An improved analytical solution for interface upconing around a well

Interface models of two-phase flow to a well usually apply vertical equilibrium assumptions to capture the vertical pressure variation in the two fluids. When large gradients in interface height occur, this leads to poor approximations. To deal with large-gradient interfaces, a variety of correction factors have been proposed on the basis of single-phase flow analogies. Herein we propose to include the effects of vertical flow directly through a nonlinear vertical pressure variation. This more complex formulation captures significantly more of the flow dynamics in the near-well region.