1. Amit Suman and Tapan Mukerji
Joint Inversion of Production and Time-Lapse Seismic Data: Application to Norne Field
Amit Suman and Tapan Mukerji
SCRF Annual Meeting
8 - 9th May 2013
Stanford University
My dissertation focus on different aspects of join inversion with an application to the Norne field.

2. Joint Inversion Loop Predicted flow and seismic response
Generate
multiple
models
Evaluate
misfit .
Reservoir
Model
Observed flow and seismic response
Predicted flow and seismic response

3. Δ Pressure Δ Saturation Production data at time t
Research Motivation
Dynamic modeling
Δ Pressure Δ Saturation
Production data at time t
Rock physics modeling
Seismic data at time t=0
Seismic data at time t
Optimize mismatch
Update parameters

4. Problem
Uncertainties attached with parameters present in the dynamic and seismic simulator: ignoring them can give misleading results in history matching
Joint inversion of both data sets are complex and computationally expensive: sensitive parameters should be identified to reduce the computational cost in the large history matching process

5. Approach
Develop a systematic workflow for joint inversion that not only update porosity or permeability model but all sensitive parameters and such that it can be applied to a real field
Generation of a set of history matched models

6. Research Overview
Focus on developing a systematic workflow for joint inversion
Sensitivity study for join inversion of production and time-lapse seismic data (2011)
Sensitivity study of rock physics parameters for time lapse seismic modeling (2012)
Application of the workflow on Segment-E of Norne field situated in the Norwegian Sea

7. Segment-E of Norne Field
Southern part of Norwegian sea
Five prime zones
Garn
Not
Ile
Tofte
Tilje
3 producers and 2 injectors in the Segment-E
Gas
Oil and water

8. Data Available Well logs Horizons Well data 3D Seismic data (2001,2003
Oil, gas and water flow rate
Bottom hole pressure (BHP)
3D Seismic data (2001,2003
2004,2006)

9. Sensitivity Parameters in Joint Inversion
Pore Compressibility
1.5X10-10 (Pa-1)
3X10-10 (Pa-1)
5X10-10 (Pa-1)
Relative permeability
Curve 1
Curve 2
Rock physics models
Cemented
Uncemented
Fluid mixing
Uniform
Patchy
Porosity
Model 1
Model 2
Model 3
Total number of cases = 3 X 3 X 2 X 2 X 2 = 72

10. Sensitivity of 4D Seismic
Median of normalized P-wave impedance change in Layer 10
Rock physics model
Relative permeability
Fluid mixing
Porosity model
Pore compressibility

11. Sensitivity of 4D Seismic

12. Sensitivity of Production
Relative permeability
Porosity model
Pore compressibility
Median cumulative oil production

13. Sensitivity of Production

14. Sensitivity Parameters in Modeling 4D Response
Clay content
Gas-oil ratio (GOR)
Coordination number
Cement fraction
Effective pressure model
Fluid mixing (Uniform or Patchy)
The sensitivity of varying above parameters to variations in Response
Response: L1 Norm of change in seismic P-wave impedance after 4 years

15. Results Median of normalized P-wave impedance change in Layer 5
Coordination number
Fluid mixing
Clay content
Effective pressure model
Cement fraction

16. Results Response Sensitivity to clay content20 40 5 7 9
175
200
225 1 3
Model 1
Model 2
Uniform
Patchy
Response
Sensitivity to clay content
Sensitivity to coordination number
Sensitivity to GOR
Sensitivity to cement
Sensitivity to effective pressure model
Sensitivity to fluid mixing

17. Sensitive Parameters Based on previous studies Relative permeability
Porosity model
Coordination number
Clay content
Fluid mixing
Pore compressibility

18. Particle Swarm Optimization (PSO)
Successfully used in other braches of engineering
Use in geosciences still remains restrained
Three tuning parameters
Inertia, local acceleration and global acceleration

19. PSO Analysis and Design
PSO belongs to a family
GPSO (General PSO)
CC-PSO (Centered-centered PSO)
CP-PSO (Centered-progressive PSO)
PP-PSO (Progressive-progressive PSO)
RR-PSO (Regressive-regressive PSO)
(Fernández et al., 2010)

20. Application to Synthetic Case
(Δ AI)normalized
50 X 50 = 2500 cells
Observed time-lapse seismic data
Reference porosity
Observed production data
Objective: Jointly invert production and time-lapse seismic data to obtain porosity model using different particle swarm optimizers

21. Dimensionality Reduction
Reconstruction
Using 50 PCA coefficients

22. Methodology

23. Swarm size = 20 No. of iterations = 100
Results
Swarm size = No. of iterations = 100
Production
Seismic
Total
RR-PSO, PP-PSO and CP-PSO achieved lower seismic, production and total misfit as compared to CC-PSO and GPSO
RR-PSO has achieved lowest seismic, production and total misfit among all of particle swarm optimizers
RR-PSO has the highest convergence rate among all of particle swarm optimizers

24. Results CC-PSO CP-PSO GPSO PP-PSO RR-PSO Initial Best
Reference porosity

25. Results
CC-PSO
CP-PSO
GPSO
PP-PSO
RR-PSO

26. Results Initial Best Initial Best CC-PSO CP-PSO (Δ AI)normalized
observed
GPSO
PP-PSO
RR-PSO

27. Model Sampling To obtain a set of history matched models tolerance MDS
PP-PSO
(Δ AI)normalized
observed
Reference porosity

28. Oil, Water and Gas rates and BHP in wells E-2H, E-3H and E-3AH
Production data
E-2H
E-3H
E-3AH
Oil, Water and Gas rates and BHP in wells E-2H, E-3H and E-3AH

29. Time-Lapse Seismic Data
∆ (𝐴𝐼) 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 = 𝐴𝐼 2004 − 𝐴𝐼 𝐴𝐼 2001
Acoustic impedance in 2001
Impedance inversion and depth conversion using Hampson-Russell
Seismic in 2001
Used for joint inversion
Acoustic impedance in 2004
Seismic in 2004
Increase in impedance due to change in the fluid saturation (water replacing oil)

30. Methodology
𝑂= 𝑖=1 𝑁 𝑃 𝑜𝑖𝑙 𝑜𝑏𝑠 − 𝑃 𝑜𝑖𝑙 𝑠𝑖𝑚 𝑃 𝑜𝑖𝑙 𝑜𝑏𝑠 𝑃 𝑤𝑎𝑡𝑒𝑟 𝑜𝑏𝑠 − 𝑃 𝑤𝑎𝑡𝑒𝑟 𝑠𝑖𝑚 𝑃 𝑤𝑎𝑡𝑒𝑟 𝑜𝑏𝑠 𝑃 𝑔𝑎𝑠 𝑜𝑏𝑠 − 𝑃 𝑔𝑎𝑠 𝑠𝑖𝑚 𝑃 𝑔𝑎𝑠 𝑜𝑏𝑠 𝑊 𝑏ℎ𝑝 𝑜𝑏𝑠 − 𝑊 𝑏ℎ𝑝 𝑠𝑖𝑚 𝑊 𝑏ℎ𝑝 𝑜𝑏𝑠 (∆AI) 𝑛𝑜𝑟𝑚 𝑜𝑏𝑠 − (∆AI) 𝑛𝑜𝑟𝑚 𝑠𝑖𝑚 (∆AI) 𝑛𝑜𝑟𝑚 𝑜𝑏𝑠 2 2

31. Total 75 parameters for optimization
Parameters Variations
Relative permeability – One
Coordination number – One
Porosity models – 70 PCA coefficients
Clay content – One
Fluid mixing – One
Pore compressibility – One
Total 75 parameters for optimization

32. Swarm size = 20 No. of iterations = 50
Results
Swarm size = No. of iterations = 50
RR-PSO, PP-PSO and CP-PSO achieved lower total misfit as compared to CC-PSO and GPSO
RR-PSO has achieved lowest seismic, production and total misfit among all of particle swarm optimizers
RR-PSO has the highest convergence rate among all of particle swarm optimizers

33. Results: Production Match (E-3H)
CC-PSO
CP-PSO
GPSO
PP-PSO
RR-PSO
All of the optimizers provided a satisfactory match of production data in well E-3H

34. Results: Production Match (E-2H)
CC-PSO
CP-PSO
GPSO
PP-PSO
RR-PSO
All of the optimizers provided a satisfactory match of production data in well E-2H

35. Results: Production Match (E-3AH)
CC-PSO
CP-PSO
GPSO
PP-PSO
RR-PSO
All of the optimizers provided unsatisfactory match of water and oil rates
CP, PP and RR-PSO have provided satisfactory match of gas production rates

36. Results: 4D Seismic Match
Initial guess
Best match
CC-PSO
CP-PSO
Improvement in the match from initial guess to best match
GPSO
PP-PSO
RR-PSO

37. Results

38. Model Sampling
tolerance
RR-PSO

39. Summary
A family of PSO have been applied successfully for join inversion of production and 4D data of the Norne field
RR-PSO has performed best among all particle swarm optimizers
Mismatch of production data in the well E-3AH still needs to be further investigated
A satisfactory history match of 4D data is achieved in some layers but mismatch in matching the whole pattern is still needs to be investigated

40. Contributions
A systematic and practical workflow for join inversion that can be and has been applied to a real field
Sensitivity study for joint inversion of production and 4D seismic data
Sensitivity study of rock physics parameters in modeling the 4D seismic response
joint inversion using a family of particle swarm optimizers, comparison of their behavior in terms of history match and convergence

41. Acknowledgements
SCRF
NTNU and Statoil for providing Norne data set