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

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

EOR : Enhanced Oil Recovery process

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

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

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

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

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)

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

Error Estimators  

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

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;

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.

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

Interpolator, Upscaling Operator  

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

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)

Performance analysis

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

SPE10 layer 85 : Space Error vs Water Saturation

SPE10 Layer 85 : AMR results

Spe10 Layer 85

SPE10 layer 85 : production well curves vs AMR ratio

Adaptative linear stop criteria SPE10 full mesh : production well curves

Adaptative linear stop criteria SPE10 full mesh : performance results

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

AMR space error criteria : SPE10 full mesh : performance results

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

Énergies renouvelables | Production éco-responsable | Transports innovants | Procédés éco-efficients | Ressources durables www.ifpenergiesnouvelles.fr