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<p>In rough-walled fractures, solute dispersion is controlled by flow heterogeneity: transverse heterogeneity across the fracture aperture promotes Taylor dispersion (∝ <i>v</i>²), whereas longitudinal heterogeneity along the fracture plane promotes macrodispersion (∝ <i>v</i>, where <i>v</i> is the mean velocity). Two widely used models for the longitudinal dispersion coefficient, the power-law relation (<i>D</i><sub><i>L</i></sub>, with <i>D</i><sub><i>L</i></sub> ∝ <i>v</i><sup><i>n</i></sup>, 1 ≤ <i>n</i> ≤ 2) and the linear-quadratic relation (<i>D</i><sub><i>L</i></sub> ∝ <i>v</i> + <i>v</i><sup>2</sup>), reflect the interplay between macrodispersion and Taylor dispersion but have been evaluated mainly under low Reynolds numbers (<i>Re</i> ≪ 1). A critical knowledge gap remains as to which model more accurately captures solute dispersion at higher velocities. To address this unresolved issue, this study employs high-resolution microscopic Particle Image Velocimetry to directly measure spatial variations in fluid velocity within a rough-walled rock fracture over <i>Re</i> = 0.1, 1, 10, and 30. At <i>Re</i> ≤ 1, longitudinal and transverse velocity gradients scaled nearly linearly with <i>Re</i>, indicating comparable contributions to solute dispersion and supporting the applicability of both dispersion models. At <i>Re</i> = 10, eddy onset initiated divergence between the two gradients, and by <i>Re</i> = 30, transverse gradients steepened markedly, exceeding longitudinal values by nearly an order of magnitude, confirming a transition toward Taylor-dominated dispersion. This mechanistic shift highlights the limitation of the power-law formulation, which cannot capture regime transitions, and points to the linear-quadratic model as a more realistic representation of solute dispersion in rough-walled fractures.</p>

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Velocity-based evidence for the transition from macrodispersion to Taylor dispersion in rough-walled rock fractures

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Dahye Kim,
  • In Wook Yeo

摘要

In rough-walled fractures, solute dispersion is controlled by flow heterogeneity: transverse heterogeneity across the fracture aperture promotes Taylor dispersion (∝ v²), whereas longitudinal heterogeneity along the fracture plane promotes macrodispersion (∝ v, where v is the mean velocity). Two widely used models for the longitudinal dispersion coefficient, the power-law relation (DL, with DL ∝ vn, 1 ≤ n ≤ 2) and the linear-quadratic relation (DL ∝ v + v2), reflect the interplay between macrodispersion and Taylor dispersion but have been evaluated mainly under low Reynolds numbers (Re ≪ 1). A critical knowledge gap remains as to which model more accurately captures solute dispersion at higher velocities. To address this unresolved issue, this study employs high-resolution microscopic Particle Image Velocimetry to directly measure spatial variations in fluid velocity within a rough-walled rock fracture over Re = 0.1, 1, 10, and 30. At Re ≤ 1, longitudinal and transverse velocity gradients scaled nearly linearly with Re, indicating comparable contributions to solute dispersion and supporting the applicability of both dispersion models. At Re = 10, eddy onset initiated divergence between the two gradients, and by Re = 30, transverse gradients steepened markedly, exceeding longitudinal values by nearly an order of magnitude, confirming a transition toward Taylor-dominated dispersion. This mechanistic shift highlights the limitation of the power-law formulation, which cannot capture regime transitions, and points to the linear-quadratic model as a more realistic representation of solute dispersion in rough-walled fractures.