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

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-Gupta
MCERI: 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 vectors
Reservoir 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 L22
Permeability fields (Multiplier .* Prior):
MCERI 8/23

11. Production data misfit Lower
WATERCUT
OWC
E-3H E-2H E-3AH
OIL 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 techniques
MCERI 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 Z
Prior  Numerical differencing
Model 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
dr
Transform to streamline coordinates
Sw  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 Model
Difference:
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 integration
WATERCUT
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. 2004
Tracing from
Producers
Aquifer
Tracing from
Aquifer outside
Injectors
of E-segment
MCERI 18/23

21. Base Case Production Strategy
Production Constraints
Max. Inj FBHP 450 Bar
1) Produce at last available rates
Min. Prod FBHP 150 Bar (Dec. 2004)
Max. Water Inj Rate 12000 Sm3/day
Max. 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 volume
Econom ic Param eters
Discount Rate 10 %
Oil Price 75 $/BBL 3) F-1H gas injection
Gas Price 3 $/Mscf
Water Prod/Inj Cost 6 $/BBL  Higher NPV than water injection
Gas Inj Cost 1.2 $/Mscf
Sidetrack 65 MM$ – 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
55 500
Recovery 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-Gupta
MCERI: Model Calibration and Efficient Reservoir Imaging

27. Backup slides: GCT
MCERI 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 development
Concept: Develop as generalization of discrete Fourier basis
KEY: 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 frequencies
MCERI 30

31. Basis functions: Examples
Corner-point Grid
(Brugge) • Modal shape  modal frequency
• Constant basis
 Zero frequency
• Discontinuities honored
Basis 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 misfit
MCERI 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 integration
MCERI 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 20
MCERI 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 misfit
Oil rate
Gas rate
44/X
MCERI

45. Backup slides:
Production Optimization
MCERI 45/X

46. Reservoir Flow Pattern
Aquifer
Aquifer
MCERI

Based on calibrated model at end of history ( Dec-2004)
46

47. Base Case
Production Constraints
Max. Inj FBHP 450 Bar
Min. Prod FBHP 150 Bar
• E-3H sidetrack in layer 10
Max. Water Inj Rate 12000 Sm3/day
Max. Liquid Prod Rate 6000 Sm3/day  Highest remianing oil pore volume
Max. Water Cut 95 %
Sm3/Sm3
Max. GOR 5000
• F-1H gas injection
Econom ic Param eters  Shut-in of E-2H (Feb. 2008) and E-
Discount Rate 10 % 3H-sidetrack (Feb. 2007)
Oil Price 75 $/BBL
Gas Price 3 $/Mscf  Higher NPV than water injection
Water Prod/Inj Cost 6 $/BBL • Lower injection/production costs
Gas Inj Cost 1.2 $/Mscf
Sidetrack 65 MM$
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