HDR J.-R. de Dreuzy Géosciences Rennes-CNRS. PhD. Etienne Bresciani (2008-2010) 2 Risk assessment...

HDRJ.-R. de Dreuzy

Géosciences Rennes-CNRS

PhD. Etienne Bresciani (2008-2010) 2

Ris

k ass

ess

ment

for

Hig

h L

evel R

adio

act

ive W

ast

e s

tora

ge

ran g e o f scén a rio s (~ 1 0 .0 0 0 )

P erm eab ility

Im p erv io u s m ed ia P erm eab le m ed iam /cen tu ry m /y ea r m /d ay

L eakag e riskN a tu ra l m ed ium (un kn ow n )

C lay

G ran ite

P erm eab ility

Im p erv io u s m ed ia P erm eab le m ed iam /cen tu ry m /y ea r m /d ay

L eakag e riskN a tu ra l m ed ium (un kn ow n )

G ran ite

Predictions for a complex system Mean behavior Uncertainty

Relevant knowledge from a lack of data Determinism of large-scale structures Stochastic modeling of smaller-scale

structures Relation between geological structures

and hydraulic complexity What are the key hydro-geological structures? How to identify them (directly & inversely)?

J.-R. de Dreuzy, HDR 3

1. Framework Field observations

2. What is the relevant flow structure? (1996-)

From fracture characteristics to hydraulic properties

3. Operative modeling approach (2006-) Discrete double-porosity models

4. Inverse problem (2005-) Channel identifications Optimal use of a data network

5. Numerical simulations (1996-)6. Transport (2000-)7. Mid- to long-term projects (2009-)J.-R. de Dreuzy, HDR 4

1. Framework Field observations

2. What is the relevant flow structure? (1996-)

From fracture characteristics to hydraulic properties

3. Operative modeling approach (2006-) Discrete double-porosity models

4. Inverse problem (2005-) Channel identifications Optimal use of a data network

5. Numerical simulations (1996-)6. Transport (2000-)7. Mid- to long-term projectsJ.-R. de Dreuzy, HDR 5

3 site-scale examples Livingstone Yucca Mountain Mirror Lake

Blueprint of fracture flow Channeling Permeability scaling

Fracture geological characteristics

6

J.-R. de Dreuzy, HDR 7

Mixed built-in and natural wastes confinement [Hanor,1994]

Artificial large-scale permeameterWhat is really permeability?

J.-R. de Dreuzy, HDR 8

Consequence of data scarcityFractures in the confining clay layer have not been observed

but are dominant

10-5 10-4 10-310-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

-1

-1

Keq

(m

/s)

a (m)

mm100 m

Perméabilité du site

-1

L/n

L

Km

W

Infl

uen

ce o

f fr

actu

res o

n t

he

perm

eab

ilit

y o

f th

e c

lay layer

a

J.-R. de Dreuzy, HDR 10

36ClPermeability increases with scaleHigh flow channeling

PERMEABILITY SCALING FLOW STRUCTURE

11

Permeability decreases with scaleHigh flow channeling

12

10-1 100 101 10210-710-610-510-410-310-210-1100101102

n(l)~L1.75 l-2.75

n(l)/

LD

fracture length, l

a=2.75

Odling, N. E. (1997), Scaling and connectivity of joint systems in sandstones from western Norway, Journal of Structural Geology, 19(10), 1257-1271.Bour, O., et al. (2002), A statistical scaling model for fracture network geometry, with validation on a multiscale mapping of a joint network (Hornelen Basin, Norway), Journal of Geophysical Research, 107(B6).

O. Bour, Ph. Davy

Horn

ele

n,

Norw

ay 

Ph. Davy, C. Darcel, O. Bour, R. Le Goc 13

D2D=1.7

Correlation between fracture

positionsPhD C. Darcel (1999-2002)

Joint set in Simpevarp (Sweden)

Mechanical interactions between

fracturesPh. Davy

1. Framework Field observations

2. What is the relevant flow structure? (1996-)

From fracture characteristics to hydraulic properties

3. Operative modeling approach (2006-) Discrete double-porosity models

4. Inverse problem (2005-) Channel identifications Optimal use of a data network

5. Numerical simulations (1996-)6. Transport (2000-)7. Mid- to long-term projects (2009-)J.-R. de Dreuzy, HDR 14

J.-R. de Dreuzy, HDR 15

Simple flow equation Complex medium structure

+

Simple flow equationComplex parameters

Identified flow structures

Complex flow equationSimple parameters

Flow structure?

K~exp[(p,a).(log K)/2]

r

hr

rr

T

t

hS wdD

D21

1

qhKt

hS

J.-R. de Dreuzy, HDR 16

Simple flow equation Complex medium structure

+

Simple flow equationComplex parameters

Identified flow structures

Complex flow equationSimple parameters

Flow structure?

K~exp[(p,a).(log K)/2]

qhKt

hS

J.-R. de Dreuzy, HDR 17

de Dreuzy, J. R., P. Davy, and O. Bour (2001), Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 1-Effective connectivity, Water Resources Research, 37(8).

p (scale, fracture density)

No connected networks

Fracture superposition a<2

[Stauffer, 1991]

Percolation theory a>3

x

Two scale-model 2<a<3:

Non c

orr

ela

ted f

ract

ure

s

D=1.75 a=2.75

D=d a=2.75

Corr

ela

ted f

ract

ure

s

At threshold Far above threshold

Same permeabilitySame flow structure

Close Permeability Different flow structure

de Dreuzy, J.-R., et al. (2004), Influence of spatial correlation of fracture centers on the permeability of two-dimensional fracture networks following a power law length distribution, Water Resources Research, 40(1).

J.-R. de Dreuzy, HDR 19

Simple flow equation Complex medium structure

+

Simple flow equationComplex parameters

Identified flow structures

Complex flow equationSimple parameters

Flow structure?

K~exp[(p,a).(log K)/2]

r

hr

rr

T

t

hS wdD

D21

1

qhKt

hS

D=1

10 h

100 h

1<D<2

D=2

)( 12/12/ r

hr

rr

T

t

hS dwndw

ndw

D : dimension fractaledw : dimension de transport anormal

Transport dans les fractals

21

Le Borgne , T., O. Bour, J.-R. de Dreuzy, P. Davy, and F. Touchard, Equivalent mean flow models for fractured aquifers: Insights from a pumping tests scaling interpretation, Water Resources Research, 2004.

normal fault zone

contact zone

Anomalous diffusion exponent

dw= 2.8

Fractional flow dimension

n=1.6

Fractional flow dimension

n=1.6

Meaning of n and dw?

22

1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,00,5

1,0

1,5

2,0

2,5

3,0

3,5

AO Conjecture

Cayley Trees

n=d s

dw

Infinite cluster Sierpinski Gasket Fragmentation Fractal Backbone Continuum percolation Infinite cluster Homogeneous Backbone Sierpinski Gasket Sierpinski Lattice [Karasaki,2002] Continuum percolation Correlated percolation [Prakash, 1992] Correlated percolation [Sahimi, 1996] Generalized Radial Flow [Barker, 1988] Continuous Multifractal Self affine [Saadatfar, 2002] Sierpinski lattice

Ploemeur

Integrated information on flow structurede Dreuzy, J.-R., et al. (2004), Anomalous diffusion exponents in continuous 2D multifractal media, Physical Review E, 70.

de Dreuzy, J.-R., and P. Davy (2007), Relation between fractional flow and fractal or long-range permeability field in 2D, Water Resources Research, 43.

Blueprint of structures on data Sensitivity of well tests on structure

organization Classical upscaled hydraulic approaches

Strong homogenization Strong localization

Intermediary flow structures Deterministic versus statistical structures

depending on available data and objectives

J.-R. de Dreuzy, HDR 23

1. Framework Field observations

2. What is the relevant flow structure? (1996-)

From fracture characteristics to hydraulic properties

3. Operative modeling approach (2006-) Discrete double-porosity models

4. Inverse problem (2005-) Channel identifications Optimal use of a data network

5. Numerical simulations (1996-)6. Transport (2000-)7. Mid- to long-term projects (2009-)J.-R. de Dreuzy, HDR 24

J.-R. de Dreuzy, HDR 25

J.-R. de Dreuzy, HDR 26

Geological dataFracture characteristics

Hydraulic data geochemical data

Geometrical structuresDFN-stochastic

Homogenized permeabilitiesContinuous models-deterministic

DATA

MODEL

PREDICTIONS

dir

ect

invers

e

ParameterizationCalibration

Mean behaviorUncertainty

Equilibrium between data, model and predictions (objectives)

J.-R. de Dreuzy, HDR 27

Geological dataFracture characteristics

Hydraulic data geochemical data

DISCRETE DUAL-POROSITY MODEL

Stochastic smaller fractures Deterministic larger fractures

DATA

MODEL

PREDICTIONS

directINVERSE

Mean behaviorUncertainty

Equilibrium between data, model and predictions (objectives)

INV

ER

SE 0

INVE

RSE

J.-R. de Dreuzy, HDR 28

PhD

Delp

hin

e R

ou

bin

et

(2008

-20

10)

PhD D. Roubinet (2008-2010) 29

y

x

yyyx

xyxx

y

x

h

h

KK

KK

q

q

y

y

x

x

yyyyxyxy

yyyyxyxy

yxyxxxxx

yxyxxxxx

y

y

x

x

h

h

h

h

aaaa

aaaa

aaaa

aaaa

q

q

q

q

Tensor

EHM

X - X +

Y-

Y +

K y+ x-K x+ y+

K y-x+K x-y-

K x-x+

K y+ y-

30

Rough fracture experimentsPhD. Laure Michel

Importance of gravity

LB pore-scale simulation of advection, diffusion and

gravityWith L. Talon, H. Auradou

(FAST)

Gravity dominantAdvection dominant

1. Framework Field observations

2. What is the relevant flow structure? (1996-)

From fracture characteristics to hydraulic properties

3. Operative modeling approach (2006-) Discrete double-porosity models

4. Inverse problem (2005-) Channel identifications Optimal use of a data network

5. Numerical simulations (1996-)6. Transport (2000-)7. Mid- to long-term projects (2009-)J.-R. de Dreuzy, HDR 31

32PhD. Romain Le Goc (2007-2009)

Minimization of an objective function = mismatch between data and model

data

2i ifield model

model1 iteration

N

obj ii h

d dF p

PhD. Romain Le Goc (2007-2009) 33

First step

data

2i ifield model

model1 iteration

N

obj ii h

d dF p

Objective Function (classical least-square formulation):

Solving direct problem

Parameter estimation in optimizing Fobj using simulated annealing

PhD. Romain Le Goc (2007-2009) 34

Second step

data

0

2i ifield model

model1 iteration

2j j0 model

j1 0

param

N

obj ii h

N

j

d dF p

p p

Objective Function with regularization term

Regularization term: values from previous step as a priori values

PhD. Romain Le Goc (2007-2009) 35

i-th step

data

0

1

2d dfield model

model1

2j j0 0

j1 0 0

2j ji-1 i-1

j1 i-1 1

+

param

iparam

N

obj dd h i

N

j

N

j i

d dF p

p p

p p

Objective Function with regularization term

Regularization term is build at each iteration

The refinement level is controlled by the information included in the data (accounting for under- and over-parameterization)

36PhD. Romain Le Goc (2007-2009)

-2 -1 0 1 2

-2

-1

0

1

2

Y

X

0.0000.013310.026620.039940.053250.066560.079880.093190.1065

FLOW

Flow structure in a 2D synthetic fracture network

1. Framework Field observations

2. What is the relevant flow structure? (1996-)

From fracture characteristics to hydraulic properties

3. Operative modeling approach (2006-) Discrete double-porosity models

4. Inverse problem (2005-) Channel identifications Optimal use of a data network

5. Numerical simulations (1996-)6. Transport (2000-)7. Mid- to long-term projects (2009-)J.-R. de Dreuzy, HDR 37

38J. Bodin, G. Porel, F. Delay, University of Poitiers

39

Niveau piézométrique

105 m

14 m

17 m

3 m

34 m

FRACTURES

J. Bodin, G. Porel, F. Delay

KARST

J.-R. de Dreuzy, CARI 2008 40

LARGE NUMBER OF WELLS

J. Bodin, G. Porel, F. Delay

Modeling exercise: Prediction of doublet test from all other available information

Collaboration with J. Erhel (INRIA) & A. Ben Abda (Tunis)

101 102 103 104 105 1060,0

0,2

0,4

0,6

0,8

MONOPOLE DIPOLE TRIPOLE

difference

DISK HOMOGENEOUS

diffe

renc

e (%

)

draw

dow

n

t

drawdown

0

2

4

6

8

10

Point-wise head and flow data (PhD. Romain Le Goc) Monopole and dipole tests (with J. Erhel & A. Ben

Abda) Dipole nets Tripoles do not bring additional facilities

Flow-metry (with T. Le Borgne & O. Bour) Identification of 3D flow structures

Use of travel-time and geochemical data (with L. Aquilina) In situ fracture-matrix interactions on 222Rn and 4He data

on Ploemeur site (M2 N. Le Gall) Long-term chronicle of nitrates and sulfates on Ploemeur

(C. Darcel & Ph. Davy)J.-R. de Dreuzy, HDR 42

1. Framework Field observations

2. What is the relevant flow structure? (1996-)

From fracture characteristics to hydraulic properties

3. Operative modeling approach (2006-) Discrete double-porosity models

4. Inverse problem (2005-) Channel identifications Optimal use of a data network

5. Numerical simulations (1996-)6. Transport (2000-)7. Mid- to long-term projects (2009-)J.-R. de Dreuzy, HDR 43

Balance between precision and efficiency 3D fracture flow simulations

B. Poirriez (PhD INRIA 2008-2010) G. Pichot (Post-Doc Géosciences Rennes 2008-2009)

Transient-state simulations Large-scale intensive transport simulation

A. Beaudoin (Univ. of Le Havre) Parallelization

Sub domain methods D. Tromeur-Dervout (Univ. of Lyon)

Platform development E. Bresciani (INRIA, 2007) N. Soualem (INRIA, 2008-2010)

J.-R. de Dreuzy, CARI 2008 44

45

Broad power-law length distribution n(l)~l-a with lmin<l<L

Large number of fractures: ~103 to 105

a=3.4L=50 lmin

~15 103 fractures

Post-Doc Géraldine Pichot (2008-2009)

PhD Baptiste Poirriez (2008-2010)

Post-Doc G. Pichot (2008-2009) 46

Head distribution in a simple fracture network Matching Fracture meshesNon-Matching Fracture meshes

1. Framework Field observations

2. What is the relevant flow structure? (1996-)

From fracture characteristics to hydraulic properties

3. Operative modeling approach (2006-) Discrete double-porosity models

4. Inverse problem (2005-) Channel identifications Optimal use of a data network

5. Numerical simulations (1996-)6. Transport (2000-)7. Mid- to long-term projects (2009-)J.-R. de Dreuzy, HDR 47

Transport in fractured media The example of percolation theory (2001)

Pre-asymptotic to asymptotic regimes Collaboration with A. Beaudoin & J. Erhel

(2006-) Velocity field structure

Collaboration with T. Le Borgne & J. Carrera Reactive transport

Simulation means Fluid-Solid and Fluid-Fluid reactivity

J.-R. de Dreuzy, HDR 48

J.-R. de Dreuzy, HDR 49

Advection-diffusion in highly heterogeneous media (2=9)

50

=1, n=0.9, D=0, Ka=1, 2=1.5

Influence of heterogeneity on: - Sorption reactivity (PhD. K. Besnard 2001-2003)- Dynamic of mixing (T. Le Borgne, M. Dentz, J. Carrera)

Particles Concentration

1. Framework Field observations

2. What is the relevant flow structure? (1996-)

From fracture characteristics to hydraulic properties

3. Operative modeling approach (2006-) Discrete double-porosity models

4. Inverse problem (2005-) Channel identifications Optimal use of a data network

5. Numerical simulations (1996-)6. Transport (2000-)7. Mid- to long-term projects (2009-)J.-R. de Dreuzy, HDR 51

3D “Theoretical” studies

Geological & physico-chemical complexities Chemical transport Multiphase flow Numerical Simulation tools

Inverse problem Broader range of data and heterogeneity structures From flow to transportConnection between theory and field

Application to existing well-documented fractured media field-scale models ORE H+ HLRW, CO2 sequestration, remediationFIELD SITES

J.-R. de Dreuzy, HDR 52

J.-R. de Dreuzy, HDR 53

Gary Larson, The far side gallery 54

PhD. Etienne Bresciani (2008-2010) advised by Ph. Davy 55

Example of protection zone delineation

Pochon, A., et al. (2008), Groundwater protection in fractured media: a vulnerability-based approach for delineating protection zones in Switzerland, Hydrogeology Journal, 16(7), 1267-1281.

J.-R. de Dreuzy, HDR 56

“Essentially, all models are wrong, but some are useful”

Which ones?Box, George E. P.; Norman R. Draper (1987).

Empirical Model-Building and Response Surfaces, p. 424