In the petroleum industry, multiphase flows occur during production and transportation of hydrocarbons in horizontal, vertical, and inclined wellbores and pipelines. The behavior of multiphase flows is significantly more complex than that of single-phase flows because of the variations of phase distribution in the pipe, known as the flow pattern or flow regime. The flow pattern that exists at a certain location in the pipe depends on the relative magnitudes of the forces acting on the fluids. Buoyancy, turbulence, inertia, and surface tension forces vary significantly with flow rates, pipe diameter, inclination angle, and fluid properties of the phases involved. As a result of large pressure and temperature variations in wellbores and pipelines, several flow patterns can exist along the flow path. The accurate prediction of multiphase flow patterns as a function of flow parameters is important because it plays a significant role in the calculation of the pressure drop in the pipe.
Of particular interest is the dispersed bubble regime that can occur for any pipe inclination at high liquid flow rates. Dispersed bubble flow consists of a liquid matrix that convects small, non-interacting gas bubbles. Although apparently simple, the dispersed bubble regime can conceal very complex phenomena associated with the bubble distribution within the liquid carrier and bubble size limits before coalescence and/or breakage. Simplified models assuming homogeneous liquid-gas bubble mixtures employ volumetric averages of the thermophysical properties of the phases. At the simplest level these phenomena are accounted for through empirical correlations. The volumetric-averaged property approach introduces errors especially associated with the estimation of mixture viscosity. A poor choice of closure equations can render significant errors in pressure drop prediction.
In this study, computational fluid dynamics (CFD) simulations are used as numerical experiments for selection of the best closure equations for 1D mechanistic modeling of dispersed bubble flows.
Transient, 3D pipe flow simulations were implemented in ANSYS Fluent. Translational periodicity in the downstream direction was employed, enabling the capture of “fully developed” periodic flows for a prescribed pressure drop. The pressure drop values were estimated from experimental observations of the dispersed flow regime. Several mesh size sensitivity and domain length periodicity studies were run to ensure accurate modeling.
The volume fraction of the gas phase was assumed within the limits prescribed by Barnea’s mechanistic model  for dispersed bubble flows and was implemented by volume patching. Once fully developed flows were achieved, the frictional component of the pressure drop was identified and used to calculate the effective mixture viscosities.
The results of CFD and mechanistic models demonstrate plausible combinations of mixture density and mixture viscosity closure relations. For example, the choice that at first might appear most logical, namely a combination of volume-weighted density with liquid viscosity, proves surprisingly unsatisfactory. This case could be expected to give good results because only liquid is in contact with the pipe. However, the friction factor resulting from this model does not change with superficial gas velocity. In contrast, both the Taitel and Dukler model  of simply using the liquid properties and the use of volume-weighted average for both the density and viscosity predict the same physically satisfying result. In this case, the friction factor decreases with the dispersed bubble Reynolds number in an expected manner.
 Barnea, D., 1987, “A Unified Model for Predicting Flow-Pattern Transitions for the Whole Range of Pipe Inclinations,” Int. J. Multiphase Flow, 13(1), pp. 1-12.
 Taitel, Y. and Dukler, A.E., 1976, “A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow,” AIChE Journal 22(1), pp. 345-354.
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