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

•Search for a model of unusual water movement during permeability tests is discussed.•Laboratory model of water flow through a dual-permeability medium is proposed.•Observations of rate-of-rise curves for different formations are presented.•Experimental curves are compared to theoretical curves determined by the model.•Good convergence between experimental results and math model was obtained.

SummaryThis 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.