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An effective reservoir management by streamline based simulation, history matching and rate allocation optimization

S
Shusei Tanaka

The document discusses advancements in streamline-based reservoir management through a simulator that incorporates capillarity and gravity effects for improved prediction and optimization in mature fields. It highlights challenges and methodologies for history matching and flow diagnostics, demonstrating applications on a benchmark case to optimize well allocation and enhance net present value (NPV). Key findings indicate that the developed simulation method offers computational efficiencies and improved results compared to traditional methods.

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An Effective Reservoir Management by Streamline-based Simulation, History Matching and Optimization Shusei Tanaka May, 2014
• Development of a general purpose streamline-based reservoir simulator:  Inclusion of diffusive flux via Orthogonal Projection  Illustration by black oil model  Extension to a multicomponent system • Application to Brugge benchmark case:  Streamline-based simulation  Streamline-based BHP/WCT data integration  Flow diagnostics for streamline-based NPV optimization • Conclusion Outline 2/50
Streamline Technology: Overview 3/50 • Key concept of Streamline:  Fast IMPES-based reservoir simulation  History matching(HM) by calibration of travel time  Improves sweep efficiency by streamline information Pressure field Streamlines Connection map
Problem Statement: SL-based Reservoir Management 4/50 • Challenges for mature field, multiple well…  Quick forecasting  HM for individual well  Improve NPV by reallocating well rate • Streamline is efficient, but can we apply all the time?  What if flow is not convective dominant?  How about prior to breakthrough for HM?  Can we improve NPV? Mature field with multiple wells
Development of a General Purpose Streamline- based Simulator
Motivation 6/50 Solve 1D Convection EquationsCalculate Diffusive Flux on Grid Compute Pressure & Velocity Field • Streamline simulation is difficult to apply if…  System of equation is highly nonlinear (ex. Gas injection)  Capillary and gravity effects are dominant Error by Operator-Split Error by IMPES
;0   w w u t S  Why Split the Equation? • Water velocity does not follow total velocity with capillary (and gravity) 7/50 tuwu Streamline cowowtww pkFuFu  
• Split equation by physical mechanisms Convective Transport Capillary Diffusion   0   cowow w pkF t S  0   w w u t S    0   wt w Fu t S  cowowtww pkFuFu   Saturation Transport Equation 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.2 0.4 0.6 0.8 1 WaterSaturation Normalized Distance Correct Solution Convection Flow Too much diffusion with large time step (SPE 163640) Operator Splitting Capillary after convection 8/50
  0 ~    wtw w Fuu t S    cowowtwwwtw pkFuFFFuu   ~~ • Split equation by physical mechanisms • Anti-diffusive corrections Computationally expensive: Function of (P, T, composition, Initial state) for each grid, time step 0   w w u t S    0   wt w Fu t S  Splitting with anti- diffusive flux Convection Eq. Corrected Operator Splitting Anti-diffusive concave envelope 9/50
0   w w u t S   wtww uufu Parallel component, calculate along streamline Anti-diffusive correction not needed Orthogonal Projection • Split equation into parallel and transverse flux terms twf u wu tuwu Streamline 10/50
twf u wu 0   w w u t S    0   tw w uf t S  0   w w u t S  tuwu Orthogonal Projection Parallel to Ut (Solve along streamline) Transverse to Ut (Solve on grids) Streamline • Split equation into parallel and transverse flux terms  wtww uufu Parallel component, calculate along streamline Anti-diffusive correction not needed 11/50
1.Compute pressure & velocity field Include capillary effects 2.Trace streamlines Solve 1D convection equations Include capillarity and gravity 3.Map back saturation to grid Calculate corrector term Predictor-Corrector Workflow Iterative IMPES Orthogonal Projection 12/50
• Pressure equation(IMPES) • Transport equation (along SL) Orthogonal Projection: Application to Multicomponent System 0                      owgj j owgj j owgj jj owgj jjr Qupuc t p Scc i sl ii fm t           cfgDpFy u k yFfSym sl ii owgj owgj jogwmm m jmjmcmjjij t jijj sl ij ogwj jiji 1 ,2 ,,               Δ • Transport equation (on Grid, corrector)          ogwj jmogwm m jmcjmmjjijtt i DgpFykuuI t m , ˆˆ  Pc,Gravity along streamline Transverse Pc,Gravity on grid   0         owgj ijijjjijjjij qyuySy t  • Governing equation 13/50
Illustrative Example 100 mD 5 mD • Water injection 0.2PVI, then CO2 0.2PVI • Single time step for each injection period • Observe capillarity by parallel/transverse to Ut tw uf  wu 14/50
Water Saturation and Capillary Flux Distributions • Capillarity traps water at center by J-Function • Capillarity flows back water towards injector during gas injection period Sw after water injection Arrow: water capillary flux Sw after gas injection Arrow: water capillary flux 1 )(   kSwJpcow  15/50
Water Capillary Flux: Parallel and Transverse to Total Velocity Total capillary flux Capillary flux transverse to total velocity Capillary flux along total velocity • Most of the capillary effects can be included along the streamlines cow t tt t ow t w p u uu I u k u        2   Along streamline On grids 16/50 cow t t t ow p u u k 2  
Water Saturation Distribution Commercial, FD Operator Splitting (no correction) Orthogonal Projection • OP can take large time step without anti-diffusive correction 17/50
Injection :: CO2 10 rb/D – 1000 [Days] Production :: BHP (1900 psi) 2D Cross-Section CO2 Flooding Model Pc, Convection Pc, Gravity Simulation model: • 7 HC component + Water • Rel-Perm by Corey • Water-wet Capillarity Initial & Boundary Condition • 2000+ psi , 212F˚ • Constant production BHP, constant CO2 injection at 10 rb/D • 1000 days 18/50
CO2 Mole Fraction Distribution: Along Streamline Including Pc & GravityConvection only 19/50
Production Mole Fraction of CO2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 200 400 600 800 1000 ProductionMoleFraction(CO2) Time [Days] Streamline Commercial Simulator Number of time step: Commercial FD = 56 Streamline = 21 20/50
CO2 Mole Fraction Distribution: Final Distribution Orthogonal Projection (After corrector term) Commercial FD (E300) 21/50
0 50 100 150 200 250 300 350 400 450 500 2D Areal 2D Cross-Section 2D Cross- SectionHetero Goldsmith Field E300 FIM Streamline Previous case Comparisons of Number of Time Step NumberofTimeStep Tested simulation cases in the paper 10× 2× 4× 3× 22/50
0 50 100 150 200 250 300 350 400 450 500 2D Areal 2D Cross-Section 2D Cross- SectionHetero Goldsmith Field E300 FIM Streamline Previous case Comparisons of Number of Time Step NumberofTimeStep Tested simulation cases in the paper 10× 2× 4× 3× 23/50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 180 360 540 720 900 1080 ProductionMoleFraction(CO2) Time [Days] Streamline Commercial Simulator 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0E+00 2.5E+04 5.0E+04 7.5E+04 1.0E+05 ProductionMoleFraction(CO2) Time [Days] Streamline Commercial Simulator
Conclusions 24/50 • Developed a new SL-based simulation method to incorporate capillarity and gravity and applied to CO2 injection cases • Computational advantages: • Minimizes the saturation correction term • Can take large time steps without anti-diffusive corrections • Demonstrated by synthetic and field case: • Iterative IMPES approach handles nonlinearity • Larger time stepping obtained compared with commercial FD simulator
Application to Brugge Benchmark: - Streamline-Simulation - History Matching - NPV Optimization
Brugge Benchmark Example 26/50 • Benchmark model for HM, optimization problem • 20 producers, 10 injectors in complex geometry • Conduct 40 years of waterflood, 1000 stb/d per wel Oil saturation and well location Initial So Net gross ratio Porosity Rock table ID
ECLIPSE vs. Streamline Simulation: Water-Cut (4 producers) 27/50 Circle : ECLIPSE 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 7500 15000 ProductionWaterCut Time [Days] BR-P-18 ECL BR-P-8 BR-P-12 BR-P-1 BR-P-18 SL BR-P-8 BR-P-12 BR-P-1 Line: Streamline - ECLIPSE without NNC option
Comparisons of Oil Saturation Distribution 28/50 Initial oil saturation After 20 years Streamline Commercial (ECL)
Presented at student paper contest 2013 Application to Brugge Benchmark: - Streamline-Simulation - History Matching - NPV Optimization
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 500 1000 1500 2000 WaterCut Time [Days] Streamline-based Inverse Modeling 30/50 min 𝛿𝐝 𝑤𝑐𝑡 − 𝐒 𝑤𝑐𝑡 𝛿𝐤 𝛿𝐝 1. Run reservoir simulation by given model 2. Trace Streamlines and calculate parameter sensitivity 3. Update parameters to satisfy: Observation Prediction
Motivation and Objective 31/50 Streamlines 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 500 1000 1500 2000 WaterCut Time [Days] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 500 1000 1500 2000 CO2MoleFraction Time [Days] WCT • What can we tell prior to breakthrough?  Pressure data can be used while not considered previously • Study objective  New approach to calculate pressure sensitivity along SL  Simultaneous inversion of pressure and water-cut data 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 50 100 150 200 BottomHolePressure Time [Days] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 50 100 150 200 BottomHolePressure Time [Days] BHP Observation Initial
ik 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 500 1000 1500 2000 WaterCut Time [Days] 𝛿𝒕 𝑤𝑐𝑡 Production WCT Parameter Sensitivity Along Streamline 32/50 • TOF( ): Travel time of neutral tracer along streamlines    , , , , x y z Inlet ds x y z u     𝜕𝑡 𝜕𝑘𝑖 = − 𝜕𝑆 𝜕𝜏 𝜕𝜏 𝜕𝑘𝑖 ∙ 𝜕𝑆 𝜕𝑡 −1 = 1 𝑓′(𝑆) ∆𝜏𝑖 𝑘𝑖 • Water-cut travel time sensitivity: injector Producer [He et. al,2003] 𝜕𝑝 𝑏ℎ𝑝 𝜕𝑘𝑖 = 𝜕∆𝑝𝑖 𝜕𝑘𝑖 ≈ ∆𝑝𝑖 𝑘𝑖 • Bottom hole pressure sensitivity: [new] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 50 100 150 200 BottomHolePressure Time [Days] Production BHP 𝛿𝒑 𝑏ℎ𝑝 𝜕𝑝 𝑏ℎ𝑝 𝜕𝑘𝑖 ≈ 𝜏𝑖 𝜏 𝜕∆𝑝𝑖 𝜕𝑘𝑖 ≈ 𝜏𝑖 𝜏 ∆𝑝𝑖 𝑘𝑖 Rate-Rate constraint Rate-BHP constraint
Sensitivity Results: 1D CPG (3phase Gas Injection) -20.0 -15.0 -10.0 -5.0 0.0 0.0 0.5 1.0 PressureSensitivity,wrtk Normalized Distance Analytical (Stremaline) Adjoint Method 0.0 5.0 10.0 15.0 20.0 0.0 0.5 1.0 PressureSensitivity,wrtk Normalized Distance Analytical (Stremaline) Adjoint Method 33/50 Inj: Gas Rate Prd: Rate Producer BHP sensitivity to k Injector BHP sensitivity to k
Sensitivity Results: 2D Areal 34/50 Inj P1 P2P3 P4 Injector BHP sensitivity by k P1 BHP sensitivity of by k Permeability field (Wells by rate constraint) Adjoint Proposed
Inversion of Permeability by LSQR 35/50 • Run simulation and get following parameter • Solve LSQR Matrix : • Advantages: • Find pressure/WCT sensitivity during SL simulation • Localized (high resolution) changes in permeability min 𝛿𝐝 𝑤𝑐𝑡 − 𝐒 𝑤𝑐𝑡 𝛿𝐤 + 𝛿𝐝 𝑏ℎ𝑝 − 𝐒 𝑏ℎ𝑝 𝛿𝐤 + 𝛽1 𝐈𝛿𝐤 + 𝛽2 𝐋𝛿𝐤 ෠𝐒 𝑤𝑐𝑡 ෠𝐒 𝑏ℎ𝑝 𝛽1 𝐈 𝛽2 𝐋 ∆𝐤 = 𝛿𝐝 𝑤𝑐𝑡 𝛿𝐝 𝑏ℎ𝑝 0 0 Water-Cut Pressure - Smoothness - Consistency with static model Scaled by stdev
History Matching of Brugge Field • Use simulation result of Real.77 as observed data • Use Real.1 as initial model • Assume 3 years of data is available Reference model Initial model 36/50
Available Observation Data 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 144.0 644.0 1144.0 ProductionWaterCut[-] Time [Days] BR-P-11 BR-P-12 BR-P-15 BR-P-18 BR-P-11 BR-P-12 BR-P-15 BR-P-18 • Only 4 producers have water breakthrough • Pressure data is available for 30 wells Water cut: Initial Observed 37/50
Reference kx Initial kx Change of kx, WCT Change of kx, WCT&BHP High perm at middle layer Change of Permeability 38/50
Reduction of Data Mismatch 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 20 40 60 80 100 NormalizedAbsoluteError.Pressure Number of Iteration 0.0 0.3 0.6 0.9 1.2 1.5 0 20 40 60 80 100 NormalizedAbsoluteError,WaterCut Number of Iteration Pressure RMSE error WCT RMSE error Individual well Mean 39/50
• Have developed a new SL-based method to integrate pressure data into prior geologic models • Same advantages as prior streamline work: • Analytic calculation of streamline sensitivities • Requires only a single flow simulation per iteration • Can be applied to field pressure/rate data prior to water breakthrough • Can be integrate pressure with water-cut or GOR simultaneously, for black-oil and compositional simulation Conclusion 40/50
Presented at student paper contest 2014 Application to Brugge Benchmark: - Streamline-Simulation - History Matching - NPV Optimization
Overview 42/50 • Problem:  Determining optimal injection/production rates to maximize NPV • Solution:  Developed a new streamline and NPV-based rate allocation method • Advantages:  Visualize efficiency of injector and producer  Extensible to any secondary recovery process with commercial simulator
- Improve oil production rate - Works only after breakthrough SL-based Flow Rate Allocation Optimization: Previous Study 43/50 • Use of Well Allocation Factors (WAFs):[Thiele et. al, 2003] Well Allocation Factor map [SPE84080] [SPE113628] - WAFs: 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
Proposed Optimization Method: Overall Workflow 44/50 2. Trace Streamlines and Find connection map 3. Calculate NPV diagnostic plot 4. Reallocate well rate via efficiency 1. Run simulation model
I1 I2 I3 I6 I5 I7 I8 NPV-based Efficiency of Streamline P1 P2 P3 P4 P5 P6 P7 Hydrocarbon value, along SL NPV along SL, integrate over reservoir life time 𝑣 𝑠𝑙 = 𝑞 𝑠𝑙 ෍ 𝑛𝑜𝑑𝑒 𝑆 𝑜 𝑏 𝑜 𝑅 𝑜 ∆𝜏 𝑟𝑠𝑙 = 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 and NPV along streamline Pore volume × Saturation × FVF × Price Discount rate Reservoir life I4 45/50
NPV-based Flow Diagnostics I1 I2 I3 I6 I5 I7 I8 P1 P2 P3 P4 P5 P6 P7 𝑒 𝑝𝑎𝑖𝑟 = σ 𝑠𝑙 𝑟 𝑠𝑙 σ 𝑠𝑙 𝑣 𝑠𝑙 Total value NPV 5-connection from Inj-4 Total value (Normalized) NPV(Normalized) 𝑰 𝟒 𝐆𝐨𝐨𝐝 𝑷 𝟒 𝑰 𝟒 𝐏𝐨𝐨𝐫 𝑷 𝟕 NPV-based diagnostic plot I4 46/50
NPV(Normalized) Streamline-based Rate Allocation: A New Approach 47/50 𝑞 𝑛𝑒𝑤 = 𝑞 𝑜𝑙𝑑 𝑒 𝑝𝑎𝑖𝑟 ҧ𝑒𝑓𝑖𝑒𝑙𝑑 ത𝐞 𝐟𝐢𝐞𝐥𝐝 decrease rate Increase rate Before update After update Total value (Normalized)
NPV(Normalized) Total value (Normalized) Streamline-based Rate Allocation: A New Approach 48/50 𝑞 𝑛𝑒𝑤 = 𝑞 𝑜𝑙𝑑 𝑒 𝑝𝑎𝑖𝑟 ҧ𝑒𝑓𝑖𝑒𝑙𝑑 ത𝐞 𝐟𝐢𝐞𝐥𝐝 decrease rate Increase rate Before update After update • Advantages: • Dynamically visualize efficiency of the injector and producer • Able to propose ‘better’ well rate during SL-simulation
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 $/bbl Brugge Benchmark Application • Compare developed model with 3 approaches: • Uniform injection (Uniform), Well allocation factors (WAFs), Equalize Arrival Time (EqArrive), Developed model (SLNPV) 49/50
0.00 0.04 0.08 0.12 0.16 0.20 0 1200 2400 3600 4800 6000 7200 RecoveryFactor[-] Time [Days] SLNPV EqArrive WAFs Uniform 0.E+00 5.E+06 1.E+07 2.E+07 2.E+07 3.E+07 3.E+07 4.E+07 0 1200 2400 3600 4800 6000 7200 NetPresentValue[$] 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 50/50
Streamlines by Sw SLNPVUniformInjection Streamlines by Injector Example of SLs: After 10 Years Not sweep aquifer region Sweep aquifer region Increased Inj-Prd connection 51/50
MCERI • 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, with low computational cost Conclusions 54

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An effective reservoir management by streamline based simulation, history matching and rate allocation optimization

  • 1. An Effective Reservoir Management by Streamline-based Simulation, History Matching and Optimization Shusei Tanaka May, 2014
  • 2. • Development of a general purpose streamline-based reservoir simulator:  Inclusion of diffusive flux via Orthogonal Projection  Illustration by black oil model  Extension to a multicomponent system • Application to Brugge benchmark case:  Streamline-based simulation  Streamline-based BHP/WCT data integration  Flow diagnostics for streamline-based NPV optimization • Conclusion Outline 2/50
  • 3. Streamline Technology: Overview 3/50 • Key concept of Streamline:  Fast IMPES-based reservoir simulation  History matching(HM) by calibration of travel time  Improves sweep efficiency by streamline information Pressure field Streamlines Connection map
  • 4. Problem Statement: SL-based Reservoir Management 4/50 • Challenges for mature field, multiple well…  Quick forecasting  HM for individual well  Improve NPV by reallocating well rate • Streamline is efficient, but can we apply all the time?  What if flow is not convective dominant?  How about prior to breakthrough for HM?  Can we improve NPV? Mature field with multiple wells
  • 5. Development of a General Purpose Streamline- based Simulator
  • 6. Motivation 6/50 Solve 1D Convection EquationsCalculate Diffusive Flux on Grid Compute Pressure & Velocity Field • Streamline simulation is difficult to apply if…  System of equation is highly nonlinear (ex. Gas injection)  Capillary and gravity effects are dominant Error by Operator-Split Error by IMPES
  • 7. ;0   w w u t S  Why Split the Equation? • Water velocity does not follow total velocity with capillary (and gravity) 7/50 tuwu Streamline cowowtww pkFuFu  
  • 8. • Split equation by physical mechanisms Convective Transport Capillary Diffusion   0   cowow w pkF t S  0   w w u t S    0   wt w Fu t S  cowowtww pkFuFu   Saturation Transport Equation 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.2 0.4 0.6 0.8 1 WaterSaturation Normalized Distance Correct Solution Convection Flow Too much diffusion with large time step (SPE 163640) Operator Splitting Capillary after convection 8/50
  • 9.   0 ~    wtw w Fuu t S    cowowtwwwtw pkFuFFFuu   ~~ • Split equation by physical mechanisms • Anti-diffusive corrections Computationally expensive: Function of (P, T, composition, Initial state) for each grid, time step 0   w w u t S    0   wt w Fu t S  Splitting with anti- diffusive flux Convection Eq. Corrected Operator Splitting Anti-diffusive concave envelope 9/50
  • 10. 0   w w u t S   wtww uufu Parallel component, calculate along streamline Anti-diffusive correction not needed Orthogonal Projection • Split equation into parallel and transverse flux terms twf u wu tuwu Streamline 10/50
  • 11. twf u wu 0   w w u t S    0   tw w uf t S  0   w w u t S  tuwu Orthogonal Projection Parallel to Ut (Solve along streamline) Transverse to Ut (Solve on grids) Streamline • Split equation into parallel and transverse flux terms  wtww uufu Parallel component, calculate along streamline Anti-diffusive correction not needed 11/50
  • 12. 1.Compute pressure & velocity field Include capillary effects 2.Trace streamlines Solve 1D convection equations Include capillarity and gravity 3.Map back saturation to grid Calculate corrector term Predictor-Corrector Workflow Iterative IMPES Orthogonal Projection 12/50
  • 13. • Pressure equation(IMPES) • Transport equation (along SL) Orthogonal Projection: Application to Multicomponent System 0                      owgj j owgj j owgj jj owgj jjr Qupuc t p Scc i sl ii fm t           cfgDpFy u k yFfSym sl ii owgj owgj jogwmm m jmjmcmjjij t jijj sl ij ogwj jiji 1 ,2 ,,               Δ • Transport equation (on Grid, corrector)          ogwj jmogwm m jmcjmmjjijtt i DgpFykuuI t m , ˆˆ  Pc,Gravity along streamline Transverse Pc,Gravity on grid   0         owgj ijijjjijjjij qyuySy t  • Governing equation 13/50
  • 14. Illustrative Example 100 mD 5 mD • Water injection 0.2PVI, then CO2 0.2PVI • Single time step for each injection period • Observe capillarity by parallel/transverse to Ut tw uf  wu 14/50
  • 15. Water Saturation and Capillary Flux Distributions • Capillarity traps water at center by J-Function • Capillarity flows back water towards injector during gas injection period Sw after water injection Arrow: water capillary flux Sw after gas injection Arrow: water capillary flux 1 )(   kSwJpcow  15/50
  • 16. Water Capillary Flux: Parallel and Transverse to Total Velocity Total capillary flux Capillary flux transverse to total velocity Capillary flux along total velocity • Most of the capillary effects can be included along the streamlines cow t tt t ow t w p u uu I u k u        2   Along streamline On grids 16/50 cow t t t ow p u u k 2  
  • 17. Water Saturation Distribution Commercial, FD Operator Splitting (no correction) Orthogonal Projection • OP can take large time step without anti-diffusive correction 17/50
  • 18. Injection :: CO2 10 rb/D – 1000 [Days] Production :: BHP (1900 psi) 2D Cross-Section CO2 Flooding Model Pc, Convection Pc, Gravity Simulation model: • 7 HC component + Water • Rel-Perm by Corey • Water-wet Capillarity Initial & Boundary Condition • 2000+ psi , 212F˚ • Constant production BHP, constant CO2 injection at 10 rb/D • 1000 days 18/50
  • 19. CO2 Mole Fraction Distribution: Along Streamline Including Pc & GravityConvection only 19/50
  • 20. Production Mole Fraction of CO2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 200 400 600 800 1000 ProductionMoleFraction(CO2) Time [Days] Streamline Commercial Simulator Number of time step: Commercial FD = 56 Streamline = 21 20/50
  • 21. CO2 Mole Fraction Distribution: Final Distribution Orthogonal Projection (After corrector term) Commercial FD (E300) 21/50
  • 22. 0 50 100 150 200 250 300 350 400 450 500 2D Areal 2D Cross-Section 2D Cross- SectionHetero Goldsmith Field E300 FIM Streamline Previous case Comparisons of Number of Time Step NumberofTimeStep Tested simulation cases in the paper 10× 2× 4× 3× 22/50
  • 23. 0 50 100 150 200 250 300 350 400 450 500 2D Areal 2D Cross-Section 2D Cross- SectionHetero Goldsmith Field E300 FIM Streamline Previous case Comparisons of Number of Time Step NumberofTimeStep Tested simulation cases in the paper 10× 2× 4× 3× 23/50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 180 360 540 720 900 1080 ProductionMoleFraction(CO2) Time [Days] Streamline Commercial Simulator 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0E+00 2.5E+04 5.0E+04 7.5E+04 1.0E+05 ProductionMoleFraction(CO2) Time [Days] Streamline Commercial Simulator
  • 24. Conclusions 24/50 • Developed a new SL-based simulation method to incorporate capillarity and gravity and applied to CO2 injection cases • Computational advantages: • Minimizes the saturation correction term • Can take large time steps without anti-diffusive corrections • Demonstrated by synthetic and field case: • Iterative IMPES approach handles nonlinearity • Larger time stepping obtained compared with commercial FD simulator
  • 25. Application to Brugge Benchmark: - Streamline-Simulation - History Matching - NPV Optimization
  • 26. Brugge Benchmark Example 26/50 • Benchmark model for HM, optimization problem • 20 producers, 10 injectors in complex geometry • Conduct 40 years of waterflood, 1000 stb/d per wel Oil saturation and well location Initial So Net gross ratio Porosity Rock table ID
  • 27. ECLIPSE vs. Streamline Simulation: Water-Cut (4 producers) 27/50 Circle : ECLIPSE 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 7500 15000 ProductionWaterCut Time [Days] BR-P-18 ECL BR-P-8 BR-P-12 BR-P-1 BR-P-18 SL BR-P-8 BR-P-12 BR-P-1 Line: Streamline - ECLIPSE without NNC option
  • 28. Comparisons of Oil Saturation Distribution 28/50 Initial oil saturation After 20 years Streamline Commercial (ECL)
  • 29. Presented at student paper contest 2013 Application to Brugge Benchmark: - Streamline-Simulation - History Matching - NPV Optimization
  • 30. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 500 1000 1500 2000 WaterCut Time [Days] Streamline-based Inverse Modeling 30/50 min 𝛿𝐝 𝑤𝑐𝑡 − 𝐒 𝑤𝑐𝑡 𝛿𝐤 𝛿𝐝 1. Run reservoir simulation by given model 2. Trace Streamlines and calculate parameter sensitivity 3. Update parameters to satisfy: Observation Prediction
  • 31. Motivation and Objective 31/50 Streamlines 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 500 1000 1500 2000 WaterCut Time [Days] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 500 1000 1500 2000 CO2MoleFraction Time [Days] WCT • What can we tell prior to breakthrough?  Pressure data can be used while not considered previously • Study objective  New approach to calculate pressure sensitivity along SL  Simultaneous inversion of pressure and water-cut data 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 50 100 150 200 BottomHolePressure Time [Days] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 50 100 150 200 BottomHolePressure Time [Days] BHP Observation Initial
  • 32. ik 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 500 1000 1500 2000 WaterCut Time [Days] 𝛿𝒕 𝑤𝑐𝑡 Production WCT Parameter Sensitivity Along Streamline 32/50 • TOF( ): Travel time of neutral tracer along streamlines    , , , , x y z Inlet ds x y z u     𝜕𝑡 𝜕𝑘𝑖 = − 𝜕𝑆 𝜕𝜏 𝜕𝜏 𝜕𝑘𝑖 ∙ 𝜕𝑆 𝜕𝑡 −1 = 1 𝑓′(𝑆) ∆𝜏𝑖 𝑘𝑖 • Water-cut travel time sensitivity: injector Producer [He et. al,2003] 𝜕𝑝 𝑏ℎ𝑝 𝜕𝑘𝑖 = 𝜕∆𝑝𝑖 𝜕𝑘𝑖 ≈ ∆𝑝𝑖 𝑘𝑖 • Bottom hole pressure sensitivity: [new] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 50 100 150 200 BottomHolePressure Time [Days] Production BHP 𝛿𝒑 𝑏ℎ𝑝 𝜕𝑝 𝑏ℎ𝑝 𝜕𝑘𝑖 ≈ 𝜏𝑖 𝜏 𝜕∆𝑝𝑖 𝜕𝑘𝑖 ≈ 𝜏𝑖 𝜏 ∆𝑝𝑖 𝑘𝑖 Rate-Rate constraint Rate-BHP constraint
  • 33. Sensitivity Results: 1D CPG (3phase Gas Injection) -20.0 -15.0 -10.0 -5.0 0.0 0.0 0.5 1.0 PressureSensitivity,wrtk Normalized Distance Analytical (Stremaline) Adjoint Method 0.0 5.0 10.0 15.0 20.0 0.0 0.5 1.0 PressureSensitivity,wrtk Normalized Distance Analytical (Stremaline) Adjoint Method 33/50 Inj: Gas Rate Prd: Rate Producer BHP sensitivity to k Injector BHP sensitivity to k
  • 34. Sensitivity Results: 2D Areal 34/50 Inj P1 P2P3 P4 Injector BHP sensitivity by k P1 BHP sensitivity of by k Permeability field (Wells by rate constraint) Adjoint Proposed
  • 35. Inversion of Permeability by LSQR 35/50 • Run simulation and get following parameter • Solve LSQR Matrix : • Advantages: • Find pressure/WCT sensitivity during SL simulation • Localized (high resolution) changes in permeability min 𝛿𝐝 𝑤𝑐𝑡 − 𝐒 𝑤𝑐𝑡 𝛿𝐤 + 𝛿𝐝 𝑏ℎ𝑝 − 𝐒 𝑏ℎ𝑝 𝛿𝐤 + 𝛽1 𝐈𝛿𝐤 + 𝛽2 𝐋𝛿𝐤 ෠𝐒 𝑤𝑐𝑡 ෠𝐒 𝑏ℎ𝑝 𝛽1 𝐈 𝛽2 𝐋 ∆𝐤 = 𝛿𝐝 𝑤𝑐𝑡 𝛿𝐝 𝑏ℎ𝑝 0 0 Water-Cut Pressure - Smoothness - Consistency with static model Scaled by stdev
  • 36. History Matching of Brugge Field • Use simulation result of Real.77 as observed data • Use Real.1 as initial model • Assume 3 years of data is available Reference model Initial model 36/50
  • 37. Available Observation Data 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 144.0 644.0 1144.0 ProductionWaterCut[-] Time [Days] BR-P-11 BR-P-12 BR-P-15 BR-P-18 BR-P-11 BR-P-12 BR-P-15 BR-P-18 • Only 4 producers have water breakthrough • Pressure data is available for 30 wells Water cut: Initial Observed 37/50
  • 38. Reference kx Initial kx Change of kx, WCT Change of kx, WCT&BHP High perm at middle layer Change of Permeability 38/50
  • 39. Reduction of Data Mismatch 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 20 40 60 80 100 NormalizedAbsoluteError.Pressure Number of Iteration 0.0 0.3 0.6 0.9 1.2 1.5 0 20 40 60 80 100 NormalizedAbsoluteError,WaterCut Number of Iteration Pressure RMSE error WCT RMSE error Individual well Mean 39/50
  • 40. • Have developed a new SL-based method to integrate pressure data into prior geologic models • Same advantages as prior streamline work: • Analytic calculation of streamline sensitivities • Requires only a single flow simulation per iteration • Can be applied to field pressure/rate data prior to water breakthrough • Can be integrate pressure with water-cut or GOR simultaneously, for black-oil and compositional simulation Conclusion 40/50
  • 41. Presented at student paper contest 2014 Application to Brugge Benchmark: - Streamline-Simulation - History Matching - NPV Optimization
  • 42. Overview 42/50 • Problem:  Determining optimal injection/production rates to maximize NPV • Solution:  Developed a new streamline and NPV-based rate allocation method • Advantages:  Visualize efficiency of injector and producer  Extensible to any secondary recovery process with commercial simulator
  • 43. - Improve oil production rate - Works only after breakthrough SL-based Flow Rate Allocation Optimization: Previous Study 43/50 • Use of Well Allocation Factors (WAFs):[Thiele et. al, 2003] Well Allocation Factor map [SPE84080] [SPE113628] - WAFs: 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
  • 44. Proposed Optimization Method: Overall Workflow 44/50 2. Trace Streamlines and Find connection map 3. Calculate NPV diagnostic plot 4. Reallocate well rate via efficiency 1. Run simulation model
  • 45. I1 I2 I3 I6 I5 I7 I8 NPV-based Efficiency of Streamline P1 P2 P3 P4 P5 P6 P7 Hydrocarbon value, along SL NPV along SL, integrate over reservoir life time 𝑣 𝑠𝑙 = 𝑞 𝑠𝑙 ෍ 𝑛𝑜𝑑𝑒 𝑆 𝑜 𝑏 𝑜 𝑅 𝑜 ∆𝜏 𝑟𝑠𝑙 = 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 and NPV along streamline Pore volume × Saturation × FVF × Price Discount rate Reservoir life I4 45/50
  • 46. NPV-based Flow Diagnostics I1 I2 I3 I6 I5 I7 I8 P1 P2 P3 P4 P5 P6 P7 𝑒 𝑝𝑎𝑖𝑟 = σ 𝑠𝑙 𝑟 𝑠𝑙 σ 𝑠𝑙 𝑣 𝑠𝑙 Total value NPV 5-connection from Inj-4 Total value (Normalized) NPV(Normalized) 𝑰 𝟒 𝐆𝐨𝐨𝐝 𝑷 𝟒 𝑰 𝟒 𝐏𝐨𝐨𝐫 𝑷 𝟕 NPV-based diagnostic plot I4 46/50
  • 47. NPV(Normalized) Streamline-based Rate Allocation: A New Approach 47/50 𝑞 𝑛𝑒𝑤 = 𝑞 𝑜𝑙𝑑 𝑒 𝑝𝑎𝑖𝑟 ҧ𝑒𝑓𝑖𝑒𝑙𝑑 ത𝐞 𝐟𝐢𝐞𝐥𝐝 decrease rate Increase rate Before update After update Total value (Normalized)
  • 48. NPV(Normalized) Total value (Normalized) Streamline-based Rate Allocation: A New Approach 48/50 𝑞 𝑛𝑒𝑤 = 𝑞 𝑜𝑙𝑑 𝑒 𝑝𝑎𝑖𝑟 ҧ𝑒𝑓𝑖𝑒𝑙𝑑 ത𝐞 𝐟𝐢𝐞𝐥𝐝 decrease rate Increase rate Before update After update • Advantages: • Dynamically visualize efficiency of the injector and producer • Able to propose ‘better’ well rate during SL-simulation
  • 49. 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 $/bbl Brugge Benchmark Application • Compare developed model with 3 approaches: • Uniform injection (Uniform), Well allocation factors (WAFs), Equalize Arrival Time (EqArrive), Developed model (SLNPV) 49/50
  • 50. 0.00 0.04 0.08 0.12 0.16 0.20 0 1200 2400 3600 4800 6000 7200 RecoveryFactor[-] Time [Days] SLNPV EqArrive WAFs Uniform 0.E+00 5.E+06 1.E+07 2.E+07 2.E+07 3.E+07 3.E+07 4.E+07 0 1200 2400 3600 4800 6000 7200 NetPresentValue[$] 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 50/50
  • 51. Streamlines by Sw SLNPVUniformInjection Streamlines by Injector Example of SLs: After 10 Years Not sweep aquifer region Sweep aquifer region Increased Inj-Prd connection 51/50
  • 52. MCERI • 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, with low computational cost Conclusions 54

Editor's Notes

  • #2: Allow me start presentation.
  • #3: This is the outline of this presentation and it has 3 main chapters: 1st, Development of a streamline simulator. Im going to show basic formulation and validation by 1D case Then, Im going to show the methodology to incorporate capillary ad gravity, with case study of 1D to 3D SPE10 model 3rd, Im going to show the data integration of pressure and water-cut and application on synthetic case, And the last, future work plan Last, Im going to show some demonstration on developed model.
  • #4: The objective of this study is as follows 1st, Develop a streamline-based simulator which can handle black oil and multi-component simulation 2nd , generally, streamline method has difficulties to incorporate capillary effect, but we present novel approach to incorpolate.. 3rd, Apply simulator for history-matching problem, focusing on not only water-cut but also pressure data integration.
  • #5: The objective of this study is as follows 1st, Develop a streamline-based simulator which can handle black oil and multi-component simulation 2nd , generally, streamline method has difficulties to incorporate capillary effect, but we present novel approach to incorpolate.. 3rd, Apply simulator for history-matching problem, focusing on not only water-cut but also pressure data integration.
  • #6: Allow me start presentation.
  • #7: Streamline based method has been used for simulation, history-matching or optimization, however, we often ignore diffusive flux especially capillary. The main reason is that because streamline is traced along total velocity and cannot take into account transverse flux caused by capillary and gravity. To take into account for this, the operator splitting method is used, however, it has some difficulties for the practical application, such as time-stepping restriction. For this study, we present an approach to take into account these effect by Orthogonal projection, and since this method take into account gravity and capillary along streamline, we might able to use same analogy for history matching and optimization problem.
  • #8: Orthogonal Projection. In orthogonal projection, we split equation by physical phenomena but this approach will split flux along streamline and transverse flux. The parallel component, which expressed by total fractional flow, including convection flow as well as capillary and gravity. Since we cannot consider every transverse flux along streamline, we split equation for transverse term calculated on grid.
  • #9: Let me start talking about operator splitting and its problem. The basic idea of operator splitting is that we split equation into several pieces, this is caused by numerical scheme that we take or coupling two softweare might end up with this situation. This paticular example, we have convection diffusion equation,…
  • #10: In order to prevent this problem, we have corrected operator splitting, which we have same equation in convection but give treatment to prevent diffusive flux as shown this equation. This is called anti-diffusive correction. The too much diffusive flux was caused by fractional flow following this green line, and we give anti-diffusive flux shown in red, will give you original fractional flow curve shown in blue. This approach will solve issues about overestimation of diffusive flux,however, the concave construction is computationally expensive and it is not feasible to use this for every grid, and time step.
  • #11: Orthogonal Projection. In orthogonal projection, we split equation by physical phenomena but this approach will split flux along streamline and transverse flux. The parallel component, which expressed by total fractional flow, including convection flow as well as capillary and gravity. Since we cannot consider every transverse flux along streamline, we split equation for transverse term calculated on grid.
  • #12: Orthogonal Projection. In orthogonal projection, we split equation by physical phenomena but this approach will split flux along streamline and transverse flux. The parallel component, which expressed by total fractional flow, including convection flow as well as capillary and gravity. Since we cannot consider every transverse flux along streamline, we split equation for transverse term calculated on grid.
  • #13: This slide shows the schematic flow of my simulator. Simulation is based on conventional IMPES-based streamline approach, solve pressure on, trace streamlines and solve 1D transport equations. The black character shows the standard streamline simulation approach, and red character shows the one I added for my research. we have a capillary effects in pressure equation, which Im not going to cover this presentation. Then, I calculate fluid transport on streamline. Here we have capillary and gravity effects, instead of using operator splitting technique. Then, reminder tem is also calculated but on grid. Let me talk about transverse flux and 1D equations.
  • #14: The approach is applied for Black oil system, and we observed that orthogonal projection is effective and we will have time stepping advantage, so we apply this for multi component system. Im not going into detail but we solve pressure by IMPES method, and transport equation is solved for total mole fraction shown as here. In terms of capillary and gravity, we solve parallel part along streamine and non-parallel part on grid.
  • #15: The study objectives becomes follows. Firstly I am going to develop new streamline simulator and apply ‘orthogonal projection method’ for transverse flux. The effect of capillary is also included in pressure equation. Then, I test my approach by comparing ECLIPSE, which will validate my solution I also compare the solution with conventional operator-splitting approach. It is well known that the operator splitting approach cannot take nonlinearity when the time-step is large.
  • #16: The study objectives becomes follows. Firstly I am going to develop new streamline simulator and apply ‘orthogonal projection method’ for transverse flux. The effect of capillary is also included in pressure equation. Then, I test my approach by comparing ECLIPSE, which will validate my solution I also compare the solution with conventional operator-splitting approach. It is well known that the operator splitting approach cannot take nonlinearity when the time-step is large.
  • #17: The study objectives becomes follows. Firstly I am going to develop new streamline simulator and apply ‘orthogonal projection method’ for transverse flux. The effect of capillary is also included in pressure equation. Then, I test my approach by comparing ECLIPSE, which will validate my solution I also compare the solution with conventional operator-splitting approach. It is well known that the operator splitting approach cannot take nonlinearity when the time-step is large.
  • #18: The study objectives becomes follows. Firstly I am going to develop new streamline simulator and apply ‘orthogonal projection method’ for transverse flux. The effect of capillary is also included in pressure equation. Then, I test my approach by comparing ECLIPSE, which will validate my solution I also compare the solution with conventional operator-splitting approach. It is well known that the operator splitting approach cannot take nonlinearity when the time-step is large.
  • #19: The result of cross-sectional model. Model has capillary and gravity effects.
  • #20: This is the results of water saturation distribution, x is normalized distance and y-axis shows water saturation.
  • #21: This is the results of water saturation distribution, x is normalized distance and y-axis shows water saturation.
  • #22: This is the results of water saturation distribution, x is normalized distance and y-axis shows water saturation.
  • #23: This is the results of water saturation distribution, x is normalized distance and y-axis shows water saturation.
  • #24: This is the results of water saturation distribution, x is normalized distance and y-axis shows water saturation.
  • #25: Outline is as follows. First, Secondly, Then, Last, …….
  • #26: Allow me start presentation.
  • #30: Allow me to start the presentation.
  • #31: Before start talking about study background, let me briefly overview the workflow of streamline-based history matching. This approach is deterministic method, so our target reservoir is water/gas flooded and objective of the history matching is to match production profile such as WCT,GOR. So, the first step is to run simulation on given model. 2ndstep, streamlines are traced by given flux field and calculate parameter sensitivity for production profile. There is to advantages here: One is computational efficiency. Sensitivity is calculated by single simulation run using streamline properties. 2nd , streamline trajectory will automatically confine the reservoir into connection pair. This will make minimization problem easier. 3rd step is to update reservoir parameters to minimize production error by solving equation shown here. Our objective function is single number, shifting time and thus dimension of this matrix is small. Thus, this calculation has very small computational cost. After updating reservoir parameter, we will continue this process until we get history match. This approach has lots of advantages, however, one and biggest disadvantages of this method is we will not think about pressure during history matching. If we want to match pressure, we need to add additional process inside this loop.
  • #32: Same behavior can be seen in production profile. We can match production concentration of CO2
  • #33: Let me briefly overview previous work that former student established. First, we have Time of flight sensitivity which describe relationship between time of flight and reservoir parameter by combining darcy’s law. For instance, permeability and time of flight has negative relationship. By combining this time of flight sensitivity and Buckley Levelette concept. We will have travel time sensitivity. For incompressible system, this is combined form of saturation speed and time of flight sensitivity. More general form is developed including solution gas. This equation can be used for miscible compressible flow problem.
  • #42: Allow me to start the presentation.
  • #43: The same behavior can be seen in production profile. We can match the production concentration of CO2
  • #44: 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.
  • #45: Let me start from motivation and objective of this study. Streamline method is used for flow simulation, optimization and history-matching, and the one of the advantage of the streamine simulation is visualization of the flow dynamics and its application. 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. 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.
  • #46: 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.
  • #48: 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.
  • #49: 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.