S t a n f o r d Geothermal Program
I n t e r d i s c i p l i n a r y Research
i n Engineering and E a r t h S c i e n c e s
Stanford University
Stanford, California
c
THE EFFECTS OF TEMPERATURE AND PRESSURE ON
ABSOLUTE PERMEABILITY OF SANDSTONES
c
by
Muhammadu Aruna
April 1976
T h i s r e s e a r c h was c a r r i e d o u t
under Research Grant GI- 34925
by t h e N a t i o n a l Science Foundation
-
ACKNOWLEDGEMENT
I
T h e a u t h o r would l i k e t o e x p r e s s h i s s i n c e r e a p p r e c i -
I
a t i o n t o h i s a d v i s e r , D r . Henry J. Ramey, Jr., for h i s i n s t r u c t i o n and g u i d a n c e t h r o u g h o u t t h e r e s e a r c h work.
He
I
made it p o s s i b l e f o r t h e a u t h o r t o come t o S t a n f o r d U n i v e r s i l y
I
and c o m p l e t e h i s g r a d u a t e s t u d i e s s u c c e s s f u l l y .
I
I I
I
The a s s i s t a n c e and p r a c t i c a l s u g g e s t i o n s from t h e
I
I
f a c u l t y o f t h e Department o f P e t r o l e u m E n g i n e e r i n g , p a r t i c u I
l a r l y from Dr. W. E . Brigham and D r .
a r e g r a t e f u l l y acknowledged.
S u l l i v a n S . Marsden,
1
The c o o p e r a t i o n I e n j o y e d from
t h e d e p a r t m e n t s e c r e t a r i e s , e s p e c i a l l y from A l i c e Mansouria4,
I
w i l l not be forgotten.
I
Many t h a n k s a r e due t o m y f r i e n d s , p a r t i c u l a r l y R o r i o
A r i h a r a , H. K . Chen, and P a u l A t k i n s o n , f o r t h e i r h e l p f u l
~
I
comments and Timely h e l p t h r o u g h the d a y s of e x p e r i m e n t a l w&k.
C r e d i t f o r m d i f i c a t i o n of t h e a p p a r a t u s b u i l t by Wei4
b r a a d t and Cass6 i s due Jon Grim, t h e P e t r o l e u m E n g i n e e r i n g 1
Dezs-tnent m a c h i n i s t .
F i n a l l y , Dr. F. Ca.ss6 reviewed t h i s m a n u s c r i p t and ma&
E?--: ? s l p f u l
I
sugg3stions'.
~
?>lis w s ~ kwas fund.ed u n d e r N a t i o n a l S c i e n c e Foundatiovl
pm=
_-'7.3L..-r-
GI- 34925.
I
i
T h i s r e p o r t was p r e p a r e d o r i g i n a l l y as a
d i s s e r t a t i o n sub,mitted to t h e Department of
Petroleum E n g i n e e r i n g and t h e Committee on t h e
Graduate D i v i s i o n of S t a n f o r d U n i v e r s i t y i n
p a r t i a l f u l f i l l m e n t of the requirements f o r the
d e g r e e of Doctor of Philosophy.
ii
DEDICLTED TO MY PARENTS AND
ALL THE GOOD PEOPLE I N MY L I F E
I
iii
J
J
J
J
J
ABSTUCT
The s t a n d a r d procedurle f o r d e t e r m i n i n g t h e p e r m e a b i l i t y
c
of porous media a c c o r d i n g t:o API Code Mo. 2 7 i s b a s e d on t h e
fundamental a s s u m p t i o n t h a t : , as l o n g as v i s c o u s f l o w p r e v a i l s ,
I
I '
t h e a b s o l u t e p e r m e a b i l i t y of a porous medium i s a p r o p e r t y of
t h e medium, a n d i s independlent of t h e f l u i d u s e d i n i t s deter-11
m i n a t i o n , s l i p e f f e c t b e i n g t a k e n i n t o a c c o u n t i n t h e case of
gas f l o w .
Absolute permeability has, t h e r e f o r e , been t r a d i t i o d -
a l l y measured a t room c o n d i t i o n s , w i t h t h e a s s u m p t i o n t h a t it
I
changes o n l y w i t h o v e r b u r d e n p r e s s u r e and n o t w i t h t e m p e r a t u r e +
R e s u l t s o b t a i n e d a t room t e m p e r a t u r e may t h e n b e u s e d t o p r e d i c t performance a t r e s e r v o i r c o n d i t i o n s a f t e r c o r r e c t i o n f o r
I
1
~
r e d u c t i o n by s t r e s s e f f e c t s .
11
Although t h i s a s s u m p t i o n i s t r u e for m o s t f l u i d s , r e s u l t s of r e c e n t a b s o l u t e p e r m e a b i l i t y measurements of water
flow t h r o u g h p o r o u s media a t h i g h t e m p e r a t u r e s
I
I
I
and h i g h
o v e r b u r d e n p r e s s u r e s d i f f e r from room c o n d i t i o n v a l u e s .
Not
o n l y was t h e a b s o l u t e p e r m e a b i l i t y t o water a t h i g h c o n f i n i n g
p r e s s u r e l o w e r t h a n t h a t to1 o t h e r f l u i d s u s e d a t room t e m p e r a -
t u r e , b u t also, t h e r e was a s i g n i f i c a n t p e r m e a b i l i t y r e d u c t i o n
~l
a t elevated temperatures.
An e x i s t i n g p e r m e a n e t e r w a s m o d i f i e d t o e n a b l e f l o w o f
I
d i f f e r e n t f l u i d s t h r o u g h s e p a r a t e flow l i n e s .
Distilled
water, a w h i t e m i n e r a l o i l , n i t r o p e n and 2 - o c t a n o l were t h e
iv
I
f l u i d s u s e d , and t e s t s were c a r r i e d o u t on n a t u r a l c o n s o l i d a t e d s a n d s t o n e s and u n c o n s o l i d a t e d s i l i c a s a n d .
With t h e e x c e p t i o n of w a t e r , t h e a b s o l u t e p e r m e a b i l i t i e s
of t h e cores t o o t h e r f l u i d s showed l i t t l e o r no t e m p e r a t u r e
dependence.
The r e d u c t i o n i n p e r m e a b i l i t y t o w a t e r w i t h
11
t e m p e r a t u r e i n c r e a s e w a s a t t r i b u t e d t o i n t e r a c t i o n between
water and s i l i c a .
I n t h e case of water f l o w t h r o u g h geothermd 1
s y s t e m s o r i n t h e r m a l r e c o v e r y p r o c e s s e s which c a u s e l a r g e
I
c h a n g e s i n f o r m a t i o n t e m p e r a t u r e s , t h e e f f e c t of t e m p e r a t u r e s
l
on a b s o l u t e p e r m e a b i l i t y s h o u l d be c o n s i d e r e d i n e n g i n e e r i n g
calculations.
I
V
TASLE
-
OF CONTENTS
Page
...................
ABSTRACT, . . . . . . . . . . . . . . . . . . . . . . .
TABLE OF CONTENTS . . . . . . . . . . . . . . . . . .
L I S T OF TABLES. . . . . . . . . . . . . . . . . . . .
L I S T OF FIGURES . . . . . . . . . . . . . . . . . . .
ACKNOWLEDGEMENT
iv
V
vii
X
xi
CFAPTERS
INTRODUCTION.
1
2.
FLOW
4
2.1
2.2
......
2 . 4 V i s c o - I n e r t i a l Flow. . . . . . . . . .
LITERATURE. . . . . . . . . . . . . . . . .
EXPERIMENTAL EQUIPMENT. . . . . . . . . . .
4 . 1 General D e s c r i p t i o n . .
.. . .
4 . 2 C o r e Holder. . . . . . . . . . . . . .
4.3
A i r B a t h and T e m p e r a t u r e C o n t r o l . . .
4.4
L i q u i d and Gas S o u r c e s . . . . . . . .
2.3
3.
4.
c
...............
I N POROUS YEDIA. . . . . . . . . . . .
D a r c y ' s Law. . . . . . . . . . . . . .
D a r c y ' s Law for Gas Flow . . . . . . .
1.
c
4.5
4.6
4.7
S l i p Phenomena i n G a s F l o w
.............
Hydraulic Hand P u n y . . . . . . . . . .
Heat Exchangers. . . . . . . . . . . .
Liq,uid Pumps
L
vi
4
5 '
6 1;
7
9
15
1
15
~
18
18
20
21
21
21
'
T a b l e of C o n t e n t s , c o n t i n u e d
Page
.....
4.8
B a c k p r e s s u r e Valve
4.9
Flow Rate M e a s u r i n g D e v i c e s .
Liquid Flow
22
4.9- 2
Gas F l o w
23
PROCEDURE
5.1
Core
.
23
............
Preparation . . . . . .
5.1- 1
5.1- 2
6.
22
4.9- 1
4 - 1 0 Pressure R e c o r d i n g D e v i c e s
5.
22
25
25
25
U n c o n s o l i d a t e d O t t a w a Sand
26
.
5.2
E s t a b l i s h i n g Run C o n d i t i o n s .
5.3
Measurements and C a l c u l a t i o n s .
6.2
6.3
6.4
6.5
27
28
5.3- 1
Liquid Flow
28
5.3- 2
Gas Flow
37
ANALYSIS OF RESULTS AND DISCUSSION.
6.1
J
C o n s o l i d a t e d M a s s i l l o n Sands t o n es
Water Flow
...........
.
41
41
6.1- 1
Consolidated Sandstones
41
6.1- 2
U n c o n s o l i d a t e d Sand
43
...........
48
6.2- 1
Consolidated Sandstones
50
6.2- 2
U n c o n s o l i d a t e d Sand
56
G a s Flow
.........
2-Octanol Flow . . . . . .
Discussion . . . . . . . .
O i l Flow
3
56
58
62
7.
C ONC LU S I O N S AND R.EC OIWENDAT I O N S
65
8.
REFERENCES.
..........
67
vii
3
J
Table of C o n t e n t s , c o n t i n u e d
9.
APPENDICES.
.. ....
.- ...
.... ......
9.1
L i s t of T a b u l a t e d Data
9.2
C o r e Data.
70
..
.... .
9.4
L i s t of M a n u f a c t u r e r s . . . . . . . .
NOMENCLATURE.
.... .....
9.3
10.
Page
D e r i v a t i o n s of E q u a t i o n s
,
c
viii
71
90
94
99
102
-
'LI'ST OF TABLES
I
I
Table
1
Page
D e n s i t y a n d V i s c o s i t y of Water v s .
Temperature
72
2
Viscosity
73
3
V i s c o s i t y of Chevron . O i l No.
Temperature
74
Density of
75
.................
of N i t r o g e n vs. Temperature . .
.
. . . . . . . . .3 .vs.. . . . . . .
2-Octanol vs. T e m p e r a t u r e . . . . .
V i s c o s i t y of 2-Octanol v s . Temperature.
...
10
11
12
13
14
15
F l o w D a t a for M a s s i l l o n S a n d s t o n e Core N o .
Water Flow.
. . . . . . . . . . . . . . . .3 ,.
78
Flow D a t a for M a s s i l l o n S a n d s t o n e Core No. 4,
Water Flow.
80
.................
Flow Data for M a s s i l l o n S a n d s t o n e Core N o . 5,
N i t r o g e n Flow . . . . . . . . . . . . . . . .
F l o w D a t a for M a s s i l l o n Sandstone Core N o . 6 ,
N i t r o g e n Flow . . . . . . . . . . . . . . . .
F l o w Data for P ? a s s i l l o n S a n d s t o n e Core N o .
1 0 , O i l Flow. . . . . . . . . . . . . . . . .
Flow Data for M a s s i l l o n S a n d s t o n e Core N o .
11, O i l Flow.
F l o w Data f o r
Sand Core N o .
Flow Data f o r
Sand Core No.
................
Unconsolidated O t t a w a S i l i c a
1 4 , Water Flow. . . . . . . . .
Unconsolidated O t t a w a S i l i c a
1 5 , Water Flow. . . . . . . . .
!I
I
76
77
,
11
1
iI
81
I
82
84
I
85
I
I
I
86
87
F l o w Data for U n c o n s o l i d a t e d O t t a w a S i l i c a
Sand Core N o . 1 6 , N i t r o g e n Flow a n d Water
Flow..
88
I!
Flow Data f o r U n c o n s o l i d a t e d O t t a w a S i l i c a
Sand Core No. 1 7 , 2-Octanol Flow.
89
'I
...................
16
1
F l o w D a t a f o r M a s s i l l o n S a n d s t o n e Core N o .
Water Flow.
. . . . . . . . . . . . . . . .2,.
I I
......
ix
LIST
-
OF FIGUP,ZS
Page
-
Figure
4
5
D e n s i t y of Water1 v s . T e m p e r a t u r e of 2 0 0 p s i g
6
Water V i s c o s i t y v s . T e m p e r a t u r e a t 2 0 0 p s i g
7
2
3
8
9
10
11
12
c
..
..
..
..
.........
D e t a i l s of Assembly i n t h e A i r B a t h . . .
S c h e m a t i c Diagra.m o f A p p a r a t u s . . . . . .
Schematic Diagram of t h e Core H o l d e r . . .
1
13
14
15
P h o t o g r a p h of A p p a r a t u s
16
16
17
19
31
.
32
D e n s i t y v s . T e m p e r a t u r e for Chevron White
Oil No. 3 a t 14.7 p s i
.........
33
V i s c o s i t y v s . Temperature for Chevron White
OilNo. 3 . .
34
D e n s i t y of 2-Octanol v s . T e m p e r a t u r e a t 1 4 . 7
psi
35
..
...... .........
.....................
V i s c o s i t y of 2-Octanol v s . T e m p e r a t u r e . . . .
V i s c o s i t y of N i t r o g e n v s . T e m p e r a t u r e .
..
~
36
39
Water P e r m e a b i l i t y v s . T e m p e r a t u r e , M a s s i l l o n
S a n d s t o n e Core No. 2 .
42
Water P e r m e a b i l i t y
S a n d s t o n e Core No.
44
...........
vs. Temperature, Massillon
3. . .
.........
Water P e r m e a b i l i t y v s . T e m p e r a t u r e a t a
C o n s t a n t C o n f i n i n g P r e s s u r e of 3000 p s i g ,
M a s s i l l o n S a n d s t o n e Core No. 3 .
.......
45
Water P e r m e a b i l i t y vs. T e m p e r a t u r e , M a s s i l l o n
S a n d s t o n e Core No. 4 .
46
............
16
Water P e r m e a b i l i t y v s . T e m p e r a t u r e , Unconsolid a t e d O t t a w a S i l i c a Sand Core N o . 1 4 .
47
17
Water P e r r r - e a h i l i t y v s . T e m p e r a t u r e , O t t a w a
S i l i c a Sand Core No. 1 5
....
......... .
X
49
,
J
L i s t df €Figures, c o n t i n u e d
Figure
18
Page
Apparent P e r m e a b i l i t y vs. Xeciprocal
Mean P r e s s u r e a t S e v e r a l T e m p e r a t u r e s
for M a s s i l l o n Core No. 5.
51
M o d i f i e d V i s c o - I n e r t i a l Graph, M a s s i l l o n
C o r e N o . 5 w i t h N i t r o g e n Flow
52
..........
19
20
21
........
A p p a r e n t P e r m e a b i l i t y v s . I i e c i p r o c a l Mean
P r e s s u r e a t S e v e r a l T e m p e r a t u r e s for M a s s i l l o n
S a n d s t o n e Core N o . 6 , C o n f i n i n g P r e s s u r e =
1000 p s i g
53
..................
P e r m e a b i l i t y v s . R e c i p r o c a l Mean
Apparent
P r e s s u r e a t S e v e r a l T e m p e r a t u r e s for Mass i l l o n S a n d s t o n e Core 110. 6 , C o n f i n i n g Pressure
3000 p s i g .
.
22
...............
54
J
A p p a r e n t P e r m e a b i l i t y vs. R e c i p r o c a l Mean
P r e s s u r e a t S e v e r a l Temperatures for M a s s i l l o n
S a n d s t o n e Core No. 6 , C o n f i n i n g P r e s s u r e =
4000 p s i g
55
..................
23
24
A p p a r e n t P e r m e a b i l i t y v s . R e c i p r o c a l Mean
P r e s s u r e a t S e v e r a l T e m p e r a t u r e s for O t t a w a
S i l i c a Sand Core No. 1 6 , C o n f i n i n g P r e s s u r e =
2000 p s i g
..................
O i l P e r a e a b i l i t y 'vs. T e E p e r a t u r e for M a s s i l l o n
Core So. 10 . . . . . . . . . . . . . . . . .
J
57
59
25
O i l P s r n e a b i l i t y v s . T e m p e r a t u r e for M a s s i l l o n
CcFe KO. 11
60
26
2 - O c ~ z n o l P e r m e a b i l i t y vs.
.................
Temperature f o r
U n c c r - s o i i d a t e d O t t a w a S i l i c a Sand Core N o . 1 7
61
J
J
J
1,.
L?VIiODUCTION
A long held conclusion t h a t t h e absolute permeability
of a p o r o u s medium i s a c o n s t a n t d e t e r m i n e d o n l y by t h e
s t r u c t u r e of t h e medium i n q u e s t i o n i s t h e s u b j e c t of t h i s
study.
Experiments d e s i g n e d t o m e a s u r e t h e a b s o l u t e p e r -
m e a b i l i t y of porous media h a v e shown
t h a t the absolute
,
~
p e r m e a b i l i t y t o water f o r c e r t a i n s a n d s t o n e c o r e s v a r i e s w i t +
t h e l e v e l of c o n f i n i n g p r e s s u r e as w e l l as w i t h t e m p e r a t u r e .
F o r w a t e r f l o w , p e r m e a b i l i t y r e d u c t i o n s of up t o 6 0 % were
I
o b s e r v e d when t e m p e r a t u r e was i n c r e a s e d f r o m 7OoF t o 30OoF.
I
This i m p o r t a n t d i s c o v e r y m y h a v e s i g n i f i c a n t r a m i f i I
c a t i o n s i n many o i l r e c o v e r y by thermal p r o c e s s e s .
The i n -
1
1
I
j e c t i o n of h o t water and steam i n t o o i l r e s e r v o i r s , underg r o u n d c o m b u s t i o n , i n j e c t i o n of f l u i d s i n t o w e l l s , t h e prod u c t i o n of g e o t h e r m a l e n e r g y , and t h e d i s p o s a l o f atomic
waste p r o d u c t s i n p o r o u s f o r m a t i o n s a l l c a u s e changes i n
I
formation temperatures.
I n r e s e r v o i r engineering, a b s o l u t e permeability i s a
b a s i c p a r a m e t e r which h a s o f t e n b e e n measured a t room con-
~1
d i t i o n s , w i t h t h e i m p l i c i t assumption t h a t only confining
p r e s s u r e affected the r e s u l t .
(Of c o u r s e w e i g n o r e t h e w e 1 4
known r e a c t i o n s between w a t e r and c l a y s . 1
Hitherto, there-
f o r e , a s i n g l e value of a b s o l u t e p e r m e a b i l i t y throughout a
r a n g e of r e s e r v o i r t e m p e r a t u r e s has b e e n used in r e s e r v o i r
engineering calculations.
t
d
Weinbrandtl'
found foir water f l o w , t h a t t h e a b s o l u t e
p e r m e a b i l i t y of c o n f i n e d , f i r e d s a n d s t o n e cores w a s s t r o n g l y
temperature dependent.
2
J
Casse v e r i f i e d t h e Weinbrandt r e s u l t .
I n r a i s i n g t h e t e m p e r a t u r e l e v e l of a f i r e d c o n s o l i d a t e d
s a n d s t o n e core u n d e r a c o n f i n i n g p r e s s u r e of 2 0 0 0 p s i f r o m
J
room t e m p e r a t u r e t o 3OO0F, h e o b s e r v e d a r e d u c t i o n i n a b s o l u t e
p e r m e a b i l i t y of as much as 65%.
With m i n e r a l o i l flow, or
i n e r t g a s f l o w , he found t h a t t e m p e r a t u r e had no a p p r e c i a b l e
J
e f f e c t on a b s o l u t e permeabilt i t y .
Recently, Arihara2 r e p o r t e d
t h a t i n h i s w a t e r f l o w e x p e r i m e n t s t h r o u g h s y n t h e t i c cementc o n s o l i d a t e d s a n d cores, h e d i d n o t o b s e r v e t e m p e r a t u r e
J
e f f e c t s on a b s o l u t e p e r m e a b i l i t y .
However, h e a p p l i e d l o w
confining pressures.
Cassgl suggested t h a t clay- water i n t e r a c t i o n caused t h e
permeability r e d u c t i o n he observed.
I
However, G r e e n b e r g , e t al.
4
i n 1 9 6 8 r e p o r t e d d a t a o n t h e p e r m e a b i l i t i e s t o w a t e r o f core
samples a r t i f i c i a l l y c o n s o l i d a t e d w i t h p h e n o l i c r e s i n o r by
sintering.
J
The g e n e r a l t r e n d showed s l i g h t t o moderate de-
creases i n p e r m e a b i l i t y w i t h i n c r e a s i n g t e m p e r a t u r e .
f i n i n g p r e s s u r e w a s a p p l i e d to the core.
N o con-
They a t t r i b u t e d t h e
J
observed changes t o m i c r o - s t r u c t u r a l re- arrangements i n t h e
m a t r i x geometry of t h e sampl-es which had a rough and i r r e g u l a r
surface.
They o b s e r v e d no c h a n g e s i n p e r m e a b i l i t i e s f o r
J
samples w i t h r e l a t i v e l y smooth s u r f a c e s .
The p u r p o s e of t h i s work w a s (1) t o v e r i f y t h e r e s u l t s
of p r e v i o u s s t u d i e s , ( 2 ) t o e x t e n d t h e p r e v i o u s work t o o t h e r
s y s t e m s , and ( 3 ) t o i n v e s t i g a t e t h e r e a s o n f o r t e m p e r a t u r e
J
i
-2d
--
I ,
e f f e c t s on a b s o l u t e p e r m e a b i l i t y .
I n order t o provide a
c l u e as t o what a c t u a l l y c a u s e d t h e p e r m e a b i l i t y t o d e c r e a s e
w i t h i n c r e a s i n g t e m p e r a t u r e , it was d e c i d e d t o u s e c l a y - f r e e
r o c k s and o t h e r p o l a r l . i q u i d s , such as 2 - o c t a n o l .
\-
I.
c.
c
L
-3-
2.
FLOW IN POROUS WDIA
I n 1 8 5 6 , as a r e s u l t of e x p e r i m e n t a l s t u d i e s on t h e f l o
7
of water t h r o u g h u n c o n s o l i d a t e d s a n d f i l t e r b e d s , Henry Darcyk
f o r m u l a t e d a flow l a w which now b e a r s h i s name.
T h i s l a w hag
been extended t o d e s c r i b e , w i t h some l i m i t a t i o n s , t h e movemeqt
of o t h e r f l u i d s , i n c l u d i n g t w o or more i m m i s c i b l e f l u i d s , i n
c o n s o l i d a t e d r o c k s and 0 t h r p o r o u s media.
2.1
Darcy's' L a w
Darcy's law, f o r t h e h o r i z o n t a l , v i s c o u s f l o w o f a f l u i d
i n a l i n e a r medium, s t a t e s t h a t t h e flow v e l o c i t y of a homogeneous f l u i d i s p r o p o r t i o n a l t o t h e p r e s s u r e g r a d i e n t , and
i n v e r s e l y p r o p o r t i o n a l t o t h e f l u i d v i s c o s i t y , or:
(2-
where v i s t h e v e l o c i t y i : n cm/sec, a_ i s t h e f l o w r a t e i n c c /
sec, p i s t h e f l u i d v i s c o s i t y i n c p , d p / d s i s t h e p r e s s u r e
gradient i n atm/cm,
t a k e n i n t h e f i r e c t i o n o f f l o w , and k
i s t h e rock permeability, d a r c i e s .
A r o c k of one d a r c y p e r -
m e a b i l i t y i s one i n which a f l u i d of o n e c e n t i p o i s e v i s c o s i t j
w i l l move a t a v e l o c i t y o f o n e c e n t i m e t e r p e r second under a
p r e s s u r e g r a d i e n t of o n e a t m o s p h e r e p e r c e n t i m e t e r .
D a r c y ' s l a w a p p l i e s o n l y i n t h e r e g i o n of l a m i n a r f l o w .
F o r " t u r b u l e n t " or n o n - l a m i n a r f l o w s which o c c u r a t h i g h e r
velocities, the pressure gradient increases at a greater rate
t h a n d o e s t h e flow r a t e .
-4-
A c o r r e l a t i o n produced by F a n c h e r , L e w i s , and Barnes 5
may b e used t o e s t i v a t e t h e r e p i o n of v i s c o u s flow f o r a
p o r o u s medium.
I n g e n e r a l , 9 a r c y ' s l a w is v a l i d f o r p o r o u s
media when a m o d i f i e d Reynolds' number
IJ
R e = vd P
i s less t h a n one.
v i s v e l o c i t y , p i s f l u i d d e n s i t y , 1.1 i s
t h e f l u i d v i s c o s i t y , and d i s t h e d i a m e t e r of t h e a v e r a g e
grain size.
A r e c e n t s t u d y by Geertsma'
showed t h a t t h e a v e r a g e
g r a i n s i z e s h o u l d b e r e p l a c e d by a r a t i o of p e r m e a b i l i t y t o ' '
porosity t o provide a b e t t e r correlation.
The r e q u i r e m e n t t h a t t h e p e r m e a b i l i t y be d e t e r m i n e d
for c o n d i t i o n s of v i s c o u s flow i s b e s t s a t i s f i e d 7 by o b t a i n i h g
d a t a a t s e v e r a l flow rat:es and g r a p h i n e f l o w r a t e v e r s u s prtelss u r e d r o p f o r l i q u i d and f o r gas by p l o t t i n g t h e p r o d u c t of
mean f l o w r a t e and p o r e p r e s s u r e v e r s u s p1 2
-
~
*
p 2 where p1 ,
i s t h e u p s t r e a m p r e s s u r e and p 2 i s t h e downstream p r e s s u r e .
For c o n d i t i o n s of v i s c o u s flow, t h e d a t a s h o u l d p l o t a s t r a i g h t
l i n e , passing through t h e origin.
Turbulence i s i n d i c a t e d
I
by c u r v a t u r e of t h e p l o t t e d p o i n t s .
2.2
D a r c y ' s Law f o r G a s Flow
I n t h e case of f l o w of g a s e s , t h e f l o w r a t e i s n o t
I
constant, but increases with t h e pressure drop, according t o
Boyle's l a w .
T h e i n t e g r a t e d form o f D a r c y ' s l a w which d e s -
c r i b e s h o r i z o n t a l l i n e a r . p a s flow, u n d e r s t e a d y s t a t e , i s o thermal c o n d i t i o n s i s :
- 5-
I
i
2
(2-3)
J
2.3
S l i p Phenomena i n G a s Flow
Kundt and Warburg*
f i i ~ s tshowed
t h a t a l a y e r of g a s
J
n e x t t o a s o l i d s u r f a c e m!y h a v e a f i n i t e v e l o c i t y w i t h
respect t o t h e w a l l .
I n case o f c a p i l l a r y f l o w , t h i s would
g i v e a g r e a t e r r a t e t h a n would b e computed f r o m P o i s e u i l l e ' s
J
law.
I n e f f e c t , t h e g a s stream l l s l i p s " w i t h r e s p e c t t o t h e
wall.
T h i s i s n o t t h e case f o r l i q u i d f l o w .
This "slip"
phenomena i s d e p e n d e n t upon t h e mean f r e e p a t h of t h e g a s
J
molecules; t h e r e f o r e , gas permeability should b e a f u n c t i o n
of t h e f a c t o r s c o n t r o l l i n g t h e mean f r e e p a t h .
These f a c t o r s
a r e p r e s s u r e , t e m p e r a t u r e , and t h e n a t u r e o f t h e g a s i t s e l f .
When t h e mean f r e e p a t h s ar*e small, e . g . ,
4
at high pressures,
t h e p e r m e a b i l i t y t o g a s s h o u l d be e x p e c t e d t o a p p r o a c h t h a t
t o liquids.
T h i s i d e a w a s s u p p o r t e d by t h e K l i n k e n b u r g 9
J
study.
Based upon a t h e o r e t i c a l a n a l y s i s o f t h e s l i p phenomenon
i n c i r c u l a r c a p i l l a r i e s , arid assuming a n a n a l o g o u s b e h a v i o r
i n a p o r o u s medium, K l i n k e n b e r g '
J
developed the r e l a t i o n s h i p
between t h e p e r m e a b i l i t y of a p o r o u s medium t o g a s and t o a
J
n o n r e a c t i v e l i q u i d as follows:
(2-411
.J
I
I.
.J
where ka i s t h e apparent: o r o b s e r v e d p e r m e a b i l i t y t o g a s , k
i s t h e a b s o l u t e permeability t o gas a t h i g h pressures (presumed e q u a l t o t h e a b s o l u t e p e r m e a b i l i t y t o a s i n g l e l i q u i d
-
phase)
,X
i s t h e mean fr5ee p a t h of t h e g a s m l e c u l e s , r i s
t h e r a d i u s of a c a p i l l a x - y (assumed t o b e c o n s t a n t )
i s a proportionality factor.
, and
c
The mean f r e e p a t h c a n b e
e x p r e s s e d as:
where d i s a c o l l i s i o n diameter, n i s t h e c o n c e n t r a t i o n of
m o l e c u l e s p e r u n i t volume, N i s Avogadro's N u m b e r , p,
i s the
mean p r e s s u r e , T i s a b s o l u t e t e m p e r a t u r e , and R i s t h e u n i versa1 gas constant.
k
a
~
F ~ o mEa_. 2 - 5 , Eq. 2- 4 becomes:
= k(l+- 4c'T
)
= k(l+-)b
2
Pm
m r N d pm
c.
where b i s r e f e r r e d t o as t h e K l i n k e n b e r g f a c t o r , and is
u s u a l l y t a k e n as a c o n s t a n t f o r a g i v e n gas and a g i v e n
c
p o r o u s medium.
From E q . 2 - 6 , t h e K l i n k e n b e r g f a c t o r appear\$
d i r e c t l y p r o p o r t i o n a l t o temperature.
2.4
V i s c o - I n e r t i a l F l o wD a r c y ' s l a w and t h e p r e c e d i n p e q u a t i o n s a r e v a l i d when
c o n d i t i o n s of v i s c o u s f l o w p r e v a i l .
A t h i g h flow r a t e s , f L b w
has b e e n shown t o b e d e s c r i b e d by a q u a d r a t i c e q u a t i o n .
a n e q u a t i o n was proposed by Forchheimer''
C o r n e l l a n d K a t z l l as f o l l o w s :
-7-
and m o d i f i e d by
Su
Dranchuk and Kolada12 have shown how t o d e l i n e a t e t h e v i s c o -
i n e r t i a l f l o w r e g i o n from flow measurements, and how t o
d e t e r m i n e t h e a b s o l u t e p e r m e a b i l i t y of a r o c k c o r e ( s e e
Appendix 9 . 3 ) .
2-7 is some-
The v i s c o - i n e r t i a l f l o w d e s c r i b e d by E q .
t i m e s r e f e r r e d t o as " t u r l b u l e n t " flow.
The d e p a r t u r e from
J
l a m i n a r flow d e s c r i b e d by E q . 2- 7 i s n o t c a u s e d by physical
f a c t o r s which (cause t u r b u l e n t flow i n p i p e .
i s u s u a l l y r e f e r r e d t o as "non-Darcy,"
i n e r t i a l " flow.
T h i s phenomenon
I
" i n e r t i a l , " or "visco-r
W
e s h a l l u s e t h e l a t t e r term.
J
I
I
J
J
J
J
Y
I
-8-
.J
..
LITE-WTURE
3.
I n 1 9 3 7 , Muskat4 s t a t e d t h a t t h e a b s o l u t e p e r m e a b i l i t y
of a porous medium " i s t h u s a c o n s t a n t d e t e r m i n e d o n l y by
t h e s t r u c t u r e of t h e medium i n q u e s t i o n and i s e n t i r e l y i n d e t
pendent of t h e n a t u r e o f t h e f l u i d . "
Also, t h e standard p r a t
c e d u r e f o r d e t e r m i n i n g t h e p e r m e a b i l i t y of p o r o u s medium
a c c o r d i n g t o A P I Code No. 2 7 1 5 ( f i r s t e d i t i o n , October 1935)
w a s based on t h e f u n d a m e n t a l a s s u m p t i o n t h a t as l o n g as t h e
r a t e of flow w a s p r o p o r t i o n a l t o t h e p r e s s u r e g r a d i e n t , t h e I
p e r m e a b i l i t y c o n s t a n t of a p o r o u s medium w a s a p r o p e r t y of
~
t h e medium and w a s i n d e p e n d e n t o f t h e f l u i d used i n i t s detdLmination.
A major s t u d y by K l i n k e n b e r g appeared i n 1 9 4 1 .
...
Klinkefi-
b e r g 9 performed l i q u i d p e r m e a b i l i t y measurements on J e n a
f i l t e r s i n order t o avoid c l a y swelling o r erosion.
The
were n o t c o n f i n e d n o r w e r e v a r i a t i o n s i n t e m p e r a t u r e studiedl.
From h i s a n a l y s i s o f gas, f l o w t h r o u g h t h e same c o r e s , he t h e p e f o r e supported t h e n o t i o n t h a t t h e permeability c o n s t a n t of
a porous medium w a s a p r o p e r t y of t h e medium, and w a s i n d e p e n -
dent of t h e f l u i d used.
I n a d d i t i o n , he w a s t h e f i r s t persdn
~
t o e x p l a i n s l i p phenomena.
I n 1 9 4 3 , Grunberg and N i s s a n 1 3 s t u d i e d t h e e f f e c t of
f l o w of aqueous s o l u t i o n s t h r o u g h l i m e s t o n e and s a n d s t o n e
c o r e s o v e r a r a n g e of t e m p e r a t u r e s .
-9-
Four s o l u t i o n s w e r e t e s t e d :
(1) d i s t i l l e d water, (2) a 2 % n-amyl a l c o h o l s o l u t i o n , and
( 3 ) two s o d i u m c h l o r i d e s o l u t i o n s ( 0 . 9 6 0
and 0.614N).
The
c h o i c e o f t h e s e s o l u t i o n s was made s o as t o o b s e r v e t h e i n f l u e n c e o f s u r f a c e f o r c e s on t h e f l o w of l i q u i d s t h r o u g h
p o r o u s media.
The core t e m p e r a t u r e s were v a r i e d from 6OC
I
t o 3OoC.
1
Pe rmeab i1.it y d ecr e a:; e d w i t h i n c r e as ing t e m p e r a t u r e f o r
a l l of t h e four, aqueous s o l u t i o n s .
1
1
A l l f o u r gave l i n e a r
p e r m e a b i l i t y t e m p e r a t u r e c u r v e s w i t h a p p r o x i m a t e l y t h e same
1
The slope of t h e g r a p h s o f p e r m e a b i l i t y v s . tempera-
slope.
t u r e w a s 0 . 8 mcV0C.
Thus:
k =
if
-
( 3-1
0.8(t,OC)
I
where a i s a c h a r a c t e r i s t i c c o n s t a n t o f t h e l i q u i d used.
As
t h e f l u i d v i s c o s i t y w a s considered properly i n c a l c u l a t i n g
~
I
p e r m e a b i l i t y , t:hey concluded t h a t v i s c o s i t y w a s n o t t h e o n l y
p r o p e r t y i n f l u e n c i n g flow.
1
I n a d d i t i o n , a l o g - l o g g r a p h of
2
I
k/k ,vs.(-) lJ
g a v e a s t r a i g h t l i n e . kl i s a base p e r m e a b i l i t y ;
1
Pa
1.1 i s f l u i d v i s c o s i t y , p i s f l u i d d e n s i t y , and Q i s s u r f a c e
1
tension.
A c o n c l u s i o n reached w a s t h a t the e f f e c t i v e c r o s s - s e c t i t
under
v i s c o u s flow was d i f f e r e n t f o r d i f f e r e n t l i q u i d s due
ti
d i f f e r e n c e s i n s u r f a c e e n e r g y , and t h u s d i f f e r e n c e s i n t h e
t h i c k n e s s of a d s o r b e d l a y e r s .
I n 1 9 4 6 , Calhoun and Y u s t e r "
p r e s e n t e d r e s u l t s of flow
t h r o u g h a r t i f i c i a l p o r o u s b o d i e s , some made of p y r e x g l a s s
and o t h e r s of f'used q u a r t z .
No c o n f i n i n g p r e s s u r e was a p p l i e
-10-
I
L
They d i s a g r e e d w i t h G r u n b e r g ' s and N i s s a n ' s r e s u l t s and confirmed Klinkenberg's r e s u l t s .
Calhoun a n d Y u s t e r found t h a t water g a v e a s l i g h t l y
lower v a l u e for p e r m e a b i l i t y t h a n b e n z e n e .
A s u s p i c i o n of
a n e l e c t r o - k i n e t i c e f f e c t w a s r u l e d o u t b e c a u s e a d d i t i o n of
a t r a c e of H C 1 or C a C 1 2 t o t h e water c a u s e d no a p p a r e n t i n crease i n p e r m e a b i l i t y .
c.
F u r t h e r m o r e , n a p h t h a gave a permea-
b i l i t y as low as t h a t of w a t e r , a n d , w i t h this h y d r o c a r b o n
l i q u i d a n e l e c t r o - k i n e t i c e f f e c t should have been a b s e n t .
Calhoun and Y u s t e r were unable t o g i v e an e x p l a n a t i o n of
c.
t h i s anomaly.
They were t h e f i r s t t o o b s e r v e a dependency
od
K l i n k e n b e r g ' s f a c t o r , b on t e m p e r a t u r e .
1
I n t r y i n g t o correlate Klinkenberg b values a t d i f f e r e n t
c.
t e m p e r a t u r e s , Calhoun and Y u s t e r assumed t h a t e q u a l mean fred
I
p a t h s would o c c u r a t e q u i v a l e n t m o l e c u l a r c o n c e n t r a t i o n s a t
d i f f e r e n t temperatures,
.
,
A g a s a t p r e s s u r e p1 and T1 s h o u l d
~
h a v e t h e same m o l e c u l a r c o n c e n t r a t i o n as t h e same g a s a t a
p r e s s u r e p z a n d T2, i f
P:1
~1
were
equal t o
p2
T
.
Therefore, e q u i jI
2
v a l e n t p e r m e a b i l i t y v a l u e s s h o u l d e x i s t f o r t h e same g a s , whcin
.
two d i f f e r e n t t e m p e r a t u r e s were u s e d ,
a t a mean p r e s s u r e p,
T1
and t e m p e r a t u r e T1, and a t mean p r e s s u r e p (-1
a t a temperad
T2
t u r e of Tz.
c
'
This correLation at d i f f e r e n t temperatures w a s
n o t i n c l u d e d i n e i t h e r K l i n k e n b e r g ' s or Grunberg and Nissan'B
presentation.
I n t h e l a t e 1960s, Greenberg, e t a1.,3 and Weinbrandt
18
a g a i n o b s e r v e d a p e r m e a b i l i t y dependency on t e m p e r a t u r e l e v e a .
G r e e n b e r g , e t a l . , d i d n o t r e s t r a i n t h e i r cores and o b s e r v e d
-11-
i
I
J
o n l y small t e m p e r a t u r e e f f e c t s .
Weinbrandt
16
, in
h i s experi-
ments on t h e e f f e c t of t e m p e r a t u r e on r e l a t i v e and a b s o l u t e
p e r m e a b i l i t y of s a n d s t o n e s , s u b j e c t e d h i s cores t o 2 0 0 0 p s i
confining pressure.
J
H e a l s o f i r e d t h e cores a t 94OoF p r i o r
I
t o u s e t o o x i d i z e o r g a n i c matter i n t h e cores and t o d e a c t i - '
vate the clays.
H i s e x p e r i m e n t s f o r B o i s e s a n d s t o n e core
J
s a m p l e s a t room t e m p e r a t u r e and a t 175OF showed t h a t w i t h a n
increase i n temperature:
(1) t h e i r r e d u c i b l e water s a t u r a t i o f a
J
increased; ( 2 ) t h e r e s i d u a l o i l s a t u r a t i o n decreased; ( 3 )
t h e r e l a t i v e permeability t o w a t e r a t flood- out increased; (
t h e r e l a t i v e perrneabi1it:y t o o i l i n c r e a s e d ; ( 5 ) t h e r e l a t i v e
J
p e r m e a b i l i t y i q a t i o , kw/ko, d e c r e a s e d ; and ( 6 ) t h e a b s o l u t e
p e r m e a b i l i t y to w a t e r d e c r e a s e d .
1 v e r i f i e d t h e WeinCasse.
I
b r a n d t f i n d i n g s and s u b s t a n t i a l l y e x t e n d e d t h e work.
J
The e f f e c t of m e c h a n i c a l stresses on t h e p e r m e a b i l i t y
of r o c k s has h e e n s t u d i e d b y s e v e r a l i n v e s t i g a t o r s .
I n 196711
I
I
Wilhelmi and Somerton17 i n v e s t i g a t e d t h e e f f e c t of overburdefl
1
p r e s s u r e on r o c k p e r m e a b i l i t y .
J
They c o n f i r m e d e a r l i e r work
b y F a t t and D a v i s 1 8 i n 1!352, and r e p o r t e d t h a t p e r m e a b i l i t y
'
a t 1 5 , 0 0 0 p s i c o n f i n i n g p r e s s u r e c o u l d be 2 5 t o 6 0 % smaller
J
t h a n t h e permeability a t a z e r o c o n f i n i n g p r e s s u r e , dependin
PP
I t
o n t h e t y p e of r o c k s s t u d i e d .
Generally speaking, t h e h i g h e l
t h e permeability, t h e higher t h e percentage of reduction.
J
About 6 0 % of t h e t o t a l r e d u c t i o n o c c u r r e d d u r i n g t h e f i r s t
3000 p s i confining p r e s s u r e .
In 1963!, G r a y , --e t a1
,19
a l s o measured t h e e f f e c t of
o v e r b u r d e n p r e s s u r e on p e r m e a b i l i t y .
~
I
I
J
Perneability reduction
was shown t o be a f u n c t i o n of t h e r a t i o of r a d i a l t o a x i a l
- 12-
J
s t r e s s , w i t h t h e maximum r e d u c t i o n o c c u r r i n g u n d e r a u n i f o r m
stress, i . e . ,
stress.
when t h e a x i a l stress i s e q u a l t o t h e r a d i a l
The p r e s e n t work r e p o r t e d h e r e w a s accompanied undeth
c o n d i t i o n s of u n i f o r m s t ~ e s s .
Zoback and B y e r l e e (1975aI2'
showed t h a t d u e t o t h e
p r e s e n c e of c o m p r e s s i b l e m a t r i x material i n a r e l a t i v e l y
i n c o m p r e s s i b l e g r a n u l a r framework, t h e p e r m e a b i l i t y o f s a n d s t o n e i s n o t simply a f u n c t i o n of e f f e c t i v e stress, b u t i s
~
highly s e n s i t i v e t o changes i n pore p r e s s u r e .
The e f f e c t of t h e r m a l stresses on r o c k p r o p e r t i e s a n d
t h e e f f e c t of o v e r b u r d e n p r e s s u r e on p o r o s i t y h a v e a l s o b e e n
of p a r t i c u l a r i n t e r e s t .
Somerton, e t a l . , * ' L h e a t e d a number of s a n d s t o n e s t o
a b o u t 150OOF u n d e r b o t h a t m o s p h e r i c and s i m u l a t e d r e s e r v o i r
pressures.
P e r m e a b i l i t y w a s measured a t room t e m p e r a t u r e
u s i n g a s t a n d a r d a i r perimeameter, b e f o r e and a f t e r h e a t i n g
t h e samples.
I
No p e r m e a b i l i t y c h a n g e s were r e p o r t e d i n t h e
r a n g e of 75-350°F.
A t t e m p e r a t u r e s w e l l a b o v e 5OO0F, t h e y
showed t h a t permanent s t i r u c t u r a l damage and d e c o m p o s i t i o n ofi1
r o c k minerals o c c u r r e d d u e t o thermal stresses.
Wyble22, w o r k i n g om t h e e f f e c t o f a p p l i e d p r e s s u r e on
s a n d s t o n e ' s p r o p e r t i e s , o b s e r v e d a s y m p t o t i c d e c r e a s e s i n cond u c t i v i t y , p o r o s i t y , and p e r m e a b i l i t y o v e r a 0 p s i t o 3,500
p s i range.
A t 2000 p s i c o n f i n i n g p r e s s u r e , about a 10% reduc-
t i o n i n p o r o s i t y w a s obslerved, and beyond t h i s , t h e p o r o s i t y
v a l u e remained e s s e n t i a l l y c o n s t a n t .
-13-
I n s u m m r y , many s t u d i e s i n d i c a t e t h e l i k e l i h o o d of
a b s o l u t e p e r m e a b i l i t y of r o c k s b e i n g a f u n c t i o n o f t e n p e r a -
t u r e beyond t h e e f f e c t s c a u s e d b y a c h a n g e i n t h e v i s c o s i t y
I
of t h e f l u i d .
The r e c e n t works of Weinbrandt’‘
and Cass6 1 1
i n d i c a t e d an e f f e c t o f major i m p o r t a n c e for r e s t r a i n e d c o r e s 4
N o obvious explanation existed.
The main p u r p o s e of t h i s
I
s t u d y w a s a v e r i f i c a t i o n of and s t u d y o f p o s s i b l e e x p l a n a t i o o s
1
of t h e s e e f f e c t s .
I
-14-
i
4.
EXPERIMENTAL EQUIPMENT
The e x p e r i m e n t a l eciuipment
used w a s s i m i l a r t o t h a t
.. d e s c r i b e d p r e v i o u s l y by Cass6’ and Weinbrandt 1 6
.
f i c a t i o n s were made i n t h e a p p a r a t u s , however.
Some modi- 1
A description
of t h e a p p a r a t u s f o l l o w s .
I
I.
4.1
General Descriptioh
F i g . 1 i s a photogriaph of t h e l a b o r a t o r y , and F i g .
2 p r e s e n t s t h e d e t a i l s of t h e a i r b a t h assembly.
diagram o f t h e a p p a r a t u s i s shown i n F i g .
3.
A schematic
T h e flow l i n e s ,
h e a t e x c h a n g e r s , and f i t t i n g s were c o n s t r u c t e d o f 316 s t a i n l e 6S
s t e e l material.
c.
Three p a r a l l e l flow l i n e s were c o n s t r u c t e d for- g a s ,
o i l , water, or 2 - o c t a n o l i n j e c t i o n .
For e a c h e x p e r i m e n t , t h e 1
d e s i r e d f l o w l i n e w a s c o n n e c t e d t o t h e c o r e ; a new c o r e b e i n g
used f o r e a c h e x p e r i m e n t .
Liquid flow w a s s u p p l i e d by a p u l -
s a t i n g pump, and gas f l o w w a s s u p p l i e d f r o m h i g h p r e s s u r e
c y l i n d e r s and d e l i v e r e d t‘hrough p r e c i s i o n p r e s s u r e r e g u l a t o r s .
L i q u i d f l o w r a t e th:rough t h e c o r e w a s measured by
a weighing b a l a n c e .
Depe:nding upon t h e l e v e l of f l o w r a t e ,
gas flow r a t e w a s measured e i t h e r by t h e use of a b u b b l e f i l m 1
flowmeter o r by a Wet T e s t Meter.
A thermocouple w a s placed
a t t h e i n l e t f a c e of t h e c o r e , and t e m p e r a t u r e w a s r e c o r d e d
continuously during t h e runs.
The c o r e h o l d e r a s s e m b l y was
p l a c e d i n an air b a t h t h a t maintained r u n t e m p e r a t u r e .
Mea-
s u r e m e n t s of u p s t r e a m p r e s s u r e and p r e s s u r e d r o p across t h e
-15-
f
i !I. 1. PhotoF,raph o f A p p a r a t u s
I
c.
W
- 17-
I
I
I
I
c o r e were a c c o m p l i s h e d by t h e u s e of p r e s s u r e t r a n s d u c e r s
connected t o p r e s s u r e i n d i c a t o r s and r e c o r d e r s .
The d e s i r e d c o n f i n i n g p r e s s u r e l e v e l was a t t a i n e d
by u s i n g a h y d r a u l i c hand pump.
Chevron No. 15 h e a v y
O i l
was used as a c o n f i n i n g f l u i d and a " V i t o n A" r u b b e r s l e e v e ,
J
l / S " t h i c k , s e p a r a t e d t h i s f l u i d from t h e core.
I
A d e s c r i p t i o n of t h e major components o f t h e a p p a r a t u s
follows.
4.2
Core H o l der
- -_
F i g . 4 s ' h o w s t h e d e t a i l s of t h e c o r e h o l d e r which
i s a Hassler r u b b e r sleeve t y p e .
The r o c k specimen t o be
s t u d i e d i s h e l d i n a " V i t o n A" r u b b e r s l e e v e , 1/8" t h i c k ,
between a n u p s t r e a m p l u g , which i s immobile, and a downstrean
p l u g which moves h o r i z o n t a l l y and a d j u s t s t o t h e core l e n g t h .
The u p s t r e a m p2ug h a s two p r e s s u r e t a p s A and D , one tap B
f o r i n l e t f l o w : , and a t h e r m o c o u p l e w e l l C .
E i t h e r l i q u i d o r g a s p r e s s u r e c a n be a p p l i e d t o
t h e Viton s l e e v e , b u t thrloughout t h e s e e x p e r i m e n t s , Chevron
White O i l No. 1.5 w a s u s e d .
Both a x i a l and r a d i a l c o n f i n i n g
p r e s s u r e s are a.pplied s i m u l t a n e o u s l y t o t h e core b e c a u s e t h e
downstream plug, i s m o b i l e and s u b j e c t t o t h e c o n f i n i n g p r e s sure.
A p e r f o r a t e d aluminum t u b e i s f i t t e d around t h e core
rubber s l e e v e t o p r e v e n t l a t e r a l deformation of core d u r i n g
loading.
The s l e e v e w a s
1 . 9 4 6 i n . OD by 3 . 0
i~
t h i c k c y l i n d e r 1 . 2 2 5 i n . I D by
i n . long.
I
4.3
A i r Bath and T e m p e r a t u r e C o n t r o l
J
An a i r b a t h w i t h a w o r k i n g s p a c e of 2 4 c u b i c f e e t
housed t h e core h o l d e r a s s e m b l v .
-18-
Four kilowatts of power may
.d
NO-
Icy 9
w o o
00
00
.- 0 0.
, - a .
a+
*
I
+
Ex
1
I
a
1
be a p p l i e d t o t h e h e a t i n g e l e m e n t s by a n A P I model 4010
power pack and a n API model. 2 2 8 t e m p e r a t u r e c o n t r o l l e r .
The
t h e r m o c o u p l e t h a t c o n t r o l s t h e o u t p u t o f the h e a t e r c o n t r o l l e r
~
c a n b e p l a c e d a t any l o c a t i o n i n s i d e t h e o v e n , b u t t h e most
e f f i c i e n t h e a t i n g c y c l e w a s found t o r e s u l t when t h e thermoc o u p l e s e n s o r w a s f a s t e n e d t i g h t l y t o t h e core h o l d e r .
A fan
I
I
p r o v i d e d a d e q u a t e a i r c i r c u l a t i o n and t h e a i r b a t h w a s equipped'
w i t h a l i g h t and a window.
~
Temperature was monitored by a 2 4 - p o i n t thermocouple
r e c o r d e r w i t h i r o n - c o n s t a n t an t h e r m o c o u p l e s
were a c t u a l l y used.
.
I
Two thermocouple$'
One thermocouple measured t h e t e m p e r a t u r e
o f t h e c o r e , and t h e o t h e r measured t h e a i r b a t h t e m p e r a t u r e .
The a i r b a t h t e m p e r a t u r e r e a c h e d t h e d e s i r e d t e s t t e m p e r a t u r e
i n a b o u t 1 - 1 / 2 h o u r s , b u t a.t l e a s t a n o t h e r four h o u r s were
r e q u i r e d f o r t h e r o c k specimen t o r e a c h t h e t e s t t e m p e r a t u r e .
4.4
-
L i q u i d and Gas' Sources
A d e a e r a t e d l i q u i d was s t o r e d i n a 4 0 0 0 cc c a p a c i t y
vacuum f l a s k .
A Lapp "Microflo" P u l s a f e e d e r pump w a s used
t o pump t h e l i q u i d t h r o u g h t h e c o r e .
The pump h a s a d i a l
i n d i c a t o r , c a l i b r a t e d i n 1 0 0 0 i n c r e m e n t s which e n a b l e d f i n e
a d j u s t m e n t s i n f l o w r a t e t o be made.
Three t y p e s of l i q u i d s
w e r e u s e d : w a t e r , o i l , and 2 - o c t a n o l .
Gas flow t h r o u g h t h e samples w a s s u p p l i e d from h i g h
p r e s s u r e c y l i n d e r s , and r e g , u l a t e d by a t w o - s t a g e a d j u s t -
a b l e r e g u l a t o r equipped w i t h a r e l i e f v a l v e .
The i n i t i a l
c y l i n d e r p r e s s u r e w a s 2 5 0 0 p s i , and d e l i v e r y p r e s s u r e s ranged
from 5 p s i t o a maximum o f 4 0 0 p s i .
-20-
I
c
4.5
L i q u i d Pumps
The pumps w e r e a Lapp "Microflo" P u l s a f e e d e r t y p e w i t h
a d i a l i n d i c a t o r c a l i b r a t e d i n 1000 increments.
Both pumps
I
created l a r g e p r e s s u r e p u l s a t i o n s when d e l i v e r i n g a t h i g h
I
pressures.
Accumulators, i n s e r t e d a l o n g t h e f l o w l i n e s ,
eliminated t h e s e pulsations.
I
A steady flow could b e estab-
l i s h e d and c o n s t a n t p r e s s u r e s m a i n t a i n e d a t b o t h e n d s o f the
core.
4.6
H y d r a u l i c Yand P u r 2
An E n e r p a c h v d r a u l - i c hand pump w i t h a r a n g e of 0 t o
1 0 , 0 0 0 p s i provided adjustment o f t h e c o n f i n i n g p r e s s u r e .
The pump w a s c o n n e c t e d to t h e c o r e h o l d e r and Chevron White
M i n e r a l O i l No, 1 5 was used t o o b t a i n t h e d e s i r e d c o n f i n i n g
pressure.
4.7
Heat E x c h a n g e r s
To m a i n t a i n t h e t e m p e r a t u r e o f t h e f l o w i n g f l u i d conI
s t a n t d u r i n g a r u n , l a r g e r e s e r v o i r s were i n s t a l l e d on each1
f l o w l i n e i n s i d e t h e oven b e f o r e t h e c o r e h o l d e r .
e n t e r e d a t t h e bottom of t h e r e s e r v o i r .
Cold flu1
Because o f t h e larj
s i z e o f t h e r e s e r v o i r arid t h e s m a l l flow r a t e s that were
I
used w i t h l i q u i d f l o w , h o t f l u i d l e f t from t h e t o p .
The
t e m p e r a t u r e o f t h e l i q u i d s l e a v i n g t h e r e s e r v o i r and e n t e r i d g
I
t h e c o r e w a s measured and found t o remain c o n s t a n t a t t h e
1
I
I
d e s i r e d test t e m p e r a t u r e d u r i n g t h e e n t i r e r u n .
The g a s r e s e r v o i r i n s i d e t h e oven w a s f i l l e d w i t h s t a i n I
l e s s s t e e l wool.
T h i s improved h e a t exchange and e n a b l e d
t h e gas t o r e a c h t h e t e s t t e m p e r a t u r e b e f o r e e n t e r i n g t h e c b r e .
-21-
The e f f l u e n t f r o m t h e c o r e and t h e a i r b a t h w a s c o o l e d
p r i o r t o f l o w rate determination.
This w a s accomplished by
l e t t i n g t h e e f f l u e n t flow t h r o u g h a c o i l immersed i n a con-
~
s t a n t room t e m p e r a t u r e water b a t h .
4.8
Backpressure Valve
B a c k p r e s s u r e was r e g u l a t e d by means of a f i n e m e t e r i n g
needle valve.
T h i s v a l v e , i n a d d i t i o n t o b e i n g used t o c h a n g e I/
I
t h e f l o w r a t e , served t o maintain a s u f f i c i e n t l y high pressure
i n t h e s y s t e m t o keep t h e o p e r a t i n g l i q u i d i n t h e l i q u i d
state.
I
I
By a d j u s t i n g t h e v a l v e and t h e pump r a t e , a c o n s t a n t
i
mean p o r e p r e s s u r e could b e m a i n t a i n e d .
M a i n t a i n i n g a con-
s t a n t mean p o r e p r e s s u r e l e v e l w a s i m p o r t a n t because e x p e r i m e n t a l work by Zoback*'
,
showed t h a t a change i n mean pore
p r e s s u r e c o u l d a f f e c t a b s o l u t e p e r m e a b i l i t y t o an even g r e a t e r
e x t e n t t h a n d i d a change i n c o n f i n i n g p r e s s u r e .
A constant
,
mean p o r e p r e s s u r e of 2 0 0 p s i w a s m a i n t a i n e d f o r a l l l i q u i d
runs.
4.9
Flow Rate Measuring D e v i c e s
l i
4.9- 1
Liquid F l o w :
A t s t e a d y s t a t e , t h e mass f l o w r a t e
w a s c o n s t a n t t h r o u g h o u t t h e system.
The mass f l o w r a t e w a s
measured by weighing small volumes o f t h e e f f l u e n t l i q u i d by
a n a n a l y t i c a l b a l a n c e o v e r a known p e r i o d of trime.
Repeated
measurement p e r m i t t e d c h e c k i n g d e t e r m i n a t i o n of s t e a d y s t a t e .
T h e v o l u m e t r i c flow r a t e w i t h i n t h e c o r e was determined as
t h e ratio of t h e mass flow ]?ate t o t h e d e n s i t y of t h e l i q u i d
a t r u n t e m p e r a t u r e and mean p r e s s u r e .
- 2 2-
The flow r a t e c o u l d
be changed by a d j u s t i n g t h e pump r a t e a n d / o r by a d j u s t i n g
t h e needle valve.
4.9- 2
Gas Flow: Gas p r e s s u r e w a s r e g u l a t e d u p s t r e a m
by a two- stage p r e s s u r e r e g u l a t o r and g a s flow w a s r e g u l a t e
downstream by means of a n e e d l e v a l v e .
T h e c h o i c e of t h e
I
a p p r o p r i a t e flowmeter w a s made a c c o r d i n g t o t h e l e v e l o f f l
i . e . , l a m i n a r flow (low r a t e ) , or v i s c o - i n e r t i a l flow ( h i g h
rate).
A b u b b l e f i l m flowmeter w a s u s e d for a l l l a m i n a r f l
measurements and a Wet T e s t Meter was used f o r v i s c o - i n e r t :
f l o w measurements.
L
0.2
A s t o p watch, graduated i n d i v i s i o n s of
second, w a s used as a t i m i n g d e v i c e .
I
The bubble f i l m flowmeter w a s t h e m o s t a c c u r a t e o f t h $ /
1
two d e v i c e s , and was used t o check t h e Wet T e s t Meter a t lod
flow r a t e s .
The b u b b l e f i l m flowmeter w a s made as follows.
I
The v e r t i c a l p a r t of a Y-shaped t u b e i s plunged j u s t up t o
t h e t h r o a t i n a s o a p s o l . u t i o n (see F i g . 1).
The g a s f l o w
I
t o b e metered e n t e r s t h r o u g h one of t h e b r a n c h e s and bubble$'
i n t o t h e o t h e r b r a n c h arid t h e n up i n t o t h e v e r t i c a l b u r e t t e
The flow r a t e i s o b t a i n e d by m e a s u r i n g t h e t i m e it t a k e s f o
a b u b b l e t o t r a v e r s e a known volume i n t h e b u r e t t e .
This
method e s s e n t i a l l y provj-ded f l o w r a t e measurements a t room
c o n d i t i o n s because t h e p r e s s u r e r e q u i r e d t o d i s p l a c e t h e
b u b b l e s was always less t h a n 0 . 0 1 p s i .
4.10
P r e s s u r e Recording D e v i c e s
Upstream p r e s s u r e and p r e s s u r e d r o p a c r o s s t h e c o r e
w e r e measured w i t h a Pace Model KP15 d i f f e r e n t i a l p r e s s u r e
-23-
I
J
t r a n s d u c e r and a Pace '-%del C D 2 5 t r a n s d u c e r i n d i c a t o r .
The
a p p r o p r i a t e p l a t e (1 p s i , 5 p s i , 2 5 p s i , 1 0 0 p s i , o r 500 p s i )
J
w a s u s e d f o r t h e working r a n g e of pressure o r p r e s s u r e d r o p .
An e l e c t r o n i c two-pen mult i - r a n g e r e c o r d e r , " C h e s s e l l ,I'
was
c o n n e c t e d t o t h e i n d i c a t o r and p r o v i d e d a permanent r e c o r d
of t h e p r e s s u r e .
A B a r n e t t Dead Weight T e s t e r w a s used t o
c a l i b r a t e t h e pressure recording devices.
I
J
l i
J
.J
'i
-
-24-
5.
PROCEDURE
Core s a m p l e s t o b e s t u d i e d were h e l d , c o m p l e t e l y sat&a t e d w i t h t h e d e s i r e d l i q u i d , i n a Hassler, r u b b e r s l e e v e
t y p e c o r e h o l d e r , i n an a i r b a t h .
The t e m p e r a t u r e of t h e
air
b a t h and t h a t o f t h e c o r e were t h e n b r o u g h t t o t h e d e s i r e d
Flow w a s e s t a b l i s h e d , and a f t e r r e a c h i n g a s t e a d y -
level.
I
s t a t e c o n d i t i o n , t h e n e c e s s a r y p r e s s u r e measurements and f l b w
r a t e s were measured.
With t h e n e c e s s a r y c o r r e c t i o n s f o r thlh
I
L
e f f e c t o f t e m p e r a t u r e on f l u i d v i s c o s i t y and d e n s i t y , absol u t e p e r m e a b i l i t y o f t h e c o r e w a s computed a t run t e m p e r a t
The l i q u i d s u s e d were water, Chevron White O i l N o .
octanol.
5.1
3 , and 2
N i t r o g e n was t h e gas used.
II
Core P r e p a r a t i o n
The t w o t y p e s of ‘rocks used i n t h i s s t u d y were c o n s o l
I
d a t e d M a s s i l l o n S a n d s t o n e s , and u n c o n s o l i d a t e d O t t a w a S i l i c h
Sand.
i.e.,
With t h e e x c e p t i o n o f t h e f i r s t run w i t h e a c h t y p e ,
2 and No. 1 4 , t h e cores were f i r e d f o r
experiments No.
a t l e a s t 1 2 h o u r s i n a 5OO0C f u r n a c e s o as t o o x i d i z e any
o r g a n i c matter p r e s e f i t
5.1- 1
.
Consclidated Massillon Sandstones :
The c o r e s
were c u t w i t h a o n e - i n c h d i a m e t e r diamond d r i l l , trimmed on
a l a t h e , e x t r a c t e d i n a Dean S t a r k t y p e a p p a r a t u s , and i g n i y e d
i n a 5OO0C f u r n a c e .
F u l l d e t a i l s o f t h e p r o c e s s are g i v e n
i n Ref. 1.
- 25-
2
A f t e r i g n i t i o n , thle c o r e s were s a t u r a t e d under vacuum
w i t h t h e d e s i r e d flowing l i q u i d .
T h e d i f f e r e n c e i n weight
J
a t 1 0 0 % l i q u i d s a t u r a t i o n and a t o t a l l y d r y c o n d i t i o n w a s
used t o c a l c u l a t e t h e c o r e p o r o s i t y .
For n i t r o g e n f l o w , t h e a i r - s a t u r a t e d c o r e w a s mounted
II
i
i n t h e core h o l d e r and f l u s h e d w i t h s e v e r a l p o r e volumes of
nitrogen.
I
I
D e t a i l s of t h e p h y s i c a l and m i n e r a l o g i c a l p r o p e r t i e s
1
~
of t h e s e c o r e s a p p e a r i n Appendix 9 . 2 .
5.1- 2
i
I
U n c o n s o l i d a t e d O t t a w a Sand: The sand was s i e v e d 1j
and s e p a r a t e d i n t o uniforbmly g r a d e d s i z e s .
For o n e run, ex-
b u t r e t a i n e d i n s i e v e No. 4 5 w a s u s e d .
J
35
p e r i m e n t No. 1 4 , t h e sand t h a t p a s s e d t h r o u g h s i e v e N o .
F o r all t h e o t h e r
r u n s , t h e sand s i z e t h a t p a s s e d t h r o u g h s i e v e No.
8 0 b u t was
,
d
r e t a i n e d i n s i e v e No. 1 0 0 w a s used.
T h i s g i v e s a v e r a g e sand I
g r a i n s i z e s of 0.385 mm and 0.156 rrun r e s p e c t i v e l y .
The
I !
s a n d w a s i g n i t e d a t 50OoC.
4
T h e upstream p l u g was i n s e r t e d i n t o t h e r u b b e r s l e e v e and
'1
t i g h t l y t i e d t o it w i t h 2 0 gage s t a i n l e s s s t e e l w i r e .
11
The c o r e l o a d i n g and assembly p r o g r a m w a s as follows:
With
t h e assembly h e l d v e r t i c a l l y u p r i g h t , a No. 4 0 0 s t a i n l e s s
4
I
s t e e l mesh, one i n c h i n d i a m e t e r , w a s s e a t e d on t h e u p s t r e a m
p l u g , and t h e sand w a s poured i n t o t h e s l e e v e slowly.
When
t h e s a n d was a b o u t 2 i n c h e s h i g h i n t h e s l e e v e , a n o t h e r
I
I
Y
s i m i l a r mesh w a s p l a c e d on t o p of s a n d pack and t h e downI
stream p l u g was i n t r o d u c e d and a l s o f a s t e n e d i n t h e same
manner.
~
3
The assembly w a s t h e n p l a c e d i n t h e core h o l d e r and
-26u
a g a i n w e l l compacted and t i g 5 t e n e d w i t h t h e h e l p o f a v i c e .
The f i n a l o v e r a l l measurtenent o f t h e c o r e h o l d e r w a s used t o
c a l c u l a t e t h e a c t u a l l e n g t h of t h e c o r e i n p l a c e .
The d i a m e t e r
of t h e c o r e w a s t h e same as t h a t of t h e end p l u g s ( 1 - i n c h
diameter).
With t h e core h o l d e r p l a c e d i n t h e a i r b a t h and conn e c t e d t o t h e flow l i n e , t h e c o r e and t h e f l o w l i n e were
c o m p l e t e l y e v a c u a t e d and, w h i l e under vacuun?, f l o w w a s s t a r d k d
s o as t o c o m p l e t e l y s a t u r a t e t h e c o r e and f i l l t h e l i n e s w i t l
the liquid.
1
I
The d e t a i l s of t h e p h y s i c a l and m i n e r a l o g i c a l p r o p e r t i e s
o f t h e s e c o r e s a l s o a p p e a r i n Appendix 9 . 2 .
5.2
E s t a b l i s h i n g Run C o n d i t i o n s
With t h e core i n t h e c o r e h o l d e r , t h e e n t i r e asserrbly
w a s p l a c e d i n a c r a d l e i n t h e a i r b a t h and a l l n e c e s s a r y
c o n n e c t i o n s w e r e made t o t h e flow l i n e s , p r e s s u r e t a p s , and
c o r e temperature probe.
C o n f i n i n g p r e s s u r e w a s t h e n a p p l i e d s l o w l y by pumping
Chevron White O i l N o .
1 5 around t h e c o r e s l e e v e , care b e i n g
t a k e n t o d i s p l a c e a l l t h e a i r i n t h i s l i n e by o p e n i n g t h e
1
c o r e end o f t h e l i n e d u r i n g t h e i n i t i a l s t a g e o f pumping.
A decreasing confining pressure with t i m e u s u a l l y indicated
l e a k a g e o f t h e c o n f i n i n g f l u i d i n t o t h e c o r e and flow s y s t e m ,
To a v o i d l e a k a g e , a 2 0 gage s t a i n l e s s s t e e l w i r e w a s always
t i e d around t h e r u b b e r s l e e v e between t h e end p l u g s and t h e
r o c k b e f o r e assembly.
A i r t h a t might have been t r a p p e d i n t h e c o r e and t h e
flow s y s t e m w a s removed by c o n n e c t i n g a vacuum pump t o
-27-
t h e o u t f l o w end of t h e s y s t e m , a n d a p p l y i n g vacuum f o r a t
l e a s t f i v e hours.
Before t h e vacuum pump w a s d i s c o n n e c t e d ,
f l o w w a s s t a r t e d s o t h a t t h e whole s y s t e m w a s c o m p l e t e l y
f i l l e d w i t h t h e l i q u i d t o be used.
The assembled system w a s t h e n h e a t e d t o t h e d e s i r e d
r u n t e m p e r a t u r e a f t e r takfing room c o n d i t i o n measurements.
The a i r b a t h t e m p e r a t u r e I?eached t h e d e s i r e d t e s t t e m p e r a t u r e
~
J
I
i
i n a b o u t 1-1/2 h o u r s , b u t a t l e a s t a n o t h e r f o u r h o u r s were
J
r e q u i r e d f o r t h e r o c k specimen t o r e a c h t h e t e s t t e m p e r a t u r e .
During t e m p e r a t u r e changes
t h e c o n f i n i n g f l u i d underwent
d
t h e r m a l e x p a n s i o n or contr3act i o n d e p e n d i n g upon whether h e a t i g
J
or c o o l i n g .
l
Repeated manual a d j u s t m e n t s were made t o keep
t h e overburden pressure within t h e d e s i r e d l e v e l .
When e q u i l i b r i u m t e m p e r a t u r e was r e a c h e d , f l u i d flow
4
w a s s t a r t e d and c o n t i n u e d f o r a b o u t a n h o u r b e f o r e measurements w e r e t a k e n .
I
R e p e a t e d measurement:s of t e m p e r a t u r e , p r e s s u r e s
and
I
I
flow r a t e w e r e made a t r e g u l a r t i m e i n t e r v a l s .
Steady state
w a s assumed when no change w a s o b s e r v e d i n t h e r e a d i n g s and
~
t h e s t e a d y v a l u e s were r e c o r d e d .
A l l f l o w r a t e measurements
were t a k e n a t room conditi.ons.
5.3
Measurements and C a l ~ c u l a t i o n s
5.3- 1
L i q u i d Flow:
Three k i n d s o f l i q u i d s were used
i n t h i s w o r k : d i s t i l l e d w a t e r , m i n e r a l o i l , and a l c o h o l .
Tap w a t e r w a s d i s t i l l e d i n a B a r n s t e a d s t a i n l e s s s t e e l
still.
The o i l used w a s Chevron White M i n e r a l O i l No. 3 ,
!
I
i
I
I
and w a s c o m m e r c i a l l y a v a i l a b l e .
- 2 8-
The p h y s i c a l p r o p e r t i e s of
1
t h e o i l v a r i e d s l i g h t l y from one c o n t a i n e r t o a n o t h e r .
a l c o h o l used w a s 2 - o c t a n o l ( P r a c t i c a l ) .
The
Before u s e , each
l i q u i d w a s d e a e r a t e d u n d e r a vacuum of a b o u t 0.3 p s i a and
f i It e r e d
.
To keep t h e f l u i d i n t h e l i q u i d s t a t e a t h i g h t e m p e r a +
t u r e s , t h e e x i t f l o w i n g p r e s s u r e was k e p t c o n s t a n t at 2 0 0
p s i f o r a l l runs.
An a c c u m u l a t o r , c h a r g e d t o 200 p s i , h e l p e p
dampen pump p r e s s u r e p u l s a t i o n s and a l s o h e l p e d t o keep t h e
f l o w i n g p r e s s u r e from c h a n g i n g d r a s t i c a l l y when t h e flow w a g
s t a r t e d or s t o p p e d .
Darcy's l a w f o r v i s c o u s f l o w i n a h o r i z o n t a l and l i n e a r
I
I
p o r o u s medium i s :
iI
where q i s i n c c / s e c , k i s i n d a r c i e s , 1.1 i n c p , A i s i n c m2
and
li
i n atdcm.
Eq. 5- 1 c a n b e e x p r e s s e d as:
k = - 14700
-aLvw
PAP
where k i s i n m d , Ap i s i n p s i , w i n gm/sec, p i n gm/cc, a n d !I
t h e o t h e r u n i t s and symbols a r e as d e f i n e d p r e v i o u s l y .
Thia
e q u a t i o n was used i n all c a l c u l a t i o n s .
I n a d d i t i o n t o u s i n g Q e f s . 5 and 6 t o estimate t h e
r e g i o n of v i s c o u s flow w l h e r e p o s s i b l e , c o n d i t i o n s o f viscousl
,
~
f l o w were a l s o d e t e r m i n e d by o b t a i n i n g d a t a a t s e v e r a l f l o w
r a t e s a t each t e m p e r a t u r e l e v e l and g r a p h i n g f l o w r a t e , q,
- 2 9-
versus pressure drop,
p.
F o r c o n d i t i o n s of v i s c o u s flow,
t h e d a t a should f a l l on a s t r a i g h t l i n e , p a s s i n g t h r o u g h t h e
origin.
The o n s e t of non--Darcy f l o w was i n d i c a t e d by a down-
ward c u r v a t u r e of t h e p l o t t e d p o i n t s f r o m t h e s t r a i g h t l i n e .
I t i s n e c e s s a r y t o know t h e v i s c o s i t y and d e n s i t y of
e a c h l i q u i d a t each working t e m p e r a t u r e l e v e l .
Water d e n s i t y
and v i s c o s i t y v e r s u s t e m p e r a t u r e were found i n t h e Steam
T a b l e s z 3 and are p r e s e n t e d i n F i g s . 5 and 6 , and i n T a b l e 1,
'
i
1
Appendix 9 . 1 .
A c a p i l l a r y t u b e v i s c o m e t e r w a s c o n s t r u c t e d t o measure
o i l and a l c o h o l (2-octanol.) v i s c o s i t i e s v e r s u s t e m p e r a t u r e
a t t h e working p r e s s u r e l e v e l of 200 p s i .
11
The p r o c e d u r e f o r
t h e s e measurements i s p r e s , e n t e d i n d e t a i l i n Appendix 9.3.
The r e s u l t s of t h e s e measurements checked v e r y c l o s e l y w i t h
I!
t h e d a t a s u p p l i e d by t h e m a n u f a c t u r e r s and t h o s e found i n
Iief. 39.
The d e n s i t y of a l c o h o l a t v a r i o u s t e m p e r a t u r e s w a s
measured w i t h a Bingham t y p e pycnometer.
The d e n s i t y o f t h e
o i l was measured a t 6OoF and t h e t a b l e s i n R e f . 2 4 were u s e d
t o estimate t h e d e n s i t i e s a t h i g h e r t e m p e r a t u r e s .
Results
a r e shown i n F i g s . 7 t h r o u g h 1 0 , and T a b l e s 3 t h r o u g h 5 i n
Appendix 9 . 1 .
-30-
'1
~
,
I
0
In
M
c.
0
0
M
0
Ln
N
0
0
cv
0
Ln
4
0
0
d
0
Ln
0
0
0
0
t
n
!n
0
00
-31-
0
-
00
0
110
019
0,8
017
016
0 5
0 4
013
01
2
011
60
I
100
I
I
I
150
200
TEMPERATURE,
250
O F
'=i~. F.
!!ater
lliscosityvs. TemDerature a t 290 n s i g
-32-
?do
I
O185
\
OI84
0183
0
O182
\
0
O1 81
\
0
0.80
o179
OI78
100
Fig.
7.
150
200
250
300
lEMPERATURE, O F
9ensityvs.Temperature for Chevron White O i l ‘*e. 3
-33-
a
II- a
a a
c3
a
w
n
5-
-
w
cn
L
2
0
Q:
zI
V
w
v)
0
u
0
'
0
v)
W
>
0 0 0
L n r f M
o
N
m
4
omx)I\co
4
S3XOlS IlN33
F ~ F .8 .
m
a-
M
6.k
All S O X I r\ 3 I l V W 3 N I ]
Viscosity v s . Temperature for Chevron White O i l No. 3
-34-
c
\0
\0
\0
\
0
'\ 0
50
100
200
TEMPERATURE,
150
250
O F
Fip. 9 .
q e n s i t y of 2-nctanol v s . TemDerature a t
1 4 . 7 psi.
-35-
300
10
9
8
7
6
5
4
3
0
\
2
0 5
04
I
I
4
I
I
1
I
50
Fi.p. 10.
100
150
200
TEMPERATURE,
250
300
I
O F
l ’ i s c o s i t v o f 2 - k t a n o l vs. T e m e r a t u r e at
14.7 n s i
-36-
i
5.3-2
Gas Flow: Gas w a s s u p p l i e d f r o m h i g h p r e s s u r e
c y l i n d e r s , and f l o w r a t e c o u l d b e r e g u l a t e d u p s t r e a m o f t h e
c o r e by a t w o - s t a g e a d j u s t a b l e r e g u l a t o r equipped w i t h a r e -
l i e f v a l v e , and downstretsm. hy means o f a n e e d l e v a l v e .
Most
experiments involved larrhar flow i n o r d e r t o o b t a i n a b s o l u t e
p e r m e a b i l i t y and t h e Kliiikenberg s l i p f a c t o r .
One v i s c o -
i n e r t i a l r u n w a s made.
I
I n a d d i t i o n t o measuring p r e s s u r e d r o p , Ap, a s e p a r a t e
I
I
t r a n s d u c e r w a s used t o measure t h e u p s t r e a m p r e s s u r e , p l .
From t h e s e v a l u e s , t h e mean p r e s s u r e pm =
p1
-
I
1
AP
7 was corn-
p u t e d , and t h e d i f f e r e n c e (p12-p22) w a s c a l c u l a t e d as 2pmAp.
Low flow r a t e s w e r e measured w i t h a b u b b l e f i l m t y p e
flowmeter and a Wet T e s t Yeter w a s used f o r h i g h flow r a t e
measurements.
Atmospheric p r e s s u r e and room t e m p e r a t u r e
were a l s o r e c o r d e d t o pe:rmit c o r r e c t i o n s t o f l o w i n g c o n d i I
tions.
The i n t e g r a t e d f o r m o f Darcy's l a w which d e s c r i b e d
s t e a d y h o r i z o n t a l l i n e a r g a s flow under i s o t h e r m a l c o n d i t i o n $
I
is:
where :
= g a s f l o w r a t e a t room c o n d i t i o n s , cc/sec
9,
k
= absolute permeability, darcies
A = c r o s s s e c t i o n a l area of porous medium, c m
L = l e n g t h of p o r o u s medium, c m
Ta
= room t e m p e r a t u r e ,
OK
-37-
2
T = f l o w i n g t e m p e r a t u r e , OK
P a = room p r e s s u r e , a t m . a b s .
Ap = p r e s s u r e d r o p across porous Fedium, atrr..
pm = mean p r e s s u r e w i t h i n porous medium, a t r . abs.
v
-z
I
= g a s v i s c o s i t y a t T and pm, c p
= mean g a s c o m p r e s s i b i l i t y f a c t o r
N i t r o g e n w a s t r e a t e d as a n i d e a l g a s and
b e c a u s e of t h e l o w working p r e s s u r e r a n g e .
t a k e n as 1
The r i g h t hand
s i d e of Eq. 5-3 w a s d i v i d e d by 1 4 , 7 0 0 b e c a u s e , i n t h e l a b o r a
t o r y , p r e s s u r e s were measured i n p s i and p e r m e a b i l i t i e s
lated i n millidarcies.
Thus:
k, md
=:
14,700
"
7
calc -
-L1J.QaPaT
AAPPmTa
Gas v i s c o s i t y v e r s u s t e m p e r a t u r e i s g i v e n by S u t h e r l a n Q ' s
25
formula
.
For n i t r o g e n , N2:
VN2
where T i s i n
0K
- -1.3.85(10 -4 I T1 . 5
102+T
and V is i n cp.
Nitrogen v i s c o s i t y versus
,
I
t e m p e r a t u r e a t atm0spheri.c p r e s s u r e i s p r e s e n t e d on F i g . 11 1
and i n T a b l e 2, Appendix 9 . 1 .
No s i g n i f i c a n t i n c r e a s e i n
n i t r o g e n v i s c o s i t y o c c u r s from a t m o s p h e r i c p r e s s u r e t o t h e
I
o p e r a t i n g l e v e l s , 2 0 0 p s i . , used i n t h i s s t u d y .
E q s . 5-4 and 5-6 were used i n g a s f l o w c a l c u l a t i o n s
I
I I
for v i s c o u s f l o w .
See Appendices, s e c t i o n 9.3-2,
-38-
f o r analysis
0
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d 3 ‘AlIS03SII\
- 39-
t-l
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4
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of v i s c o - i n e r t i a l flow.
A l i n e a r g r a p h of (p12-p22),
( p s i a )2 ,
where p1 i s upstream p r e s s u r e ( p s i a ) , p2 i s downstream p r e s s u r e ( p s i a ) , v e r s u s g a s flow r a t e , g, ( c c / s e c ) , w a s used t o
d e t e r m i n e c o n d i t i o n s for v i s c o u s flow.
-40-
6.
ANALYSIS O'F P,ESULTS AND DISCUSSION
The f o l l o w i n g p r e s e n t s t h e r e s u l t s found f o r t h e
e f f e c t of t e m p e r a t u r e l e v e l and c o n f i n i n g p r e s s u r e on s i n g l e *
phase f l o w i n sandstones.
C o n f i n i n g p r e s s u r e had t h e e f f e c t
of r e d u c i n g t h e a b s o l u t e p e r m e a b i l i t y o f s a n d s t o n e s f o r a l l
t y p e s of f l u i d s used.
S l i p f a c t o r f o r g a s flow w a s found t o
be t e m p e r a t u r e dependent as p r e d i c t e d by t h e o r y .
A change
( d e c r e a s e ) i n a b s o l u t e p e r n e a b i l i t y w i t h t e m p e r a t u r e increasles
w a s o b s e r v e d o n l y i n t h e case o f water flow.
6.1
Water Flow
Both c o n s o l i d a t e d and u n c o n s o l i d a t e d s a n d s t o n e s were
used i n t h i s study.
6.1- 1
C o n s o l i d a t e d S a n d s t o n e s : The f i r s t experiment
was c a r r i e d o u t w i t h a core t h a t was h e a t e d t o 3OO0C for 3
h r s and allowed t o c o o l o v e r n i g h t b e f o r e use.
sents the r e s u l t .
F i g . 1 2 pre-
The r o c k w a s f i r s t h e l d a t 1 0 0 0 p s i con-
I
f i n i n g p r e s s u r e , and t h e a b s o l u t e p e r m e a b i l i t y was r e c o r d e d
w i t h t e m p e r a t u r e i n c r e a s i n g t o 30OoF.
The r o c k was t h e n
a l l o w e d t o cool t o room t e m p e r a t u r e .
Confining p r e s s u r e
w a s i n c r e a s e d t o 2 0 0 0 p s i and t h e p r o c e s s o f h e a t i n g and
measurement r e p e a t e d .
The core h o l d e r used i n t h e work re-
p o r t e d h e r e i n i s ra.ted a t 5 0 0 0 p s i a t 35OoF s a f e l y , b u t a
maxinum of 4 0 0 0 p s i and 3OO0F w a s u s e d .
-41-
,
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;
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I t c a n be s e e n from t h e graph t h a t a t e a c h l e v e l o f
c o n f i n i n g p r e s s u r e , t h e a b s o l u t e p e r m e a b i l i t y t o water dec r e a s e d a t a n a p p r o x i m a t e r a t e of - 1.0 nd/OF.
The n e x t s e r i e s of e x p e r i m e n t s w e r e performed on cores
f i r e d a t 5OO0C i n o r d e r to i n v e s t i g a t e h y s t e r e s i s and r e p r o d u c i b i l i t y of r e s u l t s .
1 4 , and 1 5 .
The r e s u l t s a r e shown on F i g s . 1 3 ,
A l l showed a d e c r e a s e of a b s o l u t e p e r m e a b i l i t y
t o water w i t h t e m p e r a t u r e i n c r e a s e , b u t t h e s l o p e d e c r e a s e d
with i n c r e a s i n g temperature.
t o - 1.6 & / O F
c
w a s observed.
An a v e r a g e s l o p e of - 1 . 3 rnd/OF
The r e s u l t s a l s o show t h a t t h e
t e m p e r a t u r e e f f e c t w a s e s s e n t i a l l y r e v e r s i b l e (see F i g . 1 3 ) .
The f i r s t c o o l i n g c y c l e f o r t h e M a s s i l l o n S a n d s t o n e Nol
3 ( F i g . 14) a t 3 0 0 0 p s i g c o n f i n i n g p r e s s u r e i n d i c a t e d h y s t e r d -
..
sis.
On t h e f i r s t c o o l i n g c y c l e , t h e pern-!eability
with respect t o the f i r s t : heating cycle.
increased
~
On h e a t i n g and cool/ing
a g a i n , r e s u l t s f o l l o w e d t:he f i r s t c o o l i n g r u n , i n d i c a t i n g telrp e r a t u r e r e v e r s i b i l i t y arid good r e p r o d u c i b i l i t y .
No r e a s o n
for t h e i n c r e a s e i n p e r m a b i l i t y after t h e first h e a t i n g r u n
I
w a s found.
6.1-2
U n c o n s o l i d a t e d Sand: The f i r s t e x p e r i m e n t i n t h q s
s e r i e s w a s r u n w i t h u n c o n s o l i d a t e d O t t a w a S i l i c a Sand of
a v e r a g e g r a i n s i z e of 0 . 3 8 5 mm,
T h i s core w a s n o t s u b j e c t e d
t o h e a t t r e a t m e n t and was l o a d e d as o u t l i n e d i n t h e p r o c e d u r
s e c t i o n 5.
,
~
3,
Data were not: o b t a i n e d f o r t h e c o o l i n g c y c l e s .
The r e s u l t s a r e shown i n F i g . 1 6 .
1 0 0 0 , and 1500 p s i g were u s e d .
C o n f i n i n g p r e s s u r e s o f 500i,
A b s o l u t e p e r m e a b i l i t y t o watw
1
- 43-
I,
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0
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decreased w i t h an increase i n confining pressure.
"he r a t e
of c h a n g e was - 0 . 5 rnd/OF a t a11 l e v e l s of c o n f i n i n g p r e s s u r e c
As t h e a b s o l u t e p e r m e a b i l i t y of t h i s core w a s v e r y h i g h ,
(1
2 2 , 0 0 0 md a t 500 p s i g c o : n f i n i n g p r e s s u r e , t h e a v e r a g e s a n d
g r a i n s i z e was r e d u c e d for t h e n e x t e x p e r i m e n t .
1
See Ref. 26 1
f o r methods of c o n t r o l o f p e r m e a b i l i t y and p o r o s i t y of synt h e t i c sands.
6.2
1
Gas F l o w
Gas f l o w e x p e r i m e n t s were c o n d u c t e d a t t h r e e d i f f e r e n t
t e m p e r a t u r e l e v e l s and a r a n g e of c o n f i n i n g p r e s s u r e s .
1
1
Abso-
l u t e p e r m e a b i l i t i e s were measured w i t h n i t r o g e n flow under
c o n d i t i o n s of v i s c o u s flow and g r a p h e d as a f u n c t i o n of t h e
r e c i p r o c a l mean p r e s s u r e on a c o n v e n t i o n a l K l i n k e n b e r g graph.
One r u n w a s conducted i n t h e v i s c o - i n e r t i a l flow r e g i o n for
a consolidated sandstone.
D e t a i l s of t h e a n a l y s i s of t h i s
I
1 1
1
g a s flow d a t a are g i v e n i n T a b l e 9 and i n Appendix ( s e c t i o n
9.3- 2).
I n a l l cases, t h e absolute permeabilities at d i f f e r e a t
t e m p e r a t u r e s b u t for t h e same c o n f i n i n g p r e s s u r e , e x t r a p o l a t e d
t o t h e same i n f i n i t e p r e s s u r e v a l u e .
The s l o p e s o f t h e s e
!
g r a p h s are, however, p r o b a b l y n o t t r u e K l i n k e n b e r g s l i p c o e f ficients.
I
The h i g h s l o p e s a r e a r e s u l t of t h e e f f e c t s of a
i
c o m b i n a t i o n of b o t h s l i p and mean p o r e p r e s s u r e - c o n f i n i n g p r e s *I
I
s u r e stress e f f e c t s on p e r m e a b i l i t y .
Although t h e c o n f i n i n g
p r e s s u r e was h e l d c o n s t a n t a t 1000. psi o r more, t h e p o r e p r e s s u r e changed from n e a r l y a t m o s p h e r i c t o s e v e r a l hundred p s i
for e a c h s e r i e s of r u n s .
3 e t e r m i n a t i o n of s l i p c o e f f i c i e n t s
w a s n o t a m a j o r o b j e c t i v e of t h i s s t u d y .
'I
The v a l u a b l e informadl
t i o n from t h e s e graphs is t h a t t e m p e r a t u r e has no a p p a r e n t effect
o n a b s o l u t e p e r m e a b i l i t y t o gas.
-49-
0
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CD
-49-
6.2-1
Consolidatetl Sandstones: The r e s u l t s of t h e
f i r s t r u n i n t h e v i s c o u s and v i s c o - i n e r t i a l f l o w r e g i o n s on
M a s s i l l o n C o n s o l i d a t e d Sandstone Core Yo. 5 are shown on
F i g s . 18 and 19, r e s p e c t i v e l y .
On Fig. 1 8 , t h e Klinkenberg
s l i p f a c t o r s a t 6 8 , 1 5 0 , and 25OoF a r e 2 . 2 6 4 ,
psi, respectively.
I
3.587,
and 4.351
This shows t h a t t h e a p p a r e n t Klinkenberg
s l i p f a c t o r depends upon t e m p e r a t u r e .
T h e a p p a r e n t permea-
I
b i l i t i e s a t d i f f e r e n t t e m p e r a t u r e s and p r e s s u r e s e x t r a p o l a t e d
t o t h e same v a l u e o f 9 6 0 md and a g r e e r e a s o n a b l y w i t h t h e v i s c
i n e r t i a l a n a l y s i s v a l u e o f 9 3 2 md shown on F i g . 1 9 .
The t u r b u d
l e n c e f a c t o r 8 , which may be o b t a i n e d from F i g . 1 9 , was 1 . 7 x
7
10 f t - l , and i s i n agree,ment w i t h a c o r r e l a t i o n proposed i n
Ref.
27.
1
The c o n f i n i n g p r e s s u r e was h e l d c o n s t a n t a t 1 0 0 0 p s i
i n these runs.
Another s e r i e s o f experiments w a s conducted on Massillon
Sandstone Core N o . 6 a t room, 15OoF, and 25OoF t e m p e r a t u r e
i
!I
l e v e l s and a t c o n f i n i n g p r e s s u r e s of L O O O , 3000, and 4000 p s i g . !
R e s u l t s are shown on F i g s , , 2 0 - 2 2 , and a r e similar t o t h o s e of
11
Fig. 18.
1, 1
Absolute permeability decreased w i t h an i n c r e a s e i n
c o n f i n i n g p r e s s u r e ; and at: t h e same l e v e l of c o n f i n i n g p r e s s u r q
I
t h e a p p a r e n t p e r m e a b i l i t i e s e x t r a p o l a t e d t o t h e same i n f i n i t e
p r e s s u r e v a l u e a p p a r e n t s l i p f a c t o r s a t room and 15OoF tempera-i
t u r e l e v e l s w e r e e s s e n t i a l l y t h e same for a l l l e v e l s o f conf i n i n g p r e s s u r e , b u t h i g h e r a t 2 5OoF t e m p e r a t u r e .
The v a l u e s o f a b s o l u t e p e r m e a b i l i t i e s o b t a i n e d w i t h
ni.trop,cn flow a n d wstcr flow for t h c c o n s o l i d c i t e d s a n d s t o n e
cores w e r e different.
I
I
I
P e r m e a b i l i t i e s t o water a t room t e m ~
perature ranged between 550 rrd and 4 5 0 md f o r a l l of t h e
-50-
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confining p r e s s u r e l e v e l s , while absolute p e r m e a b i l i t i e s t o
n i t r o g e n were c o n s i d e r a b l l y h i g h e r and r a n g e d from 9 6 0 md t o
800 md f o r t h e same c o n d i t i o n s .
T h i s s u g g e s t s t h a t t h e phen-
d
omena c a u s i n g t h e p e r m e a . b i l i t y r e d u c t i o n w i t h w a t e r f l o w a t
room t e m p e r a t u r e may also be r e s p o n s i b l e for t h e p e r m e a b i l i t y
reduction a t high temperatures.
The M a s s i l l o n S a n d s t o n e has
a low c l a y c o n t e n t , a n d had been f i r e d at 50OoC.
6.2- 2
U n c o n s o l i d a t e d Sand: F i g .
tained with f i r e d s i l i c a sand.
4
i
23 shows r e s u l t s ob-
A 2000 p s i g c o n f i n i n g p r e s s u ri e
J
w a s a p p l i e d , and t h e t e m p e r a t u r e l e v e l s used were 68OF, 150af,
and 25OoF.
The r e s u l t s were s i m i l a r t o t h o s e for t h e consol,!-
dated sandstones.
4
I
P e r m e a b i l i t y t o w a t e r w a s a l s o measured f o r t h i s core.'
While t h e e x t r a p o l a t e d a b s o l u t e p e r r e a b i l i t y t o n i t r o g e n w a s /
4,260 md, t h e p e r m e a b i l i t y t o water was o n l y 2 , 1 2 7 md a t r o q
temperature.
6.3
1"
J
O i l Flow
~
.J
Because of t h e d i f f e r e n c e between t h e r e s u l t s o b t a i n e d
~
a t e l e v a t e d t e m p e r a t u r e s w i t h water f l o w and g a s f l o w , s i m i l g r
experiments w e r e r u n w i t h another f l u i d .
Chevron White O i l
~
J
No. 3 w a s c h o s e n for i t s h i g h e r v i s c o s i t y and i t s n o n - p o l a r
j
characteristics
as opposed t o w a t e r , which i s a n i n t e r m e d i d t e
v i s c o s i t y p o l a r f l u i d a n d may i n t e r a c t w i t h t h e r o c k s u r f a c e l
d
Experiments (see 3.ef. 1) had a l r e a d y been c a r r i e d o u t w i t h
Chevron White O i l No. 1 5 , which i s v e r y v i s c o u s .
A s i n water
I
f l o w or g a s f l o w e x p e r i m e n t s , t h e combined e f f e c t of temperait
I
t u r e and o v e r b u r d e n p r e s s u r e was i n v e s t i g a t e d .
-56-
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4
11
-t
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a
0
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3
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3
a-
J
F i g s . 2 4 and 25 show t h e r e s u l t s w i t h o i l f l o w for
c o r e s No. 1 0 and 11.
solidated sandstones.
O i l flow w a s cofiducted o n l y on con-
Absolute permeability t o o i l w a s
J
a f f e c t e d by c o n f i n i n g p r e s s u r e , as e x p e c t e d , b u t t h e r e w a s
only a s l i g h t decrease i n a b s o l u t e permeability t o o i l w i t h
temperature increase.
Hysteresis effects i n cooling cycles
J
were more pronounced a t h i g h c o n f i n i n g p r e s s u r e s o f 3 0 0 0 p s i
and 4 0 0 0 p s i .
J
P e r m e a b i l i t y l e v e l s a t room t e m p e r a t u r e a g r e e c l o s e l y 1
I
with t h o s e o b t a i n e d w i t h n i t r o g e n flow.
T h e a b s e n c e of
r o c k - o i l i n t e r a c t i o n i s b e l i e v e d t o b e r e s p o n s i b l e for the
i
I
d i f f e r e n c e between water and o i l p e r m e a b i l i t i e s .
T h i s sug-
1
g e s t s a d e f i n i t e i n t e r a c t i o n between water and s a n d s t o n e ,
I
consolidated or unconsolidated.
I
6.4
J
i)
I
2- Octanol Flow
I n view of t h e r e s u l t s w i t h water, it a p p e a r e d
u s e f u l t o run s i m i l a r e x p e r i m e n t s w i t h a n o t h e r polar l i q u i d .
.J
2- octanol a l c o h o l w a s chosen.
E x p e r i m e n t s were c o n d u c t e d w i t h commercial g r a d e 2o c t a n o l , and t h e r e s u l t s a r e p r e s e n t e d i n F i g . 2 6 .
The un4
c o n s o l i d a t e d O t t a w a S i l i c a Sandcore used was f i r e d a t 50OoC.
I
I
The a v e r a g e s a n d g r a i n s i z e w a s 0 . 1 5 6 mm.
The c o n f i n i n g
p r e s s u r e a f f e c t e d t h e a b s o l u t e p e r m e a b i l i t y as e x p e c t e d , b u t
i
~
-4
t e m p e r a t u r e a p p e a r e d t o c a u s e a. small i n c r e a s e i n a b s o l u t e
permeability.
I n a d d i t i o n , t h e r e w a s a permanent r e d u c t i o n
I
i n absolute p e r n e a b i l i t y on each cooling cycle.
These r e s u l d s
J
a r e d r a m a t i c when compared t o t h e water d a t a on F i g s . 1 6 and,117.
-58.
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The s l i g h t i n c r e a s e i n p e r m e a b i l i t y t o o c t a n o l w i t h temperat u r e i n c r e a s e f o r b o t h h e a t i n g and c o o l i n g r u n s emphasizes
t h e i m p o r t a n c e of t h e d e c r e a s e i n k w i t h t e m p e r a t u r e i n c r e a s e
for water.
3
R e c e n t d i s c u s s i o n s between Ramey and Dreher (Yara-
thon O i l Co.,
Denver) r e v e a l e d t h a t o c t a n o l o f t e n behaves more
l i k e an o i l t h a n a n aqueous w e t t i n g p h a s e i n s a n d s t o n e s .
In
d
r e t r o s p e c t , it might have been b e t t e r t o h a v e s e l e c t e d b o p r o p y l a l c o h o l (IPA) as t h e second p o l a r s u b s t a n c e .
It i s
recommended t h a t I P A be c o n s i d e r e d f o r f u t u r e s t u d i e s .
6.5
J
Discussion
Cass6’ c o n c l u d e d t h a t c l a y - w a t e r i n t e r a c t i o n s may
I
h a v e b e e n o n e r e a s o n for t l h e e f f e c t o f t e m p e r a t u r e l e v e l upon 1I
J
i
a b s o l u t e p e r m e a b i l i t y t o w a t e r f o r sandstones h e observed.
I
~
Grim3’
31 p r e s e n t e d a comprehensive r e v i e w of t h e m e c h a n i s m
involved i n clay- water i n t e r a c t i o n s .
J
Because t h e r o c k s u s e d
i n t h i s work w e r e t o t a l l y or n e a r l y c l a y - f r e e , c l a y - w a t e r
~
i n t e r a c t i o n i s c o n s i d e r e d r e s p o n s i b l e f o r o n l y a minor role
1
.d
i n t h e phenomenon o b s e r v e d i n t h i s s t u d y .
I t i s almost c e r t a i n t h a t water- cilica i n t e r a c t i o n s
a r e r e s p o n s i b l e f o r t h e mafior e f f e c t s o b s e r v e d w i t h w a t e r .
In!
3
a d d i t i o n t o t h e r e s u l t s of t h i s s t u d y , G r u n b e r g and N i s s a n 13
I
rrd a t room t e m p e r a t u r e ) ’I \
u s e d a q u e o u s s o l u t i o n s ( i n c l u d i n g Amyl Alcohol) w i t h J e n a
Glass F i l t e r s of low p e r m e a b i l i t y ( 1 6 0
and found a l i n e a r d e c r e a s e i n a b s o l u t e p e r n e a b i l i t y w i t h a n
1
J
increase i n temperature.
F l u i d f l o w mechanisms
32
often fit t w o c a t e g o r i e s :
3
(1) mechanisms which a r e e s s e n t i a l l y m e c h a n i c a l i n n a t u r e , t h e
-62-
1 1
f l o w d e p e n d i n g on t h e b u l k p r o p e r t i e s of t h e f l u i d s c o n c e r n e d
and upon the m e c h a n i c a l f o r c e s e x e r t e d upon t h e f l u i d b o d i e s ;
mechanisms which a r e e s s e n t i a l l y m o l e c u l a r i n char&-
and ( 2
t e r , t h e f l o w d e p e n d i n g l a r g e l y o n t h e motion of t h e i n d i v i d u a l
m o l e c u l e s , t h e moleculair, w e i g h t , t h e c o l l i s i o n cross- section,
t h e mean f r e e p a t h , r o c k - f l u i d a t t r a c t i v e f o r c e s , e t c . , r a t d e r
t h a n upon t h e d e n s i t y , p r e s s u r e v i s c o s i t y , e t c . , of t h e f l u i d
i n bulk.
The l a t t e r mechanisms may be d o m i n a n t i n t h e case
of t h e e f f e c t of t e m p e r a t u r e upon w a t e r f l o w i n s a n d s t o n e s
under p r e s s u r e .
S u r f a c e a t t r a c t i v e forces between s i l i c a and w a t e r
m o l e c u l e s may be l a r g e enough t o l e a d t o c h e m i - s o r p t i o n .
In
s u c h a case, t h e a d s o r b a t e m o l e c u l e s become p r a c t i c a l l y a
p a r t o f t h e solid s u r f a c e a n d , compared with o t h e r rnolecules
..
i n t h e l i q u i d , s u c h chemfi-sorbed m o l e c u l e s may be l a r g e l y
immobilized.
The e f f e c t i v e c r o s s - s e c t i o n u n d e r v i s c o u s f l o w
I
c o u l d t h e n b e d i f f e r e n t f o r water from t h e o t h e r f l u i d s t e s t & .
I n c r e a s e s i n t e m p e r a t ~ r eseem
~ ~ t o i n c r e a s e t h i s e f f e c t from
t h e r e s u l t s of t h i s s t u d y .
An e x h a u s t i v e l i t e r a t u r e s u r v e y
i n d i c a t e d n o known p h e n o m n a c a p a b l e of e x p l a i n i n g t h e magnit u d e of t h e e f f e c t s o b s e r v e d i n t h i s s t u d y .
It is b e l i e v e d
t h a t a major, a n d h e r e t o f o r e u n s u s p e c t e d a t t r a c t i o n between
water and s i l i c a h a s been d i s c o v e r e d .
It is p o s s i b l e t h a t
t h i s a t t r a c t i o n i s e s s e n t i a l l y r e s p o n s i b l e for t h e l a r g e
t e m p e r a t u r e e f f e c t s on p r a c t i c a l i r r e d u c i b l e water s a t u r a t i o n
and r e l a t i v e p e r m e a b i l i t i e s 34916,35, and on c a p i l l a r y p r e s !
-
s u r e s 36-38 and r e s i s t i v i t y p r e v i o u s l y r e p o r t e d .
- 6 3-
1
J
If a s t r o n g a t t r a c t i o n between water and s i l i c a i s
_.
t h e major t e m p e r a t u r e e f f e c t , s e v e r a l new e x p e r i m e n t s w i t h
v,
g a s - o i l flow i n s a n d s t o n e s w i l l show no t e m p e r a t u r e e f f e c t ,
I
~
w h i l e g a s - w a t e r f l o w i n s a n d s t o n e w i l l depend on t e m p e r a t u r e .
I n a d d i t i o n , e x p e r i m e n t s of any s o r t i n l i m e s t o n e s s h o u l d
J
n o t depend s t r o n g l y on t e n p e r a t w e .
i
J
d
J
J
J
J
J
-64J
7.
C O N C L U S I 3 N S AND RECOY!!!TYIkTIONS
E x p e r i m e n t a l r e s u l t s i n d i c a t e t h a t t h e a b s o l u t e perm e a b i l i t y t o water f o r c o n f i n e d s a n d s t o n e s i s s t r o n g l y t e m p e r a t u r e dependent.
The a b s o l u t e p e r m e a b i l i t y of s a n d s t o n e s
t o other f l u i d s (nitrogen, mineral o i l , octanol) i s e i t h e r ,
u n a f f e c t e d o r o n l y s l i g h t l y a f f e c t e d by t e m p e r a t u r e l e v e l .
Temperature increase has t h e e f f e c t of d e c r e a s i n g t h e a b s o l u t e permeability t o w a t e r f o r sandstones remarkably.
T e m p e r a t u r e c h a n g e h a s l i t t l e o r no e f f e c t on t h e abeol u t e p e r m e a b i l i t y o f s a n d s t o n e s t o n i t r o g e n , m i n e r a l oil, qr
octanol.
I n t h e case o f water
flOt7,
permeability reductiohs
o f up t o 6 0 % were o b s e w e d o v e r a t e m p e r a t u r e r a n g e o f 70-$OO0F.
~
R e g a r d l e s s of t h e t y p e of f l o w i n g f l u i d , t h e l e v e l o f
c o n f i n i n g p r e s s u r e a f f e c t e d a b s o l u t e p e r m e a b i l i t y i n t h e s@ne
manner , i . e .
, permeability
d e c r e a s e d w i t h i n c r e a s i n g confizhing
For water f:Low e x p e r i m e n t s , i n c r e a s i n g t h e c o n f i n i n g
pressure.
p r e s s u r e had t h e a d d i t i o n a l e f f e c t of i n t e n s i f y i n g t h e tembera-
t u r e dependence o f a b s o l u t e p e r m e a b i l i t y i n many cases (but
not a l l ) .
I n t h e l i g h t o f t h e r e s u l t s o b t a i n e d , it seems t h a t wnsuspected f l u i d - s o l i d s u r f a c e a t t r a c t i v e f o r c e s between w a t e r
,
m o l e c u l e s and s i l i c a were l a r g e l y r e s p o n s i b l e for t h e m a j o r
e f f e c t s observed.
pertinent
The f o l l o w i n g r e c o m n e n d a t i o n s a p p e a r
.
-65-
-66-
J'
I t i s r e c o r n e n d e d t h a t t h e r e s u l t s o b t a i n e d by G r u n 13
b e r g and N i s s a n
b e r e c h e c k e d for t h e same a a u e o u s s c l u t i o n s
and for c o n f i n e d p o r o u s media.
It i s also r e c o r n e n d e d t h a t
J
e x p e r i m e n t s b e r e p e a t e d f o r h i g h e r t e m p e r a t u r e s and c o n f i n i n , g
pressures.
S i n c e o c t a n o l behaves more l i k e a n o i l t h a n a n aq-ueous
J
w e t t i n g p h a s e i n s a n d s t o n e s , it i s recommended t h a t i s o p r o p y l
alcohol b e used as t h e second polar s u b s t a n c e for f u t u r e
studies.
R e s u l t s from such s t u d i e s may h e l p t o e x p l a i n whether
A
t h e d e c r e a s e i n water p e r m e a b i l i t y w i t h i n c r e a s i n p t e m p e r a t q h e
I
is due t o t h e p o l a r i t y o f water.
d
I f a s t r o n g a t t r a c t i o n between w a t e r and s i l i c a c a u s e s '
t h e t e m p e r a t u r e e f f e c t , e x p e r i m e n t s d e s i g n e d t o i s o l a t e watap
a n d / o r s i l i c a w i l l be e n l i g h t e n i n g .
E x p e r i m e n t s w i t h water
I
f l o w i n l i m e s t o n e s s h o u l d n o t depend s t r o n F l y o n t e m p e r a t u r a
I n a d d i t i o n , e x p e r i m e n t s w i t h g a s - o i l f l o w i n s a n d s t o n e s may
show n o t e m p e r a t u r e e f f e c t w h i l e g a s - w a t e r f l o w i n s a n d s t o n d
w i l l depend on t e m p e r a t u r e .
J
i
J
J
-66-
8.
1.
REFERENCES
Cassg , F. J . : "The E f f e c t o f T e m p e r a t u r e and C o n f i n i n g
P r e s s u r e on F l u i d Flow P r o p e r t i e s of C o n s o l i d a t e d Xocks ,"
Ph.D. D i s s e r t a t i o n , S t a n f o r d U n i v e r s i t y ( 1 9 7 4 ) .
2.
A r i h a r a , N . : "A Stud17 of N o n - I s o t h e r m a l S i n g l e and TwoPhase Flow t h r o u g h C o n s o l i d a t e d S a n d s t o n e s ,!' Ph.D. D i s s e r t a t i o n , Stanford University (1974).
3.
Greenberg, D . B . , C r e s a p , R.S:, and Malone, T.A.: " I n t r i n s i c P e r m e a b i l i t y of H y d r o l o g i c a l P o r o u s Mediums: V a r i a t i o n
w i t h Temperature," Water R e s o u r c e s R e s e a r c h (Aug. 19681,
4 , No. 4, 7 9 1 .
-
4.
Muskat, M. : Flow o f Homogeneous F l u i d s t h r o u g h Porous
Media, M c G r a w - H i l l Book Company, I n c . , 1937, C h . 11.
5.
F a n c h e r , G.H. ? L e w i s , J . A . , and B a r n e s , K.: "Some P h y s i c a l C h a r a c t e r i s t i c s of O i l S a n d s , " I n d . Eng. C h e m . , 2 5 :
1139 (1933).
6.
Geertma, J. : " E s t i m a t i n g t h e C o e f f i c i e n t o f t h e I n e r t i a l
R e s i s t a n c e i n F l u i d F l o w t h r o u g h P o r o u s Media,"
SOC.
- P e t . Eng. J o u r . ( O c t . 1 9 7 4 1 , 465.
7.
Amyx, J . W . ,
Bass, D.M., J r . , and W h i t i n g , R.L.: P e t r o l e u l
R e s e r v o i r E n g i n e e r i n , & , M c G r a w - H i l l Book Company, I n c . ,
1 9 6 0 , Ch 2
,
'
'
. .
8.
Kundt, A . , and Warbu:rg, E. : P o g p e n d o r f ' s Ann. P h y s i k , pp
1 5 5 , 337, 525.
9.
K l i n k e n b e r g , L . J . : "'The P e r m e a b i l i t y of Porous Media t o
L i q u i d s and Gases," D r i l l . and P r o d . P r a c . , API (19411,
200.
10.
F o r c h h e i m e r , P.: " H y d r a u l i k , " L e i p z i g a n d . B e r l i n , C h . 1s
S e c t i o n s 1 1 6 - 1 1 8 , Druck and V e r l a g von B.G. Teubner
(1914).
11.
C o r n e l l , D . , and K a t z , D.L.: "Flow o f Gases t h r o u g h
C o n s o l i d a t e d Porous Media," I n d . Eng. Chem. (19531,
Vol. 4 5 , p . 2145.
12.
Dranchuk, P.H., and K o l a d a , L . J . : " I n t e r p r e t a t i o n o f
S t e a d y L i n e a r V i s c o - I n e r t i a l Gas F ~ O W
Data," J o u r . ' Can.
P e t . Tech. ( 1 9 6 8 1 , -.7 , No. 1, p. 36.
-67-
i
13.
G r u n b e r g , L . , and N i s s a n , A . H . : "The P e r m e a b i l i t v of
Porous S o l i d s t o Gases and L i q u i d s , " J o u r . of . I n k . of
P
e t . ( 1 9 5 3 1 , 2 9 , No. 2 3 6 , p . 1 9 3 .
-
-
14.
Calhoun, J . C . , J r . , and Y u s t e r , S.T.: "A S t u d y of t h e
Flow of Homogeneous F l u i d s t h r o u p h I d e a l P o r o u s Media,"
D r i l l a n d 'Pro'd. Prac., API ( 1 9 4 6 1 , 335.
15.
A P I RP 2 7 : "Recommended P r a c t i c e for D e t e r m i n i n g Permeab i l i t y o f P o r o u s Media," Am. P e t . I n s t . (Aug. 1956).
16.
Weinbrandt , R.M. : "The Effect of T e m p e r a t u r e on R e l a t i v e
P e r m e a b i l i t y , " Ph .D. D i s s e r t a t i o n , S t a n f o r d U n i v e r s i t y
(1972).
17.
W i l h e l m i , B . , and Somerton, W.H.:
" S i m u l t a n e o u s Measurement of P o r e and E l a s t i c P r o p e r t i e s of Rocks u n d e r T r i a x i a l S t r e s s C o n d i t i o n s , " SOC. P e t . Eng. J o u r . ( S e p t .
1 9 6 7 1 , 240, 283.
-
18.
19.
20.
,
F a t t , I. and D a v i s , : D . H . : "Reduction in P e r m e a b i l i t y
w i t h Overburden Pressure," T r a n s . , AIME ( 1 9 5 2 ) , -13 9 5
329.
G r a y , D . H . , F a t t , I:, and Bergamini, G.: "The Effect of
S t r e s s o n P e r m e a b i l i t y of S a n d s t o n e Cores," SOC. P e t .
Eng. J o u r . ( J u n e 1 9 6 3 ) , 9 5 .
Zoback, M . D . ,
and Byeiqlee, J . D . :
" P e r m e a b i l i t y and E f f e c t i v e S t r e s s , " A m e r . Assoc. P e t . Geol. B u l l . , 59 (1)
(1975a1, 1 5 4 .
21.
S o m e r t o n , W.H. , Mehta,, M.M.,
and Dean, G.W. : "Thermal
A l t e r a t i o n of S a n d s t o n e s , " J. P e t . Tech. (May 19651,
589.
22.
Wyble, D.O.: "Effect of A p p l i e d P r e s s u r e o n t h e Conduct i v i t y , P o r o s i t y , and P e r m e a b i l i t y of S a n d s t o n e s ," T r a n s
AIME (19581. 213. 430.
23.
Meyer, C.A., McClintock, R.B., S i l v e s t r i , G . J . ,
and
S p e n c e r , R . C . , Jr.: 19167 ASME S t e a m T a b l e s , Am, SOC.
Mech. E n g r s .
2nd e d . , New York, N . Y . ,
1968.
,
J
J
J
I
kJ
I
I
I
d
i
1
J
.,
4
I
I
24.
ASTM-IP-Petroleum Measurement T a b l e s , ASTM, P h i l a d e l p h i a
(19521
25.
P e r r y , J H. : Chemical E n g i n e e r ' s Handbook, M c G r a w - H i l l
Book Company, I n c . (19691, pp. 2 3 - 1 0 .
26.
Larman, H . J . : " V a r i a t i o n s i n P e r m e a b i l i t y a n d P o r o s i t y
of S y n t h e t i c O i l R e s e r v o i r Rock--!<ethods of C o n t r o l , "
SOC. of P e t . Eng. J o u r . (Dec. 19651, 329.
.
J
.
.J
I
-6 8-
I
.J
27.
K a t z , D . L . , and C o a t s , K . H . :
F l u i d s , U l r i c h s Books, I n c
28.
J o n e s , S .C : "A R a p i d , A c c u r a t e U n s t e a d y - S t a t e K l i n k e n b e r g Permeameter," SOC. P e t . Eng. J o u r . ( O c t . 1 9 7 2 1 ,
483.
29.
Sax, N. I. : Dangerdus P r o p e r t i e s of I n d u s t r i a l Materials ,
R e i n h o l d P u b l i s h i n g C o r p o r a t i o n (1963)
30.
G r i m , R.E.:
Company, I n c
31.
G r i m , R.E. : C l a y M i n e r a l o g y , M c G r a w - H i l l
Inc. (1968).
32,
F l o o d , E . A . : " I n f l u e n c e o f S u r f a c e F o r c e s o n F l o w of
F l u i d s t h r o u g h C a p i l l a r y Systems ,I' Highway Research
Board, Spec. Rep. N o . 4 0 (19581,
33.
B a r t e l l , F . E . , Thomas, T . L . , and Fu, Y.: "Thermdynam$cs
of A d s o r p t i o n from S o l u t i o n , i v . T e m p e r a t u r e Dependenae
of A d s o r p t i o n , " J o u r . of Phys. Chem. (19511, 55, 1456,
Underground S t o r a g e of
M i c h i g a n c19 6 8 )
., Ann Arbor,
.
.
.
Mineralogy, M c G r a w - H i l l
Book
Book Company,
-
34.
P o s t o n , S . W . , Ysrael, S. , H o s s a i n , A.K.M.S. , Montgomery,
E . F . , 111, and Rarney, H . F . , Jr.: "The E f f e c t o f Tempevat u r e on I r r e d u c i b l e Water S a t u r a t i o n and R e l a t i v e Permedb i l i t y of U n c o n s o l - i d a t e d Sands," SOC. of P e t . Eng. Joqr.
(June 19701, 1 7 1 .
35.
Weinbrandt, R.M., Casse, F , J . , and Ramey, H . J . , Jr.:
"The E f f e c t o f T e m p e r a t u r e on R e l a t i v e and A b s o l u t e
P e r m e a b i l i t y of S a n d s t o n e s , " SOC. of P e t . Eng. J o u r .
( O c t . 1 9 7 5 1 , 376.
,
'
36.
S i n n o k r o t , A.A. , Ramey, Hi;
J . , Jr, , a n d Marsden, S.S ,, J r , :
"Effect of T e m p e r a t u r e L e v e l upon C a p i l l a r y P r e s s u r e '
Curves," SOC. o f P e t . Eng. J o u r . (March 19711, 1 3 .
37.
J r . , and Ramey, H.J., Jr. E
Okandan, E . , Marsden, S .S.,
" C a p i l l a r y P r e s s u ~ eand C o n t a c t Angle Measurements at
E l e v a t e d T e m p e r a t u r e s , I 1 p r e s e n t e d a t AIChE M e e t i n g , FLlsa,
Oklahoma, March 1:2, 1 9 7 4 .
38.
S a n y a l , S . K . , Ramey, H . J . , J r . , and Marsden, S . S . , Jri. :
"The E f f e c t o f T e i n p e r a t u r e on C a p i l l a r y P r e s s u r e P r o p k r t i e s of Rocks," S:PWLA 1 4 t h Annual Logging Symposium
(May 1 9 7 3 ) .
39.
N a t i o n a l R e s e a r c h C o u n c i l o f U. S .A. : " I n t e r n a t i o n a l
C r i t i c a l T a b l e s o f Numerical Data, P h y s i c s , C h e m i s t r y
and Technology," 'Vol. I-1111, 1 9 3 3 ,
~
-69-
J
9.
APPENDICES
J
3
c
9.1
L:st
of Tabulated ! l a t a
J
T a b l e 1.
D e n s i t y and V i . s c o s i t y of Water v s . Temperature
r'
(from Steam
Pressure = 200 p s i g
J
Temperature
. '
Density
gm/cc
Viscosity
60
0.9990
1.100
100
0.9931
0.679
150
0.9803
0.426
200
0.9632
0.300
250
0.9423
0.228
300
0.9180
0.183
350
0.8904
0.152
OF
cp
J
4
J
4
4
3
4
-72-
c
T a b l e 2.
V i s c o s i t y of N i t r o g e n vs. T e m p e r a t u r e
I
Pr-essure = 14.7
Temperature
OF
'
psia
Temperature
Viscosity
cp
OK
60
288.7
0.01739
100
310.9
0.01839
150
338.7
0.01959
200
366.5
0.02074
2 50
394.3
0.02185
300
422.0
0.02291
I
OK
-73-
= T(°F)-32
1.8
+
273.16
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Table 5.
Viscosity of 2-Octanol vs. T e m p e r a t u r e
J
Pressure = 200 psig
I
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Temp.
“T
A
P
Q
lJ
cpTsec
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66
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150
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m O c v ~ N ~ b O O L o Q m c v c - ~ c - f ~ m c o b m a , ~
mco03mWmcvfm0ammcvmOcvNmfm~cvl~Cu
0 0 0 0 0 b 0 0 0 0 0 f 0 0 a 0 - 00 0 0 0 0 0110 0
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m d a o m C D m m 3 ~ m m b
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0 0 0 0 0 0 0 0 0 0 0 0 0
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9.2
Core Data
J
J
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J
J
3
J
-904
N
l
l
c-4
N
ri
rl
N
c4
0
rl
CJ
N
N
hl
o
m
m
. . . . .
o C I ( D m D I
L D N O O O
a,
a
N
N
C3
W
cv
3
m
m
N
c
0
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+,
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ri
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cn
-91-
J
9.2- 1- 3
D e s c r i p t i o n : The M a s s i l l o n s a n d s t o n e i s found
i n Holmes County, Ohio, and h a s been e x t e n s i v e l y q u a r r i e d
for a v a r i e t y of p u r p o s e s .
The s t o n e is medium- to- coarse
.J
g r a i n e d and i s composed m s t l y of q u a r t z g r a i n s , which are
s u b a n g u l a r t o subrounded i n s h a p e .
The cementing materials
d'
a r e i r o n o x i d e , c l a y m i n e r a l s , and s e c o n d a r y s i l i c a .
T e s t s made for t h e Briar Hill S t o n e Company show t h a t
t h e s t o n e h a s a n a b s o r p t i o n of water of a p p r o x i m a t e l y 6 % b y
weight.
.J
The c r u s h i n g s t r e n g t h r a n g e s from 4 0 0 0 t o 6 0 0 0 p s i ,
5000 p s i being about average.
p e r cubic foot.
The s t o n e weighs 1 3 5 pounds
The a v e r a g e p e r m e a b i l i t y of t h e s a m p l e s
J
used i n t h i s s t u d y w a s 8 0 0 md, and t h e a v e r a g e p o r o s i t y a b o u t
22%.
9.2- 2
Uncons'olidated O t t a w a S i l i c a
9.2- 2- 1
Physical Properties
Core No.
14
15
16
17
Length, c m
5.696
5.590
5.657
5.894
C r o s s - S e c t i o n a l Area, c m
5.067
5.067
5.067
5.067
Average G r a i n S i z e , mm
(35- 45
mesh)
(80- 100
mesh 1
1
(80- 100
(80- 100
mesh)
mesh)
J
3
9.2.2- 2
M i n e r a l o g i c a l Composition
Weight %
99.806
Silicon dioxide (SiO,)
Aluminum o x i d e (A1203)
0.047
I r o n oxide (Fe203)
0.019
Titanium dioxide (Ti02)
0.018
Calcium o x i d e ( C a O )
<o. 01
Magnesium o x i d e (MgO)
<0,01
3
4
0.09
Loss on I g n i t i o n (LO11
- 92-
J
9.2- 2- 3
D e s c r i p t i o n : The O t t a w a s a n d used i n
t h i s s t u d y i s t h e No. 1 7 s i l i c a g r a d e and i s c o m m e r c i a l l y
a v a i l a b l e from t h e O t t a w a D i v i s i o n , P a r k e r I n d u s t r i a l and
Foundry S u p p l y , Rurlingame, C a l i f o r n i a .
I t i s more t h a n 9 9 %
w e i g h t q u a r t z and t h e g r a i n s a r e f a i r l y w e l l rounded.
The
d i s t r i b u t i o n of g r a i n s i z e s i s as f o l l o w s :
U.S.
Opening, ! l i l l i m e t e r
P e r c e n t Weight R e t a i n e d
40
0.420
8.1
50
0.297
44.5
70
0.210
28.8
100
0.149
12.7
140
0.105
4.4
200
0.074
1.1
270
0.053
0.2
Sieve No.
The s a n d w a s s i e v e d and o n l y u n i f o r m l y s i z e d g r a i n s w e m
used t o p r e p a r e a core f o r t h i s s t u d y .
-93-
9.3
D e r i v a t i o n of E q u a t i o n s
-94-
9.3- 1
C a p i l l a r y Tube V i s c o m e t e r : Because l i q u i d v i s -
c o s i t y d a t a o b t a i n e d f r o m s u p p l i e r s are a v e r a g e p r o d u c t q u a n t i -
t i e s and t h o s e from c o n v e n t i o n a l r e f e r e n c e s were n o t g i v e n at
h i g h working t e m p e r a t u r e s , it was n e c e s s a r y t o d e t e r m i n e v i s c o s i t y v e r s u s t e m p e r a t u r e a t o p e r a t i n g pressures.
A c a p i l l a r y t u b e v i s c o m e t e r , whose o v e r a l l l e n g t h w a s
62.875 i n c h e s and whose i n t e r n a l d i a m e t e r was 0.033 i n c h e s ,
w a s c o n s t r u c t e d from a 316 s t a i n l e s s s t e e l t u b e .
c o e f f i c i e n t of t h e r m a l e x p a n s i o n w a s 8 . 9 x
The l i n e a r
in/in-OF.
The l a m i n a r f l o w o f l i q u i d s t h r o u g h c i r c u l a r c o n d u i t s
obeys P o i s e u i l l e ' s l a w :
'
4
rr Ap
= 8pR
where q = f l o w r a t e , cc/sec; r = i n s i d e r a d i u s , cm; Ap =
p r e s s u r e d r o p , d y n e s / c m2 ;
?J
= liquid viscosity, poises, 2 =
l e n g t h of c a p i l l a r y , c m .
For r and R i n i n c h e s , Ap i n p s i , and
i n cp u n i t s , Eq.
9 - 1 becones:
q = 4.437 x 1 0
7 r
4
A2
(9-2)
RP
and
?J
(9-3)
= 0 . 5 2 3 0 !&
9
Knowing t h e a c t u a l v a l u e o f v i s c o s i t y a t 7OoF, and f r o m
measurements of
t o be 0.5113.
p and q , t h e m u l t i p l y i n g c o n s t a n t w a s f o u n d
Therefore:
'70
= 0.05113
-95-
%
(9-4)
p,
T h e r e f o r e , a graph of Y =
Ap (l+--)
b
Dm
;&a Pa
vs
9,
.x
J
a
1
(1+b
prn
s h o u l d y i e l d a s t r a i g h t l i n e o f s l o p e rj and i n t e r c e p t E
1
,
d
p r o v i d e d t h a t t h e v a l u e of b is known.
J
J
3
J
J
J
J
J
E q . 9- 10 was t h e w o r k i n g e q u a t i o n for t h i s a p p a r a t u s .
The r e s u l t s a g r e e c l o s e l y w i t h t h o s e found i n t h e I n t e r n a t i o n a l
Critical Tables. 39
9.3-2
V i s c o - I n e r t i a l Flow o f G a s : The q u a d r a t i c e q u a t b h
as proposed by F o r c h h e i m e r and m o d i f i e d by C o r n e l l and Katz
(see r e f s . 1 0 and 11) i s :
-8=
avq
+
BPq
2
(9-11)
for t h e case of v i s c o - i n e r t i a l flow o f g a s .
For v i s c o u s flea,
t h e q u a d r a t i c t e r m o f 9 - 1 1 i s small enough t o b e n e g l e c t e d ,
and a h a s t o b e t h e r e c i p r o c a l o f p e r m e a b i l i t y , i . e . ,
Q
= l/k.
The i n t e g r a t e d form o f E q . 9 - 1 1 f o r h o r i z o n t a l l i n e a r
flow i n t h e a b s e n c e of s l i p p a g e i s :
When t h e r e i s g a s s l i p p a g e , a becomes
):+
kl(
_I
b
k(l+-
and s i m p l i f y i n g ,
Pm
or
Y = E + fix
-97-
1
b
'
R e p l a c i n g a by
A t t e m p e r a t u r e s , T , o t h e r t h a n room t e m p e r a t u r e , t h e
l e n g t h of t h e t u b e i s :
(9-5)
and
rT 4 = r 7 0 ‘[l
+ B (~-7011~
(9-6)
or
(9-7)
Because B , t h e l i n e a r c o e f f i c i e n t of t h e r m a l e x p a n s i o n , i s
small, Eq. 9- 7 c a n be approximated as:
4
4
’-T= -
‘T
r70
‘70
6
+ 3B ( T - 7 0 1 7
For t h e a p p a r a t u s :
UT
= 0,05113 l l + 2 . 6 7 x
(T-70)3
Q
(9-9)
T h e r e f o r e , t h e v i s c o s i t y a t any t e m p e r a t u r e i s :
(9-10)
Where :
aT = 0 . 0 5 1 1 3 l l
t
2 . 6 7 x 10’’
-96-
(T-7011
9.4
L i s t of M a n u f a c t u r e r s
-99-
LIST OF YANUFACTURERS
The f o l l o w i n g i s a l i s t of t h e v a r i o u s p i e c e s of e q u i p ment or s u p p l i e s t h a t were used i n t h i s work, t o g e t h e r w i t h
t h e c o r r e s p o n d i n g names of m a n u f a c t u r e r s a n d / o r s u p p l i e r s
from whom t h e y were a c q u i r e d .
Chevron White M i n e r a l O i l N o .
San Francisco.
3
-
Van Waters E Rogers, I n c .
-
Pressure Transducers
D y n a s c i e n c e s Corp. , Model KP 1 5 , c/o
Gaco I n s t r u m e n t S a l e s , 655 Castro S t r e e t , S u i t e 2 , Mountain
V i e w , C a . , 94040 ( 9 6 1 - 2 2 2 2 ) .
B a r n e t t I n d u s t r i a l Dead Weight T e s t e r
-
c / o Gaco I n s t r u m e n t
, 94040
Sales, 6 5 5 C a s t r o S t r e e t , S u i t e 2 , Mountain V i e w , C a .
(961-2222).
P r e s s u r e I n d i c a t o r - Pace Node1 CD 25, c / o Gaco I n s t r u m e n t
S a l e s , 6 5 5 C a s t r o S t r e e t , S u i t e 2 , Mountain V i e w , C a . , 9 4 0 4 0
(961-2222).
P r e s s u r e R e g u l a t o r - V o l u m e t r i c s , Model V R C - 4 0 0 , 1 0 2 5 A r b o r
Vitae S t r e e t , Inglewood, C a . , 90301 ( 2 1 3 ) 6 4 1 - 3 7 4 7 , o r c / o
Gaco I n s t r u m e n t S a l e s , 6 5 5 C a s t r o S t r e e t , S u i t e 2 , F o u n t a i n
V i e w , C a . , 94040 ( 9 6 1 - 2 2 2 2 ) .
-
High P r e s s u r e R e g u l a t o r
Newark, C a . (793-2559).
Model 4-580, Matheson Gas P r o d u c t s ,
-
V a r i a b l e R a t e O i l Pump
Model PC, Whitey Tool E D i e Company,
3 6 7 9 Landregan Emvl., Oakland, C a , (653-51001, loan from USBM.
-
H y d r a u l i c Hand Pump
E n e r p a c , Model P- 39, P a u l Monroc H y d r a u l i c s ,
I n c . , 1 5 7 0 G i l b r e t h Road, Burlinganre, C a . , 9 4 0 1 0 (697-2950).
-
C o n s t a n t R a t e Pump
Hand-made e q u i v a l e n t t o Ruska 2 2 0 0 s e r i e s .
Uses Viton 0 r i n g w i t h machined t e f l o n b a c k - u p . r i n g .
Accumulators ( G r e e r o l a t o r ) , Model No. 20- 30 TMR-S-% WS, Hyd r a u l i c C o n t r o l s , I n c . , 1330 6th S t . , E m e r v v i l l e , C a . , 94608
(658- 8300).
Recording P o t e n t i o m e t e r (for t e m p e r a t u r e )
Model Speedo Max
v, Leeds E N o r t h r u p , 1 0 9 5 Market S t . , S a n F r a n c i s c o , C a ,
(349-6656).
3-
-100-
-
Thermocouples
I r o n - C o n s t a n t a n , C o n a x , c / o I n s t r u m e n t Labo r a t o r y , 6 4 4 Emerson S t . , P a l o A l t o , C a . , 9 4 3 0 3 ( 3 2 8 - 1 0 4 0 ) .
-
Temperature C o n t r o l l e r
API Model 2 2 8 w i t h 4 0 1 0 Power P a c k ,
A P I I n s t r u m e n t s , 2339 C h a r l e s t o n R d . , Mountain V i e w , Ca.,
94040 (964-0512).
-
L a b o r a t o r y Flowrator K i t
Model No. 10A3565ALK2, F i s h e r E
P o r t e r C o . , 1 3 4 1 North Main S t . , Walnut Creek, C a . , 94596
(933-8880).
Core S l e e v e - V i t o n A t u b i n g , \?‘estAmerican Rubber Co.,
North Main S t . , O r a n g e , Ca., 9 2 6 6 8 ( 7 1 4 - 5 3 2 - 3 3 5 5 ) -
750
-
0 !ings
V i t o n A w i t h t e f l o n b a c k - u p r i n g s , ABSCOA I n d u s t r i e s , 8 8 0 B u r l i n g a m e A v e . , Redwood C i t y , C a . (369-4897) OR
1 0 7 1 W. Arbor Vitae S t . , Znglewood, C a . , (213- 7764561).
-
Tubin
T u b e s a l e s , 5 0 0 Sansome S t .
d l 9 1 9 ) .
,
S a n F r a n c i s c o , Ca.
F i t t i n g s E V a l v e s - Van Dyke E F i t t i n g C o . ,
Oakland, C a . (658-1700).
5 5 2 5 M a r s h a l St.,
Gas A n a l y z e r - Gas Master, Laboratory Model, GOW-MAC I n s t r t k ment C o . , 1 0 0 Kings F.d., M a d i s o n , N . J . 0 7 9 4 0 (201-377-34501 o r
A p p l i e d I n s t r u m e n t C o . , 1 9 9 1 s t S t r e e t , Los A l t o s (941-592k3).
-
Recording P o t e n t i o m e t e r ( f o r p r e s s u r e )
r e c o r d e r , L e e d s and N o r t h r u p , BD-9, P.O.
Ca. (593-8392).
Two pen m u l t i - r a n g e
Box 6 3 4 , B e l m n t ,
-
Alundum Core
N o r t o n Co., I C D , 2555 L a y a f e t t e S t . ,
Clara, C a . 95050 ( 2 3 4 - 7 7 1 0 ) .
Santa
-
Lapp P u l s a f e e d e r Pump
Model LS- 20, 316SS, 1 / 6 h p , 94 Natoma
S t . , S a n F r a n c i s c o , Ca. 94105 ( 3 9 1 - 7 6 5 0 ) .
O t t a w a S i l i c a , No. 1 7 S i l i c a , P a r k e r I n d u s t r i a l and F o u n d r y
S u p p l y , 1 8 8 1 R o l l i n g Rd., Burlingame, C a . , 94010 ( 6 9 7 - 8 8 6 5 ) .
Massillon S a n d s t o n e - T h e B r i a r H i l l S t o n e C o . ,
Ohio, 4 4 6 2 8 ( 2 1 6 - 2 7 6 4 0 1 1 ) .
-101-
Glenrnont,
NOMENCLATURE
10.
English
A = area, c m 2
k = p e r m e a b i l i t y , md
L = l e n g t h of c o r e , c m
p = pressure, p s i
q = flow r a t e , cc/sec
w = flow r a t e , g m / s e c
T = temperature,
0K
or
OF
r = radius, c m
v = flow v e l o c i t y , cm/sec
Greek
p
= d e n s i t y , gm/cc
u =
viscosity, cp
4 = porosity, fraction
A = increment
Subscr i D t s
a = atmospheric condition
c = c o r e or c o n f i n i n g
m = mean v a l u e
T = temperature
-102-