Speaker
Description
Immiscible two-phase flows in geological fractures are relevant to various industrial contexts, including subsurface fluid storage and hydrocarbon recovery. Direct numerical simulations (DNS) of first-principle equations, which resolve three-dimensional (3-D) fluid-fluid interfaces, can address various flow regimes but are computationally intensive. To retain most of their advantages while reducing the computational cost, we propose a novel two-dimensional (2-D) approach based on depth-integrating the 3-D first principle equations over the local fracture aperture. Such existing models have, so far, been restricted to single-phase permanent flow in rough fractures [1,2] and two-phase flow in 2-D porous media [3]. Considering a description of two-phase flow relying on the Navier-Stokes equations coupled with the volume-of-fluid method for interface capturing, we derive a depth-integrated model based on the lubrication approximation and assuming a parabolic out-of-plane velocity profile. Wall friction and out-of-plane capillary pressure are incorporated as additional terms in the 2-D momentum equation. The model then relies on a geometric description reduced to the fracture’s aperture field and mean topography field. Implemented in OpenFOAM, it is validated against experimental [4] and 3-D DNS simulation results [5] for viscous fingering in a Hele-Shaw cell, and subsequently applied to a synthetic geological fracture geometry over a wide range of capillary numbers (Ca). With a tenfold reduction in computational cost compared to 3-D DNS, the model accurately predicts key flow metrics, such as macroscopic pressure drops and various statistical observables of the fluid displacement morphologies. The 2-D model performs best at intermediate Ca, demonstrating a potential for bridging hydrodynamic and continuum-scale models.
References:
[1] S. R. Brown (1987), Fluid flow through rock joints: the effect of surface roughness. J. Geophys. Res. Solid Earth 92 (B2), 1337-1347.
[2] Y. Méheust & J. Schmittbuhl (2001), Geometrical heterogeneities and permeability anisotropy of rough fractures. J. Geophys. Res. Solid Earth 106 (B2), 2089-2102.
[3] A. Ferrari, J. Jimenez‐Martinez, T. Le Borgne, Y. Méheust & I. Lunati (2015). Challenges in modeling unstable two‐phase flow experiments in porous micromodels. Water Resour. Res. 51 (3), 1381-1400.
[4] P. G. Saffman & G. I. Taylor (1958). The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proceedings Royal Soc. London Series A. 245 (1242), 312-329.
[5] R. Krishna, Y. Méheust & I. Neuweiler (2024). Direct numerical simulations of immiscible two-phase flow in rough fractures: Impact of wetting film resolution. Phys. Fluids, 36 (7).
| Country | France |
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