The phenomenon of relative permeability hysteresis is observed during the process of developing the oil field by methods where the flow direction changes. In this case the displacement of oil by water changes into the displacement of water by oil and vice versa. This work is devoted to modeling of relative permeability hysteresis for drainage and imbibition based on percolation theory.

The phenomenon of active oil components adsorption on the rockforming minerals is considered as the first mechanism of hysteresis origin. In the process of drainage this causes surface hydrophobization of initially hydrophilic rock which leads to each phase relative permeability change. To describe this phenomenon percolation model for media with microheterogeneous wettability is used. The second mechanism is fluid rheological properties change, caused by the fluids mixing during drainage. It is described by percolation model for fluids with different rheological properties.

Obtained numerical solution is represented as relative permeability curves and is qualitatively confirmed by the experimental data. The behavior of relative permeability hysteresis is analyzed for various differential radius distribution curves, capillary network coordination numbers, saturation models, hydrophobization degree and fluid rheological properties. It allows to establish general tendencies of relative permeability hysteresis behavior. Introduced methodology can be put into practice for relative permeability calculation in any porous media to reduce the time spent. Also this approach can be embedded in hydrodynamic modeling programs to consider the relative permeability hysteresis effect.


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