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This is the period from water breakthrough to floodout.
After breakthrough, the water–oil ratio increases with a subsequent decline in the oil flow rate. The swept area will continue to increase as additional water is injected. The incrementally swept area will contribute additional oil production, while the previously swept area will continue to produce both oil and water.
The performance calculations, for this stage, are given by the following steps:
| 1. | Assume several values for the ratio Winj/WiBT and calculate the cumulative water injected for each ratio from the following |
| 2. | Calculate the areal sweep efficiency at each assumed ratio from the following equation : |
| 3. | Calculate the ratio Qi/QiBT that corresponds to each value of Winj/WiBT using the following equation : |
where,
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and Ei is the exponential integral function.
| 4. | Determine the total pore volumes of water injected from the following : |
| 5. | Calculate the slope dfw/dSw for each value of Qi from the following : |
| 6. | Calculate the value of Sw2, the water saturation at the producing well, that corresponds to each value of dfw/dSw. |
| 7. | Calculate the reservoir water cut at the producing well for each value of Sw2, from the following equation : |
| 8. | Determine the average water saturation in the swept area, from the following : |
| 9. | Calculate the surface water–oil ratio that corresponds to each value of fw2, from the following : |
| 10. | Calculate cumulative oil production incorporating for the oil lost to the unswept area of the flood pattern, from the following : |
where,
ED is the displacement efficiency, and is calculated from the following :
| 11. | Calculate cumulative water production from the following : |
| 12. | Calculate krw at Sw2 and determine the mobility ratio M after breakthrough from the following : |
| 13. | Calculate the conductance ratio γ. |
| 14. | Calculate the water injection rate, from the following : |
| 15. | And finally, calculate the oil and water production rates, from the following : |
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