Prediction of oil-water relative permeability with a fractal method in ultra-high water cut stage

•A new analysis model of Oil-water relative permeability was put forward.•This new model can reflect more residual oil information.•This new model is more suitable to describe characteristics of the seepage. Relative permeability is a concept used to convey the reduction in flow capability due to the presence of multiple mobile fluids. The study of the mechanism and characteristics of discontinuous flow in multiphase flow have great significance in reservoir engineering, geotechnical engineering, biomedical engineering, chemical engineering. In this article, considering the oil/water micro-distribution characteristic in the ultra-high water cut stage and the self-similar fractal characteristics of porous media, an analytical model of relative permeability curve in porous media with discontinuous phase is derived based on capillary bundle model. The new expression contains the characteristic parameters of both porous media and fluid in it. The accuracy of the model is verified by fitting the available experimental data and comparing with other similar models. By changing the value of each parameter (the length ratio of oil drops to water drops, the radius of oil drops, the ratio of oil-water viscosity, fractal dimension for pore size, tortuosity fractal dimension) in the new mathematical analysis model, the influence of each parameter on the characteristics of relative permeability curve has been investigated, thus help reveal the law of two-phase seepage in the porous media of the ultra-high water cut period.