Working Report
99~33
Measurements
with the He-gas methods of
the disturbed zone caused by boring
Mika Laajalahti
Tapani Aaltonen
Kalle Kuoppamaki
Jani Maaranen
Jussi Timonen
Jorma Autio
April 1999
POSIVA OY
Mikonkatu 15 A, FIN-001 00 HELSINKI, FINLAND
Tel. +358-9-2280 30
Fax +358-9-2280 3719
Working Report 99-33
Measurements
with the He-gas methods of
the disturbed zone caused by boring
Mika Laajalahti
Tapani Aaltonen
Kalle Kuoppamaki
Jani Maaranen
Jussi Timonen
Jorma Autio
April 1999
Working Report 99-33
Measurements
with the He-gas methods of
the disturbed zone caused by boring
Mika Laajalahti, Tapani Aaltonen,
Kalle Kuoppamaki, Jani Maaranen,
Jussi Timonen
University of JyvaskyU:i
Department of Physics
Jorma Autio
Saanio &
Riekkola Consulting Engineers
April 1999
Working Reports contain information on work in progress
or pending completion.
The conclusions and viewpoints presented in the report
are those of author(s} and do not necessarily
coincide with those of Posiva.
SAATE RAPORTIN TARKASTAMISESTA JA HYVAKSYMISESTA
Saanio & Riekkola 0 y
Laulukuja 4
00420 HELSINKI
TEKIJA-ORGANISAATIOT:
JyvaskyHin yliopisto
Fysiikan laitos
PL 35
40351 JYV ASKYLA
TILAAJA:
POSIVAOy
Mikonkatu 15 A
00100 HELSINKI
TILAUSNUMERO:
9535/98/JPS
TILAAJAN YHDYSHENKILO:
Jukka-Pekka Salo
PosivaOy
KONSUL TIN YHDYSHENKILO:
Jorma Autio
Saanio & Riekkola Oy
t/, i, 'i<t:J
TYORAPORTTI
MEASUREMENTS WITH THE HE-GAS
METHODS OF THE DISTURBED ZONE
CAUSED BY BORING
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Tapani Aaltonen
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Kalle Kuoppamaki
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Mika Laafalahti
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Jussi Timonen
FT HYVAKSYJA
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Timo Kirkkomaki
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TARKASTAJA:
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Reij6 Riekkola
toimitusj ohtaj a
/c~
~PREFACE
This work is part of the characterisation of the experimental full-scale deposition holes
bored in the Research Tunnel at Olkiluoto, a project commissioned by Posiva Oy and
SKB (Svensk Karnbdinslehantering AB) in co-operation. The work was managed and
supervised by Jorma Autio at Saanio & Riekkola Oy on behalf of Posiva Oy and SKB.
The contact person at Posiva Oy was Jukka-Pekka Salo and at SKB Christer Svemar.
TIIVISTELMA
Olkiluodon tutkimustunnelin tiiviiseen granuttun on porattu kolme koereikaa, jotka
vastaavat mitoiltaan (syvyys 7.5 m ja halkaisija 1.5 m) KBS-3 -tyyppista
loppusijoitusreikaa.
Reikien
pinnoista otetuista naytteista mitattiin
Hekaasumenetelmilla pinnan suuntainen efektiivinen diffusiviteetti ja permeabiliteetti,
seka naytteiden huokoisuus. Jokaisen porauksesta aiheutuvan hairiopinnan sisaltavan
naytteen tuloksia verrattiin vastaavaan ehjan vertailunaytteen tuloksiin.
He-pyknometrilla mitattujen hairiopinnallisten naytteiden huokoisuus oli selvasti
suurempi (0.45%) kuin ehjien vertailunaytteiden (0.24% ). Myos permeabiliteetit ja
diffuusiokertoimet
olivat
selvasti
suurempia
hairiopinnallisilla
naytteilla.
Hairiopinnallisten ja ehjien naytteiden permeabilitteettien suhde oli 3.2 ja vastaavien
diffuusiokertoimien 3 .1.
Permeabiliteetit ja diffuusiokertoimet olivat selvasti riippuvaisia mittaussuunnasta si ten,
etta suuremmat arvot mitattiin kiven liuskeisuuden suunnassa ja pienemmat noin
45°:een kulmassa liuskeisuutta vastaan. Naiden kahden suunnan diffuusiokertoimien
suhde oli 2.8 seka hairiopinnallisille etta ehjille naytteille. Edella mainituille suunnille
mitattujen permeabiliteettien suhde oli suurempi ehjille kivinaytteille (7 .4) kuin
hairiopinnallisille (1.8).
AVAINSANAT: He-kaasumenetelma, pyknometri, huokoisuus, diffusiviteetti,
permeabiliteetti, hairiovyohyke
ABSTRACT
Three experimental holes the size of deposition holes in a KBS-3 type repository (depth
7.5 m and diameter 1.5 m) were bored in hard granitic rock in the Research Tunnel at
Olkiluoto and the porosities, effective diffusivities and permeabilities of rock in the
excavation-disturbed zone were determined in a direction parallel to the disturbed
surface using permeability, through-diffusion and pycnometer techniques based on the
He-gas. Those properties had previously been determined in direction perpendicular to
the disturbed surface.
Permeability and diffusivity parallel to the rock orientation were found to be clearly
larger than in a direction perpendicular to the rock orientation. The porosity of disturbed
rock samples obtained by using He-pycnometry (0.45%) was clearly higher than that of
the undisturbed ones (0.24% ). The permeabilities and diffusion coefficients obtained for
the disturbed rock samples were also clearly higher than those obtained for the
undisturbed ones. The ratio between the average permeabilities of the disturbed and
undisturbed rock samples was 3.2, and the ratio between the diffusion coefficients was
3.1.
The permeabilities and diffusion coefficients were also clearly oriented, being larger in
the direction of the schistosity of the rock than at an angle of approximately 45° to the
schistocity. The ratio between the average diffusion coefficients in these two directions
(2.8) was the same in both the disturbed and the undisturbed rock samples, whereas the
ratio between the average permeabilities was larger in the undisturbed (7 .4) than in the
disturbed rock samples ( 1.8).
KEYWORDS: He-gas methods, pycnometer, porosity, diffusivity, permeability,
disturbed zone
1
CONTENTS:
PREFACE
TIIVISTELMA
ABSTRACT
1
INTRODUCTION ..................................................................................................3
2
SAMPLES ............................................................................................................5
2.1 Ring samples ............................................................................................. 5
2.2 Cubic samples ............................................................................................ 5
2.3 Sealing of the disturbed surface ................................................................. 7
3
POROSITY MEASUREMENTS ............................................................................9
3.1 General ...................................................................................................... 9
3.2 Drying of the samples ............................................................................... 10
3.3 Measuring techniques .............................................................................. 11
3.3.1 Pycnometer .................................................................................. 11
3.3.2 Grain volume ................................................................................ 11
3.3.3 Bulk volume .................................................................................. 12
3.4 Error analysis of the He-pycnometer measurements ................................ 13
3.4.1 Error propagation .......................................................................... 13
3.4.2 Standard deviation ........................................................................ 14
3.4.3 Calibration samples ...................................................................... 15
3.5 Results of porosity measurements ........................................................... 16
3.5.1 Cubic samples .............................................................................. 16
3.5.2 Test samples ................................................................................ 17
4
TROUGH-DIFFUSION MEASUREMENTS ......................................................... 19
4.1 Measuring techniques .............................................................................. 19
4.2 Ring samples ........................................................................................... 19
4.3 Cubic samples .......................................................................................... 21
4.4 Modelling .................................................................................................. 22
4.5 Results ..................................................................................................... 24
4.5.1 Sealing of the samples .................................................................. 24
4.5.2 Ring samples ................................................................................ 25
4.5.3 Cubic samples .............................................................................. 26
5
PERMEABILITY MEASUREMENTS ..................................................................29
5.1 Measuring techniques .............................................................................. 29
5.2 Interpretation ............................................................................................ 29
5.3 Results ..................................................................................................... 30
5.3.1 Ring samples ................................................................................ 30
5.3.2 Cubic samples .............................................................................. 31
6
CONCLUSIONS .................................................................................................33
REFERENCES ...........................................................................................................35
2
APPENDICES:
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
The drying curves for the cubic and test samples ...................... 37
The bulk volume determination ......................................... .40
Diffusivity measurements on the ring samples ........................ .42
Diffusivity measurements on the cubic samples ...................... .46
Permeability measurements on the ring samples ...................... 69
Permeability measurements on the cubic samples ..................... 71
3
1 INTRODUCTION
In a nuclear waste repository, rock in the excavation-disturbed zone adjacent to the
walls of deposition holes for waste canisters is a potential pathway of transport of
corrosive agents and radionuclides. Rock in this zone may also act as a mixing tank, or,
in the case of low axial conductivity and dead-end type radial fissures, efficiently sorb
and retard the radionuclides that diffuse through the bentonite buffer. Rock
characteristics in the excavation-disturbed zone may also play a role in saturation of the
bentonite buffer and in gas release. To assess the characteristics of rock in the disturbed
zone, investigations have taken place in three experimental holes of the size of
deposition holes (depth 7.5 m and diameter 1.5 m) in a KBS-3 type repository in hard
granitic rock in the Research Tunnel at Olkiluoto. Details of the boring technique
(Autio&Kirkkomaki 1996), previous characterisation of the excavation disturbance
caused by boring (Autio 1996, Autio&Siitari-Kauppi 1997), and the He-gas method
(V~HiHiinen et al. 1993, Hartikainen et al. 1994, Hartikainen et al. 1995a, b, Hartikainen
et al. 1996a, b) have been reported earlier. He-gas methods were used in this study to
establish the degree of rock disturbance in terms of porosity, effective diffusion
coefficient and permeability. Measurements were based on either the diffusion or flow
of helium through a rock sample saturated with nitrogen gas, and included porosity
determinations using He-gas pycnometry.
Two types of sample geometry were used in the He-gas measurements. Disc samples
with a central hole (i.e. rings) were used to establish the undirectional averaged
permeability and diffusion coefficient. Cubic samples were used to measure the same
properties in two different perpendicular directions.
5
2 SAMPLES
2.1
Ring samples
The shape and dimensions of the two ring samples from the Research Tunnel at
Olkiluoto, measured by the through-diffusion method, are shown in Figure 2.1-1. The
upper side of the sample comprised the disturbed zone sealed by fluorescent epoxy.
The intention by using this measuring geometry was to obtain results averaged over all
possible lateral directions, and thus independent of any possible orientational effects
caused by the structure of the samples. The accurate dimensions of the samples are
given in Table 2.1-1.
I
I
d
I(
I
I
>I
D
Figure 2.1-1. Ring sample.
Table 2.1-1. Dimensions of the peiforated disc samples D12 and D13.
Sample
D12
D13
2.2
h [mm]
31.8±0.5
31.2±0.5
D[mm]
89.3±0.5
89.5±0.5
d[mm]
38.1±0.5
38.3±0.5
Cubic samples
Parallelepiped samples were sawn from cylindrical core samples as shown in Figure
2.2-1. After measuring the porosity with the helium pycnometer, these samples were cut
into two approximately cubic parts as shown in Figure 2.2-2 so that one part included
the disturbed zone (Samples A) and the other part was intact rock (Samples B). Codings
of the samples are shown in Figures 2.2-3.
6
40 mm
40 mm
Figure 2.2-1. Sawing of cylindrical samples into parallelepiped samples.
Disturbed zone
D5.1 A
I~rnm
h
05.1
.........
a
05.1 B
WI~rnm
Figure 2.2-2. Further cutting into cubic samples.
Upper side of the sample cylinder
Direction arrows
Sample codes
Figure 2.2-3. Coding of the parallelepiped and cubic samples.
7
Table 2.2-1. Dimensions of the cubic samples.
In measurements perpendicular to the structural orientation
h [mm]
a[mm]
b [mm]
D5.1 A
39.5±0.5
29.3±0.5
40.0±0.5
D5.1 B
38.9±0.5
40.6±0.5
38.9±0.5
D 14.2 A
39.5±0.5
32.5±0.5
40.0±0.5
D 14.2 B
40.5±0.5
40.6±0.5
39.8±0.5
D 15.1 A
39.4±0.5
33.9±0.5
39.9±0.5
D 15.1 B
37.9±0.5
40.5±0.5
39.4±0.5
Sample
In measurements parallel to the structural orientation
h[mm]
a[mm]
b [mm]
D5.1 A
39.2±0.5
29.0±0.5
37.8±0.5
D5.1 B
38.7±0.5
40.6±0.5
36.8±0.5
D 14.2A
39.2±0.5
32.0±0.5
37.5±0.5
D 14.2 B
40.5±0.5
40.6±0.5
37.6±0.5
D 15.1 A
39.4±0.5
33.4±0.5
37.7±0.5
D 15.1 B
37.8±0.5
40.5±0.5
37.3±0.5
Sample
The detailed dimensions of the cubic samples are given in Table 2.2-1. The upper part
of the table shows the dimensions of the samples measured perpendicular to the
structural orientation, and the lower part those measured parallel to the structural
orientation. The dimensions are slightly different in the two cases because removal of
excessive epoxy was made in two phases, the second of which took place in between the
two measurements.
2.3
Sealing of the disturbed surface
The material used for sealing the disturbed surface was a fast-curing epoxy resin, brand
name Caldofix HQ by Struers NS, which is composed of two fluid components.
Caldofix has to be heated to at least 70°C to cure and it is characterised by minimal
shrinkage. The resin/hardener mixing ratio is 20/6. The pot life of the mixed resin at
20°C is 4 hours. The curing time at 70°C is 90 minutes. The gelation time when the
material begins to polymerise is approximately 50 minutes. Fluorescent dye, brand
name EpoDye by Struers, was mixed with the epoxy.
8
The resin and hardener were mixed at room temperature. Before carrying out the actual
sealing of the samples, the polymerisation time (assumed here to be 50 minutes) of the
specific batch was checked. The sealing procedure after drying of the samples was the
following:
1)
The sample is heated to 70°C.
2)
The dye (1.2 g) is mixed with the hardener (69.5 g).
3)
The two components of the epoxy (233 g resin and 69.5 g hardener)
are mixed together.
4)
The sample and the epoxy are kept in an oven at 70°C for 46 minutes.
5)
When 46 minutes have elapsed from the mixing of the epoxy, the
polymerising mixture is poured onto the disturbed surface of the rock
sample so that a layer of epoxy of less than 1 mm thick is formed.
6)
The coated sample is kept in an oven at 70°C until the resin is
complete!y cured.
The procedure described here was used for all rock samples taken from the Research
Tunnel at Olkiluoto. However, at the time of writing of this report, the exact penetration
depth of the epoxy sealant into the samples used was not measured. It will be
quantitatively investigated by fluorescent microscopy before the end of 1998. If needed,
the penetration depth of the epoxy can be adjusted by lengthening the settling time or by
using a different type of polymer.
9
3 POROSITY MEASUREMENTS
3.1
General
Porosity measurements were carried out using the He-gas pycnometer method which is
based on the equation of state of ideal gas. Helium gas is used because it is non-reactive
and penetrates easily small pores, and because it very accurately fulfils the ideal gas
law. Also, a porosity value obtained by helium gas will obviously be closer to that
measured in a He-gas diffusion experiment, than a value obtained by using some other
media such as water. The values obtained by He-gas pycnometry are complementary to
those of the diffusion measurements. The latter are quite insensitive to porosity because
it only appears in Equation 4.4-3 through parameters Da and h.
Before any measurements were made, samples were cleaned by pressurized air and
dried in a vacuum oven. After drying, grain (i.e. solid) volumes of the samples were
measured using a helium gas pycnometer developed in the Department of Physics at the
University of JyvaskyHi (Vgrain= Vbulk- V pore). Bulk volume determinations were based
on the water-immersion method. The procedure of porosity measurements is shown in
Figure 3.1-1.
After the first porosity measurements for the rectangular through-diffusion samples,
samples were cut into two halves. One half, which represented undisturbed rock, was
used as a reference sample for the second half which included the disturbed zone.
Vacuum drying at 45 °C,
weight measurements at
regular intervals
Grain volume measurement
by the helium-gas pycnometer
Bulk volume measurement
by the water-immersion
method
Figure 3.1-1. The procedure of porosity measurements.
10
3.2
Drying of the samples
All samples were dried in a vacuum oven at a temperature of 45°C. This slightly
elevated temperature is not expected to cause any damage to the rock structure. Before
drying, samples were carefully cleaned by pressurized air and weighed with a balance
in ambient conditions. In order to follow the drying process, samples were weighed
after suitable intervals. For weighing the temperature of the oven was switched back to
room temperature, the oven was filled with nitrogen, and the sample was left in the
nitrogen atmosphere for four hours. The purpose of nitrogen saturation of the samples
was to decrease the absorbtion of water vapour from the air. After weighing, vacuum
drying was immediately continued. The level and rate of drying were estimated from the
weight measurements by using a fit of two exponentials to the drying curve. An
example of the drying curves is shown in figure 3.2-1. All the drying curves measured
are given in Appendix A.
Drying of rock samples takes a long time. The samples from the Research Tunnel at
Olkiluoto of size 4x4x8 cm3 e.g. were dried for about 2500 hours. Drying time can be
significantly reduced by increasing the temperature, and it is suggested that the drying
temperature should be increased in the future to 105°C or, if alteration are expected to
occur, to 80°C.
40.992 ~~
I
40.990
I
m= 40 9608+0 0186
40.986
'
40.980
~
8
I
I__
56 841
'
e(-tJme/
\0 0123
'
413 029
>
'
· ··
e(-tJme/
.. .
.
. .
.
.
.
....
\
40.976
40.974
40.972
I
.. I···
. \
.. \.
~
tZl
~
'
:
40.984
,........, 40.978
I
1
. . .
40.988
40.982
I
.
40.970
40.968
\
'*·'\.
40.966
..
..
..
~
·~
40.964
.~
40.962
.
40.960
0
.
250
.
500
.
.
..
--
~ .....
.
750
..
"' ..
1000
time [h]
Figure 3.2-1. The drying curve of sample C9.1.
I
1250
1500
1750
2000
11
3.3
3.3.1
Measuring techniques
Pycnometer
The experimental arrangement of the pycnometer used in the porosity measurements is
shown in Figure 3 .3-1. The volumes of the cells, V R and Vs, are first determined by
using calibration samples. A polished aluminium calibration sample of volume V N is
inserted into the sample cell Vs, the whole system is evacuated, and the pressure Pv and
temperature T v are measured after stabilisation. The reference cell is then pressurised
with helium. The pressure PR and the temperature T R are measured after stabilisation,
whereafter the helium is allowed to expand into the measuring chamber. After
stabilisation, the resulting pressure Ps and temperature T s of the whole volume are
measured. The unknown volumes in the system can be determined when the volume
VN, pressures Pv, PR and Ps, and temperatures Tv, TR and Ts are known for at least two
calibration samples. The same procedure is then repeated on the sample to be measured.
~-----------------------
------------1
I
I
Data aquisition
I
---------------,
I
Figure 3.3-1. Experimental set-up of the He-pycnometer.
3.3.2
Grain volume
According to the ideal-gas law, the porosity of the sample can be determined when the
pressures Pv, PR and Ps, the temperatures T v, T R and Ts, the volumes of the cells VR
and Vs, and the bulk volume of the sample Vb are all known. The porosity Ep [%] can
then be expressed in the form
12
£
P
=
V -V
b
g ·100
V
,
(3.3-1)
b
where the grain volume Vg is given by
(3.3-2)
3.3.3
Bulk volume
Bulk volume was measured using the water-immersion method. The sample was
weighed in ambient conditions and then in water. The temperature of the water was also
measured to determine its density. The density of water Pw [kg/m3 ] as a function of
temperature T [°C] is given by [Kell G. S. 1967]
Pw
= 0,99995 + 0,00005 · T -7,545 ·10-6 · T 2 + 3,6131·10-8 • T 3 •
(3.3-3)
Using the difference in the two masses and the density of water, the bulk volume of the
sample can be determined from
(3.3-4)
where Illct is the mass of the sample in ambient conditions [kg], and mr is the mass of the
sample in water [kg].
a)
b)
33.102
22.898
33.101
c;
:§i
i22,896
33.101
<tl
fll
fll
E
<tl
E
33.100
33.100
-10
10
20
30
Time[s]
40
50
60
time[min]
Figure 3.3-2. The short time behaviour of a typical wet-weighing curve (a test sample)
(a), and the wet-weighing curve of sample L 10.1. (b).
13
The masses of the samples were determined with a Metier Toledo AT400 balance. The
balance resolution was 0.1 mg and measuring accuracy was 0.2 mg. The mass of the
sample at the moment of immersion was determined by using a polynomial fit to the
measured points. The mass of the sample grows rapidly during the measurement as
water penetrates the open pores. The time of stabilization of the balance is about one
minute which sets the first value measured (Figure 3.3-2a). Deionized water was used in
the immersion measurements to reduce bubble formation. An example of the wetweighing curves is shown in Figure 3.3-2b, where the first point (t=O) has been
extrapolated from the curve fitted from measured points. All the wet-weighing curves
measured are shown in Appendix B.
3.4
3.4.1
Error analysis of the He-pycnometer measurements
Error propagation
The general formula for error propagation in the dependent quantity q(x, ... ,z), with
independent uncertainties dx , ... ,dz in the measured quantities x, ... ,z, is given by
(3.4-1)
The effective porosities of the samples were determined from Equation (3.3-1) where
the grain volumes Vg were determined from Equation (3.3-2).
The uncertainties of the grain volumes were determined from Equation (3.4-1). The
relevant quantities and their uncertainties are explained in Table 3.4-1.
Table 3.4-1. Uncertainties of the quantities involved.
Uncertainty of the volume of the measuring cell
d Vs
0.002
[cm3 ]
Uncertainty of
Uncertainty of
Uncertainty of
Uncertainty of
Uncertainty of
Uncertainty of
Uncertainty of
d VR
dPR
d TR
d Ts
dPs
dPv
dTv
0.002
10
0.02
0.02
10
10
0.02
[cm3 ]
[Pa]
the volume of the reference cell
the pressure in the reference cell
the temperature in the reference cell
the temperature in the measuring cell
the pressure in the measuring cell
the pressure in the whole system
the temperature in the whole system
[K]
[K]
[Pa]
[Pa]
[K]
14
The uncertainties in volumes Vs and VR were estimated from the standard deviations in
the calibration measurements. All pressures were measured by the same Beamex PC
106 pressure calibrator. Its accuracy was 10 Pa. Temperature measurements were made
by J-type (lron-Constantan) thermocouples, and the accuracy of the measurements was
0.02 Kin the measuring range 292-298 K.
The partial differentials involved are given by
avg
avs
--·dV
s
= dVs,
(3.4-2)
(3.4-3)
(3.4-4)
(3.4-5)
(3.4-6)
(3.4-7)
(3.4-8)
(3.4-9)
3.4.2
Standard deviation
Uncertainties in the poros1t1es of the samples were also estimated statistically by
standard deviation of the independent measurements. The formula of the standard
deviation (j:x used here is given by
15
8- =
X
where
L,.~ (x.- :X)2
t=J
(3.4-10)
I
N(N -1)
is the result of an independent measurement,
N is the number of the measurements done,
x is the average of the measured values Xi.
X;
The term N -1 in the denominator is used because N 2 has a tendency to underestimate
the uncertainty for small N.
A summary of the uncertainties for the cubic samples is given in Table 3.4-2. Samples
A have a disturbed zone. Samples without a label A or B are the original uncut samples.
Table 3.4-2. Summary of uncertainties for the cubic samples.
Porosity [0/o]
SAMPLE
~-4_2_1
l
014.2
015.1
05.1A
05.18
014.2A
014.28
015.1A
015.18
3.4.3
0.32
0.25
0.30
0.44
0.22
0.42
0.29
0.49
0.22
Uncertainty
by error
propagation
± 0.020
± 0.012
± 0.018
± 0.024
± 0.025
± 0.012
± 0.008
± 0.028
± 0.006
Uncertainty by
standard
deviation
± 0.011
± 0.004
± 0.004
± 0.036
± 0.023
± 0.007
± 0.004
± 0.015
± 0.004
Calibration samples
Measuring uncertainties in the volumes of the cylindrical aluminium calibration samples
were also determined by Equation (3.4-1). Their total difference dVb is
dmd dm
(m-mv)dp
dVb = - - - - -1 - _ __;____;__
p
p
p2
(3.4-11)
where dllld and dmf both were 0.2 mg.
With an uncertainty in the water density dp = ± 0.1% in the used temperature range, the
maximum uncertainty in Vb was within± 0.2%.
16
3.5
3.5.1
Results of porosity measurements
Cubic samples
Porosity was measured for the three orginal parallelepiped and six cubic samples,
described in Section 2.2, and the results are shown in Table 3.5-1. The original samples
and cubic samples with label A include a disturbed zone.
It is evident from these results that the behaviour of samples D5 .1 and D 14.2 is
consistent under cutting in two, because the porosities of the original samples are very
close to the averages of the corresponding A and B samples. It is also evident that the
disturbed zone has a markedly increased porosity. If one assumes that the depth of the
disturbed zone is approximately 6 mm [Autio 1996], it is easy to estimate from the
measured porosities that the average porosity of the disturbed zone in sample D5 .1 is
about 1.5%, and that in sample D14.2 about 2.5%.
In the case of sample D15.1, the porosity of the original sample is not consistent with
those of its halves. Either there has been a technical complication in the measurements
which was left unnoticed, or the porosity of especially the intact sample B has increased
in the cutting.
The uncertainty in the measurements done with the He-pycnometer were estimated by
the general formula for error propagation [Taylor 1997] and by statistical analysis. The
accuracy of porosity by this formula was within± 12%, whereas the standard deviations
of repeated measurements were within± 10%.
Table 3.5-1. Bulk volumes, grain volumes and porosities of the rectangular and cubic
samples.
Sample
D 5.1
D 14.2
D 15.1
D5.1 A
D5.1 B
D 14.2 A
D 14.2 B
D 15.1 A
D 15.1 B
Bulk volume
10-6 [m3 ]
125.409
130.080
126.146
60.143
59.235
61.035
58.956
60.425
63.362
vb
Grain volume V~ Porosity £p
10-6 [m3 ]
[%]
125.008
0.32±0.02
129.687
0.30±0.01
125.829
0.25±0.02
59.880
0.44±0.04
59.103
0.22±0.03
60.780
0.42±0.01
58.783
0.29±0.01
60.130
0.49±0.03
63.224
0.22±0.01
17
The main source of possible systematic errors is in the calibration of the pycnometer. As
explained before, calibration was done with two calibration samples whose volumes
were known very accurately. The volumes of the calibration samples were determined
by the water immersion method in the same way as the bulk volumes of the rock
samples. This may have caused a systematic error in the porosity measurements
depending on the measuring accuracy of the water-immersion method. Measuring
uncertainties in the volumes of the calibration samples were estimated to be within
±0.2% of the volume.
The He-pycnometer method is sensitive to errors in the measurement of both pressure
and temperature. The temperature measurement is based on thermocouples and
computer-based data acquisition. The measuring system provides a resolution of 0.01 K
which means that the uncertainty in temperature is ± 0.02 K. This uncertainty and the
possible systematic error in calibration affect most the total error.
3.5.2
Test samples
In addition to the cubic through-diffusion samples, the porosities of eight drill-core
samples were measured by the He-pycnometer method. The samples used were about
25 mm thick slices of drill cores with a diameter of about 27 mm. These samples were
also taken from the full-scale experimetal deposition holes in the Research Tunnel at
Olkiluoto. Four of the samples included a disturbed zone from the surfaces of the hole,
and these samples are denoted by an affix 1 in the Table 3.5-2 below.
Before the porosity measurements, the samples were dried as described in Section 3.2.
The drying curves are shown in Appendix A.
The bulk and grain volume measurements and the error analysis were done as described
in the previous sections, and the results together with the related porosities are given in
Table 3.5-2. The error values shown were found by the error propagation formula
Equation 3 .4-1.
Table 3.5-2. Bulk volumes, grain volumes and porosities of the test samples by the Hepycnometer method.
Sample
c 9.1
C9.2
D 16.1
D 16.2
L 10.1
L 10.2
L 11.1
L 11.2
wd [gl
40.962
39.312
38.956
40.584
37.292
37.508
40.054
30.900
Wa[g]
26.285
25.160
25.244
26.383
22.963
23.196
26.110
26.020
3
[cm ]
14.716
14.183
13.747
14.232
14.421
14.346
13.978
13.910
Vbulk
V
3
grain [cm
14.591
14.105
13.649
14.155
14.331
14.275
13.901
13.861
]
tp[%]
0.85 ± 0.07
0.55 ± 0.07
0.71 ± 0.07
0.54±0.07
0.62±0.07
0.49 ± 0.07
0.55 ± 0.07
0.35 ±0.07
18
19
4 TROUGH-DIFFUSION MEASUREMENTS
4.1
Measuring techniques
In the through-diffusion measurements the injection chamber is first flushed with
nitrogen and then evacuated by using a vacuum pump. This is continued until the Heconcentration from the air in the sample is stabilized at a very low level. After
evacuation the pressure of the injection chamber will be less than 0.08 bar.
During the evacuation, helium flows through the injection loop. After the evacuation,
the loop containing helium is connected to the injection chamber by using a 6-way valve
and an injector valve. At the same time the other end of the loop is connected to
nitrogen flow that goes through a pressure equalizer. Because of this, only the helium in
the loop (5 ml) will be injected. Helium is sucked from the loop to the injection
chamber by the vacuum. After connecting the loop to the injection chamber, the system
is let to stabilize for two minutes. In that time all helium is transferred to the injection
chamber, and the valve is turned off. Helium now diffuses through the sample to the
sniffer chamber, which is continuously flushed with nitrogen. The helium concentration
of this nitrogen is then measured with a Leybold helium-leak tester. During the throughdiffusion, the injection chamber is sealed. The whole through-diffusion measurement
takes about 1200 minutes. The purity of the helium used is 99.995% and that of the
nitrogen is 99.9%. It is important in the through-diffusion method that there is no
pressure difference between the injection and sniffer chambers, and that helium
migrates through the sample only by diffusion.
The sealing material used in the through-diffusion and permeability measurements is
He-tight Terostat by Wiirth GmbH. Terostat is widely used in vacuum technology, and
in these measurements it is used between the boundary surfaces of the sample and the
measuring chamber (Figures 4.2-1 and 4.3-2). The sealing tests of Terostat are reported
in Section 4.5.1.
4.2
Ring samples
In the case of ring samples the helium pulse is injected into the hole at the centre of the
sample. The outer cylindrical surface is flushed with nitrogen to remove the helium
molecules that have diffused through the sample, and the helium concentration of the
nitrogen is then measured. The geometry of .the measuring chamber is shown in Figure
4.2-1, and the experimental set-up is shown in Figure 4.2-2. The approximate
dimensions of the samples are: hole diameter 38 mm, core diameter 90 mm, length of
core 32 mm. The exact dimensions of the samples are given in Section 2.
20
60mm
90mm
Terostat sealing
89.4mm
1/16 capillary
Figure 4.2-1. The measuring chamber for ring samples.
nitrogen
chamber
selector valve
injector valve
Pump
Figure 4.2-2. The experimental set-up for ring samples.
21
4.3
Cubic samples
In principle, measurements on the cubic samples are similar to those on the ring
samples. In the case of cubic samples, the helium pulse is injected into the injection
chamber so that one rectangular face of the sample is exposed to a concentration of
helium. The opposite face of the sample is continuously flushed with nitrogen in order
to collect the helium molecules that have diffused through the sample. The helium
concentration of the nitrogen is then measured. Samples are kept at ambient temperature
and pressure. The experimental set-up for cubic samples is shown in Figure 4.3-1, and
some details of the measuring chamber are shown in Figure 4.3-2.
Pump
selector valve
injector valve
He
Figure 4.3-1. The experimental set-up for cubic samples
22
' - - - - - - Rock sample
?Omm
' - - - - - - Aluminiun
Terostat sealing
I(
)I
40mm
Figure 4.3-2. The aluminium parts that transfonn the cube to a cylindrical fonn, and the
end plates of the measuring chamber.
4.4
Modelling
Modelling of the through-diffusion measurements is based on the solution of an
appropriate diffusion equation. Because of the planar geometry of the samples and
reflective boundary conditions in the transverse directions, one can use a onedimensional approximation, and the diffusion equation to be applied for the
concentration of helium C(x,t) [kg/m3] is simply
ac
at
Ep
ax
2
'
(4.4-1)
where t [s] is time, De [m2/s] is the effective diffusion coefficient, Ep is the porosity and
x is the position inside the sample.
The boundary conditions in the direction of helium transport are such that the
concentration of helium in the injection chamber is assumed to decrease according to
the diffused amount. It is also assumed that there is no sorption and that the helium
concentration at the outer surface of the sample is zero due to continuous flushing with
nitrogen.
23
Porosity Ep and the effective diffusion coefficient De [m 21s] can both be determined from
the breakthrough curves of helium by fitting the curves with the relevant solution of
Equation (4.4-1 ). In this one-dimensional approximation it is in fact possible to derive
(Vaatainen et al. 1993, Carslaw 1959) an analytical expression for the mass flow of
helium through the sample,
m= - D A ac I
e
dx
[kg 1 s] ,
(4.4-2)
x=l
in the form
(4.4-3)
where A [m2] is the cross-sectional area of the sample, lllo [kg] is the mass of the
injected helium, Da = De/Ep [m2/s] is the apparent diffusion coefficient, h = epfs, s [m]
being the average length of the injection cell, an, n = 1, 2, ... , are the roots of
atan(al) = h [1/m], and 1 [m] is the average length of the sample. The average length of
the injection cell (s) and the length of the sample (1) are both needed as input
parameters.
Once the above mentioned parameters have been fixed, the theoretical model is fitted to
the breakthrough curves by varying the effective diffusion coefficient De and the
porosity Ep. Another possibility is to infer the value of porosity from independent
measurements, in which case the effective diffusion coefficient is the only parameter to
be fitted.
Although measurements are carried out in the gas phase, the corresponding diffusion
coefficients for the water-saturated case can be derived. This is based on the fact that in
both cases, the diffusion equation is the same apart from the actual values of the
diffusion coefficients. Significant changes in the pore space are not expected to occur
upon drying of the samples.
For helium diffusing in free nitrogen gas at 22°C, the diffusion coefficient De(N2) is
6.75*10-5 m 2/s, and for helium diffusing in free water at 22°C the diffusion coefficient
De(HzO) is 5.8* 10-9 m 21s. The ratio De(HzO) I De(Nz) is therefore 1111 600. Scaling of
the measured diffusion coefficients by this factor should provide a good estimate of the
corresponding coefficients for helium atoms diffusing in rock samples saturated with
water. If other inert molecules are considered, their mass and size should also be taken
into account. For typical molecules consisting of only a few atoms, the diffusion
coefficient in free water is close to 2* 10-9 m 21s. Measurements can therefore be scaled
to the diffusion coefficients of these heavier molecules in water-saturated samples by
using an approximate scaling factor of 1135 000 (Hartikainen et al. 1996b).
24
X 10-4
051A1_3; De= 1.50e-9, ep1 = 0.12'¥..
X 10-4
D51A1_3; De= l.SOe-9, ep2 = 0.21%
0=-~~~--~--~~--~
0
10
20
30
50
60
Time(min(
30
Time(min)
40
50
Figure 4.4-1. Two different ways to determine the porosity.
In practice the whole breakthrough curves of helium were measured and the results
were fitted by model calculations. In these fits the effective diffusion coefficient and the
porosity of the sample were used as the fitting parameters. The decay part of the
breakthrough curve determines the effective diffusion coefficient while porosity is
decisive for the rising part of the curve. In most cases there is no ambiguity as to the
value of the diffusion coefficient, but the early rise and the levelling off of the
breakthrough curve may be sensitive to inhomogenities within the sample. These
inhomogenities are not included in the model, and the calculated and measured curves
usually have a slightly different form at short times. There is therefore no unique way to
do the fitting there, and two different ways of fitting were used for a consistency check.
The first method was to fit the model curve to the very beginning of the measured
breakthrough curve (Figure 4.4-1.). Porosities defined in this way were labelled by Ept·
The other method used was to fit the model curve at the turning point in the
breakthrough curve (Figure 4.4-1.). Porosities defined in this way were labelled by £p 2 .
One expects that if there are microcracks in the sample, Ept will underestimate the
porosity. Otherwise the two values should be rather similar.
4.5
4.5.1
Results
Sealing of the samples
To begin with one had to make sure that terostat sealing between the rock surface and
the measuring chamber was He-tight. This test was carried out by comparing terostat
sealing with sealing by He-tight epoxy resin. The measurements were done by using the
through-diffusion method (Chapter 4.1 ). The results of these measurements are shown
in Table 4.5-1. The first four measurements were done with terostat sealing. In the last
two measurements the surface of the ring sample was covered with an epoxy resin. The
space between the aluminium parts and the epoxy resin were filled with terostat. It is
evident from these results that there is no detectable effect on the measured quantities
caused by sealing.
25
Table 4.5-l.Results of the Terostat-Epoxy -comparison for ring sample D12.
Sealing
Terostat
2
De [m /s]
Ep [%]
5.75*10-~
0.20
0.15
0.15
0.16
0.17
0.18
9
Epoxy resin
4.5.2
5.30*105.10* 10-9
5.00*10-9
5.60*10- 9
5.60*10-9
Ring samples
Two ring samples were measured and the average diffusion coefficient of sample D 12
was 6.12·10-9 m 2/s and that of sample D13 was 5.55·10-9 m 2/s. The porosity of sample
D12 was 0.16% and that of sample D13 0.15%. The data of six measurements are given
in Table 4.5-2. Diffusion coefficients are also given for typical bigger molecules (M) in
samples saturated by water (scaled by 1/35000). The measured and fitted breakthrough
curves are shown in Appendix C.
Table 4.5-2. Porosities and effective diffusion coefficients of the ring samples.
Sample/
Meas. no.
D12/1
/2
/3
/4
/5
/6
Average:
D13/1
/2
/3
/4
/5
/6
Average:
Porosity Ep
[%]
0.18
0.17
0.13
0.14
0.18
0.18
0.16
0.16
0.16
0.14
0.13
0.17
0.14
0.15
De [m2/s]
(He/N2)
6.75·10-9
6.05·10-9
6.45·10-9
6.20·10-9
5.70·10-9
5.55·10-9
6.12·10-9
6.50·10-9
6.00·10-9
4.60·10-9
4.60·10-9
6.00·10-9
5.60·10-9
5.55·10-9
De [m2/s]
(M/H20)
1.93·10- 13
1.73·10- 13
1.84·10- 13
1.77·10- 13
1.63·10- 13
1.59·10- 13
1.75·10-13
1.86·10- 13
1.71·10- 13
1.31·10- 13
1.31·10- 13
1.71·10- 13
1.60·10-U
1.59·10-13
26
4.5.3
Cubic samples
All cubic samples were measured by through diffusion of helium in the two main
directions as shown in Figure 4.5-1. Both flow directions for each orientation were
measured.
Direction
.l
Figure 4.5-1. The four measuring directions.
The measured effective diffusion coefficient De (He/N2) of the cubic samples varied
between 0.54·10-9 and 8.50·10-9 m2/s (Appendix D). The measured porosities Ep by
through-diffusion method of the samples were in the range 0.12- 0.62% (Appendix D).
There seems to be a rather clear orientation dependence in the measured diffusion
coefficients due to the structure of the samples, and also in the connectivity of the pore
space, as indicated by the apparent orientation dependence of the porosity. The averages
of the measured values for each sample and direction are shown in Table 4.5-3. The all
measured and fitted breakthrough curves with the determined parameters are shown in
Appendix D.
The directions perpendicular to the structural orientation of the sample (directions 3 and
4) are labelled by _l and those parallel to the structural orientation (directions 1 and 2)
by t. The actual flow direction within either structural direction did not affect the
measured values. Therefore the values for directions 1 and 2 (similarly for directions 3
and 4) have not been distinguished in calculating the averages (see Figure 4.5-1).
It can be seen from the results shown in Table 4.5-3 that the effective diffusion
coefficients are larger for the samples with a disturbed zone (samples A) than for the
intact samples (samples B). Also, the diffusion coefficients are smaller in direction _l
than in direction ! , and thus there is evidence of structure dependent orientational
effects. Porosities are also bigger in direction ! but there is no clear difference between
samples A and B. Porosities Ept and £p2 are close to each other for the intact samples B,
but differ somewhat for samples A with a disturbed zone. This is expected to be a result
of inhomogeneties appearing in samples A.
27
Table 4.5-3. The effective diffusion coefficients and porosities for the cubic samples.
Sample
Direction
De [m2/s]
(He/N2)
De [m2/s]
(M/H20)
Ept [%]
Ep2 [%]
DS.l
A
..l
2.38·10-9
7.38·10-9
6.79·10- 14
21.1·10- 14
0.22
0.30
0.34
0.54
0.60·10-9
2.17·10-9
1.70·10- 14
6.21·10- 14
0.15
0.28
0.19
0.29
Direction
De [m2 /s]
(He/N2)
De [m /s]
(M/H20)
tpl [%]
Ep2 [%]
..l
2.03·10-9
4.17·10-9
5.80·10- 14
11.9·10- 14
0.19
0.20
0.29
0.30
0.79·10- 9
2.16·10-9
2.26·10- 14
6.16·10- 14
0.19
0.40
0.23
0.45
t
B
..l
t
Sample
2
D14.2
A
t
B
..l
t
Sample
Direction
2
De [m /s]
(He/N2)
De [m /s]
(M/H20)
Ept [%]
Ep2 [%]
DlS.l
A
..l
1.68·10-9
5.31·10-9
4.80·10- 14
15.2·10- 14
0.13
0.22
0.25
0.38
1.17·10-9
2.76·10-9
3.34·10- 14
7.87·10- 14
0.25
0.31
0.29
0.39
t
B
..l
t
2
The samples were first measured in the ..l direction, after which they were further sawed
before doing the measurements in direction 1.
29
5 PERMEABILITY MEASUREMENTS
5.1
Measuring techniques
The experimental set-up of permeability measurements is similar to that of the throughdiffusion measurements.
The surface of the sample in the injection cell is exposed to an elevated pressure of
helium. This is the inner surface of the central hole in the case of the ring samples and
one of the rectangular faces in the case of the cubic samples. A constant pressure
difference is maintained between the opposite surfaces. The outer surface of the sample
is flushed with nitrogen, and the concentration of helium in the nitrogen is measured.
The flow rate of helium through the sample is measured for several pressure differences.
For each pressure difference, the flow rate is let to stabilize before reading its value. The
purity of the helium used was 99.995% and that of the nitrogen 99.9%.
5.2
Interpretation
In the case when a pressure difference exists across the sample, helium transport
through the sample is mediated by diffusion and also by flow induced by the pressure
gradient. According to Pick's and d' Arcy's laws for a compressible fluid, the volume
flow of helium through the sample is then given by (Dullien 1979)
(5.2-1)
where Q [m3/s] is the flow rate through the sample, Qdiff [m3/s] is the flow rate due to
diffusion only, K [m2] is the permeability coefficient, A [m2] is the cross-sectional area
of the sample, fl [Pas] is the dynamic viscosity of helium gas, 1 [m] is the length of the
sample, p2 [Pa] is the pressure of helium in the injection cell, and p 1 [Pa] is the pressure
of helium at the outlet. The total flow rate through the sample is measured for several
pressure differences, and the permeability coefficient is determined from a fit to the
measured points by Equation (5.2-1) (Figure 5.2-1).
30
/
/
1.2X10.
~
:u
:[
1.0x10"
1.ox10·•
5
(j)
i
a.ox10•
8.0x10"
9
~
2
~ 6.0X10~
6.0X10"
<I)
I
<I)
I
9
4.0x10''
4.0X10•
10
20
JO
40
50
0.0
S.OX10'
Time [min)
1 .OX10'
1.SX10'
2.0X10'
2.5x10'
3.0X10'
3.5x10'
Pressure difference [Pa)
Figure 5.2-1. Permeability measurement and fitted curve.
The measured permeabilities, K [m2], can be used to determine the hydraulic
conductivities, KH [m/s], of the samples. These are given by (Dullien 1979)
(5.2-2)
where p is the density of water (p = 997.08 kg/m3 at 25°C (Kell 1967)), g is the
acceleration of gravity at sea level (g = 9.81 m/s 2 ), and Jl is the dynamic viscosity of
water (J.L = 8.9042*10-4 kg/ms at 25°C (Weast 1974-1975)).
5.3
5.3.1
Results
Ring samples
The averages of the measured permeabilities and hydraulic conductivities, KH, for the
ring sample are shown in Table 5.3-1. The measured permeability coefficients of the
ring samples varied between 4.61·10- 19 and 1.19·10- 18 m2 . The error in the permeability
coefficients was within 10%. The measured and fitted permeability curves for the ring
samples are shown in Appendix E.
Table 5.3-1. Measured permeabilities and hydraulic conductivities of the ring samples.
Sample
D12
D13
K[m2 ]
1.04·10- 18
5.25·10- 19
KH [m/s]
1.14·10- 11
5.77·10- 12
31
5.3.2
Cubic samples
The permeabilities of the cubic samples varied between 0.26·10- 19 and 8.83·10- 19 m2 .
Permeabilities were larger for the samples with a disturbed zone, and larger in direction !
than in direction _L The permeability coefficients did not correlate exactly with the
diffusion coefficients. This means that there are some differences between the channels
that play an important role in diffusion and in permeability. The average values of these
quantities for each sample and direction are shown in Table 5.3-2. The measured and fitted
permeability curves for the cubic samples are shown in Appendix F.
Table 5.3-2. Measured permeability coefficients and hydraulic conductivities of the cubic
samples.
Direction
K [m2 ]
KH [m/s]
j_
2.92·10- 19
6.62·10- 19
3.21·10- 12
7.27·10- 12
!
0.35·10- 19
3.03·10- 19
0.38·10- 12
3.33·10- 12
Sample
D14.2
Direction
K [m2 ]
KH [m/s]
A
j_
5.44·10- 19
7.50·10- 19
5.98·10- 12
8.24·10- 12
!
0.26·10- 19
3.16·10- 19
0.29·10- 12
3.47·10- 12
Direction
K [m2 ]
KH [m/s]
j_
4.12·10- 19
8.83·10- 19
4.53·10- 12
9.70·10- 12
0.73·10- 19
3.68·10- 1\}
0.80·10- 12
4.04·10- 12
Sample
DS.l
A
!
B
j_
!
B
Sample
Dl5.1
A
j_
!
B
j_
t
32
33
6
CONCLUSIONS
Previous studies (Hartikainen et al. 1995b, Autio 1996, Autio&Siitari-Kauppi 1997)
have shown that there is a disturbed zone caused by boring adjacent to the experimental
full scale deposition holes in the Research Tunnel at Olkiluoto. The properties of the
disturbed zone in a direction perpendicular to the disturbed surface have previously
been measured using also He-gas methods (Autio et al. 1998, Hartikainen et al. 1995b).
In this study the degree of disturbance was established in terms of porosity, effective
diffusion coefficient and permeability parallel to the disturbed surface. The directions
parallel to the disturbed surface are obviously of more importance for migration than the
direction perpendicular to it, because there is a continuous disturbed zone of
microfracturing and porosity parallel to the surface forming a continuous migration
pathway. The porosity of disturbed rock samples obtained by using He-pycnometry
(0.45%) was clearly higher than that of the undisturbed ones (0.24% ). By assuming the
depth of approximately 6 mm for the disturbed zone, found in the previous similar
analyses, this means that the average porosity of the actual zone was about 1-2%. The
permeabilities and diffusion coefficients obtained for the disturbed rock samples were
also clearly higher than those obtained for the undisturbed ones. The ratio between the
average permeabilities of the disturbed and undisturbed rock samples was 3.2, and the
ratio between the diffusion coefficients was 3.1, even for the relatively large samples
used (so that the disturbed zone only comprised a small part of sample A).
The permeabilities and diffusion coefficients were also clearly oriented, being larger in
the direction of the schistosity of the rock than at an angle of approximately 45° to the
schistocity. The ratio between the average diffusion coefficients in these two directions
(2.8) was the same in both the disturbed and the undisturbed rock samples, whereas the
ratio between the average permeabilities was larger in the undisturbed (7 .4) than in the
disturbed rock samples ( 1.8). The averages of the measured values for the cubic samples
are shown in Table 6-1. The original data are given in Appendices D and F.
The values obtained for permeability and diffusion coefficient depend on the
penetration of the epoxy based sealing material in the pores and fractures in the
disturbed surface, preventing rapid gas flow along the immediate surface layer. The
degree of penetration of epoxy in the disturbed surface of rock samples will later be
quantitatively studied by fluoroscene microscopy.
34
Table 6-1. The averages of the measured values for the cubic samples.
[m2/s] tpl [%)
De
(He/N2)
K [m2]
Direction
Sample
Total
A
B
3.83·10-9
1.61·10-9
0.21
0.26
0.35
0.31
5.91·10- 19
1.87·10- 19
t
A
B
5.62·10-l)
2.36·10-9
0.24
0.33
0.41
0.38
7.65·10-ll)
A
B
2.03·10-9
0.85·10-9
0.18
0.19
0.29
0.24
4.16·10- 19
0.45·10- 19
j_
tp2 [%]
3.29·10- 19
Another conclusion which can be drawn from the present analysis is that the structure of
rock induces marked orientation dependence in the migration properties. In the samples
with a disturbed zone, there was a difference in the diffusitivity and permeability in the
two main directions by a factor of 2 - 4. In the intact samples, however, there was an
order of magnitude difference in the permeability, while in the diffusitivity the
difference was again a factor of two or three. In the disturbed zone orientational effects
were weaker.
In through-diffusion measurements one should thus pay attention to the oritentational
effects due to the structure of rock. Otherwise it is not possible to relate the measured
values with representative averages. It is obvious that the ring geometry provides a
convenient way to directly measure values which are averages over all possible
migration directions.
35
REFERENCES
Autio, J., Characterization of the excavation disturbance caused by boring of the
experimental full scale deposition holes at TVO-Research Tunnel, Report POSIV A96-09, Posiva Oy, Helsinki and similar report TR 97-24 in SKB's (Svensk
Kambraslehantering AB) report series, 1996
Autio, J ., Kirkkomaki, T, Boring offull scale deposition holes using a novel dry blind
boring method. Report POSIV A-96-07, Posiva Oy, Helsinki and similar report PR
D-96-030 in SKB 's (Svensk Kambraslehantering AB) report series, 1996
Autio, J., Siitari-Kauppi, M., in Scientific Basis for Nuclear Waste Management XXI,
edited by I.G. McKinley&C. McCombie. (Mater.Res.Soc.Proc 506 , Warrendale,
PA,1997) pp. 597-604
Autio, J., Siitari-Kauppi, M., Timonen, J., Hartikainen, K.& Hartikainen, J.,
determination of the porosity, permeability and diffusitivity of rock in the
excavation-disturbed zone around full-scale deposition holes using the 14 C-PMMA
and He-gas methods. Contam. Hydr. 763, (1998)
Carslaw, H.S., Jaeger, J.C., Conduction of Heat in Solids, 2nd. Ed., Oxford University
Press, Oxford, 1959
Dullien, F.A.L., Porous Media Fluid Transport and Pore Structure,Academic Press,
Inc., San Diego, California, 1979
Hartikainen, K., Vaatainen, K., Hautojarvi, A., and Timonen, J ., in Scientific Basis
for Nuclear Waste Management XVII, edited by A. Barkatt & R. Van Konynenburg
(Mater.Res.Soc. Proc., Pittsburgh, PA, 1994) pp. 821-826
Hartikainen, K., Hautojarvi, A., Pietarila, H. and Timonen, J ., in Scientific Basis for
Nuclear Waste Management XVIII, edited by T. Murakami and R.C. Ewing (Mater.
Res. Soc. Proc., Pittsburgh, PA, 1995a) pp. 435-440
Hartikainen, K., Hautojarvi, A., Pietarila, H. and Timonen, J., Permeability and
diffusivity measurements with the He-gas method of disturbed zone in rock samples
cored from the full-scale experimental deposition holes in the TVO research tunnel,
Report YJT-95-19, Nuclear Waste Commission of Finnish Power Companies, and
similar report AR D-95-018 in SKB's report series, 1995b
Hartikainen, K., Pietarila, H., Rasilainen, K., Nordman, H., Ruskeenniemi, T.,
Holtta, P., Siitari-Kauppi, M., and Timonen, J., Characterization of the altered
zone around a fracture in Palmottu natural analogue, pp. 839-846 in Scientific
Basis for Nuclear Waste Management XIX, W. M. Murphy and D. A. Knecht (eds.),
MRS, Pittsburgh, 1996a
Hartikainen, J., Hartikainen, K., Hautojarvi, A., Kuoppamaki, K. and Timonen,
J., Helium gas methods for rock characteristics and matrix diffusion. Report
Posiva-96-22. Posiva Oy, Helsinki, 1996b
36
Kell G. S., Precise Presentation of Volume Properties of Water at One Atmosphere,
Journal of Chemical and Engineering Data, Vol.12 (1967) pp.66-69
Taylor, J.R., An Introduction to Error Analysis, 2nd. Ed., 1997
Vaatainen, K., Timonen, J., Hautojarvi, A., in Symp. Scientific Basis for Nuclear
Waste Management XVI, edited by C.G. Interrante & R.T. Pabalan (Mater. Res.
Soc. Proc., Pittsburgh, PA, 1993) pp. 851-856
Weast, R.C., (ed.), Handbook of Chemistry and Physics, 55th. Ed., p. F49, Chemical
Rubber Comppany Press, Cleveland, Ohio, 1974-1975
37
Appendix A
The drying curves for the cubic samples and test samples
D 5.1
drying cmve
m= 350,9169+0,1465 e(-unVSoJ.4459>
-ftl--'----+----'----f---,----+---:-----ii---
3~1.06
363900
~----- -- ---<----- ----- f-------- __ ,___ --- -----f-- __ 111_ '=/-~-3,6_99_6:+:0_, 1:8_52 e< :~~&7.9282)
363.8'7~ 1\
3~1.04 +--'I~_\'_\~,-~.t--~-~--~-~f~---~--:-~-~-,-f~-~--~-~--:-~-~-~-1-f--~-~-~-~l-~-~--~--~fl--­
¥'
--·\-+----------""'"··-i··----·---·f----·----+· .. ·----·-f----------;·-----·-·--f
3~1.01 -+-__;__ _\~-:-i~-:-..~-::-~-::.-:--::_-:-~,-:-..~-:--~-:-..~-:-__~:.,_~-:---~~-~-:--~-:-..~-:-__~-::-~1--­
::§
363.81~
\.
351.00
~ 350.98
=
----------1'··-----
'r.
~ 363.-::-75
....
t---------:-----------1~~----i----------f---------i---·----f---i--------+
"'h
35094 +----'----f-~"-'-...,:-r--~rl-----'---l------'----+-3509l
_______, , -
::§ 363.800 + - - _ , - - - f - - - + - - - + - - - + - - t - - . . ; - - - + - -
t----------+-·-''•··:--l---------<----------1-------·<---------l------<-----------f
35096
:
,J.-------,::·----------I----------<,-----------I---------+----------I-------·---<-----------f
363.8~0
363.750
.....
+:J:~
1000
D 14.2A ch-ying ctu-ve
~.®
-t-___,--+--+--4-~-t-~-=-+16_8~,6~2_0_9+0
__~,0_7_3r2-~--~-+--~~_>
1 7
4
drying cmve
6
m= 168,8667+0,0878l.,._JJ 2J
-1-----+--+-+---t--+--+---+--+-+---t--+-1~.94~ -HIV.-----_.----_---_---·+-·--_-----+·-:--_·-_---t--·--_---·-+--·i-_----t-----+--'_____---+
____
---_-----+-i-·-_----t--_----+-:---t-----:--------1-------->------+-------•-------t -----!------- t------+-------1---------:--------168.937 +--'
__ -\1------+:---__-__ -___t---+--t----:----+-~-j----+-__-__ -i
__ ----------~;---____-___ _
-----\+-·----- ---·---->------- ----
168922 ·----·\------·
:§ 168915
~
1~.690
----·- _______ ,_____ _
1~.675 +---'-\--'--+--'--4-~-t----'---+------''---+--+---
----~-\--i--------l--------:-------+-------·-------+-------<--------l-------i---------l--------:---------
1~.007-!-~--+--+--4-~-t---+--+----i~-+--+---
:§
~
::::::::-:-__.---;---::::-_----:---~·-_----:--_,--+.:---:--_---~:-:=
1~.ooo +------------<-x-\-·-_------t-__,__-------+--_--_-----<·-·_--_------+-·-__,__---_----+---------<·--,...---_--_-·-t--+-
=
: : : : :::--_--;·:,__'---_-'<--\--:---:--:--_----:+_----:---=-
----"·---·-r·------
-111\-r-____---<_+------+-+--4---<c--t---+---+-->----t---+--
168.~2~---------i---+---+--4----i------t--+--+--l---t----+---
--- _______ ,_ ------ --------,---------
---·---+----- ---------·-----
-------+\---- ---
4000
time [h]
1~.952
1~.930
3000
2000
time [h]
D 5.1 A
: ......
363."'00 +----'-----f------'----l--~-=+===::t::==l---
4000
3000
2000
____ -., __
\.-----
+-------;------!"-~:------+---+----+--f----+---+--
363.715
+---+---l---:------t~__:--::__j~==-i---;-.......=~=:==
1000
1--
1~.6~2
1----- ~\---t--------->-·----+-------·--------+-------·-------+------·--------1-------->-------­
+----------i___,,rt---i---4----i------t----i---+----------il---+---+---
1~-~5+---:--___~1-~~---~+---------1--_--:---t---~--1--~--+-~---
~~-~--~~---_-___4_~..-..-...~l-----...+...-...-;-1-----------~---------~+--------j-------------~:----_-_.. _
::::: +--t---__-__-1-__-__->-i
__ ~
...
_,_____,_--+--+--+-----1--t----t---+--
168.87i -+---;--___-+
___ -_------:----~~~---'k------.----:----f_-----+-----:-----+--------:-----_-----+----_______--;_____
_
1~.622 i-------<--------1-------->-------~-~+-..._--.---·--------l--------·--------l-------:-------·-
::::;+-.._-___
-_+,__.
__-.. -. .. ..
1~.870 t==t:=·::::;·-~---=·--:::;-+=·--=·--4--~=---~
.. :t'-~---~---+:-·::!·----=·-·l=:~:::::;~~;;;;;;;;;;;;:9
lOO
lOO
400
300
500
lOO
300
lOO
600
.<oo
400
600
time [h]
time [h]
D 14.2 B chyi.ng cmve
D 5.1 B ch-ying cmve
m= 177,5408+0,0625
m= 165,2704+0,0627 e(-timo'll 6.0)
16.<J37
:
·······t··-----
---j-·-------------j-----·--------:-----
177.600
16.<330 -ll\r--____...,_1i-----------t:::-::-.:-::-.:::-::-.t:::::::.::::::j:::-::-::::.:::-::-~-::-.:::-::-.~::::::t-::-:::~_:::-::-::::
165J22 +-\----\+-:-+-~-+--+--+--+---1--+---+--t----
+-: :-: -:-\:~i->1:\,---:__+.-...-.. ~- - - - - t_-_-__-_.. ~- - - - -+j....--..
---i
..
--+_f----------
~ 16.<JOO +--,i---\+----i-----t---i---t---+-----!-----i----t--,__-
= 165.292 +--:---+\.__,____,__t-----;----t---t----1--+---t--:---
-------~---- -- ---~----·+-----·-·------+------i--------f-------i-------+-----·-i---------
16.<.285 +--,i---+-...,.,."<:......_-t---+---'l---__,_-----l-_ _,__--t-----<--
16~.lT.,,_ -t---+'--+-+---1--.......~""""'--t-__,_--+-----<~-t---+-;
- - - _,.._
------- - -·-
---1-----·-
16~.2~0 +----.~-1---+--l-~---l--=--i-=l===::::;:=::f==;i==;
500
100
lOO
300
400
600
time [h)
-------~--------
;
:
:
m.•" \~···············
1-::i.~~u;
-1
__ -__ -___-__ +-,__- __ -. . _-+_1--·------·-t---:-------·
----·-·1······-·
9
e<-umo'lll.5S )
····-··t········
1-::7592 -+__,-\t--t----+---;--t----t---+--,____-+---+--t-----;---
1 -+----i-----+---i---+--+---1--+---+--:----16~Jl.< +----_-\-'t-i--
::§ WJ07
1\
·······+·-····· --------~-------
:§
~ 1-::-7..<70
:
+·
i
+---c\---f-------;--+--,__-+---+--f---+-+---'-.....
-------+ .............. f-·-·-·- -------1----·-.................. -------+--------
--t\·-\
10 562
.
1-----------·-- __ \.,..._t:---------l-------+------t·------<------+-------<--------1--------:--------1-::!555
+--:---+-____,.,......_---f-----'--+---'--+-_._-f----+--
10..<47 +--'----+---'--l---~-""""=-----1---'---+------'--+-~-
l ~- - =:·- ·-~,-~-t.~·-·~--~--f~---~--~--~--~---~--:+~~~---~-~~
..~--=--::::+:~~=-t··:··=-·-~-=--·=--~---
1-::-7.~40-+
0
. . ..
lOO
200
300
time [h]
400
500
600
38
Appendix A
The drying curves for the cubic samples and test samples
Drying curve
drying ctuve
m= 351,3983+0,1779 e(-limo'8S 6•318 2J
3~U7~
+---t---+-----i--f---...,___:_-t---__:__,..--!--
3~15~0 +1-'l\.----'---+----'--+----:---+--'---l-3~U2~ -l----_-'t',_;.--+------i----+-----;.----11---..;---+---
\
35UOO -1----_----~
......- - + - - - ; - - f - - . . . _ - - l - - - + - - - - 1 - -
f----------1\---
:§
~ 351.4~5
~
·~
::::
~ m=40,9630+0,0277l'i"' 9' 197
40.984
~
~ :~::::~:\:==::====:====:====:====:===·=:====:====
.=!! 40.976-+-t._:- - + - - - - 1 - - - + - - - - 1 - - - + - - - - 1 - - - + - - -
"'~
tt.
3~1.42~ ~---··-----+-·-------I-~-~
:
+--+--+--+'-!-·-=-=~--:....;.--~--=-···=···::j--==i=-.J..-1000
2000
3000
.• .I
•
40.974-+-~.~~-+----!-_.-+-~--1---+-~--1-__ --1
..-~
...
\..
.
·~
40.968 I··
40.966
40.964
40.962
40.960
3~1.4~0
351.400
C9.1
m = 40,9608+0,0186ltintcl56.8411+0,0123 eH'"""413 '0291
- - - · - · - - - - ·..F··-·····-·-··T·······-~
____ ____:__!---
!:i 40.972
40.970
'\..
...
40 992
'
40.990
.......
. ..
...
. •·
' ...--..... . .
..
.. ·~!L:.:····· ...•..........
.. :.
. ....
250
0
500
750
1000
1250
1500
1750
2000
time[h]
4000
t.ime [h]
D 15.1 A
drying cmve
Drying curve
00 00
_"5)
170.l 5 i-.--.,..--..,.--,--.,..----,---;:.m:...=~17:._::0:.z.:,1~6::..7.=-1+0~,0::.:8~9~9..:e~<-~>_""',....'_
.....'-------- ........ ,
-- ....... , ....... ·------<
----·>·1~0.250
170.242
1!'0..23~
39.336
39 334
.
39.332
··\~--+------- ·····---~-----·- ···-----~---·-·· ····---~-------- -------+------- --------~·-·······
-~-·.._·-\-l"._;--_
.. --+---'--_..._..+.._.._......;..._..._.. _.. ~--~--+---'--+--+--
PO.ll~ +-·--_--_.. ~:.l,:
170.212
+--·--->i-~-------\1-\·--i---+.._.._···-:-·'_·--_·-+--·_---+<-_-._..-1.. _.._..._...;.."l··_--_
.. +--;.--
~ 170.20~ +--;.----Pt---i-------+-.._
.. _...+..._.._---_·f----i--+--;.--+--:--:::: 170.197 +---+-·---+---\-\.. -+---+---i---+---+---l--i-·---j--..1--------'--...,__
...._....
........:________ ,\-f------- .... ·+-- ...... i .......
-----+-
170.190 +--i----+....-'
.. 'ti~~-------~---...-..+_,_-_---11---+-..-+.-___-..---"+.. -+----i'---170.182 +--i----+---i--~ol-------;.-+-..;--t--+--+----i'---170.17~ -1--'---+-·-'--~-----------~-~-'
...-....
-~-""'-·,..... ·-j---'-'--+--'---+---'---
.... ··.
_·I
C9.2
._
1225 9841
'
rr1\ •·••• _. . m = 39,3126+0,0222l""''
--·
· ··
..
39.330 \
..
39.328 -+-.-\--_--1---+--'---1-~-+---'+---'+-~--+-~
f-----:..-+---':---+--'---l--'---l----:..1'70..220 +..._.._.. ,....
:--\_)-- lc-f--+--+--+--+--+---j---i-·_
.. _...-+._---_-_..,__
..._.._····
- - , ·.·._.
:§
...
m= 39,3093+0,0107 e<1.,.,n4 '0061+0,0162 e<-tiln'l564.5 191
~\
39.326
:§
39.324
~ 39.322
6
..... ,. ------ ........f------- .....~--f-~f--t=L-
39.320
39.318
39.316
39.314
170.167 i=:::::;~=t=:t=i=::t=:t:::t:=t:::t:=t::::j=:::;
100
200
300
400
500
600
39.312
39.310
\.
-+--~
·\. +--~--··--~---··-+---'--t--'--.:-1---'-f--\
•..
.•
.. . . . "- ··. ..
·~
..•
. ~
..
•.
..
.
....
~--- .................... .
~:;:::+=:;::
'~:t::::;:::=t::::::;:'--~~--=--;:::::j:--:.._::::;=~:=:t=:::::::·~
+
250
time [h]
. ...
....
500
750
1000
1250
1500
1750
2000
time [h]
D 15.1 B
dJying cmve
m= 164,1687+0,0703
Drying curve
e(-lim<lll<,JJJ)
,r·_...__
..
1~.235~\-\-r-,-+__
.. _...~
.. 'r---+--~---~-·---+-,--..-~-·~·-_···_
..+j··_··_
...-+._···_--_-......
38.982
1~.227~·\~'---+----'---+-~---+--..;.......--i----'----l---'----
···\·+······· ....... +·--···· ·--····+······ ......+..............;...............+...... ..
1~.ll0
38.98o
38 ·978
1~.212 +--··_··_-\·,\-:.._..._.. +_,__.. :_..~·t_.._·:_--+'·:_--:_·:_.-::_-:_..:_-~·-:_.._.. :,_:·_.. :_..-l·~..:_·:_··~:-:_..:_·4·!:_·:_··:_-t":_"__
.. ..
··t\-.. ,........;......
:§ 164.20~
~ 1~.19~
::::
......
.......+······· --···-- ,....
~ ............,
.. j ........ , ........l.. -.... -; ........ f ........,......... f ........, ...... ..
+--+---+--i--..,.,_+-.......,.--+-+---i--+--+--+--~---····-'------ .. 1-........ c:_ ......
+---... ;........ ,....... .; ........ .
jN::----·f--.....;......
1~.11~ r.::_::.:.::_;:.::.~::.:..::.~'~~::.:..::.::;.::.::.:..::.r.:~:.:::...:_ =+~-·::. ;>--=--=.. -:f.::·--=--=.. :=~
-:r:
1~.167~
0
100
38.976-l+--+---+-'---+----jl-~-+--+--___:_.+-_;_-
~---+------1--'---1---'+.......:..-1--~·-1---'--1----
bil 38.970 4-~:!Jt.,...---j---J-----ii---,--1-~,-f.--,,-+---..-+-..---
..l\,,....;....... j .......... ; .......l........ ;........f-------i--------1---- ... .; ....... .
1~.190 +---'----+---',.:--+-~--+-..;.......---1r--'---l---'----
1~.182
lOO
300
t.ime [h)
400
500
Dl6.1
38.974 -++._
·i·.
.....•
·.·.
.•.
38.972 +-1,1'• .• -.. - + - - + - - - + - - , - + - - - ' - - + - - - - + - - + - - -
+-----+ .. --- ..1--.. ···-·- .. ··--+------..:······-+···· .. --:....... ..
+-\
f ....... , .....
A
~~ =38,9S5+0,ods eH'In'lsf.ws>+0,0133 e<.. ~4t5.977}-+--I
I
I , . L
.
+---m= 38,9576+0,0235l"""i' 44 '8141'--+-~-+-~-+-----
600
-;;; 38.968 -+-4\-~:. --1---1--___:_---if.----1-___:_,-1-----1-~-f---­
~
38.966 +---1;.-,, _-1---+
...-.-'--.::-.-+.. -_1---'-.---i~_-_~... -----+
...-'---._+--~..
38.964 -+----'1~-•• +---+--:-'---+------i!--...:..-+----+-'---.-+----.
-.
.
38.962 -+--..-!,ll~..,_~-- +,~-+---,-l--~-1-_- ..--..-+---..+---38.960 -+-------1....:.....-'1...
_....-l.t:--6.-.
----'----if--.-l-----'--l--..,--l-----'--l--..,-38.958 -+--..-+-..--'.4.....
. ::>....,..,j~~-.~
...~.~-~-i_.~~~-:"""•.'""':.~: l---o---1..-.-'..-.-.1..-.~---..-.
38.956 +--t---+-:-+__.,.t9F'8'~-t--=.J=;;:::;:;:=l:==
38.954 +--.---1--.--+-r---+--r-jc---r---+---.-+---r--t--..---.
250
500
1000
1250
1500
750
1750
2000
time[h)
39
Appendix A
The drying curves for the cubic samples and test samples
Drying curve
"-
Drying curve
D16.2
40.071
40.610 ~m= 40,~804+0,~109 c(·r<i73.358).:0,o192 ~(-timo/625 ../ssr--40.608 ~
I . 1
.1.
40 "606 Ir~-~1m = 40,5846+0,0243 CHom<nlL504
.
..
:~::
40600
.
40.598
:§ 40.596
~ 40.594
'·
•
I
!
.
I
L ..
63 90
~m= 40,0515+0,0077 erm</
40.070
I
Lll.l
I . 638I
' 1)+0,0120 e141md '12 1)
:::63-+~1---t---f---
I m= 40~0545-Hi,o 156 et-1
40.068
.t.c::·md22=··
:::
..
J
1
!
\'.
...
I
I
.
40.064~~-t---t-~-r-~~~-r---+~-+---­
•.
\.1
ia...
::~:
:§ 40.062 +-_,.r-t---+---i---:--1--:--+---+--+-----
.
~ 40.060-f--4-:---t-f---f---~---:---+-----'--+~-+----
~
40.588 -+---t----=--t..:c.•.~-•. -.+-----'--1--+--:---f--+-~··_
40.586-t-~-t--+----"-'-"111~-+---1--+-~-t---
40.584 -t--'--f---t---'--f-~--""'·"t·•;;;:-+-'._._.·..:...·'+'·. :. .·:cc•·.:..·'+'·..:...··:cc·.:..··c:.·
~~:~:~=·=:=·~·====~====··~==:··=~==·=-·=~-. . ;=·~.· ==~====~=·=··;·=~
250
500
750
1000
1250
1500
1750
40.052 -t--.--f-..---t----i--..,f---i-~--T-+--r--+---i=T=.....-,
250
1000
0
500
750
1250
1500
1750
2000
2000
time[h]
time[h]
Drying curve
"I
.
1215641'
4
31' 4451
m= 3~,29134,0031 cr""'
)+0,0021 e( Und9 '
I
I
Drying curve
LlO.l
...
'·
39.916
37.296+-----1...:m'"--:-=-"3C:,7F,2"'-92::.:3::_:+'-'i0F,004:_--_:.1o_e"'1Hf-Hn<f7-l-.36~3f----t-......,--f----
39.914
39.912
.I . . . I..
.. .
.I
r----- m= 39, 8962+0, 0048 eT'""'
5 25
l .. · . I .
.2 l ~,0140
~m= 39,9000+{),0140 e<·•md359'8311
1
<·•m<~
Lll.2
I
' l
855 061
1
·
..
39.910 +--'i\':.. --t.---+------'i---:--l---+---+--:-+-----
:§
~
39.908 -t---='t-1---t----r--~--+---+--+---37.294
00
'a.
-;;; 39.906 +----f""'c---+---i--...,.._-1----,.-+--.---+--+--~-
~
·~·-·~·. .,.··---t---,--t-----+
. ,.
-·-·-+
···--:-+----
39.904 -t--+-·- . .:..·
1
-~
39.902 +----l---+---'41k-~--t-~-+-~--+-~+-~39.900 I
..
······· . .
~::.;i_'·.:.
--~r---..
500
250
750
1000
1250
1500
1750
39.898-t------1---t---t-----+--+---+----"=--t-o;;;:_=
2000
250
time [h]
500
750
1000
time [h]
Drying curve
37.516
"-
L10.2
m= 3/5075-Hl,0044/''...,m· 104>~,0036 e<-ti.;..,n'fl,oo8 >
1
I········ I·· ...
l ...
m= 37,5091+0,0062 e(·tmV94, 389)
:§ 37.512 +\-":------if---~.......i.-+---+---t------1--~--'-
~
250
500
750
1000
time [h]
1250
1500
1750
2000
1250
1500
1750
2000
40
Appendix B
The bulk volume determinations
D 5.1
hulk vohune deteunination
D 14.2 Bulk volume determination
~~::: -l---'---f-----'--J.----'-·-··1--··_···+-'-+----+-·--1··f-..._..;-,.._.+.-..y+-~--- ~-·: : ; : ·:::-:::f~=--·+:_····
- -1.
...
22~.83~ ~-'---1-----'-----1-----'-1---.;_~--'----l
__ f--.y..-'-:-.....,....:::::.....J-'---I---'--22~.830
____:_________ +··
.:.........
-l---'--f--'--l-----'-l--+--l---i--,*':::..;....-+---+---i-i--+--'+---~-------!---------·---------+·-
22<.82~ ~-+---1-__-___.;..i-J.---i-___ l--~-+,.,.._....._::__. . -i_+---1---i--+-+----1-i---1--i---
22~.820 ~-----'-+------1--__-___-'-;....-+.-.. y.-'.
:--""
__ ~
__...:
__-'-;____-+
__-__--'_.:___ --1
__ f.-___-__;-;__-__ +
__-___+.:_-___-!_-___-__:-___-___+_-___+__-____ _
:§ 22~.81~
,,
..,. . . . . . . ;. ._;
~ m.810 .....:.... ... )' __ ·····:- . _ ···+
-
--!-- .. -·--·:·---
22~.80~
--·+···
-l---i---I-P.----1-i--+--+-+--+--+-+--+----i-1-+-+--+---. . . -. t
.. - .... -!
. -- . ----! ---- ---- -·- ---- ---22~.800 +--+--A----+-1-;.._-1-...;-+-+-+--+-+--;-j-.;.-+--+---~----.
~~;: rtL~;~;.;.:;~
;:
+
10
ti.me[min]
,
12
,
14
233.940 ~ ....., .... -~ .....;...... ~ .....;.... .f- .. -<i·-- ... j ..... ; ..... ----j----- -----~~:d.~-233. 935 ~-'--l---'--l--'--l---'----1---+--+---+-~~--+--+--+-+-233.930
i
./ ..
~
:_~V:.. ;..... 1..... ;...
233.925
...../
V
··-+/··•
233.920 ..... ··-·
Vc:...; .... jf .....;..... j ...... ; ..... j ..... ; ..... j ...•. ; .•..• l·---·<--··l---··i----·
233. 915 -l--'--1-4L=-+---'----l---'---+---'--l--'--+---'--l-----'---+----'--
····· ... [7
233.910 -~----,j~~-l---i-ll----ii--l-i--+-+--+-+-+--i--+--i--233.905 )
_
....
233 900
•
16
0
18
D 5.1 A bulk vohune detennination
108.9r
-j----~~j
108~0-l--'---l----'---l----+-...-..--~-~---------~:.."-~-~-l--+--108.927 -l----+--l------i-__-_-1
__ 1___-___...:yi-.
___,.
__ ~-i--l--+--+--+---
.... y. .....
108.920
108.Jq
14
16
18
bulkvohune deteuninati.on
t---------i----------J.---------f---------l----~---1---------i----------l----------~---------·
~ 108.1~0 ~--+--•./,E.
..._.---+--+----+--+----+--+---+--
108910 ~b7~--------;:In~~~-=~1~08~,9~l~O~g~---------+·f-_--_-----l-------~--+-~--~--+--.
0
108.148
108.146
I-------; ........
6
10
'/
108.144
·/xnl· = 108,143
g-I
·
10
ll
time [min]
D 5.1 B
12
::::
-----/------l--------f------·1--------f-----·+------i-------+---·---<-----·+-------:.........
108.912
8
10
ti.me[min]
V
-----·+/------+-
108.91~
6
+-
:§ 108.152 -1----_;____.j...__-!,./L..
/_·..j..._-+---1--+---1--+--
------+----- ./7:___ ,·_ ..... j ........ ; ....... j ........ ; ......... f....... ,........ f ........, ...... .
108.917
4
2
g
108.1~6 t ......... ;......... +......... ;......... l......... .;, ........ f~-----+---------'---------·
108~2-1--+-----1---+--+--+--1--+--+-~~~--+---
108.922
'
::::: --------+------- -------+-------- --------+-------- --------+-------~
108.93~ -1--'-----l----'---___-__-+
__-___-__ -'
__ ,--+--_-'-,.-...-...+-....-...-'-;.-.7...-+v--..-::;
...~.+""..=.. -
~
'
--·fm~=233.901
D 14.2 A
t--------C-------I-------->-------1···--·--·f---·--·+-------i--------lf------<-------l-------~~---~
:§108.92~~~~=+~~~t/~~=i~=t~t=~~j[~~~
,,
j ..... ; ..... l----!----l----i----·
time (min]
D 14.2 B
bulk vohune detemrination
106 190
.
t------+--------l-------+------1-------·i-----·+-----:':------+----··i'·-·--·--l~
::::: ~-::.-:-:.-:-_.,~_-::-:-:..i.-:-:..-::~_-:-:-::.-:-:tl-:-:.-::~_-::-:-:..-:-+f---:-:_-::~.-::-:-:...-+f[?=+?-----_:,....,
.. "'
___...
__f:l_=-_____--'"-..-
113.96~
yj........;.....
106.176 ~-------7-:;..,..~..-...t.-::-:-:~_-:-:_-::-:-:jt-:-:..-::t.-:-:-:-..j~-:-:.-::t,_-::-::.t-::-:-:.~~---::-:-..t-::.-::~.-::-::.-:::
106.174 -l--l-'----+---'---+---'--+--'--+--'--+----'--~ 106,PI ~- ..........
106.172 -h£.-;._...:..:.-.J..--i---1----+-+-+--+--i---+--+--
-/-1n...,
bulk vohune detennin.11tion
-----··-r-·----- --------:------- -------:-------- -------:--------
~ ....... , ......... !........, ....... j .......+:
106.184 ~--------~-------l ......... ;....... !.........; ....... +brr----1------·;________ l....... ,........ ..
106.182
---~-:§
1------- ;................
-+------·i--------1-----· j ....... -f-.......;....... ..
,, 106.180 -l----+---1--#:.___+--+--+-+--+---+--+-----i-~
1------- "------ !'./''"/"-·'··-----·1--------'-------+--------:--------f-------:------+·-----+-------106.178 -l----'---~L...-'--+----'---+--'--+---!--+---:-I-------c--/·1--------f---·---·j- .. -- ... f.....,.+ ....... ;....... f ....... {....... -f-.......;........ .
....... , .......
----~
f-;_;;IF21-------:... .
113.96~
~--! ....... ; ......... ! ......... .:. ........ .
::::
J~-~~-,~~--~J·~~--~~f-~~--..~..1-.L!.·~~---·
,,_'._.. _---j:~~:.:.'l~~j:~:.:_j~·~:.:.t:.:.~j~:.:.=
:§ 113.958
,,,,
§
........j. ....... J.........
-~~------_.__------~---------....--YL~---_---J:.:.~·:.:.c':.:.~.t:.:.·:.:.:.:.'c:.:.·~t~:.:.·~c.~:.:.l:.:.~J~:.:.=
_/
~ -------~/-j ........c....... j........ ~--------J.------~-----·+-----·+------il-------+--------
1139 5
113.9~3
113.9~0 ··;f:.
113.948 /J .... .:. ....... I------·--'-------I--------'-------+------'------+·------:-----·+------+-------·
m;;o ~ 113,947 ~
113.94~ -J..-._=..;.---1--....;:....--1---;r------l---+--+---;~-+--+---,
10
time [min]
ll
6
time [nun]
10
ll
41
Appendix B
The bulk volume determinations
D 15.1
D 15.1 B
bulk vohune detenniuntion
:::::
_:_______ ·-+- ____;______ ·--+-······:________ +········:_________ f .... %
+--+--+-__+-j... +_-__.__. ;,_-__-__ f-__-___+-!_-_+
__-__ -+_,_-___--1_______ +--,j_-+
____-7-+-_,____-+~----j-·t""··----'~"-=-...-+-,____ _
22~58~ +--+--l----+---t-+-t-+--+--+--t--+---....-4---j--f-t---+-22!'.!'80 +----+---!-------+-!-_···-+------!·:·_--_--1--·----+-!·_·---+-_·--+·:_---=··-,~~-""~'---t-·
_··-+·----+·:-_-----~-->--·-·--+·----+~---22~.~-::-!' -----:-----22~-~90
ll~57o -----:-----
:§ 22~.56~
~
·---·:----- -
m560
22~ 5 ~ ~
m5~0
·:: :.:::
vf
1049~2
----7
. .,._ _
40
~
~
-
: :::::::·_
A
i
10
12
14
16
:;r~: ······--f-------4--·······-------+---·-··i-····-·+······-i-------- ·-··--·· :·-···
~nl = 104,939 g···-
i
i
i
t---··--~-------l----··-·'··-----il-----·--·-····-+-·----!----___.--...~4-·------·-----
1@JJ~+---t----+--~-t----+--r-~~-~-+---r---
··-····+-··· ·K·····-·
/
:§1@Jl7+---~-+-~~+-~-~-~--~-~-+-~~­
!·-------:-------· ·-----.Y·-i-·-····+
'-·--·-if----·-+·----+------<··-----+·-·····-·:·····---·
·······f······· /+······ ······+······ f·······
······· ······+············-·····
1@Jll+---~~~~-+-~-~-~---~-~-+-~~-
·······t·11'-l -·--····•,······+-------i···-···+···-·--i--------1····-·+······1·--·--·-i-----·--·
_ _-___
1@J~+_-____-j/~-~ +-~---r--+-~r-~--~--~-+--~-1®J18+-~~-+---i---+--+---r--+---t---+---+-~~-
109,314 g--
1@J1~1C~~=f==~==t=~==~==+==4===t==f=~~~
10
time [min)
-······i··-··-·· -···-· ; ...
10
time [min]
bnl.kvolnmedetennination
i
L -~n;,.;; =
..
0
1@JJ2 ······-+---··-- ···-····f--·--·--·-··-!·--··---·----··· ····
1@J3o t-------·•---··--+-------f·-·····i-·-··)./-+-··----'·-----+-----·'·--·---·t·--···-.:--------·
~ 1@Jl~
·--·-------f·-·-<··------1-·-·---7-----·
.:/r-------j--------•-·--··+·--····i-------l------+·-·--+------~---------
1049J8+-~~-+---i---l----+---+---+---l----i---+--i~~
18
1@JJ7+---t----+--~--t----+--r-+----t-~~~+----~~:~---
::
_____ _ _____
1049~+.~+---+---t---+-___,.-~-+---1----;----+---~-
time [min)
D 15.1
~ i·------:-------·1-··-·--·>~--7~-------->·---·+--
104946
104942
11----im;;o = 225,536 g--
22~-~J~ +--i-~-r----1----r~I-T---+--i--t---i--+--+---t-it---t---i----,
~~
1049
104944+---r--~L___,__+--+-~-+---+-~-+----,..._-
·-·+/-----!---·
:;t::: --·--i-----
~
7___
:
.• --- .,
v---
:
1049~0 ~-~~--~~--~--:-..r~~-:-~--~~-j+----/--· """_t::-.::-.-:-_::-.~-~.~-::--~-~-~::--~::-.::-.~r-~.:=:
+----t---¥--t---+----:-t----:--+----t--+----;----+___,_--t____,,..._+---t--
m.w
m.~
----/--
~
{--------:-----··+·------:-----·-+··---->-·---·-+--·-··-<·---_..,..,--·L·--"'.c'f-----1·-··--
----V---V---
-----!-----
bulk vohune detennination
12
12
42
Appendix C
Diffusivity measurements on the ring samples
D 12; De= 6.75e-9, ep = 0.18%
D 12; De= 6.75e-9, ep = 0.18%
2.5
0.5
0.5
8
10
time[min]
12
14
16
18
20
100
200
300
400
500
600
time[min]
700
800
900
1000
D 12; De= 6.05e-9, ep = 0.17%
D 12; De= 6.05e-9, ep = 0.17%
~
lJ:
1
0.5
0
~
8
10
Time[min]
12
14
16
18
20
200
400
600
Time[min]
800
1000
1200
3
D 12; De= 6.45e-9, ep = 0.13%
X 103~~---.-----,,-----,------,------,------,-----,,
D 12; De= 6.45e-9, ep = 0.13%
2.5
0.5
0.5
8
10
Time[min]
12
14
16
18
20
200
400
600
800
Time [min]
1000
1200
1400
43
Appendix C
Diffusivity measurements on the ring samples
X
10-3
D 12; De = 6.20e-9, ep = 0.14%
X
3~T----,--~----.----,--~----.----,---.----.---,
D 12; De= 6.20e-9, ep = 0.14%
10-3
3~-----r------r------r----~,-----,-----~------,
2.5
c
~
c
~
'i'1.5
'i'1.5
0
,g
J,
1:c
J:
0.5
0.5
8
10
Time[min]
12
14
16
18
20
200
D 12; De= 5.70e-9, ep = 0.18%
400
600
800
Time [min]
1000
1200
1400
1200
1400
D 12; De= 5.70e-9, ep = 0.18%
c1.5
~
3:
,g
-1.
1
0.5
8
10
Time[min]
12
14
16
18
20
3
D 12; De= 5.55e-9, ep = 0.18%
X 102.5~T----,--~----.----,---.----.----,---,----.---,
r
c1.5
~
200
X
400
600
800
Time[min]
1000
D 12; De= 5.55e-9, ep = 0.18%
10-3
2.5,.-------..,.-------r------,-------,r--------.-----~-----,
3:
,g
-1.
1
0.5
0.5
J
8
10
Time[min]
12
14
16
18
20
200
400
600
800
Time[min]
1000
1200
1400
44
Appendix C
Diffusivity measurements on the ring samples
d13; De= 6.50e-9, ep = 0.16%
d13; De = 6.50e-9, ep = 0.16%
x1o-"
3~------.-----~r------,-------.-------.------,
-
(
2.5
c
~
--;1.5
.g
::c
"'
0.5
0.5
J
-1
4
5
Time[min]
200
d13; De= 6.00e-9, ep = 0.16%
_ X 10-3
25
--...
400
600
Time[min]
800
1000
1200
d13; De= 6.00e-9, ep = 0.16%
..---.......
..,..-:-.......
c1.5
~
~
Ql
::c
~
1
0.5
.J
-1
0
4
5
Time(min]
200
d13; De= 4.60e-9, ep = 0.14%
20 X 10-4
20
400
600
Time[min]
800
1000
1200
d13; De= 4.60e-9, ep = 0.14%
X 10-4
18
16
14
.Ec
14
12
c:12
.E
2::.10
:::.1o
s:
.g
Ql
::c
~
"'
8
::c
8
4
0
J
-1
0
4
5
Time [min]
7
200
400
600
Time[min]
800
1000
1200
45
Appendix C
Diffusivity measurements on the ring samples
X
20
d13; De= 4.60e-9, ep = 0.13%
d13; De= 4.60e-9, ep = 0.13%
10-4
18
16
14
12
c
.E
~10
~
C1l
J:
4
J
4
5
nme[min]
-1
2.5 X
200
7
600
800
1000
1200
Time[min]
d13; De= 6.00e-9, ep = 0.17%
d13; De = 6.00e-9, ep = 0.17%
10-3
400
c1.5
;[
~
~
1
0.5
J
4
-1
5
0
200
400
Time[min]
d13; De= 5.60e-9, ep = 0.14%
X 10-3
600
800
1000
1200
Time[min]
2.5~~----~---.--~--~,---.---~---.---.---.---.
3
d13; De= 5.60e-9, ep = 0.14%
X 102.5 ...--------y--------.-------,------~--------.--------,
c1.5
;[
~
C1l
J:
1
0.5
0
-1
J
0
4
5
Time [min]
9
200
400
600
Time[min]
800
1000
1200
46
AppendixD
Diffusivity measurements on the cubic samples
D 5.1 A lJ 1
D 5.1 Al12
W51A1_a; De 1.67e-9, ep2 = 0.29%
W51A1_2; De= 2.48e-9, ep2 = 0.35%
0~--~----~----~----~----L---~----~----~
0
200
400
600
800
1000
1200
1400
1600
0~--~~--~-----L----~----~----L---~----~
0
200
400
600
Time[min]
800
1000
1200
1400
1600
Time [min]
W51A1_a; De 1.67e-9, ep1 = 0.18%
4
W51 A1_2; De = 2.48e--9, ep 1 = 0.20%
X 10
16~~----~----~------~------~----~----~
r
14
12
10
-
06L------~----~------~----~~-----L----~
10
15
20
25
0
30
10
20
30
40
50
60
Time[min]
Time [min]
4
W51A1_2; De= 2.489-9, ep2 = 0.35%
X 10
16~~----~----~------~------~------~-----,
W51A1_a; De 1.67e-9, ep2 = 0.29%
14
12
0~------L-----~------~------~----~~----~
30
Tlme[mln]
40
50
60
0
10
20
30
Time[min]
40
50
60
47
Appendix D
Diffusivity measurements on the cubic samples
D 5.1 A lJ 3
D 5.1 A lJ 4
W51A2_2; De= 3.70e-9, ep2 = 0.43%
W51 A2_3, De = 1.669-9, ep2 = 0.27%
0~--~-----L----~----~--~-----L----J---~
200
400
600
800
1000
1200
0
1600
1400
200
400
600
Time [min]
1000
1200
1400
1600
W51A2_3, De= 1.669-9, ep1 = 0.14%
W51A2_2; De= 3.70e-9, ep1 = 0.35%
c
800
Time [min]
1.5
~
~
~
1
0.5
10
15
20
Time[mln]
25
30
35
15
Time(min]
40
25
30
50
60
W51A2_3, De= 1.669-9, ep2 = 0.27%
W51A2_2; De= 3.70e-9, ep2 = 0.43%
c
20
-
1.5
c
~
~
6
~
~
<ll
~
I
0.5
0
J
0
10
15
20
Time [min]
25
30
35
40
0
10
20
30
Time[mln]
40
48
AppendixD
Diffusivity measurements on the cubic samples
D 5.1 A !/1
D 5.1 A !/2
W51A3_2; De= 6.72e-9, ep2 = 0.53%
W51A3_3; De= 7.56e-9, ep2 = 0.57%
500
nme[min]
X
10-3
W51A3_2; De= 6.72e-9, ep1 = 0.26%
X
r
1.5
'"E'
~
~
1000
1500
Time[min]
10-3
W51A3_3; De= 7.56e-9, ep1 = 0.29%
2.5
'"E'
~1.5
~
Q)
Q)
I
I
0.5
0.5
J
10
X
10-3
15
nme[min]
20
25
30
10
W51A3_2; De= 6.72e-9, ep2 = 0.53%
X
10-3
15
Time[min]
20
25
30
W51A3_3; De= 7.56e-9, ep2 = 0.57%
2.5
1.5
c:
'"E'
~
~
~1.5
~
Q)
Q)
I
I
0.5
0.5
10
15
nme[min]
20
25
30
10
15
Time[min]
20
25
30
49
AppendixD
Diffusivity measurements on the cubic samples
D 5.1 A l/3
D 5.1 A l/4
3
W51A4_2; De= S.SOe-9, ep2 = 0.62%
X 103.-------------,-------------~-------------,
W51A4_3; De= 6.75e-9, ep2 = 0.44%
1000
Time [min)
Time[min)
W51A4_2; De= 8.50e-9, ep1 = 0.37%
X 10-3
W51A4_3; De= 6.75e-9, ep1 = 0.29%
2.5
1.5
0.5
0.5
10
3
x 10-3
15
Time [min)
20
25
30
10
15
20
25
30
W51 A4_3; De = 6.75e-9, ep2 = 0.44%
W51A4_2; De= 8.50e-9, ep2 = 0.62%
2.5
1.5
c:
~
~
~
i1.5
~
:r
"'
0.5
0.5
10
15
Time [min)
20
25
30
10
15
Time [min)
20
25
30
50
AppendixD
Diffusivity measurements on the cubic samples
D 5.1 B JJ 1
X
D 5.1 B JJ 2
D5181_3; De= 0.659-9, ep2 =0.22%
10-4
D5182_1; De= 0.54e-9, ep2 = 0.15%
c1.s
f
~
~
1
0.5
0.5
200
600
400
BOO
1000
1200
1400
1600
200
Time[minl
400
600
BOO
1000
1200
1400
1600
Time[minl
D5181_3; De= 0.65e-9, ep1 = 0.16%
X
10-4
D5182_1; De= 0.54e-9, ep1 = 0.13%
2.s;;..:.:=-----r------.----.----.-----.------,
10
20
30
40
50
60
70
80
90
100
10
nme [mini
20
30
40
50
60
Time [mini
X
D51 81_3; De= 0.659-9, ep2 = 0.22%
10-4
X
10-4
D5182_1; De= 0.549-9, ep2 = 0.15%
2.s;;..:.:=-----r------.----.----.-----.----,
10
20
30
40
50
Time[minl
60
70
60
90
100
10
20
30
Time[minl
40
50
60
51
Appendix D
Diffusivity measurements on the cubic samples
D 5.1 B !/1
D 5.1 B l/2
W51B3_2; De= 1.85e-9, ep2 = 0.29%
W51 83_1; De= 2.60e-9, ep2 = 0.33%
0~--~-----L----~----L---~----~-----L--~
0
200
400
600
800
Time[min]
1000
1200
1400
1600
W51B3_1; De= 2.60e-9, ep1 = 0.38%
20
30
Time[min]
40
0~--~~--~----~----~----~----L---~~--~
0
200
400
600
800
Time(min]
1000
1200
1400
1600
W51B3_2; De= 1.85e-9, ep1 =0.20"/o
50
60
W51B3_1; De= 2.60e-9, ep2 = 0.33%
10
15
Time[min]
20
25
30
W51B3_2; De= 1.85e-9, ep2 = 0.29%
12
10
10
20
25
30
30
Time[min]
40
50
60
52
AppendixD
Diffusivity measurements on the cubic samples
D 5.1 B !/3
D 5.1 B !/4
W51B4_2; De= 3.16e-9, ep2 = 0.37%
W51 84_3; De= 1.08e-9, ep2
=0.18%
10
0~--~----~-----L----~----L-----L---~----~
0
200
400
600
BOO
Time[min]
1000
1200
1400
1600
200
400
W51 84_2; De= 3.168-9, ep1 = 0.39%
600
800
Time[min]
1000
W51B4_3; De= 1.08e-9, ep1
1200
1400
1600
=0.15%
10
15
Time[min]
20
25
30
=
W5184_2; De= 3.16e-9, ep2 0.37%
X 10-1
15~~----.------,-------.------.------.------~
20
30
Time[min]
40
50
60
10
20
30
Time[min]
40
50
60
50
60
W51B4_3; De= 1.08e-9, ep2 =0.18%
30
Time[min]
40
53
AppendixD
Diffusivity measurements on the cubic samples
D 14.2 A lJ 2
D 14.2 A lJ 1
W142A1_1; De= 1.97e-9, ep2 = 0.33%
W142A1_2; De= 2.35e-9, ep2 = 0.30%
0~--~-----L----~----L---~-----L----~--~
0~---J----~----~----~----~----~---J----~
0
200
600
800
1000
1200
1400
1600
400
0
400
200
600
Time[min]
800
Time [min]
1000
1200
1400
1600
W142A1_2; De= 2.35e-9, ep1 = 0.22%
W142A1_1; De= 1.97e-9, ep1 =0.19%
12
10
10
0~------L------J-------L------~------L-----~
10
20
30
Time [min]
40
50
0
60
10
20
30
Time [mln]
40
50
60
W142A1_2; De= 2.35e-9, ep2= 0.30%
W142A1_1; De= 1.97e-9, ep2 = 0.33%
10
c
;["
l
~
.
:I:
0~------~-----L------~------~-----L----~
20
30
Time [min]
40
50
60
0
10
20
30
Time[min]
40
50
60
54
AppendixD
Diffusivity measurements on the cubic samples
D 14.2 A !/1
D 14.2 A lJ 3
W142A3_1; De= 4.27e-9, ep2 = 0.38%
W142A2_3; De= 1.77e-9, ep2 = 0.25%
16
0~--~-----L----~----~--~~--~-----L--~
0~--~-----L-----L----~--~~---L-----L--~
0
200
400
600
800
Time [minj
1000
1200
1400
0
200
400
600
1600
800
Time[minj
1000
1200
1400
1600
W142A3_1; De= 4.27e-9, ep1 = 0.24%
W142A2_3; De= 1.77e-9, ep1 = 0.15%
10
0~------L-----~------~----~~-----L----~
0
10
20
30
Time [minj
W142A2_3; De
40
50
10
60
20
25
30
W142A3_1; De= 4.27e-9, ep2 = 0.38%
X 10-4
=1.77&-9, ep2 =0.25%
15
Time [min]
16
.J
14
12
I
c1o
I
~
.
8
J:
0~------L-----~-------L------~------L-----_d
0
10
20
30
Time[minj
40
50
60
10
20
30
nme[min]
40
50
60
55
Appendix D
Diffusivity measurements on the cubic samples
D 14.2 A!/ 2
D 14.2 A
!I 3
W152A3_3; De = 4.656-9, ep2 = 0.30%
W142A3_2, De= 3.30e-9, ep2 = 0.22%
12
0~------------~------------~------------~
0
500
1500
1000
Time[min]
x10....
0~-------------L--------------~-------------0
500
1500
1000
Time[min]
W142A3_2, De= 3.306-9, ep1 = 0.15%
X 10""
W152A3_3; De= 4.658-9, ep1 = 0.22%
18
16
14
12
10
15
Time [min]
20
25
30
8
W142A3_2, De= 3.306-9, ep2 = 0.22%
10
Time[min]
12
14
16
18
20
16
18
20
W152A3_3; De= 4.656-9, ep2 = 0.30%
18
16
14
12
15
Time[min]
20
25
30
8
10
Time[min]
12
14
56
Appendix D
Diffusivity measurements on the cubic samples
D 14.2 A !/4
D 14.2 A !/5
W142A4_1; De= 4.17e-9, ep2 = 0.22%
W142A4_3; De= 5.05e-9, ep2 = 0.44%
12
14
10
c12
c:
I
~.,
.E
;:.10
8
~
~ 8
J:
0
o~----2~o~o--~4~oo~--~oo~o--~8~oo~--1~oo~o~~12~o~o---1~4~oo~~1soo
Time(min]
W142A4_1; De= 4.17e-9, ep2 = 0.17%
200
W142A4_3; De= 5.05e-9, ep1 = 0.24%
14
12
10
10
15
Time(min]
20
25
30
W142A4_1; De= 4.17e-9, ep2 = 0.22%
10
15
Time(min]
20
25
30
25
30
W142A4_3; De= 5.05e-9, ep2 = 0.44%
14
12
c
10
I
~
.,
8
J:
0
J
10
15
Time(min]
20
25
30
10
15
Time(min]
20
57
AppendixD
Diffusivity measurements on the cubic samples
D 14.2 A 1/6
D 14.2 B lJ 1
W142A4_4; De= 3.556-9, ep2 = 0.24%
014281_1; De= 0.78e-9, ep2 = 0.23%
58
Appendix D
Diffusivity measurements on the cubic samples
D 14.2BJJ2
D 14.2 B JJ 3
D142B1_2; De= 0.76e-9, ep2 = 0.24%
D142B2_1; De= 0.83e-9, ep2 = 0.22%
1.5
0.5
0.5
0
0
200
400
600
BOO
1000
1200
1400
1600
OL---~~--~----~----~----~----~--~~--~
0
Time[min]
4
X
10
4
200
400
D142B1_2; De= 0.76e-9, ep1 = 0.19%
600
BOO
Time[min]
1000
1200
1400
1600
D142B2_1; De= 0.83e-9, ep1 = 0.20%
3.5
2.5
c
E
~
~
2
"'
J: 1.5
0.5
10
4
X
10
4
20
30
Time [min]
40
50
60
40
D142B1_2; De= 0.76e-9, ep2 = 0.24%
50
60
50
60
D142B2_1; De= 0.83e-9, ep2 = 0.22%
3.5
3.5
2.5
c
t
2
"'
J: 1.5
1.5
0.5
0.5
10
20
30
Time[min]
40
50
60
10
20
30
Time[min]
40
59
Appendix D
Diffusivity measurements on the cubic samples
D 14.2 B l/2
D 14.2 B l/1
W142B3_3; De= 2.159-9, ep2 = 0.46%
W142B3_1; De= 2.48e-9, ep2 = 0.34%
0~--~-----L----~--~----~----~----L----d
0
200
400
600
800
Time [min]
1000
1200
1400
1600
0~--~----~----~-----L----~----~--~----~
0
W142B3_1; De= 2.48e-9, ep1 = 0.39%
20
30
Time[min]
40
X
50
200
400
600
800
Time[min]
1000
1200
1400
1600
W142B3_3; De= 2.159-9, ep1 = 0.41%
10-4
60
30
40
50
60
50
60
Time[min]
W142B3_3; De= 2.159-9, ep2 = 0.46%
W14283_1; De= 2.48e-9, ep2 = 0.34%
10
20
30
Time [min]
40
50
60
10
20
30
Time[min]
40
60
AppendixD
Diffusivity measurements on the cubic samples
D 14.2 B !/3
D 14.2 B !/4
W142B4_1; De =2.339-9 , ep2 = 0.53%
W142B4_3; De= 1.669-9, ep2 = 0.46%
0~--~----~----~----~----~--~~--~----~
200
0
400
600
800
nme[min]
1000
1200
1400
1600
40
10-4
W142B4_3; De= 1.669-9, ep1 = 0.33%
50
60
40
40
50
60
W142B4_3; De= 1.66e-9, ep2 = 0.46%
W142B4_1; De =2.339-9, ep2 = 0.53%
30
Time[min]
o~---2~oo----~4~oo~---6oo~---a~oo-----1ooo~---1-2~oo----1~400----~1600
nme[min]
W142B4_1; De =2.33&-9 , ep1 = 0.45%
X
0
50
60
40
50
60
61
AppendixD
Diffusivity measurements on the cubic samples
D 15.1 A JJ 1
D 15.1 AJJ2
W151A1_3; De= 1.51e-9, ep2 = 0.22%
W151A2_2; De= 1.85e, ep2 = 0.27%
"'
J:
Ot---~~--~----~----~----~----~--~~--~
0
200
400
600
BOO
1000
1200
1400
1600
Time[min]
0~--~----~-----L----~--~L---~-----L--~
0
200
400
W151A1_3; De= 1.51e-9, ep1 = 0.12%
600
800
Time[min)
1000
1200
1400
1600
W151A2_2; De= 1.85e, ep1 = 0.14%
10
r
~4
J:
20
25
0~------~----~-------L------~------~----~
30
0
W151A1_3; De= 1.51e-9, ep2 =0.22%
10
20
30
Time[min)
40
50
60
W151A2_2; De= 1.85e, ep2 = 0.27%
10
c:
~
6
~
"'
J:
20
30
Time[min)
40
50
60
0~------L-----~------~------~----~----~
0
10
20
30
40
50
60
Time[min]
62
Appendix D
Diffusivity measurements on the cubic samples
D 15.1 A !12
D 15.1 A t/1
W151A3_2; De= 7.07e-9, ep2 = 0.46%
W151A3_1; De= 5.57e-9, ep2 = 0.39%
c
~1.5
~
<D
:c
200
400
600
800
Time[min]
1000
1200
1400
1600
Time[min]
W151A3_1; De= 5.57e-9, ep1 = 0.25%
W151A3_2; De = 7.07e-9, ep1 = 0.26%
2.5
1.5
c
~
c
~1.5
~
~
<D
<D
:c
:c
0.5
0.5
10
15
Time[min]
20
25
30
8
W151A3_1; De= 5.57e-9, ep2 = 0.39%
10
Time[min]
12
14
16
20
18
W151A3_2; De= 7.07e-9, ep2 = 0.46%
2.5
1.5
c
~
~<D
:c
0.5
0.5
0~------L-----~------~----~-------L----__j
10
15
Time[min]
20
25
30
0
10
20
30
Time [min]
40
50
60
63
AppendixD
Diffusivity measurements on the cubic samples
D 15.1 A
!I 3
D 15.1 A !I 4
W151A4_1; De= 3.67e-9, ep2 = 0.25%
W151A3_3; De= 6.40e-9, ep2 = 0.52%
g
a>
::c
1
OL---~----~-----L----~----~----L---~-----d
500
1500
1000
0
800
Tlme[mln]
W151A3_3; De= 6.409-9, ep1 = 0.27%
W151A4_1; De= 3.67e-9, ep1 = 0.17"/o
200
400
600
1200
Time [min]
1000
1400
1600
10
<:1.5
~
g
a>
::c
1
0.5
10
15
Time [min]
20
25
30
10
W151A3_3; De= 6.40e-9, ep2 = 0.52%
15
Time[min]
20
25
30
25
30
W151A4_1; De= 3.67e-9, ep2 = 0.25%
c:
~
2
a>
::c
0.5
0~------~----~-------L------~------L-----_J
0
10
20
30
Time[min]
40
50
60
15
Time[min]
20
64
Appendix D
Diffusivity measurements on the cubic samples
D 15.1 A
!I 5
D 15.1 B lJ 1
W151A4_2, De= 3.85e-9, ep2 = 0.27%
D15181_1; De= 1.11e-9, ep2 = 0.26%
1.5
0.5
200
400
600
800
Time [mln]
1000
1400
1200
Oc___~----~--~~--~----~--~----~--~~-400
600
800
1000
1200
1400
1600
0
200
1600
Time[min]
W151A4_2, De= 3.85e-9, ep1 = 0.17%
D15181_1; De= 1.11e-9, ep1 = 0.22%
14
12
10
0.5
10
15
Time [min]
20
25
30
10
W151A4_2, De= 3.85e-9, ep2 = 0.27%
20
30
Time[min]
40
50
60
50
60
D15181_1; De= 1.11e-9, ep2 = 0.26%
S X 10-<
4.5
14
12
3.5
10
c
~
~
~
3
f·5
8
"'
"'
:I:
:I:
2
1.5
0.5
10
15
Time [min]
20
25
30
10
20
30
Time[min]
40
65
AppendixD
Diffusivity measurements on the cubic samples
D 15.1 B lJ 3
D 15.1 B lJ 2
D15182_1, De= 1.439-9, ep2 = 0.28%
D15181_2; De= 1.55e-9, ep2 = 0.44%
0~--~----~----~----~----~----~--~----~
0
200
400
600
800
Tlme(min]
1000
1200
1400
1600
OL---~----~----~----~----~----~--~-----J
600
800
1000
1600
1200
0
200
400
1400
Time [min]
D15182_1, De= 1.43e-9, ep1 = 0.26%
D15181_2; De= 1.55e-9, ep1 = 0.36%
<D
J:
40
50
30
Time]min]
60
40
50
60
50
60
D15182_1, De= 1.43e-9, ep2 = 0.28%
D151 81_2; De= 1.55e-9, ep2 = 0.44%
<D
J:
40
50
60
10
20
30
Time[min]
40
66
AppendixD
Diffusivity measurements on the cubic samples
D 15.1 B !/1
D 15.1 B .l/ 4
W151 83_2, De= 2.25e-9, ep2 = 0.34%
D15182_2; De= O.SBe-9, ep2 = 0.18%
.,
:J:
0.5
0~--~----~----L----L----~--~-----L--~
200
0
200
400
600
BOO
Time[min]
1000
1200
1400
400
600
1600
BOO
Time [min]
1000
1200
1400
1600
W151 83_2, De= 2.25e-9, ep1 = 0.25%
D15182_2;De=0.5Be-9,ep1 =0.14%
2.5
c:
~1.5
~.,
:J:
0.5
10
X
20
30
nme [min]
40
50
20
60
40
50
60
W151 83_2, De= 2.25e-9, ep2 = 0.34%
D15182_2; De= O.SBe-9, ep2 = 0.18%
10-4
30
nme[min]
10
2.5
c:
~1.5
~.,
:J:
0.5
0~----~~-----L------L------L------~----~
10
20
30
nme[min]
40
50
60
0
10
20
30
nme[mln]
40
50
60
67
Appendix D
Diffusivity measurements on the cubic samples
D 15.1 B l/2
W15183_3; De= 2.67e-9, ep2
D 15.1 B l/3
=0.36%
W151B4_1; De= 1.87e-9, ep2 = 0.29%
0~--~----~----L---~----~----~----L---~
0
200
400
600
800
1000
1200
1400
1600
0~--~----~----L---~----~--~~---L--~
0
200
400
600
Time[min]
X
10-4
W151B3_3; De= 2.67e-9, ep1 = 0.30%
=0.36%
1000
1200
1400
1600
W151B4_1; De= 1.87e-9, ep1 = 0.20%
10
W151 83_3; De= 2.67e-9, ep2
BOO
Time [min]
15
Time [min]
20
25
30
W151B4_1; De= 1.87e-9, ep2 = 0.29%
30
Time[min]
40
50
60
68
AppendixD
Diffusivity measurements on the cubic samples
D 15.1 B l/5
D 15.1 B l/4
W15184_3; De= 3.97e-9, ep2 = 0.49%
W151B4_2; De= 3.02e-9, ep2 = 0.47%
14
c
.E
12
2::.10
~
(I)
~
::t:
::t:
(I)
0~--~-----L----~----L----J----~----~--~
0
200
400
600
BOO
1000
1200
1400
1600
Time[min]
X
8
OL---~----~-----L----~----L-----~--~----_.
0
200
400
W151B4_2; De= 3.02e-9, ep1 = 0.37%
10-4
600
BOO
Time[min]
1000
1200
1400
1600
W151 84_3; De = 3.97e-9, ep1 = 0.42%
14
18
16
12
14
10
12
0~------~----~-------L------L-----~------~
0
10
20
30
Time[min]
40
50
60
10
W151 84_2; De = 3.02e-9, ep2 = 0.47%
15
Time[min]
20
25
30
W151 B4_3; De= 3.97e-9, ep2 = 0.49%
14
18
12
16
14
10
12
0~------~----~-------L------~----~~----~
0
10
20
30
Time[min]
40
50
60
0~------~----~-------L------~----~~----~
0
10
20
30
Time[min]
40
50
60
69
AppendixE
Permeability measurements on the ring samples
1.2x10""'
Permeabimy for sample 012
Permeabil~y
for the sample d12
6.0x10-e
~
(;j
:§.
4.0x1o•
~
Q)
J: 2.0x1o•
30
20
10
50
40
15
20
25
Time[min]
Time[min]
1.1Sx1o•
1.4x1o•
Permeabil~y for the sample 013
Permeability for the sarrple 013
1.50x10'
1.2X10'
1.25x10'
~ 1.0X10'
~
:§.(;j
a.ox1o•
~
;:
s.ox1o•
2
.s
~
Q)
Q)
J:
J: 4.0X1o•
1.00X10'
7.50x10.
5.oox1o•
2.SOx1o•
2.ox1o•
0.00
10
20
30
40
50
Permeabil~y for the sample 013
Ui'
~
7.50x10...
.0
.s
~
5.oox1o•
Q)
J:
10
20
30
nme[min)
0
10
20
30
nme[min)
Time[min]
40
50
40
50
70
Appendix E
Permeability measurements on the ring samples
Scaled (1060) permeability K = 8,89*1o·•• for sampleD 12
4 sx1o•
Scaled (1000) permeability K =1,19*10·" for sampleD 12
4 0x1o•
3 5x1o•
3 0x1o•
'"'~
~
'"'.s 2 sx1o•
~
2 0x1 o•
Q)
1 5x1o•
.§.
q:::
q:::
I
60x10'
~ 5 Ox1o·•
~
4.0x1o·•
1.0x1o•
Y =9,4922E-1 0+3,24842E-14 X+9,90343E-20 X'
s.ox1o•
Y =1,66347E-10+6,94192E-14 X+1 ,31608E-19 X'
00
0.0
5.0x10
4
1.0x10'
1.5x10°
2.0x10'
2.5x10°
3.0x10'
2 Ox10
3.5x10'
4
4 Ox10
4
6 Ox10
4
4
8.0x10
1 Ox10°
1 2x10°
1 4x10'
1 6x10°
Pressure difference [Pal
Pressure difference [Pa]
Scaled (940) permeability K = 4,61'1 o·"fa sample D 13
Scaled (940) permeability K = 5,70'10"" for sampleD 13
14x1o•
1.0x1o·•
1.2x10.
~
"'.§.
(i)
"':§. s.ax1o·•
.g
6.0x1o·•
~
(l)
I
6.0x1o·•
~
:t
40x10'
I
4.0x1o·•
2.0x10"'
Y =7,20304E-10+2,69842E-14 X+4,8773BE-20 'Jf
2 Ox10''
Y =9,64487E-10+2,46562E-14 X+7,00089E-20 X:
00+---~---r----.---~--~--~r---~--~--~--,
00
5.0x10
4
1.0x10°
1 5x10'
2 0x10'
2 5x10'
3.0x10°
3.5x10'
Scaled (890) permeability K = 5,43'1 cr" for sampleD 13
U>
a.0x1o•
"'E
;
6.0x10'
0
<;:::
(l)
I
4.0x10•
2.0x10"'
0.0
Y =5,34234E-10+2,21567E-14 X+5,93135E-20
X:
+---.----,----.----r---.-----r----.----r---.----,----.----,
00
4
5 Ox10
1.0x10'
1 5x10'
2.0x10'
Pressure difference [Pa]
00
5.0x10'
1.0x10'
1 5x10'
Pressure difference [Pa]
Pressure difference [Pa]
2 5x10'
3 Ox10'
2.0x10'
2 5x10'
71
Appendix F
Permeability measurements on the cubic samples
Permeabili1y for the sarrple 0 5.1 A (parallel)
s.0x10"
Permeabil~y
7ii'
::::.
3.5x10
for the sarrple 0 5.1 A (perpendicular)
~ s.0x1o-~
4
(ij 3.0x10"1
.0
§.
2.5x1o·•
~
2.0x10''
§.:u
4.0x10
~
3.0x1o"
4
Q)
~ 1.5x10''
J: 2.0x1o•
1.0x10''
1.0x10
s.0x1o•
0.0
0
50
40
20
80
4
0.0
IL..__.__~...-_.____JI...-_.____JI...-_.____JL--_.____JL--_.____JL--_,
IL..__
_,__ __J__
0
120
100
__._ _...J.__ _.___
50
Time[min]
Time[min]
Permeability for the sarrple 0 5.1 A (parallel)
S.Ox1o·•
3
5.5x10-
_ L_ _. . . _ _
40
20
Permeabili1y for the sample 0 5.1 A (perpendicular)
3
5.0x10'
4.5x10. 3
6.0x10''
4.0x10''
~ 3.5x10ea a.ox1o·3
3
i-g
2.5x10.
~ s.0x1o•
'
3
0::::
2.0x10
~
1.5x10'
§.:u
4.0x10"
~
3.0x1o•
Q)
J: 2.0x1o•
1.0x10'
5.0X10-4
0.0 L__.____,_
0
__._
___,__
20
_,__
1.0x10''
_J...._
40
_.__
50
_.__~___J
80
100
10
Time [min]
30
20
50
40
Time [min]
Permeabili1yforthe sarrple 0 5.1 A (perpendicular)
4.0x10"
3.5x10
3.0x10
~
~
§.
s.ex1o•
4
1.0x1o•
Ul
::::.
2.0x1o•
4
1.5x10
Q)
J:
1.0x10
.
6.0x10...
2.Sx10'3
3::
.g
Permeabili1y for the sarrple 0 5.1 B (perpendicular)
4
4
~
5.0x10
§.
4.0x1o•
~
3.0x1o•
J:
2.0x1o•
Q)
5.0x10 ...
0.0 .___..___
0
_J__
20
_.__
_.__
_.__
__,_ _. _ __
50
40
1.0x10...
_u___.
80
30
Time[min]
50
90
120
150
180
210
240
Time[min]
9.0x10''
Permeabili1y for the sarrple 0 5.1 A (parallel)
1.2x10''
Permeabili1y for the sample 0 5.1 B (perpendicular)
8.0x10''
7.0x10''
~
4
6.0x10
(i) S.Ox10...
~ S.Ox10
::::.
4
§.
4.0x10''
~
3.0x10
§."'
~.,
4
J: 2.0x10 4
s.0x1o•
4.0x1o•
J:
2.0x1o•
0.0 l -_
0
_.__
_ L_
20
__._ _.L-_
_.__
40
Time[min]
___,__ _.___...J...__
50
80
0.0
L.a...__._-.~..
0
30
_
_.__...J...__.._____JL-.-___._
50
90
Time [min]
_ L_
120
_.__
_J__
150
72
AppendixF
Permeability measurements on the cubic samples
3.0X1o·'
Permeability for the sampleD 5.1 B (parallel)
Permeabil~yforthe sampleD 14.2
6.5x1o·•
6.0X10
4
5.5x10
4
A (perpendicular)
5.0X10"'
4.5x10
~
4
3
4.0x10'
~ 3.5x10~
§.
3.0X10"'
~ 2.5x1o·•
Cl>
J:
2.0X10"'
3
1.5x10'
4
1.0X10
0.0
_
LL.__.___L-._._____,L-.__.~__.
0
20
40
_
____._--~.
__.
60
30
eo
60
90
2.2x10"'
120
150
180
Time[min]
Time[min]
Permeabil~ for the sample D 14.2 A (perpendicular)
s.ox1o·'
Permeability for the sample D 5.1 B (parallel)
4.5x10
2.0X10"'
4
4
1.8x10
3.5x10"'
1.6X10"'
~
~
~
1.4x10-:s
11.2x10"'
i
1.0X10"'
_g
B.OX10""
;'l
s.ox1o•
3.0x10
2.5x10
~ 2.0X10
Q)
4
4
4
4
1.5x10
J:
20
40
20
60
100
80
Time[min]
Time [min]
Permeabil~y for the sample D 5.1
B (parallel)
Permeabilily for the sampleD 14.2 A (perpendicular)
s.ox1o·'
2.7ll1o"'
5.5x1o·'
2.4x10-
3
3
5.0x10'
2.1x1o·l
~
1l
§.
4.5x10
3
(i) 4.0x10
1.8x10"
::::.
(;j
1.5x10"'
~
1.2x1o"'
;'l
9.ox1o•
~
i
-
6.0X10..,
4
4
35x10_,
.
3.0X10"'
4
2.5x10
<~>
2.ox1o•
J:
1.5x10
4
3
1.0x10"
3.0X10...
40
20
60
100
80
S.OX1o•
0.0 L_____._
0
120
_J__
_,__.t____._
20
40
nme[min]
Permeabil~y for the sample D 5.1
_,__~--'--------'~--1..-~
60
80
100
Time(min)
B (parallel)
Permeabil~ for 1he sampleD 14.2 A (parallel)
3
1.6x10'
4.0X10"'
1.4xto·'
en
:::.
3.5x10"
3
ea 3.ox1o·'
.0
§. 2.5x104
~
2.0X10
;'l
1.5x10
4
4
1.0X10"'
S.Ox10..
0.0
20
40
nme[min]
60
eo
IL._~--1.-~...J....__._..J..___.__L-.~--l.-~....1....__.___1
0
10
20
30
40
Time[min]
50
60
70
73
Appendix F
Permeability measurements on the cubic samples
Permeabili1y for the sampleD 14.2 A (parallel)
6.0x1o·•
1.2x10•
Permeabili1y for the sampleD 14.2 B (perpendicular)
1.1x10-3
4
1.0x10
9.0x10""
'iij' 8.0xt0•
~ 4.0x10''
==
«;
:§.
3.0x10''
~
2.0x1o•
"'
7.0x10..
~ s.axto•
~ s.ax1o•
~
Q)
Q)
J:
J:
10
40
30
20
100
50
50
150
300
250
200
nme(min]
nme[min]
s.ex1o•
Permeabili1y for the sample D 14.2 A (parallel)
Permeability for the sampleD 14.2 B (perpendicular)
4.9x10""
5.0x10·'
4.2x1o•
;w 3.5x10""
:§."' 2.ax1o•
~
j!_
2.1x10...
1.4x1o•
7.0X10-6
0.0
L--~--'----'-.....1....-~--L-~--'-~-.L...-~____J
100
50
50
40
20
0
150
250
200
Time (min]
nme[min]
Permeability for the sample D 14.2 B (parallel)
4
7.0x10
Permeabili1y for the sampleD 14.2 A (parallel)
2.5x10''
2.0x10''
~
~
.§.
~
1.5x1o·l
1.0x10''
Q)
J:
40
20
20
50
40
ao
60
100
120
140
nme[min]
Time[min]
Permeabili1y for the sample D 14.2 A (parallel)
2.2x10''
Permeability for the sampleD 14.2 B (parallel)
2.0x1o•
1.ex1o•
~ 1.4x1o·l
~
4
1.2x10
f
1.0x10''
2
s.ax1o•
Q)
J: 6.0x10.
4.0X1o•
0.0 u.__.__
0
_.__~--'--~-'--~---l.-~-L..-_.___.
10
20
30
nme(min]
40
50
2.ox1o•
60
20
40
60
Time(min]
ao
100
120
74
Appendix F
Permeability measurements on the cubic samples
Permeability tor the sample D 15.1 A (perpendicular)
9.0x10"'
Permeability tor the sample
D 15.1 A (parallel)
6.0x10"'
7.0x10-3
~ 5.0X10.;)
!
........ 6.0x10
4
4.0X10°
;lg
(ij
5.0x10
~ 3.0X1o•
.S
4.0x1o•
~
.c
2.0X10°
4
~
3.0x1o•
I
2.0x1o•
Q)
1.0x10-3
0.0
"--~-...L-~---'--~-'--~--'--~-...JL.._~__...J
0
20
40
60
100
80
120
10
15
20
Time[min]
S.Ox10-~
4.5x10'
4.0x10
25
30
35
40
45
50
55
60
Time [min]
Permeability for the sample D 15.1 A (perpendicular)
a.ex1o·'
Permeability tor the sample D 15.1 A (parallel)
3
8.0X10''
4
7.2x10''
6.4x10.,
~
5.6x10'
~
4.8x10''
3
.§.
4.0X10"'
~
3.2x10'
.j!,
2.4x1o·'
3
3
1.6x10'
8.0X10...
20
60
40
80
10
20
Time[min]
30
40
60
50
Time [min]
7.0X10"'
Permeability for the sample D 15.1 A (parallel)
Permeability tor the sample D 15.1 A (parallel)
6.0X10"'
5.0X10"'
Time [min]
9.0X10.;)
Time[min]
Permeability tor the sample D 15.1 A (parallel)
4
1.1x10
8.0X10""
9.0x10""
7.0X10-,'I
8.0x10""
~ 6.0x10-3
(ij
5.0x10-3
.c
.S
Permeability tor the sample D 15.1 B (perpendicular)
3
1.0x10'
~
7.0x10""
~
6.0x10...
~
.S
5.ox1o•
3.0X10°
~
4.0X1o•
I
2.0X10'
~
3.0X1o•
4.0X1o•
Q)
2.ox1o•
1.ox10•
10
20
Time [min]
30
40
50
50
100
150
Time[min]
200
250
300
75
Permeability measurements on the cubic samples
1.ax 10·•
Permeability for the sa"l'le D 15.1 B (perpendicular)
~ 1.2x1o·•
~
4
~ t.Ox10
.§_
B.Ox10"
~
6.0xt0"
I
4.0xto"
Ql
2.0x10"
50
150
100
200
250
300
100
120
nme[min]
Pernneabilny 1or the sample D 15.1 B (parallel)
3.0X10
~
!
~
4
4
2.5x10
2.0xto·•
t.Sx1o·•
Ql
I
1.0x1o·•
S.OX10~
20
60
40
80
Time[min]
Permeabilny for the sampleD 15.1 B (parallel)
3.Sx1o·•
40
20
80
80
100
Time[min]
J.Ox
4
10
~ 2.1x10
Permeabilny for the sampleD 15.1 B (parallel)
4
~
1.8x10-~
.§.
1.5xto·•
~
1.2x1o·•
Ql
I
9.0x1o•
s.0x1o•
3.0xto•
20
40
60
Time[min]
80
100
120
Appendix F
76
Appendix F
Permeability measurements on the cubic samples
Scaled (0.0365) permeability K = 3.31' ta"
for the sample D 5.1 A (perpendicular)
3,8x10·'
3,3x10'
1 2x1o·"
3,0x10'
~ 1 Ox1o·'o
M.§.
~
90xW"
~E
8 Ox1o·' 1
,g
i
~
g
Q)
I
Scaled (0.0560) permeability K = ?.61•10"
fatho "mpO D 5.1 A(po•OO) /
2,7x10"'
Q)
7 Ox10"
I
y =3,11437E-11+1,05867E-15 X+4,57213E-21
5.0xW"
10000
20000
30000
40000
50000
60000
70000
X
2,4x1o·'
2,1x1o·
x'
80000
1 0000
Pressure difference [Pa)
20000
30000
40000
50000
Pressure difference [Pa]
Scaled (0.0450) permeability K = 2.46*1 o·••
S<oOd (0 0782) P'""""''~ K • 6.61'10·"
fa"'"""'' D 5.1 A (po•I•O
/
5,4x10'
for the sampleD 5.1 A (perpendicular)
2 6x10-' 0
/-10>3,78916E-15X•5.654BE-2f
2 4x10-' 0
/~
5,1x10"'
2 2x1o·"
4,8x10
2.0x10-
~
M.§.
11
'
~ 4,5x10
"§.
1 8x1o·"
~
~ 1 6x1o·"
-=
q::
Ql
I
1.4x10""
I
1.0x10-'
0
s.ox1 o·"
4,2x10
1
Q)
3,9x1o·
3,6x1o·'
Y =7,72426E-11+1,51831 E-15 X+3,39305E-21 X'
1--..---.----.----.---.---.--...--..---.-----.--,
20000
40000
60000
80000
Y =2,62579E-10+5,53167E-15 X+4,91118E-21 X'
3,3x1 o·'1---4----.--r--.----.-..---.---.-..---.--,.-.---.----.--..--.
10000
20000
25000
30000
35000
15000
40000
45000
50000
100000
Pressure difference [Pa)
Pressure difference [Pa]
3 4x10- 18
1.4x1o·"
Scaled (0.0360) penneability K = 3.00'10""
for the sample D 5.1 A (perpendicular)
Scaled (0.0500) penneability K = 5.65•10""
for the sample D 5.1 A (parallel)
3.2x10'' 0
1.2x10""
2.8x10"
1.1x1o·"
M~
1.Qx1Q·10
E
'i' 9.0x10""
2.6x10.u:~
~
2 4x10""
~
22x1o·"
q::
.Q
-; 8.0x10'''
I
10
~
'".§.
7.0x10""
Y =1 ,76543E-1 0+3,16754E-15 X+4,20196E-21 X'
6.0x10""
5.0x10"" +--r---.--.---r--r---r--,.---r--r---r---,
10000
20000
30000
40000
Pressure difference [Pa)
50000
60000
10000
20000
30000
Pressure difference [Pa)
40000
50000
77
Appendix F
Permeability measurements on the cubic samples
Scaled (0.0705) permeability K = 4.55*10"'
for the cubic sample D 5.1 B (perpendicular)
4.2x1o·''
8,0x10~
Scaled (0.0350) permeability K =2.22*10·"
for the sample D 5.1 B (parallel)
7,0x10''
6,5x10
~
~.§. 3 3x10~"
~
.g
iii 6 0x1o·'
"'"E.
-; 5,5x10'"
3.0x10~"
0
Cl)
'; 5,0x10
I
4,5x10~'
I
Y=2.00991E-11+2.74033E-16 X+4.34372E-22 X'
4,0x10~"
2
Y =3.08069E-11+6.31961 E-16 X+2.3088E-21 X
3,5x10~'
80000
60000
40000
20000
Pressure difference [Pa]
3,0x1 o~"'--..-----.--.....--r--..-----.--.....--r--..-----.--.
50000
10000
20000
30000
40000
0
Pressure difference [Pa]
Scaled (0.0698) permeability K = 2.49'1 o·"'
for the sample D 5.1 B (perpendcular)
6 Ox10~"
Scaled (0.0762) permeabifity K =2.91*10~
2,2x10''
19
for the sample D 5.1 B (parallel)
2,1x10
U) 6.0x1o·''
~"E
(jj' 2,0x10'
"'i
i' 5.0x10~"
.g
~ 1,9x10
Cl)
I
<+=
4.0x1o·"
Q)
I
3.0x10""
2.0x10~"
1,8x10~'
Y =2.1039E-11+2.62109E-16 X+2.37873E-22 X'
1,7x1 0~
...L,r----,----.---..------.---,----.----,
Y =1.18716E-10+1.45515E-15 X+3.01836E-21 X'
200000
150000
100000
50000
Pressure difference [Pa]
30000
35000
40000
45000
50000
55000
60000
65000
Pressure difference [Pa]
2,1x10''
2,0x10~'
Scaled (0.0717) permeability K =3.67*10~
19
for the sample D 5.1 B (parallel)
5,7x10''
1,9x10~'
5,4x10~'
Scaled (0.0297) permeability K = 3.31*10'
19
for the sample D 5.1 B (parallel)
1,8x10~'
5,1x10~
~ 1,7x10~'
4,8x10~
""E
-; 1,6x10~'
0
<+=
)!f 4 5x10~'
'"'E ,
1,5x10~'
Q)
I
-; 4,2x10''
1,4x10~
0
1,3x1o·'
Y =1.06191E-10+1.37226E-15 X+3.80905E-21 X'
1,2x10'
'; 3,9x10
I
3,6x10'
3,3x10~'
2
10000
20000
30000
40000
50000
60000
Y =2.73723E-11+4.69114E-16 X+3.43937E-21 X
3,0x10~'
Pressure difference [Pa]
10000
20000
30000
Pressure difference [Pa]
40000
50000
78
Appendix F
Permeability measurements on the cubic samples
Scaled (0.0490) permeability K = 6.27*10·"
for the sample D 14.2 A (perpendicular)
2,4x10
Scaled (0.0465) permeability K = 6.04*10. 19
for the sample D 14.2 A (paraUel)
2,4x1o·'
2,2x1o·
2,1x10
2,0x1o·'
~
~
1,8x10'
"§. 1,8x10'
"§. 1,5x10'
~
~
~
~ 1,2x10'
1,6x1o·'
I
I
1,4x1o·
Y =4,24534E-11+1,19717E-15 X+7,81737E-21 X
6,0x10'
Y =9,6854E-11+2,47208E-15 X+4,95489E-21 X
2
10000
20000
40000
60000
80000
20000
100000
30000
40000
50000
Pressure difference [Pa]
Pressure difference [Pa]
1,4x10'
Scaled (0.0275) permeability K = 6.12*10·"
for the sample D 14.2 A (parallel)
Scaled (0.0482) permeability K = 5.29*10·"
for the sampleD 14.2 A (perpendicular)
2,4x10
2
1,2x10
1,3x1o·'
2,2x10
2,0x10
~
7ii' 1,8x10
"''E
~
2
1,4x10'
I
1,2x1o·'
~
1,2x10
"§.
~
1,6x1o·'
0
1,1x10
,.::::
Q.l
I
Q)
Y =6,43167E-11+1,73358E-15 X+6,62958E-21 X
1,0x10
Y =7,49159E-11+1,35118E-15 X+5,01504E-21 X'
2
8,0x10"'
~,-~~--~,-~~--~~~~~~~~~~
10000
20000
30000
40000
50000
60000
70000
10000
80000
20000
30000
40000
Pressure difference [Pa]
Pressure difference [Pa]
Scaled (0.0306) permeability K = 4.05*10'
for the sampleD 14.2 A (perpendicular)
1,Bx10'
19
2,0x1 o·'
1,6x1o·
1,8x10
1,4x10'
~1,6x10'
"'.s
~
"§. 1,2x10'
,g~
~
,g
1,0x10"
1,4x10
Q)
I
Q)
I
Scaled (0.0325) permeability K = 8.22*10·"
for the sample D 14.2 A (parallel)
1,2xW'
8,0x1o·'
Y =4,6744E-11+9,30555E-16 X+5,05044E-21 X'
4,0x10""t---r----r--r---,--~--,-----.--.--~--,
0
20000
40000
60000
Pressure difference [Pa]
80000
Y =8,94248E-11+1 ,61764E-15 X+6,7443E-21 X'
1,0x10
100000
10000
20000
30000
40000
Pressure difference [Pa]
50000
60000
79
Appendix F
Permeability measurements on the cubic samples
6.0x10' 11
Scaled (0.0445) permeabifity K = 8.57*10'"
, x o·' for the sample D 14.2 A (parallel)
24 1
5.7x1o·"
Scaled (0.0982) permeability K = 2.55.10.
for the sampleD 14.2 B (perpendicular)
20
5.4x1o·"
5.1x10'"
2,2x10''
4.8x10'"
~
"'E
~
M~
4.5x10-
E
i' 4.2x10'
2,0x1o·'
~
,g
""' 1,Bx10'
11
11
3.9x10'"
Q)
Q)
J: 3.6x1o·"
I
3.3x10'11
Y =1,59036E-10+2,40133E-15 X+7,02541 E-21 X'
3.0x10'11
1,6x10'
2. 1x1 o·" +----.--.----.--.----.--.----.--.---,,--.....----,,--.....----,,---,
20000
30000
40000
50000
60000
70000
80000
10000
30000
20000
Pressure difference [Pa)
Pressure difference [Pa)
2,1x1o·'
Scaled (0.0355) permeability K = 8.54*10·"
2,0x10''
for the sample D 14.2 A (parallel)
1,8x1o·
Scaled (0.0805) permeability K = 3.36*10'
for the sampleD 14.2 B (parallel)
19
1,9x10'
1,8x10
1,6x10
7jj' 1,7x10''
.,--
7jj'
.s 1,6x10''
"§. 1,4x10
~ 1,5x10
.;::
:;=
0
""'~ 1,2x10''
Q)
1,4x1o·
I
1,3x10''
Y =1 ,08341 E-10+1,6576E-15 X+7,00631E-21 X'
1,0x10''
1,2x10''
Y =7,55247E-11+1 ,41955E-15 X+3,46696E-21 X2
1, 1x1o'+----"T--..---,-----.---.----.-----,,---~---,
20000
30000
40000
50000
10000
B,Ox1Q''4--r----r---.----r-.....--..---.--~---.--.--..--,
10000
Pressure difference (Pa)
20000
30000
40000
50000
60000
Pressure difference [Pa)
Scaled (0.0757) permeability K = 2.62*10.
for the sample D 14.2 B (perpendicular)
8,5x1o·
1,4x10'
20
Scaled (0.0682) permeability K = 3.35*10.
for the sample D 14.2 B (parallel)
19
8,0x10
1,3x10''
7,5x1o·
7,0x10'
~
~ 1,2x10''
6,5x10''
..a
7jj'
i. 6,0x10'
:;=
.s
~
5,5x10
0
:r:
1,1x10''
""'
I
~ 5,0x10''
Q)
4,5x1o·
1,0x10''
2
Y =8.63348E-11+1.15724E-15 X+3.58058E-21 X
4,0x10
Y =3,23123E-11+3,63267E-16 X+2,66438E-22 X
3,5x1o·
2
3,0x10''"!--..----.---.---.----.r---r-~-.----,...--.--..---,-----.
0
20000
40000
60000
80000
Pressure difference [Pa)
100000
120000
9,0x1 o·'+---.--.---.----,.----.--,--..--,----.--.---.--.----.--,
5000
10000
15000 20000
25000 30000
35000 40000
Pressure difference [Pa)
80
Appendix F
Permeability measurements on the cubic samples
9,5x10"
Scaled (0.0485) permeability K = 2.70•1o·"
for the sample D 14.2 B (parallel)
2,6x10''
2,4x1o·'
8,5x1o·
2,2x10'
8,0x10'
'"'i
7,5x10·'
~
7,0x10
~
"".s 2,0x10'
~
1,8x10'
li=
li=
Q)
Cl)
I
Scaled (0.0410) permeability K = 9.15*10'"
for the sample D 15.1 A (parallel)
6,5x10'
I
1,6x1o·'
1,4x1o·•
Y =4,96318E-11+6,66636E-16 X+2,80277E-21 X:
Y =1,16145E-10+2,27251E-15 X+7,82974E-21 X
2
5,5x10'
1,2x10'"i---,----r---r---.--..---..---,.---.---.------..----,
10000
20000
30000
40000
50000
60000
5,0x10'''4---.---.--..---..--.------.-----..-----..----,------.
10000
30000
40000
20000
50000
Pressure difference [Pa)
Pressure difference [Pa]
4,0x10''
2,2x10''
2,0x10'
Scaled (0.0352) permeability K = 3.73*10'"
for the sample D 15.1 A (perpendicular)
Scaled (0.0505) permeability K = 9.40*1 o·"
for the sample D 15.1 A (parallel)
3,8x10''
3,6x1o·•
1,8x10''
3,4x10'
w
1,6x10''
""i
:w 1,4x10
"g
~
li=
1,2x10'
:!1!. 2,8x10
li=
~
3,2x10'
~ 3,0x10
1,0x10
2,6x10'
2,4x10
Y =6,1864E-11+1 ,01802E-15 X+4,43282E-21 X'
6,0x10'
Y =1 ,98504E-1 0+3,35856E-15 X+8,04369E-21 X
2
2,2x10"·~----.------r--.----.----.-----.------..--.---..----..
10000
20000
40000
60000
80000
100000
20000
30000
40000
50000
Pressure difference [Pa)
Pressure difference [Pa)
1,8x10"
Scaled (0.0422) permeability K = 4.51*10'
for the sample D 15.1 A (perpendicular)
3,9x10
19
Scaled (0.0455) permeability K = 8.44*1o·••
for the sample D 15.1 A (parallel)
3,6x1o·•
3,3x10
1,6x10'
:w 3,0x10
"g
:w
"g 1,4x10'
~
~
2,7x1o·•
li=
li=
Q)
:!1!. 1,2x10''
I
2,4x10
2,1x1o·•
1,0x10''
Y =1,82635E-10+3,24601E-15 X+7,22474E-21 X
2
Y =7,39043E-11+1,21318E-15 X+5,35531E-21 X'
a,Ox1 o·'4-:':....._..-----..-,--.-----.---.---.---.--..------.--r--..----,
10000
20000
30000
40000
50000
Pressure difference [Pa)
60000
70000
10000
20000
30000
Pressure difference [Pa]
40000
50000
81
AppendixF
Permeability measurements on the cubic samples
Scaled (0.0312) permeabiHty K = 8.82*10'
2,6x1o·'
19
for the sample D 15.1 A (parallel)
6,5x1o·'
2,4x10'
S,OxW
~
E.
2,0x10''
'iii' 5,0x10'
Scaled (0.0338) permeability K = 7.16*10.'
for the sampleD 15.1 B (perpendicular)
0
5,5x10"'
"§. 4,5x10'
3:
3:
.g
.g 1,8x10'
4,0x10
Q)
Q)
I
I
3,5x10'
1,ex1o·'
3,0x10
1,4x10''
1
Y =1,19269E-10+1 ,73884E-15 X+7,54448E-21 X
20000
10000
30000
40000
2,5x10
1,ex1o·'
1
X+:,76759E-22 X
2,0x10 Uf----.---.---.---.----.---.----.---.---.---.---.
100000
40000
60000
80000
20000
0
50000
Pressure difference [Pa)
Pressure difference [Pa)
Scaled (0.0302) permeability K = 8.34*10.
for the sampleD 15.1 (parallel)
~224E-11+3,07045E-16
1,4x10
1,4 xw'
19
Scaled (0.0425) permeability K = 3.07*10.
for the sampleD 15.1 B (parallel)
19
1,3x1o·'
1,3x10'
1,2x10.
~ 12x1o·'
""E
,
;1,1x10''
2
1,1x10
Q)
I
1,0x10'
1,0x10'
9,5x1o·'
1
2
Y =8.10348E-11+9.88166E-16 X+3.1806E-21 X
9,0x10·'
Y =1,06889E-10+1,65772E-15 X+7,13559E-21 X
8,5x1o·"'---.---r--...---...--,.--.-----,r----.---r----.
50000
20000
30000
40000
10000
5000
10000
15000
20000
25000
30000
35000
40000
Pressure difference [Pa)
Pressure difference [Pa)
2,4x10''
Scaled (0.2110) permeability K = 7.35*10.
for the sampleD 15.1 B (perpendicular)
20
=
1,1x10''
Scaled (0.0355) permeability K 2.77*10'
for the sample D 15.1 B (parallel)
19
2,2x10
1,1x1o·'
2,0x10
1,0x10'
1,ex1o·'
'iii' 1 Ox10''
""e.
"; 9,5x10"'
0
~ 9,0x10
I
8,5x1o·
8,0x1o·'
Y =6,8668E-11+1,0969E-15 X+7,36751E-22 X'
20000
40000
60000
80000
100000 120000
Pressure difference [Pa)
1
Y =6,65371E-11+8,13401E-16 X+2,87161E-21 X
7,5x1o·'
140000 160000
7,0x1o·Uf----r---.----.--.--..---..---.---.---.
20000
30000
40000
50000
10000
Pressure difference [Pa]
82
Permeability measurements on the cubic samples
1,6xW'
Scaled (0.0575) permeability K =3.53*1
for the sample D 15.1 B (parallel)
a·••
1,5x1o·'
1,4xW'
"jjj'
~1,3x10'
~
10:: 1,2x10'
Q)
I
1,1x10"
1,0x10''
Y =8,53062E-11+1,32389E-15 X+3,65899E-21 X
2
9,0x1o'4---.---.--...--...--.---r---r--.-----.
10000
20000
30000
40000
50000
Pressure difference [Pa]
Appendix F