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Conservative models: parametric entropy vs. temporal entropy in outcomes.

Lumeng Huang1, Robert W Ritzi, Ramya Ramanathan

  • 1Department of Earth and Environmental Sciences, Wright State University, 3640 Coln. Glenn Hwy., Dayton, OH 45435, USA.

Ground Water
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Summary

Stochastic aquifer models must be three-dimensional and include geologic structure to accurately represent fluid flow and mass dispersion. This approach ensures a conservative and realistic representation of high-permeability pathways within the aquifer system.

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Area of Science:

  • Hydrogeology
  • Geostatistics
  • Environmental Engineering

Background:

  • Aquifer systems exhibit complex geologic architectures influencing fluid flow and mass dispersion.
  • The spatial distribution and connectivity of high-permeability facies are critical factors in aquifer behavior.
  • Existing models often simplify geologic structure, potentially reducing entropy and underrepresenting system complexity.

Purpose of the Study:

  • To explore the relationship between geologic structure, spatial disorder (entropy), and mass residence times in aquifer models.
  • To quantify and compare model parametric spatial disorder using Shannon entropy.
  • To determine the necessary dimensionality and structural representation for conservative stochastic aquifer modeling.

Main Methods:

  • Utilized Shannon entropy as a metric to quantify spatial disorder in permeability fields.
  • Compared predictions from models with and without explicit geologic structure.
  • Investigated the impact of model dimensionality (2D vs. 3D) on entropy representation, referencing percolation theory.

Main Results:

  • Models incorporating geologic structure show reduced entropy compared to unstructured models.
  • Maximum prediction variance (conservatism) does not solely depend on maximum permeability field disorder.
  • Three-dimensional models are essential to capture the full connectivity of high-permeability sediments at certain volume fractions, unlike 2D models.

Conclusions:

  • Geologic structure, particularly preferential-flow pathways, significantly impacts mass residence time distributions.
  • Two-dimensional models can profoundly underrepresent the entropy of real, three-dimensional aquifer systems.
  • Conservative stochastic modeling of aquifer systems necessitates three-dimensional representations that include detailed geologic structure.