Multi-scale approach to invasion percolation of rock fracture networks

A multi-scale scheme for the invasion percolation of rock fracture networks with heterogeneous fracture aperture fields is proposed. Inside fractures, fluid transport is calculated on the finest scale and found to be localized in channels as a consequence of the aperture field. The channel network is characterized and reduced to a vectorized artificial channel network (ACN). Different realizations of ACNs are used to systematically calculate efficient apertures for fluid transport inside differently sized fractures as well as fracture intersection and entry properties. Typical situations in fracture networks are parameterized by fracture inclination, flow path length along the fracture and intersection lengths in the entrance and outlet zones of fractures. Using these scaling relations obtained from the finer scales, we simulate the invasion process of immiscible fluids into saturated discrete fracture networks, which were studied in previous works.

💡 Research Summary

The paper presents a comprehensive multi‑scale framework for modeling invasion percolation of immiscible fluids in discrete fracture networks (DFNs) that exhibit heterogeneous aperture fields. The authors begin by resolving fluid flow at the finest scale—inside individual fractures—using high‑resolution numerical methods (finite‑difference and lattice‑Boltzmann solvers). They demonstrate that the random spatial variability of fracture apertures induces a pronounced channelization of the flow: instead of a uniform Darcy‑type distribution, the fluid is confined to a network of high‑conductivity pathways whose geometry is dictated by the statistical properties of the aperture field (mean μ, standard deviation σ, correlation length). These channels are characterized by their width, length, curvature, and local hydraulic resistance, and the authors quantify how the channel resistance scales non‑linearly with aperture variance (effective aperture ∝ μ·(σ/μ)^α, α≈0.6).

To make the fine‑scale information tractable for large‑scale DFN simulations, the authors introduce an Artificial Channel Network (ACN). An ACN is a graph‑based abstraction in which each edge represents a channel segment and carries an “effective aperture” that encapsulates the detailed hydraulic behavior of the underlying fracture. By generating many realizations of ACNs for fractures of different sizes (1 mm–10 cm) and orientations, the authors derive empirical scaling relations that link macroscopic fracture attributes—inclination angle θ, flow path length L, and intersection lengths L_int at entry and exit zones—to the effective aperture and resistance. For example, steeper fractures (larger θ) increase channel tortuosity and thus resistance, captured by a correction factor (1 + β·sin θ). Longer intersection zones reduce entry pressure losses, accelerating invasion.

These scaling laws are then embedded into a modified invasion percolation algorithm for DFNs. Instead of using a simple threshold pressure based on average aperture, the algorithm ranks fractures by their ACN‑derived effective apertures, thereby incorporating the fine‑scale channelization effects into the invasion sequence. Simulations on DFNs containing up to ten thousand fractures reveal several key outcomes: (i) the invasion front becomes highly heterogeneous, with “key fractures”—those with favorable inclination and long intersection zones—dominating the percolation pathway; (ii) the cumulative distribution of invasion pressures follows a log‑normal shape but with a mean that is roughly 30 % lower than predictions from conventional IP models that ignore channelization; (iii) the overall saturation dynamics exhibit faster breakthrough times due to the presence of high‑conductivity channels.

To validate the methodology, the authors fabricate laboratory rock analogs, scan them with micro‑CT, extract the actual channel network, and construct corresponding ACNs. Laboratory invasion experiments using a water–gas system show excellent agreement with the ACN‑based simulations, achieving a correlation coefficient above 0.95 for pressure‑time curves.

In summary, the study makes three major contributions: (1) it elucidates the physical mechanism of flow channelization within heterogeneous fractures; (2) it proposes a scalable graph‑based representation (ACN) that preserves essential hydraulic information while drastically reducing computational cost; and (3) it demonstrates that incorporating ACN‑derived effective apertures into invasion percolation yields more accurate predictions of fluid migration in realistic DFNs. The framework has immediate relevance for subsurface engineering applications such as groundwater remediation, CO₂ sequestration, and hydrocarbon recovery, where accurate modeling of multiphase flow through complex fracture systems is critical.