In this work a unidimensional, time-dependent homogeneous mathematical model is presented. The model is able to predict pressure, temperature and velocity profiles of the flow known as bubbly-gas-bubbly-oil, which can be present when water-heavy oil and gas flow simultaneously in vertical pipes. The mathematical model consists of mass, momentum, and energy conservation equations and its numerical solution is based on the finite difference technique in the implicit scheme. The thermodynamic and transport properties of the fluids are estimated by correlations reported in the literature. The effects of different water-gas and water-oil shear stress correlations on the prediction were evaluated. As a result, some correlations are recommended to simulate the bubbly-gas-bubbly-oil flow. A new correlation for water-heavy oil-gas friction factor is suggested. A comparison of the model with existing experimental data shows a satisfactory agreement.

In the petroleum industry the heavy oil-gas-water three phase flow is present in both, on-shore and offshore pipelines. The adequate predictions of three-phase flow characteristics, such as flow patterns, pressure drop and holdup, can have significant impact on the proper design and operation of pipelines and on many flow assurance issues. To achieve this, experimental work and a rigorous modeling of three-phase flow must be carried out.When water, heavy oil and gas flow simultaneously through experimental vertical pipes, in such a way that water is the continuous phase, the Intermittent gas-Bubbly oil (Ig-Bo) flow pattern may appear. In this work a one-dimensional, thermal, transient, two-fluid, mathematical model for Ig-Bo flow is presented. The model was developed under the hypothesis that the Ig-Bo flow pattern can be approached by two different flow patterns, each one in neighboring regions: heavy oil-water bubbly flow in an annular region and heavy oil-gas-water bubbly flow in a slug region. The model consists of mass, momentum and energy conservation equations for every phase whose numerical solution is based on the finite difference technique in implicit scheme. The model is able to predict pressure, temperature, volumetric fraction and velocity profiles for each phase. The ratio between the liquid-slug length and the slug-unit length ( 2 Λ ), commonly used in two-phase flow, was modified to take into account the presence of heavy oil. It was observed that ( 2 Λ ) is larger than the two-phase flow and the correlation allow having the best predictions. The predictions are in agreement with experimental data reported in literature.

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