Characterization of Pore Structures in a Volcanic Rock from Permeability Measurements

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1 /- ( 2) / - Characterization of Pore Structures in a Volcanic Rock from Permeability Measurements Yuhta S HIMIZU and Tohru W ATANABE 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 in magma 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 in volcanic rocks A volcanic rock has a wide variety of pores in size and shape The conventional equivalent channel model is not useful for estimating pore structures from permeability We thus have made a new permeability 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 the separation of tubes are parameters of characterizing pore geometry Tube radii can be estimated through microstructural 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 are left in the estimation we can obtain a reasonable structural image Electrical conductivity and other physical properties can provide us with additional information to constrain geometrical parameters Key words : permeability pore structure bubble escape of gas + Jaupart and Allegre +33+ (Eichelberger et al +320 ; Klug and Cashman +330 ; Melnik and Sparks +333 ; Saar and Manga +333) Fig + Klug and Cashman ( +330) 3-2/// -+3 Department of Earth Sciences University of Toyama Graduate School of Science and Engineering Univer- Gofuku -+3 Toyama 3-2/// Japan sity of Toyama Gofuku -+3 Toyama 3-2/// Japan Corresponding author: Tohru Watanabe 3-2/// twatnabe@sciu-toyamaacjp

2 100 Dullien ( +33 ) + : (m) : S(m ) Fig + The relationship between permeability and porosity reported in previous studies Eichelberger et P (Pa) : h (Pa s) al ( +320) measured the permeability of Obsidian Q Dome and related rhyolite samples (solid circles) - m s Measurements of Klug and Cashman ( +330) were q (m/s) made on pumice tu # blast dacite and submarine material (open circles) Saar and Manga ( +333) Q k P measured the permeability of basaltic andestite q S h () + flows and cinder cones in the Oregon Cascades (triangles) An empirical power-law relationship proposed by Klug and Cashman ( +330 ) is also () + shown k m (Fig + ) Eichelberger et al ( +320) Saar and Manga ( +333) + q k P h Klug and k Cashman ( +330) Kozeny-Carman Kozeny ( +31) : f C f q h A P () (Klug and Cashman +330 ; Saar and A Manga +333) C v P h ACf m () - -

101 Fig Simple geometrical models of a permeable medium (a) Circular tube model (b) Rectangular tube model (c) Elliptical tube model q f v m A f A () 0 v m (hydraulic radius) Scheidegger +31

3 101 Fig Simple geometrical models of a permeable medium (a) Circular tube model (b) Rectangular tube model (c) Elliptical tube model q f v m A f A () 0 v m (hydraulic radius) Scheidegger +31 (-) A () 0 () - ( + ) () Kozeny - f kc A - () m C b Kozeny m f k () / b -+ () / Fig (a) n : r Carman ( +3-2) : A AA + f pr P Q () Kozeny-Carman - C f nq npr P k () 0 q () 1 A + f S 2 h () + () 1

4 102 npr ac nc k () 2 fn 2 a f - npr r n ac c f f - np () 3 k ( ++ ) - - () 2 () 3 r f k ( + ) 2 ac ac c m a c ac + a ( ++ ) pr r mf m k pr -+ a ( + ) + () / b- m f k b b () / b Bernabe et al ( +32 ) : a : c ca : a : c : : n n (Fig (c)) (Fig (b)) ca P + ca - - pa c P pc P Q a c h a+ a h : w - w Q + h P pac npc fn a w c a + c a a - ac P Q -h a n k pc c f a + a + a c a a

5 103 r c a + b / - Fig - A tube tilted to the length of a sample by the angle q q (Fig -) -+ cos q cos q cos q fcn fis q k ffcnfis k kkcos q ( + ) fde e fpmfcnfde e + cos q f fpm ( + ) fcn + k k e fpmf cn e t ( +-) Bernabe +320 (tortuosity) - - Guéguen and Palciauskas +33 Bear ( +31 ) ffpm ( +- ) ( + ) f f + + k k t ( + )

6 104 - f ff t pm ff t cn -- Fig The e# ective radius as a function of the length fraction of narrow part Two circular tubes with di# erent radii are connected in series Wright et al 0 (inset) The e# ective radius is normalized by the small radius + The radius ratio is set to be P P r r r : r r ( +/ ) : (Fig + ) pr Q P pr Q+ pr Q P P r + r r x Fig + +/ ( +0) Q Q Q + + PP+ P Q p r r eff + + pr+ P Q+ r eff + i + dr pr r r r + eff + ( +0) ( +1) p() r r + + p + p + P : r+ r Q P r r r r + + : ( +/ ) eff + + eff i

7 105 pr Q P () / () / p P QQ+ Q r+ r ( +2) mff k bt cn (+) r m r r r eff ( +2) pr Q + eff P f f b t m s s ( +3) r eff ri r prdr eff ( +3) ff s t pr () r () (+) () s m k sf b Paterson ( +32- ) Bernabe ( +320) m () - () (Equivalent m Channel Model) b Paterson b - (Bernabe +320) -+ - Fig -+ cn s f () () cn f (-)

8 106 r + Fig (2) r R b brr l x P (3) + ( +/ ) pr b P Q 2 h + b + x l + l + x l Q npr b P q r b l 2 hl + b + x x l pr b k 2 l + b + x (/) (0) ( 3) f r r (-) prxprb + x pr f xb + x (0) l l l l (/) (0) (-+) r l r f b k ( ) ( ) 1-2 xb + x+ b + x x ( ) rr -- x (-) ( ) rr x ( f f) (--) cn f + t+ - A+ b + b r B+ b + b b x b l Cb b t + k r t r f (0) (1) r

9 107 r trr t x l t b b xbt lbt (-) (--) x (Fig /) x l (-+) l b l Fig / (a) The relation between the length fraction of narrow tube x and the radius ratio b for various t ( xbt 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 ( lbt diagram) The tube separation is normalized by the separation l calculated for the uniform radius tube model Circles indicate estimated values of ll / for samples NPFD-+ and NPFD- 0

with dyed-resin Images are captured with a transparent- light image scanner Abbreviations are Pl plagioclase ; Bt biotite ; Hb

10 108 Table + Density porosity and permeability of rock samples x l b ( ) rr ( t+ ) r x b (Fig / (a)) x r l b l ( ) rr ( t+ ) (--) b Fig 0 Porphyritic texture of samples from MtYakedake : (a) NPFD-+ and (b) NPFD- 0 The length of a scale bar is mm Pores are colored blue with dyed-resin Images are captured with a transparent- light image scanner Abbreviations are Pl plagioclase ; Bt biotite ; Hb hornblende; Qz quartz + / mm - mm Fig 1 O Table + KE/ T (FEP) (Keyence AP- -) - 0 gcm Fig 0 +/ ( Q) ( Q) - P P +/ mm P high P low high QPlowQ low

11 109 Fig 1 A schematic of permeability measurement system kpa r Wannier l ( + + kpa) (2) (3) m t Table + r l fg NPFD-0 0 h( Pa s) (2) (3) f ffcn t T (Cole and Wakeham +32/ ) h-1 1 T / / Pa s + + : / + m r l (Table ) g f gf fg f t ABS g+ / mm - mm + mm f+ - t+ + + kpa 0 0 mm + + mm (// / ) (Fig 0) m g f t - ( + + cm /s) r l NPFD-+ ( ) / - cn ff t cn

110 Table Estimated geometrical parameters of rock samples g + + g + f t + f + t 0 - - t + fg ( tfg-) r 1

parts of pores are indicated with arrows (a) NPFD- + The length of a white bar g + f+ - is + micron (b)

12 110 Table Estimated geometrical parameters of rock samples g + + g + f t + f + t t + fg ( tfg-) r 1 0 l / + + mm x b t lb t (Fig /) x l r r f g t Fig 2 Photomicrographs of samples from Mt Yake- dake Narrow parts of pores are indicated with arrows (a) NPFD- + The length of a white bar g + f+ - is + micron (b) NPFD- 0 The length of a t+ white bar is + micron - tfg g - mm -- (2 mm) r b (Fig 0 ) + mm (Fig 2) + mm (Fig 2)

13 111 g+ r - t - (Scott and (Table ) Barker -) R x l xbt lbt (Fig /) (Table ) Takeuchi et al / NPFD-+ g+ t2 b +3 x / 2 (Fig / (a)) + - x + + mm mm - + mm + + mm NPFD-0 b+ t + b x / + + (Fig + ) - x+ / mm (Fig 0) + mm g/ r + x x NPFD- + (Fig 0 (a)) NPFD-0 NPFD- 0 (Fig 0 (b)) NPFD-+ NPFD-+ r x b l r b xbt lbt (Fig /) x l x l (Okumura et al 0) mm g / f t

14 112 pore structure nd ed Academic Press San Diego +0p Eichelberger JC Carrigan CR Westrich HR and Price RH ( +320) Non-explosive silicic volcanism Nature -- /320 Guéguen Y and Palciauskas V ( +33 ) Introduction to the physics of rocks Princeton University Press Princeton 3 p Jaupart C and Allegre C J ( +33+ ) Gas content eruption r x rate and instabilities of eruption regime in silicic R l volcanoes Earth Planet Sci ett Klug C and Cashman KV ( +330) Permeability development in vesiculating magmas: implications for fragmentation Bull Volcanol / Kozeny J ( +31) Uber Kapillare eitung der Wasser in Boden Royal Academy of Science Vienna Proc Class I Melnik O and Sparks RS J ( +333) Nonlinear dynamics of lava dome extrusion Nature -1 + () +/ +1 () +2 0+/ 0- Okumura S Nakamura M and Tsuchiyama A (0) Shear-induced bubble coalescence in rhyolitic melts with low vesicularity Geophys Res ett -- doi: + +3/ 0 G 1-1 Paterson MS ( +32-) The equivalent channel model for permeability and resistivity in fluid-saturated rock A re-appraisal Mech Mater -/ -/ : +/-22 Saar MO and Manga M ( +333) Permeability-porosity relationship in vesicular basalts Geophys Res ett Scheidegger AE ( +31 ) The physics of flow through porous media University of Toronto Press Toronto -0 p Bear J ( +31 ) Dynamics of fluids in porous media Scott JBT and Barker RD (-) Determining pore- Elsevier New York 10 p throat size in Permo-Triassic sandstones from low- Bernabe Y ( +320) Pore volume and transport properties frequency electrical spectroscopy Geophys Res ett changes during pressure cycling of several crystalline -doi: + +3 /- G +03/+ rocks Mech Mater / -/ 3 Takeuchi S Nakashima S Tomiya A and Shinohara H Bernabe Y Brace WF and Evans B ( +32 ) Permeabil- (/) Experimental constraints on the low gas permeaity porosity and pore geometry of hot-pressed calcite bility of vesicular magma during decompression Geophys Mech Mater Res ett -doi: + +3 // G 3+ Carman PC ( +3-2 ) Determination of the specific surface Wannier GH ( +300) Statistical physics John Wiley & of powders I Transactions J Soc Chemical Industries Sons New York /- p /1 / - Wright HMN Roberts J J and Cashman KV (0) Cole WA and Wakeham WA ( +32/ ) The viscosity of Permeability of anisotropic tube pumice: model calculanitrogen oxygen and their binary mixtures in the limit tions and measurements Geophys Res ett -- doi: of zero density J Phys Chem Ref Data /0 G 1 Dullien FA ( +33 ) Porous media: fluid transport and

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