Laboratory longitudinal diffusion tests: 1. Dimensionless formulations and validity of simplified solutions.

Area of Science:

• Geochemistry
• Materials Science
• Environmental Science

Background:

• Diffusion testing is vital for understanding solute transport in materials.
• Simplified analytical solutions are commonly used for interpreting diffusion tests.
• Internal consistency and valid conditions for these solutions require thorough investigation.

Purpose of the Study:

• To explore the feasibility of steady, quasi-steady, equilibrium, and transient-state analyses in diffusion testing.
• To determine the valid conditions, potential errors, and experimental time for each analytical solution.
• To provide a framework for designing, performing, and interpreting diffusion experiments.

Main Methods:

• Numerical analyses using unified dimensionless parameters.
• Relating results to dimensionless reservoir volume (DRV) with sorption as the unknown.
• Systematic reformulation of analytical models for comparison.

Main Results:

• Steady, quasi-steady, and equilibrium-state analyses are applicable for non-highly sorptive tracers.
• Quasi-steady and equilibrium-state analyses are inefficient for non-sorbing tracers in low porosity materials.
• Analytical models allow comparison of experimental times and assessment of applicability/error.

Conclusions:

• The study provides insights into the applicability and limitations of different diffusion analysis states.
• Dimensionless reservoir volume (DRV) can be deduced to guide experimental design and interpretation.
• This research aids in obtaining reliable diffusion parameters and optimizing diffusion testing methodologies.