Earth and Planetary Science Letters 400 (2014) 123–129
a ,
a
a
a
a , b , c
c a b
Physics of Geological Processes, Departments of Geoscience and Physics, University of Oslo, P.O.
Box 1048 Blindern, 0316 Oslo, Norway
ISTerre, Université Grenoble Alpes, BP 53, F-38041, France
ISTerre, CNRS, BP 53, F-38041, France a r t i c l e i n f o
Article history:
Received 31 January 2014
Received in revised form 14 May 2014
Accepted 23 May 2014
Available online 6 June 2014
Editor: J.
Brodholt
Keywords: andesite pore space distribution power law scaling transport properties weathering reactions a b s t r a c t
The pore structure of magmatic rocks records processes operating during magma solidification and cooling.
It has first order effects on the petrophysical properties of the magmatic rocks, and also influences mass transfer and mineral reactions during subsequent metamorphism or weathering.
Here, the pore space characteristics of an andesitic sill intrusion were determined by multiscale resolution computed X-ray microtomography (μ-CT), and the 3D structure was used for transport modeling.
Unaltered andesite has a power law distribution of pore volumes over a range of five orders of magnitude.
The probability distribution function (PDF) scales with the inverse square of the pore volume ( V ),
PDF
V
− 2
.
This scaling behavior is attributed to the coalescence of pores at crystal–melt boundaries.
Large pores are concentrated on the outer margins of amphibole and plagioclase phenocrystals.
Incipient weathering of the andesite is associated with preferential growth of weathering products in the largest pores.
This can be explained by a model in which diffusion of external components into the porous andesite is controlled by a random network of grain boundaries and/or microfractures.
This network preferentially links the larger pores to the system boundaries and it is the major fluid transport pathway, confining incipient weathering into a small fraction of the rock volume only.
2014 Elsevier B.V.
All rights reserved.
The porosity and pore space distribution in rocks provide first order controls on several petrophysical properties, including elastic moduli, diffusivity and permeability (e.g.
Guéguen and Palciauskas,
1994 ).
A broad pore size distribution may also drive internal redistribution of mass due to curvature effects on chemical potentials
( Emmanuel and Berkowitz, 2007 ).
This may furthermore control the extent to which crystallization processes in the pores of rocks or porous building materials cause fracturing due to growth related stress generation
( Scherer, 2004 ).
It is likely that the rate and progress of any fluid infiltration driven volatilization process in porous rocks, including weathering of igneous and metamorphic rocks, serpentinization of oceanic lithosphere, and carbon sequestration by
mineral carbonation, is to a large extent affected by the spatial distribution of the pore space as well as by the total porosity.
Corresponding
E-mail address: author.
Tel.: +47 2256612; bjorn.jamtveit@geo.uio.no
fax: +47 http://dx.doi.org/10.1016/j.epsl.2014.05.042
0012-821X/
2014 Elsevier B.V.
All rights reserved.
22855101.
(B. Jamtveit).
Recent advances in technology that enable 3D pore structure characterization over a large range of length scales (X-ray tomography, focused ion beam – scanning electron microscopy, neutron scattering, etc.) have dramatically increased our ability to study rock porosity and its effects on rock properties (cf.
Zhu et al., 2011;
Baker et al., 2012a; Renard, 2012; Keller et al., 2013 ).
In igneous rocks, porosity is generated when a low-density fluid exsolves from the host magma upon cooling and/or decompression.
Bubble formation in rising magmas is a key element in many volcanic processes and has been studied extensively – both experimentally and theoretically (e.g.
Sparks et al., 1994; Blower et al., 2002; Yamada et al., 2005; Gonnermann and Manga, 2007;
Baker et al., 2012b ).
Porosity formation during the comparatively slow cooling and crystallization of intrusive rocks has received less attention (see, however
Simakin et al., 1999 ),
although it is likely to have a major effect on the petrophysical properties of the magmatic rocks as well as on post magmatic metamorphic or weathering related alteration process.
Here we present a 3D pore space characterization of an andesitic sill intrusion from the Neuquén Basin in Argentina obtained by computed X-ray microtomography.
We then analyze the

124 B. Jamtveit et al. / Earth and Planetary Science Letters 400 (2014) 123–129 transport properties of a system in which diffusion takes place through a non-percolating pore space, and a matrix in which diffusion is controlled by 2D planar objects such as microfractures and grain boundaries.
Our analysis shows that large pores have a higher probability of being part of the transport network than small pores, and thus that large pores will be preferential sites of reaction during post magmatic alteration.
This provides a new explanation of why weathering reactions is localized onto only a fraction of the porosity, and why the pore space does not get clogged after incipient reaction.
The 8–10 m thick sill intrusion investigated here is andesitic to dacitic in composition (62–65 wt% SiO
2
) and it was sampled near
Cuesta del Chihuido in southern Mendoza, Argentina.
The intrusion is hosted in the Vaca Muerta Formation of the Medoza Group, a marine limestone-shale unit of Upper Jurassic to Lower Cretaceous age
( Leanza and Hugo, 1978 ).
Field relations were described by
Jamtveit et al. (2011) .
Mineral analysis was performed using the Cameca SX100 electron microprobe at the Department of Geosciences, University of
Oslo (see
Jamtveit et al., 2011
for details).
The magmatic mineralogy is dominated by euhedral plagioclase, amphibole, ilmenite, and apatite with interstitial quartz, albite and K-feldspar
( Fig. 1 ).
Plagioclase crystals commonly display oscillatory zoning with a range in composition from An
30–40 to An
40–50
.
Grain sizes range from about 50 μm to
5 mm.
Amphiboles are dominated by pargasites and pargasitic hornblende.
Even in the best preserved rocks, chlorite occurs among the interstitial minerals and it is presumably formed by deuteric alteration during the late stages of cooling of the magmatic rocks.
During spheroidal weathering, the magmatic minerals undergo hydrolysis and oxidation to produce ferrihydrite and carbonates as the main weathering products
( Jamtveit et al.,
2011 ).
The total porosity of fresh magmatic rocks measured by He porosimetry was 7.5–7.8%.
The He-porosity is consistent with density measurements which indicate a total porosity in the 7–9% range
( Jamtveit et al., 2011 ).
Fig. 1
shows back scattered electron (BSE) images of a fresh andesite.
A large number of isolated small pores can be observed both within the plagioclase phenocrysts and within the grains comprising the fine grained groundmass
( Fig. 1 b).
However, the largest pores ( > 100 μm) are concentrated near the phenocrystgroundmass interface.
They often contain chlorite crystals interpreted to have formed at the expense of the original magmatic minerals during the cooling of the magmatic body.
Two samples of unweathered homogeneous andesite were characterized by multiscale X-ray computed micro-tomography (μCT).
Three datasets were obtained at different spatial resolutions.
Low resolution data were obtained using a Nikon Metrology model XT
H 225 LC industrial type μCT scanner at the Norwegian Geotechnical Institute with a voxel size of 6.6 μm for a 6 mm sized cubic sample.
Two additional data sets from a single sample were obtained at spatial resolutions of 0.56
and 2.8 μm on beamline
ID19 at the European Synchrotron Radiation Facility (Grenoble,
France).
For the synchrotron runs, a cylindrical sample of 7 mm diameter and 7 mm height was scanned, and a set of 1500 to 3000 radiographs was reconstructed using a filtered back-projection algorithm into 32-bit gray-level volumes, and then rescaled to
8-bit volumes consisting of 1900
1900
1000 voxels.
A multiresolution technique was applied allowing imaging of the sample
Fig. 1.
Back scattered electron (BSE) images of a fresh andesite.
(a) Amphibole (amp) and oscillatory zoned plagioclase (plg) crystals are embedded in a groundmass of albite (ab), K-feldspar (ksp) and quartz (qz).
(b) Chlorite crystals (brightest color) are observed growing into the largest pores (black).
Linear arrangements of small pores within the plagioclase phenocrysts are interpreted as partly healed microcracks formed by thermal contraction of the magmatic rock.
with a large field of view (5.7 mm wide and 2.8 mm high with a voxel size of 2.8 μm) and high resolution imaging of a smaller region near the center of the sample (1.1 mm wide and 0.56 mm high with a voxel size of 0.56 μm).
An automatic change of X-ray optical system allowed the position of the sample to remain fixed during these two scans.
Having the same reference frame facilitated later comparison and analysis of pore structure at two magnifications.
The software package AvizoFire© was used for data analysis and image processing.
The following segmentation procedure was performed to analyze the tomography data.
A mask was applied in order to remove the background, and a 3D Gaussian median filter was applied to the original gray-level images to reduce the noise.
Then filtered gray images
( Fig. 2 a,b)
were thresholded into binary form.
Finally, additional filtering and morphological closing was applied to the binary images before they were segmented into clusters of connected components (pores).
Fig. 2 c
shows the distribution of connected porosity in a
300 μm thick slice, where each connected pore cluster is marked by a different color.
The 3D volumes of connected pore clusters were measured and used to plot the pore size distribution shown in
Fig. 3 .
The three data sets were used to analyze the pore size distribution in the andesite.
For each data set an upper and lower cut

B. Jamtveit et al. / Earth and Planetary Science Letters 400 (2014) 123–129 125
Fig. 2.
(a), (b) Original gray-level X-ray images of the rock matrix, 2D slices perpendicular to the axis of the sample cylinder (7 mm in diameter) shows the contrast between pores (black) and minerals (grey).
Phenocrystals of plagioclase (plg) and amphibole (amp) are visible as areas of low porosity.
(c) Clusters of connected porosity in a
∼
300 μm thick slice identified by different colors.
Note the larger pores near the margin of the amphibole phenocrystal (amp).
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) facilitate analysis and plotting of such data, a logarithmic binning procedure was applied.
Histogram intervals were binned based on the logarithm of the pore sizes, such that each bin width is a constant percentage of the mean bin value.
After binning, the histograms were normalized, and the pore volume probability distribution functions (PDFs) for the three different resolutions are presented in
Fig. 3 .
The normalized distributions were rescaled by the mean pore volume (
).
When rescaled, all three datasets collapse onto a common probability distribution with the form
PDF (
)
α
, and
2 ( Fig. 3
inset).
The total data set covers almost eight orders of magnitude in pore volume and produces a convincing power law distribution over at least five orders of magnitude.
Fig. 3.
Pore volume probability distribution function (PDF) measured from 3D Xray images obtained with three spatial resolutions (0.56, 2.8
and 6.6
μm voxel sizes).
Inset: Data collapse of the pore volume distributions rescaled by their mean values at different pixel resolutions.
The dashed line corresponds to a power-law
(PDF ( V )
∝
V
α
, with α = −
2).
off pore size is given by the respective resolution (voxel size) and sample size.
Pore size distribution data, obtained by using different imaging resolutions, range over eight orders of magnitude (1–10 8 μm 3 ).
To
Most studies of pore size distribution in magmatic rocks have been conducted using vesicular volcanic rocks, and both exponential and power law size distributions have been reported (cf.
Baker et al., 2006 ,
and references therein).
Models that include nucleation and diffusion controlled growth of vesicles lead to an exponential size distribution
( Mangan and Cashman, 1996 ) un-
less multiple nucleation events are invoked
( Blower et al., 2002 ).
Power law distributions on the other hand are often ascribed to coalescence during collision of bubbles
( Gaonac’h et al., 1996;
Lovejoy et al., 2004 ) analogous
to the behavior predicted by the coagulation theory of
Smoluchowski (1917) .
The coalescence model predicts a probability distribution with a power law exponent

126 B. Jamtveit et al. / Earth and Planetary Science Letters 400 (2014) 123–129 of
2, as observed in this study.
In the multiple nucleation model, the bubble size distribution evolves from a unimodal form, to an exponential and then to a power law distribution with an exponent that increases with the number of nucleation stages.
In a viscous and partly crystalline andesitic intrusion, the gravitational mobility of vesicles will be very limited and a coalescence mechanism driven by ‘self-propagated’ bubble motion seems implausible.
The observed spatial association between large pores and the grain boundaries of phenocrystals of plagioclase and amphiboles
( Fig. 2 )
does, instead, indicate that bubble growth is connected to coalescence at crystal–liquid interfaces.
This could be driven by crystal growth or melt movements relative to the crystals during emplacement.
Similar mechanisms have been proposed for less viscous, highly porous systems (cf.
Bai et al., 2011 ).
Few experimental studies of bubble growth have been performed in partly crystallized systems.
However, experiments on the decompression of granitic melts under subliquidus conditions conducted by
Simakin et al. (1999)
produced power law vesicle size distributions (PDF (
)
α
), although with a somewhat smaller exponent than reported here (
1 .
5).
The total porosities produced in these experiments were also similar to that of the andesite used in this study, and Simakin et al.
concluded that “our data confirm observations that crystals in the melt give rise to bubble coalescence”.
Our μCT-data and petrographic observation support Simakin et al.’s conclusions that crystal–vesicle interactions control the pore size distributions of intrusive rocks.
An intersting implication of this is that the largest pores tend to be localized at or near the boundaries of the largest crystals.
This may have implications for the transport properties of the rock following cooling and complete crystallization as we will discuss below.
The pore size distribution and pore connectivity is clearly important for the access of external fluids to magmatic rocks, and thus to the rate at which such rocks undergo post-magmatic alteration and subsequent weathering.
Jamtveit et al. (2011)
showed that incipient weathering of the andesite described above is associated with growth of weathering products, notably ferrihydrite and calcite, in the andesite pores (their Fig. 7).
They furthermore showed that the progress of pore filling increases nearly linearly with pore volume for pores in the 10–100 μm diameter range, so that most pores larger than 100 μm in diameter were completely filled by weathering products whereas pores smaller than 10 μm were nearly empty.
Several explanations have been put forward to explain the commonly observed preferential growth of secondary minerals in large pores during reactive transport in porous rocks.
Pore size dependent solubility has been suggested as a viable mechanism by many authors, including
Putnis and Mauthe (2001) ,
Emmanuel and
Berkowitz (2007)
and
Emmanuel et al. (2010) .
This phenomenon depends on the effect of surface curvature and it is well known for systems with very small ( < 1 μm) pore sizes (cf.
Scherer, 1999 ).
However, for larger, low surface curvature, pores like those in the andesite investigated in this work, this mechanism is much less likely to play an important role.
Alternatively, it has been shown that the probability of nucleation increases with pore size
( Chen et al., 1998 ),
and
Jamtveit et al. (2011)
suggested that this as a possible explanation of their observations.
A third alternative is that the supersaturation of the pore fluid is higher in the largest pores.
The growth of weathering products in the andesite depends on both dissolution of local magmatic minerals and the introduction of externally derived components (notably oxygen and carbonate bearing species).
Thus the relevant supersaturation in a given pore will depend on both the rate of dissolution of the minerals comprising the pore walls, and the rate of influx of external components.
In the following, we analyze the transport properties of a porous rock with non-percolating porosity to investigate the feasibility of transport-controlled variation in supersaturation between large and small pores.
The pore space of the andesite described above is not percolating.
Indeed, the volume of individual pores is defined as the size of the locally connected region, and the largest measured connected pore volumes typically extend over a distance of a few hundred micrometers.
Diffusion-controlled transport through the rock is therefore, to a major extent, controlled by transport in the
surrounding the pores.
This matrix is comprised of mineral grains with negligible diffusion coefficients, grain boundaries, and possibly microfractures with apertures below the resolution of our
CT-technique.
In the following, we will examine how the nature of the rock matrix influences the overall transport properties of the entire porous medium.
We first assume that the matrix is homogeneous and can be characterized by a ‘bulk’ matrix diffusion coefficient.
The effective diffusion coefficient for 2D models with variable porosity and with pore size distributions similar to that of the studied andesite samples was analyzed using the MILAMIN Finite
Element Solver of
Dabrowski et al. (2008) .
The diffusion equation was solved in a square domain representing a porous medium model
( Fig. 4 a, b).
The boundary conditions for concentration (
) were
0 and 1 at the left and right boundaries, and zero flux boundary conditions were applied to the top and bottom.
The diffusion coefficient of the matrix was set to
m
1.
In natural systems, the diffusion coefficient in the pores is many order of magnitude higher that of the matrix.
However, as shown by
Krotkiewski et al. (2011) ,
to accurately calculate the effective diffusion coefficient for models with isolated pores embedded in a homogeneous matrix, it suffices to set
p
10
4
m
.
Increasing
p even further does not change the effective diffusion coefficient significantly.
Fig. 4 c
shows that the effective diffusion coefficient (
eff
) increases linearly with porosity for the small porosities relevant to this study.
The increase is higher for the studied pore geometries and power law pore size distributions
( Fig. 4 a)
than for a medium comprised of non-overlapping circular pores
( Fig. 4 b),
for which
eff is well predicted by
Bruggeman’s (1936)
differential effective medium (DEM in
Fig. 4 c)
model.
However, even at nearly 20% porosity, the effective transport coefficient for a porous medium with power-law distributed pore sizes is only a factor of 2 higher than that of the non-porous, homogeneous matrix.
We conclude that for a homogeneous matrix with slow diffusivity, a porosity of 8% has a negligible effect on the overall transport rates and that the local fluid composition is effectively independent of pore size.
However, as pointed out above, the rock matrix is heterogeneous and matrix transport will occur along grain boundaries and possibly along microfractures that cannot be resolved by our μCT-measurements.
Furthermore, as demonstrated by
Jamtveit et al. (2011) ,
weathering related growth in the pore space causes dilation of grain boundaries and drives both intra-granular and trans-granular fracturing.
The rock matrix is thus characterized by a complex network of more or less two-dimensional transport path segments.
To investigate the consequences of diffusive transport through a porous medium in which matrix transport is controlled by diffusion through grain boundaries or fractures, we developed a simple geometrical model based on the superimposition of a fracture network

B. Jamtveit et al. / Earth and Planetary Science Letters 400 (2014) 123–129 127
Fig. 4.
(a) A 2D porous medium model with a power law pore size distribution comparable to that observed in this study (synthetic model).
(b) Porous medium made of non-overlapping spheres.
(c) Computed relative effective diffusion coefficients ( D eff
) for the models shown in (a) and (b).
The diffusion coefficient of the non-porous matrix is D m
=
1, and the diffusion coefficient in the pores is D p
=
10
4
.
Further increasing D p does not change D eff significantly.
Fig. 5.
Randomly generated fractures overlapping a 2D porous medium with a pore size distribution similar to that of the andesite.
Pores connected to a boundary by the fracture network are shown in white.
Pores shown in yellow are not connected to any boundaries.
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) model and a pore space model.
The fracture network model consists of segments of random location and orientation, and with lengths randomly selected from a distribution similar to the distribution of the pore sizes described above (a power law with a cutoff length comparable to the diameters of the largest pores).
The pore size distribution was statistically similar to the distribution of pore sizes in the 2D sections through the porous andesite.
Fig. 5
shows how the fracture network overlaps the pore space of the porous medium.
It is evident from visual inspection that most of the small pores are not connected to the domain boundaries.
In contrast, large pores are often connected to the boundaries,
in this model where there is no correlation between the location of large pores and the superimposed grain boundary/fracture network.
In reality, as discussed above, large pores tend to be concentrated on grain boundaries where they may have formed by coalescence of smaller pores during the magmatic stage.
Consequently, the probability that large pores will be connected to the boundaries is higher for the andesite than for this random model.
Assuming that the filling of pores requires connection to the domain boundaries, and that pores are effectively filled during weathering when connected to the grain boundaries, we computed the ‘extent of pore filling’ as a function of pore size as shown in
Fig. 6 .
This figure is qualitatively similar to an analogous diagram based on the pore filling of a weathered andesite specimen (inset in
Fig. 6 ),
in which it was observed that the fraction of filled pores tends to increase with the pore size.
Note that some large pores were not filled, presumably because they were isolated.
Our model is also able to reproduce a pore size distribution function with a larger negative exponent for the unfilled pores in weathered rocks than for fresh andesite, as observed
( Jamtveit et al., 2011 ).
In this analysis we ignore possible precipitation and clogging within the fractures network.
This is at least partly justified by the observed dilation of grain boundaries and small-scale fractures during growth in the larger pores.
Thus, even if some precipitation

128 B. Jamtveit et al. / Earth and Planetary Science Letters 400 (2014) 123–129
Fig. 6.
Ratio of filled pores as a function of pore size, assuming that all pores connected to the domain boundaries in
Fig. 5
are completely filled by reaction products.
The pore size is given relative to a domain length scale of 1.
Inset: Percentage fill versus pore size measured (from
Jamtveit et al., 2011 ).
occurs along grain boundaries or microfractures, reaction generated stresses might keep the network open and possibly generate new fractures.
It is also possible that the growth of secondary minerals in fracture apertures does not completely occlude them.
This study shows that degassing of partly crystalline intrusions may give rise to a power law distribution of pore volumes over a volume range exceeding five orders of magnitude.
This scaling behavior may reflect coalescence of pores at the crystal–melt boundaries.
As a consequence, large pores tend to be localized near grain boundaries.
Weathering and, by inference, other fluid infiltration driven alteration processes in andesite is associated with preferential mineral growth in the largest pores.
Diffusion through a porous, but otherwise homogeneous medium below the percolation threshold is only to a very limited extent influenced by the rapid transport in the pores, and cannot explain preferential growth in large pores.
However, diffusion through a polycrystalline porous aggregate, such as a rock, is controlled by a complex network of enhanced diffusivity pathways, such as grain boundaries and microfractures in the otherwise impermeable rock mass.
Such a network can preferentially connect larger pores to the system boundaries, and leave small pores isolated from any infiltrating fluids, confining the weathering to a small portion of the rock volume.
This is particularly relevant for magmatic rocks where the largest pores tend to be localized along grain boundaries due to coalescence processes taking place during crystallization.
We thank Paul Meakin who made several improvements to the manuscript and Elodie Boller at ESRF for the technical help during the tomography scans.
We also thank Marcin Dabrowski and
Dani Schmid for insightful comments regarding modelling, and
Don Baker and an anonymous reviewer for valuable comments that helped us to clarify the paper.
This study was supported by a
Center of Excellence grant to PGP (grant no.
146031) from the Norwegian Research Council.
BJ also benefited from support from the
Alexander von Humboldt-Stiftung through an Alexander von Humboldt Research Award during the final stages of work on this paper.
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