A first principle model for multiphase slugging flow in vertical risers

In this paper, we propose a simple model to represent the slugging flow regime appearing in vertical risers. We consider a one dimensional two-phase flow composed of a liquid phase and a gaseous compressible phase. The presented model can be applied to a wide class of systems, ranging from pure vertical risers to more complex geometries such as those found on actual sub sea petroleum facilities. Following ideas from the literature, we introduce a virtual valve located at the bottom of the riser. This allows us to reproduce observed periodic regimes. It also brings insight into the physics of the slugging phenomenon. Most importantly, this model reveals relatively easy to tune and seems suitable for control design. A tuning methodology is proposed along with a proof of the existence of a limit cycle under simplifying assumptions.