One-dimensional solute transport for uniform and varying pulse type input point source through heterogeneous medium

Area of Science:

• Environmental Science
• Hydrogeology
• Chemical Engineering

Background:

• Understanding solute transport in porous media is crucial for environmental management and contaminant remediation.
• Heterogeneity in porous media significantly influences fluid flow and solute dispersion patterns.
• Existing models often simplify flow velocity, limiting their applicability to real-world scenarios.

Purpose of the Study:

• To develop an analytical solution for conservative solute transport in a 1D heterogeneous porous medium.
• To investigate the impact of spatially dependent seepage velocity and variable retardation factors on solute movement.
• To analyze solute transport under different input source conditions (uniform and varying pulse) and boundary conditions.

Main Methods:

• Developed an analytical solution using the Laplace transform technique (LLT).
• Introduced a novel space variable to simplify the problem formulation.
• Considered spatially dependent seepage velocity and a retardation factor inversely proportional to the square of flow velocity.

Main Results:

• Obtained analytical solutions for two distinct input source types (uniform and varying pulse).
• Graphical illustrations demonstrate the influence of medium heterogeneity on solute transport.
• Analyzed the effects of heterogeneity with and without the presence of a source pollutant.

Conclusions:

• The developed analytical solution accurately describes conservative solute transport in heterogeneous porous media.
• Medium heterogeneity and flow velocity variations significantly alter solute dispersion and breakthrough curves.
• The Laplace transform technique provides an effective method for solving complex solute transport problems.