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A permeability study of sand

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a ferm eab ilx tv stu d y
or mm
by
w i l l i a m Lee H ershelm an
A d i s s e r t a t i o n su b m itte d in p a r t i a l f u l f i l l m e n t of the
r e q u ir e m e n ts f o r the Degree o f D octor o f P hilosophy*
in th e D e p artm en t o f G eology, in th e G ra d u a te
C o l l e g e o f t h e S t a t e U n i v e r s i t y o f Iowa
June,
1940
ProQuest Number: 10598673
All rights reserved
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uest
ProQuest 10598673
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ii
TABLE OF CONTENTS
Page
INTRODUCTION * * * * * * * ♦ * , * * * * * * * * . *
1
STATEMENT OF THE PROBLEM.........................
*
I
REVIEW OF LITERATURE * .................................................. , * * .
*
3
V oids , * * « « • * •
d ra in S lae
.....................
* • * » * * * • * ...........................
P o r o s ity and d r a i n S is e
P e r m e a b 11 i ty
* * » » « • * *
..
3
*
• * * * » » * * * # • *
« « •
The T h e o r y o f F l o w E q u a t i o n s
* « *
10
13
•
16
*
ZO
Form ulae f o r P e r m e a b il i t y * • # • * * * * * » *
£8
E m p iric a l M easurem ent o f P e r m e a b i l i t y * * * * *
37
APPARATUS AND PROCEDURE
U n c o n s o lid a te d Sands
. » « » • • * * • « * * * #
42
* . * * * # * * . * * . #
4Z
P o r o s i t y and P e r m e a b ility o f U n ig rad e Sands * »
44
M ix tu r e s o f G rades o f U n c o n s o lid a te d Sands
47
G r a i n S l s e o f t h e Mixed G ra d e s
# * » # « * » *
Procedure for C o n so lid ated M a te ria ls
INVESTIGATION AND RESULTS
U n c o n s o lid a te d Sands
* .
* . . * * * . *
.....................
52
.....................
57
* • * * # * * • # * # * •
The E f f e c t o f G r a i n S i z e on p o r o s i t y
47
57
in
U n ig r a m ila r ? U n c o n s o lid a te d Sands * * * * * *
58
The E f f e c t o f C o n t a i n e r D i a m e t e r o n t h e
P o r o s i t y o f U n ig ra n u la r# U n c o n s o lid a te d Sands
82
The E f f e c t o f G r a i n Slsse o n P o r o s i t y o f
M ix tu r e s o f U n c o n s o lid a te d Sands
* * * * * *
64
iiI
Page
The E f f e c t o f G r a i n S i z e o n P e r m e a b i l i t y o f
U n lg ra n u la r* U n c o n so lId a te d Sands * * * * * *
The E f f e c t o f G r a i n S i z e on P e r m e a b i l i t y
M ix tu r e s o f U ncona& lIdated Sands
in
* * * * * *
The E f f e c t o f P o r o s i t y o n p e r m e a b i l i t y
6?
69
* # » *
1Z
The E f f e c t o f P o r o s i t y on t h e P e r m e a b i l i t y o f
U nigr& nular* U n c o n s o lid a te d Sands * * * * * *
73
The E f f e c t o f P o r o s i t y on t h e P e r m e a b i l i t y o f
M ix tu re s of U n c o n s o lid a te d Sands
* * * * * *
76
E q u a tio n o f th e P e r m e a b i l i t y from G ra in S iz e
and P o r o s i t y
* * * * » * * * # * # * * # «
D e riv a tio n o f th e E quation
*
BZ
* * * * * * * * * *
S t u d y o f t h e p e r m e a b i l i t y o f Some S a n d s t o n e ©
61
*
63
I n v e s t i g a t i o n o f t h e ^ E f f e c t i v e D i a m e t e r 11 * * *
66
SUMMARY ADD CONCLUSIONS
*■ * * * * * * * * * * * *
*
93
FURTHER RESEARCH * * * * * * * * ..................... * . * * ,
94
SELECTED BIBLIOGRAPHY
96
* * * * * * * * * * * * * * *
A P P E N D I X ..........................................* * * * * .............................* * *
96
Iv
L I S T OF ILLUSTRATIONS
P age
F igure
1*
P e r m e a b i l i t y Kook-*up
* « » * * * * * « »
45
F i g u r e Z*
P e r m e a b i l i t y H e ad • * * • # » # « « • « »
54
F i g u r e 3*
P o ro slm eter * * * * . * * . . * . ♦ • * «
55
F i g u r e 4*
E f f e c t o f G r a i n Sis:® on P o r o s i t y o f
U n ig ra n u la r# U n c o n s o lid a te d Sands * * *
F i g u r e 5*
E f f e c t o f C o n t a i n e r D ia m e te r on P o r o s i t y
o f U n ig ra n u la r* U n c o n s o lid a te d Sands
F i g u r e 6*'
E f f e c t o f G r a i n 'Slate o n P o r o s i t y
*
63
- * «
65
in
M ix tu re s o f U n c o n s o lid a te d Sands
F i g u r e 7*
E f f e c t o f G r a in Sis® on P e r m e a b i l i t y o f
U n ig ram ilar* U n c o n so lid a te d Sands * • #
F i g u r e 0*
F i g u r e 9*
S a m p l e s C o n t a i n i n g b u t One G r a d e S i z e
F igure
T e s t Sam ples C o n t a i n i n g G ra d e s
«4%
F igure
11*
”2 %
* *
W5 W, a n d w6 " * * * * * * * * * * *
77
76
IE* T e s t S a m p l e s C o n t a i n i n g G r a d e s ”4 %
*
*
*
*
M5 %
..............................................
13* T e s t S a m p l e s C o n t a i n i n g G r a d e s
"6"
Figure
74
T e s t S a m p l e s C o n t a i n i n g G r a d e s tt3 ri# * 4 " ,
and »6M * *
F igure
70
*3%
* 5 % a n d *e*
F igure
66
The E f f e c t o f G r a i n S i z e o n P e r m e a b i l i t y
In M ix tu r e s o f U n c o n s o l i d a t e d Sands * *
10*
59
*
*
*
*
*
*
*
*
*
* .
.
79
f,5 w a n d
*
*
*
*
*
60
14* E f f e c t o f G r a i n S i z e o n t h e O r d i n a t e
In tercep t
* * * * *
* • * .
64
Pag©
F igure
15# R e l a t i o n o f G r a i n S I m
F igure
16# T h e R e l a t i o n
to th e Tan
0 «*
# #
18* The S i i c h t e r
» * * # • • • • » * » • • *
88
90
( W i l s e y ) ^ E f f e c t i v e S i s © 1*
from M easured G ra in S i z e
P late 1
.
17* T h e H a z e n ^ E f f e c t i v e S i e e M f r o m M e a s u r e d
G r a i n Sis©
F igure
85
of G rain S is e and P o r o s ity
t o t h e Perm eability o f S a n d s t o n e s
F igure
.
........................................................
* • * • » » #
91
6
ABSTRACT
A P e r m e a b i l i t y S t u d y o f Sa nd
T his s t u d y is a r e p o r t o f th e
in v estig atio n ©
made a t t h e S t a t e U n i v e r s i t y o f Iowa u p o n t h e q u a n t i t a t i v e
r e l a t i o n s w hich e x i s t betw een g r a i n
size,
p o rosity#
and
p e m e a b i IIty*
The
l i t e r a t u r e was r e v i e w e d a n d a n a l y s e d w i t h
1*
The v a r i a t i o n ©
reg ard tot
p ro d u ced in t h e p o r o s i t y and
p e r m e a b i l i t y by s i x d i f f e r e n t m e t h o d s o f p a c k i n g s p h e r e s *
Z+
A d is c u s s io n o f the v a rio u s d e f i n i t i o n s
of
a v e r a g e and e f f e c t i v e g r a i n d i a m e t e r o f a sand*
3*
The e f f e c t
of g r a i n s i z e of n a t u r a l
©and®
upon t h e p o r o s i t y *
4*
The e f f e c t o f g r a i n s i z e
upon th e
p e rm e a tb i 1 i t y #
5«
A th eo retical
developm ent o f th e flo w
e q u a t i o n s em ployed in d e t e r m i n i n g p e r m e a b i l i t y *
6*
The
lim it©
of th o se e q u atio n s*
7*
Form ulae d e v is e d to d e te rm in e
the
p e r m e a b i l i t y b y method© o t h e r t h a n d i r e c t f l u i d m e a s u r e m e n t *
The e x p e r i m e n t a l
i n v e s t i g a t i o n was d e s i g n e d t o
do w h a t h a d n o t b e e n a t t e m p t e d b e f o r e r e l a t i v e
t o th e manner
o f asse m b ly o f th e g r a i n s i z e and p o r o s i t y d a ta *
B oth
c o n s o l i d a t e d and u n c o n s o 1 i d a t e d m a t e r i a l s w ere u t i l i z e d
th e experim ents*
in
The u n c o n s o l i d a t e d s a m p l e s w e r e f r o m t h e
v ii
Io w a R i v e r a t Iow a C i t y *
Io w a, a n d from t h e f r i a b l e
P e te r sa n d sto n e o f the n o r th e a s te r n p a r t o f - t h e
St*
sa me s t a t e *
The c o n s o l i d a t e d s a m p l e s w e r e c o r e d f r o m o i l - p r o d u c i n g
h e r I e o n s i n P e n n s y l v a n ia and Kentucky*
E m p i r i c a l d a t a were g a t h e r e d from th e u n c o n s o l i ­
d a te d sand sam ples by t r e a t i n g
sy ste m s o f g r a i n s composed
o f s i n g l e grade® and m i x t u r e s o f grade® and m a i n t a i n i n g
the fo llo w in g
o u tlin es
1*
The
e f f e c t o f g r a i n e l s e on p o r o s i t y *
2*
The
effect
3*
The ' e f f e c t o f p o r o s i t y
o f g r a i n s i z e on p e r m e a b i l it y #
The r e s u l t s - o f t h e
on p e r m e a M 1 i t y *
in v e s ti g a t i o n dem onstrated
that*
1*
As t h e g r a i n s i z e
in creases
the p o ro s ity
2*
As t h e g r a i n s i z e d e c r e a s e s
3*
The p e r m e a b i l i t y d e c r e a s e s a s
decreases*
the p e rm e a b ility
decreases*
when
the p o r o s i t y
t h e p o r o s i t y 1® d e c r e a s e d b y c o m p a c t i o n * a n d t h a t
the r a t e
of decrease
4*
in c re a s e s as the g r a in s iz e
The p e r m e a b i l i t y v a r i e s
p o r o s i t y w hen t h e p o r o s i t y
is a l t e r e d
decreases*
In v e rs e ly as
the
by c h a n g e o f g r a i n
size.
From t h e g e n e r a l i t i e s
d erived fo r
p orosity*
observed*
a f o r m u l a was
th e p e r m e a b i l i t y from t h e g r a i n s i z e and
The e q u a t i o n
la*
vi i i
/" /& # 3 V S -
L og / f - L
qj
P ~
a
I_______________ / . / s o y
The f o r m u l a d e r i v e d f o r
)
/
the p e r m e a b ility o f the
u n c o n s o l i d a t e d s a n d s was f o u n d t o be i n v a l i d
for
the
c o n s o l i d a t e d sam ples*
An i n v e s t i g a t i o n o f
the
in d u r a t e d sam ples d i s c l o s e d
d e f i n e d b y H a s e n was t h e
least
the e f f e c t i v e
th at
d iam eter o f
th e diam eter as
i n a c c u r a t e one w hich c o u ld
be d e t e r m i n e d from a c u m u l a t i v e p e r c e n t c u rv e *
A PERMEABILITY STUDY OF SAND
INTRODUCTION
Tliis t h e s i s
i s th e r e p o r t o f an i n v e s t I g a t i o n
o f th e r e l a t i o n s h i p w hich e x i s t s
s i z e and p e rm e a b i1ity*
1939 p e r u s i n g
summer* f a l l
and
the
grain
The a u t h o r s p e n t t h e s p r i n g o f
lite ra tu re
on t h e s u b j e c t ,
a n d w i n t e r o f t h e sa m e y e a r
in terp retstio n
of the
and the
in e x p e rim e n ta tio n
e x p e rim e n ta l d ata*
s u r v e y was c a r r i e d o u t u n d e r
F* T* M a v i s *
betw een p o r o s ity *
The l i t e r a t u r e
the s u p e r v is io n o f P ro fe s s o r
t h e n o f t h e D e p a rtm e n t o f M e c h a n ic s and
H y d r a u l i c s a t t h e S t a t e U n i v e r s i t y o f Iowa*
The r e m a i n d e r
o f t h e w o r k was u n d e r t h e s u p e r v i s i o n a n d g u i d a n c e o f
P r o f e s s o r s A* C* T r o w b r i d g e a n d A . C* T e s t e r *
The a u t h o r
is
h i s many
d e e p ly in d e b te d to P r o f e s s o r T row bridge fo r
h elp fu l
su gg estio ns a t
the
I n c e p t i o n o f th e p r o b le m and
to P r o f e s s o r T e s te r fo r h is c r i t i c i s m s and
as
t h e work r e a c h e d i t s
in te rp retatio n s
f i n a l stages*
STATEMENT OF PROBLEM
It
i s g e n e r a l l y know n t h a t
sandstones possess
v o i d s a n d t h a t t h o s e v o i d s when i n c o m m u n i c a t i o n may s e r v e
as c o n d u its fo r
the
tran sm issio n of flu id s*
some o f t h e q u a n t i t a t i v e
rela tio n s
determ ine the ease o f th a t
Unknown a r e
o f th e f u n c t i o n s w hich
tran sm issio n *
2
E a s e o f t r a n s m i s s i o n d e p e n d s u p o n two d i f f e r e n t
sets
of fu n c tio n s,
and, t h o s e o f
e.e# j
those of the
the f l u i d b e in g
t r a n s m i t t i n g m edium
tran sm itted #
A ssum ing t h e
t r a n s m i s s i o n m ed iu m t o be a s a n d o r s a n d s t o n e ,
the c o n d u it
fu n ctio n s are
the p a ssa g e s
resu ltin g
th e d ia m e te r s and f r e q u e n c i e s
from p o r e com m u n icatio n *
U n fo rtu n ately n e ith e r
o f t h e s e c o n c e p ts c a n be m e a s u re d d i r e c t l y ,
lo g ical
but
it
is
t o a s s u m e th em t o b e r e f l e c t e d b y t h e p o r o s i t y ,
the g ra in s iz e ,
and th e g r a i n a n g u la r ity *
f u n c t i o n s which a i d or h i n d e r
are
of
the v i s c o s i t y ,
The f l u i d
the ease of i t s
the d e n s i ty ,
the
tran sm issio n
te m p e ra tu re , and the
pressure*
S ingly a l l
of th e se fu n c tio n s a r e f a m i l i a r , and
th e h y d r a u l i c e n g in e e r and th e p h y s i c i s t have u n i te d
flu id fu n ctio n s
advantageously
m echanics, but advances
in the f i e l d
in th e q u a n t i t a t i v e
c o n d u it f u n c t i o n s have been r e l a t i v e l y few .
recent
the
of f l u i d
u n io n o f the
However,
im provem ents in p r o d u c t i o n m ethods f o r gro u n d w a te r
and o i l have p l a c e d a s t r o n g
th e c o n d u i t , and so a s
demand on i n f o r m a t i o n r e g a r d i n g
the u t i l i t y
has
in c re a se d the
in v e s tig a tiv e r e lu c ta n c e has decreased*
T herefore,
rela tio n s
m edium ,
it
is
our p u r p o s e
o f two o f t h e f u n c t i o n s
i.e .;
to
in v estig ate
the
of the tran sm issio n
p o r o s i t y and g r a i n s i z e ,
and to e x p re s s
th e m a s f u n c t i o n s o f t h e p e r m e a b i l i t y *
The f u n c t i o n o f g r a i n a n g u l a r i t y h a s n o t b e e n
3
in clu d ed
in t h i s
i n v e s t i g a t io n *
The r e a s o n s f o r
th is
e x c 1u s i on b e i n g j
1#
There e x i s t s #
a t present#
no m ethod o f
m e a s u r i n g g r a i n a n g u l a r i t y o r r o u n d n e s s w h i c h I®
su fficie n tly
d u p licated
in o th e r
Zm
expressed
lab o rato ries*
The a n g u l a r i t y o r r o u n d n e s s
is p a r t i a l l y
in th e p o r o s i t y *
3*
series
f r e e o f t h e human e l e m e n t t h a t r e s u l t s may b e
When o n e t y p e o f s a n d
of experlm ents#
is used throug hou t a
the a n g u la r ity
is m ain tain ed as a
c o n s t a n t a n d n e e d n o t be d e te r m i n e d *
REVIEW OF LITERATURE
Voids*
The v o i d s b e t w e e n g r a i n s
in sands or sa n d sto n e s#
when i n c o m m u n i c a t i o n # may s e r v e a s c o n d u i t s
tran sm issio n of flu id s*
shape#
T h e s e v o i d s may v a r y
the
in s i z e and
d e p e n d in g upon th e m anner o f p a c k in g and upon t h e
s i z e and shape o f th e g r a i n s d e f i n i n g
in itia l
d iscussion
grains#
upon t h e v o id s # w i l l
w ill
for
be d i r e c t e d
the e f f e c t of
them#
the s i z e
For the
and sh ap e o f th e
he n e g l e c t e d a n d
in te rest
tow ards th e v a r i a t i o n s produced
v o id s by a v a r i e t y
o f m ethods o f g r a i n
fu rth er
the d isc u ssio n #
fac ilita te
packing*
the g r a in s
b u t w i l l be i n tr o d u c e d
is n o t to
in a l a t e r
To
of the sand
w i l l be c o n s i d e r e d a s s p h e r e s o f a u n i f o r m s ize*
o f g r a i n s iz e and shape
in t h e
The e f f e c t
be c o m p l e t e l y n e g l e c t e d #
discu ssio n *
The b e s t d i s c u s s i o n o f t h e r e s u l t s
c o n d itio n s
i s t h a t o f G r a t o n a n d F r a s e r *#
o f the above
They b a s e t h e i r
1* G r a t o n , L . C* a n d F r a s e r , H- J * # S y s t e m a t i c p a c k i n g o f
s p h e r e s w i t h p a r t i c u l a r r e l a t i o n to p o r o s i t y and p e r m e a b i l i t y
J o u r * G e o l * , V o l . 4 3 , 1 9 3 5 , pp* 7 8 5 - 9 0 9 *
i d e a s upon s i x
ty p e s o f p a c k in g w hich a r e c o l l e c t e d
in to
two g r o u p s o f t h r e e e a c h , a n d p r o p o s e s u n i t o f p a c k i n g
co n sist
to
o f e i g h t s p h e r e s and t h e v o id s p a c e c r e a t e d by
them#
In the f i r s t
a bottom
fashion
w ith
layer of four
th at
its
case or ty p e, the a u th o rs v i s u a l i z e
s p h e r e s which a r e p l a c e d
the s u r f a c e o f an y one s p h e r e
two n e i g h b o r i n g
from t h e
s p h e r e s andt h a t
c e n t e r o f a n y one s p h e r e
two w h i c h a r e
in c o n t a c t w ith
is
in c o n ta c t
lin es p ro jected
to the c e n te r s o f
I t form a 90° a n g le *
the c e n te r s of th e sp h eres r e p r e s e n t the c o rn e rs
square#
The s e c o n d
arranged s im ila r ly
each g rain c o n ta c ts
lay er of four sp h e re s,
to
those
in such
in th e f i r s t ,
the
Thus,
of a
w ith the g r a in s
is p la c e d so th a t
t h e b o t t o m l a y e r a t b u t one p l a c e *
The c e n t e r s o f t h e e i g h t s p h e r e ® t h u s r e p r e s e n t
the c o r n e r s
of a cube.
C a s e 1 may b e r e p r e s e n t e d b y t h e f o l l o w i n g d i a g r a m s
or th e th r e e d im en sio n al f i g u r e
on P l a t e
I*
Top
vie w
S id e
v ie w
Case 1
in
the second c a s e ,
f i r s t and second l a y e r s
form t h e c o r n e r s
the sp h e res of both th e
are arran g ed so th a t
of sq u a res,
but th is
i s p l a c e d on t o p o f t h e f i r s t
row s p h e r e s
the
other
touch the f i r s t
two a t
so t h a t
tim e
th e ir cen ters
the second
layer
two o f t h e s e c o n d
row s p h e r e s a t
two p o i n t s a n d
b u t one p o in t*
Top
v lew
\/
The t h i r d c a s e f i n d s
second la y e r s a g a in a rra n g e d a t
b u t the second la y e r
g r a i n of the second
a t four p o in ts ,
p oint*
th e g r a i n s o f the f i r s t and
the c o rn e rs o f s q u a re s ,
i s p l a c e d on t h e f i r s t
layer c o n ta c ts
two a t
so t h a t one
th e grain® o f th e f i r s t
two p o i n t s a n d t h e f o u r t h a t o n e
Plate I
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
A f t e r 3 - r a t on a n d F r a s e r
Top
view
Side
view
Case 3
The s e c o n d d i v i s i o n o f t h r e e c a s e s h a s t h e
cen ters
o f th e s p h e r e s o f t h e f i r s t and s e c o n d l a y e r s
f o r m in g t h e c o r n e r s o f a rhombus r a t h e r t h a n a s q u a r e *
Thus,
l i n e s p r o j e c t e d from t h e c e n t e r s
two a n g l e s o f 6 0 ° a n d two o f 1 2 0 ° w i t h
o f th e s p h e r e s form
i t s n eig h bo rs of
t h e same l a y e r #
In c a se 4 the g r a in s
th o se
of th e f i r s t
of th e second
layer co n tact
a t o n ly one p o in t#
3 id e
v iew
Case 4
T h i s may b e r e c o g n i s e d a s c a s e Z a f t e r r o t a t i o n #
C a s e 5 h a s t h e s e c o n d l a y e r rhom b p l a c e d on
th a t of the f i r s t
lay er
in su c h f a s h i o n
second lay e r spheres c o n ta c t
th at
two o f t h e
those of th e f i r s t
lay er a t
vrj*
tw o p o i n t s *
a n d tw o a t o n l y o n e p o i n t *
Top
Side
v iew
v lew
\f
Case 5
Case 6 has
the second
l a y e r p l a c e d on t h e f i r s t
in su c h a manner t h a t one g r a i n o f th e seco n d l a y e r c o n t a c t s
t h o s e ox" t h e f i r s t a t t h r e e p o i n t s *
one g r a i n a t
two p o i n t s *
a n d two a t o n l y o n e p o i n t *
Top
view
Side
v iew
Case 6
T h i s may b e r e c o g n i s e d a s a r o t a t e d
The r e a s o n f o r
the f a c t
its
I t w ill
in tro d u c in g
t h a t th e y a re m erely r o t a t e d
may be j u s t i f i e d
in
f o r m o f c a s e 3*
c a s e s 4 and 6 d e s p i t e
form s o f o t h e r c a s e s
if the s p h e ric a l sequence
e n t i r e t y w ith a f lu id
be s e e n t h a t
the
flow ing
th ro ats
grain s are v a s tly d iffe re n t#
is v i s u a l i z e d
from r i g h t
left*
o f th e v o id s betw een t h e
T his fe a tu re *
ha® n o a f f e c t u p o n t h e p o r o s i t y *
to
would a l t e r
although
It
the ease o f
tra n s m is s io n of the flu id *
In r e la tio n
to th e t h r o a t s
betw een t h e s p h e re s #
S l i c h t o r ^ has sta te d *
2*
S i i c h t e r # C. $ • # U* S. G e o l *
No# 140# 1905# p# 10*
BXf t h e p a r t i c l e s
Survey W ater-S upply P aper
o f sand or g r a v e l w hich
make u p t h e w a t e r b e a r i n g m ediu m a r e w e l l
form th e p o r e s a r e somewhat t r i a n g u l a r
s e c t i o n and th e d ia m e te r o f th e
only o n e -f o u r th
so il
to o n e -s e v e n th
rounded in
in c ro s s
in d iv id u al pores
is
the d ia m e te r of th e
p articles* * 1
The a b o v e g r o u p o f c a s e s g i v e some i n d i c a t i o n o f
what m o d ific a tio n s
th e v a r io u s m ethods o f p a c k in g can
p ro d u c e on th e p o r o s i t y and a l s o
the p e rm e a b ility #
The
e f f e c t u p o n t h e p o r o s i t y h a s b e e n w e l l d e m o n s t r a t e d by
G r a to n and F r a s e r ,
3#
and r e s u l t s
G r a t o n , L* C*# a n d F r a s e r ,
in th e f o llo w in g v a r i a t i o n s
H# J . ,
op* c i t . # p# 805*
C a s e Number
P o r o s i.ty
Case 1
4 7 * 6 4 <?£
Case Z
3 9 * 5 4 <&
Case 3
25*95 %
Case 4
39* 54 %
Case 5
30.1 9 %
Case 0
2 5.95 %
ic
H o w ev e r*
to th is
d iscu ssio n
v isu a lise d
occurring
three
of void space;
reserv atio n s
ap p licab le
(Z ) th e g r a i n s
were
©s p e r f e c t s p h e r e s w h i c h a r e s e l d o m f o u n d
in n a tu re *
in n a tu re *
of g rain s
th e re are
1* Z , 4 ,
(2) cases
and 5 r a r e l y e x i s t
(3) n a tu ra l d e p o sits p r a c t i c a l l y never c o n s is t
o f one u n ifo rm s ize*
6# a l t h o u g h
t h e y g i v e some i d e a
a rra n g e m e n t upon p o r o s i t y
ap p lied d ir e c tly
G rain S iz e #
co n d itio n s
T hu s*
of the e f f e c t
1 through
of g rain
can n o t be
and p e r m e a b i l i t y *
to n a tu r a l
A tten tio n
the c a s e s
sands#
i s now t u r n e d f r o m a n
ideal
se t of
t o one o f t h e m o st d i f f i c u l t p ro b le m s o f a s t u d y
o f th e s u b j e c t of p o r o s i t y and p e r m e a b i l i t y #
It
is
th e
e f f e c t o f t h e g r a i n a l e e upon, t h e s e f u n c t i o n s #
The common p r a c t i c e
a n a l y s i s has been t o s e p a r a te
g ra d e s by th e
trlb u tio n
D espite
the u n ifo rm ity
of p r a c t ic e
th is
ex p erim en ters as
th e c o n c e p t has been p la c e d
d efin itio n s
in to
of e ffe c tiv e
o u tstanding e ith e r
H ow ever*
s i z e * 1*
t h e r e has been
a v erag e or e f f e c t i v e
d is re p u ta b le p o sitio n *
or
th e g r a in s o f th e sand
to d eterm in e an ^average or e f f e c t i v e
co n stitu tes
size
u se of s i e v e s and from t h e s i z e - g r a d e d is~
h a r m o n y among t h e v a r i o u s
resu lt
in m aking a g r a i n
little
t o what
diam eter*
and a s a
in a c o n fu s e d and
from t h e
tu rm o il*
four
or a v e rag e d ia m e te r have been
i n t h e i r u s e by o t h e r e x p e r i m e n t e r s *
in t h e i r a c c u ra c y under s p e c i a l
One o f t h e e a r l i e s t
co n d itio n s#
experim enters#
Kazen^# s e t
11
4*
H ag en * A l l e n * Some p h y s i c a l p r o p e r t i e s o f s a n d s a n d
g r a v e ls w ith s p e c i a l r e f e r e n c e to t h e i r use in f i l t r a t i o n :
M a s s a c h u s e t t s S t a t e B o a r d o f H e a l t h * T w e n t y * * F o u r t h Ann*
R e p t * , 1 8 9 3 , p* 451*
fo rth h is
i n t e r p r e t s ! i o n o f the e f f e c t i v e
**A® a p r o v i s i o n a l
w ith
t h e known f a c t s *
curve c u ts
the
the
b a s i s w hich b e s t a g r e e s
th e s i z e o f g r a i n where th e
10 p e r c e n t l i n e
is c o n s id e re d
♦ e f f e c tiv e d i a m e t e r 1 o f the m a te ria l*
is such t h a t
10 p e r c e n t o f t h e m a t e r i a l
sm aller g ra in s
than the s is e
«
d iam eter a s :
a n d 90 p e r c e n t
Is o f
to be
T h is s i z e
is of
larg er grains
g iv en .%
Hasen used c u m u la tiv e p e r c e n t curves*
F o l l o w i n g H a g en * S I i c h t e r ^ p o s t u l a t e d
5*
S l i c h t e r * C* S * * U* $* Q e o l*
P a p e r 6 7 , 1902* pp* 2 2* 2 3*
e ffectiv e
size
as the g ra in s ls e
homogeneous m a t e r i a l
a t t h e sa m e r a t e
as
o f one s i z e
the m a t e r i a l
the
Survey* W a te r-S u p p ly
o f a t h e o r e t i c a l body o f
t h a t w ould t r a n s m i t w a te r
under c o n sid eratio n *
W ilse y * in a s tu d y of th e v a r i o u s e f f e c t i v e
6« M a v i s * F* T ** a n d W i l s e y * E* F** A s t u d y o f t h e
p e rm e a b ility o f sand:
U n i v e r s i t y o f Iowa S t u d i e s , S t u d i e s
i n E n g i n e e r i n g * B u l l . 7* 1936*
IZ
d iam eters#
determ in ed the e f f e c t i v e
by S l i c h t e r
diam eter as d e fin e d
t o b e s u c h t h a t 31 p e r c e n t o f t h e m a t e r i a l
was o f s m a l l e r g r a i n s #
More r e c e n t l y F a n c h e r a n d L e w i s 7 a s w e l l a s
7#
F a n c h e r # G* H* # a n d L e w i s # J . A## F l o w o f s i m p l e f l u i d s
through porous m a te r ia 1st
The P e n n s y l v a n i a S t a t e C o l l e g e
M ineral I n d u s t r i e s E x p erim en tal S ta tio n # T ec h n ic al Paper
H o . 7# 1333*
F a i r a n d Hatch® h a v e d e v e l o p e d f o r m u l a e f o r
a v erag e and
8*
F a i r # G# M. # a n d H a t c h , L* P . # F u n d a m e n t a l f a c t o r s
g o v ern in g th e s tr e a m lin e flo w o f w a te r th ro u g h sands
Jour*
Amer* W a t e r Works A s s * , V o l . 25# No* 1 1 , 1 3 3 3 , p p . 1 5 5 1 1585*
effectiv e
diam eters
resp ec tiv e ly .
F a n c h e r an d Lew is c a l c u l a t e d a v e r a g e g r a i n
d i a m e t e r from s c r e e n a n a l y s e s and t h e fo rm u la s
d
=
\7
v
z»
#
T h i s f o r m o f <| was p r o p o s e d t o b e u s e d o n l y w i t h t h e
f o r m u l a f o r p e r m e a b i l i t y a d v a n c e d b y t h e sa m e a u t h o r s i n
t h e same p a p e r *
The n u m b e r o f g r a i n s n f o r a n y a v e r a g e d i a m e t e r
d s was c a l c u l a t e d
by a ssu m in g
th at
the g ra in s
o f opening
were
sp h erical and o f m average density o f Z* 65*
Fair and Hatch developed the formula?
c/c (e/7r; =
Z />
« )
# Jiickox, 0* M*.# Flow through granular M ierlala®
Amr* Qeophye# Union* Ft# 11 # 1934, pp* 567*571#
They d e s i g n a t e
th e i r diam eter as an e f f e c ti v e
a u n iform group o f p a r t i c l e s
and shape fa c to r m
vo Iw e #
tlw
having
the f ix tu r e #
e la b o r a t i o n o f $ 1 lo ftier* a d e f i n i t i o n
Porosity,
&r*ln
md
of packing o f
fir s t
facto r
grain®
were
genera-1
& l ij>*
P o ro sity
c o n s id e re d to he p e r f e c t
of
for a case 6 o rie n ta tio n
The
mm
Illu stra tio n #
w ould p ro d u c e a
fo r
than
a m m
of t h e s e v a lu e s m ight be e i t h e r g r e a t e r
th an t h a t given
fo r th e p e rf e c t spheres*
w ould he upon th e o r i e n t a t i o n
g ra in s w ith in th e
u n it
The
g rain s,
By w a y o f
low er p o r o s i t y
dependency
Is on
b y t h e mode
epheree#
of non*spherical grain*
less
it
the grain*#
neis* spherical
bridging were present#
both
T h u s#
e ffe c te d
la
a packing u n i t
H ow ever,
s u rfa c e area#
u n d e r c o n d i t l erne i n w h i c h t h e
e f f e c t w ould h o ld f o r
p r o v i d e d no
diam eter of
o f e f f e c t i v e diam eter#
th e g ra in * and th e a le e
m e dlecueeed
m tm
Trane*
of
th e
1*
or
The
in d iv id u al
o f packing*
The r e s u lts produced by bridging In non*spheric*I
g rain s are s t a r t l i n g and w ill
even though
constant*
the p o r o s i t y m a rk e d ly
th e rem ain in g f u n c t i o n s of the system a re h e ld
Further#
b r i d g i n g may a p p e a r
in the s m a lle r s iz e - g r a d e s
cause
increase
of the
th an
in th e
to a g r e a te r
larger
grades*
l a t t e r may b e a c c o u n t e d f o r b e c a u s e
g e n e r a l l y m ore ro u n d e d l a r g e g r a i n s w ould h av e
to bridge*
Or
the d e cre a se
i t may b e t h a t
in g r a i n
size
th e
increase
degree
The
the
less
tendency
In p o r o s i t y w ith
is due to an e f f e c t r e s u l t i n g
from a s c r e e n m ethod o f g r a d e s e p a r a t i o n *
If
th e W entworth*
*
W e n t w o r t h , C* K* , A s c a l e o f g r a d e a n d c l a s s t e r m s f o r
c l a s t i c sedim ents®
J o u r * & e o l * , Vol# 3 0 , 1 9 £ £ , pp# 3 7 7 ^ 3 9 2 *
in terp retatio n
is used,
o f th e T y ler s ie v e
series
for
the d ia m e te rs of th e s ie v e o penings
increm ents
o f 1*414*
T herefore,
the
the sand s i z e s
i n c r e a s e by
l a r g e r s ie v e s have a
w ider range
in the s i z e
illu stra te ,
t h e to p s i e v e o f a s e r i e s m ight have o p e n in g s
1 mm* a c r o s s ,
siev e
o f g r a i n s c a p t u r e d u p o n them*
the second sie v e
l / 4 mm*, e t c *
l / Z mm*, a n d t h e
The d i a m e t e r o f t h e
To
th ird
g r a i n s on t h e
s e c o n d s i e v e c o u l d h a v e a r a n g e o f i / Z mm* a n d t h o s e on
the
th ird
size*
s i e v e c o u l d h a v e o n l y a 1 / 4 mm* v a r i a t i o n
T he
trend
o f s u c h a s e r i e s would r e s u l t
n e a r ly uniform d ia m ete r f o r
s iz e - g r a d e s w ith
fill
less
tendency fo r
th e v o id s betw een th e
s ire*grade*
the g r a i n s
in
i n m ore
on t h e s m a l l e r
the sm a ller g ra in s
larg er g rain s
o f t h e same
to
One o f t h e f i r s t men t o d e s c r i b e
p o r o s ity w ith a d e c re a se
the
increase
in
Q
i n t h e g r a i n s i z e was C* H* L e e «
9*
E l 1 i s , A . J * , a n d L e e , C« H * , G e o l o g y a n d g r o u n d w a t e r s
o f th e w e s t e r n p a r t o f San D iego C o u n ty , C a l i f o r n i a *
U* S*
G e o l . S u r v e y W a t e r - S u p p l y P a p e r 4 4 6 , 1 9 1 9 , pp* 1 2 1 - 1 2 3 *
H is o b s e r v a t i o n s
to s i l t ,
showed th e p o r o s i t y
co arse sand,
in f i n e
f r o m 36 s a m p l e s ,
sand,
41-48 per c en t
to
ra n g in g from c o a r s e sand
t o be 3 9 - 4 0 p e r c e n t f o r
i n m ed iu m s a n d ,
44«*49 p e r c e n t
5 0 - 5 4 p e r c e n t o f a f i n e s a n d y loam*
T e r z a g h i * ^ d e m o n s t r a t e d t h e sa m e t r e n d w i t h a
10*
T e r z a g h i , C # , E n g i n e e r i n g N e w s - R e c o r d , V ol* 9 5 , No*
2 3 , Dec* 3 , 1 9 2 5 , p* 914*
p o r o s i t y o f 50 p e r c e n t f o r p a r t i c l e s
mm* t o a b o u t 95 p e r c e n t f o r p a r t i c l e s
larg er
th a n 0*02
sm aller
than
0 * 0 0 2 tern*
T r a s k w h i l e
w orking w ith th e co m p actio n o f
11#
T r a s k , P . D*, C o m p a c t i o n o f s e d i m e n t s *
P e t * G e o l * B u l l * 1 5 , 1 9 3 1 , p* 273*
sed im en ts,
follow ss
Amer* A s s o c *
found th e e s t im a t e d w a ter c o n te n t to v a ry as
E stim ated
W ater C o n t e n t
S ize-O rouo
nun*
45*0
%
* 125 •*
* 2 5 0 sun*
45*4
%
*004 -
*125 s o u
46*9
%
* 0 1 6 -*
*0 6 4 mna*
51*9
%
*004 -
. 0 1 0 mm*
60*2
%
* 00 1 •*
. 0 0 4 mm*
65 # 6
%
*000 -
*0 0 1 mm*
96* Z
%
*25
-
The p a r t i c l e s
Trask s t a t e s
*5
sm aller
th at
than
the
one m ic r o n w e re f l o c c u l a t e d *
f i g u r e s may n o t a p p l y t o
n o n - f l o c c u l a t e d s e d im e n ts w hich a r e s m a l l e r
th a n one
m icron*
Fraser
12
sta te d !
12*
F r a s e r * H* J . , P o r o s i t y a n d p e r m e a b i l i t y o f c l a s t i c
sed im en ts!
J o u r * G e o l * * V o l . 4 3 , 1935* p* 917*
^A ctually* as
frictio n *
ad h esio n ,
im p o rtan ce,
area
th e grain**size d e c re a s e s *
and b r i d in g
because of the h ig h er
to volum e and m assj
the g r a i n - s i z e ,
Perm eaM i I t y *
become o f
and t h e r e f o r e
the g r e a te r
P erm eab ility
is
ratio
is
in creasin g
of su rface
u*e s m a l l e r
the p o r o s i t y . w
a m easure of th e e a se w ith
w h i c h a f l u i d may move t h r o u g h a p o r o u s m e d iu m u n d e r
in flu en ce
of a d riv in g
pressure#
the
More f o r m a l l y ,
p e r m e a b l 1 i t y may b e s t a t e d a s a u n i t v o l u m e o f a f l u i d
of
u n i t v i s c o s i t y m o v in g t h r o u g h a p o r o u s medium o n e u n i t on
17
a side#
in u n i t
pressure
darcy*
tim e,
g rad ien t*
and I t
contain®
and u n d e r
The u n i t
the
in flu en ce
of p e rm e a b ility
of a u n it
is
the
I s a c o n s t a n t o f t h e p o r o u s m edium a n d
no f a c t o r s
of th e f l u i d
being
tran slated ^ #
The
& The name* D a r c y # wa s o r i g i n a l l y s u g g e s t e d i n a p a p e r
b y W y c k o f f # B o t s e t # M u s k a t a n d Heed (Rev* s c i # I n s t r * # 4*
1935* p* 3 9 4 ) a n d wa s a c c e p t e d i n 1935 b y t h e A m e r i c a n
P etro leu m i n s t i t u t e t o g e th e r w ith the fo llo w in g s e t o f
u n its*
K =
1 d a r c y — ' l ( c # c * / s e c # )cm »^/{atm ,/crru )
H ow ever* H u t t i n g (A«A#P»G» B u l l * 14# 1930# p* 1 3 4 9 )
s u g g e s t e d t h e sa me u n i t s f o r t h e p e r m e a b i l i t y # e x c e p t t h a t
t h e p r e s s u r e was e x p r e s s e d I n 10® d y n e s o r 0 * 9 9 a t m o s p h e r e s *
N e v i n ( a *A*P*G* B u l l * 10* 1932# p* 3 8 2 ) d e f i n e d
p e r m e a b i l i t y w i t h some s i m i l a r i t y # t h e e x c e p t i o n s b e i n g
t h a t he u s e d a r a t i o f o r t h e f l u i d v i s c o s i t y v a l u e a n d
e x p re s s e d th e d i f f e r e n t i a l p r e s s u r e in pounds p e r sq u a re
inch*
K r u m b e l n a n d P e l t l j o h n ( M a n u al o f S e d i m e n t a r y P e t r o g r a p h y #
A p p l e t o n - C e n t u r y * 1933* p* 5 1 3 ) d e f i n e d p e r m e a b i l i t y a s
**‘t h e f a c u l t y o f a l l o w i n g p a s s a g e o f f l u i d s w i t h o u t i m p a i r ­
m e n t o f s t r u c t u r e o r d i s p l a c e m e n t o f p a r t s ” * The d e f i n i t i o n
d o e s w e l l t o s t r e s s t h a t t h e p a r t s o f t h e medium b e s t a t i c
a t th e tim e of p e r m e a b i l it y d e te r m in a tio n .
Ho w ev er* p e r ­
m e a b i l i t y th u s d e fin e d le a d s to the c o n v i c t i o n t h a t i f
a n y o f t h e p a r t s o f t h e m edium a r e d i s p l a c e d t h e r e i s no
p e r m e a b i l i t y # l . e * * I t becomes im p erv io u s# w hereas*
a c t u a l l y such a d is p la c e m e n t o n ly r e s u l t s in a d i f f e r e n t
v alu e o f th e p e rm e a b ility #
The e f f e c t o f d i s p l a c e m e n t o f
p a r t s o f t h e m edium may e i t h e r i n c r e a s e o r d e c r e a s e t h e
p e r m e a b i l i t y o f t h e m edium d e p e n d i n g u p o n t h e t y p e o f
d isp lacem en t experienced#
dim ensions of p e r m e a b ility ares
thus
it
i s an a re a #
being
the sq u a re o f a l i n e a r
dim ension#
10
T h is a r e a
is ex p ressed
com m unicating
pores
in th e number and s l g e
th ro u g h w hich
W ith a few e x c e p t i o n s ,
o f the
t h e f l u i d m oves#
the g e n e ra l consensus of
o p in io n r e l a ti v e
t o p o r o s i t y a n d p e r m e a b i 1 i t y , was
1%
in a u g u ra te d by S I i c h t e r
when he s t a t e d t h a t t h e
13*
S l i c h t e r , C- S . , U* S* G e o l *
P i * 2 , 1 0 9 7 - * 9 6 , pp* 3 0 1 - 2 , 3 2 6 .
p e r m e a b i l i t y was p r o p o r t i o n a l
to
Survey,
1 9 t h Ann# R e p t # ,
the p o ro s ity *
b e e n f o l l o w e d more r e c e n t l y by B a r b ^
He h a s
and P e ttk e * ^ #
14*
B a r b , C# F « , P o r o s i t y a n d p e r m e a b i l i t y r e l a t i o n s i n
A p p a la c h ia n sands*
P e r m a • S t a t e C o l l * B u l l * . No* 9* 1 9 3 0 ,
pp* 4 7 - 5 9 *
15*
F e t t k e , C* R** A#A*P*G* B u l l * , V o l . 1 8 , 1 9 3 4 , p p .
1 9 9 - 2 0 6 ; O i l a n d G a s J o u r * , A u g . 5 , 1 9 3 7 , pp# 2 0 - 2 5 , a n d
35n*
Both of t h e s e a u t h o r s d e r i v e d
from t h e
sin g le
is one p h a s e
un ifo rm ity
P ra c tic a lly
determ ined
of
for p erm eab ility
fu n c tio n of porosity#
G r a i n sisse a l s o
T his
eq u atio n s
has
its
of the q u e s tio n
effect
on p e r m e a b i l i t y *
in w hich s u r p r i s i n g
th o u g h t and r e s u l t has been d is p la y e d #
every experim enter sin c e P o is e u ille
the p e rm e sb i1 ity
Square o f th e d ia m e te r of
to be p r o p o r t i o n a l
the c o n d u its
f l u i d moves and e x p r e s s e d by t h e
term
has
to the
th ro u g h w hich
However,
the
it
is
19
im p o ssib le
to m easure the d ia m e te rs
sand o r sa n d sto n e ,
size
i t had been
a s a n e x p r e s s i o n o f <S#
c o n fro n te d w ith
size*
and d e s p i t e
to use g r a in
inam edlately
o f the
th at
th ere
g rain
is a d iv e r s ity
th e a v e ra g e and e f f e c t i v e
the agreem ent
th at
t h e p e r m e a b i 11 t y
is
t e r m jd, n o o n e h a s s u f f i c i e n t l y
e s t a b l i s h e d what c o n s t i t u t e s
S lich ter
16
d#
S h e d some l i g h t on t h e c o m p l e x i t y
16*
S l i c h t e r , C* S » , U* 8* G e o i #
P a p e r 1 4 0 , 1 9 0 5 , p* 10*
of
Is
in a
th e pro b lem of a v e ra g e and e f f e c t i v e
on w hat c o n s t i t u t e s
a fu n ctio n
the custom
H ere one
I t was d e m o n s t r a t e d a b o v e
of o p in io n
size
so
of the c o n d u its
S urvey, W ater-S upply
t h e p r o b le m when he s t a t e d ?
"If
t o a mass of n e a r l y
larg er p a rtic le s
to
be a d d e d ,
th e flow of w ater w ill
the
uniform sand p a r t i c l e s
effect
be o n e o f tv/o k i n d s ,
dep en d in g p r i n c i p a l l y upon th e r a t i o
of
the p a r t i c l e s
g rain s
in th e
a re only s l i g h t l y
g rain s,
and
added b e a rs
o rig in al
the sand to
a re added,
p a rticles
seven to ten
be t h e
of th is
increase
the e f f e c t
tim es
the p a r t i c l e s
of
added
the o r i g i n a l sand
t r a n s m i t w ater*
p a rticles
o rig in a l
than
w hich th e s i z e
the a v e ra g e s i z e
If
t h e m ore p a r t i c l e s
added th e g r e a te r w i l l
of
to
sand*
larg er
on t h e r e s i s t a n c e
If,
is
kind
in the c a p a c i t y
how ever,
larg er
the re v e rs e *
the diam eter
sa n d g r a i n s be a d d e d ,
th a t are
each of
o f the
t h e new
if
to
p articles
tends
to b lo ck the course
o f th e w ater*
T h u s* f o r e x a m p l e * a l a r g e b o u l d e r p l a c e d
of fin e
sand w ill
ten d
w ater*
As m o re a n d m o r e o f
to b lo c k th e p a ssa g e
the
to a mass o f u n if o r m sand*
w ater
through
of
the
the
t o t a l mass*
w hole to
tra n s m it w ater
q u a n tity
o f the
n eg lig ib le*
presence
of
the
to
for
th is
t o t a l mass*
the
o f the
so th a t
the
becomes r e l a t i v e l y
tra n s m it w ill approach
alone*
The
is n o t n e c e s s a r i l y
a high
is
co n stitu te
of
large
be added*
larg e p a r tic le s
in d icatin g
large p a r tic le s
if a very
p articles
larg e p a r t i c l e s
o f the m a te ria l*
of th e
u n til*
the c a p a c i t y
i n t e r p r e t e d as
t h e amount
th e c a p a c ity
larg e p a r tic le s
t h a t o f t h e mass o f
of flo w of
tim e on th e a d d in g
increase
o r i g i n a l mass of f i n e
are
e q u a l s a b o u t 30 p e r c e n t o f
From t h i s
larg e p a r tic le s w ill
the r a t e
be d e c r e a s e d u n t i l
larg e p a r t i c l e s
of the
large p a r tic le s
added
i t w ill
in a mass
t o be
tran sm issio n c a p a c ity
in d ic ate d
a larg e
a s would be th e
o n l y w h en t h e
fra c tio n per
c a s e where
cent
the
*
larg e p a r tic le s
The
th esis
the p e rm e a b ility
dim ensions
e q u a l s 40 t o 50 p e r c e n t o f t h e w h o le * '1
of
th e
d i s c u s s i o n shows t h a t *
is p ro p o rtio n a l
of th at
g r a i n or group
to a g ra in
of g ra in s
n or h a s any m ethod o f c a l c u l a t i o n o f th e
sise*
although
the
i s n o t known*
d esired g rain
s i e e been d e v e lo p e d w hich h a s p ro v ed s a t i s f a c t o r y *
The T h e o r y o f F l o w E q u a t i o n s #
Any f l u i d m e th o d s
for
the
determ ina tio n
of perm eability are
b a s e d on a s e r i e s
e x p e r i m e n t s b y H# D a r c y a n d p u b l i s h e d a s *
Fubl iques
stated
d e l a V I 1 l a de D i j o n '1* P a r i s *
that
the r a t e
of flow of water
b e d was d i r e c t l y p r o p o r t i o n a l
to the
heads
inversely proportional
at
the
ffL e s F o n t a i n e s
1656*
H e r e he
through a f i l t e r
t wo d i m e n s i o n a l a r e a
of th e sand f a c e exposed to the water*
between th e f l u i d
of
and to
the
difference
i n l e t and o u t l e t f a c e s ,
to the d ep th of
and
t h e p o r o u s medi um*
A n a l y t i c a l l y e x p r e s s e d D a r c y * s Law i s ;
Q
where Q is
outlet
the r a t e
faces
gradient
= _ c £ ijx _
iLj
(3)
of flo w j A th e
(provided both are
between th e
of t h e sa n d column;
the
of the
same);
i n l e t and o u t l e t
i n l e t and
the p re s s u re
f a c e s ; jt t h e
length
c © constant*
C ertain considerations
D a r c y * s Law a n d t h e s e a r e
valid*
area
I n g r e s s may be
the
attend
lim its
the a p p l i c a t i o n
t o which th e
i n i t i a t e d when i t
is
of
law is
realised
that
\
fluids
h a v e t wo m a i n t y p e s o f f l o w *
i s c o n t r o l l e d by b o t h
an eddying or
of which
t h e v e l o c i t y o f movement a n d t h e
d i a m e t e r and r o u g h n e s s
the s o - c a lle d viscous
the s e l e c t i o n
of the conduit#
cor l a m i n a r :
turbulent
type
The f i r s t
flow,
of flow*
type
is
and th e second
is
The l a w s g o v e r n i n g
t h e two t y p e s a r e q i i i t e d i f f e r e n t #
D a r c y * s Law h o l d s o n l y f o r
s in c e Darcy d e fin e d the discharge/1
first
power o f t h e head#
the
lam inar
; i ow
proportionafpio the
In tu rb u le n t
f le w .th e tiischarge
zz
varied
as
t h e s q u a r e r o o t o f t h e head#
In the determ ination
flow,
it
la n e c e s s a r y to
hydrodynamics*
of
the
introduce
“R e y n o l d s * n u m b e r 11#
lim its
the w ell
lam inar
known t e r m
in
When o r i g i n a l l y
presented*
R e y n o l d s * n u m b e r was p o s t u l a t e d
pipes*
t h e same c o n d i t i o n s
but
of
for
sand-free
hold m ic ro sc o p ic a lly in a
17
M uskat and Wyckoff
p re s e n t t h e i r ideas
p o r o u s medium#
17# M u s k s t * M#* a n d W y c k o f f * R# 13#, Th e F l o w o f
H o m o g e n e o u s F l u i d s t h r o u g h P o r o u s M e d i a , pp# 5 7 - 5 8 ,
M c G r a w - H i l l * 1937*
ins
“One may n o t e h e r e a g a i n
difference
between
t u b e and w h a t w i l l
flow —
filled
be d e n o t e d h e r e a s
w i t h p o r o u s medium.#
section
circular
to
flow through a sa n d -fre e
g o v e r n e d b y D a r c y * s Law —
the v e lo c ity
the
the v is c o u s
traverse
(exactly
tube),
zero a t
the fundamental
so
in
the
while
flux
cross
sectional area,
f r o m a maximum a t
that
on ly to the
to
the
the c e n te r
In a
flow the
sq u are of the
in © l i n e a r
first
a
the c ro ss
for P o iseu ille
is p ro p o rtio n a l
is p ro p o rtio n a l
case of
the m acroscopic v e l o c i t y
Thus, w h ereas,
total
in the form er
parabolic across
special
l i n e a r p o r o u s medium I s u n i f o r m o v e r
section#
“v i s c o u s M
through a tube
is e s s e n t i a l l y
failing
the w a lls ,
For,
the
p o r o u s me d i u m
power of the a re a*
23
The r e a s o n
for
this
difference
tremendous s u r f a c e exposed
its
uniform d isse m in a tio n
thus g iv in g
lies
in
i n a p o r o u s medium,
throughout
in a rough se n se
enormous number o f p a r a l l e l
in each having
evidently
the
the
and
t h e medium,
equivalent
capillaries,
of an
the
t h e sa me a v e r a g e v e l o c i t y ,
fluid
although
w ith in each th ere
are undoubtedly m icroscopic v e lo c ity
traverses
to those
sim ilar
in a s a n d - f r e e c a p i l l a r y * ”
The b r e a k f r o m
l a m i n a r to t u r b u l e n t
18
w e l l d e s c r i b e d by Tolman
as follows*
flow
is
18#
T o l m a n , C* P * , a r o u n d W a t e r # C h a p t e r 8# M c G r a w - H i l l #
1937*
" I n R e y n o l d 1® e x p e r i m e n t s w i t h
increasing
p i p e f l o w t h e v e l o c i t y a t w h i c h e d d y i n g c omme nc e d i s
called
the h igher c r i t i c a l
dem onstrated
that
velocity*
turbulent
f l o w c o u l d be c h a n g e d t o
l a m i n a r f l o w by g r a d u a l l y r e d u c i n g
This change always
does
This second c r i t i c a l
the
lower c r i t i c a l
to
velocity
lower c r i t i c a l
velocity
points
With v e l o c i t i e s
the m otion
turbulent
veloc ity .
flow*
velocity
out
Be 1 ow t h e
I® a l w a y s
between the
is u n sta b le
than
a t which e d d ie s d i e
the m otion
and above t h e h i g h e r c r i t i c a l
turbulent*
the velo city #
o c c u rs a t a lower v e l o c i t y
the change from lam inar
I s k n o wn a s
He a l s o
it
laminar
is always
t wo c r i t i c a l
a n d may b e e i t h e r
lam inar or t u r lm le n t# depend Ing upon th e i n i t i a l
c o n d i t i o n o f flow#
**A c r i t e r i o n k n o w n a® R e y n o l d s * n u m b e r
o ften used
flow
in h y d r a u l i c a n a l y s e s
in a p ip e
particular
la
laminar
relationship
or
turbulent for
the •
pipe dlane ter#
of water#
I n v e s t I g a t o r s h a v e s h o wn t h a t
is com pletely
to determ ine w hether
of v e lo c ity #
and d e n s i t y and v i s c o s i t y
is
V arious
flow of f l u i d s
in p ip e s
lasairtar b e lo w R e y n o l d s * number o f £#000#
T u r b u l e n t f l o w o c c u r s u s u a l l y when R e y n o l d s * number
is g re a te r
t h a n 3#000#
Between th e
lim iting
o f £ # 0 0 0 a n d 3 # 0 0 0 t h e f l o w may be e i t h e r
or
lam inar# depending upon the
values
turbulent
i n i t i a l condition of
flow* *
A nalytically
e x p r e s s e d R ey no ld s* number
1st
/? = a y f
(4)
where v r e p r e s e n t s
the v elo city *
of the pipe#
t h e c a s e o f a p o r o u s m e d i a some
appropriate
or
in
grain
the d e n s ity o f
the
«S r e p r e s e n t s t h e d i a m e t e r
a le e ; j£ the v i s c o s i t y
t h e f l u i d ; j jf
fluid#
In porous media#
the break, from
t u r b u le n t flow does not appear e i t h e r
t h e same R e y n o l d s * number a s
M ushat and W y c k o f f d e s c r i b e
19#
of
it
does
lam inar
to
as a b r u p t l y nor a t
in s e n d - f r e e c o n d u its#
the former as follow s*
M u s k a t # &§*# a n d W y c k o f f # Ft* D## op# c l t # #
p# 03#
**lt i s #
indeed#
not
t r a n s i t i o n between s t r i c t l y
turbulent
unlikely
f l o w i n a p o r o u s medium c o n s i s t s
d isse m in a tio n of
throughout a l l
the pores
deviations
beginning
local
regions
t h e medium#
the
of
turbulence
in c o n t r a s t
to the
turbulent s ta te
tremendous w all
losses.
rise
as compared to
of
radius
1 cm.
f r e e volume
Thus# w h e r e a s
the r a t i o
I s Z cm.~*#
to p o r e volume
of
linear
turbulence#
where t h e
t o be a t t r i b u t e d
the
to
the
the r a t i o
in
f r e e pore
in a f r e e
the w all
fluid
to
the v iscous
in which th e eddy m otion can g ive
friction
until
by t h e s i n g l e
exposed to
a p o r o u s medium a n d w h i c h g i v e s
rise
capillary
surface
of w a ll
to
to
the
surface
i n a ZO p e r c e n t p o r o s i t y s a n d c o m p o s e d
of uniform s p h e r ic a l
be
of the
of complete
is probably
surface
to
throughout the
case of sand~frec pipes
t e r m # b*\r^#
the
larger
increased#
The p e r s i s t e n c e
is c h ara c terize d
d r a g on t h e f l u i d #
is
to
spreading
is dissem in ated
term a /v under such c o n d itio n s
volume
Thus t h e
in the
turbulence
the v e lo c it y
w h o l e o f t h e medi um#
the
turbulence
of a p p r e c ia b le eddy lo s s e s
the sm a ller pores as
quadratic
the
essentia lly
f r o m L a r c y * s Law w o u l d c o r r e s p o n d
the
finally
of
the
v i s c o u s and c o m p l e t e
in the g ra d u a l
pores,
that
grains
o f C # 1 mnu r a d i u s w o u l d
I # £ 0 0 cm#" * . tt
The m a g n i t u d e o f
the Reynolds*
number a t w h i c h
26
turbulence appears
in sand f i l l e d
o f mu c h e x p e r i m e n t a t i o n *
20*
L indquist,
1933*
1934,
p i p e s has been the s u b j e c t
20
L indquist^
experim enting w ith
E*# P r e m i e r C o n g r e s s
des Grands B a r r a g e s *
N e m e n y x i P* , W a s s e r . k r a f t u n d W a s s e r w i r t s c l i a f t , No* 2 9 ,
p* 1 5 7 , e r r i v e d a t a s l m i l a r " Y i n u r e *
—
S c h a f f e r n a k , F*, and F a c h l e r , R*, D i e W a s s e r w i r t a c h a f t ,
No* 1 , 1 9 3 4 , p* 1 4 5 , e x p e r i m e n t i n g w i t h g r a v e l ”, found '"tEe "
b r e a k t o o c c u r b e t w e e n R e y n o l d s 1 n u m b e r s o f 3 a n d 6*
t h e f l o w o f w a t e r among s h o t o f u n i f o r m s i z e ,
found the
b r e a k t o o c c u r a t a R e y n o l d s 1 n u m b e r o f 4*
Muskat and
e x p erim en tin g w ith the flow
21* M u s k a t , M*, a n d B o t s e t ,
pp* 2 1 * 4 7 *
H* G* , P h y s i c s ,
1,
1931,
of a ir
among g l a s s b e a d s d i s c e r n e d a R e y n o l d s * n u m b e r o f
12 f o r
the break
t o t u r b u l e n t flow*
Ehrenberger
e x p e r i m e n t e d on t h e f l o w o f w a t e r
22*
E h r e n b e r q e r , R*,
p* 71*
Eeits*
O ster ,
through heterogeneous
sands,
with g rain
a s 3 * 0 mm*,
a fluid
v e lo c ity corresponding
is
that
t o h o l d up t o
t o a R e y n o l d s ’ n u m b e r o f 5*
th e most p e r t i n e n t
of F a n e h er,
1938,
diam eters as high
i n w h i c h D a r c y * s Law was f o u n d
Perhaps
subject
1n g * A r c h * V e r * ,
Lewis,
piece
o f w o r k on t h e
and B a r n e s ^ .
These
z?
23*
F a n e h e r * 0* H - , L e w i s , J* A # , a n d B a r n e s , K* B#,
P e n n a * S t a t e C o l l - M l n - l n d - Exp# S t a # B u l l . 2 2 , 1933#
a u t h o r s w o r k e d m o s t l y on c o n s o l i d a t e d
Pennsylvania*
sa nds from
and a few u n c o n s o l i d a t e d
a variety
o f homogeneous f l u i d s *
i.e.,
and gas#
Their r e s u lts
the
indicate
neighborhood of a value of
types.
oil,
They used
w ater,
air,
break to occur
in t h e
1 f o r R e y n o l d s ’ number#
T his v a l u e of F a n e h e r , Lewis and Barnes has
24
been checked
i n t h e f i e l d by r e c o r d i n g t h e f l o w f r o m
24# M u s k e t , M#, F l o w o f H o m o g e n e o u s F l u i d s ,
M c G r a w - H i l l , 1937#
gas and o i l
w ells,
flow r e s u l t s
and
in n e a rly a l l
gave a R e y n o l d s ’ number
Having e s t a b l i s h e d
cases
less
the upper
the a c tu a l
than
M e in s e r and F i s h e l
1*
l i m i t of v a l i d i t y
f o r D a r c y ’ s Law, we now t u r n o u r a t t e n t i o n
lim it#
pp# 6 7 - 6 8 ,
to the
lower
have worked from t h i s
angle
25#
M e i n s e r , O* £ # , a n d F i s h e l , V* G*, T e s t o f p e r m e a b i l i t y
w i t h low h y d r a u l i c c r a d l e n t s t
T r a n s . Artier. G e o p h y s , U n i o n ,
P t # 2 , 1 9 3 6 , pp# 4 7 1 - 4 7 4 ,
and r e p o r t s
wThe r e s u l t s
that
least
for
the
of the
type of sand used
investigation
the
indicated
flow v a rie d at
approxim ately w ith the h y d ra u lic
gradient,
down
to a g r a d i e n t o f a f o o t p e r m i l e and p r o b a b l y t o a
lower g r a d ie n t#
Moreover,
th ere appears
some m o v e m e n t t o a g r a d i e n t a s
MThe t h e o r y o f
obtained
in
preem ption
low a s
laminar
Investigations
evidence of
1 inch per mile#
f l o w and t h e r e s u l t s
of v i s c o s i t y
establish a
t h a t D a r c y ’ s Law h o l d s p r e s u m a b l y f o r
flow through permeable m a te r ia ls
under
the
indefinitely
l o w g r a d e s * 11
F o r m u l a e f o r Perinea M l i t y #
to determ ine p e rm e a b ility
Ma ny a t t e m p t s h a v e b e e n made
from
i n d i r e c t methods*
th e a t t e m p t s were of a p u r e l y t h e o r e t i c a l
were s t r i c t l y
along
em pirical,
particular
have d e lim ite d
types of f l u i d
sh ap es and p o r o s i t i e s ,
Many o f
w ithin
or
techniques.
some o f t h e i r
attem pts
lim its
specific
The
to
flow,
particular
grain
local
geographic
environm ents.
th e fo rm u la e have been s u r p r i s i n g l y
their
some
o t h e r s were developed
l i n e s which employed b o th o f t h e s e
experim enters
their
and s t i l l
nature,
Some o f
conditions,
but
sir.es,
accurate
the narrowness of
of a p p l i c a t i o n has e x e r c is e d a r e s t r i c t e d
usage#
The g o a l
set
fo r a formula f o r
would be one w h i c h w o u ld a p p l y r e g a r d l e s s
conditions*
Some o f
employment,
and o t h e r s
portion
of
perm eability
of
the m odifying
the a u th o rs have a ttem p ted such
the problem
have a tte m p te d
in hope t h a t
w ould c a r r y on t h e work from where
to solve
the next
only a
experim enter
i t had been h a lte d #
When t h e a c c u r a t e
it w ill
form ula u l t i m a t e l y has been derived*
n o t be t h e r e s u l t s
but rather
of th e work o f any i n d iv i d u a l*
a sm all a d d itio n
to*
or a unique assem blage of
t h e d a t a w h i c h h a s b e e n c o m p l i e d b y t h e many who h a v e
spent
long hours
evolving
factual
knowledge f o r
the use
o f mankind#
The f i r s t w o r k e r
in the f i e l d
t h r o u g h p o r o u s m edia was D a r c y ^ .
of f lu id
Up o n h i s
results
Z&#
D
a r c yV* K**^ H‘L
ejWs'W F o n t a i n e s >P
a de
,
-j
HM’W
11 u b l i q u neil mill
D l J o n f * P a r i s * 1856*
been based a l l
flow
have
l a v i lIIIlI MW
e nde
—m
—H i 1 ■»
other attem pts.
Hasen
2*7
working w ith
the flow of w ater
through
£7*
Ha g e n * A l l e n * Some p h y s i c a l p r o p e r t i e s o f s a n d s a n d
g r a v e ls w ith s p e c i a l r e f e r e n c e to t h e i r use in f i l t r a t i o n *
M a s s * S t a t e B o a r d o f H e a l t h * £ 4 t h A n n . K e p t . * 1893*
filter
beds
d e v ised a formula as
c h c t z( O ^ O + O . O S t )
^ =
where v is
the v e lo c ity
1*000$
(5 )
in m eters per day in a s o l i d
co lu m n o f t h e same d i a m e t e r a s
constant about
follows*
th a t of
d ^effective
the
sand; £ a
diameter®
i n mm* $ h
head measured
i n a n y u n l t $ jjJ d i s t a n c e
of p e rc o latio n
s a me u n i t s
the head; £
i n d e g r e e s C.
as
in
tem perature
1898* C h a r l e s S .
S lichter^
attem pted a
in th e
30
Z&*
S l i c h t e r , C* 5 * , U* S# G e o i #
P t * I I , 1 8 9 7 - 1 6 9 6 , pp* 3 0 1 - 6 8 4 #
m athem atical
Survey,
t r e a t m e n t o f th e problem#
1 9 t h Ann# R e p t # ,
Pie s a y s *
**The f o l l o w i n g p a g e s c o n t a i n a t h e o r e t i c a l
Investigation
water
of
the g e n e ra l problem of the flow of
through porous
*'ln C h a p t e r
from p u r e l y
for
the
soil
1 an a t t e m p t
theoretical
flow of w ater
or rock#
c o n s i d e r a t i o n s an e x p r e s s i o n
or o t h e r f l u i d
o f s o i l ma d e up o f g r a i n s
of t h i s
pores of the
ideal
relation
the g ra in s
is
f orm#
form ula,
shown,
and
For the purpose of
a study
spherical-graIned
of p o ro s ity
t h r o u g h a column
of n e a r ly uniform s iz e
of ap p ro x im ately s p h e ric a l
construction
i s made t o d e r i v e
i s made o f t h e
soil,
and the
to the average arrangement o f
a n d made a f a c t o r
the formula
in the r e s u l t i n g
formula#
I devise as
of the q u a n tity of
w ater per
s e c o n d t r a n s m i t t e d by a c o l u m n o f s o i l
follow ing
expressions
c p = C / 0 0 9 ¥ ) _^lcL ^
„ -C .frlv
se c.
the
(6 )
i n wh i c h —
=*■ t h e q u a n t i t y
P
*
i n cm*
the d iffe re n c e
3
in p r e s s u r e a t
of the c y lin d e r
the ends
I n cm* o f w a t e r a t
4 d e g r e e s C*
d
=■ t h e me a n d i a m e t e r
of the s o i l
grains
i n cm.
s
- thea re a
h
= the h e ig h t
-
of the c ro s s s e c tio n
in
cm.^
o f t h e column o f san d in
the c o e f f i c i e n t
cm*
of v i s c o s i t y o f the
fluid
K
= a constant
(1*0094)
*
S lichter,
- the
C* S . ,
f r o m T a b l e XI «■
lo g a r ith m of th e f a c t o r 10.22 u
op* c I t * , p .
Terzaghi
taken
326.
developed a formula
for p e rm e a b ility
29.
T e r z a g h i , C*, P r i n c i p l e s o f s o i l m e c h a n i c s :
III,
De t e r m i n a l I o n o f p e r m e a b i l i t y o f c l a y :
Eng. News-Record,
V o l . 9 5 , No* 2 1 , 1 9 2 5 , pp* 6 5 2 - 8 3 6 *
from h i s
studies
of so ils*
He s a i d *
d e r i v e a semi**empirics 1 f o r m u la ba sed
on t h e f o l l o w i n g
lary channels
least
five
ones*
percolates
unit
the e f f e c t i v e
volume,
the c r o s s - s e c t i o n
of the n arro w est
t h r o u g h one o f th e c a p i l l a r y c h a n n e l s ,
the channel
loss per
of the c a p il
if a d e f i n i te q u a n tity of w ater
lo ss of head per
of
The w i d e s t p a r t s
th rough which th e w a te r flow s have a t
times
Hence,
facts*
unit
Is a t
length of the narrow est s e c tio n s
l e a s t 25 t i m e s
le n g th of the w id e st
size
vQ and v t
of
the
the g r a i n s
greater
ones...
(cm .),
the c o e f f i c i e n t s
than
the
L e t dw b e
n the void
of v i s c o s i t y
of
3Z
the w ater a t
10 d e g r e e ® € ,
and a t
tem perature
respectively*
and C an e m p i r i c a l
by e x p e r i m e n t
to rang© f r o m 800 v Q t o 4 6 0
t
c o e f f i c i e n t found
d e p e n d i n g b o t h on t h e s h a p e o f t h e g r a i n s a n d o n t h e
uniform ity
of the sand;
then
3
. ^ Z' n - 0 . / 3 \ d
A " = ( 8 0 0 to 9 6 o V
) {vv°
' W t J K v r7 ^ 7 T )
Barb
30
experim enting w ith
(3)
i n d u r a t e d sands from
30*
B a r b * C* P * , P o r o s i t y a n d p e r m e a b i l i t y r e l a t i o n s i n
A ppalachian o i l sands:
P e n n a * S t a t e C o l l * B u l l * 9* 1930*
pp* 4 7 - 5 9 *
w e s t e r n P e n n s y l v a n i a made t h e f o l l o w i n g
statem ent of the
problem:
NThe m a t h e m a t i c a l
p e r m e a b i l i t y and p o r o s i t y
to the graph
general
(draw n on
relation
can be e x p r e s s e d ,
logarithm ic paper)*
e q u a t i o n y - kxn where y r e p r e s e n t s
perm eability
represents
according
by t h e
the
in the whole numbers as p l o t t e d ,
t h e p o r o s i t y a s w h o l e number®*
o f n c a n b e f o u n d by d e t e r m i n i n g
straight
between
l i n e makes w i t h
up t h e n u m e r i c a l
tangent*
the angle
the h o riz o n ta l
For
the
line
and x
The v a l u e
the
and lo o k in g
given,
the
33
im
tangent
w h i c h m a y h e t a k e n ass t h e v a l u e o f n*
As v a l u e s f o r y a n d
k
a r e a lr e a d y k n o wn ,
it
I® a
s im p le n a t t e r t o s o l v e ; f o r k w h i c h i s a b o u t . 0 * 0 0 0 0 0 0 0 *
The r e l a t i o n
r o u g h l y , y « 0#0000066
is
p e r m e a b ility v a r ie s a s a s e a I I
porosity
power*
{m
fraction
a w h o l e number) r a i s e d
Between t h e working
E astern fie ld s
t i me © th e
the seventh
lim its of p o r o s i t y
the p e rm e ab ility a t
v a r i e s about a s
to
th e
or
i n th e
10 p e r c e n t p o r o s i t y
th e s q u a r e a n d a t 2 0 p e r c e n t a b o u t
a s th e c u b e o f t h e p o r o s it y *
th a t th e v a r ia tio n
I t c a n © a s I i y b e se e n
i s much g r e a t e r
b e l i e v e d by m ost o f t h e o p e r a t o r s *
t h a n would be
n
f a i r and Hetch^* developed a formula f o r
31#
f a i r , 0* M»# a n d H a t c h , t * P * * f u n d a m e n t a l f a c t o r s
g o v e r n i n g th e s t r e a m l i n e ' f l o w o f w a t e r t h r o u g h s a n d t
Jour#
Aiaer# W a f e r Wo r k s Aaeoe** Vol# 2 3 , Ho# 1 1 , 1 9 3 3 , pp# 1531*
1365*
pernteah i i i t y
wh
ic h la s
K
=
_________ /
_
(9)
where,
K
-
t he c o e f f i c l e n t o f p ©rma a b i l l t y
Cv = a f i l t r a t i o n
T =
c o n s t a n t d eterm in ed a s 5 / g r a v i t y
t h e tem p e ra tu r e c o r r e c t i o n t a k e n as v i s c o s i t y /
density
34
F = i h e p o ro ftity f a c t o r ,
where £ S«
porous I t y
S -
ehep* f a c t o r # varying, from 0 fo r s p h e re s to
7*7 f o r a n g u l a r grsline
W =* p e r c e n t a g e by weight, of m t e r la I of a g iv en
diem te r
4 = d i a m e t e r ( f o r sands I t i s taken as the g eo m etric
mean of the a d j a c e n t s c r e e n ai&ee)*
In th e F a i r and H atch e q u a t i o n ,
.ones,
the s l i t #
proportion,
-unlike p r e v i o u s
and d i s t r i b u t i o n
of
the vo id s
a r e e x p r e s s e d In t e r r a o f h y d r a u l i c r a d i u s a n d p o r o s i t y #
f a i r and Hatch found t h a t
t h e p e r a e f t b l 11 t y o f a n
a s s e m b l a g e o f s p h e r e s o f t h e same d i a m e t e r v a r i e s d i r e c t l y
a s f V t S - f } ^ , w h e r e jf i s t h e p o r o s i t y #
Fan eh er and L e w l * ^ e vo lv ed th e fo llo w in g formula
$Zm F a n e h e r , G* u * $ a n d L e w i s , J* A * , F l o w o f s i m p l e
f l u i d ® t h r o u g h p o r o u s mm t e r l a l e t
inri# Eny* Ch e m# , V o l #
Wo* 10, 1930, pp* 1139-1147*
f a n e h e r , 0# H*# and Lewis, J# A* § fenna* S t a t e Coll*
tsln* tndm Exp* S t a t i o n Tech* Paper Ho* 7, 1933*
£ or pm rmea M 1 1t y s
/( "
2rC yu
where,
H = th e c o e f f i c i e n t of p e r m e a b i l i t y
y -
the a c c e l e r a t i o n o f g ra v ity
35
d
=
the average diam eter
of
the g ra in s
found from
the equation
G
S*
= a coefficient
=
the v i s c o s i t y
o f th e fluid*.
H u i b e r t and Feben
n *>
d e r iv e d an e q u a tio n f o r
the
33*
H u i b e r t , R* , a n d F e b e n , D*, H y d r a u l i c s o f r a p i d f i l t e r
sands
J o u r * Amer* W a t e r Wor ks A s s o c # , Vol # 2 5 , 1 9 3 3 , pp*
19*65*
flow of water
Hasten* 9*
t h r o u g h s a n d w h i c h was v e r y s i m i l a r
However,
evaluate several
Separate#
factors
Another
head v a r i e d as
form ula,
Instead
of using
one c o n s t a n t t o
th eir porosity coefficient
difference
is
t h a t whereas
the sq u are of the diam eter
it varied
to
the
the
A difference
tem perature fa c to r s
o f t h e t wo e q u a t i o n s *
in Hazen*s
also e x ists
The f o r m u l a
where#
~
the
loss
of head
d
-
the depth of th e
r
-
rate
S
-
the sand s i z e
of flow
sieve
size)
In f e e t
sand
in
Inches
in m i l l i o n g a l l o n s p e r
i n mm*
for
between the
iss
L
is
loss of
1*39 p o w e r o f t h e d i a m e t e r
H u i b e r t a nd Feben*
o f H u l b e r t and Feben
to
day
( 5 0 p e r c e n t o f me
±
36
t
=
the
tem perature of the w ater
Fettke
34*
Fettke,
199*206*
i n d e g r e e s F*
experim ented w ith sands
C. R . , A . A . P . G *
from th e
I d , No* Z ,
Bull*
1934, pp.
F e t t k e , C* R* * O i l a n d Gas J o u r . , Aug* 5 ,
Z 0 -Z 5 a nd 35ru
Bradford,
equation
Pennsylvania o i l
fields
f o r p e rm c a b i1i t y as
/ r = 6. v s
1 9 3 7 , PP*
and f o r m u la te d an
foilowes
(U )
*/o ~/o •/=>*“ '
wheret K th e perraeabi1i t y j
P the poro sity *
33
Mavis and W ilsey
a rr iv e d a t the
follow ing
35* M a v i s , F* T * , a n d W i l s e y , £* F * , A s t u d y o f t h e
p e r m e a b i l i t y o f sand*
U n i v e r s i t y o f Iowa S t u d i e s , S t u d i e s
i n E n g i n e e r i n g , 1936*
conclusions
regarding
the p e rm eab ility !
“ The p e r m e a b i l i t y o f u n i g r a n u l a r
proportional
to
the square
of th e average
sands
Is
diam eter
of th e sand grains*
“ The p e r m e a b i l i t y o f g r a d e d s a n d
portional
si^e
to the
square of the
is pro­
10 p e r c e n t e f f e c t i v e
a s d e f i n e d b y Ha e e n* w
An a t t e m p t
unusual s ig n ific a n c e
by u s e o f u n u s u a l m e t h o d s ,
is
that
of Ryder
*
and o f
His words follow*
37
36*
R y d e r , H* M#* P e r m e a b i l i t y m e a s u r e m e n t s w i t h o u t c o r e s ;
Penna* S t a t e C o ll# B ull* 2 0 , 1936, pp. 4 3 - 5 9 ,
ul f a l l
would e x p e c t
than
if
of
t h e g r a i n s w e r e o f o n e s i z e we
the sp a ce s between the
w ell packed w ith sm all
ones,
m athem atically not only th a t
that
t o h e v e r y much g r e a t e r
the p e rm e a b ility
l a r g e r g r a i n s were
it
h a s b e e n shown
this
be t h e c a s e ,
the p e r m e a b ility should v ary ,
sand.
Inversely
of small
grains
as
but
in any p a r t i c u l a r
t h e f o u r t h powero f t h e p e r c e n t a g e
in th e a g g re g a te ,
f,The f o l l o w i n g
fo rm u la has been d e v e lo p e d
em pirically,
a n d b a s e d on a l a r g e
experim ental
w o r k a n d on p e r m e a b i l i t i e s made by t h e
u s u a l m e t h o d s on s p e c i m e n s
amount o f
from c o r e s ,
U i 11 i d a r c i e s = /Oo (
L___________ )
Vu * ir ■
h*8 )
total
s a n d on 1 4 0 m e s h
(13)
where,
L
-
and
weightof a l l
l a r g e r me s h s i e v e s
S
=w e i g h t
o f s a n d on 325 m e s h s i e v e
B
=w e i g h t
o f s a n d on
bottom *”
Bm pirica 1 Measurement of Perm eabi1i t y *
the q u a n t i t i e s ,
form ula f o r
and t h e i r
relations,
th e e m p ir ic a l measure
been a long tim e
sieve
in being s e t
The d e v e l o p m e n t o f
which c o n s t i t u t e
of p e r m e a b i l i t y have
forth.
However,
at
the
the
38
present
time th e s e
relationships
are
fairly
By t h e u s e o f t h e p r i n c i p l e s
analysis
37*
37
it
is possible
to r e s o lv e
w ell understood#
of dim ensional
the f a c t o r s
B r i d g e m a n , P# W*, D i m e n s i o n a l A n a l y s i s ,
Buckingham, E d g ar, S i m i l i t u d e s
Mec* E n g * , V o l . 3 7 , 1 9 1 5 , p* £63*
flo w of' f l u i d s
w h e r e aJ£ i s
of the
19ZZ»
T r a n s * Amer* Soc*
t h r o u g h a p o r o u s medium i n t o :
the p re s s u re
d ro p o v e r a column o f
length d s ;
of v i s c o s i t y ^ * and dens i t y j f 'w i t h a v e l o c i t y
of a f l u id
v$ a n d d e x p r e s s i n g
a diam eter c h a r a c t e r i s t i c
of a c e rta in
g ra in size*
I t has been alm o st u n i v e r s a l l y
the argument o f /
is
of
the f i r s t
a g r e e d upon t h a t
dlinension^,
so the
38* M u s k a t , M#, a n d B o t s e t , H* E * , F l o w o f g a s
porous m a te r ia ls }
P h y s i c s , 1, 1 9 3 1 , p p . £ 7 - 4 7 *
M u s k a t , M*, F l o w o f H o m o g e n e o u s F l u i d s ,
M c G r a w - H i l l , 1937*
through
pp.
56*57,
e q u a t i o n becomes
A fr. where
is
For
th e argument
co/?st.
the p re s su re
M z
of v ^ )
gradient*
l o w v a l u e s o f d!, v ,
of th e
(Z )
f u n c t i o n P,
and
which
(lam ellar
is
flow)
re c o g n iz e d as
39
"Reynolds** number"# e q u a l s
the f u n c t i o n and th e e q u a t io n
becomes^ t
39*
M u s k a t # M*# op* c i t * #
Zbo.
4S
C O H < st.
p* 57#
y K
{3 )
\/
c/ *
by i n v e r s i o n
V — co*i&?7
A rbitrarily
d
2.
o/ * 4 / d
s44
4s
choosing K to 'a b s o r b
(4)
the values
of
and th e c o n s t a n t #
^
= - %
yU
- -J /b
As
(5 )
a n d by i n v e r s i o n
XT' =
In which K Is
the c o e f f i c i e n t
><
V
(6)
AS
of perm eability#
(7 )
=_£
4
(8)
40
($)
-
By s u b s t i t u t i o n
of e q u atio n s
A'
7,
8, and 9 in 6 r e s u l t s
=-------------------------------r
in:
U ° )
where*
yU. s v i s c o s i t y
of the f l u i d
Q
s flow i n cm#' Vsec*
L
-
A
=: a r e a
le n g th of sand sample
of
the
sample
P |#
pressure
in c e n t l p o i s e s
i n cm#
i n f l o w or o u t f l o w end of
i n era*
2
(provided
in atm ospheres a t
they are
10 t o
their
reduction of
dimensions*
the
=: cm* ^
Length
= cm#
Time
= sec*
Pressure
=
V iscosity
These u n i t s
th e sample*
fundam entals
the follow ing
Vo 1time
the same)
the r e s p e c tiv e
in flo w and o u tflo w ends of
In the
the sand
units
of e q u a tio n
are used:
atmosphere
=r c e n t i p o i s e a
lead
to a dim ensional
expression
for
/ c
-
AA X C *r?3 * C+r?
s e o X C»? z x <3.T*h ,
_
the p e r m e a b ility c o n s ta n t:
^
x C&? 2
je c
_
c
X j
or e x p re ss e d
in fundam ental
perm eability
ares
/-Se s
jec
units,
* - £ 1 7
f
> c/>7 ¥
c/y *?e &
the dimensions
of the
41
Equation
I f a gas
f o r use w ith
is used as the flu id *
be o b s e r v e d s i n c e
sample
10 i s
o u tf lo w end o f the
The r e d u c t i o n
sample r e s u l t s
gas and thus an i n c r e a s e
However*
of
flow channel
it
the
In p r e s s u r e a t
the
in an e x p a n s io n o f t h e
In t h e v e l o c i t y *
tim es d e n s i t y )
of the p r e s s u r e s
*
throughout
has been e s t a b l i s h e d
(velocity
the sq u a res
c e r t a i n m o d i f i c a t i o n s must
the v e lo c ity g ra d ie n t
Is n o t c o n stan t*
mass v e l o c i t y
incom pressible fluids*
Equation
10 i s
th a t both th e
and t h e g r a d i e n t
rem ain c o n s t a n t along
the
then e x p re ss e d ass
40*
wyckoff* B o i s e t , h i u s k a t , a n d Re ed* P e r m e a b i l i t y o f
p o r o u s m a t e r i a i s 5 A*A*P.G* B u l l * 18* 1 9 3 4 , pp* l o l - 159*
C h a l m e r s , J * , T a l i a f e r r o , D. B#, a n d R a w l i n s , E* L * ,
Flow o f a i r a n d g a s t h r o u g h p o r o u s rnedias
T r a n s * Amer#
I n s t * fcieck* E n g . , P e t r o l e u m D i v i s i o n , Ch* 5 , 1 9 3 2 , p* 332*
/t
=
m
QL
( U )
A f P ~/°»)
where Q r e p r e s e n t s
7
the
total
fluid
o u tflo w as reduced to
in w hich,
P
= 8+Pz
(12)
(13)
APPARATUS AND PROCEDURE
The e q u i p m e n t u s e d
b e d i s c u s s e d was a s s e m b l e d
of
for
obtaining
the
results
to
in th e S e d im e n ta tio n L a b o ra to ry
the Departm ent o f Geology a t
the S ta te U n iv e r s ity
of
I owa#
Sands used
in- t h e
experim ents were both
c o n s o lid a te d and unco n so lid ated #
came f r o m t w o g e o g r a p h i c
I owa C i t y a n d f r o m t h e
northeastern
consisted
Iowa*
localities*
friable
A third
St*
of o il
and Kentucky*
Venango O i l
t h e I o wa R i v e r a t
P e ter sandstone of
s e t o f u n c o n s o l id a te d samples
of c ru s h e d q u arts;!te*
were c o r e s
The u n c o n s o l i d a t e d s a n d s
The i n d u r a t e d s a m p l e s
producing sandstones
T hirteen
of the
from P e n n s y lv a n ia
c o r e s were from th e T h ird
Sand o f W arren County* P e n n s y l v a n i a !
cores were from t h e J e t t
sandstone
and te n
of t h e Owensboro D i s t r i c t *
Kentucky*
The p r o c e d u r e f o l l o w e d
s a m p l e s wa s q u i t e
different
u n c o n so lid a te d samples*
procedure*
it
than
in t r e a t i n g
the
indurated
t h a t fo llo w ed w ith the
Because of the d i f f e r e n c e
is necessary
in
to c o n s id e r each group
individually*
Unconsolidated Sands*
the u n c o n s o l i d a t e d
The f i r s t
step
sands c o n s is te d
p erio d in an e l e c t r i c
oven a t
removed a n y w a t e r a d h e r i n g
in the h a n d lin g o f
of a 24 hour d ry in g
a tem perature
t o t h e grain®#
of
180°F#
This
43
The s a n d s w e r e s e p a r a t e d b y s i e v e s
Ro-Tap m e c h a n i c a l
were used*
shaker*
g ra d u a te d as
No*.
Standard*
placed
Tyler wire sc ree n s
follow s!
Opening
i n ram*
Mesh
U.S. S e r i e s
Equivalent
1
9
1.981
10
z
16
*991
18
3
3Z
.495
35
4
60
* £48
60
5
US
,124
120
6
250
*061
230
7
Fan
The g r a i n s
were s i e v e d
£0 m inutes*
in a
i n 100 g r a m m a s s e s f o r p e r i o d s o f
and t h e g r a d e s s t o r e d
separately
for future
use*
The s p e c i f i c
gravity
o f e a c h g r a d e was d e t e r m i n e d
by a w a t e r d i s p l a c e m e n t method*
T h i s v a l u e was u s e d
in t h e
p o ro sity determ inations*
Next*
grain size
i t was n e c e s s a r y
to determ ine
f o u n d on e a c h s i e v e *
To t h i s
the average
end a p e t r o g r a p h i c
m i c r o s c o p e f i t t e d w i t h a m i c r o m e t e r o c u l a r was e m p l o y e d *
G rains were s e l e c t e d
f o r m e a s u r e m e n t by p l a c i n g a few* a s
c a p t u r e d a t random by a s p a t u l a *
microscope*
poured back
A fter
into
these grains
their
on t h e
stage
of th e
had been m ea su re d t h e y were
container*
The c o n t a i n e r was
s h a k e n w i t h a r o t a r y m o t i o n f o r a f e w r, o m e n t s a n d a f r e s h
batch s e le c te d
f o r measurement*
This p ro ce d u re
continued
44
until
100 g r a i n s ha d b e e n m e a s u r e d a l o n g
axes*
The t h r e e
average g rain
th re e major
s e t s of f i g u r e s were th en a v e ra g e d and
the a v e ra g e g r a i n . s i a e
diam eter equal
their
concluded
to the average
to
be a s p h e r e w i t h a
of the
An
300 f i g u r e s #
s i s © wa s d e t e r m i n e d f o r e a c h g r a d e *
F o r o s i t y a n d JPermeafcl 1 i t y o f U.n l q r a d a * * S a n d s #
For the
*
In t h i s p a p e r # a u n i g r a d e sand is one composed of b u t
a s i n g l e grade as c o n tr a s t e d w ith m ix tu res of grades*
The
t e r m s u n i g r a d e a n d u n i g r a n u l a r a r e synonymous*
determ inetion
individual
weight*
grades*
1*
and p e r m e a b i l i t y
in th e g l a s s
tubes w ith diam eters
of 1-7/8
l e n g t h s o f 3 0 i n* a n d 18 in*
to
after
and r o l l e d
to
into
perm eability
the
the c o n ta in e r
in such
of the grade*
t h e t u b e was
in the permeaxaeter w i t h a s
little
was d e s i r e d s o
a maximum p o r o s i t y f o r
trial*
in* a n d
inverted
tu be and sam ple w ere p l a c e d
A m i n i mu m o f j a r r i n g
s a n d would be a t
in g l a s s
th e mixing*
At th is p o in t,
correct position
in
respectively*
in su re a thorough m ixture
to add
the
o f the
illustrated
i n* a n d 1 - 1 / 4
irnpiacement o f th e san d ,
as p o s s ib le *
Is
sam p les were h e l d
The ©a mpl e was p o u r e d
Also*
sample c o n t a i n e r
The p e r m e a m e t e r h o o k * u p
The u n c o n s o l i d a t e d
fashion as
of each of
c o n v e n i e n t sa m p le s were s e l e c t e d by
and p l a c e d
permearaeter*
Figure
of p o ro sity
the
first
in
jarring
that
the
TO AIR
PERMEABILITY
W'
SET
UP
PS
The p e r m e a b i l i t y o f e a c h o f t h e
d e t e r m i n e d by m e a s u rin g
the
the q u a n tity
s a m p l e s was
of a ir
passing
s a n d c o l u m n o f known l e n g t h a n d e n d a r e a s
gradient
through
under a
e s t a b l i s h e d by a m e r c u r y or w a t e r manometer*
r a t © o f f l o w wa s d e t e r m i n e d by c o n d u c t i n g
the a i r
The
from
t h e t o p o f t h e column t o a g r a d u a t e d b u r e t t e from which
w a t e r wa s d i s p l a c e d *
b u re tte with a i r
Prior
captured
allow ed
least
in th e
in o rd e r
three
The t i m e r e q u i r e d
to f i l l
the
was r e c o r d e d by a s t o p w a t c h *
to each p e rio d
burette#,
an
interval
to e s ta b lis h
tirals
d u rin g which th e a i r
was
o f f r e e b u b b l i n g was
a s t e a d y flow*
Also#
w e r e c o m p l e t e d on e a c h s a m p l e t o
at
insure
t h e s t e a d y flow*
P o r o s i t y wa s d e t e r m i n e d b y t h e u s e o f t h e
follow ing
formulas
/OCP =
L
l/2
(1)
_ _
wherei
W
sp*gr*
= th e w e ig h t of th e sample
- the s p e c i f i c
r. t h e v o l u m e o f t h e
Pg
- the gross p o ro s ity
outside
This
g r a v ity of the grade
VZ
Following
in grams
sand in
the
being used
tube
in per cent*
the completion of the f i r s t
run,
the
o f t h e c o n t a i n e r wa s t a p p e d w i t h a r u b b e r hammer*
resulted
p o ro sity for
in a s e t t l i n g
of the
sand and a lower
the second p e rm e a b ility
run*
This p ro ce d u re
wa s r e p e a t e d f o u r
c o u l d no
or f i v e
tim es u n t i l
the
l o n g e r be s h o r t e n e d by t a p p i n g
A decrease of five
sand column
on t h e c o n t a i n e r *
t o s e v e n p e r c e n t c o u l d be p ro d u c e d
t h e p o r o s i t y by t h i s
treatm ent*
fy§i x t u r e # o f G r a d e s o f U n c o n s o l i d a t e d S a n d s *
sands are p r a c t i c a l l y
u n k n o wn i n n a t u r e *
r e c o n s t r u c t more n e a r l y
the n a tu ra l
be u s e d
the
on e g r a d e a s 80^ #
neighboring
grades#
found f o r
the
A full
grades#
o f a n y one g r a d e
to
t o mix a n y
and f i li a l l y
sequence of m ix tu res
Rather*
g ra d e s and th e s e f o r
five
in the
they were
treated
the purpose of
o f p o r o s i t y and p e r m e a b i l i t y
rounded grains*
The p r o p o r t i o n s
1*
the grades
Also# m ix tu r e s were
g r a i n s was n o t d e v e l o p e d *
in s i n g l e
to
Twenty p e r c e n t
was p o s s i b l e
side*
four
comparison w ith the v a lu e s
Table
it
In ord er
75%, 6 6 ^ # 5 0 %, 35%, Z5%, a n d ZQ% o f t h e
g r a d e s o f ZQ% e a c h #
only
Thus
g r a d e on e i t h e r
made w i t h t h r e e
angular
lowest p e rc e n ta l
in a m ixture#
Uni g r a d e
conditions#
were mixed in p r e d e t e r m i n e d p r o p o r t io n s *
wa s s e l e c t e d a s
in
of the m ix tu res a re given
The m i x t u r e s a r e
in which the nu m era to r
and th e d e n o m in ato r
represented
represents
in f r a c t i o n a l
in
fora
t h e number o f t h e g r a d e
the per cent of th a t grade p resen t
the m ixture*
G rain Size of the
ixed G rades*
samples a w eighted g r a in
the follow ing
formulas
For e ac h of t h e mixed
s i z e was d e r i v e d b y t h e u s e o f
in
48
TABLE I
G ra d e C o n t e n t o f M i x t u r e s o f U n c o n s o l i d a t e d Sand Samples
S a m p l e No,
aft.
2
S3
2
SB
2
£Ci
2D
EE
m
2G
£K
EL
20
EP
2V*
'
1.098
0.937
0*734
0*835
0*997
5
E
3
1 *E96
2
20
2
60
2
3
80
3
0.905
4
1.08E
3
4
0*8S3
1 .£6
20 "IF
2
3
4
2 0 "IF 6 0
2
3
4
40
4 0 ^S5
E
3
4
40
2 0 4$
2
3
4
1 wU
s>b ’.in
TffiV 40
*isv
EH
0.855
E
"IF "Ҥ0 "IF
EM
2TJ
4
~33
2
3
50
e
s
2 5 75
2
3
4
2 5 "*25* 50
2 _3_ 4
25
50 "IS*
2
3 4
‘ab ~
23*
2T
1.S06
"75 "IF
21
26
"■W
Weight©
S ize in
0.990
~5Q TST
2H
ER
3
66
3
33
3
“T>6
SC
2Q
Grade P r o p o r tio n s
S 3 4
5
“SET 20 20 20
2 3 4
5
“fET “15- “SET"SIT
2
3 4
5
"ST *15' " 4 0 "15
2
3 4 5
" s o 1 5 1 5 ~W
2 3 4
5 6
26 20 20 20 1 5
2
3 4_ 5
T S T 5 “fe 25
0*660
0*953
0*871
0.74S
0.841
0*711
0.630
0.599
0.583
0*695
49
TABLE L ( C e n t . )
S a m p l e No#
3A
SB
SO
3CX
SB
31
3F
3G
3H
31
3J
Gr a d© P r o p o r t i o n s
3
I S
3
“S I
3
“S I
3
U
3
25
3
“I I
3
“I I
3
“ SI
3
75
3
80
3
20
4
“SI
4
“ SI
4
“SI
4
“ SI
4
H
4
H
4
50
4
1 1
4
1 1
4
H
4
80
0.504
0.639
5
“SI
3M
3N
50
5P
3Q,
3R
38
3T
31?
0.453
0.5 7 8
0.4 6 8
5
“ SI
5
“I I
5
H
3K
3I»
W eighted G rain
S i z e i n ra.m*
0 .3 9 4
0.432
0 .5 3 4
0.6 7 3
0 .6 9 4
0*450
0*582
60
3
20
3
3
H
3
n
3
20
3
“V
K
*cU
3
~ l0
3
80
3
H
3
(M
m
ton****
20 1 l
4
5
60 20
4
5
"m'r"pQ ""'rQ (j
4
5
H
H
4
5
u
n
4
5
40 40
4
5
6
pK
V-/ ' "pn
<&y “To
wU
4
5
6
*40 T5ET
4
5
6
80 40 80
4
5
6
H
H
“3 1
4 _5____6
r*
«*»*"■
0 «419
0.359
0*500
0 .470
0.389
0.453
0.37 1
0.341
0.385
0.373
50
TABLE I ( O o n t *)
S a m p l e No*
4A
4B
40
4GX
40
4E
4E
4G
4H
41
4J
4L
4ri
m
40
4P
G rade P r o p o r tio n s
4
5
66
4
5
^ 5
4
5
S 3 33
4
5
50
4
5
25 75
4
5
25 25
4
5
“IS - 5 0
4
5
50
25
5
4
4
“ SET
4
*1o
’"’W
4
20
4
20
4
..4 0
4
40
4
20
W eighted G ra in
S i z e i n m#m*
0*267
0*318
6
'.s’s 1
0*239
0*291
0*254
6
53“
6
25
6
25
5
20
5
80
5
6
~W
20
5
6
~
~20
5
6
20
60
5
6
40
20
5
3
20 4 0
5
6
40 40
0*213
0*233
0*272
0*331
0*339
0*247
0*291
0*228
0*197
0*261
0 *2 4 4
0*213
51
TABLE I
S a m p l e Bo#
5A
5B
50
5D
51
5F
5G
( G o u t *)
G rade P ro p o rtio n ®
5
6
3 3 "53“
5
6
"66 ~W
5
6
~W
s
e}
"25
75
5
6
" 7 5 £5
5
6
8 0 " "20
5
6
~ 2Q
W eighted G ra in
S i z e i n num .
0*161
0* 188
0*174
0*154
0*195
0*199
0*149
w here,
x
-
th e s m a l l e s t p e r c e n t by w e ig h t o f any g ra d e
present *
Q,,G,,G*,
=
p e r c e n t by w e ig h t o f
=
the
siee
siev e,
i n mm* o f t h e a v e r a g e
fro m w hich
s-
Procedure
g r a i n on e a c h
a s d e te rm in e d by d i r e c t m easu rem en t, and
the n u m erica l
Gm,
the g ra d e s p r e s e n t .
su b scrip ts sig n ify
the
g r a i n s were s e l e c t e d *
w e i g h t e d g r a i n sl&© o f
th e sam ple
for C o n so lId ated M a terlals*
sam ples w ere c u t p a r a l l e l
the grades
i n mm*
The p e r m e a b i l i t y
to the bedding p la n e s
ro c k fro m a b i s c u i t w h i c h was o b t a i n e d
of th e
In th e f i e l d
by
th e u se o f a Baker c o r e - b a r r e l *
The p e r m e a b i l i t y s a m p l e s w e r e c l e a n e d b y w a s h i n g
them i n c a r b o n
by p l a c i n g
tetrach lo rid e*
th em in a S o x h l e t e x t r a c t o r and r e t o r t i n g
so lv en t fo r
a p erio d
the sam ples w ere c u t
d eterm in in g
d istrib u tio n *
180°F f o r
where
o f e i g h t hours*
fo llo w in g
in to
one f o r
th e p o r o s ity
w h i c h wa s c r u s h e d f o r
of
The w a s h i n g was a c c o m p l i s h e d
tw o p i e c e s ,
the
the w ashing,
use
in
and p e r m e a b i l i t y and th e o th e r
t h e p u r p o s e o f m aking a g r a d e - s i & e
The s a m p l e s w e r e d r i e d
two d a y s b e f o r e p l a c i n g
th e y w ere k e p t w h ile n o t
a t a tem p eratu re
them i n a d e s i c c a t o r
i n use*
53
Th e c r u s h i n g
its
sep arated
the
In d u rated
p o r c e l a i n m o r t a r and a s o f t wooden p e s t l e #
t h e g r a i n s was c o n t i n u e d u n t i l
clu ste rs
From tim e
Into
T h i s was a c c o m p l i s h e d b y u s e o f a
c o n s titu e n t grains#
iso lated #
rock
to tim e
a ll
S ep aratio n of
o f th e g r a i n s w ere
t h e © a m p le was
In spected fo r
o f g r a i n s w hich w ere p ic k e d o u t and s e p a r a t e d
in to g rain s#
Follow ing
the
se p ara tio n
w a s s i e v e d f o r ZO m i n u t e s
of the
on a Ro~Tap«
grains#
E a c h g r a d e , was
w e ig h e d and r e c o r d e d a s a p e r c e n t o f t h e whole#
th e g r a d e s w ere p l o t t e d
i n d u r a t e d sa m p le s by e s s e n t i a l l y
the u n c o n so lid a te d
being t h a t
the
©ample h o l d e r
F in ally #
as c u m u la tiv e p e r c e n t curves*
The p e r m e a b i l i t y was d e t e r m i n e d f o r
used f o r
th e mass
in d u rated
t h e same m e th o d a s
sam ples#
th at
the d if f e r e n c e
sam ples w ere h e ld
Illu stra te d
the
by F ig u re £j
a l a r g e p r e s s u r e g r a d i e n t was r e q u i r e d #
and
in th e s p e c i a l
In c a s e s w h e re
th e p r e s s u r e s were
d e t e r m i n e d by t h e it©a o f a d i a l g a g e r a t h e r
t h a n t h e m ano-
me t a r s #
For
the d e te rm in a tio n of th e p o r o s ity
in d u r a te d sam ples# a g a s
p iece of a p p aratu s
fo r o p eratio n of
1*
Is
e x p a n s i o n m ethod was used*
Illu stra te d
i n F i g u r e 3*
t h e p o r o s i m e t e r was a s
The l e v e l
of the
T his
The r o u t i n e
follow s*
o f t h e m e r c u r y was b r o u g h t t o C
by m a n i p u l a t i o n o f th e r e s e r v o i r *
£♦
placed
in th e
S t o p c o c k s A and B were op en ed and
c o n ta in e r behind
th e sam ple
s t o p c o c k A# a n d t h e
top o f
RUBBER STO PPER
PERM
SAMPLE
& s
P O P O S /P E T E R
—c
/=Ag. 3
5©
th e c o n t a i n e r t i g h t l y re p la ced *
3*
s t o p c o c k A was c l o s e d a n d
m ercury r a i s e d
4*
in to
5*
to drop
c l o s e d and th e
level
to C by l o w e r i n g
S t o p c o c k A was
stopcock A allo w ed
le v e l of the
t h e f u n n e l a b o v e s t o p c o c k B*
S t o p c o c k B was
m e rc u ry was a ll o w e d
the
to expand
the re s e rv o ir*
o p e n e d and t h e
in to
of the
air
behind
th e sp a ce above
the
m ercury*
6#
m easured
S t o p c o c k A was c l o s e d a n d
i n t h e g r a d u a t e d c o l u m n b e l o w s t o p c o c k B* w h en
the s u r f a c e
of th e m ercury
r e s e r v o i r were a t
7*
t h e same
A fter
0*
the
in th e
g r a d u a t e d colum n and t h e
level*
th e volum e o f a i r
s t o p c o c k B was o p e n e d and
in to
the expanded a i r
The l e v e l
had been rec o rd ed *
th e a i r a llo w e d to escape*
o f t h e m e r c u r y was a g a i n r a i s e d
funnel*
9*
S t o p c o c k B was
c l o s e d and t h e
m ercury le v e l
d r o p p e d t o C*
10*
S t o p c o c k A was o p e n e d !
etc*
The a b o v e p e r f o r m a n c e was r e p e a t e d u n t i l
was c a p t u r e d o v e r
P rio r
to rem ove
the m ercury
i n t h e g r a d u a t e d c o lu m n *
to e a c h sam ple run* a t r i a l
a ir adhering
no a i r
to th e w alla
r u n was made
of the a p p aratu s#
The g r o s s v o l u m e o f t h e s a m p l e s was d e t e r m i n e d ,
as
the
in to a
d ifference
b e tw e e n t h e volume o f w a te r
in troduced
Z 5 c c * g r a d u a te f r o m a g r a d u a t e d p i p e t t e ,
and th e
volume o c c u p i e d i n t h e g r a d u a t e b y t h e s a m p l e a n d t h e
57
in tr o d u c e d w a te r w hich c o v e re d
the
sam ple*
The " e f f e c t i v e p o r o s i t y " was t h e n d e t e r m i n e d
by use o f th e form ulas
in w hich*
V*
W
*
t h e v o l u m e b e h i n d s t o p c o c k A i n cm#^
s
th e g r o s s volum e o f th e c o r e
=
the
t o t a l volum e o f a i r
colum n
Fe
*
I n cm*^
cap tu red
in th e
graduated
i n cm*^
the e f f e c t i v e
p o ro sity
in per cen t
INVESTIGATION AND RESULTS
l i n e o n s o 1|i d a t e d S a n d s »
d eterm in e
the
effect
perm e& M lity *
For
w h i c h c a n be f o u n d
1*
The
i n v e s t i g a t i o n was d e s i g n e d
of p o ro sity
th is
in the fo llo w in g
g rain siz e
b*
V aria tio n s
o u tlin e?
s i z e upon p o r o s i t y *
of p o ro sity
in u n ig ra n u la r*
V ariatio n s
upon th e
p u r p o s e a p r o c e d u r e was f o l l o w e d
The e f f e c t o f g r a i n
a*
and g r a i n s i z e
to
from v a r i a t i o n o f
u n co n so lid ated
sands*
of p o r o s ity produced
in m ix tu re s
of u n c o n so lId a te d sands*
Z*
The e f f e c t o f g r a i n
a*
V ariatio n s
the g ra in s iz e
b#
size
of p e rm e a b ility
of unlgranular*
V ariatio n s
of u n c o n s o lid a te d sands*
upon p e r m e a b i l i t y *
from v a r i a t i o n o f
u n c o n s o lid a te d sands*
of p e r m e a b i l i t y p ro d u c e d by m ix t u r e s
sa
3*
The e f f e c t
a*
o f p o r o s i t y upon perrr.eabll ity *
V a ria tio n s
of p o ro sity
of unlgranular*
b*
V ariatio n s
p o ro sity v a ria tio n s
4#
o f p e r m e a b i l i t y from v a r i a t i o n s
u n c o n s o l id a te d sands#
o f p e r m e a b i l i t y p ro d u c e d from
of m ix tu res
o f u n c o n s o l id a te d sands#
D e r i v a t i o n o f a form ula
g rain s is e
in ten d ed
of the f u n c tio n s
rela tio n s*
i*e«*
relatio n sh ip ©
t o show i n i t i a l l y
upon each o t h e r
in
u n i g r a n u l a r com ponents*
had been e s t a b l i s h e d *
lig h t of
u nigrade
types
th eir
A fter
and
F in a lly *
sim p lest
th ese
in te rp reted
th e e v id e n c e s u p p l i e d from t h e
system s*
the
t h e more c o m p l i c a t e d
sy ste m s o f m ixed g r a d e s w e re i n v e s t i g a t e d
in t h e
from
and p o r o s i t y *
The d e s i g n was
effects
for p erm eab ility
after a ll
sim pler*
the d a ta
from b o th
o f sy ste m s w ere a sse m b le d an e q u a tio n f o r
the
p e r m e a b i l i t y was d e r i v e d *
The E f f e c t o f l i r a i n $ l % e on p o r o s i t y
The e f f e c t o f g r a i n s i z e o n t li e
Unconso 1 Ida t e d Sands*
p o ro sity of u n ig ran u lar,
i n F i g u r e 4*
g rain
s ize
The g r a p h
decreases
For
in Uni g r a n u l a r *
u n c o n so lid a te d sands
illu stra te s
the p o r o s i t y
the
fact th at as
the
in creases*
th e p u rp o se o f com parison o f each o f th e
g r a d e © some p a r t i c u l a r p o i n t o f r e f e r e n c e
selected *
i s show n
S ince
and t h e p o r o s i t y *
h a d t o be
t h e c o m p a r i s o n wa s b e t w e e n t h e
the
th e p o r o s i t y and th e
only v a ria b le
grain s iz e
i n a n y o n e g r a d e was
o n l y common p o i n t o f r e f e r e n c e b e t w e e n
ss
E f f e c t o f Grain S l z « on P o r o s i t y In U n l ft r a n u l a r , U n o o n s o l l d a t e d Sands
/ 2 7S
I 2 oo
M
■r-i
03
7 Jo
C 7J
od
u
o
3 7S'
CP
3/
3„
73
Jy
37
3C
37
38
33
rc
y/
P o r o s i t y in
Percent
/5».y
Only s m a l l e s t p o r o s i t y
per g ra in s i t e p l o t t e d
t h e g r a d e s was t h e s m a l l e s t p o r o s i t y
grade*
T h u s * a s shown b y F i g u r e 4*
ex h ib ited
in t h e
the v a r io u s
grades*
co m p aciab iiity *
the p o r o s i t y
fo r each
rela tio n sh ip
t h e maximum
There
tr a n s p o s itio n o f the c o n p a c ta b il i ty
p o ro sity sin ce
th is
the
is a c t u a l l y a com p arison of
com pactaM 1i ty o f
obtained
i s no e r r o r
in to
the
is a m easure o f the d e g re e o f
and r e f l e c t s
same m e th o d o f r e f e r e n c e
it
ex actly *
la
l a t e r case®
is em ployed*
A tab u lar rep re se n ta tio n
o f F i g u r e 4 follow ® ?
T a b l e 11
G r a d e $ i« e
Average Measured
Grain Diameter
H in imum
Foros it y
aiR
1*422 mm#
30*03 % .
SIR
*775 mm*
30*55 %
41R
*338 mrn*
34*3
%
4StP^
*359 mm*
35*5
%
5$tP
*216 mm*
36*9
%
6StP
* 133 mm*
' 39.1
%
*
i n F i g u r e 4 o n l y one v a l u e is u se d t o e x p r e s s th e
p o r o s i t y a n d g r a i n s i & e o f g r a d e 4*
T h i s was d o n e b e c a u s e
t h e S t * F e t e r a n d lowm R i v e r s a n d s w e r e m i x e d I n e q u a l
p r o p o r t io n s and used in t h i s m ix tu re f o r a l l l a t e r
d e term in e !io n s*
G rade 4 o f F ig u r e 4 is an a v e r a g e o f th e
p o r o s i t i e s a n d g r a i n s i g e e o f t h e two s a n d s #
T he s h a p e o f t h e c u r v e o f F i g u r e 4 m i g h t b e d u e
to a n y one o r c o m b in a tio n
in flu en ce
the p o ro s ity *
of th ree
The t h r e e
f a c t o r s w hich c o u ld
facto rs
are*
(1)
61
M ethod o f s e p a r a t i o n ,
resu ltin g
(2 ) Shape o f th e g r a i n s ;
actu ally
{3 } T h e r e l a t i o n s h i p
fillin g ;
as e x h ib ited
e v id e n c e co u ld he found to s u p p o rt the
two p o s s i b i l i t i e s *
diam eter o f th e
if
$1ic h te r
is
Introdu ced g ra in s
req u ired
to f i l l
v o id s betw een th e
th at of
in te rstitia l
exist® *
L ittle
first
in
the
in itia l
In itia l
For*
follow ed *
the
the
g r a i n s m ust be from 1 /4 t o l / l
grain s*
a c t u a l l y m e a s u r e d , no g r a i n s
A fte r rech eck in g
o f the re q u ire d
the g r a i n s
l/4
to
l/?
d i m e n s i o n s c o u l d b e f o u n d i n t h e g r a d e 2 , 3# a n d 4 screen**
ings*
or
N e i t h e r w ere a n y g r a i n s fo u n d w hich w ere s p l i n t e r
l a t h shaped*
h a d no r a d i c a l
shape*
The s h a p e s o f
dep artu re
B oth t h e
the g r a in s
from th e r e g u l a r
o f rounding*
the
g rain s
H ow ever,
flu ctu atio n
in
to s u b - r o u n d , w ith
hav in g a s l i g h t l y
in b o th s a n d s ,
the cu rv e a t
I t w ould a p p e a r
in crease g rain
as t h e r e
th at
the
rela tio n sh ip a c tu a lly
p o ssib le
to produce
rep e titio n
o f the
d iffe re n t siee
size
the o v erlap#
T h i s d e c i s i o n wa s r e a c h e d b e c a u s e
n o n -ex isten ce
degree
i s no m a j o r
ex ists*
Its
b e tter
t h e o v e r l a p o f g r a d e s 4 a b o v e shows
tren d of d ecrease p o ro s ity w ith
to be p r e s e n t
e llip so id a l
l a r g e and s m a ll g ra d e s , p o s s e s s e d g r a i n s
w hich c o u ld be d e s c r i b e d a s c u r v i l i n e a r
some o f t h e s m a l l
in th e g ra d e s
i t was n o t
o t h e r e v i d e n c e by w h ich t o a c c o u n t f o r
and th e f a c t
resu lts
g rain s
th at
these r e s u lts
are a
o f o t h e r o b s e r v e r s who e m p l o y e d
and d i f f e r e n t
shapes
w e ll a s d i f f e r e n t m ethods o f s e p a r a t i o n
of p a r t i c l e s
than
as
t h o s e em ployed
in t h i s
paper#
The E f f e c t o f C o n t a i n e r . D i a m e t e r o n t h e
U n i g r a n u l a r # l i n e o n e o 1 i 4.a.t ed S a n d s #
d ata f o r
Poros i t y o f
W hile a c q u i r i n g
the p © ro s liy * g r® in s is e r e l a t i o n s h i p s
w as l e a r n e d a b o u t t h e s i z e
be used#
of the
the
som ething
c o n t a i n e r w hich s h o u ld
The o b s e r v a t i o n made i n d i c a t e d t h a t a s a f e
was r e a c h e d
i f t h e c o n t a i n e r d i a m e t e r wa s
of the average
100 t i m e s
that
grain#
The e f f e c t
of
the c o n ta in e r
c o m p a r i s o n o f F i g u r e s 4 a n d 5*
F i g u r e 5* a s m a l l
size
For the
t u b e was u s e d a n d
decrease o f p o ro s ity w ith
i s sh ow n b y a
d eriv atio n
of
the norm al tr e n d
to the c o n ta in e r
s i z e was o n e t o
The e x p l a n a t i o n o f t h i s
obvious#
F urnas^
has
sta te d
of
o f g r a i n s i z e was
increase
o b se rv e d to a p o i n t a p p ro x im a te ly a t w hich th e r a t i o
grain siz e
lim it
of
100#
phenomenon i s f a i r l y
t h a t when a c o n t a i n e r w a l l
41#
F u r n a s # C« C## F l o w o f g a s e s t h r o u g h b e d s o f b r o k e n
so lids?
U* ' $-« B u r e a u o f M i n e s B u l l . 307# 1929*
is
in tro d u ced
in to
so lid m aterial
leav in g
in
the v o id s
If
a bed o f m a te r ia l#
the s e c t i o n n e x t to th e w a ll
in t h a t
the g ra in s
a re p laced
the c o n t a i n e r
th an
effect
is p ro d u c e d and to ab o u t
is a d i s t o r t i o n
of
is
se c tio n co rresp o n din g ly
rath er
there
30 p e r c e n t o f t h e
in se rte d
the
removed#
larg er*
in th e c o n t a i n e r
in to
the sand,
same d e g r e e *
the p a c k in g w hich r e s u l t s
t h e sa me
T h u s#
in an
63
C o n t a i n e r D i a m e t e r on P o r o e i t y i n U n i g r a n u l a r , U nooneol i d a t e d Sands
i. 2 7S
(. Zoo
f. os o
©
N
«*-*
CA
,7 so
B
. 6 7S
600
■3oo
0.00
3Z
33
jy
3J
36
37
33
P o r o s i t y in
Percent
F/%. 3
Only s m a l l e s t p o r o s i t y
per grain s iz e p lo tte d .
64
In p o r o s i t y w here th e g r a i n s c o n t a c t
in crease
the p lan e
of th e c o n ta in e r w alls*
The d i s t o r t i o n
p erip h ery
several
tow ards
to
If
o f t h e c o l u m n a n d may h e
th e g r a in s have sm all
the diam eter o f
packing a re a
of
the c e n te r
g r a i n s deep*
rela tiv e
o f p a c k in g e x te n d s from th e
the c o n ta in e r *
i s r e p r e s e n t e d by a
the san d and th e w a ll e f f e c t s
th e norm al
la rg e core a t
increases*
the c o n ta in e r
m aining
t h e sa me*
t h e wave o f d i s t o r t e d p a c k in g
tow ards
the c e n te r
increased*
o f d i s t o r t i o n may b e co m e e q u a l
c o n tain er*
w ill
a t w hich p o i n t
he e q u a l
th e zone
of the
o f t h e e n t i r e colum n
For th e
i n g r a d e Z r e p r e s e n t e d an i n c r e a s e o f 2 6 *Z p e r
o f 23*8 p e r c e n t*
The E f f e c t o f O r a . i n S i z e on F o r e s i t y
U n c o n so lid ated Sands*
in m ix tu res
The r e l a t i o n
h e r © a s was o b s e r v e d f o r
the p o r o s ity d e c re a se s as
th ere
pronounced sag
is
in M ix tu re s o f
of g rain siz e
of u n c o n so lid a te d sands
d e r a o n s t r a t e d b y F i g u r e 6*
H ow ever,
same t i m e
in t h i s p a p e r th e d i s t o r t i o n
c e n t and f o r g ra d e 3 an in c r e a s e
p o ro sity
the
F in a lly
to the ra d iu s
the p o r o s i t y
encroaches
to t h a t o f the d i s t o r t e d p o rtio n *
sand and equipm ent u sed
resu ltin g
d iam eter re ­
o f th e s a n d colum n an d a t
is
the c e n te r
a r e p r o p o r t i o n a l l y sm all*
As t h e g r a i n s i z e
t h e p o r o s i t y o f t h e colum n
diam eters
The same g e n e r a l
is g ra p h ic a lly
tren d
th e u n ig ra n u la r sam p les,
the g r a i n s i z e
a strik in g
to
is
found
i* e* ,
increases*
d e p a r t u r e r e p r e s e n t e d by th e
in th e m id d le o f
the curve*
Effect
of
Grain
Size
on Porosity
in Mixtures
of
G
O
px,
^
M
OC
o
px,
c
0)
o
»
Sands
Only s m a l l e s t p o r o s i t y
per strain size p l o t t e d
U n co n so lid a ted
6 S
Q
6
66
T h e s a g may h e a c c o u n t e d f o r
in te rstitia l
The
fillin g
low est p o r o s ity
£2#6 p e r
cent for
by th e
in
the l i g h t of
sm aller g ra in s
illu stra te d
s a m p l e 2V*
in th e m ixture#
in F ig u re 6 is
The s y s t e m
one o f
is rep re se n te d
a s jl
6 4
5 w i t h a g r a i n d i a m e t e r o f 0 * 6 9 5 mm#
The
25 25 25
s e c o n d l o w e s t p o r o s i t y i s one o f 2 3 * 4 p e r c e n t f o r s a m p l e
3U#
T h is system
is r e p r e s e n te d by 3
4
5
6 and a g r a i n
Tfir
d i a m e t e r o f G * 3 ? 3 mm.
The c o n d i t i o n s m e t b y t h e s y s t e m s c o m p o s e d o f
25 p e r
c e n t o f e a c h o f f o u r c o n s e c u t i v e g r a d e s se e m t o
represent
the g r e a te s t
d i s t o r t i o n ' of packing
in te rstitia l
of the
fillin g
la r g e r grains#
e x p e c t a sy s te m composed o f 5 g r a d e s
to have
the
w ithout
low est p o r o s ity #
but
One w o u l d
in e q u a l p r o p o r tio n
th is
does n o t appear
to
b e t h e c a s e * S a m p l e 2U w i t h a c o m p o s i t i o n o f Z 3 4 5 6
1 5 1 5 W IS' 2 5
a n d a g r a i n s i z e o f 0 * 5 6 3 mm* h a s a minim um p o r o s i t y o f
26*2 p e r c en t*
I n t h i s c a s e t h e n u m b er o f s m a l l g r a i n s
m u s t b e more t h a n s u f f i c i e n t
l a r g e r g r a i n s and r e s u l t i n g
to f i l l
th e v o id s betw een
i n some d i s t o r t i o n
p a c k in g accom panied by a c o rre s p o n d in g
the
of th e ir
in crease
in th e
poros ity #
As th e p r o p o r t i o n
in creases
la titu d e
th ere
in
is
less
o f sm all g r a d e s
and le s s void
the s iz e o f th e g rain s
s i e v e s becomes
less re s u ltin g
uniform siz e*
T h u s*
an in c re a s e
the curve
to
fillin g
larg e
grades
because
the
r e t a i n e d on t h e s m a l l e r
in g r a i n s o f m ore n e a r l y
t e n d s t o sweep b a c k to w a rd s
in p o r o s ity w ith a d e c re a se
in g r a in
size*
67
T here
is
one o t h e r t h in g
o f F i g u r e 6 w hich r e q u i r e s
of n ote about the cu rv e
i n t e r p r e t a t i o n and t h a t
w ide s p r e a d o f p o i n t s a b o u t th e c u rv e f o r
sizes
the
and the c l o s e c o n f o r m ity to t h e c u rv e
g r a i n s izes*
of g rain s iz e
( 1 ) The l a t i t u d e
p e r g ra d e p ro d u c e d by th e s i e v e m ethod o f
( 2 ) An e r r o r
grade s iz e ;
( 3 ) The a m o u n t o f v o i d f i l l i n g .
The a u t h o r
In th e m ethod o f e x p r e s s i n g
feels
may b e d i s c a r d e d b e c a u s e ;
th at
fit
some o f t h e
any re a so n a b le curve;
the curve produced
H o w ev e r*
in the
the second so u rc e
the curve
in
sm all g ra d e s
the
of e r r o r
{1} R e g a r d l e s s o f a n y g r a i n
s i z e w h ich m ig h t be a s s ig n e d *
about
g rain
in the sm all
i.e .;
se p ara tio n ;
to
larg e
the
The d e v i a t i o n may b e a c c o u n t e d f o r b y a n y
one o r c o m b in a tio n o f t h r e e e f f e c t s *
w ould n o t
is
in th e
lo w est p o r o s i t ie s
( Z } T he c l o s e c o n f o r m i t y
low est grad e s iz e s #
b o th t h e wide s p r e a d o f th e p o i n t s
th e l a r g e g r a d e s and th e c l o s e c o n f o r m ity
can be r e a l i z e d from t h e amount o f
v o id s p a c e a v a i l a b l e and th e amount o f t h a t s p a c e w hich
is f i l l e d
by t h e s m a l l e r g r a i n s
The E f f e c t o f G r a i n S i z e
U n c o n so l I d a t e d Sands*
p erm eab ility
of a m ixture*
on P e m e a b i l i t y o f U n i g r a n u l a r *
The e f f e c t o f g r a i n
in u n lg ra n u la r,
7* w h i c h d e m o n s t r a t e s
decreases
t h e p e r m e a b i 11t y a l s o d e e r e a s e s *
for
on
u n c o n s o 1 Ida te d sa n d s
In F i g u r e
p erm e ab ility
size
th a t as
the g r a in
eac h g ra d e or g r a i n s i z e
is
sh o w n
size
The s m a l l e s t
shows s u r p r i s i n g
u n i f o r m i t y a n d may b e r e p r e s e n t e d b y t h e e q u a t i o n ;
The
Effect
of
Grain
Size
on Permeability
in U n ig r a n u l a r ,
z£ >
Sanda
Only s m a l l e s t p e r m e a b i l i t y
per grain size p l o t t e d .
Unconsolidated
€8
so
0 9)® !'
19
•H
CQ
a b
CO &
U
i
o
'■O
®
S7g.7
—4
-CO
rO
o
aS C
<D
B
Q
69
b o g /C
— 3. /6
+
bog fO COr
(1 )
O. ¥ G G 3 /
where*
K
'
th e p e rm e a b ility
Q
= the g r a in s i z e
E q u atio n 2,
In D a r c y ’s
o f th e sam ple d e te r m in e d from
page 5 2 .,
* A l l l o g a r i t h m s u s e d i n t h i s p a p e r a r e common o r B r i g g s
lo g s o f t h e n a t u r a l numbers*
The n o t a b l e t h i n g
is
the
fact
about th e curve o f F ig u re
t h a t th e g r a i n s i z e can be so c l o s e l y p l o t t e d
as a fu n c tio n o f th e p e rm e a b ility w hile
th e sam ples v a r i e s
From t h i s
7
of
f r o m 3 0 * 5 8 p e r c e n t t o 39*1 p e r c e n t #
i t may be i n t e r p r e t e d
com pared t o th e
the p o r o s i t y
grain
size*
th at
t h e p o r o s i t y , w h en
has a s m a ll e f f e c t upon th e
min im um p e r m e a b i l i t y *
The E f f e c t o f G r a i n S i z e on P e r m e a b i 1 i t y
U ncoftso1 I d a t e d S ands *
p erm eab ility
illu stra te d
decrease
in M i x t u r e s o f
The e f f e c t o f g r a i n s i z e o n
in m ix tu re s
by F i g u r e
of u n c o n so lId a te d sands
8* w h i c h a g a i n d e m o n s t r a t e s
in p e r m e a b i l i t y w i t h t h e d e c r e a s e
A f a i r l y clo se c o rre la tio n
is
the
in g r a i n s iz e #
b e t w e e n g r a i n s i z e a n d m inim um
p e r m e a b i l i t y may foe d r a w n f r o m t h e e q u a t i o n s
LoS K
&
=
Log /.9 S
0
+
^ 9 SJL9 ° o.-V&ROl
U)
Th<’ •• i i'c o t .M
im n
S u e ’ on
Pnr moHbi ] lty
in
Mixtures
of
Only smallest, p e r m e a b il i t y
per &ram size p l o t t e d .
Un c o n s o l 1d a t e d . S a n d s
70
x g .a
w here,
K
=
the p e rm e a b ility
G
*
the g r a in s i a e
The s l o p e s o f
p rac tic ally
curve w ith
Id en tical*
th e a b sc is sa
in D arcy*s
H ow ever,
I n F i g u r e 8*
to the
left
the m ix tu re s
H ere a s
the g rain
In F i g u r e 6 ,
th e
7 and 3 a r e
In tersectio n
i n F i g u r e 7 h a s moved t o
p o sitio n
of e x p re ss in g
52.
the c u rv e s o f F ig u re s
of Its
for
E quatio n Z, page
from
size
The d i s l o c a t i o n
the
left
of the c u rv e
i s p r o b a b l y du e t o
and to
of th e
th e m ethod
in te rstitia l
fillin g *
t h e ZV s a m p l e , c o m p o s e d o f
Z 3
5 w i t h a g r a i n s i z e o f 0 , 8 9 5 ram* h a s t h e w i d e s t
Z 5 *Z5 t S Y s
d e v i a t i o n a n d t h e 3U s a m p l e p o s s e s s e s t h e n e x t l a r g e s t
T h i r d c om e s ZXJc o m p o s e d o f
d ev iatio n *
Z
3
4
5
6
To TS5 W *25 20
*
a g rain
size
o f 0 * 5 8 3 mm*
and
“
P ro b ab ly both su g g e stio n s f o r the d is lo c a tio n
of th e curve of F ig u re Q a re a c tiv e ,
stitia l
b e lief
the
fillin g
is h eld
because
fillin g #
a sam ple w i t h
in te rstitia lly
sin g le
Inter**
th e dom inant p a r t *
the curve has been d i s p l a c e d
The r e s u l t
T h is
tow ards
the g r e a t e s t
i s a low er p e r m e a b i l i t y
t h e sa m e g r a i n s i z e w h i c h h a d b e e n
fille d ,
than f o r
o ne c o m p o s e d o f b u t a
grade*
The e r r o r
be
th at of
l o c a t i o n o f th e sa m p le s w hich have s u f f e r e d
in te rstitia l
for
undoubtedly p lay s
but
illu stra te d
o n ly a fo u rth
In m ethod o f g r a i n s i z e
b y u s e o f s a m p l e ZV#
of th e sam ple and
b e tw e e n t h e grad© Z g r a i n s
e x p ressio n can
Here g r a d e Z r e p r e s e n t s
in t h a t p e r c e n t a g e c o n t a c t
is p r a c t i c a l l y
im possible*
The
1Z
dom inant or m a tr ix g r a i n s
T herefore*
and
o f som e s m a l l e r s i z e .
of grade Z a c t as
the g r a in s
im perm eable m asses
to p la c e
are
in th e p o r o u s m a trix *
the p e r m e a b i l it y ab n o rm ally
e x p re ss!o n o f the
i s o l a t e d non*porous
g rain
s i z e w hich
is
low f o r
th e volum e o f a f l u i d
one c e n l l p o i s e w h ic h w i l l *
p o r c u s medium w h ic h
d riv in g
pressure
is
ten d s
th e w eighted
used*
The E f f e c t o f P o r o s i t y on P e r m e a b i l l t y *
expressed as
T his
P erm eabl1 i t y
Is
havin g a v i s c o s i t y
of
i n one second*
on© c e n t i m e t e r
o f one atm osphere*
pass through a
on a s i d e u n d e r a
A lso*
th e dim ensions
o f p e r m e a b i l i t y w e r e d e t e r m i n e d t o be a d i a m e t e r s q u a r e d *
o r an a r e a *
w hich
is
e x p r e s s e d by t h e number and s i z e o f
the p o r e s
in
t h e medium w h ic h a r e
b o th ends
o f t h e sam ple*
in
com m unication w ith
S in c e p e r m e a b i l i t y is d e p e n d e n t upon th e
and s iz e
of th e p o re s o f the
r a t h e r c lo s e ly d en o tes
of
it*
H o w ev e r*
g rain
size.
v aried
is a lte re d
v aries
same t h i n g * m u s t b e a f u n c t i o n
to
in v erse p ro p o rtio n
the g r a in s iz e
is d e v e lo p e d from th e
in v ersely as
the p o r o s i t y
d e c re a s e d and t h a t
as t h e g r a i n s iz e *
by changes
or
the p e rm e a b ility *
I t was d e m o n s t r a t e d a b o v e t h a t
in creased as
b iliiy
th e p o r o s ity * w hich
t h e p o r o s i t y may be e i t h e r d i r e c t l y
In v ersely p ro p o rtio n a l
The
the
medium*
number
t h e perinea*
T h u s* when t h e p o r o s i t y
of g rain size,
the p e r m e a b ility
the p o ro s ity *
The d i r e c t p r o p o r t i o n
r e s u l t s when a sand*
73
w i t h i n w h i c h t h e r e a r e no a l t e r a t i o n ®
com pacted*
It
is
of g rain
p ro b ab ly e asy to v is u a liz e
size,
is
th a t a lo o sely
com p acted sa n d w ould have a h ig h p o r o s i t y and t h a t
the
and number o f t h e c h a n n e l s
of tran sm ittin g
flu id
In a l a r g e p e r m e a b i l i t y *
Then
w ould be l a r g e and r e s u l t
as the p o r o s ity o f
the s iz e
a
srae H
er
cap ab le
th e sam ple
size
is d e c r e a s e d by com paction*
and number o f t h e p a s s a g e s
decrease,
to r e s u l t
In
p e r sue ab i 1I t y *
A ctu ally
the p e rm e a b ility
o f th ese m o d ific a tio n s
of p o ro s ity ,
is
the r e s u l t
of both
and th e p o res i t y
r e p r e s e n t s a b a la n c e b e tw een th e amount o f c o m p a c tio n end
the s iz e
o f the
.The E f f e c t o f
F o r o s 1 t y on t h e F e r r o s a M l . l t y o f U n k i r a n u l a r *
Unconsolidated
m eab ility
g r a i n s w hich compose t h e sand*
$ands*
i s sh o w n on F i g u r e 9 b y s a m p l e s 2 I R ,
4 S t P , 5 S t F , a n d 0 3 tP*
sam ples v a r i e s
rep resen tin g
the g ra in
The. e f f e c t o f p o r o s i t y
size
S IR , 4IK ,
T h e p e r m e a b i l i t y o f a n y on© o f t h e
by com paction a s th e
the
upon p e r*
sam ple*
A lso ,
decreases*
the
A tab u lar
T able
ta n g e n t o f the
ta n g e n t d e c re a se s as
r e p r e s e n t a t i o n shows?
111
Sample No.
Mals—
Tangent
zm
15 °
*20
SIR
16 °
*28
4 IR
16 °
*28
45 tP
12°
*21
55 tP
10°
90
*17
SStP
lin e
. 15
7Y
SAMPLES
CONTAINING
BUT
ONE GRADE SIZE
P o r o s ity in
P e r c e n t.
So
P e r m e a b ility
D arcy*s
75
d iv e rsity
T he two v a r i a t i o n s
resu ltin g
o f the
o f th e sam ple g iv e
in d icatio n
as
sizes
some
o f t h e m eth o d t o employ in th e d e r i v a t i o n
fo rm u la f o r
resu lt
g rain
from c o m p a c tio n an d
the p e rm e a b ility *
o f an
the s iz e
increase
Add t o t h e s e
two f a c t s
i n t h e .minimum p o r o s i t y
of th e g ra in s
decreases,
s h ip c a n be s e e n betw een g r a i n s iz e *
of a
o f the
the
sam ples
and a c l o s e r re la tio n -*
p o ro sity ,
and
■ perm eabillty*
Q u a rtzite
S am ples*
© *!#, 2 Q i,
In F ig u re
3Q1# 4 Q t ,
9 th e rem aining sam p les,
3Q t, and 6Q t,
r e p r e s e n t sam ples
composed o f g r a d e s o f c ru s h e d q u a r t s i t e *
th ese
s a m p le s was t o
of p o ro sity ,
for
d eterm in e w hether or not
perm eabi1i t y ,
the c u r v i l in e a r
The p u r p o s e o f
the c o n d itio n s
and g r a i n s i z e w hich were v a l i d
t o s u b - r o u n d Iowa R i v e r a n d S t #
s a n d s w ould a l s o h o ld f o r
a very a n g u la r
sa n d *
The s a m p l e s w e r e p r e p a r e d b y c r u s h i n g
a hammer*
The s i e v i n g
sa m e a s w a s u s e d f o r
th e rounded sands*
sam ples d e m o n s tra te d
fo r p erm eab ility w ritte n
t h a t an
for c u rv ilin e a r
su b-round sand g ra in s
would r e q u i r e m o d i f i c a t i o n
w ith a n g u la r g ra in s *
A lso ,
are co m p arativ ely h ig h er,
n e ith e r as
large
sizes as fo r
It
the
th e m w i t h
p r o c e d u r e a n d a p p a r a t u s was t h e
The q u a r t z i t e
eq u atio n
P eter
t h e y show t h a t
and
nor as sm all
th at
and
fo r use
th e p o r o s itie s
the p e r m e a b i l i t i e s
are
i n t h e sa me r a n g e o f g r a d e
rounded g ra in s*
is p o ssib le
to account fo r the
latter
effects
76
from t h e
s i z e end sh a p e s o f th e
p o r o s i t y was
q u a rtz ite
i n c r e a s e d becau&et
t h e a n g u l a r g r a d e was s m a l l e r
than t h e c u r v i l i n e a r or
grade;
(Z ) The b r i d g i n g
in th e mass o f a n g u l a r g r a i n s #
I t sh o u ld
a co nchoidal
be r e m e m b e r e d t h a t q u a r t s p o s s e s s e s
f r a c t u r e w hich p r o d u c e d f l a k e s
o f the
The f l a k e s had two a l m o s t e q u a l d i m e n s i o n s a n d
qu& rt& ite*
a t h i r d w h i c h w a s m uch s m a l l e r *
The a v e r a g e - o f
t h r e e w ou ld be# a s s u m in g a s p h e r e
a g rain
T he
( 1 ) The a v e r a g e g r a i n o f
' sub-round g ra in o f the c o rre sp o n d in g
produced
g rain s#
of s m a lle r d ia m e te r than
to r e p r e s e n t
these
the. g r a d e *
th e g r a i n p ro d u ced by an
e q u iv a le n t g ra d e o f rounded g ra in s*
The r e d u c t i o n
on p e r m e a b i l i t y w a s p r o b a b l y d u e
t o tlie s h a p e a n d p o s i t i o n w h ich t h e f l a k e s assu m ed
u n i t o f packing*
rest#
the fla k e s
In s e e k in g
the m ost s t a b l e p o s i t i o n o f
p r e s e n t a broad#
of the flu id *
They w ould o v e r - l a p
g re a tly reduce
the s i z e
fiat
surface
lik e
m a t e l y 0*9 d e s p i t e an
th e flow
s h in g le s and
T h e maximum
g r a d e Z p e r m e a b i l i t y o f t h e q u a r t s it© s a m p le s
Iowa E l v e r a n d Si*
to
and number o f p o r e s w h ich would
c o m m u n ic a te w i t h t h e e n d s o f t h e colum n#
the
in th e
re la tiv e
to
P e t e r s a m p l e s was r e d u c e d a p p r o x i ­
in crease
in p o r o s i t y o f 5 p e r cen t*
The E f f e c t o f F o r o s i t y o n t h e P e r m e a b i 1 1 t y o f M i x t u r e s o f
U n co n so l Ida te d S a n d s*
The e f f e c t o f p o r o s i t y upon
p erm e ab ility
Is g r a p h i c a l l y
%Z, a n d
Here
13*
illu stra te d
t h e sa m e g e n e r a l
in F ig u re s
co n sid eratio n s
10#
II#
a r e found
Teat Staples
Containing
Permeability
Grade* " 2 *, " 3 ", " 4 ", "
5 ", and
77
Permeability
Darcy1a .
Test Samples Containing Grades "3 ”, " k ", " 5 ", and
78
Grades
Permeability
Test Samples Containing
79
F -ig tz
Permeability
Test Samples Containing Grades " 5 " and
80
^ g .1 3
to hold as
did
i n F i g u r e 9*
f o r a n y one sa m p le v a r i e d *
l*e*j
a decrease
the p e rm e a b ility
by com paction*
p o r o s i t y alo n g a ta n g e n t and t h a t
in cre ased w ith a d ecrease
th at
in the
w ith the
t h e minim um p o r o s i t y
g r a i n s i z e a c c o m p a n ie d by
In t h e p e r m e a b i l i t y *
Equ a t l . o n o f t h e
P erm eab ility
An e q u a t i o n f o r
th e p e r m e a b i l i t y fro m g r a i n s i z e and
p o r o s i t y was d e v e l o p e d f o r
f r o m O r a I n S i ze a n d F o r o s I t y *
sa n d s# having
t h e s h a pe© a n d
m W e n t w o r t h * C* K* * A s c a l e o f g r a d e a n d c l a s s t e r m s f o r
c l a s t i c sedim ents*
J o u r * G e o l * * v o l * 30* 1922* pp.* 3 7 7 - 3 9 2 *
surface
i r r e g u l a r 1t i e s
and St*
P eter
sim ilar
to
th o se found
i n Iowa R i v e r
sands*
The e q u a t i o n p r o p o s e d
is:
/ 6 t / 3 V < r -----
/ /s y o y
)
« i)
ft
where*,
K
= the c o e f f i c i e n t
of p e rm e a b ility
P
= the g ro ss p o r o s ity
Q
= the g r a in s i z e
expressed
in p e r c e n t
a s d e t e r m i n e d b y E q u a t i o n £*
page 52'
T an $
=
th e ta n g e n t of the
angle*
sam ple*
a lo n g w hich
move a s
the p o r o s i t y - i s
com paction*
for a p a rtic u la r
the p e r m e a b i l i t y v a lu e s
d e c r e a s e d by
az
D e r i v a t i o n o f th e E ouat.ion*
F igures
7# 8 ,
9#
From 'a n e x a m i n a t i o n o f
10# 11# 12# a n d 13# s e v e r a l
may b e e s t a b l i s h e d
from w h ic h an e q u a t i o n
b i i i i y may b e d e r i v e d
g e n eralitie s
for
t h e permea**
from t h e p o r o s i t y and g r a i n s iz e *
They a r e s
1*
tangent as
The
the p o r o s i t y
d e c r e a s e d by com paction*
The
p erm eab ility decreases as
3*
The
p e rm eab ility v a rie s
p o ro sity
the g ra in s izc.
in v ersely as
i s v a r i e d by c h a n g e s
the
In th e
size*
4*
as
is
d i r e c t l y alo n g a
Z•
p o r o s i t y when t h e
g rain
p erm eab ility v a rie s
the g r a in
The t a n g e n t o f t h e a n g l e o f S t a t e m e n t
s iz e decreases*
5 m From S t a t e m e n t s 2 ,
3,
a n d 4# t h e o r d i n a t e
i n t e r c e p t i o n o f th e com paction p o re s ity ~ p e rrae ah il i t y
i n c r e a s e s as
1 decreases
lin e
the g ra in s iz e decreases*
The e q u a t i o n o f a n y p a r t i c u l a r
s a m p l e may b e
e x p ressed ass
L Dg K *
Log P ~ Log
7an 0
(Z )
where#
K
~ th e c o e f f i c i e n t of p e rm e a b ility
P
= t h e g r o s s p o r o s i t y in p e r c e n t
1
- th e in te r c e p t o f the
Tan0
t a n g e n t on
theo rd in a te
= th e ta n g e n t o f th e com paction v a r i a t i o n
To make a g e n e r a l
an g le.
f o r m u l a o f E q u a t i o n 2# two
r e q u i r e m e n ts m ust be s a t i s f i e d ,
i.e .,
th o se
of S tatem en ts
63
4 a n d 5*
The v a r i a t i o n o f t h e
14 a n d t h e g e n e r a l
latter
i s shown on F i g u r e
s t a t e m e n t o f w h i c h may be e x p r e s s e d b y
th e eq u atio n s
CQ j 7" ~
/ 6 &3
3
/ O G-
(3 )
/./s-o *
S u b stitu tio n
Los
o f E q u a t i o n 3 in £ y i e l d s ?
/ . „ ■ / » - ('■“ * * *
7a>? pf
The r e f i n e m e n t o f S t a t e m e n t 4 i s
F igure
sise
15*
The v a l u e o f T an
by u se o f th e c u rv e or
Log7s.ti $
It
p o ssib le*
- /
is suggested
fi
i n d i r e c t l y by th e e q u a tio n s
o$ ./s +
(4)
lsog &
t h a t t h e c u r v e b e u s e d when
i n some s e r i o u s
m a t e r i a ls com prising
th e stu d y of a few in d u ra te d
sam ples*
T w e n t y - t h r e e sa m p le s were s t u d i e d
purpose of e s ta b lis h in g
ap p ly in g
w ere e s t a b l i s h e d
the v a l i d i t y
or
sand or sa n d sto n e
for
the
in v alid ity
of the
to u n c o n s o l i d a t e d m a t e r i a l s and w hich
above*
B r ie f ly stated *
the
From t h e
s a n d s * a t t e n t i o n was
tu rn e d to
p rin cip les
error
d r o p s b e l o w 0 * 3 5 inn*.
S t u d y o f t h e P e r m e a b i 1 i t y o f Some S a n d s t o n e s *
loose g ra n u la r
by
i s d e r iv e d from th e g r a i n
s in c e E quatio n 4 r e s u l t s
when t h e g r a i n s i e e
illu stra te d
th e m ath em atical
t e c h n iq u e s and
t e r m s a s d e f i n e d by t h e a u t h o r w e r e fo u n d t o be
8 V
The E f f e c t
o f the G rain S i z e
on t h e
O rdinate I n t e r c e p t
7 .0
5 .0
4.0
2.0
Grain
S ize
m.m.
2
4 5 6
20
In te r c e p t
Log 1 - 1 .6 4 - 3 4 5 -
ffig b T —
Hg. / v
30
40 90
8 f
The R e l a t i o n o f t h e G r a i n S i z e t o t h e Tan 0
1 .5
rfltTn
G ra in
S iz e
-5
m.iDo
0. 1
0.2
0 .3
0 .4
0 .5
.6
Tan 0
F- g. AT
.7 . 8 . 9 1 . 0
06
in ap p licab le
E q u atio n
I,
to the
study o f
p a g e 81 ,
is
i n d u r a t e d sands*
not v a lid
fo r sandstones*
However, an a t t e m p t e d c o r r e l a t i o n
( T a b l e IV a n d F i g u r e
Thus
16) r e s u l t e d
In th e
e q u a t i o n f o r p e r m e a b i l i t y from g r a i n
o f the d a ta
d e riv a tio n of an
s iz e and p e r o s ity *
The e q u a t i o n ,
QQ M
=
b o g / j p r * G e .* \ f f t j
~~ Le>S S 3 . £
(1)
0 ./6 7 3 8
w here,
0
-
w eighted g ra in
size
i n mm* a s d e f i n e d b y E q u a t i o n
£ , p a g e 52
C?6
-- p e r c e n t b y w e i g h t
o f th e g r a i n s o f g rad e 6
P@
= e ffe c tiv e p o ro sity
in p e r c e n t
K
= p erm eab ility
rep resen ts
in M illid a r c y * s
the b e s t e x p re s s io n of the
m e a b ility of the
co u ld
£3 s a n d s t o n e sa m p le s w hich
f*K f f e c t i v e D i a m e t e r 11*
o f p e r m e a b ility and p o r o s i t y a re
su b ject
em ployed
H ow ever,
to v a r i a ti o n
in th e
the sandstone
the
of d e fin itio n *
sam p les, an
The d e f i n i t i o n s
s t a b l e and n o t s u b j e c t
th ird fu n ctio n ,
foregoing
w h i c h was d e s i g n e d
per­
b e made f r o m t h e d a t a a t ha n d*
I n v e s t 1g a t i o n o f t h e
v ariatio n *
( * 0 0 1 D a r c y 1® ) ,
g rain
S ince
size,
is
the d e f i n i t i o n
s e c t i o n s was n o t a p p l i c a b l e
i n v e s t i g a t i o n was c a r r i e d
to d is c lo s e a n o th e r d e f i n i ti o n
te rm w h ich m ig h t be v a l i d *
to
to
out
of the
87
P erm ea b ility
Millidarcy*s
AS
1*04
0,0502
A13
15*05
0*158
A1S
18*9
0 ,8 5 - '
44
18*65
6,1
B4
1 8 ,6 5
7,09
1 8,76
7,71
45
19*81
12* 61
AS
81*91
18*76
B2
1 5 ,6
15*3
B9
17*0
33*7
B5
2 0 .5
34*6
BIO
86*6
3 7 .3
B8
0 2 .0 5
4 0 .7
B6
05,85
4 1 .7
B3
0 5 ,0
51 .3
A1G
0 7 .5
53,2
B1
0 1 ,9
64 ,1
All
0 5 .6
6 9 .8
A9
55*7
118,1
B7
25*9
163,4
45
35*9
1 81,0
47
rare fV
ra
VO
315*0
46
55*4
5 58.0
.
88
89
It
size
is d e s ira b le
th a t any e x p re ss io n of the g ra in
in v o lv e th e use of but a s i n g l e
fig u re
w ould th e n be r e p r e s e n t a t i v e
th e sa m p le and w ould c o r r e s p o n d t o
The d e v e l o p m e n t
figure*
Such a
o f t h e g r a i n s co m p risin g
the e f f e c t i v e
diam eter*
o f su c h a f i g u r e m ight be e i t h e r m ath em ati­
c a l or g raphical*
The two m o s t w i d e l y a c c e p t e d d e f i n i t i o n s
type a re
those
o f Hasen42 a n d S l l c h t e r 4 5 *
of th is
Hasen o r i g i n a l l y
42*
H a z e n , A l l e n * Some p h y s i c a l p r o p e r t i e s o f s a n d s a n d
g r a v e l s w i t h s p e c i a l r e f e r e n c e t o t h e i r us© i n f i l t r a t i o n *
M a s s a c h u s e t t s S t a t e B o a r d o f H e a l t h * T w e n t y - F o u r t h Ann*
R e p t * , 18 93* p* 451*
43*
S l i c h t e r , C# S * , U# S» Gaol* S u r v e y * W a t e r - S u p p l y
P a p e r 6 7 , pp.* 2 2 - £ 3 *
d efined h is
d i a m e t e r from a g r a p h i c a l s o l u t i o n ,
44
th e work o f w ils e y
, the S l i c h t e r d e f i n i t i o n
and s i n c e
effectiv e
44* M a v i s , F* T # , a n d W i l s e y , E* F * , A s t u d y o f t h e
p e r m e a b i l it y of sands
U n i v e r s i t y o f Iowa S t u d i e s , S t u d i e s
i n E n g i n e e r i n g , B u l l * 7 , 1936*
may a l s o
be d e te r m in e d g r a p h i c a l l y *
w ere em ployed a s
p lo ts
are
shown on F i g u r e s
It
accu rately
fu n ctio n s
can be seen
T h e s e two d e f i n i t i o n s
o f the p e r m e a b i l i t y and t h e i r
17 a n d 18 a n d i n T a b l e V*
t h a t the perm eab!X ity
e x p r e s s e d by e i t h e r
is not
t h e Hazen o r t h e S l i c h t e r -
The Hazen
E ffective
from Measured
Permeabil it y
in
M illid a r c y s
Size"
Grain
S iz e
So
•H
p p
fig- n
The
S lic h te r
(Wilsey)
"E ffectiv e
Size"
from Measured
Grain
Size
92.
Table V
Sample.
No*
S llo h te r (W ils e y )
P erm ea b ility
" E ffe c tiv e Diameter" " E ffe c tiv e Diameter" M illid a r c y fs
in m »m .
in m»m«
A£
. 0452
*0685
0.0502
A13
.0969
. 1344
0.152
A12
.106
.1562
0 .8 5
A4
.110
*150
6*1
B4
.0995
♦1319
7 .0 9
A1
*0955
.1355
7.71
A5
.1292
.1758
12*61
A3
*1229
.1615
12.76
BE
.084
.119
1 5 .3
B9
.1046
.1319
‘Xrs n
uO . t
B5
.1157
.155
34.6
BIO
.1813
.1446
3 7 .3
B8
.0968
*132
40.7
B6
.1319
*172
41.7
B3
.124
*155
5 1 .3
AlO
.1356
.1562
53 .2
B1
.1099
.137
6 4 .1
A ll
.1801
.1577
6 9 .8
A9
.133
.146
118*1
B7
.1099
*1452
163.4
A6
.1393
.168
181.0
A7
*1562
*172
315.0
AS
.1452
.159
558.0
93
W ilsey d e f i n i t i o n ,
to the
b u t ‘ that th e Hagen d e f i n i t i o n
lea st v a ria tio n .
S ince n e i t h e r
ex ercised s u f f ic ie n t accuracy,
i f any o th e r
d e fin itio n
was m o r e p r e c i s e *
For
o f the
th is
ex p ressio n s
I t was d e s i r a b l e
from a s i m i l a r
is s u b je c t
to disco v er
g rap h ical
so lu tio n
p u rp o s e p l o t s w ere c o n s t r u c t e d
siz e © w h ich c o r r e s p o n d e d to a
through a range of g r a in
minim um i n w h i c h 5 p e r c e n t o f t h e g r a i n s w e r e s m a l l e r a n d
a maximum i n w h i c h 6 0 p e r c e n t o f t h e g r a i n s w e r e s m a l l e r *
The r e s u l t s
o f t h e p r o c e d u r e were s a t i s f a c t o r y
In so f a r a s no g r a p h i c a l
d e fin itio n
of the e f f e c t i v e
d i a m e t e r c o u l d be fo u n d M ilc h was s u b j e c t
th an
ter
the d e f i n i t i o n
o f Ha gen*
Thus,
if
to le ss v a ria tio n
the e f f e c tiv e
diam e­
i s s o u g h t by e m p lo y in g c u m u l a t i v e p e r c e n t c u r v e s ,
Hasen d e f i n i t i o n
tim e i t
Is
the
lea st
In accu rate,
s h o u ld be rem em bered t h a t
but at
effectiv e
diam eter
is
em ployed as
t h e sa m e
the p e r m e a b ility
s u b j e c t t o w i d e e r r o r when t h e H a g e n d e f i n i t i o n
Its
the
is
of
only function*
■ StmtABY AND CONCLUSIONS
From t h e
foreg o in g
discu ssio n
the fo llo w in g
c o n c l u s i o n s a r e 3>elieved t o have b e e n s u b s t a n t i a t e d
types
o f san d from w hich t h e e m p i r i c a l
for
the
d a ta w ere g a th e r e d :
U n c o n s o lid a te d Sands
1*
In both u n ig ra n u la r and m ix tu res of g ra d e s ,
t h e minimum p o r o s i t y
However*
for
Increases
th e m ixed g r a d e s
m arked n o r so r e g u l a r
as
as
the
the g ra in
sise
decreases.
I n c r e a s e was n e i t h e r
in th e u n ig r a n tila r
sands.
so
94
2*
g rains
To a v o i d d i s t o r t i o n
in th e c o n ta in e r*
s h o u l d b e 10 0 t i m e s
3*
decreases
g rain
$ tze,
5*
the d ia m e te r of
of the g ra in s
As
As
the
g rain siz e
m ixed sam ples*
in creases*
th e p o r o s i t y d e c r e a s e s by com paction*
also
However* t h e p e r m e a b i l i t y
decreases*
d e c r e a s e s m uch m o r e r a p i d l y
of decrease of
used*
th e p o r o s i t y d e c r e a s e s by i n c r e a s e o f
t h e p e r m e a b l1 i t y
the p e rm e a b ility
siso
b ein g
u n lg r a n u l a r a n d t h e
the
o f the
the c o n ta in e r
The p e r m e a b i l i t y d e c r e a s e s a s
f o r both
4*
th at
In t h e p a c k i n g
than
the p e rm e a b ility
t h e p o r o s i t y and
i n c r e a s e s as
the r a t e
the g ra in
decreases*
6*
An e q u a t i o n f o r
d e v e lo p e d from t h e g r a i n
sise
t h e p e r m e a b i l i t y wa s
and p o r o s ity *
It
is*
/6Jy /O ff
/./ S ' o V
75/? 0
I n d u r a t e d Hocks
7*
The e q u a t i o n
s a m p l e s was f o u n d t o b e
8*
d eriv ed fo r
in v alid
the u n c o n s o lid a te d
f o r c o n s o l i d a t e d sands*
The Hagen d e f i n i t i o n o f t h e
^ effectiv e
d ia m e te r * was f o u n d t o h e t h e m o s t a c c u r a t e o n e w h i c h
c o u l d b e d e r i v e d when a s i n g l e
f i g u r e wa s s e l e c t e d
from a
cum ulative p e r c e n t c u rv e *
FURTHER RESEARCH
B efore
the
rela tio n sh ip s
of p o ro sity ,
g rain si^ e ,
95
a n d p a r m a a M 1i t y a r e
s e v e r a l problem s w i l l
A list
tio n
fin a lly
and c o m p le te ly e s t a b l is h e d *
have to be s u c c e s s f u l l y
o f t h e s e p r o b le m s w ould
of the p a r t i c l e s
of s i l t
in clu d es
in v estig ated *
( I ) an in v e s tig a ­
and c l a y s i s e s j
{Z ) t h e
d ev elo p m en t of a q u a n t i t a t i v e m easurem ent o f shape o f
p articles
g atio n
and th e e f f e c t o f shape;
o f the
rep resen ted
© mass o f
in v esti­
sand g ra d e s w hich m ight in c lu d e system s
b y two p e a k h i s t o g r a m s ,
less
(5) a f u r th e r
and system s
in w hich
t h a n ZO p e r c e n t o f t h e s a m p l e c o n s i s t s o f
one g r a d e *
The a u t h o r h a s
felt
to be th e r e l a t i v e
so lu tio n
o f th e problem *
liste d
th e s e problem s
im portance w ith r e s p e c t
in what i s
to a
96
S e lec te d B ib lio g rap h y
1*
D arcy* B, ,
rJL e s P o n t e i n a a P u b l l q u e s
D 1 J o n w, V i c t o r D a l m o n t *
P aris,
1865#
F a n c h e r * G, H« * a n d t e w i s * J»
flu id s
3*
10,
1933, pp.
G - r a t o n , L* C** a n d F r a s e r *
of sp h eres w ith p a r t i c u l a r
p e rm e ab ility :
pp.
* Flow of s im p le
through p orous m a t e r i a l s :
Z 5 9 No.
V ol.
Jour*
d© l a V i l i e cle
Ind.
Eng* C h m * *
1139-1147*
H* J . ,
S y s te m a tic packing
re la tio n
G e o l « * V o l*
to p o r o s i t y and
4 3 , Ho. 8 ,
765-909.
Ha s e n , A l l e n , Some p h y s i c a l p r o p e r t i e s
g ra v e ls w ith s p e c ia l re fe re n c e
n itra tio n s
Mass*
f o u r t h Ann, K e p t .,
5,
1935,
Johnson,
S tate
to t h e i r
Board o f H e a l t h ,
use
in
Tw enty-
1893*
T» W,.., a n d T a l i a f e r r o *
p., B, * F l o w o f a i r a n d
n a t u r a l g a s t h r o u g h p o r o u s m edia*
T e c h n i c a l P a p e r Ho* 5 9 2 ,
M u s k a t * M*, a n d B a t s e t *
porous m a te ria ls *
of sands and
B u reau o f M ines
1938,
H* G . * F l o w o f g a s t h r o u g h
P h y s ic s , V ol.
1# Mo* I ,
1 9 3 1 , pp#
£7-47.
M uakat*
F lo w o f Homogeneous F l u i d s , M c G ra w -H ill#
1936,
H e y n o I d s , O s b o r n e * On t h e
dynam ical
th e o r y of an
in co m p ressib le v isc o u s
f l u i d and th e d e t e r m i n a l io n o f
the c r i t e r i o n *
R o y a l Soc* L o n d o n * V ol* A - 1 8 6 ,
1 69 6 # p p ,
T rans,
1 £ 3 - 164,
97
§1Ic h te f . C«, Si. S. Gee1• 5u rv . 19th Ann* Hept*
1897-1898, pp, 305-325.
98
M&mDm
A© t h e e x p e r i m e n t a t i o n p r o g r e s s e d *
a p p a r e n t t h a t a p o r t i o n ot
as a receptacle:.;
i t became
t h e t h e e l a s h o u ld be r e s e r v e d
i n t o w hich c o u ld be
d a t a d e r i v e d from t h e p ro b le m .
c o llec ted
a ll
o fthe
S uch a s e c t i o n would,s e r v e a s a
a medium o f r e f e r e n c e t o w h i c h o n e m i g h t g o f o r a n y s o e c i f i e
in fo rm atio n r e l a ti n g
t o t h e d a t a upon w h ic h t h e r e s u l t s a r e
based,
W i t h t h a t f u n c t i o n i n m i n d , a n a p p e n d i x 1®
p ro v id ed w hich t r e a t s
in d iv id u ally
a ll
em ployed In t h e f o r e g o i n g e x p e rim e n ts#
in e re ss~ refe re n ee ,
For convenience
t h e sa m p le s a r e numbered in t h e
sam e m a n n e r a s was u t i l i s e d
are lis te d
o f t h e sa m p le ®
on t h e p r e v i o u s p a g e s a n d
i n t h e sam e o r d e r a s th e y w e re I n t r o d u c e d
i n t o t h e b o dy o f t h e t h e s i s *
99
S a m p l e No*
SIB
Grade S i z e s .
Grade
No.
Sieve
No.
Sieve
O pening
P e r c e n t by
We i g h t
R etain ed
1 . 9 8 1 mm.
1.
9*
2.
16»
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3*
32.
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4.
60,
.216
5.
115.
.124
6,
250.
. 0 6 1 ""
Pan
--------
7
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G
G r a i n Mean
L^W-HT
3
%
100
mm
1.422
n it
.775
ittr
tl
.369
nil
tt
.2 1 6
it It
.133
ft it
"
It
""
11
It
1.482
it it
mra9
P erm eab ility
K
1286.0
2. K
674.5
f!
3. K
5 25 #0
4. K
5* K
1.
Darcys
1.
.317
Tan
0
2 . Tan
0
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3* Tan
0
.335
536.0
u
4* Tan
0
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522.0
tt
5 , Tan
0
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- . 3 8 9 . ....
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Average
Gross P o r o s ity
1,
2,
4 0 .0
%
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3 5 .68
%
ft
4.
5 4.0
%
-
100
S a m p l e No,
5XK
Grade S i z e s ,
Grade
No,
Sieve
No.
Sieve
Opening
P e r c e n t by
W eight
R etain ed
1 . 9 8 1 mm.
1-.
9.
2,
16,
.9 9 1 ""
3.
32.
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4.
60.
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""
ft
5.
113.
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""
ft
6.
250.
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If
7.
Pan
«, «• ^
.
mm
%
.........
m
100
1.422 ""
"
773 ^^
.369 ,i"
.216
.775
titi
mm.
Permeab i l i t y
1. K
408,0
Darcys
2. K
386,1
ti
3. K
317,0
4. K
5. K
Tan
0
,326
2 . T an
0
.319
ft
3 . Tan
0
,324
259.9
If
4 , Tan
0
.320
255.3
If
5« Tan
0
,306
1,
A verage
Gross P o r o s i t y
L
4:0.2
2.
37*6
%
,n'»
.133
If
M
G
G r a i n Mean
Le^W-HC
3
3.
3 6.0
%
4.
55.42
$
101
S a m p l e No*
4IR
Grade S i z e s .
Grade
No.
Sieve
No.
Sieve
Opening
1.
9.
2.
16,
. 9 9 1 ""
tt
3,
32.
. 4 9 5 ,n’
ft
. 7 7 5 ft tr
4,
60,
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tt tt
5.
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tt it
6,
250.
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tt tt
7.
Pan
P e r c e n t by
We i g h t
R etain ed
1 . 9 8 1 mm.
___
G r a i n Mean
L+-W-KT
mm
%
_________________
100
1.422
it
tr
ti
mm mm mm mm
G
.588
tr n
mm.
Permeab i l i t y
1. K
117.3
D arcys
2. K
105.0
n
3. K
7 9 .4
4. K
5* K
Tan
0
. 247
2 . Tan
0
.244
it
3 . Tan
0
.244
7 0.9
ir
4.
Tan
0
.249
64 • 6
it
5 , Tan
0
, 236
1.
Average
•
G ross P o r o s ity
L
4 2 . 7 __ %
3*
30.2
2.
41*1
4.
3 6 .1
eg
5.
35.21
%
if tt
%
%
24 4
S a m p l e No.
4 B t »P
G-rade S i z e s .
Sieve
Opening
Grade
No.
Sieve
No.
1.
9.
1 . 9 8 1 mm.
2.
16»
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it
3.
32.
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it
4.
60.
• 216
5.
115.
6*
250.
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Pan
P e r c e n t by
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.
G r a i n Mean
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3
mm
A
.
1.422
ii
"
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n it
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ft
.216
tt tt
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it
100
tt it
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n ii
mm.
P erm eab ility
K
80*4
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1.
Tan
0
*236
63*25
ft
2 . T an
0
. 244
54*7
tt
3 . Tan
0
*238
4. K
47*65
it
4 . Tan
0
• 237
5. K
43*0
tt
5 . Tan
0
*258
2. K
3.
K
it
.775
G
1 .
m i
Average
G ross P o r o s i t y
,239
103
S a m p l e No.
531»F
G-rade S i z e s .
^ade
Jo*
Sieve
No.
Sieve
Opening
1.
9.
2.
16.
3.
32.
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it
4.
60.
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II II
tt
5.
115*
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till
7.
Pan
_M M
P e r c e n t by
We i g h t
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1 . 9 8 1 mm1.
. 9 9 1 ITIT
G
G r a i n Mean
L+*W-^T
5
mm
_____ ___ _ %
ti
1 00
1 .4 2 2
ti it
.7 7 5
it it
.3 6 9
it ti
"
.2 1 6
»i it
If
.1 3 3
it i i
II
«216
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flam9
P erm eab ility
Tan
0
*198
it
2 , Tan
0
.194
22*54
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3 . Tan
0
*189
4.. K
17*46
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4.
Tan
0
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K
16 *66
ti
5o Tan
0
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1. K
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K
3+
5m
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Average
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1,
42*9
<f0
2.
41^6
jg
3•
^
3 9 «°
%
104
S a m p l e No.
6 S t.P
Grade S i z e s .
S ieve
O pening
G-rade
No.
Sieve
No,
P e r c e n t by
We i g h t
R etain ed
1.
9.
1 . 9 8 1 mm.
2.
16*
■991 t!"
it
5,
32.
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ti
4,
60.
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5.
115.
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6 .
250.
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7-
Pan
-------------
..............
,
G r a i n Mean
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mm.
A
, .......................
100
1 .4 2 2
,Mt
J75
""
ti
,5 6 9
ti ti
tf
216
" !t
"
■135
If t!
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II
G
153
mm
P erm eab ility
1. K
1 1 .4
D arcys
1.
Tan
0
. 1 1 2 ____
2. K
8 . 87
it
2 . Tan
0
. 1 1 1 .........
3. K
6 .86
tt
3.
Tan
0
.094
4. K
6 .0 0
it
4.
Tan
0
5* K
5 .9 4
tt
5 . Tan
0
______
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Average
G ross P o r o s ity
Jj
2.
44 *
^
3. 40.5
%
43.1 _ %
4. 30.1
$
39.1
%
105
S a m p l e No.
TCt*
Grrade S i z e s »
G rade
No.
Sieve
No.
S ieve
O pening
1.
9.
2.
16,
, 9 9 1 ""
3.
32.
,4 9 5 ""
tt
4.
60,
«2l6
it
5«
115.
, 1 2 4 «"'
tt
6*
250.
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tt
7.
Pan
1 . 9 8 1 mm,
P e r c e n t by
W eight
R etain ed
G r a i n Mean
l +'W-ht
3
.... .............
%
mm
100
M
- it
186*0
D arcys
mm.
2. K
109*0
3. K
4. K
Tan
0
ti
2 . Tan
0
100*0
n
3 , Tan
0
90*4
tt
4.
Tan
0
n
5* Tan
0
5. K
1,
A verage
G ross P o r o s ity
I*
2«
415 »1
%
3.
41*9
%
^
4*
40*0
%
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tt
u
it i i
P erm eab ility
1. K
it tt
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G
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106
S a m p l e No,
G-rade S i z e s •
S ieve
Opening
P e r c e n t by
W eight
R etain ed
G-rade
No.
Sieve
No.
1.
9.
2.
16,
. 9 9 1 ""
3*
32.
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4.
60.
.216
5.
1 , 9 8 1 mm.
-
..........- ............... ..
G r a i n Mean
L'-W-HT
3
%
,
mm,
it
100
1.422
n it
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"
""
II
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115.
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6,
250.
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II tt
7.
Pan
-------------
0
11
II
I f It
mm.
P erm eab ility
1. K
69 ,6
2. K
6 2 * 0
D arcys
Tan
0
ii
2 . Tan'
0
ii
3.
Tan
0
4. K
ti
4,
Tan
0
5* K
ti
5 . Tan
0
3. K
56*6
1.
Average
.
G-ross P o r o s i t y
I.
2.
47*6
%
44*5
%
3 .
4.
*11.9
-
%
.
%
vlb
107
S a m p l e No,
40t*
G-rade S i z e s .
Sieve
Opening
P e r c e n t by
We i g h t
R etain ed
na d e
Jo.
Sieve
No.
1.
9.
2.
16.
. 9 9 1 M"
3.
32.
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4.
60.
.2 1 6
"»
5.
115*
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""
6.
250.
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7.
Pan
1 . 9 8 1 mm.
. . . . . . .
.....
mm ^
fa
n
1 . 4 2 2 n it
ti
100
.7 7 5
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II
02*0
Darcys
________ mm.
2. K
0 O'*4
3. K
46 « 2
1.
Tan
0
it
2 . T an
0
tt
3 . Tan
0
4. K
it
4.
Tan
0
5* K
it
5,. T a n
0
Average
G-ross P o r o s i t y
1.
2.
»0
%
3.
$
4.
5 .
%
4 7.7
.2 1 6
tt
tr
.1 3 3
tr
it
it ii
P erm eab ility
1. K
tt i i
:f 11
"
tt
« —-
G-
G r a i n Mean
3>W-HT
3
%
/2
S a m p l e N o , __ Sot...
G-rade S i z e s .
Sieve
No.
G-rade
No,
Sieve
O pening
P e r c e n t by
We i g h t
R etain ed
1.
9.
1 . 9 8 1 mm.
2.
16,
.991
3*
32.
. 4 9 5 11"
4.
60e
.2 1 6
G r a i n Mean
L+- Wt-T
3
mm
.... _ .....%
XX
II
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5.
115*
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6.
250.
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7.
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ii
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mm.
P erm eab ility
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1 . Tan
0
1. K
C U l ...
2. K
36*5
ti
2 . T an 0
3- K
30
t»
3 . Tan 0
ii
4 , Tan 0
tt
5 . Tan 0
4. K
5. K
_
it :
^ T1.J■’Vf.."’
-:1
Average
G-ross P o r o s i t y
L
03*1
%
49*6
%
3. 47»5
H"
n
%
$
109
S a m p l e No. _
G-rade S i z e s ,
Grade
No.
S ieve
No,
Sieve
O pening
P er c e n t by
We i g h t
R etain ed
9.
1 « 9 8 1 mm.
cf
......... A
.
16.
0991 ,,M
«
3.
32.
. 4 9 5 MU
4.
60.
.216
5.
1*
2
G r a i n Mean
L+-W-HT
3
mm
1 .4 2 2
ti
""
it
115*
. 1 2 4 »'■
ii
6e
250.
. 0 6 1 ,,ff
7.
Pan
*775 fl If
II II
.369
.2 1 6 If If
_____..... *{ If
----1 0 0 —
if
G
II If
mm.
Permeab i l i t y
1. K
16 .1 _
2a K
10*?
3. K
0*Gt>
4. K
5. K
Darcys
1,
Tan 0
ii
2 . Tan 0
n
3* Tan 0
ii
4,
ti
5 . Tan 0
Tan 0
Average
1 9 ti
G ro ss P o r o s i t y
I.
00. E
%
3*
%
2.
00.6
>S
4.
%
5.
%
M1!
110
BA
S a m p l e No,
Grrade S i z e s ,
G-rade
No,
Sieve
No.
1.
9.
2.
16,
. 9 9 1 ,l,f
3.
32.
, 4 9 5 ""
4#
60.
,2 1 6
5*
115.
.124
6.
250.
. 0 6 1 n”
7.
Pan
Sieve
O pening
P e r c e n t by
We i g h t
R etain ed
1 . 9 8 1 mm.
_ ............
G-rain Mean
L+"W+"T
3
mm
%
<LJ KrJ
66
«»
tl
ri,»
♦t
It
1.422
ir ir
.775
n i»
.369
ti i i
.2 1 6
it if
.133
ti ti
ti ii
If
a
.090
mm,
Permeab i l i t y
Tan 0
1. K
4 4 6 *5
2. K
r? p
e>
1/w'C'i &J
(i
2 , Tan 0
.275
2 44,4
tt
3.
3 . Tan 0
.2731
245.0
it
4 , Tan 0
.2714
tt
5 , Tan 0
K
4. K
5* K
Darcys
1.
*
Average
#2841
G-ross P o r o s i t y
I,
41 *4
2.
50 #4
^
4.
61 6 5
86 ,9 1
%
2 6 .V
%
Ill
Sam ple No,
BB
G rade S iz e s e
G rade
No,
S ieve
No .
S ieve
O pening
1 . 9 8 1 mm*
9.
1 .
P e r c e n t by
W eight
R e ta in e d
.
2 .
16
3.
32.
,495
4.
60.
.2 1 6
5.
115.
.124
6 *
250.
,061
7.
Pan
...
*99 1 n "
66
""
33
G
G r a i n Mean
L+-W-HT
%
mm
"
1 .4 2 2 'r,f
.775 !M
>
.569
»"
,J”
.216
,r M
""
*135 ,M
f
it tt
1*206
mm
P erm eab ility
1 .
Tan
0
*2 9 0
2.
Tan
0
,297
3.
Tan
0
*
it
4.
Tan
0
* 295
ii
5.
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0
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£346*0
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435*0
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4.
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ty
rp: #ZO
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G ross P o r o s ity
I.
35*6
%
3
2 9 .3
2.
31*4
/O
4
28*4
<•j
%
%
112
S a m p l e No,
2C
G-rade S i z e s *
Grade
No.
Sieve
No.
Sieve
Opening
9.
1*
1 .9 8 1
P e r c e n t by
We i g h t
R etain ed
mm.
G r a i n Mean
L+-W-KT
3
- *%
mm
2.
16.
. 9 9 1 rt ft
33
ii
3.
32.
.495
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33
ti
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4.
60.
*216
53
n
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113,
.124
tin
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6*
250.
.0 6 1
ntt
ti
.133
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7.
Pan
ii ii
1.422
II It
it
G
,855
mm*
Permeab i l i t y
1 .
K
376*0
D arcys
l . Tan
0
2.
K
289*0
«
2* T an
0
354*0
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5.K
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0
4* Tan 0
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0
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L
2,
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57*3
_________
%
3*
2 9 #96
%
52*85
%
4 ,
28,6
%
S a m p le No.
SC^
G-rade S i z e s .
G-rade
No.
1.
Sieve
No,
9,
Sieve
O pening
1 .9 8 1
P e r c e n t by
W eight
R etain ed
mm.
mm.
2•
16,
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113.
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1 .4 2 2
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itit
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155 ittt
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irit
mm
P erm eab ility
1. K
636.0
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1 • Tan
0
2. K
5 2 0.0
ti
2. Tan
0
.2903
3. K
3 0 3.5
tt
3 . Tan
0
.3007
4. K
289.0
tt
4. Tan
0
.2977
it
5. Tan
0
5. K
itu
A verage
G ross P o r o s it y
...29.5........
.2959
114
S a m p l e No.
gp
G-rade S i z e s *
G rade
No.
Sieve
No.
Sieve
Opening
P e r c e n t by
We i g h t
R etain ed
1 . 9 8 1 mm.
G r a i n Mean
Lh-W-KF
3
1.
9.
2.
16,
.991
3.
32.
.495
4,
60.
.216
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7.
Pan
.1 3 3 If II
II II
ii ii
25
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ti ii
75
»
1 .4 2 2
. 937
mm.
P erm eab ility
1 . K
73S .0
D arcys
2. K
4 0 5 .0
ti
3. K
3 3 7 .0
4, K
3 2 3 .9
5. K
ti ii
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mm
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0
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0
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5 . Tan
0
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Average
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Gross P o r o s it y
L
5 9.7
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3.
5 2 .55
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2.
5 4 .9 9
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4.
5 1 ♦2
£
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115
S a m p l e N o.
2B
G-rade S i z e s .
G-rade
No.
Sieve
No.
Sieve
Opening
P e r c e n t by
W eight
R etain ed
G r a i n Mean
L+’W-HT
3
/°%
1.
9.
1 . 9 8 1 mm.
2.
16.
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25
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ti rt
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P erm eab ility
1. K
180 . 6
2.
K
141*5
3. K
4. K
Tan 0
*294
If
2 . Tan 0
.288
1 1 1 .6
If
3 . Tan 0
.262
106.5
If
4.
If
5 . Tan 0
5. K
Darcys
1.
Tan 0
.2798
.2859
Average
Gross P o r o s it y
I.
35.6
%
3*
29.3
%
2.
32.3
%
4.
2 8.58
%
116
S a m p l e No.
SF
G-rade S i z e s *
G rade
10.
Sieve
G r a i n Mean
No.
Opening
u~ WKP
3
W eight
R etain ed
1*
9.
1.981 mm.
2.
16 *
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3.
32.
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50
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5m
115.
.124
6*
250.
.0 6 1
7.
Pan
--------
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ram.
*
tt
™
....151
mm.
Perm eab i l i t y
K
38 4.5
D arcys
2. K
269*0
3. K
4, K
1.
Tan
0
.270
tt
2 fe T an
0
.2742
22 3.0
tt
3* Tan
0
.278
19 7 .0
it
4* Tan
0
.266
t»
54 Tan
0
5. K
1.
.2720
Average
Gross P o r o s it y
L
5 4 .7
%
3*
31.2
2*
5 2 .2
%
4.
2 8 .3
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II II
tl
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Itt*
_
%
%
117
S am ple No,
EG
G rade S i z e s .
Grade
No,
Sieve
No.
Sieve
Opening
Per cent by
We ight
Retained
1.
9.
1.981 mm*
2.
16 *
*991 ",f
f>0
"
3.
32.
*495
25
"
4.
60.
>,216
r
Grain Mean
L*-W+-T
3
mm
7*
.........
1.422
HV
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115.
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250.
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itii
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997
ann*
Permeability
1, K
768*0
Darcys
21 K
382*0
u
3. K
323*0
ti
4, K
2 9 6 *9
(r
4. Tan 0
ii
5* Tan
5. K
1 . Tan
0
*2804
2 . Tan
0
,2814
Tan
0
*280
3*
* 27 9
0
.2802
Average
Gross Porosity
I.
8 0 .5
%
3*
30.19
2*
31 *S
%
4*
29*2
_%
. %
S a m p l e N o.
Grade S iz e s *
G-rade
No.
Sieve
No.
1 .
Sieve
Opening
1 . 9 8 1 mm.
9.
2.
16
3.
32.
4
.
P e r c e n t by
We i g h t
R etain ed
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M
60,
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115*
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6.
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7.
Pan
ur _ -m
v~ra
G
G r a i n Mean
l ^ w-kc
3
mm
1.422
.775
11
.369
.216
.133
mm*
Permeab i l i t y
Tan
0
.311
it
2 . Tan
0
.3179
3 98,1
tt
5 . Tan
0
.315
372.5
u
4„ Tan
0
.
u
5* Tan
0
1 . K
788.0
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2.
K
4 60.0
3.
K
4. K
5. K
1 .
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Average
Gross P o r o s i t y
I,
3 8 . 52
2.
34.
z
%
3.
32.06
%
4 .
3 1,1
ii tr
it it
it ii
it ti
u ii
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JL*£fL
ii ii
.
1°
1°
119
S a m p l e No .
El
G-rade S i z e s •
G-rade
No.
S ieve
No.
Sieve
O pening
P e r c e n t by
W eight
R etain ed
1.
9.
1 . 9 8 1 mm.
2.
16.
3*
G r a i n Mean
L+-W-HT
3
_____...........................
%
mm
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80
"
32.
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80
"
4.
60.
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5,
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ti
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tr
—
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mm.
P e r m e a b 11 i t y
1.058
w
704
3* K
608
4. K
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1 .. K
5* K
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0
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2 . T an
0
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t»
3.
Tan
0
.310
ii
4.
Tan
0
.3 1 1 5
ii
5. Tan 0
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.3079
Average
G-ross P o r o s i t y
I,
39,
68
%
3.
35,45
%
2.
3 5 . 72
%
4.
5 3 ,25
%
120
S a m p l e No.
SJ
Grade S iz e s <
Sieve
No,
G-rade
No*
Sieve
O pening
P e r c e n t by
We i g h t
R etain ed
1 . 9 8 1 mm.
1 .
9.
2.
1 6 *
.991
M II
32.
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4.
6 0 .
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5.
115*
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"
20
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it it
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II II
It
.3 6 9
tltl
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.2 1 6
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If II
II
.1 3 3
tl It
------G
G r a i n Mean
L+-W-HT
3
II
.9 0 5
If It
mm.
P erm eab ility
K
2 .
K
3 0 7 .a _
3.
K
3 0 3 .8
4. K
5.
Tan
0
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2 . Tan
0
.*288 . .
3.
Tan
0
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II
4* Tan
0
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5 . Tan
0
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1 .
2 9 4 .0
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it
M
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A verage
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G ross P o r o s ity
1.
59.7
2.
5 6 .79
%
%
3.
3 4 .4
%
4.
35.9
%
121
2K
S a m p l e No*
G-rade S i z e s .
Grade
No.
S ieve
No.
1.
9.
2 .
16.
3*
Sieve
O pening
1 .9 8 1
P e r c e n t by
W eight
R etain ed
mm.
G r a i n Mean
3
mm
. 9 9 1 ,,u
_____
60
52
»
1.422
it if
32.
. 4 9 5 ""
20
"
.775
it tt
4.
60.
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20
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it i t
5.
115.
.124
tt
.216 tt tv
6*
250.
.0 6 1
7.
Pan
m—**.—
G
””
If
.133
If
1*062
t t ft
mm.
Permeab i l i t y
1 . Tan
0
*
(i
2 . Tan
0
*2659
315.0
tt
3 . Tan
0
*292.
274.0
ti
4.
Tan
0
*£942
it
5.
Tan
0
K
652*0
Darcys
2. K
432.0
3. K
4. K
1
*
5. K
G ross P o r o s it y
56 . 0
Ja
2 . gl»5
%
3,
£886
*2901
Average
1.
II u
S 9.8
%
a e »8
%
122
S a m p l e No.
2L
G-rade S i z e s .
Grade
No.
Sieve
No.
Sieve
O pening
P e r c e n t by
We i g h t
R etain ed
1.
9.
2 .
16 *
.991
20
"
3.
32.
.495 n"
60
“
4.
60.
.2 1 6
""
20
11
5.
115.
.124
«"»
if
6 .
250.
.0 6 1
""
ti
7.
Pan
1 . 9 8 1 mm.
mm
%
_
1.4 2 2
. 823
.216
,133
ii h
ii if
ti ii
mm.
P erm eab ility
1. K
361.0
Darcys
1 o Tan
0
*2 8 3 4
2» K
242.1
ti
2 . T an
0
- 2 87 5
3. K
303.8
n
3.
Tan
0
.280
4. K
1 96.1
ti
4.
Tan
0
... .*2 7 9 4
it
5 . Tan
0
5. K
ii ti
. 7 7 5 tt ii
. 3 6 9 ti ii
ii
—
G
G r a i n Mean
L+-W8 T
3
Average
.8826
G ross P o r o s ity
I.
37*96
%
3,
3 1 . E5
. %
2*
34.1
/$
4.
30*75
. %
123
S a m p l e No. __21
G-rade S i z e s
G-rade
No.
S ieve
No.
S ieve
O pening
9.
1.
P e r c e n t by
W eight
R etain ed
1 . 9 8 1 mm.
G-rain Mean
L+-W-HF
mm
%
2.
16
*
. 9 9 1 H"
£0
"
3*
4.
32.
. 4 9 5 11,1
20 _
M
60.
.2 1 6
60
5.
115.
.124
.2 1 6
6,
250.
.061
7.
Pan
. 1 3 3 ,flt
itu
g
""
•
66 *
1.422
. 7 7 5 trtr
.569
mm.
P erm eab ility
1. K
261 *0
D arcys
1.
Tan 0
■ .2668
2. K
172*0
tt
2.
T an 0
.2718
3. K
1 4 5 .8
tt
3.
Tan 0
>268
4. K
115*1
it
4.
Tan 0
.8755
it
5 . Tan
5. K
0
________
Average
.8727
Gross P o r o s ity
L
07 .65
2#
*54 #4
%
0o
3,
58.24
jE
j.^
5 1 .55
Hft
%
tM>
124
S a m p l e No,
BN
G-rade S i z e s ,
G rade
No,
Sieve
No.
Sieve
O pening
P e r c e n t by
W eight
R etain ed
1.
9.
1 .9 8 1
2,
16,
.991
3.
32.
,495
,,n
40
4.
60.
.2 1 6
""
20
5.
115.
. 1 2 4 *,w
13
6,
250.
.0 6 1
ft
7.
Pan
M•»——
G
mm.
....... j. — ...
G r a i n Mean
L+-W-HT
3
mm
%
40
u
1 .4 2 2
. 7 7 5 it it
it it
____. 3 6 9
. 2 1 6 it tt
"
.133
It
%9 52
mm.
1 . Tan
0
,278
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2 . Tan
0
* 28 2
3 4 1,0
tt
3® Tan
0
.2772
329,7
it
4,
Tan
0
.2655
it
5 , Tan
0
636,0
D arcys
2. K
392 ,5
3. K
4. K
5. K
Average
.2757
Gross P o r o s ity
I.
37 *3
%
3.
3 1 ,2 2
2,
35 . 5 8
%
4.
3 0.7
it it
ii ii
Permeab i l i t y
1 , K
ti it
.
%
.
%
12 j
Sam ple No.
SO
G-rade S i z e s .
G-rade
No.
Sieve
No.
Sieve
Opening
1 .
9.
2 .
16.
. 9 9 1 ,MI
3,
32.
. 4 9 5 ""
4.
60.
.2 1 6
5.
115.
.124
6 .
250.
.0 6 1
7.
Pan
1 .9 8 1
mm.
...
M"
mm
%
________
1.4 2 2
2 0.....
"
.775
.... "
.369
If
,216
if ii
.133
ti ii
It
,nt
If
mm.
Tan
0
.2732
it
2 . T an
0
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it
3.
Tan
0
.
u
4,
Tan
0
.2flP.fi
5 o Tan
0
55 1.0
Darcys
2. K
4 1 4 .0
3. K
278*8
4.
049.0.
K
m
5. K
1 .
Sfil A
Average
.2784
Gross P o r o s ity
I.
37.6 5
%
2.
3 5 ,5
%
4.
5 . _________ %
n it
it ti
ii ii
P erm eab ility
1 . K
rt
"
40
.871
ii
40
___ _
G-
G-rain Mean
L+-W-HT
3
P e r c e n t by
W eight
R etain ed
32*72
.
%
31.9
.
%
126
S a m p l e N o,
BP
G-rade S i z e s .
G rade
No.
Sieve
No.
1.
9.
2 .
16,
. 9 9 1 ,r”
BO
"
1.4 2 2
3,
32,
. 4 9 5 18”
40
"
.775
tt tt
4,
60.
,2 1 6
""
40
0 369
i t 11
5.
115.
. 1 2 4 ""
H
it
.216
tr tt
6 .
250.
.0 6 1
tt
.133
it it
?.
Pan
Sieve
O pening
1 .9 8 1
P e r c e n t by
We i g h t
R etain ed
mm,
_______ __
G r a i n Mean
L+-W-KD
3
mm
_ %
»i
G
, 7 42
it ti
mm •
P erm eab ility
1 . K
438*7
D arcys
1 c Tan
0
,2592
2. K
269,0
is
2 . Tan
0
.2643
3. K
237*0
it
3.
Tan
0
.2643
4 . K
2 0 9.0
it
4.
Tan
0
.264
it
5.
Tan
0
5. K
h tt
A verage
......
G ross P o r o s it y
L
3 7 ,3
%
3.
32.72
.
%
2.
34 .1 3
%
4.
31.59
.
%
.2629
12 7
S a m p l e No*
&Q
G-rade S i z e s .
G rade
No,
Sieve
No.
Sieve
Opening
G r a i n Mean
L+-W-KT
3
P e r c e n t by
W eight
R etain ed
1.
9.
1 . 9 8 1 mm.
2 .
16,
, 9 9 1 ,nt
40
"
1 . 4 2 2 1H’
3.
32,
, 4 9 5 ,f"
BO
,r
. 7 7 5 M"
4,
60.
.2 1 6
,Mf
so
"
.369
3.
115.
,124
20
"
,2 1 6
6 *
250.
.0 6 1
7.
Pan
tl
»”
.841
ii
mm.
P erm eab ility
Tan
0
.306
ti
2 . T an
0
.8935
1 B1 . 6
tl
3.
Tan
0
.29 2 3
93*1
91
4 . Tan
0
.2816
5 . Tan
0
1 . K
170.5
2 . K
155*5
3. K
4. K
Darcys
ft
5* K
1.
A verage
.2933
Gross P o r o s it y
I.
3 5 .6
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S a m p le No.
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G-rade S i z e s .
Grade
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S a m p le No*
51
G rade S i z e s .
Grade
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S a m p le N o,
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159
S a m p l e No.
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S a m p l e No, __ 50
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Grade S izes*
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S a m p l e No,
5B
G-rade S i z e s .
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9*
2.
16 9
.991
it ii
II
3.
32.
.495
it ti
II
4.
60.
*216
n tt
5.
115.
.124
ti tt
6.
250.
.061
i*tt
7-
Pan
1 . 9 8 1 mm.
G r a i n Mean
L+'W+’T
mm
%
1.422
tt it
.775
it ii
tt
.369
n it
75
**
.216
it if
£5
"
.133
ti it
II
G
.195
ii
mm.
P erm eab ility
1.
D arcys
1 8 .8
K
1.
Tan
0
.197
2* K
15 .4 5
ii
2 . Tan
0
.1978
K
9*89
it
3.
T an
0
.1982
4. K
ti
4* T an
0
5. K
tt
5* T an
0
3.
A verage
*1977
G ross P o r o s it y
I.
4 5 .9
%
3,
2a
4 1 #o
%
4.
58*5
%
%
it
177
S a m p l e No.
5f
G-rade S i z e s 0
G-rade
No.
Sieve
No,
10
S ieve
Opening
9o
P e r c e n t by
We i g h t
R etain ed
1 . 9 8 1 mm.
%
ii
2.
16,
. 9 9 1 ""
3.
32.
.4 9 5 ""
4.
60.
.216
5.
115.
. 1 2 4 ""
6.
250.
.061 ""
7.
Pan
G r a i n Mean
3
mm.
1.422
n
.775
60
n
.2 1 6
SO
"
. 1 3 3 tttr
trit
II
„ . . 1 S 9 _ . am-
D arcys
1 . Tan
0
f 2 0 4 1 .........
1 3 .9
sf
2 . Tan
0
,1 9 0 9
3. K
11 *2
1?
3 . T an
0
.1991
.
4. K
10.15
II
4 ? Tan
0
.1985
..
II
5 , T an
0
1 7 . 9 ...
2. K
5. K
II II
.369
P erm eab il ity
1. K
II11
ii
" !I
<w«
G
IT1!
A verage
.1997
Gross P o r o s it y
I.
43
.6
%
3.
39.1
%
2.
40 . 6
%
4,
3 6 .3
%
1111
1 73
S a m p l e No*
5G
Grade S i z e s .
G rade
No,
Sieve
No,
1.
9.
1 . 9 8 1 mm,
2.
16,
, 9 9 1 11,1
_ .......... _ . %
vt
3*
32.
, 4 9 5 ,n’
ir
4,
60.
.216
it
5.
115.
.124
30
"
6*
250,
, 0 6 1 IMI
80
,f
7.
Pan
- - - -
Sieve
Opening
G
G r a i n Mean
L+'W’HT
3
P e r c e n t by
W eight
R etain ed
mm.
1.4 2 2
. 7 7 5 II II
II II
...... - 3 6 ^
,2 1 6 It W
.
-133
mm.
P erm eabil ity
1. K
12*63
2* K
9,84
ii
3. K
7 ,62
it
4. K
6 ,96
ti
4,
ti
5. K
Darcys
Tan
0
.1426
2 . Tan
0
.1345
3 . Tan
0
.1288
Tan
0
,1271
5 , Tan
0
1.
Average
__ . 1 3 3
Gross P o r o s i t y
j4
4 4 #65
2,
42
•3
(III
II II
ii
,149
MIt
%
3.
4 0 ,4
.
%
%
4,
3 9 .8
.
%
179
S a m p l e No.
AX
G rade S i z e s .
G rade
No,
Sieve
No.
P e r c e n t by
W eight
R etained
S ieve
Opening
1 .981mm.
G r a i n Mean
L+W^T
3
1 .
9
2.
16
.991""
%
it
3.
32
.4 95""
it
4.
60
.2 1 6 ""
5.
115
.12 4 ""
6,
250
.061""
5Z+2 -------
7.
Pan
-------
3 8 * 0 5 -----
E ffe c tiv e P o ro sity i r . r r
%
£UQ .......-
ii
it
4 0 * 6 -------------
ir
__________m.m.
1.4 2 2
" "
.775
" "
.369
11 "
.216
" "
......133. . " "
ti
P erm eab ility
m
M i l x l a a r c y 1s
S a m p l e No. ^2G-rade S i z e s .
Grade
No..
Sieve
No.
Sieve
O pening
P e r c e n t by
W eight
R etain ed
G r a i n Mean
L+W4T
1.
9
2.
16
*991"
-1-.422 it tt
3.
32
.495"
. 7 7 5 11 "
4.
60
.2 1 6 "
.369
5.
115
.124"
.216
6.
2 50
.061"
i n
7.
Pan
E ffe c tiv e P o ro sity
1 .981mm.
m.m
%
» "
If tl
P erm eab ility _ a ^ 5 0 3 _ ,
M i l l i a a r o y 1s
1 30
Sam ple no.
m
G-rade S i z e s .
G-rade
No,
Sieve
No.
1.
9 .
S ieve
O pening
G r a i n Mean
Ln WXT
3
P e r c e n t by
W eight
R etain ed
1 .981mm*
/»
2«
16
.9 9 1 ” ”
ir
3.
32
.495””
ft
4.
60
.216””
5.
115
.1 2 4 ””
6.
250
.061””
7*
Pan
E ffe c tiv e P o ro sity
5*82
3 1* 2
. 5 1 . 2 ....
11 * 2
17*5
%
ti
it
ir
m. m
1 .4 2 2
" "
.775
" "
.369
" "
.2 1 6
" "
.133
" "
ft
P erm eab ility
1 2* 7 6
M i l l i d a r c y 1s
A4
S a m p l e No*
G-rade S i z e s .
G-rade
No.
Sieve
No.
S ieve
Op en i n g
P e r c e n t by
W eight
R etain ed
1 .98lmm
d r a i n Mean
L+W+T
1.
9
2.
16
.991"
.U t2 2 .
3.
32
.4 9 5 "
.775
4.
60
. 216 "
5.
115
.124"
6.
250
.061"
7.
Pan
E ffective P o ro sity
m.m.
%
If
t|
If
If
II tt
.216
4 8 .1 5
” 11
*133 11 ”
1 7* 6
17*6
%
P erm eab ility
6 .1
M illid arcy ' s
181
S a m p l e No*
G-rade S i z e s .
G-rade
No,
Sieve
No.
Sieve
O pening
1*
9
2.
16
3*
32
* 9 9 1 m"
#4 9 5 mii
4.
60
.216”"
5.
115
.124""
6.
250
.06 1 ""
7.
Pan
G r a i n Mean
L+W+T
P e r c e n t by
We i g h t
R etained
‘jf
/»
1.981m m.
1 .422
"
.775
”
. 216
"
.133
"
A . 27
4 4.8
P erm eab ility
E ffe c tiv e P o ro sity
m. m
1 2 .61
M i l l i d a r c y *s
S a m p l e No.
G rade S i z e s .
G rade
No.
Sieve
No.
Sieve
Opening
1 .981mm.
1.
9
2.
16
.991""
3.
32
,4 95 ""
4,
60
. 2 1 6 ""
5.
115
.124""
6
.
250
.061""
7.
Pan
-----------
E ffe ctiv e P o ro sity
P e r c e n t by
W eight
R etained
2 8 .3
%
G r a i n Mean
L-W-vT
3
m.m
%
ii
ti
-1*422
" "
.775 " "
ii
.369
12 * 8
ii
.216 " "
30.1
ii
0 .3 2
6 .7 2
ii
P erm eab ility
1 31.0
M i l l i d a r c y 1s
132
S a m p l e No* ..AT.. Grade S iz e s ,
Grade
No,
Sieve
No.
S ieve
O pening
G r a i n Mean
P e r c e n t by
We i g h t
R etained
L+W^T
3
1 .
9
2 .
16
• 9 9 1 ,tu
11
1.422
" "
3.
32
.495""
11
.775
" "
4.
60
• 2 1 6 1,11
11
.369
" tf
5.
115
. 1 2 4 utt
1 .6 * 0
"
.2 1 6
” "
6 ,
250
*0 6 l ,f"
80*1
"
.133
H ,f
7.
Pan
E ffe c tiv e P o ro sity
S a m p l e No.
1 •981mm.
m.m.
_ ........ - %
__ -3 *3 6 "
2 Q . 7 __ %
P erm eab ility
315*0
M i l l i d a r c y *s
A8
Grade S i z e s .
G rade
No.
Sieve
No.
Sieve
Opening
1.
9
1 .981mm.
2.
16
.991""
3*
32
.495""
4.
60
.216""
5.
115
.124""
6.
25 0
7.
Pan
P e r c e n t by
W eight
R etained
. _| .. .... ...r /**
it
G r a i n Mean
...L-vW+T
j
.
m.m.
1.422
" "
11
.775
" "
11
.369
1 4,36
“
.216 " "
. 0 6 1 " 11
80.. 1
"
*J -T-Z *» t<
-------
___ 5 . 6 . ■
"
E f f e c t i v e P o r o s i t y __ 3 2 * 1
%
Perm eability
533*0
M i l l i d a r c y 1s
183
S a m p l e No*
G-rade S i z e s .
G rade
No,
Sieve
N o.
S ieve
Opening
G r a i n Mean
L-W^T
P e r c e n t by
W eight
R etain ed
1.
9
1 . 98lram
2.
16
• 9 9 1 f,,t
3.
32
.4 9 5 "”
4.
60
5.
m.m
1.21
1 .4 2 2
. 2 1 6 11,1
3.* 21
. 369
115
. 1 2 4 ,n!
4 .8 4
6*
250
• 0 6 l ,MI
7.
Pan
E ffe c tiv e P o ro sity
S a m p l e No.
51#2
%
"
.216
"
8 2 .8
"
IX . 2
11
P erm eab ility
1 18.1
M i l l i d a r c y 1a
AlQ
G-rade S i z e s .
G ra d e
No.
S ieve
No.
Sieve
O pening
G r a i n Mean
L+W4T
3
1.
9
2.
16
.99 1 ""
3.
32
.495""
4.
60
. 2 1 6 ""
5.
115
.124 ""
22.5
"
...369 it
.216 ti
6.
250
.06 1 ""
61.9
"
.133 tt
-------
9*2
7.
Pan
E ffe ctiv e P o ro sity
1.981mm.
P e r c e n t by
W eight
R etained
2 2 *6
%
.... ...
%
it
ii
6.42
"
P erm eab ility
-m
.1*422 ii
.775 it
53*2
M illid a rcy ' s
134
S a m p l e No*
G-rade S i z e s .
G-rade
No,
Sieve
No.
Sieve
O pening
1.
9
2.
16
.991,nt
3.
32
.4 9 5 ””
4.
60
*2 1 6 ,MI
5.
115
. 1 2 4 ,Mf
6
.
250
• 0 6 1 H"
7.
Pan
S ffe c tiv e P o ro sity
G r a i n Mean
L-W+T
P e r c e n t by
W eight
R etain ed
1 .98lram.
m. m
%
it
1.422
.775
.369
0*1
.2 1 6
6 1 .4
±121
1 2 .5
2 0 ,2
%
P erm eab ility
6 9*8
M illid arcy rs
S a m p l e No. __A12_
G-rade S i z e s .
Grade
No.
S ieve
No.
Sieve
O pening
P e r c e n t by
W eight
R etain ed
1.
9
1.9 81m m .
2.
16
• 9 9 1 ,m*
3r
32
.495”"
4.
60
. 2 1 6 ,IM
5.
115
.1 2 4 '™
2 3 .8
"
6.
250
, 0 6 l 1111
5 5.5
11
j m
P an
-------
19*2
"
S ffe c tiv e P o ro sity
1 7 »Q1 %
G r a i n Mean
I>W4T
3
m
..................- %
it
1.4 2 2
ii
tt
.775
u
,
P erm eab ility
-2SSL
.216
it
tt
tt
0*85
M i l l i d a r c y 1s
185
S a m p l e No. _ ■AX3
G-rade S i z e s .
G-rade
No,
Sieve
No.
Sieve
Opening
G -rain Mean
L +W-*-T
P e r c e n t by
W eight
R etained
1.
9
2.
16
•991""
1 .422
3.
32
.4 9 5 ""
*775
4.
60
. 216""
.369
5.
115
.124“"
1 2.0
.216
6
.
250
. 061""
£ 2 *2 .
. 133
7.
Pan
S ffe c tiv e P o ro sity
S a m p l e No.
1 .9 8lm m .
m. m
/*
25 A
16*6
%
P erm eab ility
0 .1 5 2
M i l l i d a r c y *s
31
G rade S i z e s .
G rade
No.
S ieve
No.
Sieve
O pening
1.
9
1 .981mm
2.
16
.991""
3.
32
.495""
4.
60
. 2 1 6 ""
5.
115
.124""
6
.
250
. 061 ""
7.
Pan
E ffe c tiv e P o ro sity
25#3
%
P e r c e n t by
W eight
R etain ed
„
G r a i n Mean
L+W4T
m.m.
%
II
*i
775
1.0
II
>369
.2 1 6
6 1 ^SL
P erm eab ility
-133
64 .1
M i l l i d a r c y 1s
130
S a m p l e No,
32
Grade S iz e s .
G rade
No,
Sieve
No.
1.
9
P e r c e n t by
V7e i g h t
R etained
Sieve
Opening
1 ,981mm.
G r a i n Mean
L +W+T
m.m
%
2.
16
.9 9 1 '"'
1 .4 2 2
H "
3.
32
.4 9 5 '"'
.775
M"
4.
60
. 2 1 6 ""
1 *9
.369
» "
5.
1X5
.124""
5*9
,2 1 6
» "
6.
250
. 061 ""
48*1
. 13 3
ft
7.
Pan
S ffe c tiv e P o ro sity
S a m p l e No.
H
44*0
25*0
%
P erm eab ility
15*5
M i l l i d a r c y *s
Bg
G rade S iz e s .
Grade
No.
Sieve
No.
S ieve
Opening
P e r c e n t by
W eight
R etained
1 .98lmm.
G r a i n Mean
m.m.
1.
9
2.
16
.991""
3-
32
. 4 9 5 ”"
4.
60
,216
5.
115
,124” M
11*8
.2 1 6
6.
250
.06 1"”
71*5
111
7.
Pan
S ffe ctiv e P o ro sity
%
ti
1.422
" M
.369 V *
11
"
tt
ti
16*7
22*4
%
P erm eab ility
51*3
M i l l i d a r c y *s
137
S a m p l e No,
G-rade S i z e s .
G-rade
No,
Sieve
No,
S ieve
O pening
P e r c e n t by
We i g h t
R etain ed
G r a i n Mean
L*W-T
1.
9
1 .98lmm
2.
16
.991""
1.422
" "
3.
32
.495"”
.775
11 "
4.
60
. 2 1 6 ""
, 36.9
""
5.
115
.124""
6.
250
. 0 6 1 ""
7.
Pan
E ffe c tiv e P o ro sity
m. m
%
0.6
S
bSL
.2 1 6
"
.155
""
"
s i.
*8
%
P e r m e a b i l i t y ■■Hill, ,#|
7 ..............
09
g,i
M i l l i .dar
d a rc y ’s
S a m p l e No.
G-rade S i z e s .
G-rade
No *
Sieve
No.
Sieve
Opening
P e r c e n t by
W eight
R etain ed
1 .981mm.
G r a i n Mean
L-+W+T
m.m.
1.
9
2.
16
.991,M
3.
32
.495'"
4,
60
. 2 1 6 Mf
1*7
5#
115
.124,M
23*5
.216 11
6.
250
. 0 6 1 1,1
58*6
.133 " "
7.
Pan
E ffective P o ro sity
%
M
JU.4.22., " tt
.775 ” ”
.569
"
16*8
2 3 .8
%
P erm eab ility
3 4 .6
M i l l i d a r c y 1s
138
S a m p l e No.
G rade S iz e s .
G rade
No,
S ieve
No.
1.
9
P e r c e n t by
W eight
R etain ed
S ieve
O pening
1 .981mm.
G r a i n Mean
L+W+T
m.m
%
2.
16
*991""
1 .422
" "
3.
32
.4 9 5 "”
.775
" "
4.
60
. 2 1 6 ""
.369
" "
5♦
115
.124""
3-CU&
.216
"
.
250
t0 6 l""
59*5
,r
.133
" "
7.
Pan
1 0 .4
"
6
E f f e c t i v e P o r o s i t y __ 2 5 * 2
S a m p l e No*
%
P erm eab ility
"
4 1 .7
M i l l i d a r c y *s
&7
G rade S iz e s .
G rade
No .
S ieve
NO.
S ieve
O pening
P e r c e n t by
W eight
R etain ed
G r a i n Mean
L+W+T
m.m.
1.
9
1 .98lmm
2.
16
.9 9 1 ""
3.
32
.4 9 5 ""
.775
4.
60
.216""
.369
5.
115
.124""
4 ,6
.216
6.
250
,061""
7 5.0
122.
7.
Pan
S ffective P o ro sity
%
if
JLtAS.iL.
it
»i
" "
"
"
it
it
19*5
2 2 .7
^
P erm eab ility
1 6 5 .4
M i l l i d a r c y 1s
189
S a m p l e No.
88
G-rade S i z e s .
G-rade
No,
S ieve
No.
1 ,981mm.
1.
9
2.
16
*991” "
3.
32
. 4 9 5 IHf
4.
60
. 2 1 6 " 11
0 .7
5.
115
. 1 2 4 t,,f
4 .1
6.
250
.0 6 1 ”"
7.
Pan
S ffe c tiv e P o ro sity
%
m.m.
%
ii
..... X0,5__._
2 4.9
21*8
G r a i n Mean
L +W*T
3
P e r c e n t by
We i g h t
R etain ed
Sieve
O pening
1.4 2 2
" "
it
.775
" "
ti
. 369
" "
. 216
" "
.133
" "
m
ir
u
P e rm eab ility
4 0 .7
M illid arcy rs
S a m p l e No,
G-rade S i z e s ,
G-rade
No,
Sieve
No,
Sieve
O pening
P e r c e n t by
W eight
R etained
G-rain Mean
L+W+T
%
m.m
1.
9
1 •981mm
2,
16
.9 9 1 ""
3.
32
.4 9 5 ""
Q»2
'»
. 7 7 5 11 "
4.
60
. 2 1 6 ""
0 ,4
"
5.
115
.124""
4 .9
569..." . "
It II
6.
25 0
. 0 6 1 ""
62.0
7.
Pan
E ffective P o ro sity
\\
1.4 2 2
M It
rt
it
52.5
1 8 /9 6
%
P erm eab ility
33*7
M i l l i d a r c y 1s
1?G
S am ple So.
_g10_ .
G rade S iz e s .
G rade
No,
S ieve
No.
P e r c e n t by
W eight
R etain ed
Sieve
O pening
1 .
9
1 . 981mm.
2 .
16
. 9 9 1 " 11
3.
32
. 4 9 5 ""
n
4.
60
. 2 X6 " "
it
5.
115
.124""
7 rQ
250
. 0 6 1 ""
74*0
ir
Pan
-
18*4
ti
6 .
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