Universal Relationship between Mass Flux and Properties of Layered Heterogeneity on the Contaminant-Flushing Process
Abstract
:1. Introduction
2. Problem Formulation
3. Results and Discussion
3.1. Numerical Setup
3.2. Flushing Processing
3.3. Effects of Porosity
3.3.1. Effect of Porosity for Case 1
3.3.2. Effects of Porosity for Cases 1 and 2
3.3.3. Effects of Porosity for Cases 2 and 3
3.3.4. Effects of Porosity on Temporal Distribution of the Maximum Vertical Mass Flux
3.4. Effect of Transverse Dispersivity
3.4.1. Effect of Transverse Dispersivity for Cases 4–6
3.4.2. Effect of Transverse Dispersivity on Temporal Distribution of the Maximum Vertical Mass Flux
3.4.3. Effect of Transverse Dispersivity on Total Vertical Mass Flux
3.5. Effect of Retardation Factor
4. Applications and Limitations
4.1. Applications
4.2. Limitations and Future Works
5. Conclusions
- (1)
- With all the other parameters remaining the same, increasing the porosity of layer-2 (which has a slower flushing velocity) would (a) lead to increased mass flux across the interface of two layers, (b) shift the rising limb of the mass flux-distance curve towards the left boundary where solute-free water is introduced for flushing, resulting in a larger mass flux range at a given time. Thus, the total amount of mass flux at a given time would be greater. However, if keeping all parameter unchanged but increasing the porosity of layer-1 (which has a faster flushing velocity) would (a) lead to decreased mass flux, (b) shift the falling limb of the mass flux-distance curve towards the left boundary, causing less total mass flux. Furthermore, increasing the porosity of layer-2 would also prolong the time required for completely flushing out the solute from the system.
- (2)
- When increasing the transverse dispersivity in either layer-1 or layer-2, the mass flux would increase. Changing the transverse dispersivity has little effect on the longitudinal transport, and so, the time needed for completing the flushing process will not be affected.
- (3)
- Retardation factor plays a similar role with porosity. When all the other parameters remain unchanged, the increased retardation factor of layer-2 would increase the mass flux and expand the spatial range (along the layering or bedding direction) of the vertical mass flux. In contrast, an increased retardation factor in layer-1 would decrease the mass flux and lead to a reduced range of the vertical mass flux. Furthermore, increasing the retardation factor of layer-2 would also prolong the time needed for completely flushing out the solute from the system.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Literatures | Methods | Main Points | Differences from This Study |
---|---|---|---|
[44] | Semi-analytical model | The model considers transverse dispersion and linear reactions in a layered medium, and the mass exchange between the zones is determined by the transverse dispersion across the interface. | This paper focused only on the transverse dispersion but did not consider other influence factors. |
[45] | Analytical model | The modeling results show that the pollutant concentration is more sensitive to the Peclet number than the retardation factor and the first-order decaying coefficient in uniform groundwater flow. | The model was based on 1-D ADE, and the flow direction was perpendicular to the interface of two layers. |
[46] | Laboratory model | The effects of the geometry of low-conductivity zones, conductivity contrast, and flow regime on solute flushing. | This paper focused only on the conductivity contrast but did not consider other influence factors. |
[47] | Synthetic pore-scale millifluidics simulation | They compared the length scales associated with mass transfer rate and the calculation of the Peclet number and found that the Peclet number is commonly larger than the characteristic length scale associated with mass transfer rate. | The simulations were using a millifluidics device, which might not fully represent the complex and heterogeneous nature of real-world porous media. |
Case No. | θ1 | θ2 |
---|---|---|
1 | 0.1 | 0.2 |
2 | 0.1 | 0.4 |
3 | 0.2 | 0.4 |
Case No. | αT1 | αT2 |
---|---|---|
4 | 0.01 | 0.02 |
5 | 0.01 | 0.04 |
6 | 0.02 | 0.04 |
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Chen, Z.; Zhan, H. Universal Relationship between Mass Flux and Properties of Layered Heterogeneity on the Contaminant-Flushing Process. Water 2023, 15, 3292. https://doi.org/10.3390/w15183292
Chen Z, Zhan H. Universal Relationship between Mass Flux and Properties of Layered Heterogeneity on the Contaminant-Flushing Process. Water. 2023; 15(18):3292. https://doi.org/10.3390/w15183292
Chicago/Turabian StyleChen, Zehao, and Hongbin Zhan. 2023. "Universal Relationship between Mass Flux and Properties of Layered Heterogeneity on the Contaminant-Flushing Process" Water 15, no. 18: 3292. https://doi.org/10.3390/w15183292