Flow and residence time in a laboratory aquifer recharged by rainfall

During rainfall, water infiltrates the soil, and percolates through the unsaturated zone until it reaches the water table. Groundwater then flows through the aquifer, and eventually emerges into streams to feed surface runoff. We reproduce this process in a  two-dimensional laboratory aquifer recharged by artificial rainfall. As rainwater infiltrates, it forms a body of groundwater which can exit the aquifer only through one of its sides. The outlet is located high above the base of the aquifer, and drives the flow upwards. The resulting vertical flow component violates the Dupuit-Boussinesq approximation. In this configuration, the velocity potential that drives the flow obeys the Laplace equation, the solution of which crucially depends on the boundary conditions. Noting that the water table barely deviates from the horizontal, we linearize the boundary condition at the free surface, and solve the flow equations in steady state. We derive an expression for the velocity potential, which accounts for the shape of the experimental streamlines and for the propagation rate of tracers through the aquifer. This theory allows us to calculate the travel times of tracers through the experimental aquifer, which are in agreement with the observations. The travel time distribution has an exponential tail, with a characteristic time that depends on the aspect ratio of the aquifer. This distribution depends essentially on the geometry of the groundwater flow, and is weakly sensitive to the hydrodynamic dispersion that occurs at the pore scale.