time space domain decomposition for reactive transport in porous media
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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Renewable energies | Eco-friendly production | Innovative transport | Eco-efficient processes | Sustainable resources
Time Space Domain Decomposition for
Reactive Transport in Porous Media
Anthony MICHEL
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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
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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
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Motivation
Part 1
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CO2 Geological Storage
Storage
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CO2 Geological Storage Modelling
CO2H2O CH4
CO2
H2O
Ca++H+
Gas
Salt Water
Rock
Texture
OH-
Na+
HCO3-
Cl-
Porous Media
Geological Storage = Aquifer + Seal
10 km
100 m
Connectivity
Fe++
Mg++
Chemical System
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CO2 Reactivity - Physical Distribution
( Garcia, 2008 ) CO2 Carbonatation Effects
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CO2 Reactivity – Numerical Distribution
Acid Front Reactivity Local time Stepping
High Very LowTime step reduction is due to :- Strong non linearities- High species concentration ratios- What else ??
Low
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SHPCO2 Project
Simulation Haute Performance du Stockage Géologique de CO2
ANR-CIS 2007 4 years project
From 2008 to 2011
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SHPCO2 Project Structure
SP3
SP5
CPU-Time
Newton Krylov+ Preconditioners
SP2
SP1
SP4
Time SpaceDomain Decomposition
Parallel Computing andLoad Balancing
Real StudyTest Case
Numerical Models Integration and Coupling
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Real Study Test Case
( Gaumet, 1997) Carbonates Layering
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Real Study Test Case
( Gabalda, 2010) Dogger, Paris Basin Geological Model
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Reactive Transport Modeling
Part 2
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Reactive Chemical System
T W
c
q
I
I
Scxx
z Scz
components
primary species
secondary species 0
0
0
0
c1 c2x1
x4x3
z1 z2q1 q2
x2
q -> Skc*c + Skx*x
q <- Skc*c + Skx*x (Precip) (Dissol)Rkin
Kinetic Reactions
Equilibrium ReactionsPhases and Species
solid
fluid
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Local Reactive Flash Model
q
Mass Balance Equations [w c] + Scx [w x] + Scz [z z] = T [q q] = W
Equilibrium Equations
ln(x) = ln(Kx) + Sxc [ ln(c)] ( w > 0 )
ln(z) = ln(Kz) + Szc [ ln(c)] or ( z = 0 )
Closure Equations
c + x = 1
z = 1
q = 1
c
q
z
w
z
x
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Global Reactive Transport Model
Mass Balance Equations
Closure Equations
(X)
(X)
Constitutive Laws
(X)
C
W
T
F
RT,kin
RW,kin
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Fast Upwind Local Reactive Transport Model
Mass Balance Equations
Closure Equations
(X)
(X)
Constitutive Laws
(X)
+ qout * qin*Cinlocal
local
local
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Time Space Domain Decomposition
Part 3
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T
T+t
t
x
Time Space DD – Continuous Subdomains
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T
T+t
t
x
Time Space DD – Discrete Subdomains
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T
T+t
t
x
B1B2 21
A1 u1 + R1(u1) = F1
B1 u1 =
= B2 21 u1
Time Space DD – Local Subdomain Problem
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A1 u1 + R1(u1) = F1
B1 u1 =
= B2 21 u1
A2 u2 + R2(u2) = F2
B2 u2 =
= B1 12 u2
A u + R(u) = F
Time Space DD – Global Coupled Problem
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U= 21 u1* U2*= 12 u2*
A1 u1 + R1(u1) = F1
B1 u1 =
= B1 u
A2 u2 + R2(u2) = F2
B2 u2 =
= B2 u1*
Time Space DD – Classical Nonlinear Solver
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Downwind Sweeping
1 k-1 k k+1 ncell
Bk(Ck) = Flux(Ck)in = Ck-1
0
t
Is Fast Upwind RT a Time Space DD Method ?
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- React(cell) = |Rkin|(cell) / Max (|Rkin|(cell))
- D1 = {React (cell) > TolReact } TolReact = 0.4, 0.2
- react = D2 + NCellOverLap NCellOverLap = 4
- D2 = D1 + NCellSecurity NCellSecurity = 2
High Reactive Zone
Security Layer
OverLap
Reactive Subdomain Definition
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Numerical Efficiency Results
Two Species Reactive Transport
Classical / Nested / Common … Newton Iterations
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Link with other NL Preconditionners …
Cf Jan NordbottenTalk, Yesterday
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Case Studies
Part 4
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Case study 1 – Laboratory Experiment
Plug Boundary
External Boundary
Study Domain
Aqueous Solution Fixed pCO2
Core Cement
Reacted Cement
Reactive Front
R2R1
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Case study 1 – Laboratory Experiment
Portlandite + CO2(aq) -> Calcite
Wollastonite -> CaO(aq) + Silice [CO2aq]
CaOaq + CO2aq ->Calcite
Silice -> SiO2aq [CaOaq]
Simplified Overall Reaction Scheme
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Case study 1 – Laboratory Experiment
Aqueous Species
Minerals
Reactive Subdomain
Movies …
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Case study 2 - SHPCO2 Use Case
Trapped Supercritical CO2
Barreers
Regional Hydrodynamics
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Case study 2 - SHPCO2 Use Case
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Case study 2 - Reactive Chemical System
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Case study 2 - SHPCO2 Use Case
Movies …
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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
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