РОССИЙСКАЯ АКАДЕМИЯ НАУК
Институт проблем безопасного развития атомной энергетики
RUSSIAN ACADEMY OF SCIENCES
Nuclear Safety Institute (IBRAE)
Experience in Analyzing Safety
of SNF Management Back End
in the Russian Federation
L.A. Bolshov, I.I. Linge, P.S. Kondratenko, I.V. Kapyrin, V.D. Kovalchuk
Presented by Prof.
Leonid A. Bolshov
May, 2010
Outline
 Motivation
 Experience in groundwater flow and transport modeling
 Non-classical transport processes in geologic media:
Basic physical models
Main factors determining anomalous transport in fractured media
1. Transport in random advection model
2. Random advection with finite correlation length
3. Contaminant transport over percolation media
4. Fluctuation aspects in transport over highly disordered media
 Conclusions
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Motivation
 Nuclear energy development program:
– till 2015 – 234 bln. kWh/year (2009 – 163 bln. kWh/year)
– after 2015 г. – annual grow of nuclear power
not less than 2GWt.
 Program «New generation nuclear energy techlogies
(2010-2020)»
– Innovative technologies for the conversion to closed SNF cycle
– New generation fast power reactors
 Program “Nuclear and radiation safety” (2008-2015)
– Creation of an underground lab for SNF and HLW storage
– Safe disposal of high level waste requires the solution
of complex scientific problems
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SNF management in the Russian Federation
PWR-440, FR
BilNPP
PWR-1000
Remains at
the Bilibino NPP
LWGR-1000
HOT-1
SNF
SNF
SNF
SNF
Комплекс
разделки
(SNF reprocessing)
RT-1
ODC
HOT-2
GKhK
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PA «Mayak»
( SNF storage at GKhK)
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Plans of IBRAE for groundwater flow
and transport modeling
1. Formalization of the process for constructing
hydrogeological models and making calculations
of safety parameters
2. Proper understanding of the underlying physical
processes – non-classical models
3. Systematization of existing knowledge and
software for continuum porous media models
(clay, sand)
4. Development of the software for fractured media
5. Cooperation with institutions having experience
of work at specific facilities
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Numerical modeling: model types
– Dimension: 1D, 2D, 3D.
– Media representation
Continuum porous media
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Discrete fracture network
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Model in development :
PA “Mayak” groundwater flow
Hydrogeological tasks:
 Possible reservoirs overflow
(accumulated 413 mln m3 of liquid waste).
Dangerous rise of levels observed during
the years of high precipitation (2000-2003).
 Transport of radionuclides from Karachai
lake (120 mln Ci accumulated radioactivity).
 Drainage of polluted waters into the
surrounding channels.
 Plenty of other near-surface RW storages.
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Kirovo-Chepetsk chemical combine
Groundwater flow model
using ModFlow
Radionuclide transport model
(MT3DMS)
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Experience in 3D:
prospective SNF repository in France (test case)
– Repository in clay
– Heterogeneity (~1010)
and anisotropy (~102)
in the permeability tensor
– Layer pinch-outs
– Small thickness of the domain w.r. to diameter
– Full heterogeneous (~105) diffusion-dispersion tensor.
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Modeling results: pressure and migration
3D view
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Vertical cross-section
Horizontal cross-section
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Current problems: Laboratory in granite rock
massif with possible SNF repository
Fractured media model
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Non-classical transport processes:
Key factors and physical concepts
 Key physical factors determining anomalous
transport in fractured media
1. Natural fracture networks exhibit fractal properties and can
be classified as percolation media
2. Random advection as dominating transport mechanism
3. Sharp contrast in medium characteristic distribution
4. Strong spatial fluctuations of moisture seepage
characteristics
 Concepts
1. Critical phenomena theory
2. Feynmann’s diagram techniques
3. Mesoscopic effects in semiconducting tunneling barriers
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Non-classical transport processes:
1. Transport in Random Advection Model
Statement of the problem
c
   vc   0;
t
 v  0;
 vi  r1  vk  r2   V 2  a / r1  r2 
at
2h
r1  r2  a
Results
h>1: classical diffusion
h<1: super-diffusion, exponential
decay in concentration tail
No heavy tails
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Various concentration asymptotics
at large distances (tails)
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Non-classical transport processes:
2. Random Advection with Finite Correlation Length
Kik  r1  r2   v'i  r1  v'k  r2   V 2  a / r1  r2
Statement of the problem
v  r   u  v '  r  , u is drift velocity
at a  r1  r2   ,
R t 
c  r, t 
c  0, t 

2h
 is correlation length
Classical Gaussian tail
Super  diffusion
Classical diffusion
Super  diffusive tail
t
Change of transport regimes
with time (schematic)
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r
Two-stage concentration tail
(schematic)
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Non-classical transport processes:
3. Contaminant Transport in Percolation Media
Statement of the problem
Governing equation:
c  r , t  t
  dt   t  t   c  r , t    Dc  r , t  ,
t

  t   t 1  , 0    1; t   2/
Results
R t 
c  r, t 
c  0, t 
Classical diffusion
Sub  diffusion
Sub  diffusive tail
t
Transport regimes above
the percolation threshold (schematic)
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Classical Gaussian tail
r
Two-stage concentration tail above
percolation threshold (schematic)
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Non-classical transport processes:
4. Fluctuation Aspects (cont’d)
Statement of the problem
F
N
S1
C
S
Results
Large area of Strong renormalization of the
contaminant source power (factor K)
Large area of the contact surface between medium
and contaminant source:
K 1
S
Small area:
Strong renormalization
K  1
CS contaminant source
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N
near-field zone
F
far-field zone
Large statistical scatter of the K- factor
K  K 
2
/ K  1
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Conclusions
 Either closed SNF cycle or final direct SNF
disposal require safety assessment techniques
 Numerical groundwater flow and radionuclide
transport models are regarded as the main tool
in the safery assessment. Their development is
considered as one of the key goals
 Four physical models presented above manifest
main feature of geological media giving rise to nonclassical contaminant transport. The contaminant
concentration at large distances (in tail) decays
exponentially in both super- and sub-diffusive
transport modes. Spatial fluctuations of medium
properties can lead to a significant renormalization
of contaminant source power
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РОССИЙСКАЯ АКАДЕМИЯ НАУК
Институт проблем безопасного развития атомной энергетики
RUSSIAN ACADEMY OF SCIENCES
Nuclear Safety Institute (IBRAE)
THANK YOU
FOR YOUR ATTENTION