Isothermal two-phase flow of a vapor–liquid system with non-negligible inertial effects

In this paper we consider the problem of gas/liquid extraction near the bottom well in the context of geothermal energy exploitation. In particular we develop a mathematical model for the isothermal two-phase flow of a mono-component fluid in an undeformable porous media taking into account inertial effects. We use the so-called Forchheimer’s equation to model the relation between the fluid velocity and the pressure gradient in the region of co-existence of the two phases.We formulate the problem in cylindrical geometry assuming steady state and isothermal conditions. We take into account capillary pressure and we study its influence on the whole system. We derive important formulas that allow to predict the main thermodynamical quantities in the region of co-existence of the liquid and gaseous phase and we determine constraints on the physical parameters in order to predict the behavior of the fluid in the domain of the problem. Finally, we perform some numerical simulations to investigate the dependence on the physical parameters involved in the model.