Experimental studies show that liquid drop is deformed from initial spherical shape into ellipsoid shape in annular-mist flow, and the available critical Weber number We Crit determined by the experiment can vary from 2.2 to 60 for low-viscosity liquid. On the basis of the force equilibrium and the critical-Weber-numbercalculation method proposed by Azzopardi (1985), this paper develops a new model to predict minimum gas rate. This model introduces a parameter C k,Wecrit that describes the effect of liquiddrop deformation and the maximum drop-size difference on the minimum gas rate. The effect of liquid-droplet coalescence is also considered indirectly. A function to predict drop-deformation magnitude for different critical Weber numbers is developed on the basis of energy conservation. The function-prediction results are in good agreement with experimental data from the literature and the predicted result from the drop deformation/breakup model, and the average absolute deviation is 6.1%. The C k,Wecrit calculated by the new model increases with the increase of the pressure and liquid amount and it varies from 3.99 to 7.3, which means the critical gas velocity increases with the increase of the pressure and liquid amount. Numerous gas-well data were used for the validation of these entrained models, including data from 33 low-pressure gas wells (wellhead pressure: 0.26-3.41 MPa) from Coleman et al. (1991) and 91 high-pressure gas wells (wellhead pressure: 0.7-56 MPa) from Turner et al. (1969). The result shows the new entrained model has a good comprehensive performance in judging liquid-loading status in both high-and low-pressure gas wells. Spherical-Droplet Model. Turner et al. (1969) proposed a liquid-film model and an entrained-droplet model. The liquid-film model describes the movement of liquid-film flow along the wall of tubing, whereas the entrained-droplet model describes the movement of liquid drops entrained in gas core. Those authors proved that the entrained-droplet model was more adequate to predict critical gas velocity. In the model of Turner et al. (1969), the spherical entrained droplet was adopted to calculate the critical gas velocity and rate, and values of 30 and 0.44 were used as the Weber number and drag coefficient, respectively. It was Entrained-Droplet Model

Maximum ellipsoidal magnitude of the droplet is an important basic parameter for calculating drag force, droplets axial-velocity and dispersed-phase pressure gradient in an annular-mist pipe flow. An analytical correlation to predict the maximum ellipsoidal magnitude of a low-viscosity droplet in a parallel gas stream based on energy conservation and volume conservation. Stagnant pressure distribution on droplet surface is revised from Flachsbart's formula. The proposed correlation has clear physical meaning and easy to use. The correlation captures the deformation mechanism with an average absolute percent error of 9.53. The effect of stagnant pressure distribution on the proposed correlation's accuracy is discussed.

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