1. History matching reservoir models using the EnKF/EnKS Geir Evensen

2. Date: 2004-01-16 Page: 2 Hydro: Aluminium and energy supplier Founded 1905 36 000 employees in 40 countries Leading offshore oil producer Worlds third largest aluminium supplyer Pioneer in renewable energy and energy efficient solutions

3. Date: 2004-01-16 Page: 3 Hydro Research Centre, Bergen Programs Improved Exploration 60% Recovery Small FieldsPolar Regions Climate & Renewable energy

4. Date: 2004-01-16 Page: 4 Extend lifetime of mature fields mm cm m km Program: 60% Recovery Projects: Seismic mapping Reservoir geophysics IOR Oseberg seismics Reservoir characterization Methods for tertiary recovery Well and intervention technology Unstable flow

5. Date: 2004-01-16 Page: 5 Introduction Simulation model must be consistent with the reservoir production history to be used for predicting future production. History matching = Tuning of model parameters or parameter estimation. For history mathcing we must: Define the parameter space (porosity, permeability, reservoir structure, transmissibilities,….). Define a cost fuction (prior statistical weights, norm, etc.). Chose a minimization method (gradient descent, Monte Carlo, EnKF).

6. Date: 2004-01-16 Page: 6 Minimization problem Highly nonlinear, multiple local minima. Hard to solve using traditional minimization methods. Data errors independent in time and model a Markov sequence: Reformulation as a sequence of minimization problems. Each subproblem provides a prior for the next problem. Equivalent to solving the full problem in one go for linear models. Evensen 2005 (www.nersc.no/~geir)www.nersc.no/~geir Approach used by the EnKF/EnKS.

7. Date: 2004-01-16 Page: 7 Time Updates Update procedure in EnKS/EnKF d_1 Prediction EnKF update EnKS update d_2d_3

8. Date: 2004-01-16 Page: 8 Nonlinear minimization problem

9. Date: 2004-01-16 Page: 9 Ensemble Kalman Filter (EnKF) Statistical method which solves the combined state and parameter estimation problem. Monte Carlo version of the original Kalman Filter. EnKF home page: http://www.nersc.no/~geir/EnKF The EnKF is now used for ocean and weather prediction TOPAZ system: http://topaz.nersc.no Meteorological Service of Canada Potential for history matching and reservoir management?

10. Date: 2004-01-16 Page: 10 Ensemble Kalman Filter (EnKF) Representation of uncertainty using an ensemble of model solutions and randomized measurements: Describes error covariances for the model estimate and measurements. Uncertainty predictions by ensemble integration: Each ensemble member is integrated using a stochastic version of the dynamical model. Includes the impact of model errors. Model ensemble is updated from measurements using a variance minimizing analysis scheme: Assumption about Gaussian error statistics for prediction.

11. Date: 2004-01-16 Page: 11 Time True state Initial state with errors Measurements with errors

12. Date: 2004-01-16 Page: 12 Time Model prediction with errors Measurements with errors True state

13. Date: 2004-01-16 Page: 13 Time Updated estimate with errors Measurements with errors True state Model prediction with errors

14. Date: 2004-01-16 Page: 14 Time New model prediction with errors Measurements with errors True state Updated estimate with errors

15. Date: 2004-01-16 Page: 15 Time Measurements with errors True state Updated estimate with errors

16. Date: 2004-01-16 Page: 16 EnKF-Eclipse Implementation at Hydro Suite of F90 programs controlled by unix script Modular and model independent implementation. Based on generic EnKF distribution from http://www.nersc.no/~geir/EnKF/ Simulation software for generation of the initial ensemble. Simulation of realizations based on statistical geomodel. Conditioning on log and AI data. Eclipse simulator is used as a “black box”: Only used to integrate model states forward in time. interface between ECLIPSE and the EnKF: Convert between ECLIPSE restart files and ensemble files. Differentiate between dynamic and static variables. EnKF analysis program.

17. Date: 2004-01-16 Page: 17 EnKF-Eclipse Implementation: Initialization of ensemble Statistical geomodel iniens Poro/perm ensemble Eclipse data file eclipse Grid and restart info ens0F.uf ens0S.uf ens0A.uf ens0S.uf EnKF logobs.uf

18. Date: 2004-01-16 Page: 18 EnKF-Eclipse Implementation Ensemble integration and update For j=0, data_times ens{j}A.uf ens{j}S.uf For i=1,nrens interface Eclipse restart file eclipse Eclipse restart file interface ens{j+1}F.uf ens{j+1}S.uf done ens{j+1}F.uf obs{j+1}.uf EnKF ens{j+1}A.uf done

19. Date: 2004-01-16 Page: 19 Estimation of permeability using EnKF ReferenceFirst guessEstimate 25 months Major structure of permeability field is recovered!

20. Date: 2004-01-16 Page: 20 Estimation of permeability using EnKF Information from data accumulates in time. Result is consistent with statistical input model. Definition of initial statistical model is crucial. Cross section distance Permeability Results from idealized experiments are very promising!

21. Date: 2004-01-16 Page: 21 Some previous EnKF reservoir applications Nævdal, Mannseth and Vefring (2003), Near well reservoir monitoring through EnKF, (SPE 75235). Nævdal, Johnsen, Aanonsen and Vefring (2003), Reservoir monitoring and continuous model updating using EnKF, (SPE 84372). Gu and Oliver (2004), History matching of the PUNQ-S3 reservoir model using the EnKF, (SPE 89942). Gao, Zafari and Reynolds (2003), Quantifying uncertainty for the PUNQ- S3 problem in a Bayesian setting with RML and EnKF, (SPE 93324). Liu and Oliver (2005), Critical evaluation of the EnKF on history matching of geological facies, (SPE 92867). Wen and Chen (2005), Real-time reservoir model updating using EnKF, (SPE 92991). All conclude positively regarding the use of EnKF for history matching. All consider idealized experiments.

22. Date: 2004-01-16 Page: 22 EnKF-Eclipse for Oseberg Alpha North Complex reservoir. 5 producers. 3 injectors. Simulation model hard to match. Uncertainty about faults, barriers, channels, and communication with other reservoirs.

23. Date: 2004-01-16 Page: 23

24. Date: 2004-01-16 Page: 24 Some preliminary remarks Good match for GOR at wells started early in simulation. Easy to fit unconstrained model to the first production data. Poor match for wells started late in simulation. Too large weight on early production data? Neglected model errors? Typical parameterization problem? Possible to include faults, structural errors, transmissibilities? Uncertainty in production data. 10-20% or more? QC of production data crucial.

25. Date: 2004-01-16 Page: 25 Summary Ongoing field case with new Oseberg alpha north model: Includes pluri-gaussian facies representation. Assimilates production and 4D seismic data. Ongoing field case for Rimfaks: Collaboration with Statoil.