W-tube system with bi-exponential response – A model for permeability tests in heterogeneous aquifers

This article presents the results of a search for a laboratory (physical) and the corresponding mathematical model of bi-exponential water level movement in a W-tube (triple-columned) system. Water level movement in this laboratory system resembles the behavior of the water level in piezometers installed in heterogeneous aquifers during field permeability tests, where a response to the initial disturbances is recorded. The configuration of the W-tube was set to ensure the bi-exponential return of the water level to its initial position. Throughout laboratory experiments, four types of sand samples were analyzed. The shape of the recorded rate-of-rise curve depended on hydraulic conductivities of the sands in the branches of the W-tube system. Results of the analytical mathematical model and the experiments were compared, good convergence was obtained.