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Pore scale heterogeneity in the mineral distribution and surface area of Berea sandstone
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 63 (2014) 3582 – 3588
GHGT-12
Pore scale heterogeneity in the mineral distribution and surface area of Berea sandstone Lai, P.a*, Krevor, S.a a
Imperial College London, South Kensington, London SW7 2BP, United Kingdom
Abstract The impact of pore scale heterogeneity in chemical transport and reaction is not understood in continuum (Darcy/Fickian) models of reactive transport. This is manifested in well-known problems such as scale dependent dispersion and discrepancies in reaction rate observations made at laboratory and field scales. A potential cause is the inability of the continuum approach to incorporate the impact of heterogeneity in porescale reaction rates. This results in part from pore-scale heterogeneities in surface area of reactive minerals. We use X-ray micro-tomography to describe the non-normal character and statistics of reactive surface area within a porous medium, specific mineral phases and their distribution in 3-dimensions. Using in-house image processing techniques, thin sections, nitrogen BET surface area, backscattered electron imaging and energy dispersive X-ray spectroscopy, we compare the surface area of each mineral phase to those obtained from X-ray imagery. There is little correlation between the reactive surface area fraction and the volumetric fraction of a mineral in a bulk rock. Berea sandstone has a characteristic pore size at which a surface area distribution may be used to quantify heterogeneity. The observations made contribute to the incorporation of statistical descriptions of pore scale heterogeneity in reactive transport into upscaled models. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2013 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of GHGT. Peer-review under responsibility of the Organizing Committee of GHGT-12 Keywords: Reactive surface area; pore-scale heterogeneity; micro-tomography; hydrology;
1. Introduction The flow of water or multiple fluids through porous rocks with concurrent fluid-rock chemical reactions is a dominant feature of many natural and engineered processes. These include metamorphic processes in hydrogeology, the formation of karst zones, the evolution of snow packs during melting, CO2 subsurface injection, nuclear waste remediation, near-surface contaminant transport and remediation and the transport of magma through the mantle. These so-called reactive transport processes are complex due to the coupling of chemical reactions, reactant transport through the pore space and at times the significant evolution of the pore space itself through rock dissolution and mineral precipitation. There are also known couplings between processes taking place at the pore scale and their macroscopic manifestation as shown by Boso and Battiato [1]. As a result, there are longstanding difficulties with the use of laboratory scale characterisation and predictive modelling of transport and reaction relevant to field scale processes as described by White and Brantley [2].
* Corresponding author. E-mail address: [email protected]
1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of GHGT-12 doi:10.1016/j.egypro.2014.11.388
P. Lai and S. Krevor / Energy Procedia 63 (2014) 3582 – 3588
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Recent work by Peters [3], Landrot et al. [4], Golab et al. [5] and Hezel et al. [6] have pioneered techniques registering 3D Xray imagery of rocks at the microscopic scale with 2D electron image mapping of minerals to produce 3D maps of the mineral distribution within a rock. In this paper we have sought to utilise similar techniques to provide a statistical description of the heterogeneity in the mineral surface area available for reaction from direct observations of Berea sandstone. We have built on past work in part by strengthening the basis for using ȝCT for making such observations by validating the calculation of surface area against independent measurements of surface area using N2 BET. Following from recent works [3, 4, 5, 6], we have used parallel spectroscopic and X-ray imaging observations of the rock samples to register the mineral phase identification in the 3D X-ray images. Using this validation of the approach towards mineral identification and surface area quantification in the X-ray images we were able to identify minerals directly in three dimensions and construct the statistical descriptions of mineral specific surface area heterogeneity at a range of spatial scales. Nomenclature ȝCT BET SEI BSE EDS ȝ ı
X-ray computed micro-tomography Brunauer-Emmett-Teller secondary electron imaging or image backscattered electron imaging or image energy dispersive X-ray spectroscopy mean standard deviation
2. Experiment 2.1. Rock sample The rock studied is the Berea sandstone, which has been used extensively in petrophysical research applications including Khilar and Fogle [7], Churcher et al. [8] and Shaw et al. [9]. The Berea sandstone has significant fractions of at least two mineral types, and mineral-specific characterisation was performed on it. The dominant mineral phases were distinguished in the ȝCT images to assess the impact of heterogeneity in the pore morphology and mineral distribution on surface area. From petrographic thin section analysis, the Berea sandstone is observed to be of fine to medium sand grade, with subangular, moderately spherical grains with a mixture of point and concavo-convex contacts. The composition is broadly similar between specimens: 85% quartz; 12% partially or fully dissolved alkali feldspars yielding predominantly kaolinite and some 2:1 clay minerals in relict feldspar grains and 3% plagioclase feldspar. The extent of drusy calcite cementation varies between samples and there is some silica cementation in the form of quartz overgrowths. The most abundant accessory mineral is muscovite, which was either bent or fibrous. Microcline, biotite, haematite, ilmenite, and pyrite were also observed. The visible porosity is 15%. 2.2. Adsorption surface area Surface area quantification from ȝCT imagery was grounded by parallel observations on the same samples using nitrogen adsorption and the Brunauer-Emmett-Teller (BET) method. Although a much greater understanding of the processes governing mineral reaction kinetics at the fluid-solid interface has developed since the initial proposition of the use of total surface area was made by Helgeson et al. [10], the use of BET surface areas is still generally useful and appropriate as a proxy for effective surface area in far from equilibrium reaction processes Hanchen et al. [11]. Additionally, the BET surface area is the observation of choice for calculating and modelling field scale dissolution processes as discussed by Zhu [12], Kampman et al. [13]. Thus normalisation of surface areas calculated from ȝCT images in this work by those observed using N2 BET also allows for both comparison and wider application in the use of the observations in subsequent modelling. The specific surface area of cylindrical pieces of each rock was measured, with samples sized so that they could also be imaged in the ȝCT. The dimensions of the samples were approximately 4 mm diameter and 10 mm length. The analysis was performed with a Micromeritics Tristar 3000 using nitrogen as the working gas. Figure 2 shows that the BET surface area of the rocks ranged nearly two orders of magnitude, from 0.08 m2/g for the Guelph carbonate up to 4.3 m2/g for the Edward carbonate. The surface area of Berea sandstone samples varies within the range of 0.71.4 m2/g, similar to values that can be found in the literature, e.g. Sen et al. [14].
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The calculation of specific surface area from ȝCT images were compared to those measured from bulk nitrogen BET measurements and the results are reported in Figure 2. The BET method infers surface area from observations of gas adsorption and the calculations are based on the molecular diameter of the working gas, in this case nitrogen. Thus the resolution of the surface area observations from BET was higher than the calculations from the ȝCT images that could only resolve features larger than 1ȝm. The results show that the BET measurements are consistently 1 to 2 orders of magnitude larger than calculations from ȝCT, but within a rock sample the correlation has as much repeatability as the BET surface area measurement itself. Furthermore, the ratio of BET surface area to ȝCT surface area provides an indication of the extent to which features below the resolution of the ȝCT are contributing to the total surface area. Increasing ratios indicate a larger portion of surface area associated with features below the resolution of the ȝCT. Plotting this ratio against the BET surface area it is clear that as the specific surface area increases a higher proportion of area is associated with features that are below the resolution of the X-ray images. 2.3. Minerals in 3 dimension The application ȝCT to mineral identification is not new. For example, Uesugi et al. [15], Tsuchiyama et al. [16], Tsuchiyama [17], and Tsuchiyama et al. [18] have shown that quantitative discussions of X-ray linear attenuation coefficients are possible with both mono- and poly-chromatic X-ray beams. It is possible to use information about the attenuation of X-ray light to obtain quantitative information about material densities and elemental composition. It is on this basis that we sought to create 3D mineral maps of the rocks directly from the X-ray imagery.
Fig. 1. (a) Photo of the Berea sandstone sample; (b) thin-section micrograph in cross-polarized light; (c) secondary electron image of grain-coating clays in the Berea sandstone sample.
Fig. 2. (a) The BET specific surface areas; (b) surface area correlation between BET and CT; (c) surface roughness, where the “roughness” ratio of BET surface area to CT calculated surface area plotted against BET surface area.
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Fig. 3. The mineral identification process: (a) an example label (quartz); (b) segmented Berea sandstone.
It was found that given a reasonably optimal setup, the contrast of the image was sensitive to the parameters of energy, specimen dimension, and byte scaling. Ultimately, operating the beam at 40kV and 3W, at a resolution of 1ȝm on the Xradia VersaXRM-500 produced images viable for mineral identification. The specimens were cut to less than 2 mm to minimize beam hardening, and the reconstructed data scaled to the smallest range possible. The parameters used were 2500 projections, 20s exposure time, and camera binning of 2, to collect a 109 voxel image. Once collected, the ȝCT image was processed as follows. The reconstructed volume was first de-noised using the non-local means neighbourhood filter in Avizo Fire 8.0. The minerals were identified according to their absorption or greyscale value using multiphase watershed in Avizo Fire 8 for both binary and mineral-specific segmentation. Gradient thresholding was used to mask grain boundaries with transitioning greyscale values. The threshold was chosen so that the finer features were not blotted out but it still produced a thin mask over the grain boundaries. With the mask applied, the mineral phases were categorised based on mean greyscale values. Then watershed transform was computed to establish the identity of the remaining voxels by expanding the initial labels. Figure 3 shows the initial categorisation, as an example, the quartz label, and the final segmented rock after the watershed transform. One pore phase and four mineral categories corresponding to clay, quartz, feldspar and other minerals (e.g. carbonate cement, oxides, and garnet) were identified. Finally, a cube of 600s voxels was extracted from the centre of the image for statistical analysis. 3. Analysis 3.1. ȝCT surface area The 3D X-ray images were used to generate a statistical description of the spatially varying property, surface-area-to-porevolume ratio, throughout the rock. Our workflow is to sub-sample an image at a chosen length scale, calculate the surface-areato-pore-volume ratio in that sub sample, and then repeat this process for every unique location throughout the X-ray image. For example, a 6003ȝm image contains 216 x 100ȝm unique sub samples. The surface area of mono-mineralogical (rock-pore) 3D ȝCT images were abstracted as a series of triangular mesh surfaces using a marching cubes algorithm. The meshing was carried out in Matlab R2012b using Peter Hammer's open source adaptation of Martin Helm’s Octave function [19]. The surface area was determined for each sub-sample, then normalised to the pore volume. Frequency histograms were generated for sub-sample sizes ranging from 50ȝm to 300ȝm. The frequency distributions were summarised as box plots. On each box plot the central mark is the median, x is the mean, the edges of the box are the 25th and 75th percentile, the whiskers mark 2.7 standard deviations and the red diamonds indicate outliers. With each distribution represented by a vertical box plot, the influence of sampling size on the spread and mean of each distribution was clearly observed. The distributions show a smaller spread at larger sampling scales partly due to smaller amounts of data available, but more significantly due to the increasing effect of volumetric averaging. This brings it back to the question of the effect of scale-dependent heterogeneity in determining upscaled average reaction rates. 3.2. Multi-mineralogic surface area The surface area between the solid and pore space for each mineral group was calculated using the mineral-specific images. The images were first reformed into 2 phases in order to mesh a surface. For an image with n number of phases, there are 2n-1-1 ways to binarise, and n!/2(n-2)! pairs of phases involved. The combinations constitute a system of linear equations Ax=B, where A is the pairings associated with the combination C, x are the pairs, and B is the surface area for combination C. For the 5 phase Berea images, there were 15 combinations, and 10 pairings. The surfaces were meshed for each combination, and the area, B calculated using Heron's formula. Since the pore space is group 1, the first 4 pairings, x1 to x4 represent the surface area for each mineral group; the groups 2 to 4 are clay, quartz, feldspar, and others respectively.
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Using the mineral-specific surface areas, the sub-volume sampling process described in Section 3.1 was duplicated to generate statistical distributions but this time for each mineral phase separately. Figure 5 show the surface area distributions for a range of sub-sample sizes, with separate colours for each mineral group. The clays tend to show large but not the highest mean and spread in specific surface area. This may be an effect of the segmentation process. At 1ȝm voxel size, some of the profiles of the clay could be identified. From that, only a small fraction of the complex geometries is retained during segmentation. This resulted in the clays looking more globose than stacked plates or filamentous webs. This loss is true for other complex microstructures like the fluted and partially resorbed detrital feldspar grains that were observed under SEM. Our current equipment is not fit for identifying thin structures or pore lining features such as chlorite rims and various grain coating clays. This limitation means that although some of the macro distribution properties of the clays in the spread have been captured, the mean surface area is lower than quartz because of the diminished shapes that are left with after imaging and segmentation.
Fig. 4. Mono-mineralogic surface area distributions for the Berea sandstone sample.
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Fig. 5. Multi-mineralogic surface area distributions for the Berea sandstone sample.
The natural logarithm of each distribution is also plotted alongside to evaluate their lognormal character. The natural logarithm plots also show how the lognormal fitting performs. The approximation is good with the Berea. The natural log plots also show peaks at 0 (indicated by -inf) where the sub-volume samples have no surfaces associated with that mineral. For example, in Figure 5 at 200ȝm, 7% of the sub-volume sample cubes do not have feldspar in them. This is included in the legend as 'Sampling fraction'.
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4. Conclusion The work presented is the first characterisation of pore-scale heterogeneity in the reactive surface area of minerals within a permeable rock based on direct observation of the mineral distribution and pore morphology in three dimensions. The information can be used directly in statistically based models of reactive transport including the emerging group of pore network models focused on characterising reactive processes. The data can also be used to understand constraints imposed by heterogeneity in mineral surface area on techniques for modelling field scale reaction rates and interpreting reaction rate data obtained from the field or even core-scale measurements. It was observed in this work that the nature of the heterogeneity can be highly specific to a given rock. In the Berea sandstone, clays that appeared to preferentially coat quartz grains resulted in little correlation between the modal mineral composition of the rock and the fraction of surface area at the pore interface made of a specific mineral. At the scale of thousands of pores or smaller, the combination of heterogeneity in mineral distribution and varying pore morphology resulted in a range of distribution types applicable for describing surface area heterogeneity. Surface area could be distributed log-normally with long tails. These characterisations provide useful insight into the impact that the spatial expression of reactive surface area will play in governing the overall rate of reactive processes during flow through porous geologic media. Acknowledgements The authors gratefully acknowledge funding support for this work from the Qatar Carbonates and Carbon Storage Research Centre provided jointly by Shell, Qatar Petroleum and the Qatar Science and Technology Park. References [1] Boso, F., Battiato, I., 2013. Homogenizability conditions for multicomponent reactive transport. Advances in Water Resources 62, 254–265. [2] White, A.F., Brantley, S.L., 2003. The effect of time on the weathering of silicate minerals: why do weathering rates differ in the laboratory and field? Chemical Geology 202, 479–506. [3] Peters, C.A., 2009. Accessibilities of reactive minerals in consolidated sedimentary rock: An imaging study of three sandstones. Chemical Geology 265, 198– 208. [4] Landrot, G., Ajo-Franklin, J., Yang, L., Cabrini, S., Steefel, C., 2012. Measurement of accessible reactive surface area in a sandstone, with application to CO2 mineralization. Chemical Geology 318-319, 113–125. [5] Golab, A., Romeyn, R., Averdunk, H., Knackstedt, M., Senden, T.J., 2013. 3D characterisation of potential CO2 reservoir and seal rocks. Australian Journal of Earth Sciences 60, 111–123. [6] Hezel, D.C., Elangovan, P., Viehmann, S., Howard, L., 2013. Visualisation and quantification of CV chondrite petrography using micro-tomography. Geochimica et Cosmochimica Acta et Cosmochimica Acta 116, 33–40. [7] Khilar, K.C., Fogler, H.S., 1983. Water Sensitivity of Sandstones. Society of Petroleum Engineers Journal 23, 55–64. [8] Churcher, P., French, P., Shaw, J., Schramm, L., 1991. Rock Properties of Berea Sandstone, Baker Dolomite, and Indiana Limestone. Proceedings of SPE International Symposium on Oilfield Chemistry , 1–19. [9] Shaw, J.C., Churcher, P.L., Hawkins, B.F., 1991. The Effect of Firing on Berea Sandstone. SPE Formation Evaluation 6, 72–78. [10]Helgeson, H.C., Murphy, W.M., Aagaard, P., 1984. Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. II. Rate constants, effective surface area, and the hydrolysis of feldspar. Geochimica et Cosmochimica Acta 48, 2405–2432. [11]Hanchen, M., Krevor, S., Mazzotti, M., Lackner, K., 2007. Validation of a population balance model for olivine dissolution. Chemical Engineering Science 62, 6412–6422. [12]Zhu, C., 2005. In situ feldspar dissolution rates in an aquifer. Geochimica et Cosmochimica Acta 69, 1435–1453. [13]Kampman, N., Bickle, M., Becker, J., Assayag, N., 2009. Feldspar dissolution kinetics and Gibbs free energy dependence in a CO2-enriched groundwater system, Green River, Utah. Earth and Planetary Science Letters 284, 473– 488. [14]Sen, P.N., Straley, C., Kenyon, W.E., Whittingham, M.S., 1990. Surface-to-volume ratio, charge density, nuclear magnetic relaxation, and permeability in claybearing sandstones. GEOPHYSICS 55, 61–69. [15]Uesugi, K., Tsuchiyama, A., Nakano, T., Suzuki, Y., Yagi, N., Umetani, K., Kohmura, Y., 1999. Development of microtomography imaging system for rock and mineral samples. Proc. SPIE 3772, 214–221. [16]Tsuchiyama, A., Hanamoto, T., Nakashima, Y., Nakano, T., 2000. Quantitative Evaluation of Attenuation Contrast of Minerals by Using a Medical X-Ray CT Scanner. Journal of Mineralogical and Petrological Sciences 95, 125–137. [17]Tsuchiyama, A., 2005. Quantitative evaluation of attenuation contrast of X-ray computed tomography images using monochromatized beams. American Mineralogist 90, 132–142. [18]Tsuchiyama, A., Nakano, T., Uesugi, K., Uesugi, M., Takeuchi, A., Suzuki, Y., Noguchi, R., Matsumoto, T., Matsuno, J., Nagano, T., Imai, Y., Nakamura, T., Ogami, T., Noguchi, T., Abe, M., Yada, T., Fujimura, A., 2013. Analytical dual-energy microtomography: A new method for obtaining three-dimensional mineral phase images and its application to Hayabusa samples. Geochimica et Cosmochimica Acta 116, 5–16. [19]Hammer, P., 2011. Marching Cubes (http://www.mathworks.com/matlabcentral/fileexchange/32506-marching-cubes), MATLAB Central File Exchange. Retrieved Jul 23, 2013.
ScienceDirect Energy Procedia 63 (2014) 3582 – 3588
GHGT-12
Pore scale heterogeneity in the mineral distribution and surface area of Berea sandstone Lai, P.a*, Krevor, S.a a
Imperial College London, South Kensington, London SW7 2BP, United Kingdom
Abstract The impact of pore scale heterogeneity in chemical transport and reaction is not understood in continuum (Darcy/Fickian) models of reactive transport. This is manifested in well-known problems such as scale dependent dispersion and discrepancies in reaction rate observations made at laboratory and field scales. A potential cause is the inability of the continuum approach to incorporate the impact of heterogeneity in porescale reaction rates. This results in part from pore-scale heterogeneities in surface area of reactive minerals. We use X-ray micro-tomography to describe the non-normal character and statistics of reactive surface area within a porous medium, specific mineral phases and their distribution in 3-dimensions. Using in-house image processing techniques, thin sections, nitrogen BET surface area, backscattered electron imaging and energy dispersive X-ray spectroscopy, we compare the surface area of each mineral phase to those obtained from X-ray imagery. There is little correlation between the reactive surface area fraction and the volumetric fraction of a mineral in a bulk rock. Berea sandstone has a characteristic pore size at which a surface area distribution may be used to quantify heterogeneity. The observations made contribute to the incorporation of statistical descriptions of pore scale heterogeneity in reactive transport into upscaled models. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2013 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of GHGT. Peer-review under responsibility of the Organizing Committee of GHGT-12 Keywords: Reactive surface area; pore-scale heterogeneity; micro-tomography; hydrology;
1. Introduction The flow of water or multiple fluids through porous rocks with concurrent fluid-rock chemical reactions is a dominant feature of many natural and engineered processes. These include metamorphic processes in hydrogeology, the formation of karst zones, the evolution of snow packs during melting, CO2 subsurface injection, nuclear waste remediation, near-surface contaminant transport and remediation and the transport of magma through the mantle. These so-called reactive transport processes are complex due to the coupling of chemical reactions, reactant transport through the pore space and at times the significant evolution of the pore space itself through rock dissolution and mineral precipitation. There are also known couplings between processes taking place at the pore scale and their macroscopic manifestation as shown by Boso and Battiato [1]. As a result, there are longstanding difficulties with the use of laboratory scale characterisation and predictive modelling of transport and reaction relevant to field scale processes as described by White and Brantley [2].
* Corresponding author. E-mail address: [email protected]
1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of GHGT-12 doi:10.1016/j.egypro.2014.11.388
P. Lai and S. Krevor / Energy Procedia 63 (2014) 3582 – 3588
3583
Recent work by Peters [3], Landrot et al. [4], Golab et al. [5] and Hezel et al. [6] have pioneered techniques registering 3D Xray imagery of rocks at the microscopic scale with 2D electron image mapping of minerals to produce 3D maps of the mineral distribution within a rock. In this paper we have sought to utilise similar techniques to provide a statistical description of the heterogeneity in the mineral surface area available for reaction from direct observations of Berea sandstone. We have built on past work in part by strengthening the basis for using ȝCT for making such observations by validating the calculation of surface area against independent measurements of surface area using N2 BET. Following from recent works [3, 4, 5, 6], we have used parallel spectroscopic and X-ray imaging observations of the rock samples to register the mineral phase identification in the 3D X-ray images. Using this validation of the approach towards mineral identification and surface area quantification in the X-ray images we were able to identify minerals directly in three dimensions and construct the statistical descriptions of mineral specific surface area heterogeneity at a range of spatial scales. Nomenclature ȝCT BET SEI BSE EDS ȝ ı
X-ray computed micro-tomography Brunauer-Emmett-Teller secondary electron imaging or image backscattered electron imaging or image energy dispersive X-ray spectroscopy mean standard deviation
2. Experiment 2.1. Rock sample The rock studied is the Berea sandstone, which has been used extensively in petrophysical research applications including Khilar and Fogle [7], Churcher et al. [8] and Shaw et al. [9]. The Berea sandstone has significant fractions of at least two mineral types, and mineral-specific characterisation was performed on it. The dominant mineral phases were distinguished in the ȝCT images to assess the impact of heterogeneity in the pore morphology and mineral distribution on surface area. From petrographic thin section analysis, the Berea sandstone is observed to be of fine to medium sand grade, with subangular, moderately spherical grains with a mixture of point and concavo-convex contacts. The composition is broadly similar between specimens: 85% quartz; 12% partially or fully dissolved alkali feldspars yielding predominantly kaolinite and some 2:1 clay minerals in relict feldspar grains and 3% plagioclase feldspar. The extent of drusy calcite cementation varies between samples and there is some silica cementation in the form of quartz overgrowths. The most abundant accessory mineral is muscovite, which was either bent or fibrous. Microcline, biotite, haematite, ilmenite, and pyrite were also observed. The visible porosity is 15%. 2.2. Adsorption surface area Surface area quantification from ȝCT imagery was grounded by parallel observations on the same samples using nitrogen adsorption and the Brunauer-Emmett-Teller (BET) method. Although a much greater understanding of the processes governing mineral reaction kinetics at the fluid-solid interface has developed since the initial proposition of the use of total surface area was made by Helgeson et al. [10], the use of BET surface areas is still generally useful and appropriate as a proxy for effective surface area in far from equilibrium reaction processes Hanchen et al. [11]. Additionally, the BET surface area is the observation of choice for calculating and modelling field scale dissolution processes as discussed by Zhu [12], Kampman et al. [13]. Thus normalisation of surface areas calculated from ȝCT images in this work by those observed using N2 BET also allows for both comparison and wider application in the use of the observations in subsequent modelling. The specific surface area of cylindrical pieces of each rock was measured, with samples sized so that they could also be imaged in the ȝCT. The dimensions of the samples were approximately 4 mm diameter and 10 mm length. The analysis was performed with a Micromeritics Tristar 3000 using nitrogen as the working gas. Figure 2 shows that the BET surface area of the rocks ranged nearly two orders of magnitude, from 0.08 m2/g for the Guelph carbonate up to 4.3 m2/g for the Edward carbonate. The surface area of Berea sandstone samples varies within the range of 0.71.4 m2/g, similar to values that can be found in the literature, e.g. Sen et al. [14].
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The calculation of specific surface area from ȝCT images were compared to those measured from bulk nitrogen BET measurements and the results are reported in Figure 2. The BET method infers surface area from observations of gas adsorption and the calculations are based on the molecular diameter of the working gas, in this case nitrogen. Thus the resolution of the surface area observations from BET was higher than the calculations from the ȝCT images that could only resolve features larger than 1ȝm. The results show that the BET measurements are consistently 1 to 2 orders of magnitude larger than calculations from ȝCT, but within a rock sample the correlation has as much repeatability as the BET surface area measurement itself. Furthermore, the ratio of BET surface area to ȝCT surface area provides an indication of the extent to which features below the resolution of the ȝCT are contributing to the total surface area. Increasing ratios indicate a larger portion of surface area associated with features below the resolution of the ȝCT. Plotting this ratio against the BET surface area it is clear that as the specific surface area increases a higher proportion of area is associated with features that are below the resolution of the X-ray images. 2.3. Minerals in 3 dimension The application ȝCT to mineral identification is not new. For example, Uesugi et al. [15], Tsuchiyama et al. [16], Tsuchiyama [17], and Tsuchiyama et al. [18] have shown that quantitative discussions of X-ray linear attenuation coefficients are possible with both mono- and poly-chromatic X-ray beams. It is possible to use information about the attenuation of X-ray light to obtain quantitative information about material densities and elemental composition. It is on this basis that we sought to create 3D mineral maps of the rocks directly from the X-ray imagery.
Fig. 1. (a) Photo of the Berea sandstone sample; (b) thin-section micrograph in cross-polarized light; (c) secondary electron image of grain-coating clays in the Berea sandstone sample.
Fig. 2. (a) The BET specific surface areas; (b) surface area correlation between BET and CT; (c) surface roughness, where the “roughness” ratio of BET surface area to CT calculated surface area plotted against BET surface area.
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Fig. 3. The mineral identification process: (a) an example label (quartz); (b) segmented Berea sandstone.
It was found that given a reasonably optimal setup, the contrast of the image was sensitive to the parameters of energy, specimen dimension, and byte scaling. Ultimately, operating the beam at 40kV and 3W, at a resolution of 1ȝm on the Xradia VersaXRM-500 produced images viable for mineral identification. The specimens were cut to less than 2 mm to minimize beam hardening, and the reconstructed data scaled to the smallest range possible. The parameters used were 2500 projections, 20s exposure time, and camera binning of 2, to collect a 109 voxel image. Once collected, the ȝCT image was processed as follows. The reconstructed volume was first de-noised using the non-local means neighbourhood filter in Avizo Fire 8.0. The minerals were identified according to their absorption or greyscale value using multiphase watershed in Avizo Fire 8 for both binary and mineral-specific segmentation. Gradient thresholding was used to mask grain boundaries with transitioning greyscale values. The threshold was chosen so that the finer features were not blotted out but it still produced a thin mask over the grain boundaries. With the mask applied, the mineral phases were categorised based on mean greyscale values. Then watershed transform was computed to establish the identity of the remaining voxels by expanding the initial labels. Figure 3 shows the initial categorisation, as an example, the quartz label, and the final segmented rock after the watershed transform. One pore phase and four mineral categories corresponding to clay, quartz, feldspar and other minerals (e.g. carbonate cement, oxides, and garnet) were identified. Finally, a cube of 600s voxels was extracted from the centre of the image for statistical analysis. 3. Analysis 3.1. ȝCT surface area The 3D X-ray images were used to generate a statistical description of the spatially varying property, surface-area-to-porevolume ratio, throughout the rock. Our workflow is to sub-sample an image at a chosen length scale, calculate the surface-areato-pore-volume ratio in that sub sample, and then repeat this process for every unique location throughout the X-ray image. For example, a 6003ȝm image contains 216 x 100ȝm unique sub samples. The surface area of mono-mineralogical (rock-pore) 3D ȝCT images were abstracted as a series of triangular mesh surfaces using a marching cubes algorithm. The meshing was carried out in Matlab R2012b using Peter Hammer's open source adaptation of Martin Helm’s Octave function [19]. The surface area was determined for each sub-sample, then normalised to the pore volume. Frequency histograms were generated for sub-sample sizes ranging from 50ȝm to 300ȝm. The frequency distributions were summarised as box plots. On each box plot the central mark is the median, x is the mean, the edges of the box are the 25th and 75th percentile, the whiskers mark 2.7 standard deviations and the red diamonds indicate outliers. With each distribution represented by a vertical box plot, the influence of sampling size on the spread and mean of each distribution was clearly observed. The distributions show a smaller spread at larger sampling scales partly due to smaller amounts of data available, but more significantly due to the increasing effect of volumetric averaging. This brings it back to the question of the effect of scale-dependent heterogeneity in determining upscaled average reaction rates. 3.2. Multi-mineralogic surface area The surface area between the solid and pore space for each mineral group was calculated using the mineral-specific images. The images were first reformed into 2 phases in order to mesh a surface. For an image with n number of phases, there are 2n-1-1 ways to binarise, and n!/2(n-2)! pairs of phases involved. The combinations constitute a system of linear equations Ax=B, where A is the pairings associated with the combination C, x are the pairs, and B is the surface area for combination C. For the 5 phase Berea images, there were 15 combinations, and 10 pairings. The surfaces were meshed for each combination, and the area, B calculated using Heron's formula. Since the pore space is group 1, the first 4 pairings, x1 to x4 represent the surface area for each mineral group; the groups 2 to 4 are clay, quartz, feldspar, and others respectively.
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Using the mineral-specific surface areas, the sub-volume sampling process described in Section 3.1 was duplicated to generate statistical distributions but this time for each mineral phase separately. Figure 5 show the surface area distributions for a range of sub-sample sizes, with separate colours for each mineral group. The clays tend to show large but not the highest mean and spread in specific surface area. This may be an effect of the segmentation process. At 1ȝm voxel size, some of the profiles of the clay could be identified. From that, only a small fraction of the complex geometries is retained during segmentation. This resulted in the clays looking more globose than stacked plates or filamentous webs. This loss is true for other complex microstructures like the fluted and partially resorbed detrital feldspar grains that were observed under SEM. Our current equipment is not fit for identifying thin structures or pore lining features such as chlorite rims and various grain coating clays. This limitation means that although some of the macro distribution properties of the clays in the spread have been captured, the mean surface area is lower than quartz because of the diminished shapes that are left with after imaging and segmentation.
Fig. 4. Mono-mineralogic surface area distributions for the Berea sandstone sample.
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Fig. 5. Multi-mineralogic surface area distributions for the Berea sandstone sample.
The natural logarithm of each distribution is also plotted alongside to evaluate their lognormal character. The natural logarithm plots also show how the lognormal fitting performs. The approximation is good with the Berea. The natural log plots also show peaks at 0 (indicated by -inf) where the sub-volume samples have no surfaces associated with that mineral. For example, in Figure 5 at 200ȝm, 7% of the sub-volume sample cubes do not have feldspar in them. This is included in the legend as 'Sampling fraction'.
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4. Conclusion The work presented is the first characterisation of pore-scale heterogeneity in the reactive surface area of minerals within a permeable rock based on direct observation of the mineral distribution and pore morphology in three dimensions. The information can be used directly in statistically based models of reactive transport including the emerging group of pore network models focused on characterising reactive processes. The data can also be used to understand constraints imposed by heterogeneity in mineral surface area on techniques for modelling field scale reaction rates and interpreting reaction rate data obtained from the field or even core-scale measurements. It was observed in this work that the nature of the heterogeneity can be highly specific to a given rock. In the Berea sandstone, clays that appeared to preferentially coat quartz grains resulted in little correlation between the modal mineral composition of the rock and the fraction of surface area at the pore interface made of a specific mineral. At the scale of thousands of pores or smaller, the combination of heterogeneity in mineral distribution and varying pore morphology resulted in a range of distribution types applicable for describing surface area heterogeneity. Surface area could be distributed log-normally with long tails. These characterisations provide useful insight into the impact that the spatial expression of reactive surface area will play in governing the overall rate of reactive processes during flow through porous geologic media. Acknowledgements The authors gratefully acknowledge funding support for this work from the Qatar Carbonates and Carbon Storage Research Centre provided jointly by Shell, Qatar Petroleum and the Qatar Science and Technology Park. 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