the equation as a function of Bx and By to best represent each flow pattern within the specified limits of Bx and By.

The program checks which of the flow-regime equations is best satisfied. After determining into which flow regime the values of Bx and By fall, the program identifies the flow regime and proceeds to calculate the appropriate pressure drop associated with that flow regime.

The user, in running the program, must set the calculator size to 035 with the XEQ command. The program cards are then read sequentially. The total number of program card sides read is 17.

Prior to starting the execution, press the reset button once. The printer is switched on and left on MAN mode.

Program execution is initiated by XEQ command followed by entering the program name "TPPD" in the alpha mode. Program inputs are prompted automatically in the required units. Further instructions are self-explanatory as displayed on the screen.

After each input, press the reset button to continue. At the end of all inputs, the program will automatically proceed to perform calculations for the phase chosen.

The example problem calculates the pressure drop per 100 ft of pipe in a 12-in. Schedule 40 line (ID = 11.938 in.) for the following conditions:

Vapor: Wg = 375,000 lb/hr,

mu G = 0.01 cp, and pG = 2 lb/cu ft

Liquid: WL = 275,000 lb/hr,

mu L = 0.1 cp,

rho L = 33.5 lb/cu ft,

and sigma L = 5.7 dynes/cm

### ACKNOWLEDGMENT

The author wishes to thank KTA-Global Engineering Sdn Bhd for permission to publish this article.

### BIBLIOGRAPHY

- Blackwell, W. W., "Program calculates two-phase pressure drop," OGJ, Nov. 24, 1980, pp. 116-24.
- Perry, J.H., Chemical Engineers' Handbook, 5th Edition, McGrawHill, New York, pp. 5-38, 5-39.
- Lockhart, R.W., and Martinelli, R.C., Chem. Engr. Prog., January 1949, pp. 39-48.
- Baker, O., "Simultaneous flow of oil and gas," OGJ, Nov. 10, 1954.
- Baker, O., and Swerdloff, W., "Calculation of surface tension," OGJ, Nov. 21, Dec. 5,12 and 19,1955, and Jan. 2, and 9, 1956.

*Copyright 1990 Oil & Gas Journal. All Rights Reserved.*