hdr j.-r. de dreuzy géosciences rennes-cnrs. phd. etienne bresciani (2008-2010) 2 risk assessment...
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HDRJ.-R. de Dreuzy
Géosciences Rennes-CNRS
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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
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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
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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
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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
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3 site-scale examples Livingstone Yucca Mountain Mirror Lake
Blueprint of fracture flow Channeling Permeability scaling
Fracture geological characteristics
6
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J.-R. de Dreuzy, HDR 7
Mixed built-in and natural wastes confinement [Hanor,1994]
Artificial large-scale permeameterWhat is really permeability?
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J.-R. de Dreuzy, HDR 8
Consequence of data scarcityFractures in the confining clay layer have not been observed
but are dominant
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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
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J.-R. de Dreuzy, HDR 10
36ClPermeability increases with scaleHigh flow channeling
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PERMEABILITY SCALING FLOW STRUCTURE
11
Permeability decreases with scaleHigh flow channeling
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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
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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
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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
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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
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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
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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:
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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).
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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
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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
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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?
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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.
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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
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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
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J.-R. de Dreuzy, HDR 25
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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)
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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
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J.-R. de Dreuzy, HDR 28
PhD
Delp
hin
e R
ou
bin
et
(2008
-20
10)
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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-
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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
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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
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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
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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
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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
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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)
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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
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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
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38J. Bodin, G. Porel, F. Delay, University of Poitiers
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39
Niveau piézométrique
105 m
14 m
17 m
3 m
34 m
FRACTURES
J. Bodin, G. Porel, F. Delay
KARST
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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
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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
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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
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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
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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
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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)
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Post-Doc G. Pichot (2008-2009) 46
Head distribution in a simple fracture network Matching Fracture meshesNon-Matching Fracture meshes
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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
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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
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J.-R. de Dreuzy, HDR 49
Advection-diffusion in highly heterogeneous media (2=9)
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=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
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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
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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
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J.-R. de Dreuzy, HDR 53
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Gary Larson, The far side gallery 54
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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.
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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