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

Abstract

Summary The Dykstra-Parsons method (Dykstra and Parsons 1950) is used to predict the performance of waterflooding in noncommunicating stratified reservoirs. Much interest has been shown recently in the application of the method to chemical flooding, particularly for the case of polymer injection used for mobility control. The original method assumes that the reservoir layers are horizontal; however, most oil reservoirs exhibit a dip angle, with water being injected in the updip direction. Therefore, it is important to account for the effect of inclination on the performance of the method. 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 the density difference between the displacing and displaced fluids. The derived equation that governs the relative locations of the displacement fronts in different layers is nonlinear, includes a logarithmic term, and requires an iterative numerical solution. This solution is used to estimate the fractional oil recovery, the water cut, the injected pore volume, and the injectivity ratio at the time of water breakthrough in successive layers. Solutions for stratified systems with log-normal permeability distribution were obtained and compared with horizontal systems. The effects of the gravity number, the mobility ratio, and the Dykstra-Parsons permeability-variation coefficient (VDP) on the performance were investigated. Cases of updip and downdip injection are discussed. It was found that for a positive gravity number (updip water injection), performance is enhanced in terms of delayed water breakthrough, increased fractional oil recovery, and decreased water cut as compared with horizontal layers. This occurs for both favorable and unfavorable mobility ratios but is more evident in unfavorable mobility ratios and more-heterogeneous cases. For the case of a negative gravity number (downdip water injection or updip gas injection), the opposite behavior was observed. The results were also compared with the performance of inclined communicating reservoirs with complete crossflow. The effect of communication between layers was found to improve fractional oil recovery for favorable and unit mobility ratios and decrease recovery for unfavorable mobility ratio.