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.
© 2012. Society of Petroleum Engineers
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History
- Original manuscript received:
15 December 2010
- Meeting paper published:
7 March 2011
- Revised manuscript received:
15 February 2012
- Manuscript approved:
22 February 2012
- Published online:
4 September 2012
- Version of record:
6 December 2012
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