Critical Evaluation of Holdup Prediction Methods for Gas-Liquid Flow in Horizontal Pipes
Authors: Mandhane J.M. , Gregory G.A. , Aziz K. 
Published: December 2007

This paper uses a large amount of available data for liquid holdup in horizontal, two-phase flow to compare and evaluate 12 different correlations and models. In a proposed two-step holdup prediction method, an expected flow pattern is predicted on the basis of the system variables. The correlation recommended for use with that flow regime then is used to predict the holdup.

Introduction
The complexity of the different flow regimes involved in the flow of gas and liquid mixtures in pipes has greatly hindered the development of theoretical mechanistic flow models. However, because of the industrial importance of these systems, there has been a substantial buildup of knowledge and experience, largely in the form of empirical correlations. As a result, from the pipeline designer's point of view, the task of selecting the "best" or most point of view, the task of selecting the "best" or most appropriate correlations has become rather formidable.
A need clearly exists for a periodic critical evaluation of available prediction methods. This paper presents the results of a detailed comparison of correlations and models for holdup in horizontal two-phase flow. The results of other evaluations of flow-pattern maps and pressure-drop prediction methods for two-phase flow pressure-drop prediction methods for two-phase flow in horizontal pipes, and holdup for two-phase flow in inclined pipes are reported elsewhere.
The term "liquid holdup" is used in this paper to mean "in-situ liquid volume fraction." Other definitions or measures are often used in the literature to describe the amount of liquid actually contained in a pipe under twophase flow conditions.
Previous Evaluations Previous Evaluations In 1964, Dukler et al. published a critical comparison of a number of holdup prediction methods. The correlations of Hoogendoorn, Hughmark, and Lockhart and Martinelli were tested against culled holdup data contained in the AGA/API data bank. On the basis of three statistical parameters, the Hughmark correlation was found to be best parameters, the Hughmark correlation was found to be best over all, but the agreement with the data was generally poor for all the correlations. The parameters used by poor for all the correlations. The parameters used by Dukler et al. were based on percentage errors and thus were very sensitive to incorrect predictions for low measured values of holdup.
A recent study by Vohra et al. used the data of Beggs and Eaton to compare the correlations of Beggs and Brill, Dukler, Eaton et al., Guzhov et al., Hughmark, and Lockhart and Martinelli. Perhaps not too surprisingly, they reported that the Eaton et al. correlation was in best agreement with the Eaton data, and the Beggs and Brill correlation was in best agreement with the Beggs data. Over all, the Eaton et al. correlation was found to be in best agreement with the test data, followed by the Beggs and Brill correlation. It should be noted that there were 238 data points from Eaton and only 58 from Beggs used in the study.

Approach Followed in This Study
In the early stages of this study, it was apparent that there were several aspects of the proposed comparison that should be considered in some detail.
The first point concerned the question of bias in the analysis resulting from the test data. Clearly, if a given correlation is based directly on a substantial portion of the test data being used in the comparison, it is given an unfair advantage over the other correlations being tested.
JPT
P. 1017