Preferential pathways for fluid and solutes in heterogeneous groundwater systems: Self-organization, entropy, work

This study proposes an alternative framework to quantify and explain the enigmatic emergence of preferential flow and transport in heterogeneous saturated porous media, using concepts from thermodynamics and information theory. We examined simulations of two-dimensional fluid flow and solute transport based on the methods of Edery et al. (2014) at total head differences of 100 and 10 characterized the discrete probability distribution of solute particles to cross a distinct transversal position in a plane normal to the direction of the mean flow by means of the Shannon entropy. In general, we found a declining entropy with increasing downstream transport distance, reflecting a growing downstream self-organization due to the increasing concentration of particles in preferential flow paths. Strikingly, preferential flow patterns with lower entropies emerged when analyzing simulations in media with larger variances in hydraulic conductivity, and this enhanced self-organization appeared even stronger for simulations at lower head differences. This implies that macro-states of higher order are established, despite the higher randomness of ln(K) for a range of Peclet numbers representing strong and intermediate importance of advective transport. The key to explain this almost paradoxical behavior is the finding that power in the vertical flow components grows with the variance of the hydraulic conductivity field. Due to this larger energy input, the vertical/transversal flow component may perform more work to increase the order in the flow path distribution, through steepening transversal concentration gradients as reflected in lower entropies. The emergence of spatially organized preferential transport and the related decline in flow path entropy essentially requires that the entropy is exported from the system. Consistently, we found that a declining entropy in lateral distribution of flow paths goes along with a rising entropy in the associated breakthrough curve. This space-time asymmetry in entropy implies that perfect organization and certainty about both flow paths and travel times can never simultaneously occur. This required consummation of entropy and thus violation of the second law of thermodynamics. We thus propose that the combined use of free energy and entropy holds the key to characterize, quantify and predict the self-organized emergence of preferential flow phenomena and to explain the underlying cause of their emergence.References:Edery, Y., Guadagnini, A., Scher, H., and Berkowitz, B.: Origins of anomalous transport in disordered media: Structural and dynamic controls, Water Resour. Res., 50, 1490-1505, doi:10.1002/2013WR015111, 2014.