Asymptotic behavior of a compressible two-phase model with well–formation interaction

In this work we consider a compressible gas–liquid model with a well–reservoir interaction term that is relevant for coupled wellbore-reservoir flow systems involved in e.g. drilling operations. Main focus is on deriving estimates that are independent of time. Under suitable conditions on the well–reservoir interaction term we obtain such estimates which allow prediction of the long-time behavior of the gas and liquid masses. Moreover, we also obtain a quantification of the convergence rates as a function of time and gain some insight into the role played by the rate characterizing how fast the well–reservoir interaction must die out. The model is investigated in a free boundary setting where the initial mass is a mixture of both phases, i.e., no single-phase zone exists.