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Effect of sorption intensities on dispersivity and macro-dispersion coefficient in a single fracture with matrix diffusion

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Abstract

Matrix diffusion and sorption are among the key processes impacting the efficiency of natural attenuation in the subsurface. While these processes have been studied extensively in fractured media, limited information exists on the sorption nonlinearity. To address this shortfall, a numerical model has been developed that couples matrix diffusion and nonlinear sorption at the scale of a single fracture using the dual-porosity concept. The study is limited to a constant continuous-solute-source boundary condition. The influence of sorption intensities on dispersivity and macro-dispersion coefficient is investigated using a method of spatial moments. Results suggest that mixing of solutes is significantly lowered by nonlinear sorptive behavior, with respect to the mixing caused by matrix diffusion for linearly sorbing solutes. Also, the magnitude of time dependent dispersivity during the pre-asymptotic regime is lower for nonlinearly sorbing solutes with respect to the linearly sorbing solutes. Reduced mixing is also observed for nonlinearly sorbing solutes under combined mechanisms of matrix diffusion and decay.

Résumé

Les phénomènes de diffusion et de sorption comptent parmi les processus clés qui influent sur l’atténuation naturelle en subsurface. Si ces processus ont été massivement étudiés en milieu fracturé, il existe en revanche peu d’informations sur la non-linéarité de la sorption. Afin de combler cette lacune, un modèle numérique a été développé ; il couple la diffusion dans la matrice et la sorption non-linéaire à l’échelle d’une fracture unitaire en utilisant le concept de double porosité. La seule condition aux limites fixée pour toute l’étude est une source de soluté constante et continue. L’influence de l’intensité de la sorption sur la dispersivité et sur le coefficient de macro-dispersion est étudié via une méthode utilisant les moments spatiaux. Les résultats suggèrent que les mélanges de solutés sont significativement réduits par les phénomènes de sorption non-linéaires, comparativement aux mélanges causés par la diffusion pour des solutés à sorption linéaire. C’est pourquoi la dispersivité, dépendante du temps, est plus faible pour les solutés à sorption non-linéaire que pour les solutés à sorption linéaire, lors du régime pré-asymptotique. Des mélanges réduits ont également été observés pour des solutés à sorption non-linéaire, sous les mécanismes combinés de diffusion dans la matrice et de dégradation.

Resumen

La difusión intersticial y la adsorción se encuentran entre los procesos clave que impactan la eficiencia de la atenuación natural en el subsuelo. Mientras que estos procesos se han estudiado extensamente en medios fracturados existe información limitada acerca de la no linealidad de la adsorción. Para abordar esta situación se ha desarrollado un modelo numérico que acopla la difusión intersticial y la adsorción no lineal a la escala de una sola fractura usando el concepto de porosidad doble. El estudio se restringe a condiciones limitantes de fuente de soluto constante y continuo. Se investiga la influencia de las intensidades de adsorción sobre el coeficiente de dispersión-macro y dispersividad usando un método de momentos espaciales. Los resultados sugieren que la mezcla de solutos disminuye significativamente mediante comportamiento de adsorción no lineal, en relación con la mezcla causada por difusión intersticial para solutos con adsorción lineal. Se observa que la magnitud de la dispersividad dependiente del tiempo durante el régimen pre-asintótico es más baja para solutos con adsorción no lineales en relación a los solutos con adsorción lineal. También se observa mezcla reducida para solutos con adsorción no lineal bajo mecanismos combinados de difusión intersticial y desintegración.

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Acknowledgements

Thanks are extended to the associate editor and the anonymous reviewers whose editorial and substantive comments improved the paper. Thanks also go to the Managing Editor (Prof C. Simmons) and Technical Editorial Advisor (Mrs. Sue Duncan) for their editorial comments.

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  1. Department of Civil Engineering, Indian Institute of Technology - Madras, Chennai, India , 600 036

    G. Suresh Kumar

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Suresh Kumar, G. Effect of sorption intensities on dispersivity and macro-dispersion coefficient in a single fracture with matrix diffusion. Hydrogeol J 16, 235–249 (2008). https://doi.org/10.1007/s10040-007-0234-5

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