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Using pore-solid fractal dimension to estimate residual LNAPLs saturation in sandy aquifers: A column experiment
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Abstract: : The“tailing” effect caused by residual non-aqueous phase liquids (NAPLs) in porous aquifers is one of the frontiers in pollution hydrogeology research. Based on the current knowledge that the residual NAPLs is mainly controlled by the pore structure of soil, this study established a method for evaluating the residual saturation of NAPLs by investigating the fractal dimension of porous media. In this study, the soil column experiments of residual light NAPLs (LNAPLs) in sandy aquifer with different ratios of sands and soil were carried out, and the correlation between the fractal dimension of the medium, the residual of LNAPLs and the soil structure parameters are statistically analyzed, and its formation mechanism and main control factors are discussed. The results show that: Under our experimental condition: (1) the fractal dimension of the medium has a positive correlation with the residual saturation of NAPLs generally, and the optimal fitting function can be described by a quadratic model:
${S_R} = {\text{192}}{\text{.02}}{D^2} - 890.73D + {\text{1 040}}{\text{.8}}$ ; (2) the dominant formation mechanism is: Smaller pores in the medium is related to larger fractal dimension, which leads to higher residual saturation of NAPLs; stronger heterogeneity of the medium is related to larger fractal dimension, which also leads to higher residual saturation of NAPLs; (3) the micro capillary pores characterized by fine sand are the main controlling factors of the formation mechanism. It is concluded that both the theory and the method of using fractal dimension of the medium to evaluate the residual saturation of NAPLs are feasible. This study provides a new perspective for the research of “tailing” effect of NAPLs in porous media aquifer.-
Key words:
- Residual saturation /
- NAPLs /
- Pore structure /
- Fractal /
- Tailing effect
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Figure 6. Relationship between pore structure parameters and fractal dimension
NOTES：(a) porosity - fractal dimension, (b) permeability coefficient - fractal dimension, (c) particle size variation coefficient - fractal dimension, (d) coarse grain content - fractal dimension, (e) medium sand content - Fractal dimension, (f) fine sand content - fractal dimension
Figure 7. Relationship between medium structure parameters and residual saturation of LNAPLs
NOTES: (a) porosity - residual saturation, (b) permeability coefficient - residual saturation, (c) particle size variation coefficient - residual saturation, (d) coarse grain content - residual saturation, (e) medium sand content - residual saturation, (f) fine sand content - residual saturation.
Figure 8. Schematic diagram of pore structure of sand medium
NOTES: 1-connected pores, 2-roars, 3-dead pores, 4-microcapillary pores, 5-particles, 6-isolated pores
Figure 9. The best fitting curve of fine sand content and D and SR
NOTES: (a) fine sand content - fractal dimension, (b) fine sand content - residual saturation
Table 4. Key results
Treatment 1-1 1-2 2-1 2-2 3-1 3-2 4-1 4-2 $ D $ Line 1 2.44 2.41 2.59 2.55 2.73 2.69 2.71 2.73 Line 2 2.08 2.07 2.17 2.19 2.19 2.12 2.18 2.20 Mean 2.26 2.24 2.38 2.37 2.46 2.41 2.45 2.47 $ {S_R} $ (%)
Residual saturation8.14 9.12 10.33 7.34 10.58 7.90 12.34 12.14 $ {n_0} $ (%)
Porosity46.45 44.91 47.90 47.18 51.09 50.70 49.06 48.46 K(m/d)
Permeability coefficient79.16 50.85 41.91 61.36 27.35 39.82 37.04 46.51 $ {R_{Coarse - sand}} $
Coarse sand (%)51.52 43.05 21.44 7.73 $ {R_{Medium - sand}} $
Medium sand (%)22.52 21.91 14.76 6.19 $ {R_{Fine - sand}} $
Fine sand (%)25.96 35.04 63.8 86.09 $ RS{D_{sand}} $
RSD of sand content (%)47.53 32.02 79.79 137.06 NOTE：$ RS{D}_{sand}=\dfrac{SD（{R}_{Coarse-sand},{R}_{Medium-sand},{R}_{Fine-sand}）}{Average（{R}_{Coarse-sand},{R}_{Medium-sand},{R}_{Fine-sand}）}\times 100 $. 
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Table 1. Particle ratio scheme of soil column medium
Treatment T1 T2 T3 T4 NO. 1-1 1-2 2-1 2-2 3-1 3-2 4-1 4-2
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Table 2. the observed results of the three permeability coefficients before the end of the residual LNAPLs formation experiment
1-1 1-2 2-1 2-2 3-1 3-2 4-1 4-2 Third from last 80.08 54.05 39.8 53.72 27.75 51.68 37.88 40.58 Second from last 79.83 41.84 40.37 66.06 27.3 31.2 36.23 45.89 Last 77.58 56.65 45.55 64.3 26.99 36.57 37.01 53.05 RSD% 6 16 8 11 1 27 2 13
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Table 3. Volume of samples and particle size
NO. Volume (cm3) Accumulated in particle size $ \dfrac{W}{{{W_0}}} $(%) $ {V_{soil}} $ $ {V_{sand}} $ $ {V_{oil}} $ 0.03-0.3 mm 0.3-0.4 mm 0.4-0.5 mm 0.5-0.65 mm 0.65-0.8 mm 0.8-1 mm 1-2 mm 1-1 3377.20 1808.39 127.71 8.58 7.23 6.38 6.53 4.81 3.27 63.25 1-2 3354.15 1847.72 137.35 7.97 6.88 6.09 6.40 4.74 3.46 64.46 2-1 3384.92 1763.58 167.47 12.71 9.48 7.74 7.38 4.75 2.81 55.15 2-2 3338.76 1763.58 115.66 13.05 9.41 7.76 7.56 5.09 3.27 53.87 3-1 3365.69 1646.01 181.93 22.63 15.98 12.57 11.39 6.76 3.33 27.35 3-2 3338.76 1646.01 133.73 19.82 15.68 12.81 12.01 7.40 3.90 28.39 4-1 3323.38 1692.96 201.20 24.24 19.97 16.46 15.37 9.22 4.40 10.35 4-2 3338.76 1720.87 196.39 24.86 19.93 16.39 15.24 9.00 4.02 10.56
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Table 5. Parameter relationship statistics and physical significance
Structural parameters Fractal dimension Residual saturation Significance Coarse sand content Negative correlation Negative correlation The smaller the pores, the larger the fractal dimension and the larger the residual saturation Medium sand content Negative correlation Negative correlation The smaller the pores, the larger the fractal dimension and the larger the residual saturation Fine sand content Positive correlation Positive correlation The smaller the pores, the larger the fractal dimension and the larger the residual saturation Coefficient of particle size variation Positive correlation Positive correlation The stronger the heterogeneity, the larger the fractal dimension and the larger the residual saturation. Porosity Positive correlation / The more pores, the larger the fractal dimension, but the change of residual saturation is not obvious Permeability
coefficientNegative correlation / The worse the pore connectivity is, the larger the fractal dimension is, but the residual saturation does not change significantly NOTE: / means no relationship
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