TY - JOUR

T1 - A two-dimensional depth-integrated model for immiscible two-phase flow in open rough fractures

AU - Krishna, Rahul

AU - Méheust, Yves

AU - Neuweiler, Insa

N1 - Publisher Copyright: © 2025 The Author(s). Published by Cambridge University Press.

PY - 2025/5/20

Y1 - 2025/5/20

N2 - Immiscible two-phase flows in geological fractures are relevant to various industrial applications, including subsurface fluid storage and hydrocarbon exploitation. Direct numerical simulations (DNS) of first-principle equations, which resolve three-dimensional (3-D) fluid-fluid interfaces, can address all types of 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) model based on integrating the 3-D first-principle equations over the local fracture aperture, assuming the lubrication approximation and a parabolic out-of-plane velocity profile, and relying on the volume-of-fluid method for fluid-fluid interface capturing. Such existing models have, so far, been restricted to single-phase permanent flow in rough fractures and two-phase flow in 2-D porous media. 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 3-D DNS results for viscous fingering in a Hele-Shaw cell, and applied to a realistic synthetic rough fracture geometry over a wide range of capillary numbers. We then analyse to which extent, under which conditions and why this depth-integrated 2-D model, with a tenfold reduction in computational cost, provides convincing results compared with 3-D DNS predictions. We find that it performs surprisingly well over nearly the entire range of for which 3-D DNS models are relevant, in particular because it properly accounts for the out-of-plane capillary forces and wall friction.

AB - Immiscible two-phase flows in geological fractures are relevant to various industrial applications, including subsurface fluid storage and hydrocarbon exploitation. Direct numerical simulations (DNS) of first-principle equations, which resolve three-dimensional (3-D) fluid-fluid interfaces, can address all types of 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) model based on integrating the 3-D first-principle equations over the local fracture aperture, assuming the lubrication approximation and a parabolic out-of-plane velocity profile, and relying on the volume-of-fluid method for fluid-fluid interface capturing. Such existing models have, so far, been restricted to single-phase permanent flow in rough fractures and two-phase flow in 2-D porous media. 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 3-D DNS results for viscous fingering in a Hele-Shaw cell, and applied to a realistic synthetic rough fracture geometry over a wide range of capillary numbers. We then analyse to which extent, under which conditions and why this depth-integrated 2-D model, with a tenfold reduction in computational cost, provides convincing results compared with 3-D DNS predictions. We find that it performs surprisingly well over nearly the entire range of for which 3-D DNS models are relevant, in particular because it properly accounts for the out-of-plane capillary forces and wall friction.

KW - Hele-Shaw flows

KW - lubrication theory

KW - multiphase flow

UR - http://www.scopus.com/inward/record.url?scp=105005592521&partnerID=8YFLogxK

U2 - 10.1017/jfm.2025.404

DO - 10.1017/jfm.2025.404

M3 - Article

AN - SCOPUS:105005592521

VL - 1011

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

SN - 0022-1120

M1 - A43

ER -