Improving the computational efficiency of first arrival time uncertainty estimation using a connectivity-based ranking Monte Carlo method

Morvillo, Maria; Bonazzi, Alessandra; Rizzo, Calogero B.; Barros, Felipe P. J. de

doi:10.1007/s00477-020-01943-5

Cited by 7 publications

(6 citation statements)

References 52 publications

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“…Its straightforward implementation makes the Shannon entropy a flexible means (i) for the optimization of observation networks (Fahle et al, 2015;Nowak et al, 2012);…”

Section: Calculation Of Flow Path Entropy In Concentration Patternsmentioning

confidence: 99%

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

Zehe

Loritz

Edery

et al. 2021

Hydrol. Earth Syst. Sci.

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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. 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.

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“…Its straightforward implementation makes the Shannon entropy a flexible means (i) for the optimization of observation networks (Fahle et al, 2015;Nowak et al, 2012);…”

Section: Calculation Of Flow Path Entropy In Concentration Patternsmentioning

confidence: 99%

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

Zehe

Loritz

Edery

et al. 2021

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

“…The emergence of preferential pathways of fluid flow and solute transport in saturated porous media has been explored in numerous simulation studies in heterogeneous conductivity fields, to relate the spatial correlation structures of the hydraulic conductivity and velocity fields to features of anomalous transport behavior (e.g., Cirpka and Kitanidis, 2000;Willmann et al, 2008;Berkowitz and Scher, 2010;de Dreuzy et al, 2012;Morvillo et al, 2021). While velocity correlation parameters have been successfully related to statistical moments of hydraulic conductivity, it remains challenging to delineate preferential pathways a priori exclusively based on multivariate and topological characteristics of the hydraulic conductivity field.…”

Section: Attempts To Characterize and Predict Preferential Transport ...mentioning

confidence: 99%

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

Zehe

Loritz

Edery

et al. 2022

Preprint

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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.

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“…The emergence of preferential pathways of fluid flow and solute transport in saturated porous media has been explored in numerous simulation studies in heterogeneous conductivity fields, to relate the spatial correlation structures of the hydraulic conductivity and velocity fields to features of anomalous transport behavior (e.g., Cirpka and Kitanidis, 2000;Willmann et al, 2008;Berkowitz and Scher, 2010;de Dreuzy et al, 2012;Morvillo et al, 2021). While velocity correlation parameters have been successfully related to statistical moments of hydraulic conductivity, it remains challenging or even impossible to a priori delineate preferential pathways exclusively based on multivariate and topological characteristics of the hydraulic conductivity field.…”

Section: Attempts To Characterize and Predict Preferential Transport In Groundwatermentioning

confidence: 99%

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

Zehe¹,

Loritz²,

Edery³

et al. 2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

Improving the computational efficiency of first arrival time uncertainty estimation using a connectivity-based ranking Monte Carlo method

Cited by 7 publications

References 52 publications

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

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

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

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

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