The simultaneous flow of gas and liquid in pipes is frequently encountered in industry. Consequently, considerable effort has been expended in developing reliable techniques for calculating holdup and pressure drop for gasliquid flow. Most of the recent work has concentrated on either vertical or horizontal flow. However, in some industrial environments, notably oil-and gas-gathering systems, flow is neither vertical nor horizontal.In this paper we present some results from a recent study of gas-liquid flow in pipelines inclined f 10 deg. from the horizontal. We shall concentrate our attention on the slug-flow regime because we found this regime to predominate in uphill and horizontal flows for conditions typicaliy encountered in pipeline applications. Stratified flow tends to dominate in the downhill situation but even for this pipeline orientation, slug flow can exist if the flow rate is sufficiently large.At the outset of this study it was decided that a fundamental approach would probably have the greatest potential for skcess. Therefore an extensive review was made of the two-phase literature in order to determine (1) the flow regimes encountered in two-phase flow and (2) the types of models proposed for these regimes. On'the basis of this information it was possible to develop the model for slug flow in inclined pipelines described in the next section. This model provided a guide for selecting the operating conditions in an 80-ft. test section. By judiciously combining our experimental and theoretical information, we developed correlations which were successfully validated against field data. We believe that this test of our correlations demonstrates the viability of a fundamental approach to an otherwise complex problem.

A correlation for slug frequency in horizontal gas-liquid slug flow involving the use of the input liquid quality and mixture Froude number is presented. It is based on both prior literature data and recent data collected by the authors and has been effectively used in pressure drop calculations.

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A correlation is developed for predicting in-situ (or true) liquid holdups for two-phase, gas-liquid slug flows in inclined pipes. The correlation is based on experimental data collected in pipes ranging from 2.54 to 7.94 cm in diameter with the air-water system used.The experimental data used to develop the correlation were collected at zero input liquid qualities, as previously discussed by Greskovich (1973), and extended over the entire range. These data revealed little diameter effect on holdup for diameters greater than 2.54 cm but a marked effect of angle of inclination. Predicted holdup values show good agreement with experimental data. E. J. GRESKOVICH and W. T. COOPER Department of Chemical EngineeringBucknell University Lewisburg, Pennsylvania 17837 SCOPEThe prediction of liquid holdup for two-phase, gasliquid slug flows in pipelines is a must for design engineers. Correlations, for example, based on the early work of Lockhart and Martinelli (1949) for horizontal flows have been extended to inclined flows, and predictions by Flannigan (1958) for the contribution of hills to overall line pressure drops have markedly added to the technology, but both leave a lot to be desired.The objective of the research reported here was to develop a holdup correlation for inclined two-phase flows using only operating parameters known a priori to the design engineer. The correlation was to be tested with data collected in pipes up to a diameter of 7.94 cm with the air-water system used. Rather than collect holdup data over the entire range of input liquid qualities, experimental data at zero input liquid qualities were obtained and extrapolated by using a new technique (Greskovich, 1973) based on the correlation of Guzhov et al. (1967).Once verified, the model and resulting correlation can be used for scale-up purposes. CONCLUSIONS A N D SIGNIFICANCEIt has been shown that in-situ, or true, liquid holdups for inclined two-phase slug flows can be easily obtained over the range by experimentally measuring such holdups at zero input liquid qualities and then extrapolating the data based on Greskovich (1973). Experimental holdup data from a 7.94 cm diameter pipe were compared with data from smaller diameter pipes, and, based on the correlation of true liquid holdup against input liquid quality, by using mixture Froude number and angle of inclination as parameters, there appeared to be little direct effect of pipe diameter for pipes greater than 2.54 cm other than that taken into account by the mixture Froude number.

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