Experimental validation of a depth-integrated model for immiscible two-phase flow in rough fractures

Displacement of a wetting fluid by a non-wetting fluid in fractured media is relevant to many subsurface applications, including fluid storage and groundwater contaminant remediation. Such flows are difficult to predict because they are governed by fracture-scale geometric heterogeneity embedded within complex fracture networks, which sets a large contrast of relevant length scales. The flow is also governed by the coupled action of viscous, capillary, and gravitational forces. These effects are further compounded by wetting films, contact-line dynamics, and spatial variations in wettability. As a result, developing models that are both computationally efficient and faithful to the governing physics remains challenging.

At the scale of individual fractures, two main modeling strategies are commonly employed. Fully resolved three-dimensional direct numerical simulations provide detailed descriptions of interfacial dynamics but are computationally expensive and impractical for extensive parameter exploration. Conversely, continuum-scale approaches offer efficiency but typically neglect aperture-scale hydrodynamic instabilities and geometric controls that govern displacement morphology. Recently, we introduced a two-dimensional depth-integrated model for immiscible two-phase flow in rough fractures [1], which retains the dominant hydrodynamic and capillary effects while substantially reducing computational cost. Although this model has been tested against idealized configurations and numerical benchmarks, its performance against laboratory experiments in realistic rough-walled fractures has not yet been systematically evaluated.

A direct comparison between model predictions and controlled drainage experiments was carried out using transparent fracture analogs and corresponding numerical simulations. The fracture geometry was first generated numerically as a self-affine rough fracture with a Hurst exponent of 0.8 and a domain size of 145 mm by 80 mm. The geometry has a mean aperture of 0.4 mm and a correlation length equal to one eighth of the fracture length, resulting in a strongly heterogeneous aperture field characterized by a relative closure of 0.57. The rough surfaces were fabricated by precision milling into polymethylmethacrylate plates [2]. The experimental fracture geometry was subsequently reconstructed from X-ray tomography and employed directly in the numerical simulations. Drainage experiments were conducted with three immiscible fluid pairs spanning viscosity ratios of 1/200, 1/100, and 70, and capillary numbers between 10^−3.0 and 10^−7.0, thereby covering viscous-dominated stable and unstable, as well as capillary-dominated, displacement regimes. Two-dimensional depth-integrated simulations were performed under identical flow conditions, enabling direct comparison. Model performance is assessed using quantitative descriptors of invasion dynamics, including displacement morphology, finger width, interfacial length evolution, breakthrough saturation, and longitudinal saturation profiles.

The depth-integrated model reproduces the dominant displacement features observed in the experiments while requiring substantially less computational effort than fully resolved three-dimensional simulations. This demonstrates its suitability as an efficient and physically consistent framework for studying immiscible two-phase flow in rough-walled fractures.

[1] Krishna, R., Méheust, Y. and Neuweiler, I., 2025. A two-dimensional depth-integrated model for immiscible two-phase flow in open rough fractures. Journal of Fluid Mechanics, 1011, p.A43.

[2] Amin Rezaei, Francesco Gomez Serito, Insa Neuweiler, Yves Méheust. Dynamic Displacement of Wetting Fluids by Non-Wetting Fluids in a Geological Fracture: An Experimental Study. American Geophysical Union Annual Meeting 2024 (AGU24), Dec 2024, Washington DC, United States. pp.H53K-1232