Applicability of a Fractal Model for Sandstone Pore-Fracture Structure Heterogeneity by Using High-Pressure Mercury Intrusion Tests
<p>Stratigraphic column of the study area.</p> "> Figure 2
<p>Parametric sub-sample results of high-pressure mercury testing.</p> "> Figure 3
<p>SEM Image analysis of thin sections.</p> "> Figure 4
<p>Different types of high-pressure mercury pressure curves and pore distribution. (<b>a</b>) High pressure mercury injection curve of type A; (<b>b</b>) Pore size distribution of type A sample; (<b>c</b>) High pressure mercury injection curve of type B; (<b>d</b>) Pore size distribution of type B sample.</p> "> Figure 4 Cont.
<p>Different types of high-pressure mercury pressure curves and pore distribution. (<b>a</b>) High pressure mercury injection curve of type A; (<b>b</b>) Pore size distribution of type A sample; (<b>c</b>) High pressure mercury injection curve of type B; (<b>d</b>) Pore size distribution of type B sample.</p> "> Figure 5
<p>Comparison of pore structure parameters of different types of samples. (<b>a</b>) The percentage of pore volume between 1000~10,000 in type A and type B samples; (<b>b</b>) The percentage of pore volume between 100~1000 in type A and type B samples; (<b>c</b>) The percentage of pore size less than 100 pore volume in type A and type B samples; (<b>d</b>) The pore volume percentage of total pore volume in type A and type B samples.</p> "> Figure 6
<p>Fractal dimension of the <span class="html-italic">M</span> model. (<b>a</b>) Single fractal dimension of type A sample M model; (<b>b</b>) Single fractal dimension of type B sample M model; (<b>c</b>) Single fractal dimension.</p> "> Figure 7
<p>Fractal dimension of the <span class="html-italic">S</span> model (log (dv/dp)) is the logarithm of mercury-injected volume per unit pressure; D is fractal dimension, dimensionless. (<b>a</b>) Single fractal dimension of type A sample S model; (<b>b</b>) Single fractal dimension of type B sample S model; (<b>c</b>) Single fractal dimension.</p> "> Figure 8
<p>Fractal dimension of the <span class="html-italic">T</span> model. (<b>a</b>) Single fractal dimension of type A sample T model; (<b>b</b>) Single fractal dimension of type B sample T model; (<b>c</b>) Single fractal dimension.</p> "> Figure 9
<p>Multifractal dimension of the pores of different types of samples. (<b>a</b>) Multifractal characterization of lg(ɛ) and lg[μ<sub>1</sub>(q, ɛ)]; (<b>b</b>) Multifractal characterization of pores in type A samples; (<b>c</b>) Multifractal characterization of pores in type B samples.</p> "> Figure 10
<p>Comparison of multifractal variations of different lithofacies. (<b>a</b>) Comparison of pore low value distinguishing shape dimension; (<b>b</b>) Comparison of pore high value distinguishing shape dimension; (<b>c</b>) Multiple fractal dimension.</p> "> Figure 11
<p>Relationship between fractal dimension values calculated using different fractal models. (<b>a</b>) S model diversion values <span class="html-italic">D<sub>S</sub></span> ~ Sponge model dimension values; (<b>b</b>) S model diversion values <span class="html-italic">D<sub>S</sub></span> ~ Fractal dimension value of thermodynamic model <span class="html-italic">D<sub>T</sub></span>; (<b>c</b>) Fractal dimension of sponge model <span class="html-italic">D<sub>M</sub></span>; (<b>d</b>) Relationship between <span class="html-italic">D</span><sub>0</sub><span class="html-italic">–D</span><sub>10</sub> and <span class="html-italic">D</span><sub>–10</sub><span class="html-italic">–D</span><sub>0</sub>; (<b>e</b>) Relationship between <span class="html-italic">D</span><sub>–10</sub><span class="html-italic">–D</span><sub>10</sub> and <span class="html-italic">D</span><sub>–10</sub><span class="html-italic">–D</span><sub>0</sub>; (<b>f</b>) Relationship between <span class="html-italic">D</span><sub>–10</sub><span class="html-italic">–D</span><sub>10</sub> and <span class="html-italic">D</span><sub>0</sub><span class="html-italic">–D</span><sub>–10</sub>.</p> "> Figure 12
<p>Relationship between pore volume and single fractal dimension at different stages of the process. (<b>a</b>) Total pore volume percentage; (<b>b</b>) The pore volume percentage is <1000 nm; (<b>c</b>) The pore volume percentage is between 100~1000 nm; (<b>d</b>) The pore volume percentage is >1000 nm.</p> "> Figure 13
<p>Relationship between pore volume and multifractal dimension at different stages of the process. (<b>a</b>) Total pore volume percentage; (<b>b</b>) The pore volume percentage is <1000 nm; (<b>c</b>) The pore volume percentage is between 100~1000 nm; (<b>d</b>) The pore volume percentage is >1000 nm.</p> "> Figure 13 Cont.
<p>Relationship between pore volume and multifractal dimension at different stages of the process. (<b>a</b>) Total pore volume percentage; (<b>b</b>) The pore volume percentage is <1000 nm; (<b>c</b>) The pore volume percentage is between 100~1000 nm; (<b>d</b>) The pore volume percentage is >1000 nm.</p> "> Figure 14
<p>Mercury removal efficiency as a function of single and multiple fractal dimension. (<b>a</b>) Relationship between Mercury removal efficiency and Fractal dimension <span class="html-italic">D</span>; (<b>b</b>) Relationship between Mercury removal efficiency and Multifractal dimension <span class="html-italic">D</span>.</p> ">
Abstract
:1. Introduction
2. Sample Preparation and Experimental Testing
2.1. Sample Collection
2.2. Experimental Methods
2.3. Computational Theory
3. Results and Discussion
3.1. Sample Classification Based on Pressed Mercury Basis Testing
SEM Images of Test Samples
3.2. Quantitative Characterization of Heterogeneity of Pore Distribution Based on Different Fractal Models
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Term | Significance |
D | Fractal dimension |
DT | Fractal dimension by using Thermodynamics |
DS | Fractal dimension by using the Sierpinski model |
D−10–D0 | The fractal dimension value of the pore structure with a lower pore volume |
D0–D10 | The fractal dimension value of the pore structure with a larger pore volume |
D−10–D10 | The fractal dimension value of the pore structure with a total pore volume |
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Sample No. | Pore Volume (cm3·g−1) | Porosity (%) | Permeability (mD) | Mercury Removal Efficiency (%) |
---|---|---|---|---|
1 | 0.876865 | 13.0 | 1.27 | 44.59 |
2 | 1.2908226 | 14.1 | 5.78 | 51.79 |
3 | 1.2762134 | 14.0 | 6.59 | 49.04 |
4 | 0.947973 | 12.0 | 0.804 | 46.66 |
5 | 0.165032 | 4.5 | 0.038 | 21.58 |
6 | 0.9993501 | 12.7 | 0.729 | 26.63 |
7 | 0.5983404 | 10.6 | 31.0 | 14.08 |
8 | 0.7377842 | 12.0 | 7.52 | 19.22 |
9 | 1.0976112 | 13.4 | 13.2 | 28.32 |
10 | 0.7145822 | 10.0 | 2.27 | 22.27 |
11 | 0.1632108 | 3.7 | 2.75 | 15.68 |
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Zou, S.; Sun, M.; Chen, Y.; Li, Q.; Chang, X.; Zhang, J.; Ren, G. Applicability of a Fractal Model for Sandstone Pore-Fracture Structure Heterogeneity by Using High-Pressure Mercury Intrusion Tests. Processes 2024, 12, 1658. https://doi.org/10.3390/pr12081658
Zou S, Sun M, Chen Y, Li Q, Chang X, Zhang J, Ren G. Applicability of a Fractal Model for Sandstone Pore-Fracture Structure Heterogeneity by Using High-Pressure Mercury Intrusion Tests. Processes. 2024; 12(8):1658. https://doi.org/10.3390/pr12081658
Chicago/Turabian StyleZou, Shuangying, Mingyuan Sun, Yongmei Chen, Qinglin Li, Xiangchun Chang, Junjian Zhang, and Guangying Ren. 2024. "Applicability of a Fractal Model for Sandstone Pore-Fracture Structure Heterogeneity by Using High-Pressure Mercury Intrusion Tests" Processes 12, no. 8: 1658. https://doi.org/10.3390/pr12081658