Two-phase flow in horizontal and inclined pipelines can cause significant practical operating problems. When slugs flow in a horizontal pipeline that contains sections of different inclinations they undergo a change of length and slug flow characteristics as the slug move from section to section. In addition, slugs can be generated at low elbows, dissipate at top elbows and shrink or grow in length as they travel along the pipe.

A mathematical model and a computer program were developed to simulate these phenomena. The model was based on the sink/source concept at the pipeline connections. A connection between two pipeline sections of different slopes was conveniently called elbow. An elbow accumulates liquid as a sink, and releases liquid as a source. The sink/source has a characteristic capacity of its own. This capacity is positive if the liquid can indeed be accumulated at the elbow or negative if the liquid is actually drained away from the elbow. This type of treatment effectively isolates the flow upstream from an elbow from that downstream, while still allowing flow interactions between two detailed pipeline sections. The hydrodynamic flow model was also used to calculate the film liquid holdup in horizontal and inclined pipelines. The model can successfully predict the liquid film holdup if the liquid film height is assumed to be uniform through the gas pocket. Many other models were used to calculate all the needed parameters to perform the sink/source model.

The overall effect of horizontal and inclined pipelines on slug flow depends on the operating flow rates and pipeline configurations. For special case of near constant slug frequency corresponding to moderately high superficial liquid and gas velocities, this effect was found to be small. The changes in the film characteristics between two adjacent pipeline sections were found to be mostly responsible for the pseudo-slug generation, slug growth and dissipation in the downstream pipeline sections. The film liquid holdup decreased with increasing pipe diameter. The unit slug length increased at the upstream inclined pipes and decreased at the downstream inclined pipes with increasing pipe diameter. The possibility of pseudo-slug generation was increased at large pipe diameters even at high sink capacities. At low sink capacities, no pseudo-slugs were generated at high superficial velocities. The slug flow characteristics were more affected by low superficial gas and liquid velocities, large pipe diameters and shallow pipeline inclinations.


Slug flow is one of the most common flow patterns in two-phase gas-liquid flow that is one of the frequently occurring flow situations in many problem areas of practical importance. In petroleum industry, two-phase flow is encountered during the production and transportation of oil and gas. The flow occurs in both wellbores and flow lines and involves horizontal, inclined and vertical pipes. In offshore production, the two-phase flow line can be a substantial length before reaching separation facilities such as slug catchers requires methods to predict the pressure drop, slug length, and liquid holdup in the system.

Horizontal and inclined pipeline configurations are very common in field pipelines; however, very few studies have been published for slug flow in hilly terrain pipelines. A horizontal and inclined pipeline consists of three different sections, horizontal, upward inclined, and downward inclined section. Slug flow through separate pipeline what ever the inclination is, is relatively well understood, however a lack of understanding on how flow characteristics are changed when these pipeline sections are joined together into one line.

In this study, a computer program was developed to perform all necessary calculations for slug flow characteristics in different shapes of horizontal and inclined pipelines and in all the pipeline sections, which is the last step for pressure drop calculations. A horizontal and inclined pipeline consist of more than one section, each pipeline section has different inclination. Different combinations of these pipelines can be constructed, however, the program will solve for special shapes and combinations. A mathematical model developed by using Zheng's model and the sink/source concept. Different necessary models and relations were used to complete the needed variables for calculations.

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