An Improved Revision To The Hagedorn And Brown Liquid Holdup Correlation
Authors: Abdul Majeed Ghassan H. , Abu Al-Soof Nimat Behnam , Alassal Jawad R. 
Published: March 2010

Abstract
Many two-phase flowing pressure drop evaluation studies have shown that the modified Hagedorn-Brown correlation is the best over-all predictor. However, on average, this correlation tends to under-predict pressure drop.
In this study, the Hagedorn-Brown liquid holdup correlation was revised using 51 pressure profiles containing 540 pressure loss measurements. The revised correlation gave higher value of liquid holdup than the original for the same value of correlating function. The pressure drops for 157 well test data (not used in the development of the revised liquid holdup correlation as they were taken from another field), were calculated for different cases using the original and the revised liquid holdup correlation. In comparing the calculated pressure drop results with the field data, the revised correlation gave considerably better results.

Introduction
Several published correlations can be used to predict pressure drops in vertical oil well pipes for the simultaneous flow of oil, water and gas. One of these correlations is that of Hagedorn and Brown(1). Their correlation was developed from 475 tests in a 1500-ft experimental well using fluids having viscosities up to 110 cpo An average mixture density corrected for downhole conditions was used for calculating estimates of pressure losses caused by friction and acceleration. Liquid holdup was then calculated from the total measured pressure loss and the calculated. values of friction and acceleration losses. These holdup values were correlated with arious flow variables and fluid properties. Because liquid holdup was not measured directly, values of holdup given by the correlation are not always physically significant.
Further work by Brill and Hagedorn(2) recommended that the pressure gradient should be calculated by the Griffith(3) correlation for the bubble regime. Also, they suggested that the density of the mixture calculated using the Hagedorn-Brown holdup correlation should be compared with that calculated using no-slip holdup. The largest of these two values was then considered.
Several two-phase, flowing pressure loss, evaluation studies were performed in which the modified Hagedorn-Brown correlation was included in addition to other existing correlations. A summary of hese studies is shown in Table L The results of these studies showed that, the modified Hagedorn-Brown correlation was the best over-all predictor. However, it was found, based on the statistical results presented in thesf; studies, that on average, the modified Hagedorn-Brown correlation tended to under-predict pressure drops. Rossland(S) mentioned that the under-prediction was mainly due to the under-prediction of liquid holdup. Thompson(9) added that, the modified Hagedorn-Brown correlation tended to over-predict pressure loss in bubble flow (Griffith), while it tended to under-predict for slug flow.
In the present study an attempt was made to revise the Hagedorn-Brown liquid holdup correlation using unpublished field data. The original and the revised liquid hold-up correlations were then tested against 157 well test data using different cases.

Measured Data
The well test data were drawn from unpublished sources. These data consisted of 51 field pressure profiles (for vertical wells). In each profile, the well was divided into equal depth interval and the pressure was measured at the end of each interval.