Preferential pathways for fluid and solutes in heterogeneous groundwater systems: self-organization, entropy, work
<p>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 s...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2021-10-01
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| Series: | Hydrology and Earth System Sciences |
| Online Access: | https://hess.copernicus.org/articles/25/5337/2021/hess-25-5337-2021.pdf |
| Summary: | <p>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. Simulations at lower driving head
differences revealed an even stronger self-organization with increasing
variance. While these findings appear at first sight striking, they 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
in the transversal flow component, and these pathways emerge in the vicinity
of 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.</p> |
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| ISSN: | 1027-5606 1607-7938 |