Hold up

The complexity of the different flow regimes involved in the flow of gas and liquid mixtures in pipes has greatly hindered the development oftheoretical mechanistic flow models. However, because ofthe industrial importance of these systems, there has been a substantial buildup of knowledge and experience, largely in the form ofempirical correlations. As a result, from the pipeline designer'spoint 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. Tp.is paper presents· the
res ults of a detailed comparison of correlations and models for holdup in horizontal two-phase flow. The results of other evaluations of flow-pattern maps1 and pressure-dropprediction methods2 for two-phase flow
in horizontal pipes, and holdup for two~phase flow in inclined pipes3 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 desc-ribe the amount of liquid actually contained in a pipe under twophase flow conditions.

PreviousEvaluations
In 1964, Dukler et ale 4 published a critical comparison of a number of holdup prediction'methods. The correlations of Hoogendoorn,5 Hughmark,6 and Lockhart and Martinelli7 wer~ tested against culled holdup data cqntained in the AGA/API data bank. 4 On the basis of three statistical parameters, the Hughmark correlation was found to be best over all, but the agreement' with the data wasgenerally poor for all the correlations. The
parameters used by Dukler et ale were based on percentage errors and thus were very sensitive to incorrect prediction for low measured values of holdup. A recent study by Yohra et ale 8 used the data ofBeggs9
and Eaton10 to compare the correlations of Beggs and Brill,!l Dukler,12 Eaton et al., 13 Guzhov et al., 14
B~ghmaik,6 and Lockhart andMartinelli. 7 Perhaps not too surprisingly, they reported that the ~aton et ale correlation ~as 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 ale 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 fromEaton 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 questiqn of bias in the analysis resulting from the test data. Clearly, if a given
correlation is based directly on a substantialportion of the test data being used. in the comparison, it is given an
unfair. advantage over the other correlations being tested.
To truly test an empipcal"correlation, its predictions must be compared with other than its own constitutive data.

Assuming that one has access to reliable data, as many data points as possible should be used to ensure that
bias toward anyone correlation will beminimal.
The first step in this study was to establish a comprehensive data file. The U. of Calgary Multipha~e Pipe
Flow Data Bank1 contaiils about 2,700 liquid-holdup observations·, representing a large number ofindependent
studies. This data file has· been used as the basis·for all subsequent critical evaluations.
The second point concerned choosing the most appropriate criteria as the basis for.comparing two or more
correlations. It-must be not~d that al~ost everyconceivable parameterrepresentmg some measure of the erraror
the difference between the observed data and the correlation prediction is extra sensitive to errors in some particular magnitude range of the holdup parameter. For exampie, a correlation that is mostly accurate at low values of holdup will appear superior to a...