Physical and mathematical model of a dual-permeability medium

Authors:

• Marek Andrzej Marciniak,
• Mariusz Kaczmarek,
• Filip Wolny

Abstract

This article presents a physical and mathematical model of a groundwater medium characterized by heterogeneous systems of void space. The rate of water flowing through two sand samples of different hydraulic conductivity was analyzed with a specially designed apparatus (serving for the physical model). These analyses were conducted with the use of the PARAMEX method, which relies on creating water level fluctuations within a water-bearing medium and the registration of the water level's return to the initial position. The rate at which the water returns to the initial level, presented using a rate-of-rise curve, indicates the filtration parameters of the analyzed samples. Double- and triple-columned experiments were registered. Double-columned experiments were conducted to register the rate-of-rise curve of the two sand samples separately. Triple-columned experiments were used to re-enact the filtration properties of a dual-permeability medium. Simultaneously, a mathematical model was created. Theoretical rate-of-rise curves were generated using the MATLAB numerical computing environment. Both: experimentally registered and theoretical curves are presented in this article. A good convergence between these two types of curves has been obtained. This creates an opportunity to define interpretation algorithms for dual-permeability parameters based on the PARAMEX method.