ALTON R. HAGEDORN' JUNIOR MEMBER AIME KERMIT E. BROWN MEMBER AIME A I,500-ft experimental well was used to study the pressure gradients occurring during continuous, vertical, twophase flow through I-in., 114 -in. and Ii/j-in. nominal size tubing. The test well was equipped with two gas-lift valves and four Maihak electronic pressure transmitters as well as with instruments to measure the liquid production rate, air injection rate, temperatures and surface pressures. Tests were conducted for widely varying liquid flow rates, gas-liquid ratios and liquid viscosities. From these data, an accurate pressure-depth traverse was constructed for each test in each of the three tubing sizes. From the results of these tests, correlations have been developed which allow the accurate prediction of flowing pressure gradients for a wide variety of tubing sizes, flow conditions, and liquid properties. Also, the correlations and equations which are developed satisfy the necessary condition that they reduce to the relationships appropriate to single-phase flow when the flow rate of either the gaj or the liquid phase becomes zero. All the correlations involve only dimensionless groups, which is a condition usually sought for in similarity analysis but not always achieved. The correlations developed in this study have been used to calculate pressure gradients for pipes of larger diameter than those upon which the correlations are based. Comparisons of these calculated gradients with experimentally determined gradients for the same flow conditions obtained from the literature indicate that extrapolation to these larger pipe sizes is possible with a degree of accuracy sufficient for engineering calculations. The extent of this extrapolation can only be determined with additional data from larger pipe diameters.

Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in Small-Diameter Vertical Conduits

Comparison of void fraction correlations for different flow patterns in horizontal and upward inclined pipes

Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup

This paper presents the resu[ts of an investigation of Iwo-phase, gas-liquid flow in horizontal pipelines. Experimental data were taken in three field-size, horizontal pipelines, two of which were constructed for this purpose. The data were obtained using water, distillate and crude oi! separately as the liquid phase, and natural gas as ~he second phase. Experimental pressure-length traverse, liquid holdup and f?ow-pattern data were collected jor each set of flow rates, These data were used to deve[op three correlations that are presented herein. The liquid-ho[dup values correlated with various fluw parameters without regard to the existing flow pattern. The same was true for the energy-loss factors. A new flow-pattern map is presented that appears to be quire reliable, but not required for the pressure-loss calculations. The liquid-holdup correlation and /he energy-loss factor correlation are used in conjunction with a twe-phase flow power balance, developed during this study, to predict tite pressure bsses that occur during gas-iiquid f70w in horizontal pipelines. A recommended calctdational procedure is given, as weU as a statistical analysis of the results, This procedure lends itself to computer application, since several small pressure decremen [s are needed 10 calculate a pressure-length traverse. The correlations are shown graphically, but may be curve fitted with existing curvef?tting computer programs,

The Prediction of Flow Patterns, Liquid Holdup and Pressure Losses Occurring During Continuous Two-Phase Flow In Horizontal Pipelines

Holdup in two phase flow

Vertical upward concurrent air-liquid flow was investigated under isothermal conditions in a test section of 1-in. schedule 40 pipe. Pressure drop was measured with a mercury manometer connected to two pressure taps 20 ft. apart in the section. Liquid was trapped between two quick shutoff valves activated by two solenoid valves. The liquid was druined from the section to provide the holdup data. Six liquids were used to determine the effect of density, viscosity, and surface tension.

The experimental holdup, and two-phase pressure drop data were not in agreement with Lockhart-Martinelli type of correlation for horizontal flow. A statistical correlation for holdup was developed to include fluid physical properties, total mass velocity, and the air-liquid ratio entering the pipe. Similarly a pressure drop correlation was developed which expressed the two-phase pressure drop as a function of the slip velocity, liquid physical properties, and total mass velocity. This correlation showed an average percentage error of less than 15% between the observed and the calculated total pressure drop.

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B. S. Pressburg

Papers

Holdup and pressure drop with gas-liquid flow in a vertical pipe