Dynamics of foam flow in a rock fracture: Effects of aperture variation on apparent shear viscosity and bubble morphology

There has recently been renewed interest in understanding the physics of foam flow in permeable media. As for Newtonian flows in fractures, the heterogeneity of local apertures in natural fractures is expected to strongly impact the spatial distribution of foam flow. Although several experimental studies have been previously performed to study foam flow in fractured media, none of them has specifically addressed that impact for parallel flow in a realistic fracture geometry and its consequences for the foam's in situ shear viscosity and bubble morphologies. To do so, a comprehensive series of single-phase experiments have been performed by injecting pre-generated foams with six different qualities at a constant flow rate through a replica of a Vosges sandstone fracture of well-characterized aperture map. These measurements were compared to measurements obtained in a Hele-Shaw (i.e., smooth) fracture of identical hydraulic aperture. The results show that fracture wall roughness strongly increases the foam's apparent viscosity and shear rate. Moreover, foam bubbles traveling in regions of larger aperture exhibit larger velocity, size, a higher coarsening rate, and are subjected to a higher shear rate. This study also presents the first in situ measurement of foam bubbles velocities in fracture geometry, and provides hints towards measuring the in situ rheology of foam in a rough fracture from the velocity maps, for various imposed mean flow rates. These findings echo the necessity of considering fracture wall when predicting the pressure drop through the fracture and the effective viscosity, as well as in situ rheology, of the foam.