Multifractal Analysis of Tight Sandstone Using Micro-CT Methods: A Case from the Lower Cretaceous Quantou Formation, Southern Songliao Basin, NE China
The relationships between the pore structure and a single fractal or specific region have been widely reported. However, the intrinsic relationship between multifractal parameters and physical properties have remained uncertain. In this study, micro-computed tomography scanning technology and high-p...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/6/336 |
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| Summary: | The relationships between the pore structure and a single fractal or specific region have been widely reported. However, the intrinsic relationship between multifractal parameters and physical properties have remained uncertain. In this study, micro-computed tomography scanning technology and high-pressure mercury injection technologies were applied to determine the pore structures of tight sandstone at different scales. Subsequently, the multifractal theory was applied to quantitatively evaluate the multiscale pore structure heterogeneity. An evident linear relationship exists between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mi>o</mi><mi>g</mi><mi>X</mi><mfenced separators="|"><mrow><mi>q</mi><mo>,</mo><mi>ε</mi></mrow></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><mi mathvariant="italic">log</mi></mrow><mo></mo><mrow><mo>(</mo><mi>ε</mi><mo>)</mo></mrow></mrow></mrow></semantics></math></inline-formula>, indicating the pore structure of tight sandstones exhibits significant multifractal characteristics. Multifractal parameters, including <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∆</mo><mfenced separators="|"><mrow><mi>α</mi></mrow></mfenced><mo>,</mo><mo> </mo><mo>∆</mo><mi>D</mi><mo>,</mo><mo> </mo><msub><mrow><mi>D</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>−</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><msub><mrow><mo> </mo><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></mrow></semantics></math></inline-formula>, can serve as sensitive indicators to assess the multiscale pore structure heterogeneity. In particular, the relative development degree of large-scale pores (>10 μm) can be reflected by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>−</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>0</mn><mo> </mo></mrow></msub></mrow></semantics></math></inline-formula>, which has strong heterogeneity. The heterogeneity of the multiscale structure is closely linked to the mineral components of tight sandstone reservoirs, and the heterogeneity of small-scale pores (1–10 μm) is stronger by clay mineral enrichment. Furthermore, the part of the pore structure corresponding to the combination of pore size range of 10 to 20 μm and throat size range of 20 to 40 μm in a low probability measure area may dominate the permeability of tight sandstone. The findings enhance the understanding of pore structure heterogeneity and broaden the application of multifractal theory. |
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| ISSN: | 2504-3110 |