Calculation of Water Breakthrough Time in Well Patterns of Ultra-low Permeability Reservoir

As ultra-low permeability reservoir is developed by water flooding,it always presents characteristics of non-Darcy flow and permeability anisotropy. We derived water breakthrough time formula of five-spot well pattern,inverted nine-spot well pattern and rhombic nine-spot well pattern with basic non-Darcy flow formula and streamline integral method. Breakthrough time of one actual well pattern in Ordos Basin was calculated. Calculation results accorded with production data well. Effects of threshold pressure gradient, permeability anisotropy and viscosity difference between oil and water were analyzed. It shows that the greater the viscosity ratio of oil and water,the earlier the water breakthrough time; Corner well of rhombic nine-spot well pattern can realize uniform displacement both in x direction and y direction as ratio of well spacing in x direction and y direction equals to permeability anisotropy degree; The grenter the threshold pressure gradient,the latter the water breakthrough time. Effect of threshold pressure gradient became more apparent as well spacing is larger.