Time asymptotics of non-darcy flows controlled by total flux on the boundary

We study the long term asymptotics of the diffusive capacity, the integral characteristic of a domain with respect to a nonlinear Forchheimer flow in porous media. Conditions on the boundary are given in terms of the total flux and constraints on the pressure trace on the boundary. We prove that, if the total flux is stabilizing, then the difference between the pressure average inside the domain and the pressure average on the boundary is stabilizing as well. This result can be used for calculating the productivity index of the well, an important characteristic of the well performance. To obtain the main theorem, a refined comparison of the fully transient pressure with the pseudo-steady state pressure (the time derivative of pressure is constant) was performed. These results can be effectively used in reservoir engineering and can also be applied to other problems modeled by nonlinear diffusive equations. Bibliography: 26 titles.