Two-phase gas-liquid flow with particular emphasis on holdup measurements and predictions

Abstract

The work described in this thesis is an analytical and experimental study of two-phase gas-liquid horizontal flow in a conduit with particular emphasis on holdup measurements and predictions. Holdup and pressure drop, their inter-relationships, and their flow pattern dependence were investigated. A simple method for flow pattern determination was presented so that the appropriate prediction method may be selected for a particular situation. The results were discussed by comparison with a wide range of experimental data and the relevant literature. Two simple devices for holdup measurements were developed in this work and their behaviours were also found to be flow pattern dependent. The results are as follows: In the analytical study, the original Lockhart-Martinelli formulation was treated analytically for ideal stratified flow giving equations which agree with experimental pressure drop and holdup data and the more rigorously derived relationships of Johannessen and Taitel & Dukler. For ideal annular flow, the derived equations predicted pressure drop in large diameter pipes reasonably well giving results which are in agreement with the modified equation of Baker. Poor prediction was achieved for small diameter pipes. The holdup equations derived for annular flow were also in poor agreement with experimental data although a slight modification resulted in an equation that was not only suitable for holdup prediction, but also may be used to represent the original Lockhart-Martinelli holdup correlation over the entire operating range. A correlation was presented for the frictional pressure drop in annular flow based on laboratory air-water data and geothermal steam-water data. The correlation was found to predict pressure loss values which agreed with data from various different sources. The correlation exhibited a point of inflexion which was believed to be due to the transition from a ripple wave type of interfacial disturbance to one of roll wave-droplet entrainment. An extensive literature survey showed that such a transition at high gas rate occurs at all flow orientations and is governed by a critical liquid rate given by a definite value of the Weber number defined in terms of the liquid phase. The Butterworth form of holdup equation was justified by assuming ideal stratified and annular turbulent-turbulent and viscous-viscous flows. A full set of equations for stratified flow covering the cases of liquid-gas, turbulent-viscous and viscous-turbulent were also derived. It was found that the variation in the coefficients and exponential factors in the Butterworth equation was due to at least three factors: the flow pattern, the flow regimes of the phases, i.e., viscous or turbulent, and the range of the value of the ratio of the liquid holdup to the voidage. Furthermore, experimental data were found to behave according to whether the flow pattern was stratified, slug and plug or annular. Equations for determining these flow patterns were presented, based on the derived stratified flow equations, and were checked to be in agreement with the flow pattern maps of Mandhane et al and Taitel & Dukler, and the experimental flow pattern observations of this work. Since the derivation from the original Lockhart-Martinelli formulation did not yield a completely satisfactory relationship for the holdup and pressure drop in annular flow, such a relationship was examined in terms of the film flow equations, Newton's law of viscosity and the Prandtl’s mixing length. This was also compared with the analysis of Levy of annular-mist flow using the mixing length theory. Throughout the analysis, the results were compared with various sources of laboratory air-water data and geothermal steam-water data, and the discrepancies, if any, were discussed. The rise velocity of Taylor bubbles in conduits was also examined in terms of the film flow equations, the Newton's law of viscosity, the Prandtl’s mixing length theory and the universal velocity distribution equations. The rise velocity of a Taylor bubble as derived by the Prandtl's mixing length theory has the same form as that derived by Dumitriscu and Davies & Taylor who used the classical potential flow theory. The analysis was extended to justify the Armand equation for holdup for slug and plug flows. Thus, to summarise the analytical work presented in this work, given a set of input conditions, the flow pattern may be predicted as one of three: stratified, slug and plug, annular. From a knowledge of the flow pattern, appropriate methods of holdup and pressure drop prediction may be chosen. The interrelationships between holdup and pressure drop for stratified and annular flow have also been shown. In the experimental study, the application of two simple devices, developed in this work, one of which was subsequently patented, for holdup measurement was investigated. Both devices were found to be flow pattern dependent in their behaviour and require calibrations. During the study of these two devices, pressure drop, holdup and flow pattern data were also generated and were used for the comparison with the analytical part of this work.