Abstract
Fractal geometry is widely applied in the process description of contaminant transport, but few studies quantify the complexity of contaminant plume in the time series. Although the required accuracy is outside the scope of existent characterization methods, the model of solute transport remains the most sensitive issue for researchers due to its fractal behaviour. In this paper, a synthetic model is firstly presented under the condition of homogeneous/heterogeneous aquifer with different dispersivities and numbers of continuous point leakage sources. The new Hausdorff fractal dimension for the contaminant plume in the time series is obtained by the 3D box-counting method. According to the comparison among different hydro-geologic conditions, the result shows that the complexity of the contaminant plume decreases to the constant value with the passage time when the dispersivity increases and the number of point leakage sources rises. The decreasing fractal dimension is matched with the power-exponential function. The effect resulted from the number of point sources is tended to be weak when the amount is enormous. It is showed that the number of point leakage sources does not make a noticeable distinction in the homogeneous and heterogeneous aquifers.
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The authors would also acknowledge the anonymous reviewers for detailed comments on the improvement of this paper.
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This work was supported by the National Science Foundation of China (Grant Nos. 4F180035 and U1710253).
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Chen, G., Sun, Y. & Xu, Z. A Novel Approach to Assess the Complexity of Contaminant Plume Transportation in the Aquifer Based on Hausdorff Fractal Dimension. Water Air Soil Pollut 231, 145 (2020). https://doi.org/10.1007/s11270-020-04527-9
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DOI: https://doi.org/10.1007/s11270-020-04527-9