Analytical model of reactive transport processes with spatially variable coefficients.

Area of Science:

• Environmental Science
• Geochemistry
• Applied Mathematics

Background:

• Analytical solutions for reactive transport models are crucial for understanding contaminant fate and transport.
• Existing models often simplify by using constant coefficients, limiting applicability to real-world scenarios with variable flow velocity (v(x)) or decay rates (k(x)).

Purpose of the Study:

• To develop a general framework for constructing exact analytical solutions to partial differential equation (PDE) models of reactive transport.
• To extend analytical modeling capabilities to scenarios with spatially variable coefficients.

Main Methods:

• A regular perturbation technique is employed for advection-dominant problems.
• The framework is demonstrated for one-dimensional scenarios with constant and variable coefficients.
• A symbolic worksheet is provided for evaluating solutions with different parameters.

Main Results:

• Exact analytical solutions were derived for reactive transport models with spatially variable coefficients.
• The derived solutions show good agreement with numerical approximations.
• The approach is adaptable to various initial conditions and coefficient functions.

Conclusions:

• The presented framework provides a versatile tool for analyzing contaminant fate and transport in porous media.
• The method can be generalized to multispecies transport and higher-dimensional problems.
• This approach enhances the utility of analytical models for practical contaminant transport studies.