Co-current flow of two immiscible liquids, such as oil and water in a planar fracture, exhibits nonlinear structures which become important in many natural and engineering systems such as subsurface flows, multiphase flows in lubrication joints, and coating flows. In this context, co-current flow of oil and water with variable rates is experimentally studied in a Hele-Shaw cell, various flow regimes are classified, and relative permeabilities for the phases are analysed thoroughly. Similar to multiphase pipe flows, multiphase flow in planar gaps shows various flow regimes, each having different flow rate/pressure gradient behaviour. As well as recovering the known results in the immiscible displacements in Hele-Shaw cell where the fluid-fluid interface remains stable/unstable for favorable/adverse viscosity ratios, it is found that the co-current flow of two fluids with different viscosities results in three distinct flow regimes. Before breakthrough of non-wetting phase, i.e, water, a "linear displacement" flow regime initially establishes at very low water injection rates. This stable movement turns into a "fingering advancement" flow regime at high water flow rates and Saffman-Taylor instability develops normal to the direction of the flow. After the breakthrough, a "droplet formation" flow regime is identified where the droplets of wetting phase, oil, are trapped in the water phase. For subsurface flow applications, we quantify these regimes through relative permeability curves. It is reported that as the water flow rate increases, the relative permeabilities and flow channels become smooth and regular. This behaviour of relative permeability and saturations shows dominance of capillary forces at low flow rates and viscous forces at higher flow rates. Variable injection rates provide the interface structures for both drainage and imbibition process, where the wetting phase saturation decreases and increases respectively. It is shown that relative permeability curves exhibit hysteresis, thus the process is irreversible. Published by AIP Publishing.
