The Modification of the Dykstra-Parsons Method for Inclined Stratified Reservoirs

The Dykstra-Parsons method is used to predict the performance of waterflooding in non-communicating stratified reservoirs.
Much interest was shown lately for the application of the method for chemical flooding and in particular for the case of
polymer injection used for mobility control .The original method however assumes the layers to be horizontal. Most oil
reservoirs exhibit a dip angle with the water being injected in the up dip direction. It is there for important to account for the
effect of the inclination on the performance.
A modification of the Dykstra-Parsons equations is obtained to account for reservoir inclination. The developed model
includes a dimensionless gravity number that accounts for the effect of the dip angle and density difference between the
displacing and displaced fluids. The derived equation that governs the relative locations of the displacement fronts in different
layers is non linear and include a logarithmic term. Iterative numerical solution is used to obtain the location of the front in the
different layers at the time of water breakthrough in successive layers. This solution is used to obtain values for the fractional
oil recovery, the water cut, the dimensionless time and the injectivity ratio.
Solutions for stratified systems with log normal permeability distribution were obtained and compared with 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.
It was found that the gravity (dip angle) enhances the performance in terms of delaying water breakthrough, increasing the
fractional oil recovery, and decreasing water cut as compared to horizontal layers. This occurs for both favorable and
unfavorable mobility ratios but is more evident in unfavoorable mobility ratios and more heterogeneous cases.
The results were also compared with the performance of inclined communicating reservoirs with complete crossflowand
the communication was found to improve fractional oil recovery for unit and favorable mobility ratios and decrease recovery
for unfavorable mobility ratio.