Control Optimization of Oil Production under Geological Uncertainty

1. Control Optimization of Oil Production under Geological Uncertainty ¹´²´³Agus Hasan, ²´³Bjarne Foss, ¹´³Jon Kleppe ¹Department of Petroleum Engineering, NTNU ²Department of Cybernetics Engineering, NTNU ³Center for Integrated Operations in Petroleum Industry Nordic Process Control Workshop 2009 Porsgrunn, Norway 29-30 January 2009 NPCW 2009 NTNU

2. Outline • Objectives and Motivations • Closed-loop Reservoir Management • Case Study • Part 1 Optimization • Optimization Methods • Reservoir Control Structure • Binary Integer Programming • Optimization Results • Part 2 Uncertainty • Geological Uncertainty • History Matching • Results • Conclusions and Recomendations NPCW 2009 NTNU

3. Objectives and Motivations Objectives: • Efficient: Fast enough • Accurate • Robust • Applicable: can be used in practical way • Find operating combination conditions of down-hole valve settings that • optimize the water flood. • Investigate potential for improvement as function of reservoir properties and • operating constraints. Objective function: Net Present Value (NPV) Which optimization method should we choose in our problem? NPCW 2009 NTNU

4. Closed-Loop Reservoir Management Production System (Reservoir, Well) Optimization Data Control and Optimization Identification and Updating Reservoir Simulator Calc. NPV Geological Uncertainty NPCW 2009 NTNU

5. Case Study Grid cells : 45 x 45 x 1 = 2025 2-phases : Oil-Water Assumptions: Incompressible and Immiscible fluids flow No flow boundaries No capillary pressure No gravity effect (Brouwer 2004) 1 Injector and 1 Producer well Each well was divide into 45 segments Each segments was modeled as a separated “smart well” NPCW 2009 NTNU

6. Initial Data • Porosity : 0.2 (uniformly distributed) • IOIP : 324000 sm3 = 2041200 bbl • Injection rate : 405 sm3/day • Water Injection price : $ 0 / bbl • Oil produced price : $ 60 / bbl • Water produced price : $ 10 /bbl • Discount rate : 0 • Three different permeability cases: NPCW 2009 NTNU

7. Reservoir Simulator Mass balance Darcy’s Law Saturation Equation Pressure Equation NPCW 2009 NTNU

8. Non-optimized Results NPCW 2009 NTNU

9. PART 1 Optimization NTNU 1/5/2020 NPCW 2009

10. Optimization Methods • Reactive Control Shut-in well with water cut above some threshold • Proactive Control Delay water breakthrough • Binary Integer Programming (BIP) On-off valves setting NPCW 2009 NTNU

11. Reservoir Control Structure 45 well segment aggregated into 9 control segments. Allow one segment to be closed at 200, 400, and 600 days. Which well segment should be closed? (Optimize the shut in sequence) Start Finish 200 400 600 0 800 [days] NPCW 2009 NTNU

12. Binary Integer Programming Constrain: NPCW 2009 NTNU

13. Results (Water saturation after 800 days) Non-optimize Case Reactive Proactive BIP NPCW 2009 NTNU

14. Results (Water cut and NPV) Unit in million USD NPCW 2009 NTNU

15. PART 2 Uncertainty NTNU 1/5/2020 NPCW 2009

16. Uncertainty Origins: • Mathematical model (linear model) • Measurement devices (well loging, surface facilities, etc) • Reservoir geology (porosity, permeability, fault, etc) Treatments: • EnKF • Bayesian Inversion • History matching • etc. NPCW 2009 NTNU

17. Geological Uncertainty Permeability Realizations NPCW 2009 NTNU

18. History Matching (Using 200 day production data) NPCW 2009 NTNU

19. History Matching (Cont’d) Selected permeability fields from ”Realizations” ”True” permeability fields Saturation profile from ”Realizations” (200 days) ”True” saturation profile (200 days) NPCW 2009 NTNU

20. Final Results (BIP with and without uncertainty) Unit in million USD NPCW 2009 NTNU

21. Results (Cont’d) Saturation profile without Uncertainty (800 days) Saturation profile with Uncertainty (800 days) NPCW 2009 NTNU

22. Conclusions • A new production optimization technique has been presented. • Optimization proces based onBinary Integer Programming has been • succesfuly applied and gives improvement in Net Present Value. Binary • Integer Programming gives more benets in the sense of NPV improvement • then regular Reactive or Proactive Control. • Binary Integer Programming is a robust optimization technique under • gealogical uncertainty such as permeability distribution. The optimization • process also showed that water saturation at breakthrough was observed to • be more uniformly distributed across the reservoir after the optimization • process as compared with the unoptimized case. • The scope for improvement depends on the type of heterogeneity in the • permeability field. Because the NPV performance of the optimal water • flood depends less on geological features than that of a conventional water • flood, the scope for improvement partly depends on the performance of • the conventional water flood. • The scope for improvement depends on the relative magnitudes of the oil • price and the water cost, and on the length of the optimization window. NPCW 2009 NTNU

23. Recommendations The effects of capillary pressure, compressibility, and gravity were not investigated in this study. Results obtained in this study may therefore only be representative for situations were gravity and capillary effects are relatively small. Gravity may positively or negatively affect the sweep efficiency. The scope for improvement and the shape of the optimal control functions may thus change if capillary or gravity forces are signicant. Therefore, their exact effects should be investigated. NPCW 2009 NTNU