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10
8
6
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Hexane
Heptane
Octane
Nonane
Decane
Solvent
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2*NN*4
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Solubility Parameter
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Asphaltene Precipitation
(wt% bitumen)
-
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140,000
Viscosity (mPa•s)
120,000
100,000
80,000
60,000
40,000
Cold Lake
20,000
Peace River
0
0
5
10
15
20
Asphaltene Content (%)
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68
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AD
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% /V %
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2 A.N 4K
1
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4; +, 7
9P9*
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2 A.* 4'
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− ln(1 − y s 2 ) = k1 z 2 + k 2
4; +6 7
/
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ln
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1 − ys2
1 − y s1
z1 − z 2
AF
4; +; 7
1 − ys2
1 − y s1
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2 A.*A 4
9.
2 A.*D 4
2 A.*! 4
K
ln
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1 − ys2
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1 − y s1
N sz
=
z = z1
z = z1
=
− cDsa
(1 − y s1 )
1 − y s1
z = z1
=
4; +B 7
− ln
2 A.*F 4K
1 − ys2
1 − y s1
cDsa
1 − y s2
ln
z 2 − z1
1 − y s1
P*.
z = z1
4; +C 7
z 2 − z1
K
%
N sz
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z = z1
2 A.*A 4
-
N sz
z − z1
z 2 − z1
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1 − y s1 dz
2 A.N 4
N sz
z1 − z 2
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z1
=
cDsa
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z 2 − z1
y a1
A+
4; +A 7
2 A.*H 4
K
4; +8 7
L
K
( y a )M
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2 A. ! 4
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z = z1
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K
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-
*
-
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%
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4; 6; 7
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4; 6= 7
K
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n
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AH
4; 6? 7
2 A. D 4
2= 4
2 A. " 4
2 A. * 4
) )
N sz
K
z = z1
=
(
PDsa
Pa 2 − Pa1
RT ( z 2 − z1 ) (Pa )M
4; 6B 7
)
.
'
)
2 A. F 4'
;'6
"
"
%
.
-
9
29 4
C
= 1 − erf
Co
2
/ *N+"4K
z
4; 6C 7
4 Dt
(
L
L
.
-
'
P!
' & 3
)
D! - I
@
)
2 !!*4 0
/
2 !!A4C'
2 )
4
2 A. + 4
1 = erf
AN
z
4 Dt
K
4; 6A 7
(
L
' (
-
)
;2 4
-
Qs (t ) = N s (t ) As =
K
x Vs ρ s dVtotal ,cum
Ms
dt
4; 68 7
)
2 A. F 4'
)
'
(
&
9
-
)
29P9 4
29P!4
)
K
N s (t ) =
PDsa Pai − Pa 0
RT (∆z ) (Pa )M
4; ;, 7
2 A.A! 4
'
2 A. N 4
N s (t ) =
2 A.A! 4
PDsa ,eff
RT (∆z )
Pai − Pa 0
x V ρ dVtotal ,cum
= s s
(Pa )M
As M s
dt
2 A.A* 4
Dsa ,eff =
K
4; ;+ 7
K
x Vs ρ s dVtotal ,cum RT (∆z )(Pa )M
As M s
dt
P (Pai − Pa 0 )
D!
4; ;6 7
2 !!*4 0
/
2 !!A4
-
B
2 !!A4
)
' <
2 A.A 4
K
Dsa ,eff = K
-
dVtotal ,cum
∆z
4; ;; 7
xVs ρ s RT (Pa )M
2 As M s P (Pai − Pa 0 )
4; ;= 7
dt
K
K=
&
.
2-
4
K
Pa = Ptotal − x s Psvap (T )
-
4; ;? 7
)
3
)
'
%
' &
/
K
Pa 0 = Ptotal − Psvap (T )
4; ;B 7
.
' (
K
Pai = Ptotal − x s Psvap (T )
&
4; ;C 7
' (
^' (
-
-K
D*
Dsa ,eff = Dsa
φ
τ
4; ;A 7
;';
;';'+
(
.
2,
) *NH"4K
D AB
-
L
,
1.858 x10 − 27 T 3 / 2 1
1
=
+
2
MA MB
Pσ AB Ω D
: (
?
$
XL
1/ 2
4; ;8 7
=
_?
' %
N" $K
Dsa =
1.858 x10 −27 (295 K )
3/ 2
(1 atm)(4.7475 x10 −10 m)2 (1.1105)
1
1
+
72 kg kmol 28.8 kg kmol
1/ 2
4; =, 7
Dsa = 8.29 x10 −6 m 2 / s = 0.0829 cm 2 / s
D!I
*'"K
Dso (0.40)
1 .5
= 0.022 cm 2 / s
Dsa ,eff =
Dsa ,eff
D
4; =+ 7
;';'6
$>
(
/ .
&
-
2 A.D 4
.
2,
D AB =
?
-
?
µ
) *NH"4'
1.17 x10 −13 T ξ B M B
4; =6 7
V A0.6 µ
: (
LE ?
"
$
ξ?
? 3
= J'
%
2 NH $4
2 A.D 4
K
Dso° =
1.17 x10 −13 (295 K ) (1)(400 kg kmol )
72 kg kmol
630 kg m 3
0.6
(23000 mPa • s )
4; =; 7
Dso° = 1.11x10 −13 m 2 s = 1.11x10 −9 cm 2 s
2 A.D 4
K
Dos° =
1.17 x10 −13 (295 K ) (1)(72 kg kmol )
400 kg kmol
980 kg m 3
0.6
(0.42 mPa • s )
Dos° = 1.19 x10 −9 m 2 s = 1.19 x10 −5 cm 2 s
DA
4; == 7
(
3
.
.
2,
) *NH"4K
Dso = (Dso° ) (Dos° )
xo
&
3
)
xs
4; =? 7
9
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=', .
.
(
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3
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(
2
%
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2
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)+
F+'"
4-
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4
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-
-
' =
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9
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/
-
'(
)
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D"
)
water
wire mesh
covered slit
H
packing of
corn syrup
+ glass beads
R
R
W
water +
corn syrup
!
='6
&
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)
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1 -
.
( 1
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0
(
DF
D.&'
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Z
)
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&
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3 !
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-
2
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%
D. 4' =
'
D+
= J
P
acrylic
housing
L = 20.3 cm
W = 10.6 cm
H = 52.7 cm
T
vapour sample
port
saturated
trough model
T
T
graduated
cylinder
T
water bath
liquid
pentane
!
=6
"
(
DH
*
5 Pjvap
(
V
K
Pjvap (T )
Pjvap
-
A−
= 10
B
T +C
4= + 7
,
E
5'
P A '!!! 2%
O0
%
.
?
PF'H" * ?P*!FD'FA
*NHF4' &
'
(
-
2 D. 4'
yj =
-
Pjvap
=
'
)
&
4= 6 7
P
)
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)
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6
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%
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4-
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Q+
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-
A!
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2*!A
-
4'
'
-
-
/ -
'
-
pore
space
1 – pore to pore distance = 1.79 mm
4
1
2 – pore width = 1.10 mm
3 – pore throat width = 0.30 mm
5
2
4 – particle size = 1.49 mm
6
5 – diffusion distance = 1.04 mm
3
6 – flow path length = 2.32 mm
solid
!
=? .
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.
2
=4
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G 56,,=7
(
3
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.%
2
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4
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%V-
-
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/
ν = Gt
L
4= ; 7
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2 D.D 4K
µ = νρ
=';'6
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4= = 7
)
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d
2 D." 4K
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-
,
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m Ho
mo
4= ? 7
=';'=
2/
)
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*
- 4
-
' (
-
' (
-
-
-
' (
*
'
wt % Ashpaltenes =
=';'?
3
mo 2
∗ 100%
mo1
4= B 7
2 (
0
'
)
-
-
)
)
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/
-
'
)
/
%
D.+
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/
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(
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2& &=4 -
2 D.+ 4K
"+
S or (% IOIP) =
mo ρ o
* 100
Vb φ
4= C 7
ρ
'
0 cm
Sample 1
3.8
12.7
Sample 2
Sample 6
Sample 7
15.2
Sample 5
φ
3
25.4
Sample 3
29.2
38.1
Sample 4
41.9
!
=C 3
2 ( "
"H
$
/
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. 1"
-
(
1
-
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1 (
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9
A!
%
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-
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2
*4
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Extracted
Porous Media
z(t
)
Interface
z=
Glass Beads
Saturated with
Corn Syrup
!
)
?+ .
"
-
1
"N
"
z=
z
ma
x
0
%
".
-
-
.
-
-
' (
-
/
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!'!!ND
:
2!'"FD
: 4' (
2 )
0
/
-
2 !!A4
4
2 !!*4
3
B
) )
9 2 !!"4'
5.0
y = 0.0094x + 0.2031
R2 = 0.9958
Depth of Interface (cm)
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
50
!
100
150
?6
()
200
250
Time (min)
300
-
350
!'*+
-
2 A. + 4
' %
)
*'D)*!
%
!' H 9:
2 : !a!' 4
)
450
1 #"
(
!' *N' $
400
4' (
."
: 2
"'*)*!
D!I
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F!
."
:
?'6
)
)
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-
#"
E
DE
+E
NE
( 1
A E -
!.*!!I'
?'6'+
(
0 1) 2
(
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%
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?; ( "
-
/
2
-
)
4' (
-
-
/
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F*
-
' (
N"E
(
/
-
)
A *+F
= J
*HI
2
E'
4-
-
-
N AH!
= J
E
F!I
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'
?'6'6
# "
&
%
)
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".D
-
.
' %
9
)
D! - I
' , -
D!I
-
)
'
D! - I
' %
-
E
NE
D!I
(-
'
E -
' %
-
'
(
"."
-
K
µ (cP ) = 0.37ω s −2.69
%
4? + 7
".F
-
2B
*NNN4
20
.
-
'
F
-
/
!!A4' (
FA
Dynamic Viscosity (mPa•s)
0.0
!
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
1
2
3
4
5
6
?=
-
!
&
"
(
Pentane Mass Fraction
)
0.8
T = 32°C
8
7
T = 29°C
T = 27°C
T = 24°C
T = 22°C
9
10
11
12
0.9
FD
Dynamic Viscosity (mPa•s)
!
0
5
10
15
20
25
??
0.2
3
0.3
&
0.4
0.6
)
2
Pentane Mass Fraction
0.5
.
0.7
# H 66I
0.8
T = 22°C Trial II
T = 22°C Trial I
0.9
14
Butane (Jin, 1999)
-2.12
µ (cP) = 0.95ωs
12
Viscosity (cP)
10
8
Pentane (this work)
-2.69
µ (cP) = 0.37ω
ωs
6
4
Propane (Ramakrishnan, 2003)
-1.28
µ (cP) = 1.12ωs
2
0
0.25
0.30
0.35
0.40
0.45
0.50
Mass Fraction of Solvent (ω
ωs)
!
?B
( 1
.
&
F"
"
) )( 1
#)
?';
( "" )
"
)
2
3
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4-
)
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1
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&
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.
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A"'"!
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F'++
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A
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QD4
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Q*4' (
Q+4
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FF
QH4'
QA
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(
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+
H2
-
(
".&4 ) )
)
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)
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.
3
)
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L
- /
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N'+NE
)
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2-
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)
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)
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)
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4
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%
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2
4
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-
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2
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.%
".+ 2 . 4
%
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- ' (
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A'
#
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!. %
(
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-
-
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2
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FH
2 4
2
4
2 4
2 4
2 4
2 4
2 4
2
2 4
!
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4
(
FN
1
254
2/4
2 4
2
2
2
4
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(
+!
4
1
4
7
4
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1
&
-
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&
'
-
&
/-
-
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)
%
-
".H' (
-
)
Q"
4
Q" 2
-
2
%
K
9
- -
".H4
2 4' %
/
)
-
"
2
%
&
4
*
)
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".H
' L
/
-
'
-
-
' & %
".H
P*DD!
)
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)
PD"N!
AD.AH
'
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)
9
-
'
%
".N
)
3
Q+
)
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)
+*
A
'
'
*+.*H
9
%
".H
-
%
".*!' ,
)
' 0
9
-
)
Q+
-
%
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)
2
4
%
- -
".*!
%
-
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".**
/
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(
".&&
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%
)
F
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)
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9
)
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)
9
-
'
*!
HI
-
HF'
+
H+'"I
'
0
5
360 min
3060 min
1440 min
15
4590 min
PENTANE
Distance from Top of Model (cm)
10
20
Vapex
Interface
25
30
35
40
5670 min
10
9
Capillary
Height
8
7
6
5
4
3
2
1
0
Horizontal Distance from Exposed Edge (cm)
!
?A
1
"
-
#
4
"
+A
E?7
! .
(
#"
Micromodel Filled with Bitumen
!
? 8<
Extracted
Region
!
.
"
&
4
+D
"
"
9
)EC5 H +AB, " 7
0.0
360 min
0.1
1440
min
0.3
3060
min
0.4
PENTANE
Relative Distance from Top of Interface
0.2
0.5
0.6
0.7
0.8
4590
min
0.9
1.0
1.00
0.75
0.50
0.25
0.00
Relative Horizontal Distance from Exposed Edge
!
? +,
"
G
(
1
#"
+"
"
4
#
"
E?7
! .
0.0
0.1
0.2
2820
min
0.3
0.4
0.5
PENTANE
Relative # of Pores from Top of Interface
240
min
1500
min
4740
min
0.6
0.7
0.8
0.9
1.0
1.00
0.75
0.50
0.25
0.00
Relative # of Invaded Pores from Exposed Edge
!
? ++
"
G
1
"
#"
4
+F
"
.
EA7
"
(
#
? -- # " 3 >
-
3
&
.
G 51 4 7
.
#)
E
# "
4I 7
4" 7
A*'D"
DHF
N'A"
A
4" 7
4:7
J"
4:7
D+*D
*!'
*"'
+H"
"! "
*"'F
H'
"'+H
H "
"H!!
*D'
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D
D'D*
F!"
FDF"
N'D
*D'*
"
H'*
AF!
"+""
F'A
*!'!
N'+N
D F!
"H !
+A'
HF'
N'A*
"+H"
"*H"
H*'N
H+'"
*
.
+
.
H
Z
(
/
/
'
/
/
/
%
-
".* ' (
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&
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'
/
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)
9
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-
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wall
solid
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(
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$
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$1 2
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-
%
'
)
92 4
-
'
+H
-
".*A' %
".*D
0
Vapex Interface
(centre)
5
15
PENTANE
Distance from Top of Model (cm)
10
20
Vapex Interface
(visual)
25
30
35
40
Capillary
Height
10
9
8
7
6
5
4
3
2
1
0
Horizontal Distance from Exposed Edge (cm)
!
? +;
-
"
4
+N
"
EB7
!
.
z
=
ge
d
z i,e
e
tr
n
e
z i,c 0
= z=
z
z
solvent
bitumen
extracted
porous
media
live oil
!
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-
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2
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-
45
Average # of Invaded Pores
40
Row 1
z = 0.9684 t - 16.858
Row 5
z = 0.8173 t - 14.525
Row 10
35
Row 13
z = 0.6675 t - 13.908
30
25
20
15
10
5
0
0
10
20
30
40
50
60
70
time (min)
!
? +? -
1
"
4
;
9
-
(>
"
%
EC7
".*"
-
H
%
".*F'
3
#"
80
Average # of Invaded Pores Normalized
by Model Width
1.0
0.9
Row 1
0.8
Row 10
z = 0.0218 tshift
Row 5
z = 0.0812 tshift
z = 0.0148 tshift
Row 13
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
10
20
30
40
50
60
tshift (min)
!
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10
z = 0.1776 t -2.6631
2
R = 0.9932
Interface Position, z (cm)
9
8
7
6
5
z = 0.1294 t -1.5819
2
R = 0.9493
4
3
2
20 cm
1
40 cm
0
0
10
20
30
40
50
60
".
#
70
80
Time (min)
!
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1
"
6,
HD
=, "
4
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10
Interface Position, z (cm)
9
8
7
z = 0.1775 tshift
6
R = 0.9932
2
z = 0.1295 tshift
5
R2 = 0.9493
4
3
2
20 cm
1
40 cm
0
0
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20
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%
Volume of Live Oil Produced (mL)
300
250
200
Vcum (mL) = 4.48 t - 51.23
150
100
50
0
0
1000
2000
3000
4000
5000
6000
Time (min)
!
%
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Cumulative Volume Produced (mL)
0
25
50
75
100
125
150
175
200
225
250
275
0
!
? 6,
500
"
1000
1500
"
2500
3000
1
3
Time (min)
2000
#
!
3500
"
4000
4500
T = 31.45°C
T = 29.35°C
T = 28.12°C
T = 25.78°C
T = 24.41°C
5000
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<
1 -
1.385
1.380
1.375
Refractive Index
1.370
1.365
y = 0.1377x + 1.3281
R2 = 0.9989
1.360
1.355
1.350
1.345
1.340
1.335
1.330
0%
5%
10%
15%
20%
25%
30%
Mass Percent Corn Syrup
%
*1
-
*!"
0
&
)
$
-
35%
40%
1.42E-05
1.40E-05
Diffusivity (cm2/s)
1.38E-05
1.36E-05
1.34E-05
1.32E-05
1.30E-05
1.28E-05
1.26E-05
0
%
50
100
150
1L
200
250
Time (min)
300
-
*!F
350
(
400
450
&
"
<
)
# "
0.4
y = 0.0013x + 0.018
Mass (g)
0.3
y = 0.0006x + 0.11
0.2
0.1
Heavy Oil
Heavy Oil - Ashphaltene Free
0.0
0
50
100
150
200
250
300
Time (s)
%
(
?'& 1 L
?* 1 % -
?
3
3
?
2 !
/
(
&
"
&
"
+.
+
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( !)
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*N'**
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*HN
A *+H
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*F"N
N AH!
0
0
1
*!+
"
"
( "
"
E?5 H+A,, "
Asurface = L * W
= (40 cm )(0.95 cm )
= 38.1 cm 2
3
=
A−
Pjvap (23.84) = 10
B
T +C
6.85221−
1064.63
23.08+ 232
= 10
= 476.89 mmHg
= 63.58 kPa
3
=
%
? /
vap
y s 0 = Ps (T )
P
63.58 kPa
=
102.47 kPa
= 0.62
*!H
<
G
=
%
ωs
xs
Ms
ωs 1 − ωs
+
Ms
Mb
=
0.47
72 g mol
=
0.47
1 − 0.47
+
72 g mol 400 g mol
= 0.83
3
=
%
3
)&
vap
y si = xs Ps (T )
P
(0.83)(63.58 kPa)
=
102.47 kPa
= 0.52
=
=
3
)&
Psi = x s Psvap (T )
= (0.83)(63.58 kPa )
= 52.85 kPa
% )
N s (t )
=
xs ρ s
dV
M s Asurface dt
xs ρ s
B
M s Asurface 2 t − F
=
(0.83)(0.63 g cm 3 )
4.4826 cm 3 min 0.5
(72 g mol )(38.1 cm 2 ) 2 1800 min − 11.43 min
= 1.01x10 −5 mol cm 2 min
*!N
L
Dsa ,eff
=
=
=
( N s (t )) RT (∆z ) ( Pa ) M
P
Pai − Pa 0
(1.01x10 −5 mol
cm 2 min
1000cm 3
L
)(8.314 kPaL
molK
102.47 kPa
)(296.23K )(4.91cm)
x
44.04kPa
49.62kPa − 38.89kPa
= 4.88 cm 2 min = 0.081 cm 2 s
L
=
Dsa ,eff τ
φ
(0.081 cm 2 s )(1.5)
0 .4
= 0.304 cm 2 s
=
300
Volume of Live Oil Produced (mL)
Dsa
250
200
150
Vcum = 4.56 t- 50.48
100
50
0
0
1000
2000
3000
4000
5000
Time (min)
%
*1G
=
**!
,
2 )
Q*4
Volume of Live Oil Produced (mL)
300
250
200
150
Vcum = 4.40 t - 62.48
100
50
0
0
1000
2000
3000
4000
5000
Time (min)
%
1G
=
,
2 )
Q 4
Volume of Live Oil Produced (mL)
300
250
200
Vcum = 4.93 t - 76.57
150
100
50
0
0
1000
2000
3000
4000
5000
Time (min)
%
A1G
=
***
,
2 )
QA4
6000
Volume of Live Oil Produced (mL)
300
250
200
Vcum = 4.81 t - 84.04
150
100
50
0
0
1000
2000
3000
4000
5000
6000
Time (min)
%
D1G
=
,
2 )
QD4
Volume of Live Oil Produced (mL)
300
250
200
Vcum (mL) = 4.48 t - 51.23
150
100
50
0
0
1000
2000
3000
4000
5000
6000
Time (min)
%
"1G
=
**
,
2 )
Q"4
11
10
Interface Position, z (cm)
9
z = 0.1774 t - 1.9328
R2 = 0.98
8
7
6
5
z = 0.1521 t - 1.9916
R2 = 0.94
4
3
2
20 cm
1
40 cm
0
0
10
20
30
40
50
60
70
80
Time (min)
%
F1&
!
D!
(
2 )
Q*4
11
10
z = 0.1746 t - 2.3623
R2 = 0.97
Interface Position, z (cm)
9
8
7
6
5
4
z = 0.1446 t - 2.0815
R2 = 0.94
3
2
20 cm
1
40 cm
0
0
10
20
30
40
50
60
70
80
Time (min)
%
+1&
!
**A
D!
(
2 )
Q 4
11
10
Interface Position, z (cm)
9
z = 0.1956 t - 3.4209
R2 = 0.98
8
7
6
5
4
z = 0.1598 t - 4.1941
R2 = 0.95
3
2
20 cm
1
40 cm
0
0
10
20
30
40
50
60
70
80
Time (min)
%
H1&
!
D!
(
2 )
QA4
11
10
Interface Position, z (cm)
9
8
7
z = 0.1742 t - 2.8483
R2 = 0.99
6
5
z = 0.1374 t - 3.0358
R2 = 0.96
4
3
2
20 cm
1
40 cm
0
0
10
20
30
40
50
60
70
80
90
Time (min)
%
N1&
!
**D
D!
(
2 )
QD4
10
z = 0.1776 t -2.6631
R2 = 0.9932
9
Interface Position, z (cm)
8
7
6
5
z = 0.1294 t -1.5819
R2 = 0.9493
4
3
2
20 cm
1
40 cm
0
0
10
20
30
40
50
60
70
80
Time (min)
%
*! 1 &
!
D!
(
2 )
Q"4
45
Row 1
Average # of Invaded Pores
40
Row 5
Row 10
35
Row 13
z = 0.9684 t - 16.858
z = 0.8173 t - 14.525
z = 0.6675 t - 13.908
30
25
20
15
10
5
0
0
10
20
30
40
50
60
70
80
Time (min)
%
** 1 &
0 - 2 )
**"
Q+4
45
40
# of Invaded Pores
35
Row 1
z = 0.8137 t - 9.8277
Row 5
z = 0.7690 t - 9.6237
Row 9
z = 0.6642 t - 8.8544
30
25
20
15
10
5
0
0
20
40
60
80
Time (min)
%
* 1&
0 - 2 )
QH4
10
Interface Position, z (cm)
9
8
7
z = 0.1774 tshift
6
R2 = 0.98
z = 0.1521 tshift
5
R2 = 0.93
4
3
2
20 cm
1
40 cm
0
Linear
0
10
20
tshift
%
*A 1 (
5
=
30
40
t (min) -
t0 (min)
&
!
2 )
**F
Q*4
50
D!
60
(
10
Interface Position, z (cm)
9
8
z = 0.1747 tshift
7
R2 = 0.96
6
5
z = 0.1447 tshift
4
R2 = 0.92
3
2
20 cm
1
40 cm
0
0
10
20
tshift
%
*D 1 (
5
=
30
40
t (min) -
t0 (min)
&
!
2 )
50
60
D!
(
Q 4
10
Interface Position, z (cm)
9
8
7
z = 0.1956 tshift
6
R2 = 0.98
5
z = 0.1599 tshift
R2 = 0.94
4
3
2
20 cm
1
40 cm
0
0
10
20
tshift
%
*" 1 (
5
=
30
t (min) -
&
40
t0 (min)
!
2 )
**+
QA4
50
D!
(
10
Interface Position, z (cm)
9
8
7
z = 0.1743 tshift
6
R2 = 0.99
z = 0.1202 tshift
5
R2 = 0.93
4
3
2
20 cm
1
40 cm
0
0
10
20
tshift
%
*F 1 (
5
30
=
40
t (min) -
&
50
70
t0 (min)
!
2 )
60
D!
(
QD4
10
Interface Position, z (cm)
9
8
7
z = 0.1775 tshift
6
R2 = 0.9932
z = 0.1295 tshift
5
R2 = 0.9493
4
3
2
20 cm
1
40 cm
0
0
10
20
tshift
%
*+ 1 (
5
30
=
40
t (min) -
&
50
**H
Q"4
70
t0 (min)
!
2 )
60
D!
(
45
Row 1
40
Row 5
# of Invaded Pores
35
30
z = 0.0218 tshift
Row 10
z = 0.0812 tshift
Row 13
z = 0.0148 tshift
25
20
15
10
5
0
0
10
20
tshift
%
*H 1 (
5
30
=
t (min)
40
-
50
60
t0 (min)
&
0 -
2 )
Q+4
45
40
# of Invaded Pores
35
Row 1
z = 0.8137 tshift
Row 5
z = 0.7691 tshift
Row 9
z = 0.6643 tshift
30
25
20
15
10
5
0
0
10
20
tshift
%
*N 1 (
5
=
30
40
t (min) -
t0 (min)
&
2 )
**N
50
60
0 QH4
Effective Diffusivity Dsa,eff (cm2/s)
0.12
0.10
Dsa,eff = -8.2784t-1/2 + 0.4933
0.08
R2 = 0.89
0.06
0.04
0.02
0.00
0
0.01
0.02
0.03
0.04
0.05
0.06
1/sqrt [ Time (min) ]
%
!1L
.(
0
2 )
Q*4
Effective Diffusivity Dsa,eff (cm2/s)
0.09
0.08
0.07
0.06
0.05
0.04
Dsa,eff = -3.52527t-1/2 + 0.33507
R2 = 0.81
0.03
0.02
0.01
0.00
0
0.01
0.02
0.03
0.04
0.05
1/sqrt [ Time (min) ]
%
*1L
.(
* !
0
2 )
Q 4
Effective Diffusivity Dsa,eff (cm2/s)
0.09
0.08
0.07
Dsa,eff = -7.85176t-1/2 + 0.42377
0.06
R2 = 0.96334
0.05
0.04
0.03
0.02
0.01
0.00
0
0.01
0.02
0.03
0.04
0.05
0.06
1/sqrt [ Time (min) ]
%
1L
.(
0
2 )
QA4
Effective Diffusivity Dsa,eff (cm2/s)
0.10
Dsa,eff = -5.5139t-1/2 + 0.4081
0.09
R2 = 0.913
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
0
0.01
0.02
0.03
0.04
0.05
1/sqrt [ Time (min) ]
%
A1L
.(
* *
0
2 )
QD4
0.06
Effective Diffusivity (cm2/s)
0.12
0.10
0.08
Dsa,eff = -5.36208t-1/2 + 0.43187
R2 = 0.95
0.06
0.04
0.02
0.00
0
0.02
0.04
0.06
0.08
0.1
1/sqrt(Time (min))
%
D1L
.(
0
2 )
Q"4
Effective Diffusivity, Dsa,eff (cm2/s)
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
500
1000
1500
2000
2500
tshift (min)
%
"1
G
(
2 )
*
(
=
L
Q*4
3000
3500
Effective Diffusivity, Dsa,eff (cm2/s)
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
500
1000
1500
2000
2500
3000
3500
tshift (min)
%
F1
G
(
(
=
2 )
L
Q 4
Effective Diffusivity, Dsa,eff (cm2/s)
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
500
1000
1500
2000
2500
tshift (min)
%
+1
G
(
2 )
* A
(
=
L
QA4
3000
3500
Effective Diffusivity, Dsa,eff (cm2/s)
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
500
1000
1500
2000
2500
3000
3500
tshift (min)
%
H1
G
(
(
=
2 )
L
QD4
Effective Diffusivity, Dsa,eff (cm2/s)
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
500
1000
1500
2000
2500
3000
tshift (min)
%
N1
G
(
2 )
* D
(
=
L
Q"4
3500
4000
32
Temperature (°C)
30
28
26
24
22
Pentane
20
Model Top
Model Bottom
18
0
1000
%
2000
3000
Time (min)
A! 1 (
,
2 )
4000
5000
Q*4
32
30
Temperature (°C)
28
26
24
22
Pentane
20
Model Top
Model Bottom
18
0
1000
%
2000
3000
Time (min)
A* 1 (
,
* "
2 )
4000
Q 4
5000
32
30
Temperature (°C)
28
26
24
22
Pentane
20
Model Top
Model Bottom
18
0
1000
%
2000
3000
Time (min)
A 1(
,
4000
5000
2 )
6000
QA4
32
30
Temperature (°C)
28
26
24
22
Pentane
20
Model Top
Model Bottom
18
0
1000
%
2000
3000
Time (min)
AA 1 (
,
* F
4000
2 )
5000
6000
QD4
32
Temperature (°C)
30
28
26
24
22
Pentane
Model Top
20
Model Bottom
18
0
1000
%
2000
AD 1 (
3000
Time (min)
,
4000
2 )
5000
6000
Q"4
32
30
Temperature (°C)
28
26
24
22
Pentane
20
Model Top
Model Bottom
18
0
1000
2000
3000
4000
5000
Time (min)
%
A" 1 (
,
* +
2 )
Q+4
6000
32
30
Temperature (°C)
28
26
24
22
Pentane
20
Model Top
Model Bottom
18
0
1000
%
2000
AF 1(
3000
4000
Time (min)
,
2 )
5000
6000
QH4
50
45
Surface Area (cm2)
40
35
30
25
20
15
10
5
0
0
1000
2000
3000
4000
Time (min)
%
A+ 1
3
* H
)&
5000
6000
45
Row 1
Row 5
Row 10
Row 13
Average # of Invaded Pores
40
35
30
25
20
15
10
5
0
0
1000
2000
3000
4000
5000
6000
Time (min)
%
AH 1 ;
(
.G
&
0 - 2 )
'& 1 0
Exp’t #
Q+4
G
Sample Location
4
5
1
2
3
6
7
1
6.0
3.7
6.1
22.8
3.2
4.7
5.3
2
4.1
3.4
3.8
16.8
2.7
3.9
4.5
3
4.6
4.4
3.3
15.5
2.5
3.9
4.1
4
3.8
3.0
3.3
18.6
2.3
3.6
4.0
5
4.4
3.9
4.3
24.2
3.1
4.1
5.2
* N