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This technique of calculating the extended Dykstra and Parsons method is presented below :
| 1. | From the relative permeability data and oil and water viscosities, calculate the fractional flow relationship from the following |
| 2. | Calculate the slope of dfw/dSw and determine the average water saturation at breakthrough. |
| 3. | Calculate the displacement efficiency at breakthrough, from : |
| 4. | Calculate the areal sweep efficiency at breakthrough, from : |
where.
Where coefficients a1 to a6 in the above equation depend on the waterdrive mechanism; ie., Five Spot, Direct Line Drive or Staggered Line Drive.
| 5. | Calculate the vertical sweep efficiency at assumed reservoir water–oil ratios (WOR) of 1, 2, 5, 10, 15, 20, 25, 50, and 100 bbl/bbl, using the technique of de Souza and Brigham. The vertical sweep efficiency at water breakthrough is calculated by extrapolating back to a WOR of zero. |
| 6. | Calculate the fractional flow values, and surface WOR from the above assumed reservoir WOR, from the following : |
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| 7. | Calculate cumulative water injected at breakthrough using the following equation : |
| 8. | Calculate cumulative oil produced at breakthrough, from the following : |
| 9. | Calculate the time to breakthrough, from the following : |
| 10. | Interpolate values of Sw, and calculate values of Swbar, from calculated values of fractional flow fw2, calculated previously in step 5 above. |
| 11. | Calculate the areal sweep efficiency for each value of fw2, calculated previously in step 5 above, using equations listed in step 4 above. |
| 12. | Calculate the displacement efficiency, for each value of Swbar calculated in step 10 above, using equations listed in step 3 above. |
| 13. | Calculate cumulative oil production for each assumed WOR from the following : |
| 14. | The equation to link water injection to oil and water production and fillup volume is presented below. This equation is used together with the relationship of WOR v's overall oil recovery factor to derive the oil and water production rates versus time. |
References:
Dykstra, H., Parsons, R., "The Prediction of Oil Recovery by Water Flood", Secondary Recovery of Oil in the United States, 2nd ed. American Petroleum Institute, 1950
Buckley, S., and Leverett, M., “Mechanism of Fluid Displacement in Sands” AIME, 1942
Felsenthal, M., Cobb, T., and Heur, G, “A Comparison of Waterflooding Evaluation Methods” SPE Paper 332, 1962.
de Souza, A., Brigham, W., "A Study on Dykstra–Parsons Curves", Stanford University Petroleum Research Institute, 1981
Ahmed, T., “Reservoir Engineering Handbook”, Elsevier, 2006
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