Preprints
https://doi.org/10.5194/hess-2021-254
https://doi.org/10.5194/hess-2021-254

  21 May 2021

21 May 2021

Review status: a revised version of this preprint was accepted for the journal HESS and is expected to appear here in due course.

Preferential Pathways for Fluid and Solutes in Heterogeneous Groundwater Systems: Self-Organization, Entropy, Work

Erwin Zehe1, Ralf Loritz1, Yaniv Edery2, and Brian Berkowitz3 Erwin Zehe et al.
  • 1Karlsruhe Institute of Technology (KIT), Institute of Water and River Basin Management, Karlsruhe, Germany
  • 2Technion Israel Institute of Technology, Haifa, Israel
  • 3Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot, Israel

Abstract. Patterns of distinct preferential pathways for fluid flow and solute transport are ubiquitous in heterogeneous, saturated and partially saturated porous media. Yet, the underlying reasons for their emergence, and their characterization and quantification, remain enigmatic. Here we analyze simulations of steady state fluid flow and solute transport in two-dimensional, heterogeneous saturated porous media with a relatively short correlation length. We demonstrate that the downstream concentration of solutes in preferential pathways implies a downstream declining entropy in the transverse distribution of solute transport pathways. This reflects the associated formation and downstream steepening of a concentration gradient transversal to the main flow direction. With an increasing variance of the hydraulic conductivity field, stronger transversal concentration gradients emerge, which is reflected in an even smaller entropy of the transversal distribution of transport pathways. By defining "self-organization" through a reduction in entropy (compared to its maximum), our findings suggest that a higher variance and thus randomness of the hydraulic conductivity coincides with stronger macroscale self-organization of transport pathways. While this finding appears at first sight striking, it can be explained by recognizing that emergence of spatial self-organization requires, in light of the second law of thermodynamics, that work be performed to establish transversal concentration gradients. The emergence of steeper concentration gradients requires that even more work be performed, with an even higher energy input into an open system. Consistently, we find that the energy input necessary to sustain steady-state fluid flow and tracer transport grows with the variance of the hydraulic conductivity field as well. Solute particles prefer to move through pathways of very high power, and these pathways pass through bottlenecks of low hydraulic conductivity. This is because power depends on the squared spatial head gradient, which is in these simulations largest in regions of low hydraulic conductivity.

Erwin Zehe et al.

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-254', Daniele Pedretti, 17 Jun 2021
    • AC2: 'Response to review of Daniele Pedretti', Erwin Zehe, 29 Jun 2021
  • RC2: 'Comment on hess-2021-254', Hubert H.G. Savenije, 20 Jun 2021
    • AC1: 'Response to review of Hubert Savenije', Erwin Zehe, 29 Jun 2021
  • AC1: 'Response to review of Hubert Savenije', Erwin Zehe, 29 Jun 2021
  • AC2: 'Response to review of Daniele Pedretti', Erwin Zehe, 29 Jun 2021

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-254', Daniele Pedretti, 17 Jun 2021
    • AC2: 'Response to review of Daniele Pedretti', Erwin Zehe, 29 Jun 2021
  • RC2: 'Comment on hess-2021-254', Hubert H.G. Savenije, 20 Jun 2021
    • AC1: 'Response to review of Hubert Savenije', Erwin Zehe, 29 Jun 2021
  • AC1: 'Response to review of Hubert Savenije', Erwin Zehe, 29 Jun 2021
  • AC2: 'Response to review of Daniele Pedretti', Erwin Zehe, 29 Jun 2021

Erwin Zehe et al.

Erwin Zehe et al.

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Short summary
This study uses concepts from thermodynamics and information theory to quantify and explain the enigmatic emergence of preferential flow and transport in unstructured heterogeneous saturated porous media. We demonstrate that the downstream concentration of solutes in preferential pathways implies a downstream declining entropy in the transverse distribution of solute transport pathways. Preferential flow patterns with lower entropies emerged within media of higher heterogeneity.