The formation of liquid slugs caused by the pipeline profile ("terrain induced slugs1' or "severe slugs") is an important phenomenon to be analyzed during the design stage of systems for the transport of two-phase hydrocarbon mixtures. In this work a mathematical model is developed that generates a necessary condition for the occurrence of severe slugs and an analytical. expression to calculate their length.


When slug flow" is present in a pipeline transporting two-phase hydrocarbon mixtures', the slugs length and velocity must be calculated in order to size the slug-catcher at the line outlet. The "normal slugs" (caused by flow conditions along an infinite pipeline, with constant slope and physical properties) may be described by mathematical models and semi-empirical correlations usually developed on the basis of laboratory scale data [l], [2]. These correlations may not fit the data for large pipes. A major difficulty exists in describing terrain induced slugs which are caused by downward inclined pipe segments followed by upward segments. These slugs are called "severe" because their length can be much greater than the length of normal slugs. The severe slugs generation process is described: if a dip is present along a pipeline, and the flow in the downward inclined pipe is stratified, then the liquid level in the dip grows up until gas flow blockage is attained. Consequently the trapped gas pressure and the liquid levels in both pipes (descending and ascending) will increase. This trend continues if the increase in pressure of trapped gas is less than the increase in hydrostatic head caused by the liquid column growing up in the upward inclined pipe. When liquid arrives at the top of this pipe the slug growth ends and it is pushed and accelerated along the line. While passing the top, the slug tail loses some liquid (fall-back). During the subsequent descent the slug may break into shorter slugs or join slower ones. The complexity of severe slugs dynamics further increases when a lot of dips are present along the pipeline. The problem can be studied quantitatively by means of very expensive computer codes based on the latest correlations [3]. Anyway severe slugging can exist only if specific geometrical and physical conditions are present in a pipeline. In most cases of engineering interest, these conditions are not verified. In this paper a "point model" developed by Schmidt [4] is re-formulated. A condition for the onset of severe slugging is obtained and the length of the severe slug is analytically determined. The above mentioned condition, which was already proposed by Boe [5] # can be utilized during the pipeline design stage to exclude the onset of severe slugging along the line and to study this phenomenon at the outlet terminal. In fact, many pipelines, especially those off-shore, end in a riser pipe that makes the onset of severe slugging moreprobable.

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