InterPore2026

Depth-Integrated Modeling of Immiscible Two-Phase Flow in Rough Fractures: Comparison with Experimental Observations

22 May 2026, 12:20

15m

Oral Presentation (MS09) Pore-Scale Physics and Modeling MS09

Speaker

Rahul Krishna

Description

Understanding immiscible two-phase flow in rough-walled fractures is essential for predicting subsurface fluid migration in fractured media, with direct relevance to applications such as CO$_2$ sequestration in depleted fractured reservoirs, where storage reliability must be ensured, and contaminant remediation in fractured aquifers, where safe and efficient injection, containment, and recovery are critical. Predicting such flows is complicated by fracture network-scale topological complexity, fracture-scale geometric heterogeneity spanning multiple length scales, and the coupled influence of viscous, capillary, and gravitational forces, further affected by wetting films, contact-line motion, and wettability variations. Developing computationally tractable models that still capture the essential flow physics, therefore, remains a key challenge.

At the fracture scale, existing approaches either rely on fully resolved three-dimensional (3-D) direct numerical simulations (DNS) of the Navier–Stokes equations, which capture interfacial dynamics with high fidelity but are computationally demanding [1], or on continuum-scale models that neglect aperture-scale hydrodynamic instabilities [2]. To bridge this gap, we recently developed a two-dimensional (2-D) depth-integrated model for immiscible two-phase flow [3], which reduces the governing equations to the fracture mean plane while retaining the key effects of wall friction and out-of-plane capillary pressure. Although validated against Hele-Shaw experiments and 3-D simulations, its predictive performance against laboratory experiments in rough-walled fracture analogs has not yet been assessed.

Here, we address this gap by comparing model predictions against controlled drainage experiments conducted in transparent fracture analogs. The fracture geometry was numerically generated with self-affine rough walls (Hurst exponent $H = 0.8$), mean aperture $a_\mathrm{m} = 0.4$ mm, and correlation length $l_c = L/8$, over a $145$ mm $\times$ $80$ mm domain. The resulting aperture field exhibits strong variability, characterized by a relative closure $\delta = \sigma_\mathrm{a}/a_\mathrm{m} = 0.57$. The rough topographies were engraved into polymethylmethacrylate (PMMA) plates by precision milling [4], and the experimental fracture geometry was subsequently reconstructed using X-ray tomography and employed directly in the numerical simulations. Experiments were performed with three immiscible fluid pairs spanning viscosity ratios $M = 1/200$, $1/100$, and $70$, and capillary numbers $\log Ca$ between $-3.4$ and $-6.4$, covering viscous-, capillary-dominated, and stable displacement regimes. Corresponding 2-D simulations were conducted under identical flow conditions, enabling direct comparison with experimental observations. The analysis focuses on quantitative descriptors of invasion dynamics, including phase morphology, finger width, interfacial length evolution, breakthrough saturation, longitudinal saturation profiles, and trapped cluster size distributions.

Preliminary results indicate that the depth-integrated formulation reproduces the key displacement characteristics observed experimentally at a fraction of the computational cost of fully resolved 3-D DNS. These findings highlight its potential as a practical framework for exploring a broader range of flow and geometric conditions than would be computationally feasible with high-resolution simulations alone. More broadly, this study demonstrates that reduced-order models, when rigorously verified and supported by targeted experimental validation, can provide a physically sound and computationally efficient approach for simulating immiscible two-phase flow in fractured systems.