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<p>Three-dimensional rough surface characterization was performed based on the Weierstrass-Mandelbrot (W-M) fractal function, investigating the impact of typical W-M geometric parameters on the morphology of the surface, and calculating the statistical parameters of the three-dimensional rough surfaces. The statistical parameters of the three-dimensional rough surfaces were calculated, the roughness characteristics of the fracture surfaces were quantified, and the relationship with the fractal dimension was established. A fracture seepage testing system was developed based on a self-designed structural surface and 3D engraving technology. Seepage tests were conducted on fractures with varying roughness levels. The results indicated that as the pressure gradient and roughness increased, the flow of the fluid exhibited pronounced non-linearity. The coefficients of the Forchheimer <i>A</i> and <i>B</i> equation increased with fracture roughness. Three-dimensional fracture samples exhibited overpressure drop phenomena as confining pressure increased. The surface roughness significantly influenced the non-linear fluid flow characteristics. As confining pressure increased, the flow resistance exhibited a non-linear relationship with the Reynolds number, indicating strong post-Darcy flow. As the pressure gradient gradually increased during the seepage process, the value of the non-linearity effect factor <i>E</i> increased, although the rate of increase slowed down over time. This study provides reliable analytical methods and models for studying fracture seepage characteristics.</p>

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Characterization of rough structural surface models and seepage characteristics based on 3D engraving technology

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Yi Wang,
  • Xin Bai,
  • Qiuyan Pei,
  • Hao Yuan,
  • Junhui Wang,
  • Peng Zhang,
  • Xingyu Qiu

摘要

Three-dimensional rough surface characterization was performed based on the Weierstrass-Mandelbrot (W-M) fractal function, investigating the impact of typical W-M geometric parameters on the morphology of the surface, and calculating the statistical parameters of the three-dimensional rough surfaces. The statistical parameters of the three-dimensional rough surfaces were calculated, the roughness characteristics of the fracture surfaces were quantified, and the relationship with the fractal dimension was established. A fracture seepage testing system was developed based on a self-designed structural surface and 3D engraving technology. Seepage tests were conducted on fractures with varying roughness levels. The results indicated that as the pressure gradient and roughness increased, the flow of the fluid exhibited pronounced non-linearity. The coefficients of the Forchheimer A and B equation increased with fracture roughness. Three-dimensional fracture samples exhibited overpressure drop phenomena as confining pressure increased. The surface roughness significantly influenced the non-linear fluid flow characteristics. As confining pressure increased, the flow resistance exhibited a non-linear relationship with the Reynolds number, indicating strong post-Darcy flow. As the pressure gradient gradually increased during the seepage process, the value of the non-linearity effect factor E increased, although the rate of increase slowed down over time. This study provides reliable analytical methods and models for studying fracture seepage characteristics.