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Characterization of Pore Structures in a Volcanic Rockfrom Permeability Measurements
Yuhta SHIMIZU῍ and Tohru WATANABE῍῍
We propose a new method for estimating pore structures of volcanic rocks. Permeability of ascending
magma controls the escape of gas, and greatly a#ects the style of eruption. The interconnection of bubbles inmagma must play a key role in controlling the permeability. However, the mechanism of their interconnection
has been poorly understood. In order to understand it, we must have a good understanding of pore structures involcanic rocks. A volcanic rock has a wide variety of pores in size and shape. The conventional equivalentchannel model is not useful for estimating pore structures from permeability. We thus have made a newpermeability model for volcanic rocks. Our model is composed of a bundle of parallel identical tubes. Each tube
is made of serial two circular tubes with di#erent radii. The two radii, the length fraction of narrow tube and theseparation of tubes are parameters of characterizing pore geometry. Tube radii can be estimated throughmicrostructural observation, and other two geometrical parameters can be constrained from measured permeability and porosity. We applied this method to rock samples from Mt. Yakedake, and found that the permeability
is mainly determined by narrow parts, the length fraction of which is less than *.+. Although uncertainties areleft in the estimation, we can obtain a reasonable structural image. Electrical conductivity and other physicalproperties can provide us with additional information to constrain geometrical parameters.
Key words : permeability, pore structure, bubble, escape of gas+ῌ ῐ ῎ ῑ ῏&'()*+,-'./01 +231456789:;<;=>?8@A=BC8=DE9 F =:FGFHIJA=K48L.MNOP6◊Q4RSTU+VW6 XWY Jaupart and Allegre,@ABCHIJAZ[\:FHIJA=K2+]^8+33+ ;<;4_K'./6`a*bc9 ;<;=>'. F d=()efghijk.Rl (Eichelberger?4mnop4[q r_ as tu8/nvw+l

et al., +320 ; Klug and Cashman, +330 ; Melnik and Sparks,

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Graduate School of Science and Engineering, University of Toyama, Gofuku -+3*, Toyama 3-*ῌ2///,
Japan.
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Department of Earth Sciences, University of Toyama,
Gofuku -+3*, Toyama 3-*ῌ2///, Japan.
Corresponding author : Tohru Watanabee-mail : twatnabe@sci.u-toyama.ac.jp

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Fig. +. The relationship between permeability and porosity reported in previous studies. Eichelberger etal. (+320) measured the permeability of Obsidian
Dome and related rhyolite samples (solid circles).
Measurements of Klug and Cashman (+330) weremade on pumice, tu#, blast dacite, and submarine
material (open circles). Saar and Manga (+333)
measured the permeability of basaltic andestite
ﬂows and cinder cones in the Oregon Cascades(triangles). An empirical power-law relationshipproposed by Klug and Cashman (+330) is also
shown.

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Channel Model) Q _C*+,

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106ABCDEFGHIJ , KL

M%

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107

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9XY1Z[U\  $%&']^ l 7 G (-+) 9IJ,]^ l _()* b ?@+,`a23!"#$%&']^ l* Ubc

Fig. /. (a) The relation between the length fraction of narrow tube x and the radius ratio b for various t (xῌbῌt
diagram). The parameter t denotes the ratio of the measured radius r to the uniform radius r*. Circles
indicate estimated values of x for samples NPFD-+ and NPFD-0. (b) The relation between the tube
separation l and the radius ratio b for various t (lῌbῌt diagram). The tube separation is normalized by theseparation l* calculated for the uniform radius tube model. Circles indicate estimated values of l/l* forsamples NPFD-+ and NPFD-0.

! 

108

Table +. Density, porosity and permeability of rocksamples.

"#$ %$&'()
2
(ῌ)

b

*+, x -./01 l 

345 678#-9:
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2<6=#> ?

b

= @A6BC6DE (Fig. / (a)) %$&'() +, x BC6DEF &'() * G6H I
2

2

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1l

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(῍)

rr* (t+)b;,

J (--) *K , L )MN& G  $8&'() 9 ;,
01 *  2b 6>O :G %$8&'() 9 ;,
 %$

2P7QG 01R STUVN  99WXYZ [\]^6O

Fig. 0. Porphyritic texture of samples from Mt.Yakedake : (a) NPFD-+ and (b) NPFD-0. The lengthof a scale bar is , mm. Pores are colored blue withdyed-resin. Images are captured with a transparentlight image scanner. Abbreviations are Pl, plagioclase ; Bt, biotite ; Hb, hornblende ; Qz, quartz.

. 
.ῌ+ 

_`   abc

6!O"#[d$%&'ef]ghi j( )2 ,/ mm

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

k*+ ,6 l$h 9K l

mm 6m#k*+,^ 9 [d$ - $.n/o 034efk*+p8

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C®U +/. ¯X#$  ]g6A&+$. (Qῑ) I

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O9 F$ ^W w n/ [86-~16\$³6 ´ g µ¶] ·^g g¸n/ _¹ Phigh -./ Plow  MFX

6´ g\$9ºI#$ Z° »¼
F$ +/ mm `=6aO ½  ῌPhigh Plow῎Q P Qῑ
low
῍
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,

"#$%&'()*+,

Fig. 1.

-./A schematic of permeability measurement system.

 .0$%1234 ,<=

NPFD-+ 567 , 891: ;<= .0>"/?

@AB CD >1. " E#>FG (,*) FHIJ
2#

KL= HM

*+ E/ NO P. PQ=R2;S/ TUVK1 H M W<21

XYQ" ZR= [\<=]^34H >_`,** kPa

109

P .5abHno  p  >H

qr<1 IJ>s Wannier,.ῌ- 

>cR de f-=ghijklm r*
t5uvw l*ZR xyz{| ,῍-῍,+300 FHtB]^34p h(+*0 Pa · s) >

  (,2) (,3)  f}~G T X<25e0 (Cole and  g

Wakeham, +32/)

P G/ /  !ffcn fg
 ftt

<=ghp

> +ῌ P#z4i y=R ABS  m,/ mm, e -* mm 4|4 m *.+ mm. D> g+  yk f  + ῌ -   t  + <2RA4 " : : /.*+*+. m, 

ijklm r* t5uvw l*

"#

e

KL= =H

M> +*῍+** kPa X> +*῍+** kk P6
+*+. m, 

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-./c=5

fcngfh-.1*.*.1T

+*/ Pa · s

ffcnῌtP¡ Q0="> (/./*./)

P6 ©M +*ῌ

:fª<= ©M>¬<2H M­®WYQsQ¯ °ZR= (Table ,) df-=gh m *.0 D=> 0 mm ijk

l/vw . D=> .* mm11¢k£/Q0 .0>¤¥)¦§¨ (Fig. 0) ~<2
PD67«¤ P g t5u

yk f, ± "kk ².> N t > 107³ / <1 P/P «¤#.0Q

 (*.**+  +* cm- /s) t5

uNH M (++** kPa) YQ .z4 #
N""¹> +*+0+*+* m,º»"Y !¸<2t.  (,2) (,3) 56

P

Table + ; > , ¯ ¼½#<YL=/ "> NPFD-0 /5L2´µ r* ¶ l* 

r*

ῑ
ῌ῎
t ΐ ῌ ῐ῎ l*fg
῔ ῍῏ ῔ ῒῒ/·c89:;< 

110Table ,.

  g +

Estimated geometrical parameters of rock samples.

  *.+ῌgῌ+$=> ?@1AB1CD-E f FGH
 t   ,   +,ῌfῌ  +ῌtῌ,
0-$=> I1$Jtῌ ῌ+,*,
fg

KL MN*O(07PQ (tῌfg-) *R"#r*  *.10 S l*  *./.* S1T U0$%> 0K0 VW!1XYKZ-=0#[ :Z\(1]^_`abKLcde *.*+῍+* mm fg1]^_$%hijkl!m0KnLo% p ?@-qrstu*v0# w  1xy]z{b`ab-|>7=>Ae} 1:Ze U]z{b1`ab-=> x b t F
GH l b t gl~W (Fig. /) KLCKG* %]^_1ZQ x  l $%?@1&V

W! r* 1'()*0#F  r* 1 U*G6#'()*fg1 UeM 07e6
# 1(KL f  g t * - >I$e 0% I1GXY(e 1
Gl!menLo1K=>#4G  g+ AB1CD-E f+ῌ- t+ -O(0#=>71 - UZ7PQ1

Fig. 2. Photomicrographs of samples from Mt. Yakedake. Narrow parts of pores are indicated witharrows. (a) NPFD-+. The length of a white bar
is +** micron. (b) NPFD-0. The length of awhite bar is +** micron.

'()1+,*2%#"  - 21VW!"# tῌfg $%&'()*+,-./0#%1 +,*2%#13 g 14*567

1[1 ( 1l ,*-* mm1£¤¥¦K*§G?@1 I1¨© (*.*2 mm) L %]^_1cd r, :%]^_1%]^_ , ª«¬­*®NLo% ¯°±*G²³¥¦¡¢ -῍- "7G* ´¸b1?@1¹ºLo*vcdR b -'(  ²³1´µz¶·(Fig. 2) [(© (Fig. 0) -º$  Ze + mm -|>G

% »0-0#%G°¼?@e¼

J?@[%2Ke ?@1

½C *.+ mm

1?@67 (Fig. 2) I1G°¼?@*G6#

   -   !"#$%&
5)(6.(789:6 ;<=

> 4

111

'()*+, -./01 234
?@A%

B(CD#EF%-5G @

?@A.H6I%B(CD#E JKL

A.6MN O '()PQR.

S#T H6U >%(CD#E8/6 VW X!YZ[#\ZJ (Scott and]5 ;F%^_G (Table ,) (CD#E

Barker, ,**-) ` +, M"# '()B(CD#F R $85) JKLS#T H6

EF%-a6%b5( ;+1 c6&-dFef'g%((Gh#ij( +k) &)lmn#i%o,pG , 'lmn#i B(CD#E*qrst.( ;82u+vw>,x./689:6 yx z+{CD#E|} l  xῌbῌt z+{ lῌbῌt \Yy, %~~%-5GM .:m (Fig. /) % ( ()  5G (Table ,) M 
NPFD-+'() 0 g+ 85)9:68 t2 b

 +3 7 x 85) *.,/ 8 *.2  , ' $ %  6 (Fig.

 Takeuchi et al., ,**/

(5)(R ~~/.   '()1 -6*89:6

/ (a)) @AG2%9:68 $8

.ῌ. (3(6a6CLh% (5)G

0 g*.+ %9:68 r* 4 - 5 t 4

+ ῌ - 8k) x 85) *.*, 70$%9:+(;8 '()Yn# U >*.+

6 8'CD#E *  +* mm #

mm   5G -   !"#$1 O\#./67 B(8* *.+ mm #\# +῍+** mm #\# N B(8(1*./6./, 28*95(`M* ,*ῌ70./6

M NPFD-0'() 0 b+ 85)9:68 t0( , %:G89:6 _+., b,. 7 x 85) ,./+*- 8 +  , '$%

5G;$ (Fig. +)* <.

6 @AG27 x+ = ./,> c6*/,0(%>5),./  +*- (689:6

?89:6 8'CD#E* +* mm #\#./689:68 B(8

JKLS#T (Fig. 0) %H68 U >* +* mm #\#./6 ;4?@A H

@8A5)(6;8B( @ & 6I8<#\#./6

0 g*./  /6(CD5G <r#85)E>

r r* 4 +.. 5 6 x $ #\#.6  %F+a6;8G)(6 /H /(0%I a x I 6 I ,**. , 'JKLS#T%Ua68 *85) E¡$¢Z #\#%9:6/ J (M  NPFD-+ (Fig. 0 (a))  , M  NPFD-0b,

(Fig. 0 (b)).   ( Q 0 1 M  NPFD-0  M 

NPFD-+ 8¤¥&5(%*'0>(

89:6w) 8'8'@ >( KL0I(+1Y£

H:6 ; M 

NPFD-+ ,@"MNOI(;8 ay6a6CLh B(CD#E
F r 8¨*qr x (CD#EF b ¨5)CD#E ' g|} l 8(1 . 'lmn#i+k) M 6  @A+k) r z+{ b %^¦7kG;8%§Pa6 ;+1@( 0( ay(G.(Q017 1 -2u©Q
8a6

_ xῌbῌt z+{ lῌbῌt \Y m (Fig. /) %(() x

RS +6 6&*bG  ªTa68

z+{ l %5G G x z+{ l M9:)(6 (Okumura et al., ,**0) M @A895( UV H61 I

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