Can the Maximum Power Principle predict Effective Conductivities of a Confined Aquifer? A Lab Experiment

Abstract:

Power can be performed by a system driven by a potential difference. From a given potential difference, the power that can be subtracted is constraint by the Carnot limit, which follows from the first and second laws of thermodynamics. If the system is such that the flux producing power (with power being the flux times its driving potential difference) also influences the potential difference, a maximum in power can be obtained as a result of the trade-off between the flux and the potential difference. This is referred to as the maximum power principle.

It has already been shown that the atmosphere operates close to this maximum power limit when it comes to heat transport from the Equator to the poles, or vertically, from the surface to the atmospheric boundary layer. To reach this state of maximum power, the effective thermal conductivity of the atmosphere is adapted by the creation of convection cells.

The aim of this study is to test if the soil’s effective hydraulic conductivity also adapts in such a way that it produces maximum power. However, the soil’s hydraulic conductivity adapts differently; for example by the creation of preferential flow paths. Here, this process is simulated in a lab experiment, which focuses on preferential flow paths created by piping.

In the lab, we created a hydrological analogue to the atmospheric model dealing with heat transport between Equator and poles, with the aim to test if the effective hydraulic conductivity of the sand bed can be predicted with the maximum power principle. The experimental setup consists of two freely draining reservoir connected with each other by a confined aquifer. By adding water to only one reservoir, a potential difference will build up until a steady state is reached. The results will indicate whether the maximum power principle does apply for groundwater flow and how it should be applied. Because of the different way of adaptation of flow conductivity, the results differ from that of the atmosphere.