Axisymmetric plumes due to fluid injection through a small source in a wet porous medium

Abstract

A small spherical source discharges a fluid into a porous medium that is already fully saturated with another fluid. The injected fluid has higher density than the ambient fluid, and so it forms a plume that moves downward under the effects of gravity. We present a simple asymptotic analysis assuming the two fluids do not mix that gives the width of the plume far from the source as a function of the injected volume flux. A spectral method is then developed for solving the full nonlinear problem in Boussinesq theory. Accurate numerical solutions are presented, which show in detail the evolution of the plume of heavier injected fluid over time. Close agreement with the asymptotic plume shape far from the source is demonstrated at later times.