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.

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

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

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

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

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

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

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)

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

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

Sensitivity of 4D Seismic

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

Sensitivity of Production

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

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

Results Response Sensitivity to clay content 20 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

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

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

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)

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

Dimensionality Reduction Reconstruction Using 50 PCA coefficients

Methodology

Swarm size = 20 No. of iterations = 100 Results Swarm size = 20 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

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

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

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

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

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

Time-Lapse Seismic Data ∆ (𝐴𝐼) 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 = 𝐴𝐼 2004 − 𝐴𝐼 2001 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)

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

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

Swarm size = 20 No. of iterations = 50 Results Swarm size = 20 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

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

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

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

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

Results

Model Sampling tolerance RR-PSO

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

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

Acknowledgements SCRF NTNU and Statoil for providing Norne data set