Waterflooding Performance in Inclined Communicating Stratified Reservoirs

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. The gravity number accounts for the dip angle and the density difference between the displacing, and displaced fluids. The developed fractional flow formula is used to estimate the fractional oil recovery, the dimensionless time, and the injectivity ratio at times of water breakthrough in the successive layers. The developed model allows for each layer to have its own porosity, endpoint saturations, and endpoint relative permeabilities. Solutions for the waterflooding performance in inclined communicating stratified systems with log-normal permeability distribution were obtained and compared with that of the horizontal systems. The effects of the gravity number, the mobility ratio, and the Dykstra-Parsons permeability-variation coefficient V-DP on the performance were investigated. 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 improved performance is more significant in the cases of unfavorable mobility ratio and of highly heterogeneous reservoirs. Reservoir dipping does not affect the pseudorelative permeability functions but results in a decrease in the injectivity ratio.