Effective dispersion in temporally fluctuating flow through a heterogeneous medium

Area of Science:

• Environmental science
• Hydrogeology
• Fluid dynamics

Background:

• Understanding solute transport in heterogeneous porous media is crucial for environmental remediation.
• Spatially heterogeneous media and temporally fluctuating flow conditions are common in groundwater systems.
• Existing theories often simplify flow to steady-state conditions, potentially missing key transport dynamics.

Purpose of the Study:

• To investigate the effective transport of passive solutes in temporally fluctuating flow within spatially heterogeneous media.
• To analyze the impact of temporal boundary condition fluctuations on solute dispersion.
• To develop a theoretical framework for predicting solute dispersion under complex flow conditions.

Main Methods:

• Solving the Darcy equation for incompressible fluid flow using perturbation theory.
• Distinguishing between spatial (medium heterogeneity) and temporal (boundary condition fluctuation) random processes.
• Evaluating second-order perturbation approximations for effective and ensemble dispersion coefficients.

Main Results:

• Derived dispersion coefficients include terms for local dispersion, spatial heterogeneity, and interactions between temporal fluctuations and heterogeneity.
• Temporal velocity fluctuations lead to time-evolving transverse dispersion coefficients reaching macroscopic values.
• Results are valid for moderately fluctuating fields but show wide applicability via simulations.

Conclusions:

• Temporal flow fluctuations significantly influence solute dispersion, leading to enhanced spreading.
• The findings reconcile theoretical predictions with field observations of solute transport.
• Supports remediation strategies involving temporal variations in injection/pumping rates for improved groundwater mixing.