Vol. 60 No. 3 (2021): Geofísica Internacional
Articles

How to use solutions of Advection-Dispersion Equation to describe reactive solute transport through porous media

Jetzabeth Ramírez Sabag
Instituto Mexicano del Petróleo
Bio
Dennys Armando López Falcón
Instituto Mexicano del Petróleo
Bio

Published 2021-06-24

Keywords

  • Advection-Diffusion Equation,
  • Analytical solutions,
  • Reactive Solute Transport,
  • Porous Media,

How to Cite

Ramírez Sabag, J., & López Falcón, D. A. (2021). How to use solutions of Advection-Dispersion Equation to describe reactive solute transport through porous media. Geofísica Internacional, 60(3), 229-240. https://doi.org/10.22201/igeof.00167169p.2021.60.3.2024

Abstract

Resumen
Las soluciones de la Ecuación de Advección-Dispersión son usadas frecuentemente para describir el transporte de solutos a través de medios porosos, considerando adsorción en equilibrio, de tipo lineal y reversible. Para indicar algunas sugerencias acerca de este tema, se hizo una revisión de las soluciones analíticas disponibles. Hay soluciones para Problemas con Condiciones de Frontera, de primer y tercer-tipo en la entrada así como de primer y segundo-tipo a la salida. Se analiza el comportamiento de las soluciones equivalentes, para sistemas finitos y semi-infinitos, observando que las soluciones de los sistemas semi-infinitos se aproximan a las correspondientes de los sistemas finitos conforme la condición de frontera de salida en el infinito se aproxima a la ubicación de medición del sistema finito. Solamente se presentan las soluciones analíticas con condiciones de frontera de segundo-tipo a la salida, ya que son iguales a las correspondientes soluciones analíticas con frontera de primer-tipo a la salida, para ambos tipos de condiciones de frontera de entrada usadas. Un análisis paramétrico, basado en el número de Peclet, muestra que todas las soluciones convergen cuando el número de Peclet es mayor que veinte. Los sistemas investigados deben tener un número de Peclet mayor que cinco para usar con confianza las soluciones de la Ecuación de Advección-Dispersión para describir el transporte de soluto en medios porosos.
Palabras Clave: Ecuación de Advección-Difusión, Soluciones Analíticas, Transporte de Solutos Reactivos, Medios Porosos.
Abstract
The solutions of Advection-Dispersion Equation are frequently used to describe solute transport through porous media when considering lineal and reversible equilibrium adsorption. To notice some warnings about this item, a review of analytical solutions available was done. There are solutions for Boundary Value Problems with first and third-type inlet boundary conditions as well as first and second-type outlet boundary condition. The behavior of equivalent solutions for finite and semi-infinite systems are analyzed, observing that semi-infinite system solutions approximates to the corresponding finite ones as the “infinite” outlet boundary condition approach to the finite measurement location. Because the analytical solutions with a first-type outlet boundary condition are equal to the corresponding analytical solutions with a second-type one, for both inlet boundary condition type used, only the latter is presented. A parametric analysis based on Peclet number shows that all solutions converge for Peclet number greater than twenty. Systems under research must have Peclet number greater than five to use confidently the solutions of Advection-Dispersion Equation to describe reactive solute transport through porous media.
Keywords: Advection-Diffusion Equation, Analytical solutions, Reactive Solute Transport, Porous Media.

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