time space domain decomposition for reactive transport in porous media

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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

CO2H2O

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

cq

II

Scxxz Scz

components

primary species

secondary species 00

00

c1 c2x1

x4x3

z1 z2q1 q2

x2

q -> Skc*c + Skx*xq <- 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

zx

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Global Reactive Transport Model

Mass Balance Equations

Closure Equations

(X)(X)

Constitutive Laws

(X)

C

W

TF

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) = F1B1 u1 =

= B2 21 u1

Time Space DD – Local Subdomain Problem

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A1 u1 + R1(u1) = F1B1 u1 =

= B2 21 u1

A2 u2 + R2(u2) = F2B2 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) = F1B1 u1 =

= B1 u

A2 u2 + R2(u2) = F2B2 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 ZoneSecurity 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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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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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 2 - SHPCO2 Use Case

Trapped Supercritical CO2

Barreers

Regional Hydrodynamics

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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

time space domain decomposition for reactive transport in porous media

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