Weak solutions of a gas-liquid drift-flux model with general slip law for wellbore operations

Abstract

In this work we study a compressible gas-liquid models highly rel-evant for wellbore operations like drilling. The model is a drift-ux model and is composed of two continuity equations together with a mixture momentum equation. The model allows unequal gas and liquid velocities, dictated by a so-called slip law, which is important for modeling of ow scenarios involving for example counter-current ow. The model is considered in Lagrangian coor-dinates. The difference in uid velocities gives rise to new terms in the mixture momentum equation that are challenging to deal with. First, a local (in time) existence result is obtained under suitable assumptions on initial data for a general slip relation. Second, a global in time existence result is proved for small initial data subject to a more specialized slip relation.