The Relaxation Limit of a Compressible Gas-Liquid Model with Well-Reservoir Interaction

In this paper, we are concerned with the motion of gas-kick flow in oil wells for the extreme case where the pressure is largely dictated by the surrounding reservoir pressure. Formally, the model can be obtained by taking the relaxation limit of a two-phase compressible gas-liquid model with a pressure-dependent well reservoir interaction term. Under suitable smallness assumptions upon the initial data, the global existence as well as the uniqueness of strong solutions to the model is investigated by using the energy method. In addition, the large-time behavior of the solution is studied. Our results generalize the ones in [18, S. Solem and S. Evje, Z. Angew. Math. Phys., 68 (2017), pp. Art. 23].