Entropy, fractality, and thermodynamics of groundwater pathways

Abstract

This Work deepens the issue of groundwater connectivity and the behavior of permeable (alluvial) pathways from a thermodynamic viewpoint. Groundwater pathways have been inferred from geological data upon a starting dataset of 2000 MC simulations of alluvial sediment ratios. Each MC-realization is thresholded upon a certain sediment’s ratio threshold, within the unit interval. Each ensemble of connected locations forms a subsurface pathway, and the latter is fitted through a Gibbs’ Distribution (GD). Each distribution’s best-fit exponent is proportional to the local entropy in a random point of the connected pathway. GD’s exponents decrease at the increase of the threshold prescribed for defining an alluvial pathway, proving that a higher conductivity threshold enables identifying a highly efficient pathway, where groundwater flow encounters less resistance, tending to be more conveyed. Moreover, more probable pathways return lower GD exponents. Lower GD exponents imply a lower energy dissipation within a groundwater pathway; hence the latter is thermodynamically more efficient (and colder) than its less probable counterparts. Moreover, most probable groundwater pathways are close to a thermodynamical equilibrium (zero free-energy), making their spatial (probable) structure more ordered to energetic fluctuations. In addition, the estimation of GD’s exponents for a randomly sampled connected pathways subset enables to highlight the fractal nature of a subsurface pathway; the GD’s exponent weak variation across scales underlines its role as a signature of the whole pathway as of its portions.These results, achieved only from geological data, are important for understanding the patterns of groundwater and contaminant pathways and are strikingly consistent with the latest findings of the research in hydrological systems thermodynamics. This work frames groundwater pathways’ delineation within a novel thermodynamic framework and reconciles their spatial behavior to that of their surface counterparts.