Flow models and numerical schemes for single/two-phase transient flow in one dimension

In the two-phase flow field, a traditional mathematical model for simulating the transition of severe slugging flow presents a challenge when liquid slugs completely block pipelines. Accordingly, an advanced and practical slug model that is derived from a mixture model associated with a slip closure is essential to solving the problem in cooperation with the two-fluid model. The model can offset numerical instability that arises from the discontinuous function of the friction factor across the transition from one flow pattern to the other. Two numerical schemes, the non-iterative and the iterative, are developed, and the proposed schemes can stably predict the transient problems under the Courant-Friedrichs-Lewy (CFL) condition for semi-implicit/implicit schemes. In the present work, pressure transients produced by a complex phenomenon, named water hammer effect, are captured using the single-phase flow model in one-dimension to verify the applicability of the numerical schemes and the friction factor model. At last, the analysis of the two-phase transient flow in a pipeline-riser system indicates that the significant advantage of the present schemes is the robustness that the numerical prediction of the severe slugging behaviour is accurate and stable.