Bhark, E.W., Texas A&M MCERI, Norne Field reservoir model characterization workflow
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Norne Field E-Segment: Multiscale Parameterization and Streamline-Based Dynamic Data Integration for Production Optimization

Norne Field E-Segment: Multiscale Parameterization and Streamline-Based Dynamic Data Integration for Production Optimization

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Bhark, E.W., Texas A&M MCERI, Norne Field reservoir model characterization workflow Presentation Transcript

  • 1. Multiscale Parameterization and Streamline-Based Dynamic Data Integration for Production Optimization Norne Field E-Segment Eric Bhark Alvaro Rey Mohan Sharma Dr. Akhil Datta-GuptaMCERI: Model Calibration and Efficient Reservoir Imaging
  • 2. Approach to case study• Objective  Develop optimal production strategy (2005 to 2008)  Production and seismic data integration• Conceptual approach  Deterministic perspective  Single, history matched model (to 12/2003)  Global parameters defined • Faults and transmissibility multipliers • Saturation regions – Relative perm, capillary pressure • Large-scale permeability & porosity heterogeneity with multipliers  Data integration • Minimal calibration of prior MCERI 2/23
  • 3. Structured workflow Production data integration • Calibrate permeability heterogeneity to fluid rates (to 12/04) • Multiscale parameterization (global to local scales) Seismic data integration • Match (time lapse) changes in acoustic impedance by adjusting water front movement (Sw) • Streamline-based techniques Production optimization strategy • Optimize constrained well rates through forecast period • Objective of improving sweep efficiency (fluid arrival time equality along streamlines)MCERI 3/23
  • 4. Production data integration: Overview• Calibrate prior permeability model  Multiscale approach of global-to-local adjustment  Update at sensitive locations and scales• Production data  Three-phase rates • 12/1997 to 12/2004  Producers E-3H, E-3AH, E-2H• Heterogeneity parameterization  Reduce parameter dimension of high-resolution model  Address parameter correlation, insensitivity MCERI 4/23
  • 5. Parameterization • Grid-connectivity-based transform (GCT)  Parameterization by linear transformation  Characterize heterogeneity as weighted linear combination of basis vectorsReservoir property 1 2 3 4 10 15 = + + + …+ …+ w1 w2 w3 w4 w10 w15 Calibrated parameters • GCT basis vectors  Generalization of discrete Fourier basis vectors for generic grid geometries • Parameterization analogous to frequency-domain transformation • Modal shapes, harmonics of the grid MCERI  Bhark, E. W., B. Jafarpour, and A. Datta-Gupta (2011), A Generalized Grid-Connectivity-Based Parameterization for Subsurface Flow Model Calibration, Water Resour. Res., doi:10.1029/2010WR009982 5/23
  • 6. Calibration approach• Parameterize layers individually  Maintain prior vertical variability, stratification  Prevent vertical smoothing• For each layer (21 active of 22 total):  Define perm multiplier (1) field as calibrated field  Retain prior heterogeneity at full spatial detail Prior (ln md) Multiplier m  (  w i 1 i i ) m param.  n cells MCERI 6/23
  • 7. Calibration workflow• Adaptive refinement of multiplier fields (layers)  From coarse (global) to fine (local) scale  Successive addition of higher-frequency basis vectors Layer 1 multiplier Constant (zero frequency) basis vector  21 parameters total  zonation = w1 MCERI 7/23
  • 8. Calibration workflow• Adaptive refinement of multiplier fields (layers)  From coarse (global) to fine (local) scale  Successive addition of higher-frequency basis vectors Layer 1 multiplier + +… = w1 w2 w5 MCERI 7/23
  • 9. Calibration workflow• Adaptive refinement of multiplier fields (layers)  From coarse (global) to fine (local) scale  Successive addition of higher-frequency basis vectors Layer 1 multiplier + +… +… = w1 w2 w5 w10 • Between gradient-based minimization iterates (Quasi-Newton) – Gradient from one-sided perturbation of transform parameters • Based on data sensitivity (gradient contribution)  Cease (layer-by-layer) upon data insensitivity to addition of detail MCERI 7/23
  • 10. Calibration results (71 param)Calibrated multiplier fields:L2 L10 L20 L21 L22Permeability fields (Multiplier .* Prior):MCERI 8/23
  • 11. Production data misfit LowerWATERCUT OWC E-3H E-2H E-3AHOIL RATE E-3H E-2H E-3AH MCERI 9/23
  • 12. Structured workflow Seismic data integration • Match (time lapse) changes in acoustic impedance by adjusting water flood movement (Sw) • Streamline-based techniquesMCERI 10/23
  • 13. Seismic data integration: Overview• Seismic inversion of reflection data Difference of  Acoustic impedance at grid cell resolution averages: 2003 - 2001 • Dr. Gibson of Texas A&M Geophysics Dept. • 2001 – 2003 time lapse interval • Changes in Z (dynamic changes)• Calibration to seismic data  Sequential integration of acoustic impedance • Objective function weighting – Multiple sources seismic inversion uncertainty – Limitations in PEM  Gradient-based workflow • Calibrate inter-well permeability based on streamline-derived sensitivities – Grid cell resolution  local calibration MCERI 11/23
  • 14. Streamline-based workflow Water front evolution • Positive time-lapse Data misfit changes (Sw)1 Z  G seisk  1 k   2 Lk SL-based Z Z Sw Z Sg Z P sensitivities    k Sw k Sg k P k Sensitivity formulation Model (k) • Two-phase (water-oil) Update (LSQR) PEM PEM  Z • Consider only variation (Gassman) with saturation (Kf) Simulation ZPrior  Numerical differencingModel S w S w  Streamline-derived So Sw Sg k (analytical) MCERI 12/23
  • 15. Sensitivity formulation• Well rates  Cell saturations  Acoustic impedance  Cell permeability near streamlines traced from production wells• Trace streamlines from producers  Velocity field from finite-difference simulation• At each cell  Map Sw, k,  to intersecting streamline  Compute time of flight () per segment: outlet    inlet u drTransform to streamline coordinatesSw  Sw x, y, z, t   Sw  Sw  , t Define semi-analytical formulation for Sw at each cellS w Fw Sw 1      0   Sw   t MCERI  k t t  k 13/23
  • 16. Results: Seismic data integration  Increase in acoustic impedance • Replacement of oil by water  Decrease in acoustic impedance • Occurs in areas initially water-saturated  infer pressure effect Pre-calibrated Model Observed Calibrated ModelDifference:2003-2001 K = 5-9 K = 11 MCERI 14/23
  • 17. Production data misfit revisited  No degradation in match quality • Confirmation that (local, inter-well) permeability updates for seismic data integration are consistent with calibration from production data integrationWATERCUT E-3H E-2H E-3AH MCERI 15/23
  • 18. Structured workflow Production optimization strategy • Optimize constrained well rates through forecast period • Objective of improving sweep efficiency (front arrival time equality along streamlines)MCERI 16/23
  • 19. Optimal Production Strategy: Overview• Review reservoir flow pattern, connectivity• ‘Base Case’ strategy for rate optimization  From investigation of production enhancement opportunities• Optimal rate strategy Injector 1) Maximize sweep (RF) Producer • Equalizing fluid arrival time at producers (from injectors, aquifer) 2) Maximize NPV (indirectly) • Accelerating production i.e., minimize arrival time Injector MCERI 17/23
  • 20. Reservoir Flow Pattern Calibrated model: End of history at Dec. 2004Tracing from Producers AquiferTracing from Aquifer outside Injectors of E-segment MCERI 18/23
  • 21. Base Case Production StrategyProduction ConstraintsMax. Inj FBHP 450 Bar 1) Produce at last available ratesMin. Prod FBHP 150 Bar (Dec. 2004)Max. Water Inj Rate 12000 Sm3/dayMax. Liquid Prod Rate 6000 Sm3/day  RF = 47.8%Max. Water Cut 95 %Max. GOR 5000 Sm3/Sm3 2) E-3H sidetrack well in layer 10  Highest remaining oil pore volumeEconom ic Param etersDiscount Rate 10 %Oil Price 75 $/BBL 3) F-1H gas injectionGas Price 3 $/MscfWater Prod/Inj Cost 6 $/BBL  Higher NPV than water injectionGas Inj Cost 1.2 $/MscfSidetrack 65 MM$ – Lower injection/production costs Improvement pre-optimization:  RF = 48.5%  Increment of 0.7%  Incremental NPV increase: 872 MM$ MCERI 19/23
  • 22. Rate optimization workflow• Consider 6-month time intervals• Trace streamlines (using velocity field)  Compute fluid arrival time at producers  t q  t q N p ro d J q   2• Compute obj. fn. i i 1  Penalize water, gas production t i q  t i q  1  f w,i • Minimize obj. fn. using SQP t i q   Analytical sensitivities S ij  q j  Single forward simulation MCERI 20/23
  • 23. Rate optimization workflow• Consider 6-month time intervals• Trace streamlines (using velocity field)  Compute fluid arrival time at producers  t q  t q N prod J q   2• Compute obj. fn. i i 1  Penalize water, gas production t i q  t i q  1  f w,i • Minimize obj. fn. using SQP t i q   Analytical sensitivities S ij  q j  Single forward simulation• Progress to next time interval MCERI 21/23
  • 24. Production acceleration N prod N prod J q    t q   ti q 2    ti q2 i 1 i 1 55 500Recovery Factor (based on OIIP), % Recovery factor Incremental NPV 434 400 (over base case) Incremental NPV, MM $ (up 0.3%) 344 50 48.88 49.19 49.24 300 300 200 45 100 40 0 Norm Wt.-0 Norm Wt.-100 Norm Wt.-1000 Norm Wt.-0 Norm Wt.-100 Norm Wt.-1000 Case Case • Rate opt. improves recovery factors  Delays gas breakthrough (and shut-in) at E-2H and E-3H-sidetrack • Acceleration (  ) improves NPV  Disproportionate increase – pressure support from higher gas injection rate compensates for water injection (BHP upper limits reached) MCERI 22/23
  • 25. Summary• Production data integration  Global to local permeability calibration • Multiscale parameterization  Minimally update (pre-calibrated) prior model• (Sequential) Seismic data integration  Match change in acoustic impedance between 2001 and 2003  Calibrate cell permeability based-on streamlines traced from producers • Cell saturations through water front movement  Well-captured positive changes• Production schedule optimization  Established base scenario of E-3H-sidetrack (large remaining oil pore volume) and F-1H gas injection (lower costs)  Improved RF and NPV by equalization and reduction of fluid travel times MCERI 23/23
  • 26. Norne Comparative Study Eric Bhark Alvaro Rey Mohan Sharma Dr. Akhil Datta-GuptaMCERI: Model Calibration and Efficient Reservoir Imaging
  • 27. Backup slides: GCTMCERI 27/X
  • 28. Highlights of new basis  u1  1 u     2 v  2    v     Grid-connectivity-based transform basis =                        M     v M  (1) Model (or prior) independent u   N  Can benefit from prior model information (2) Applicable to any grid geometry (e.g., CPG, irregular unstructured, NNCs, faults) (3) Efficient construction for very large grids (4) Strong, generic compression performance (5) Geologic spatial continuity MCERI 28
  • 29. Basis developmentConcept: Develop as generalization of discrete Fourier basisKEY: Perform Fourier transform of function u by (scalar) projection on eigenvectors of grid Laplacian (2nd difference matrix) • Interior rows  Second difference  Periodic operator (circulant matrix) • Exterior rows  Boundary conditions control eigenvector behavior MCERI 29
  • 30. Basis development CPG Unstructured Grid Laplacian 5 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50 2-point connectivity (1/2/3-D)• Decompose L to construct basis functions (rows of )  Always symmetric, sparse  Efficient (partial) decomposition by restarted Lanczos method  Orthogonal basis functions; Φu  v  u  Φ1 v  ΦT v• In general (non-periodic) case  Eigen(Lanczos)vectors  vibrational modes of the model grid  Eigenvalues represent modal frequenciesMCERI 30
  • 31. Basis functions: Examples Corner-point Grid (Brugge) • Modal shape  modal frequency • Constant basis  Zero frequency • Discontinuities honoredBasis vec. 1 Basis vec. 2 Basis vec. 3 Basis vec. 4 Basis vec. 5 Basis vec. 9 MCERI 31
  • 32. Structured workflow(1) START: Prior model (2) Regional update (3) Local update Prior spatial hydraulic Parameterize property model Streamline-, multiplier field sensitivity-based inversion (GTTI) Update in transform domain Multiscale iterate Gradient-based iterate Back-transform Unit-multiplier field at multiplier field to grid cell resolution spatial domain Calibrated Model FINISH Flow and transport Add higher- simulation frequency modes to basis NO Data misfit tolerance? YES Additional YES spatial detail? NO MCERI 32
  • 33. Honoring prior by basis element selection Leading basis functions by modal frequency 3D CPG 1 2 3 4 5 6 7 8 9 Coefficient spectrum: scalar proj. of prior onto 500 leading basis functions coefficient Spectral Basis function by modal frequency Basis function by compression Leading basis functions by prior model compression performance 1 2 3 4 5 6 7 8 9 MCERI 33
  • 34. Pressure misfitMCERI 34/X
  • 35. E-3AH Pressure• There is an apparent constant shift  Simulated pressure is over-estimated• Potential Solutions  Add (negative skin), completion specific • Skin required to lower pressure 20+ bars (e.g., s = -10) results in high rate fluctuation as drawdown becomes too large  Add WPIMULT < 1.0 • Same result as for skin  Lower Pinit • Improves match, but lowered to 150 bars MCERI
  • 36. E-3AH Pressure• Early FMT match indicates that Pinit is consistent with prior model specs• This is despite isolation of EQLNUM 3 (see below) which would permit a very different pressure across the NOT formation MCERI
  • 37. Backup slides: SL-based AI integrationMCERI 37/X
  • 38. Seismic inversion• Selected components Difference of averages:  QC/filtering of sonic, density logs 2003 - 2001 • Well acoustic impedance – Conditioning data  Stochastic inversion (genetic algorithm) • Solve for acoustic impedance maps at 2001, 2003 • Average of 5 realizations  Compute change at grid cell resolution • Observation data for model calibration • Focus on dynamic changes • Reduce affect of static, poorly resolved parameters 3rd Layer 10th layer Bottom layer MCERI Gao, K. Acoustic impedance inversion using Petrel for the Norne Oil Field, Texas A&M Geophysics Dept. 12/24
  • 39. (Qualitative) Results Assessment of WOC in E-segment (Ile, Tofte) Change in Z (2001 – 2003) with Sw following production & seismic integration • Orthogonal intersection of seismic volume slice and grid slice • Increase in calibrated WOC more consistent with observed acoustic impedance Pre-calibration Calibrated Pre-calibration Calibrated Slice J = 45 Slice J = 49 Acoustic Saturation impedance Changes (Seismic volume) (Cellular Grid) MCERI 15/X
  • 40. Sensitivity formulation• Well rates  Cell saturations  Acoustic Impedance  Sensitivity (Z/k) computed along streamlines traced from producers • Trace through velocity field at grid cell resolution  Sensitivity matrix is sparse • non-zero components correspond to cells intersected by streamlines (localization) Transform to characteristic coordinates Sw  Sw x, y, z, t   Sw  Sw  , t  Define semi-analytical formulation for Sw Semi-analytical Sw  Sw  , t   Sw  Sw  / t  S w 1      Sw   I J k t  t  k MCERI 13/X
  • 41. Time-lapse sensitivity• Sw depends on front location & previous state of saturation τ  Sn  Sn  , Sn -1  w w w t • Perturbation in Sw 1 n Sn Sn w  S wτ  nw1 Sn -1 w t Sw- • Mapping of Sw b/w SL’s at different ‘steady-state’ intervals Sw Fw Sw • 2-phase incompressible + =0 • perturbations in properties do t Sw τ not affect streamline geometry 1 n Sn 1 n -1 Sn -1  Sn - M 1 0   Sn w  S wτ  nw1  S w τ  n - 2 w  w S wτ  t Sw  t -  Sw  Sw t  0   MCERI 41/X
  • 42. Seismic data integration Layer 10 Layer 20MCERI 42
  • 43. Sensitivity definition• Construct sparse sensitivity matrix  Gradient-based minimization (LSQR)• For each cell at which acoustic impedance measured  Compute sensitivity for all cells along intersecting streamline(s) Sw 1      Sw   k t t  k Nparam Active model cells x x x x  Cells within seismic cube x x x x x     x x x    x x x x   x x x x x     x x x x x  x x x x   Nobs  x x x x    x x  MCERI 14/X
  • 44. Prod. data misfitOil rateGas rate 44/X MCERI
  • 45. Backup slides: Production OptimizationMCERI 45/X
  • 46. Reservoir Flow PatternAquifer Aquifer MCERI  Based on calibrated model at end of history ( Dec-2004) 46
  • 47. Base CaseProduction ConstraintsMax. Inj FBHP 450 BarMin. Prod FBHP 150 Bar • E-3H sidetrack in layer 10Max. Water Inj Rate 12000 Sm3/dayMax. Liquid Prod Rate 6000 Sm3/day  Highest remianing oil pore volumeMax. Water Cut 95 % Sm3/Sm3 Max. GOR 5000 • F-1H gas injectionEconom ic Param eters  Shut-in of E-2H (Feb. 2008) and E-Discount Rate 10 % 3H-sidetrack (Feb. 2007)Oil Price 75 $/BBLGas Price 3 $/Mscf  Higher NPV than water injectionWater Prod/Inj Cost 6 $/BBL • Lower injection/production costsGas Inj Cost 1.2 $/MscfSidetrack 65 MM$ RF NPV Increm .Case Production Strategy (%) (MM $) (MM $) 1 Do Nothing: Production based on last available voidage rates 47.8 3998 - 2 Case 1 + Sidetrack + Water Injection: Recomplete E-3H in layer 10 horizontally 48.8 4438 440 3 Case 1 + Gas Injection: Inject gas through F-1H (at same voidage as w ater inj.) 48.0 4574 576 4 Case 1 + Sidetrack + Gas Injection 48.5 4870 872 Base case for optimization MCERI 20/24
  • 48. Enhancement scenarios tested• Sidetrack (300m)  E-3H in layers 1-3  E-3AH in layer 5, 6, 7, 8, 9, 10 • Currently in layers 1 and 2  F-3H in layer 2, 3 for injection to support E-3AH • Currently in layer 20• Conversion of F-3H into gas injector  Layer 20 MCERI 48/X
  • 49. Analytical sensitivity• Producer i, well (prod. or inj.) j  i  i j• When j is producer: S ij   q j   0 i j   Assume streamlines do not shift for perturbation in well rates • Travel time at i sensitive only to change in well rate at producer j = i  N fsl ,i , j   l 1   l ,i , j  N fsl  0• When j is injector: S ij   N q fsl j    0 N fsl  0   Nfls,i,j connect wells i and j• Requires only single forward simulation MCERI 49/X