Simulations of one and two phase flow in porous media: from the pore scale description to the macroscale studies

Transcription

1 Simulations of one and two phase flow in porous media: from the pore scale description to the macroscale studies Félix Collin-Bastiani PhD - CERFACS (Master INP) Jacques Franc PhD INP Romain Guibert Research Engineer IMFT/INP Pierre Horgue Research Engineer MFEED platform Gérald Debenest Professor IMFT/INP

2 Contents Upscaling fluid flow from pore scale to Darcy scale Two phase flow and transport processes Conclusions Perspectives

3 Multi-scales: different models and issues Microscale (local scale) Possibles models: - Stokes/Navier-Stokes - VOF for multiphase - Lagrangian Particle Tracking Issues: - Complex geometries - CPU time expensive Macroscale (large scale) Related models: - Darcy-Forchheimer - Generalized Darcy s law - Convection/Dispersion equations Issues: - Effective medium properties - Upscaling local scale physics How to treat the link between scales?

4 Micro-scale : effective properties determination Upscaling : can we find the link between pore scale phenomenon and the macroscale description? Focus on some recent works Permeability determination Mesh sensitivity Method/BC comparison Parallel efficiency (Transport in Porous Media 2015) (Mathematical Geosciences 2016) Two-step Upscaling Method efficiency study (Computational Geosciences 2015) (Computational Geosciences 2017) Inertial and thermal flows Forchheimer coefficient Effective thermal conductivity (Oil Shale Symposium 2015)

5 Permeability evaluation Real Media Collaboration LFC Pau / Total REV Porosity / Permeability Guibert et al. TiPM (2015) Extracted from large volume x x mm 3 Berea standstone / Porosity 12% / 4 mm 3

6 Permeability evaluation- REV determination porosity permeability pressure velocity

7 Convergence seems to be close Permeability evaluation Guibert et al TiPM - Configuration 1 : Permeameter - Configuration 2 : Periodic Mesh Conf. 1 Conf. 2

8 Permeability evaluation Several refinements necessary : no convergence obtained yet, but possible to do (next mesh will need ~1TB of RAM) Huge computational resources (memory rather than CPU time) Possible to use direct numerical approach for billions of cells if needed Or another approach?

9 Micro-scale : effective properties determination Upscaling : from a direct problem, can we find the link between pore scale phenomenon and the macroscale description? Many recent works Permeability determination Mesh sensitivity Method/BC comparison Parallel efficiency (Transport in Porous Media 2015) (Mathematical Geosciences 2016) Two-step Upscaling Method efficiency study (Computational Geosciences 2015) (Computational Geosciences 2017) Inertial and thermal flows Forchheimer coefficient Effective thermal conductivity (Oil Shale Symposium 2015)

10 Two-step upscaling Principle : Use at Darcy-scale King TiPM (1989) Pickup et al. MG (1994) Khoury et al. JAM (2006) But what about scaling microscale to Darcy?

11 Two-step upscaling method for permeability evaluation 1) Divide in sub-domains 2) First upscaling 3) Second upscaling (Computational Geosciences 2015) Results - Drastic reduction of computational resources required (CPU, RAM) - Allows mesh refinement and large sample volumes.

12 De 2 3 à 6 3 subdomains: ~5% of maximum error Gain (for 6 3 subdomains) Memory (45G to 250M) divide by 180 Time (290 to 85h) 70% Two-step upscaling Two refinement levels K xx Kyy Kzz Local scale boxes Error compared to the classical upscaling for each refinement level

13 Micro-scale : effective properties determination Upscaling : from a direct problem, can we find the link between pore scale phenomenon and the macroscale description? Many recent works Permeability determination Mesh sensitivity Method/BC comparison Parallel efficiency (Transport in Porous Media 2015) (Mathematical Geosciences 2016) Two-step Upscaling Method efficiency study (Computational Geosciences 2015) (Computational Geosciences 2017) Inertial and thermal flows Forchheimer coefficient Effective thermal conductivity (Oil Shale Symposium 2015)

14 Extension to non-darcy flows Packing of several thousand blocks Objectives : determination of the effective permeability and inertial correction R. Guibert et al. 2015, 34th Oil Shale Symposium 2015 From 5 to 40 millions of cells

15 Extension to non-darcy flows Packing of several thousand blocks Objectives : determination of the effective permeability and inertial correction R. Guibert et al. 2014, 34th Oil Shale Symposium 2014 But, time and computational resources consuming What about TSU?

16 TSU Extension to non-darcy flows Increasing the local scale Reynolds (near wells), correction to Darcy s law? Validation on Sphere packings Long sample, particle deposition ~20 R 3 Mesh details (one refinement level)

17 TSU method applied to non-darcy flows Validation on Sphere packings Test on complex medium? Cassidy, R et al., Geological Society 2005

18 Micro-scale : transport and two-phase flows Dispersion coefficient SimpleParticleFoam Passive LPT algorithm Statistical tools to determine dispersion coefficient (EAGE, Wien, 2016) (PG sub 2017) Tube bundle experiments heleshawinterfoam Penalization for wall effects Good agreement between numerical and experimental (Chemical Engineering Science 2013) Immersed boundary penalizedinterfoam Solid domain penalization Wetting effect on immersed boundaries (Computer & Fluids 2014)

19 Dispersion using LPT Method and VAT Results # estimators in finite samples Comparison in «capillary» between methods Comparison in real sample

20 Pore scale Two phase flow : Experiments/Simulations Match? Comparison 10ml/min VOF Comparisons : VOF, VOF+ normal to the surface smoothing, VOF + interface smoothing, VOF+all corrections Comparison of # VOF solvers Drainage Water (red) Oil (blue) On going work Prediction? Not the pattern S r,w

21 Macro-scale open-source porous multiphase toolbox Water invasion in heavy oil reservoir Context : Development in OpenFOAM : => Darcy s equation : penalization term in momentum equation Missing essential features: Objectives : - phase saturations - relative permeabilities - capillary pressure laws - boundary conditions for fixed fluxes (Computer Physics Communications, 2015) (CRAS Meca, 2016) - develop solver dedicated to porous multiphase flow - make it as an evolutive toolbox (libraries, BC,...)

22 Toolbox content Boundary conditions Pressure boundary condition for fixed velocity Porous models Brooks and Corey (1964) Van Genuchten (1980) Linear model Tutorials Validation cases (analytical solutions) Practical test-cases

23 Toolbox extensions: Richards equation Model : Improvements: - pressure gradient in the non-wetting phase neglected. - Picard s algorithm, linearization - Improvement of the existing C++ classes Technical report : - Model description - Validation cases - Efficiency study (Technical report, HAL/arXiv, 2015) Water infiltration on unstructured mesh (topographic dataset)

24 Toolbox extensions: DryMethaFoam Model : Improvements: - IMPES formulation with transport equations - Incompressible two-phase flow in waste - Double porosity approach (static and mobile water) - Solute transport and transfer in water - Biodegradation model (complex, with ph) - Mixed tank boundary condition (all the process) Technical report ADEME DRYMETHA (11/2016) & PhD Shewani: - Model description - Efficiency of water injection (Shewani et al., 2015 Bioresource Tech Shewani et al. 2017, CES )

25 Recent developments: Reactive flows CombustionPorousFoam for decarbonation : - Compressible flow - Temperature equation - Gas component transport - Solid component degradation DrymethaFoam2 for dry methanation: - multicomponent liquid/gas - equilibrium calculations - explicit solver of ph : VFA production Digan et al. 2016, 2017 sub. Combustion front in oil shale semi-coke

26 On-going work and collaborations Around the toolbox - Specific stability criteria for time-step management (done, distributed) - Compressible version of the IMPES solver (on going) - Upscaling method DMM (Multiphase Darcy to Reservoir scale) Other on going works - PhD - Master internships Collaborations - New tool to determine (K, D) on larger samples (no calculation ) - Extension to double porosity medium (TSU) - Chemical flooding OMV (optimization procedures) - Combustion and upscaling of non linear reaction rates - Numerical studies for industrials - Support for students or Engineers - Dedicated developments - Open-source tools training - Many others

27 Contact Team G. Debenest : debenest@imft.fr / debenest@enseeiht.fr R. Guibert : romain.guibert@imft.fr P. Horgue : pierre.horgue@mfeed.fr / phorgue@imft.fr Toolbox MFEED informations

28 IMPES formulation t n+1 Update properties S n+1