Renewable energies | Eco-friendly production | Innovative transport | Eco-efficient processes | Sustainable resources Multi-fidelity meta-models for reservoir engineering March 23, 2016 – MASCOT-NUM Véronique Gervais (IFPEN) Mickaële Le Ravalec (IFPEN) Arthur Thenon IFP Energies nouvelles (IFPEN)

© IFP Energies nouvelles Reservoir characterization Introduction - Reservoir engineering context A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 2 Geological data Seismic data Core sample data Production data Log data Reservoir model

© IFP Energies nouvelles Introduction - Reservoir engineering context Goals of reservoir engineering  Assessment of field production potential  Management of the field development Tools 3D numerical models Flow simulator Main issues Size of reservoir models Building representative models A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse Simulated production data Reservoir model Flow simulation  time consuming flow simulations  lots of uncertainties 3

© IFP Energies nouvelles Introduction - Reservoir engineering context To handle / reduce uncertainties Identify the most influent uncertain parameters Probabilistic forecasting Incorporate all available data (dynamic data)  History-matching process A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse Simulated production data Optimization Reservoir model Measured production data Flow simulation Objective function 4

© IFP Energies nouvelles Introduction - Reservoir engineering context To handle / reduce uncertainties Identify the most influent uncertain parameters Probabilistic forecasting Incorporate all available data (dynamic data)  History-matching process Dealing with uncertainties and optimizing field production call for a huge number of flow simulations  Prohibitive computation time Solutions Using reservoir models with coarser grids  Approximate responses Using meta-models (polynomial, kriging, etc…)  Still requires a lot of simulations to be predictive A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse Good context to use multi-fidelity meta-models 5

© IFP Energies nouvelles Introduction - Multi-fidelity meta-models A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 6

© IFP Energies nouvelles Outline Introduction Numerical experiment Vectorial output modeling Sequential design strategy Conclusion and future work A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 7

© IFP Energies nouvelles Outline Introduction Numerical experiment PUNQ test case description Numerical experiment description Results Discussion Vectorial output modeling Sequential design strategy Conclusion and future work A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 8

© IFP Energies nouvelles Numerical experiment – PUNQ description The case is inspired from PUNQ S3 [Floris et al., 2001] 6 production wells (PRO-1, 4, 5, 11, 12 and 15) Produced by depletion Two reservoir models with different grid resolutions Coarse model: 19*28*5 grid blocks (average simulation time: 10s) Fine model: 57*84*5 grid blocks (average simulation time: 180s) A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse PUNQ S3 top and well positions Porosity in layer 3 for the coarse and fine PUNQ models

© IFP Energies nouvelles Numerical experiment - Description A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 10

© IFP Energies nouvelles Numerical experiment - Results A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 11

© IFP Energies nouvelles Numerical experiment - Results A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse The Q2 coefficient is computed for an independent test sample (LHS of 200 points). 12

© IFP Energies nouvelles Multi-fidelity meta-models show poor performance when approximating the OF.  Poor correlation between OF values for fine and coarse levels Similar behaviors do not imply a good correlation between the OF contributions. Numerical experiment - Discussion A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 13

© IFP Energies nouvelles Outline Introduction Numerical experiment Vectorial output modeling Methods Results Discussion Sequential design strategy Conclusion and future work A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 14

© IFP Energies nouvelles Existing method from [Douarche et al., 2014] [Marrel et al., 2015] Apply a Proper Orthogonal Decomposition on a set of responses Compute meta-models to approximate the coefficients of the reduced basis (scores) In multi-fidelity, we propose to compute coarse level scores by projecting the coarse level responses on the fine level reduced basis. Vectorial output modeling - Methods A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse Set of responses Apply PODGet the scores Design of experiment (LHS) Build kriging models Set of fine level responses Apply POD Get the fine level scores Design of experiment (nested LHS) Build co-kriging models Set of coarse level responses Projection on the fine reduced basis Get the coarse level scores 15

© IFP Energies nouvelles Vectorial output modeling - Results A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse Using this approach we approximate the OF by modeling each output involved in its definition (OF through output modeling). 16

© IFP Energies nouvelles Example: GOR at well 1 Example: BHP at well 4 Vectorial output modeling - Discussion A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 17

© IFP Energies nouvelles Example: BHP at well 4 Vectorial output modeling - Discussion A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 18

© IFP Energies nouvelles Outline Introduction Numerical experiment Vectorial output modeling Sequential design strategy Introduction Algorithms Results Conclusion and future work A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 19

© IFP Energies nouvelles How to choose the point location and the level of fidelity to be evaluated to build better multi-fidelity meta-models of the objective function? Sequential design strategy - Introduction A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 20

© IFP Energies nouvelles Sequential design strategy - Introduction A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 21

© IFP Energies nouvelles In simple fidelity context Sequential design strategy - Algorithms Initial design of experiment (small size LHS) Meta-model of the OF (output modeling) Compute the CVE on the OF Sampling of points in the Voronoï cell with the highest CVE Selection of the point maximizing the OF variance Stopping criterion Final meta-model of the OF Flow simulation 21 Stopping criterion Sufficient predictivity or end of time budget A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 22

© IFP Energies nouvelles In multi-fidelity context Sequential design strategy - Algorithms Initial design of experiment (small size nested LHS) Meta-model of the OF (output modeling) Compute the CVE on the OF Sampling of points in the Voronoï cell with the highest CVE Selection of the point maximizing the OF variance Stopping criterion Final meta-model of the OF Flow simulation Compute the CVE on the OF Sampling of points in the Voronoï cell with the highest CVE Selection of the point maximizing the OF variance Stopping criterion Fine level Coarse level Stopping criterion Sufficient predictivity Stopping criterion Sufficient predictivity or end of time budget A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 23

© IFP Energies nouvelles Sequential design strategy - Results A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 24 Coarse level evaluations Both levels evaluations

© IFP Energies nouvelles Sequential design strategy - Discussion A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 25

© IFP Energies nouvelles Outline Introduction Numerical experiment Vectorial output modeling Sequential design strategy Conclusion and future work A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 26

© IFP Energies nouvelles Conclusion The use of multi-fidelity co-kriging meta-models in reservoir engineering can save computation time, especially if the time budget is very limited. Suitable methodologies must be deployed. Efficiency depends on the correlation between the fidelity levels and the time ratio. Future work Application to a more complex test case (Brugge Field) Improvement of the proposed sequential strategy Sequential strategies for optimization Conclusion and future work A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 27

© IFP Energies nouvelles Kennedy, M., and O’Hagan, A. (2000). Predicting the output from a complex computer code when fast approximations are available. Biometrika 87, 1–13. Le Gratiet, L. (2012). MuFiKriging: Multi-fidelity co-kriging models. R package version 1.0. Floris, F.J.T., Bush, M.D., Cuypers, M., Roggero, F., and Syversveen, A.-R. (2001). Methods for quantifying the uncertainty of production forecasts: a comparative study. Petroleum Geoscience 7, S87–S96. Douarche, F., Da Veiga, S., Feraille, M., Enchéry, G., Touzani, S., and Barsalou, R. (2014). Sensitivity Analysis and Optimization of Surfactant-Polymer Flooding under Uncertainties. Oil & Gas Science and Technology – Revue d’IFP Energies Nouvelles, 69(4), Marrel, A., Perot, N., Mottet, C. (2015). Development of a surrogate model and sensitivity analysis for spatio-temporal numerical simulators. Stoch Environ Res Risk Asses, 29, Le Gratiet, L., & Cannamela, C. (2015). Cokriging-Based Sequential Design Strategies Using Fast Cross-Validation Techniques for Multi-Fidelity Computer Codes. Technometrics, 57(3), 418–427. References A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 28

© IFP Energies nouvelles A. Thenon - Multi-fidelity meta-models for reservoir engineering - MASCOT-NUM - March 23, Toulouse 29