Analytical models and experimental verifications for relative permeabilities of oil-water two-phase flow in fractures

The relative permeabilities of oil-water two-phase flow in fractures attract increasing attention in reservoir engineering. In this work, two analytical models were developed for the relative permeabilities of oil-water flow in fractures. One of the models, developed without considering oil-water interface slip, demonstrates that the relative permeabilities of oil-water flow are only dependent on saturation and wetted perimeter. The other one, developed from considering oil-water interface slip, implies that the relative permeabilities of oil-water flow are not only related to saturation and wetting perimeter, but also related to interface coefficients. Comparative experiments were conducted to verify. The experimental rectangular fractures, which were made of polymethyl methacrylate, had different hydraulic diameters from 2.06 to 5.71 mm and height-width ratios from 0.115 to 8.696. The oil-water flow was horizontal and laminar in fractures, with oil-water viscosity ratios ranged from 7.3 to 29.6. Stratified flow and dispersed flow were observed in the experiments. The analytical models developed show that oil-water interface slip has little influence on the relative permeability of oil phase, but has significant effect on the relative permeability of water phase. Both analytical models and experimental results indicate that the sum of relative permeabilities can be greater than 1.