dubrovnik meeting, 13/10/2008 1 different approaches to simulate flow and transport in a multi scale...

$: Dubrovnik meeting, 13/10/2008 1 Different approaches to simulate flow and transport in a multi scale fractured block October 2008 Bernard-Michel G. Grenier$
Dubrovnik meeting, 13/10/2008 1

DifferentDifferent approachesapproaches to to simulatesimulate flow and flow and transport in a multi scale fractured blocktransport in a multi scale fractured block

OctoberOctober 20082008

Bernard-Michel G. Bernard-Michel G. CEA/DEN – DM2S/SFME/MTMS

Grenier C.Grenier C.

CEA/DSM – LSCE

Khvoenkova N.Khvoenkova N.IFPIFP


Context – waste repository

Study the possibility to bury nuclear

wastes deep undergroung

We are insterested in fractured rocks :

scale or granite

It a is multiscale problem: fracture size

from cm to hundreds of meters

Physical parameters are based on in-situ

measures (ASPO, Cadarache)

We limite ourselves to a cubic block of 200

m.

The goal is to predict the flux of pollutants

exaping the storage facility


The User Context

Industrials : answers to practical problems

No time to develop fancy theories

We try to develop very simplified approach taking into account

most of the important physical phenomena

We nevertheless try to appropriate ourselves accademic

developpement for a better understanding of the phenomena

=> This presentation’s goal is to show the limitations of our engineer

approach but also to underline the praticle difficulties encountered

when using more evoluate accademic approach


Semi synthetic fractured block

Main features (mainly intersecting the gallery, above 10 meters):Measured features &Simulated features according to statistics

Background features (cm to few meters) :Simulated features according to statistics


Fracture complexity

undeformed host rock

unaltered altered

cataclasite

foliated rock

mini-splay

2 cm

fault gouge/ breccia/crush

mini-master

fracture coating


Modeling strategies

Explicit modeling of major fractures ( + sensitivity) Matrix diffusion treated by means of semi analytic

approach and equivalent properties Computation of flow and eulerian transport with Cast3m

(Mixed hybrid Finite Element code), fractures as discretized planes

Matrix diffusion may also be calculated with homogeneization techniques. For the moment developped only in 2D.

Major fractures either meshed or homogeneized with smeared fractures techniques.

1

2


Model at fracture scale

First level : include zones in the vicinity of the flow path by means of retention coefficients (fracture coating, infilling materials, mylonite)



Second level : include zones in the depth of the matrix blocks (altered and non altered diorite) by means of a semi analytic simulation of diffusion in the matrix


First step – determine the main fractures

50 or 70 larger conductors are sufficient for flow !Network at the percolation threshold

Flow flux function of the amount of large fractures

Flow–flux converged with 50 fractures only


Head and Flow field


Transport first level and second level, increased matrix diffusion

First level : Tmax = 107 y Second level Tmax = 109 y

4.8 1082.2 1085.5 106X5 (level 2)3 1065.63 1052.25 105X5 (level 1)56001200100.8X1 (level 2)

181.2543.7513.75X1 (level 1)T95%T50%T5%(Time in years) Water transit

time = 5.9 yearsMatrix zone 1 m


Single fracture system for equivalent model

Meshing of matrix zones

Conc. profiles

Conc. field

3 levels of PA time scale flow velocities3 tracers (non sorbing to intermediate)


Main transport paths

Preferential path for the convection and short time flow => need to mesh the main features


Half way conclusions

Strong influence of matrix diffusion and sorption for slow velocities: almost diffusive transport regime

Large storage volume of RNs in the matrix combined with retardation (retention) factor, and the small background fractures

=> Need for an accurate modelisation of background fractures in the vicinity of main features.

Green function techniques won’t be sufficient in two cases : difficulty to determine Deq (influence of the small fractures)Too many major features (percolation).

Strong influence of the main fractures (when below the percolation threshold)

=> Impossible to have a full homogeneization approach. Main fractures are to be meshed (or smeared). Only the viscinity of the main path is containing concentrations.

Dubrovnik meeting, 13/10/2008

Asymptotic approach – for the matrix

Scaling :

Strong « not so physical » hypothesis :

Strong bimodal periodic fracture distribution hypothesis


Scaled equations

Darcy law

Transport

f : fractures

m : matrix


Homogeneization (Nina Khvoenkova PhD 2007)

The Ym integral is the matrix/fracture exchange term. Very important, it is the extra information we are looking for


How to use it

We varied the “scaling exponents” m,teta and alpha

The previous expressions are simplified accordingly

We select the case for which the equations are the closest

expression of our physical intuition (or mesurement of the

problem). There’s no other way since the scaling exponents are

math based and not physical.

In the case of the granite rock : m=2, alpha=1, teta=3 or m=1,

alpha=0, teta=3 give correct exchange terms

=> We can test this set of equations on a simplified geometry for

validation.


Conclusions

Needs to be numerically improved (interpolation on local problems, parallelism for local problems).

Needs to be coded in 3D and coupled with main fractures, difficulties for the meshing.

Eventually use this approach on simple geometry to predict echange coef. In Barenblatt double porosity model.

For some species Am=1, then the matrix/fracture exchange is unstationnary. Taking into account the background fracturation improves the tracer time release evaluation (over Green functions, simple porosity approach).

For species where Am <<1 (Iodine) homogeneization approach shows an instantaneous exchange (for long times). No improvement.


Validation

We mesh explicitly a periodic network of fracture/matrix (sugar-box). We

compare the output flux with the homogeneized approach

Good agreement (5-20%) for the different parameters, on transient

calculations.

dubrovnik meeting, 13/10/2008 1 different approaches to simulate flow and transport in a multi scale...

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