We present the results of the development of a multi-fluid model for a transient multiphase flow in a wellbore. The 1D multi-fluid model governs a transient isothermal gas/oil/water flow in a deviated well.
The model is able to predict the flow regimes with a single interface between gas and liquid mixture: stratified-smooth, stratified-wavy, and slug flow regimes. The model of a stratified flow can be modified to cover the annular flow regime. The present model is an extension of the earlier work on multi-fluid models for near-horizontal pipes ,  to any inclination angle and additional phases.
The numerical algorithm is based on SIMPLE pressure-velocity coupling scheme, which is featured with the implementation of the geometry conservation based algorithm . The algorithm guarantees the compliance of balance equations together with the holdup constraint within specified tolerances. The phase appearance and disappearance is treated with specific modification of governing equations.
The code is validated on the results on transitions between the regimes from hydrodynamic stability study, and particularly on the flow patterns data from open literature. We discuss the experimental and analytical flow patterns in comparison with the results by the code. The results by the model are in a reasonable agreement with earlier published work.
Finally, we focus on the initiation of the flow inside the wellbore. The wellbore considered as a long pipe starting from horizontal section and coming to surface with steep inclination. The inflow of reservoir fluids occurs in the horizontal part of the wellbore. The change of wellbore inclination induces transition between different flow regimes. The impact of realistic wellbore trajectories on the dynamics of the wellbore flow is studied.