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Time Space Domain Decomposition for Reactive Transport in Porous Media

Time Space Domain Decomposition for Reactive Transport in Porous Media. Anthony MICHEL. Contributors. Florian Haeberlein PhD Student, IFPEN He will defend his PhD next week ( 14/11/2001) Laurence Halpern, Paris 13, LAGA L.Trenty, J.M.Gratien, A.Anciaux, IFPEN M.Kern, INRIA

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Time Space Domain Decomposition for Reactive Transport in Porous Media

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  1. Time Space Domain Decomposition for Reactive Transport in Porous Media Anthony MICHEL

  2. Contributors • Florian Haeberlein PhD Student, IFPEN • He will defend his PhD next week ( 14/11/2001) • Laurence Halpern, Paris 13, LAGA • L.Trenty, J.M.Gratien, A.Anciaux, IFPEN • M.Kern, INRIA • T.Parra, Geochemistry Dpt, IFPEN • D.Garcia, J.Moutte, ENSMSE

  3. Outlook • Part1. Motivation • CO2 geological storage modeling • CO2 reactivity distribution • ANR-SHPCO2 Project • Part 2. Reactive Transport Modeling • Reactive chemical system • Local reactive flash model • Global reactive transport model • Part 3.Time Space Domain Decomposition • Subdomains • Non linear DD Method • Reactive subdomain definition • Part 4. Case Studies • Case study 1. Laboratory experiment • Case study 2. SHPCO2 Use Case

  4. Part 1 Motivation

  5. CO2 Geological Storage Storage

  6. CO2 Geological Storage Modelling Geological Storage = Aquifer + Seal Chemical System 100 m CH4 H2O Gas CO2 10 km Na+ CO2 Cl- H2O Salt Water Porous Media HCO3- OH- Fe++ H+ Mg++ Ca++ Rock Connectivity Texture

  7. CO2 Reactivity - Physical Distribution ( Garcia, 2008 ) CO2 Carbonatation Effects

  8. CO2 Reactivity – Numerical Distribution Local time Stepping Acid Front Reactivity Time step reduction is due to :- Strong non linearities - High species concentration ratios - What else ?? Low Very Low High

  9. SHPCO2 Project • ANR-CIS 2007 • 4 years project • From 2008 to 2011 Simulation Haute Performance du Stockage Géologique de CO2

  10. SHPCO2 Project Structure Numerical Models Integration and Coupling Newton Krylov + Preconditioners SP2 SP1 SP5 SP4 Real Study Test Case SP3 CPU-Time Time Space Domain Decomposition Parallel Computing and Load Balancing

  11. Real Study Test Case ( Gaumet, 1997) Carbonates Layering

  12. Real Study Test Case ( Gabalda, 2010) Dogger, Paris Basin Geological Model

  13. Part 2 Reactive Transport Modeling

  14. Reactive Chemical System Phases and Species Equilibrium Reactions components W T x1 x2 c2 c1 fluid c I 0 x3 x4 primary species I q 0 x Scx 0 solid q2 q1 z1 z2 secondary species z 0 Scz Kinetic Reactions q -> Skc*c + Skx*x (Dissol) Rkin (Precip) q <- Skc*c + Skx*x

  15. Local Reactive Flash Model c q • Mass Balance Equations [qw c] + Scx [qw x] + Scz [qz z] = T [qq q] = W • Equilibrium Equations ln(x) = ln(Kx) + Sxc [ ln(c)] ( qw > 0 ) ln(z) = ln(Kz) + Szc [ ln(c)] or ( qz = 0 ) • Closure Equations S c + S x = 1 z = 1 q = 1 x z qw qz qq

  16. Global Reactive Transport Model C • Mass Balance Equations • Closure Equations W T F (X) • Constitutive Laws RT,kin (X) (X) RW,kin

  17. Fast Upwind Local Reactive Transport Model + qout * qin*Cin • Mass Balance Equations • Closure Equations local local local (X) • Constitutive Laws (X) (X)

  18. Part 3 Time Space Domain Decomposition

  19. Time Space DD – Continuous Subdomains t T+Dt T G1 W1 x W2 G2

  20. Time Space DD – Discrete Subdomains t T+Dt T W1 x W2

  21. Time Space DD – Local Subdomain Problem l2 l1 t B2 p21 B1 T+Dt A1 u1 + R1(u1) = F1 B1 u1 = l1 T l2=B2 p21 u1 W1 G1 x G2

  22. Time Space DD – Global Coupled Problem A u + R(u) = F A2 u2 + R2(u2) = F2 B2 u2=l2 A1 u1 + R1(u1) = F1 B1 u1 = l1 l1 =B1 p12u2 l2=B2 p21 u1

  23. Time Space DD – Classical Nonlinear Solver U1*= p21 u1* U2*= p12u2* l2* =B2u1* l1*=B1u2* A1 u1 + R1(u1) = F1 B1 u1 = l1* A2 u2 + R2(u2) = F2 B2 u2=l2*

  24. Is Fast Upwind RT a Time Space DD Method ? Bk(Ck) = Flux(Ck)in = l(Ck-1) Dt 0 ncell k-1 k k+1 1 Downwind Sweeping

  25. Reactive Subdomain Definition - React(cell) = |Rkin|(cell) / Max (|Rkin|(cell)) TolReact = 0.4, 0.2 - D1 = {React (cell) > TolReact } NCellSecurity = 2 - D2 = D1 + NCellSecurity - Wreact = D2 + NCellOverLap NCellOverLap = 4 High Reactive Zone Security Layer OverLap

  26. Numerical Efficiency Results Two Species Reactive Transport Classical / Nested / Common … Newton Iterations

  27. Link with other NL Preconditionners … Cf Jan Nordbotten Talk, Yesterday

  28. Part 4 Case Studies

  29. Case study 1 – Laboratory Experiment External Boundary Aqueous Solution Fixed pCO2 Plug Boundary Study Domain R1 Reacted Cement R2 Reactive Front Core Cement

  30. Case study 1 – Laboratory Experiment Simplified Overall Reaction Scheme Portlandite + CO2(aq) -> Calcite Wollastonite -> CaO(aq) + Silice [CO2aq] CaOaq + CO2aq ->Calcite [CaOaq] Silice -> SiO2aq

  31. Case study 1 – Laboratory Experiment Aqueous Species Reactive Subdomain Minerals Movies …

  32. Case study 2 - SHPCO2 Use Case Trapped Supercritical CO2 Regional Hydrodynamics Barreers

  33. Case study 2 - SHPCO2 Use Case

  34. Case study 2 - Reactive Chemical System

  35. Case study 2 - SHPCO2 Use Case Movies …

  36. Perspectives • Global Solver Efficiency and Robustness • Find a robust linear solver and preconditionner • Optimize local computations in the reactive flash • Improve newton convergence criterias • Re-Visit the Fast Upwind Method • Compare efficiency of the two methods • Improve Efficiency of our Time-Space DD Solver • Define good criterias for reactive subdomains • Add appropriate metrics for the nested loops

  37. www.ifpenergiesnouvelles.com

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