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Use of streamline flow diagnostics for injection production rate allocation optimization
- 1. Use of Streamline Flow Diagnostics for Injection and Production Rate Allocation Optimization Shusei Tanaka November, 2014
- 2. Background 2/19 • Determining optimal injection/production rates to maximize NPV is challenging Heterogeneous geological reservoir Reallocate well rate to sweep bypassed oil • Rate reallocation algorithm needs to be fast and robust Requires a number of simulations Handle waterflood, EOR… Improve NPV under multiple constraints • Diagnose efficiency of the well How much ‘Inj-1’ contributes to field NPV?
- 3. - Improve oil production rate - Works only after breakthrough SL-Based Flow Rate Allocation Optimization: Previous Study 3/19 • Use of Well Allocation Factors (WAFs):[Thiele et. al, 2003] Well Allocation Factor map [SPE84080] [SPE113628] - WAFs by offset oil production of well-pair • Equalize arrival time of injection fluid: [Al-Hutali et. al, 2009] Norm Wt. - 0 After2yearsAfter5yearsears Base Base Improved Norm Wt. - 0 After2yearsAfter5yearsyears Base - Control well rate to have equivalent ‘breakthrough’ time - Increase well rate of high WAFs Decrease Increase Decrease Decrease Decrease Increase - Improves sweep efficiency - Works only before breakthrough
- 4. - Improve oil production rate - Works only after breakthrough SL-Based Flow Rate Allocation Optimization: Previous Study 4/19 • Use of Well Allocation Factors (WAFs):[Thiele et. al, 2003] Well Allocation Factor map [SPE84080] [SPE113628] - WAFs by offset oil production of well-pair • Equalize arrival time of injection fluid: [Al-Hutali et. al, 2009] Norm Wt. - 0 After2yearsAfter5yearsears Base Base Improved Norm Wt. - 0 After2yearsAfter5yearsyears Base - Control well rate to have equivalent ‘breakthrough’ time - Increase well rate of high WAFs Decrease Increase Decrease Decrease Decrease Increase - Improves sweep efficiency - Works only before breakthrough • Fast • Not robust • Does not optimize NPV
- 5. Motivation and Objective 5/19 • Previous study of SL-based waterflood optimization does not optimize NPV and limited applicability • Study objective: Propose a new NPV-based flow diagnostics Develop a streamline-based rate allocation method to optimize NPV Apply model to Brugge benchmark case Brugge field: multiple well and constraints [SPE 119094] Streamlines
- 6. Proposed Optimization Method: Overall Workflow 6/19 2. Trace Streamlines and Find connection map 3. Calculate NPV diagnostic plot 4. Reallocate flow rate of unconstrained well via ‘efficiency’ 1. Run simulation model
- 7. ‘Value’ and ‘NPV’ of a Streamline 7/19 Injector Producer 𝐻𝐶𝐼𝑃𝑠𝑙 = 𝑞 𝑠𝑙 𝑛𝑜𝑑𝑒 𝑆 𝑜 𝑏 𝑜 𝑅 𝑜 ∆𝜏 𝑁𝑃𝑉𝑠𝑙 = 𝑞 𝑠𝑙 𝑛𝑜𝑑𝑒 𝑆 𝑜 𝑏 𝑜 𝑅 𝑜 + 𝑆 𝑤 𝑏 𝑤 𝑅 𝑤 ∆𝜏 ∙ 1 + 𝑑 −𝜏/365 ∉ 𝑝𝑟𝑑 𝑛𝑜𝑑𝑒 ∆𝜏 > 𝑡 𝑟𝑠𝑚 Hydrocarbon value (Maximum possible revenue) NPV along SL (Prospected revenue) • Hydrocarbon value and NPV along Streamline from time T to reservoir life, trsm 𝑷𝑽 = න 𝟎 𝒔 𝑨 𝝃 𝝓 𝝃 𝒅𝝃 = න 𝟎 𝒔 𝒒 𝒔𝒍 𝝓 𝒔 𝒖 𝒕(𝒔) 𝒅𝝃 = 𝒒 𝒔𝒍 න 𝟎 𝒔 𝝓 𝒔 𝒖𝒕(𝒔) 𝒅𝝃 = 𝒒 𝒔𝒍 𝝉 𝜏 𝜉 =0 𝑠 𝜙 𝑠 𝑢 𝑡(𝑠) 𝑑𝜉 Pore volume: Time-of-Flight (TOF): Pore volume × Saturation × FVF × Price Discount rate Reservoir life
- 8. I1 I2 I3 I6 I5 I7 I8 NPV-based Efficiency of Streamline P1 P2 P3 P4 P5 P6 P7 8/19 HCIP, integrate along SL NPV, integrate along SL, only reservoir life time 𝐻𝐶𝐼𝑃𝑠𝑙 = 𝑞 𝑠𝑙 𝑛𝑜𝑑𝑒 𝑆 𝑜 𝑏 𝑜 𝑅 𝑜 ∆𝜏 𝑁𝑃𝑉𝑠𝑙 = 𝑞 𝑠𝑙 𝑛𝑜𝑑𝑒 𝑆 𝑜 𝑏 𝑜 𝑅 𝑜 + 𝑆 𝑤 𝑏 𝑤 𝑅 𝑤 ∆𝜏 ∙ 1 + 𝑑 −𝜏/365 ∉ 𝑝𝑟𝑑 𝑛𝑜𝑑𝑒 ∆𝜏 > 𝑡 𝑟𝑠𝑚 𝑒 𝑠𝑙 = 𝑁𝑃𝑉𝑠𝑙 𝐻𝐶𝐼𝑃𝑠𝑙 • Efficiency of a SL • Streamline efficiency by hydrocarbon value and NPV using economic values I4
- 9. I1 I2 I3 I6 I5 I7 I8 NPV-based Efficiency of Well Pair P1 P2 P3 P4 P5 P6 P7 9/19 𝑁𝑃𝑉𝑝𝑎𝑖𝑟 = 𝑠𝑙 𝑁𝑃𝑉𝑠𝑙 𝐻𝐶𝐼𝑃𝑝𝑎𝑖𝑟 = 𝑠𝑙 𝐻𝐶𝐼𝑃𝑠𝑙 • Well pair efficiency by hydrocarbon value and NPV 𝑒 𝑝𝑎𝑖𝑟 = 𝑁𝑃𝑉𝑝𝑎𝑖𝑟 𝐻𝐶𝐼𝑃𝑝𝑎𝑖𝑟 HCIP NPVHCIP and NPV, integrate by SL bundle • Well pair efficiency I4
- 10. NPV-Based Flow Diagnostics 10/19 I1 I2 I3 I6 I5 I7 I8 P1 P2 P3 P4 P5 P6 P7 𝑒 𝑝𝑎𝑖𝑟 = 𝑁𝑃𝑉𝑝𝑎𝑖𝑟 𝐻𝐶𝐼𝑃 𝑝𝑎𝑖𝑟 5-connection from Inj-4 pairv pairr HCIP (Normalized) NPV(Normalized) 𝑰 𝟒 𝐆𝐨𝐨𝐝 𝑷 𝟒 𝑰 𝟒 𝐏𝐨𝐨𝐫 𝑷 𝟕 NPV-based diagnostic plot I4 (𝑁𝑃𝑉, 𝐻𝐶𝐼𝑃 are normalized by field maximum 𝐻𝐶𝐼𝑃)
- 11. MCERI NPV(Normalized) Streamline-based Rate Allocation: A New Approach 𝑞 𝑝𝑎𝑖𝑟 𝑛𝑒𝑤 = 𝑞 𝑝𝑎𝑖𝑟 𝑜𝑙𝑑 𝑒 𝑝𝑎𝑖𝑟 ҧ𝑒𝑓𝑖𝑒𝑙𝑑 𝑞 𝑤𝑒𝑙𝑙 = 𝑟 𝑝𝑎𝑖𝑟 𝑞 𝑝𝑎𝑖𝑟 𝑛𝑒𝑤 ത𝐞 𝐟𝐢𝐞𝐥𝐝 decrease rate Increase rate Before update After update Total value (Normalized) 11/19
- 12. MCERI NPV(Normalized) Total value (Normalized) Streamline-based Rate Allocation: A New Approach decrease rate Increase rate Before update After update • Advantages: • Dynamically visualize efficiency of the injector and producer • Able to propose ‘better’ well rate by post processing 12/19 𝑞 𝑝𝑎𝑖𝑟 𝑛𝑒𝑤 = 𝑞 𝑝𝑎𝑖𝑟 𝑜𝑙𝑑 𝑒 𝑝𝑎𝑖𝑟 ҧ𝑒𝑓𝑖𝑒𝑙𝑑 𝑞 𝑤𝑒𝑙𝑙 = 𝑟 𝑝𝑎𝑖𝑟 𝑞 𝑝𝑎𝑖𝑟 𝑛𝑒𝑤 ത𝐞 𝐟𝐢𝐞𝐥𝐝
- 13. 13/19 • 3 years of waterflood, 8 injectors and 7 producers • Constraint: Field water injection/production 2500 [rb/day], min/max BHP per well • Relative oil, water price = 1, -0.2 $/bbl, Discount rate = 10% • Compare developed model with 3 approaches: • Uniform injection (Uniform), Well allocation factors (WAFs), Equalize Arrival Time (EqArrive), Developed model (SLNPV) Permeability Field Initial Oil Saturation SLs by Uniform Injection I1 I2 I3 I6 I5 I7 I8 P1 P2 P3 P4 P5 P6 P7 I4 Demonstration: 2D Multi-well Case
- 14. 0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05 3.0E+05 0 180 360 540 720 900 1080 NetPresentValue[$] Time [Days] SLNPV EqArrive WAFs Uniform 0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05 3.0E+05 0 180 360 540 720 900 1080 NetPresentValue[$] Time [Days] SLNPV EqArrive WAFs Uniform 14/19 Recovery Factor Net Present Value 2D Multi-well: Recovery and NPV SLNPV: Maximum NPV at 2 years 2.5 times of uniform injection 0.0 0.1 0.2 0.3 0.4 0 180 360 540 720 900 1080 RecoveryFactor[-] Time [Days] SLNPV EqArrive WAFs Uniform
- 15. 15/19 Result of Saturation Distribution: Uniform Injection and SLNPV SLNPVUniform injection : at 0.5 yrs Reduced injection Increased injection High water saturation High oil saturation
- 16. NPV-Based Flow Diagnostics 2D Multiwell Example 16/19 𝑁𝑃𝑉𝑝𝑎𝑖𝑟 = 𝑠𝑙 𝑞 𝑠𝑙 𝑛𝑜𝑑𝑒 𝑆 𝑜 𝑏 𝑜 𝑅 𝑜 + 𝑆 𝑤 𝑏 𝑤 𝑅 𝑤 ∆𝜏 ∙ 1 + 𝑑 −𝜏/365 ∉ 𝑝𝑟𝑑 𝑛𝑜𝑑𝑒 ∆𝜏 > 𝑡 𝑟𝑠𝑚 Injector P/I 1 2 3 4 5 6 7 8 1 96879 45170 0 38964 0 0 0 0 2 0 26458 25571 0 0 0 0 0 3 77264 0 0 49230 0 40210 0 0 4 0 54433 0 53080 0 0 0 0 5 0 66903 80531 0 78445 0 0 18356 6 0 0 0 19642 0 -4292 5050 0 7 0 0 0 4419 18840 0 -6175 -21328 Producer Predicted NPV, until end of the simulation I1 I2 I3 I6 I5 I7 I8 P1 P2 P3 P4 P5 P6 P7 I4
- 17. 17/19 Oil Saturation and Well Location • Constraints: - Field water injection qt <= 20,000 bbl/d - Well flow rate qti <= 6000 bbl/d - Producer BHP > 100 psi, Injector BHP < 6000 psi • Simulation Model: - Synthetic water flooding - 20 producers, 10 injectors - 20 years of simulation - Relative oil, water price = 1, -0.2 $/bbl Brugge Benchmark Model
- 18. Streamlines by Sw SLNPVUniformInjection Streamlines by Injector Example of SLs: After 10 Years Not sweep aquifer region Sweep aquifer region Increased Inj-Prd connection 18/19
- 19. 0.00 0.04 0.08 0.12 0.16 0.20 0 1200 2400 3600 4800 6000 7200 RecoveryFactor[-] Time [Days] SLNPV EqArrive WAFs Uniform 0.E+00 5.E+06 1.E+07 2.E+07 2.E+07 3.E+07 3.E+07 4.E+07 0 1200 2400 3600 4800 6000 7200 NetPresentValue[$] Time [Days] NPV EqArrive WAFs Uniform Recovery Factor Net Present Value Recovery Factor and NPV Injection Rate Production Rate Updated Well Rate by SLNPV 0 1000 2000 3000 4000 5000 6000 7000 0 1200 2400 3600 4800 6000 7200 ProductionRate[bbl/day] Time [Days] BR-P-1 BR-P-2 BR-P-3 BR-P-4 BR-P-5 BR-P-6 BR-P-7 BR-P-8 BR-P-9 BR-P-10 BR-P-11 BR-P-12 BR-P-13 BR-P-14 BR-P-15 BR-P-16 BR-P-17 BR-P-18 BR-P-19 BR-P-20 0 1000 2000 3000 4000 5000 6000 7000 0 1200 2400 3600 4800 6000 7200 InjectionRate[bbl/day] Time [Days] BR-I-1 BR-I-2 BR-I-3 BR-I-4 BR-I-5 BR-I-6 BR-I-7 BR-I-8 BR-I-9 BR-I-10 19/19
- 20. • Have developed a new SL-based rate allocation method to improve recovery considering NPV • Proposed a new diagnostic plot to visualize the relative value and efficiency of a well in the asset • Results in greater NPV compared to prior streamline-based rate allocation methods • Can be applied to IOR/EOR simulation study with any commercial simulator by post processing Conclusions 20/19
Editor's Notes
- Allow me to start the presentation.
- Challenges of this problem. The most commonly used approach of water flooding is, injecting constant and uniform by spatial and time extent. However, the reservoir is heterogeneous and uniform injection is not the best option. We want to reallocate well rate to sweep bypassed oil. For the application side, we also have difficulties, such as it requires number of simulation, works robustly for waterflood and EOR application under multiple constraints Also it is easy to diagnose the production well since it produce oil, but difficult for injector. Can we estimate how much injector to contribute to NPV?
- Let me overview the previous streamline based rate allocation method. The first approach that we can find is the use of well allocation factors. The well allocation factors are defined as offset oil production or oil cut of the well pair. If the value is close to 1, that pair is efficient. Their approach is to update well by comparing field average efficiency. If the efficiency is higher than average, then inject more by factors. The second approach is called Equalize arrival time of injection fluid. The objective of this method is to equalize arrival time of all injection-production pair, by solving this equation. The example in right picture shows that by equaliing arrival time, we can improve sweep efficieny of the field. In addition to this assumption, these previous study does not optimize NPV.
- Let me overview the previous streamline based rate allocation method. The first approach that we can find is the use of well allocation factors. The well allocation factors are defined as offset oil production or oil cut of the well pair. If the value is close to 1, that pair is efficient. Their approach is to update well by comparing field average efficiency. If the efficiency is higher than average, then inject more by factors. The second approach is called Equalize arrival time of injection fluid. The objective of this method is to equalize arrival time of all injection-production pair, by solving this equation. The example in right picture shows that by equaliing arrival time, we can improve sweep efficieny of the field. In addition to this assumption, these previous study does not optimize NPV.
- Let me start from motivation and objective of this study. The previous study of SL-Based rate allocation optimization is done using this connection map, however, is not based on NPV and there is limitations due to assumptions. The objective is to propose new flow diagnostic plot and rate allocation optimization method to optimize NPV.
- Let me show the overall workflow first. The picture below shows the streamline contoured by TOF, the travel time of the injection fluid. The picture center is the drainage map, obtained by mapping injection to production connection to underline grid. With this we can visualize the region where injector drained. Once we superimpose all the streamline information to reprehensive line, we can obtain connection map.
- How do we measure value and NPV using streamline? First, start from time of flight, we can define pore volume as follows. Then multiply pore volume and saturation which makes it hydrocarbon volume, and make it value to
- In order to overcome limitation of the previous study, Im going to show the NPV-based flow diagonostics with example of 2D field. The goal is to find the NPV and efficiency along streamline.
- Find connection efficiency
- Then Im going to talk the procedure to update well rate according to the flow diagnostics. The flow chat is shown here, we run simulation with single step, and then… Update individual flow rate based on average efficiency of the field.
- Then Im going to talk the procedure to update well rate according to the flow diagnostics. The flow chat is shown here, we run simulation with single step, and then… Update individual flow rate based on average efficiency of the field.
- Let me show the example by 2D areal, multiwell case. The initial permeability field and oil saturation is shown in figure.
- This slide shows the streamline distribution of uniform injection by top, optimized results below. The contour is time of flight and injector index, respectively. The figure shows that the optimized results sweep less aquifer region and more streamline at the top of the reservoir. This results are reasonable because most of the oil is located at the top of the reservoir in Brugge case.
- Conclusion as follows: