Comparison of Liquid-Holdup and Friction-Factor Correlations for Gas-Liquid Flow

Abstract

Predicting expected pressure drop during two-phase, gas-liquid flow in pipes is highly significant to the petroleum industry. The relative accuracies of four published correlations are determined in terms of the constitutent liquid holdup and friction-factor prediction schemes. Liquid-holdup values predicted from two other correlations and from no-slip considerations are included in the comparisons. Introduction The prediction of pressure drop during two-phase, gas-liquid flow in pipes is of great significance to the petroleum industry. Extensive theoretical and experimental research has been conducted on horizontal, vertical, and inclined two-phase flow, but few of the resulting correlations are valid over broad ranges of flow rates, fluid properties, and pipe sizes. Most published pressure-loss prediction correlations require prediction of two parameters: the liquid holdup and a two phase friction factor. The reliability of any flowing pressure-drop correlation is, therefore, dependent on the relative accuracies of the constituent liquid-holdup and friction-factor predictions. The accuracy of these correlating schemes may be evaluated only for test cases for which simultaneous liquid-holdup and pressure-drop data are available. Beggs'2 and Eaton's5 experimental data include accurately measured pressure-loss and liquid-holdup values. These data are restricted to 1-, 1.5-, 2.067-, and 4.02-in.-ID pipes. Additional data are available in the literature or from private sources, but the accuracy of measurement is unknown or questionable, so they were not considered here. Fifty-eight tests from Beggs' study and 238 tests from Eaton's study were combined in a data bank for this investigation. Using this data bank, two separate comparison studies were pursued. The first study compared measured liquid holdup with that predicted from six commonly used correlations and a no-slip calculation for two-phase horizontal flow in pipes. The second study predicted two-phase friction factors from correlative functions of four authors and compared these factors with the friction factors calculated from their respective mechanical energy-balance equations. Some differences exist in the definition of terms used in the energy-balance equations. The four friction-factor correlations considered were developed by Beggs and Brill,3 Dukler,4 Eaton et al.,6 and Guzhov et al.7 Their liquid-holdup correlations were also compared with the correlations of Hughmark9 and Lockhart and Martinelli.10 To establish a lower bound on predicted liquid-holdup values, a no-slip holdup was also calculated. The percent differences between measured and predicted liquid holdup and between measured and predicted friction factors were computed for each test in the data bank. The mean and standard deviation of these differences were determined to evaluate the reliability of selected correlations for predicting two phase pressure drops in horizontal pipes.