Forced Imbibition in Rough Fractures

Abstract:

Although immiscible fluid-fluid displacement in smooth fractures has been investigated in depth, the hydrodynamic impact of roughness, especially under unfavorable viscosity contrast and strong imbibition, remains poorly understood.

We experimentally investigate forced imbibition in a microfluidic analogue of a rough fracture, consisting in a modified Hele-Shaw cell with one plate patterned with an array of cylindrical posts. This setup allows us to control the fracture aperture and roughness precisely. The flow cell is initially saturated with a viscous and non-wetting silicon oil, which is then displaced by less-viscous and more-wetting DI water.

We observe distinct regimes of imbibition dynamics in the cell, depending on the gap width and level of roughness: (1) water invades only through the gap initially, but later imbibes into the roughness space; (2) water imbibes only within the roughness space as if it is completely wetting; (3) water first imbibes within the roughness space for a critical distance and then starts invading through the gap at the injection point; (4) water simultaneously advances through the gap and the roughness space, like classic imbibition in smooth confinement.

We rationalize the aforementioned flow regimes, and explain the transitions among them, with a 1D gap-averaged hydrodynamic model, consisting of two parallel and interacting porous matrices, with different hydraulic conductance and characteristic capillary pressure. The model captures the trends in the filling of the cell observed experimentally as a function of the roughness and the capillary number. In ongoing work, we extend the gap-averaged model to 2D, and explore the development of a 3D phase-field model that is expected to capture both the macroscopic patterns and the pore-scale mechanisms of forced imbibition in the microfluidic fracture.