Dispersive transport of ions in column experiments: An explanation of long‐tailed profiles

Abstract

Abstract. We present a novel microscopic model of sorption and convection of ions in heterogeneous media. Our model is based on an analogy to electron transport in a semiconductor. A new feature of our model is a power law random distribution of the adsorption time of ions. Diverging standard deviation of the distribution function yields anomalous ion transport. We show that this anomalous transport explains a concentration profile with a long tail that has been observed in column experiments. We successfully fit recent experimental data. Finally, we propose new experiments by which we can check the validity of our model. IntroductionThere have been many column experiments on reactive flow in heterogeneous media. Complete understanding of these local-scale experiments is important for understanding fieldscale heterogeneity. However, previous theoretical models for column experiments have produced only limited success. In the present paper we propose a novel model with heterogeneity of a new type and thereby explain the results of recent column experiments which were carefully performed with superior precision. Nakayama et al. In the present paper we propose a novel microscopic model of sorption and convection of nuclides. The theoretical solution of our model agrees with the experimental results of JAERI very well, particularly with the long tail of the concentration profile. Our theory also predicts that concentration profiles with different water flow rates should be identical to each other when we rescale the profiles. This theoretical prediction is also realized in the JAERI experimental data. We thereby conclude that our new model captures an essential feature of sorption and convection in heterogeneous media.We assume heterogeneity of ion adsorption in our model. A new feature is a random distribution function of adsorption time with diverging standard deviation, as opposed to the randomness with finite deviation assumed in previous studies on heterogeneous media. There have been theoretical studies 1027

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