Download Alternative Modeling Approaches for Flow & Transport in Fractured

Alternative Modeling
Approaches for Flow &
Transport in Fractured Rock
Douglas D. Walker, DE&S
Jan-Olof Selroos, SKB
Supported by Swedish Nuclear Fuel and Waste
Management Co. (SKB)
Presentation Overview
• Context and Objectives of the
Alternative Models Project
• The hypothetical Aberg Repository
• 3 alternative conceptual models of
heterogeneity
• Performance measures
• Results and Conclusions
Deep Geologic Disposal of
Nuclear Waste
Cladding
Fuel Rod
Spent Fuel
Canister
Bentonite
Bedrock
Repository Tunnel
Nuclear Waste Disposal
Performance Assessment
Inhalation
Ingestion
Irradiation
CLIMATE
ENGINEERED
BARRIER
EVENTS:
Intrusion
Seismic
Volcanic
BIOSPHERE
GEOSPHERE
Uncertainty in Subsurface
Hydrology
• Uncertainty vs. variability
• Uncertainty in:
– process physics
– measurement
characterization of heterogeneity
– upscaled representation in models
The Alternative
Models Project
• Nuclear waste disposal performance
assessment uncertainty analysis
• Compare alternative representations of
flow / transport in fractured rocks
• Explicit definition of
– test problem premises
– performance measures and summary
statistics
Aberg Repository
Aberg Site and Data
• Hydrogeologic Setting:
– Inland recharge, discharge to Baltic
– Fractured granitic rocks
– Large-scale fracture zones (deterministic)
• Data:
– 53 Boreholes (hydraulic/tracer tests, chem)
– geophysics, fracture trace maps
– Äspö Hard Rock Laboratory
• Regional model / boundary conditions
Aberg: Deterministic Fracture
Zones and Repository
Alternative Conceptual Models
Channel
Network
Stochastic
Continuum
Discrete Fracture
Stochastic
Continuum
• Effective porous medium
(Darcy’s Law)
• Spatially correlated RV
+ deterministic zones
• Finite Difference flow model
• Advective particle tracking
Stochastic Continuum:
Application
• Conductivity distribution
– 3m K tests  25m, Lognormal + variogram
– Rock & Conductor distributions
– homogeneous ar = 1.2 m2/m3 rock
• Structural model
– Deterministic zones only
• Repository
– 945 canisters x 34 realizations
Stochastic Continuum:
Travel Paths
Travel Time, yr
Elevation, from south
Stochastic Continuum
• Advantages:
– hydraulic tests are volume averages
– method / software well-established
• Disadvantages:
– Scale dependence of K in fractured media
poorly understood
– Preferential paths not represented at
scales below block size
Discrete Fracture Network
Fracture Network
Flow Area
1-D Pipe Network
Discrete
Fracture
• Fracture simulation with
observed frequency, size
and orientation
• Deterministic zones
• 1-D Pipe / Finite Element
flow solution
• Pathway analysis for
transport
Discrete Fracture Network:
Application
• Fracture Distribution
– Deterministic Zones and Canister fractures
– Lognormal, with 20  R  1000m in region
and 0.2  R  20m at repository
– Lognormal transmissivity
– ar = f (area between fracture traces)
• Repository
– 50 to 90% of 81 canisters x 10 realizations
Discrete Fracture Network:
Travel Paths
Realization 9
West
Block 3
Block 4
Block 6
Top View
Discrete Fracture Network
• Advantages:
– Represents the conductive structures
(Realism)
– Allows for preferential paths
• Disadvantages:
– Data demand
– Computational demand
– Matrix permeability may be important
Flow Channeling
Areas with stagnant
water (access by
diffusion only)
Channels with
mobile water
Fracture surfaces in
contact with
each other
Channel
Network
• Channel simulation with
observed frequency and
conductance distribution
• Deterministic zones
• 3-D Finite Difference flow
solution
• Particle tracking with total
mixing at intersections
Channel Network
Intersections
Channel Network:
Application
• Conductance Distribution
– 3m K tests  30m, Lognormal
– Rock, Conductor, & EDZ distributions
– ar = 1.2 m2/m3 in Zones,  1/10 in Rock
• Structural model
– Deterministic zones
• Repository
– 229 cans x 30 real x median (200 particles)
Channel Network:
Travel Paths
Channel Network
• Advantages:
– Represents observed channels within
fracture planes, directly assigns ar
– Allows for preferential paths and dispersion
– Includes diffusion/sorption in matrix, flow
within Rock
• Disadvantages:
– Conductance is scale dependent
Application Summary
SC
CN
DFN
Zones
logK=
logK=
LogN
by zone
1.6
LogN
by zone
0.8
Constant
by zone
0
Rock
logK=
 logK=
LogN
by region
1.6
LogN
by zone
0.8
Flowwetted
surface
Homogen.
Homogen. by
Zones, Rock,
EDZ
Trunc. LogN
Radii 0.2<R<20m
20<R<1000m
LogN logT=9e-7
Heterogen, a
function of radius
and connection
Simulation Summary
Canisters
Realization
EDZ
SC
CN
DFN
945
locations
Median of 200
released at 229
locations
50 to 90% of 81
locations
34
30
10
Below
resolution
10  K of
rock mass
canister fractures
T = 1e-9
Performance Measures
• Travel time: canister to biosphere
tw = qw/f
[yr]
• Canister Flux: Darcy flux at canisters
qw
[m/yr]
• F-factor: Retardation vs. Advection
F = (dw ar) / qw [yr/m]
Performance measures:
Medians
7
6
5
4
SC
DFN
CN
3
2
1
0
Log Travel -Log
Time
Canister
(yr)
Flux
(m/yr)
Log Ffactor
(yr/m)
Performance measures:
Variances
1.2
1
0.8
0.6
SC
DFN
CN
0.4
0.2
0
Log Travel Log
Time
Canister
Flux
(yr)
(m/yr)
Log Ffactor
(yr/m)
Discussion
• Median performance measures and exit
locations similar
(Controlled by premises of BC, major zones)
• For DFN, F-factor variance greater than
tw variance (variability of ar impacts PA)
• SC variances greatest, but differences
in studies complicate comparison
Discussion II
• Modeling study differences:
– # particles released
SC = one / canister
DFN = one / canister subset
CN = median of 200 / canister subset
– # canisters with pathways
100% in SC and CN; 50 to 90% in DFN
– Not evaluated: team experience, Sensitivity of
inference to data
• SC and CN  boundary flow, DFN low
Conclusions
For this site and these performance
measures:
• Problem premises constrain the results
• Uncertainties regarding conceptual
models of flow / transport in fractured
rocks have limited effect on PA
• Chief benefit of DFN / CN is to examine
effects of ar
Acknowledgements
SC Modeling Study:
H.Widén (Kemakta), D. Walker (DE&S)
DFN Modeling Study:
W Dershowitz, S Follin, T Eiben, J Andersson (GA)
CN Modeling Study:
B. Gylling, L. Moreno, I. Neretnieks (KTH)
Swedish Nuclear Fuel and Waste Management Co.
A. Ström, J-O. Selroos (SKB)