Alternative Modeling Approaches for Flow &

Transport in Fractured Rock

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 OverviewPresentation 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

Deep Geologic Disposal of Nuclear Waste

Cladding Fuel Rod

Spent Fuel Canister Bedrock

Bentonite

Repository Tunnel

Nuclear Waste Disposal Performance AssessmentNuclear Waste Disposal

Performance AssessmentInhalation

Ingestion Irradiation

ENGINEERED BARRIER

BIOSPHERE

CLIMATE

GEOSPHERE

EVENTS: IntrusionSeismicVolcanic

Uncertainty in Subsurface Hydrology

Uncertainty in Subsurface Hydrology

• Uncertainty vs. variability

• Uncertainty in:– process physics– measurementcharacterization of heterogeneity– upscaled representation in models

The Alternative Models Project

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 RepositoryAberg Repository

Aberg Site and DataAberg 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

Aberg: Deterministic Fracture Zones and Repository

Fracture zones and tunnels0500

10001500

2000

East

0500 1000

15002000

North

0

200

400

600

800

1000

Up

0

200

400

600

800

1000

Up

Fracture zones and tunnels0500

10001500

2000

East

0500 1000

15002000

North

0

200

400

600

800

1000

Up

0

200

400

600

800

1000

Up

Alternative Conceptual ModelsAlternative Conceptual Models

StochasticContinuum

Discrete Fracture

ChannelNetwork

StochasticContinuumStochasticContinuum

• Effective porous medium (Darcy’s Law)• Spatially correlated RV + deterministic zones• Finite Difference flow model• Advective particle tracking

Stochastic Continuum:

ApplicationStochastic 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

Stochastic Continuum: Travel Paths

Elevation, from south

Travel Time, yr

Stochastic ContinuumStochastic 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 NetworkDiscrete Fracture Network

1-D Pipe NetworkFlow Area

Fracture Network

DiscreteFractureDiscreteFracture

• Fracture simulation with observed frequency, size and orientation• Deterministic zones• 1-D Pipe / Finite Element flow solution• Pathway analysis for transport

Discrete Fracture Network:

ApplicationDiscrete 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

Discrete Fracture Network: Travel Paths

Discrete Fracture NetworkDiscrete Fracture Network

• Advantages:– Represents the conductive structures

(Realism)– Allows for preferential paths

• Disadvantages:– Data demand– Computational demand– Matrix permeability may be important

Flow ChannelingFlow Channeling

Areas with stagnant water (access by diffusion only)

Channels with mobile water

Fracture surfaces incontact with each other

ChannelNetworkChannelNetwork

• 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 Intersections

Channel Network:

ApplicationChannel 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: Travel Paths

Channel NetworkChannel 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 SummaryApplication SummarySC CN DFN

Zones logK=logK=

LogNby zone

1.6

LogNby zone

0.8

Constantby zone

0

Rock logK= logK=

LogNby region

1.6

LogNby zone

0.8

Trunc. LogNRadii 0.2<R<20m20<R<1000mLogN logT=9e-7

Flow-wettedsurface

Homogen. Homogen. byZones, Rock,

EDZ

Heterogen, afunction of radiusand connection

Simulation SummarySimulation Summary

SC CN DFN

Canisters 945locations

Median of 200released at 229

locations

50 to 90% of 81locations

Realization 34 30 10

EDZ Belowresolution

10 K ofrock mass

canister fracturesT = 1e-9

Performance MeasuresPerformance 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

Performance measures: Medians

0

1

2

3

4

5

6

7

Log TravelTime

-LogCanister

Flux

Log F-factor

SCDFNCN

(yr)(m/yr)

(yr/m)

Performance measures: Variances

Performance measures: Variances

0

0.2

0.4

0.6

0.8

1

1.2

Log TravelTime

LogCanister

Flux

Log F-factor

SC

DFN

CN

(yr)(m/yr)

(yr/m)

DiscussionDiscussion

• 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 IIDiscussion 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

ConclusionsConclusions

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

AcknowledgementsAcknowledgements

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)