Instabilities, Waves and Slugs in Pipeline Two-Phase Flows

Summary

This paper is concerned with multi-phase fluid flow models that can be represented by systems of one-dimensional hyperbolic equations, with particular application to pipeline two-phase flows. It is shown how the governing equations can be rewritten in a form which enables analogies to be drawn with the flow of liquid down open, inclined channels. For such flows, smooth periodic solutions do not satisfy the basic equations but a train of piecewise smooth waves joined together by shocks can be constructed. These waves evolve non-linearly to their asymptotic form following a physical instability occurring in the flow. For pipeline two-phase flows, the top of the pipe puts a constraint on the maximum amplitude of the waves but also encourages the growth of the instability. When the wave bridges the pipe a liquid slug is formed, which is often an unwelcome problem in production facilities, especially offshore.

These ideas can be extended to other systems of multi-phase flows. For example, a third phase can be added to pipeline flows and the governing equations can be rearranged into a form enabling similar solutions to be obtained. Dispersed two-phase flows and granular flows can also be represented by analogous sets of equations with similar solutions for appropriate values of the physical parameters. These types of solutions, viz piecewise smooth waves joined together by shocks are typical for systems of hyperbolic equations with source terms indicating that instabilities and growth of waves in a wide variety of multi-phase systems are closely related phenomena.