A novel model for oil-water two-phase relative permeability of shale formation during flowback based on fractal method

As an abundant type of unconventional hydrocarbon resources on the earth, shale oil has been widely concerned by scholars across the world. During flowback period, flow-back resistance of fracturing fluids increases because of the existence of shale oil. Therefore, it is of practical significance to study the flow-back capability of frac-turing fluid for high well performance. In this paper, fractal method of porous media has been used for calcu-lation of relative permeability of oil-water two phase flow in shale pores. First, we built up flow equation of single nanopore with four layers: boundary layer, bulk wetting phase layer, oil-water two phase layer, and nonwetting phase layer. Furthermore, boundary slip, boundary, viscosity change in boundary layer and threshold pressure gradient is considered for correction flow rate equation. The pores of shale matrix can be simplified into capillary bundle model, and fractal theory is suitable for this model. Aperture fractal dimension and tortuosity fractal dimension is used to expand its scale to porosity media with fractal method. Then the model is verified by experimential results and classic models. Furthermore, serval main factors affecting the relative permeability of water are primarily analyzed, and the more essential factors out of the aforementioned ones are extracted and further studied. The results show that with the increase in the thickness of oil-water two phase layer, the relative permeability of water is affected more seriously; The relative permeability of water is positively correlated with slip length and thickness of boundary layer. This work provides a more convenient approach to calculate relative permeability with no experiments, and provide permeability for numerical simulation in flow back period.