A mathematical model is developed for performance prediction of waterflooding performance in communicating stratified reservoirs with a dip angle from the horizontal. The effect of the gravitational force is reflected by a dimensionless gravity number in the fractional flow formula that accounts forthe dip angle and density difference between the displacing and displaced fluids. The developed modelis used to estimate the fractional oil recovery, the water cut, the dimensionless time and the injectivity ratio at times of water breakthrough in the successive layers. Eqations are also derived for the case of continuous log–normal permeability distributions characterized by the Dykstra–Parsons variation coefficient VDP or the standard deviation of thelog–normal distribution σk.
Solutions for inclined communicating stratifiedsystems with log normal permeability distribution were obtained and the performance was compared withthat of the horizontal systems. The effects of the gravity number, the mobility ratio and the Dykstra-Parsons permeability variation coefficient, VDP, on the performance are investigated and discussed.
The obtained results showed that the gravity effect of the dip angle enhances the performance in terms of delayed water breakthrough, higher fractional oil recovery and lower water cut. This improvedperformance is more significant in the case of unfavorable mobility ratio. Reservoir dipping does not affect the pseudo relative permeability functions but results in a decrease in the injectivity ratio