1. ArcEOR A posteriori error estimate tools to enhance the performance of
the reservoir simulator
ArcEOR
J-M. Gratien, O. Ricois, S. Yousef
Sim-Race 2015, IFPEN December 1Oth 2015

2. Outline Introduction : EOR process overview
ArcEOR : a new general purpose simulator
Aposteriori Error Estimation
Adaptative linear solver stop criteria
Space error criteria for Adaptive MeshRefinement/Coarsening
Results
Perspective
Sim-Race 2015, IFPEN – Aposteriori error estimators in ArcEOR December 10th, 2015

3. EOR : Enhanced Oil Recovery process

4. Various Process type Primary recovery process:
Water injection
Secondary recovery process :
Improve oil recovery rate :
Gas injection
Chemical injection
Polymer, Alkaline, Surfactant chemical products
Thermal process
Heat, vapour injection

5. Various thermal EOR process
Steam Drive process
Huff’n Puff process
Steam Assisted Gravity Drainage
Toe To Heel Air Injection
Réunion Estimateurs à postériori - Arc EOR Janvier 2013

6. ArcEOR : a new general purpose Reservoir simulator
Design the next generation Parallel Reservoir Simulator for various Enhanced Oil Recovery processes.
Efficient even on full field models
Advanced thermodynamics models
Coupled with geodynamics models
Innovative simulator based on the technologies developped in the OpenFlow™ and ArcGeoSim™ projects.
Advanced linear solvers (Multi-Cores, GP-GPU,…)
Advanced mesh functionnalities :
load balancing,
AMR, AMC (Adaptative mesh refinement/coarsening)
OpenFlow environnement ( IHM, Data bases, workflow,…)
Réunion Estimateurs à postériori - Arc EOR Janvier 2013

7. ArcEOR :Various physical models
Fluid system models :
Various PVT models :
Black Oil (Di/Tri phasic model)
SteamBlackOil model (BO + water steam)
Compositional model (EOS + tabulated ki model)
Thermal Compositional model (Heat + Compositional model)
Tri Phasic KrPc model
Tabulated relative permeability curves
Tabulated Capilarity curves
Rock model
Thermal conductivity, compressibility,…
Facies and model zone management

8. Various numerical models
Numerical schemes
Two points, MPFA schemes for VF discretisation
Non linear model solved with an Interative Newton solver
Full implicit time discretisation scheme
Non linear and linear solvers
Iterative Newton Solver
Various linear solvers via ALIEN
MPI (PETSC,PMTL4,HYPRE,IFPSolver,…)
Multi-core (HARTS+MCGSolver)
GP-GPU (MCGSolver)

9. Performance issues
Thermal models are complexe
Complexe nonlinear physical models : (Flash, EOS,…)
Complexe time step management
Space and time scale problems
Performance is a key issue for full field simulation
Linear solver : up to 80% of computation time
AMR : Adaptive Mesh Refinement
AMC : Adaptative Mesh Coarsening
Adapt cells size to the need of precision
Reduce the number of unknowns for a given precision
Take into account geological data at the fine level
Compute at a coarse level if possible

10. Error Estimators

12. Aposteriori Error Estimators
Theorical implementation
Theorical aposteriori estimator can be expensive to compute
Based on RT basis function with DOF on nodes
Need interpolation between cell unknowns to node unknowns
Pratical implementation
Simplification link to the simulator numerical scheme
Based on the real discrete flux computation and flux reconstruction algorithms
More efficient algorithms

13. Application of aposteriori error estimators
Improve the performance of non linear solver;
Adaptative linear solver stop criteria :
Improve the performance of the simulator with the Adapatative Mesh Refinement/Coarsening feature:
Adapt the number of grid blocks for a given space error;

14. Adaptative linear solver stop criteria
Objectives:
Improve the performance of non linear solver;
Adaptative linear solver stop criteria :
Better estimation of linear error regarding time, space and non linear errors;
Reduce the cumulative number of steps of iterative linear solvers;
Optimisation of the Newton based Iterative Non Linear Solver.

15. Adaptive Mesh Refinement/Coarsening
Objective :
For a given precision, manage the number of unknowns adapting the mesh size
For a given number of unknowns, balance error over the all mesh
Source of errors
Sharp front, non linearities,…
Tools :
Various error estimators :
Gradient Estimators
Aposteriori Error Estimator
Interpolator, Upscaling operators

16. Interpolator, Upscaling Operator

17. Particle, Upscaling and Interpolator
Particles level
Geological data
Fine level
Medium level
Coarse level

18. Example SAGD study case
DeadOil Model
Cartesian mesh 4218 cells
Pair of horizontal wells (1 injector, 1 producer)
Heat of the two wells during 90 days
Saturated Steam Injection (90%), limit rate constraint (980 bbl/d)
Production by the lower well, limit pressure constraint (90 psi)

19. Performance analysis

20. Example : Spe10 study case
DeadOil Model
Cartesian 60x220x85
5 spots
1 water injector well
4 productor wells

21. SPE10 layer 85 : Space Error vs Water Saturation

22. SPE10 Layer 85 : AMR results

23. Spe10 Layer 85

24. SPE10 layer 85 : production well curves vs AMR ratio

25. Adaptative linear stop criteria SPE10 full mesh : production well curves

26. Adaptative linear stop criteria SPE10 full mesh : performance results

27. AMR space error criteria : SPE10 full mesh : production well curves

28. AMR space error criteria : SPE10 full mesh : performance results

29. Conclusion and future works
Aposteriori error estimators:
Interesting tools to manage adaptative algorithms:
Linear error estimations;
Space error estimations.
Future works
Improve time step management;
Numerical Scheme for semi conform mesh:
MPFA scheme
Improved Two Points Scheme
Anisotrope refinement pattern

30. Énergies renouvelables | Production éco-responsable | Transports innovants | Procédés éco-efficients | Ressources durables