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Micro-CT image calibration to improve fracture aperture measurement
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Micro-CT image calibration to improve fracture aperture measurement Hamed Lamei Ramandi ∗ , Ryan T. Armstrong, Peyman Mostaghimi School of Petroleum Engineering, The University of New South Wales, Sydney NSW 2052, Australia
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a b s t r a c t A novel technique for the accurate measurement and adjustment of fracture apertures in digital images of fractured media is presented. We utilize X-ray micro-computed tomography to image a highly fractured coal sample and collect high-resolution scanning electron microscope (SEM) images from the samples surface to facilitate segmentation of coal fractures. The gray-scale micro-CT values at the mid-point of fractures are obtained and correlated to aperture sizes measured with the higher resolution SEM data. Afterwards, the micro-CT images are upsampled to enable assignment of aperture sizes smaller than the image resolution. We initially segment the coal image, upsample the segmented image, and then re-calibrate the fracture aperture sizes. The final calibrated segmented image contains the fracture network acquired from the micro-CT data with precise aperture sizes assigned based on the high-resolution SEM data. To illustrate the importance of accurate aperture measurement, two coal subsets are tested. The permeabilities before and after applying the calibration method are measured. The results show a significant change in numerical permeabilities after applying the calibration method. This indicates that a large amount of information is potentially omitted when utilizing standard image segmentation tools to segment fractured media. © 2016 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/4.0/).
1. Introduction Coal Bed Methane (CBM) is the methane gas (CH4 ) extracted from deeply buried coal seams. Contrary to conventional reservoirs, fluid flow in coal seams is dominated by a highly permeable natural fracture network rather than pores [6, 17]. The characterization of this fracture network is important for choosing commercial CBM reservoirs [42] where there is percolation from one micro-fracture to the next [18]. Fracture aperture size is a key parameter in coal fracture characterization that has received little attention, and there are limited data available on aperture size distribution in the literature [22]. Fracture aperture size refers to the distance between two surfaces of a fracture [7,21]. Several techniques have been used to characterize the fracture geometry and/or aperture distributions, e.g. using digital profiles of the fracture surface [1] or injecting hardening resin or Wood’s metal into a fracture to make a cast [8,27]. Since these methods are destructive, it is important to develop nondestructive techniques for measuring the fracture aperture size distribution. In the last three decades a number of researchers have employed nondestructive techniques for measuring fracture aperture sizes including
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Corresponding author. E-mail addresses: [email protected] (H.L. Ramandi), [email protected] (R.T. Armstrong), [email protected] (P. Mostaghimi). http://dx.doi.org/10.1016/j.csndt.2016.03.001 2214-6571/© 2016 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/4.0/).
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transmitted light [5,30], nuclear magnetic resonance imaging [15,30] and X-ray micro-computed tomography (micro-CT) imaging [13,14,22,31,36,37,40,43]. The key advantage of micro-CT over other techniques is that, for a core-scale sample, it provides higher quality 3D images and allows for digital isolation of favorable sections in the sample. However, when using micro-CT, it is difficult to visualize and even more difficult to accurately measure micrometer-sized fracture apertures. This is because the fracture apertures usually exist near the resolution limit of the micro-CT scanner. This is a significant issue when measuring fracture apertures from segmented data by simply counting the number of pixels that transverse a fracture. Near the image resolution, mislabeling of only a few voxels can create significant error. This can often provide a gross overestimation/underestimation of aperture widths [23]. To accurately represent a fracture network at the core-scale, the sample must be large enough to contain planar fractures and their interconnectivities. However, for this situation, the image resolution in the direction normal to a fracture, is often not enough, i.e. represented by only a few voxels [14]. A few approaches have been proposed where the local gradient in pixel values from the raw and/or filtered images are used to assist fracture aperture measurements [11,14,22,26,37]. Vandersteen et al. [37] explained and compared several parameters, i.e. missing attenuation, peak height, and full width at half maximum for fracture aperture size measurement. They indicated that the advantage of peak height is that it is independent of fracture direction. Mazumder et al. [22] showed that peak height is a better parameter to calculate fracture apertures with lower widths. Using these approaches requires at least two sets of micro-CT images; one for capturing fractures of known dimensions and another for the sample of interest. Using this type of calibration curve can produce uncertainties. This is because attenuation coefficients of each substance can vary with any changes in the imaging conditions. This results in a unique calibration curve for each image obtained that is not comparable for different imaging conditions. This unique calibration curve is not applicable for other images, e.g. images of natural fractures, acquired at different imaging conditions. Another issue with studying coal samples, particularly bright coals, is that coring the sample is difficult. The coring of bright coals that contain a well-developed conductive fracture network usually results in the sample crumpling. This represents a fundamental challenge to subsurface fracture characterization. Herein, we introduce a novel method in which we image coal as a complex fractured porous medium at full core-plug scale, i.e. no additional coring is required. In this technique, we resolve the fracture apertures of the fluid-accessible fracture network. We register high-resolution scanning electron microscope (SEM) images from the samples external surface directly into the micro-CT image to generate a calibration curve. This technique eliminates the need for coring the sample to image with micro-CT at higher resolution as well as the uncertainties caused by acquiring two sets of images at different imaging conditions. We apply the calibration curve to the raw micro-CT image to measure apertures at each point where a fracture exists. Afterward, an algorithm assigns measured apertures to create a calibrated binary image. Lastly, to show the importance of fracture calibration, permeability of the new calibrated image is numerically computed and compared with the results where non-calibrated image segmentation methods are used. 2. Materials and methods 2.1. The sample and data acquisition procedure A cylindrical coal sample, 25 mm in diameter and 37 mm in length, that contains a well-developed fracture network (bright coal) surrounded by less-fractured coal (dull coal) is chosen. The geology of the region and sample specifications are discussed in [29]. A helical scanning micro-CT instrument which is build and developed at Australian National University is used for micro-CT imaging [34]. The instrument routinely acquires images with cone-angles greater than 50◦ [38,39]. Imaging parameters and specification of the instrument are shown in Table 1. In this technique, when performing micro-CT imaging the sample is moved according to a pre-defined helical trajectory, along which a series of radiographs are recorded uniformly around the sample at different viewing angles. The radiographs represent the cumulative attenuation of the X-ray beam through the sample, and are referred to as projections. This method produces a data set with complete information about the sample by collecting projection data along a helical trajectory [39]. To generate a 3D spatial representation of the sample (tomogram), the projections are reconstructed using a reconstruction algorithm based on the Katsevich [12] inversion formula for a helix trajectory. Each data point in the tomogram represents effective X-ray attenuation coefficient which in turn is associated with the density of the sample and expressed by a 16-bit gray-scale image. The micro-CT imaging begins with scanning the sample in as-received (dry) condition. The sample is then saturated with an X-ray attenuating fluid and re-imaged (wet image) to highlight all of the fluid-accessible fractures using the technique described by Golab et al. [9]. The X-ray attenuating fluid is a mixture of 1.5 molar Sodium Iodide (NaI) and 1.0 molar Potassium Chloride (KCl). The sample is initially saturated under vacuum, and then, to ensure that all the fluid-accessible pores and fractures are saturated, the fluid is injected at a high pressure of ∼670 bar. The resolution of acquired images, wet and dry, is 16.5 μm (Fig. 1a and b). In each imaging experiment a 3 mm thick aluminum filter is used to minimize beam-hardening artifacts by attenuating soft X-rays at the source. After micro-CT imaging in order to acquire a higher resolution image, the external surface of the sample is polished for SEM imaging. Secondary Electron and Backscatter Electron SEM techniques are accomplished using a Hitachi S3400 at the Electron Microscope Unit of the Mark Wainwright Analytical Centre at the University of New South Wales. Although SEM is considered as a destructive method, it does not affect the petrophysical properties of sample, i.e. porosity, permeability and aperture distribution, since the data is collected from the
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Table 1 Imaging parameters and specification of the micro-CT instrument used in this study. Scanning parameters
Specifications
Micro-focus X-ray source Radiographic field of vision Number of display voxels Detector pixel size Acquisition time Energy of X-ray Scanning operation X-ray beam form Detector Number of projection per revolution Total number of projections Pitch The angular step The vertical step
GE ns:180 28 mm × 35 mm 3040 × 3040 140 μm 23 h 120 kV (100 mA) Helical system Cone beam Perkin Elmer 2520 10106 25.938 mm 0.002493 Rad 0.010293 mm
Fig. 1. A registered 2D bedding plane section (X-slice) through the sample. a: dry micro-CT image (black = pores and fractures, gray = macerals and white = minerals), b: wet micro-CT image (white = minerals and saturated pores and fractures and black = macerals), c: the same slice from the difference image (inverted difference map, black = pores and fractures, gray = macerals and white = minerals).
external surface of the sample. In addition, the fracture aperture size reconstruction method presented herein can be used with any high-resolution imaging method, such as, region-of-interest micro-CT imaging instead of SEM. The technique developed by Latham et al. [16] is used to register the wet micro-CT image to the dry one. Subtracting the dry and wet images generates the difference image (Fig. 1c). The difference image exposes all of the fluid-accessible structures that are not readily observable with conventional imaging techniques [28,29]. This allows for extracting a more realistic fracture network. The registration technique developed by Latham et al. [16] is employed for registering SEM images to micro-CT images (Fig. 2). This technique enables a direct comparison of the high-resolution SEM image and the corresponding slice from the 3D tomographic image. This technique also assists in selection of appropriate threshold levels and generation of the calibration curve. 2.2. Image enhancement and segmentation Prior to segmentation, for sharpening the image, a nonlinear anisotropic diffusion filter [32,35] followed by the unsharp mask is applied to the difference image [35]. Image segmentation is the process of converting a grey-scale multiphase image into two or more unique well-defined regions. This process is proven to be quite challenging for complex multi-mineral fractured samples such as coal. An advanced method based on a combination of the watershed method [41] and active contour methods [3], called converging active contours (CAC) is used on the filtered difference image to obtain an acceptable segmentation result. CAC employs gradient and local intensity information simultaneously [33,35]. CAC begins by selecting two
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Fig. 2. a: A registered 2D slice of the micro-CT difference image (16.5 μm voxel length) compared to the higher resolution information (5.5 μm/pixel) in the SEM image (b), c: the enlarged portion of the registered micro-CT slice, d: the same region (c) in SEM image (43 nm/pixel).
user-defined lower and upper thresholds. The values less than the lower threshold are labeled as voids and the values above the upper threshold are labeled as solids and the values between the lower and upper thresholds are labeled as unallocated region. The labeled regions grow towards each other, within the unallocated region, to set the boundary at the points where two contours converge. At boundary regions the exact interface between phases is identified by using the image intensity gradient [33,35]. Using CAC the image is segmented into four phases: (1) fracture network (2) micro-pores (3) coal macerals (organic materials) that includes regions of the coal that are not penetrated by contrasting agent, and (4) mineral phase that includes high density regions in the coal (Fig. 3). This creates the non-calibrated segmented image. For a more detailed discussion of segmentation methods, the reader is referred to Sheppard et al. [35] and Schlüter et al. [33]. 2.3. Calibration curve Theoretically, the 2D micro-CT image of a fracture can be considered as the convolution of a box function with a Gaussian Point Spread Function (PSF) [14,37]. The response from this convolution can be matched to the raw image attenuation profile or gray-scale profile that transverses a fracture by adjusting the width of the box function once the PSF is known [14]. We first find the PSF of the micro-CT image using the SEM images as the ground truth fracture aperture measurement. To generate a calibration curve, we correlate the peak height value of numerous aperture profiles acquired from the micro-CT images to the aperture size measured, using the method presented by Ketcham et al. [14]. This provides a direct relationship between the X-ray attenuation coefficient (gray-scale value) at the mid-point of a fracture to the actual fracture aperture (Fig. 4). A distinct calibration curve must be generated for each image since the coefficients, and consequently the gray-scale values, vary with any change in imaging condition and parameters.
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Fig. 3. 2D slice of the difference image and segmented image. a: The difference image (dark = fractures and pores, grey = macerals and white = minerals), b: the non-calibrated segmented image (red = fracture network, green = micro-pores, blue = macerals, and cyan = minerals).
Fig. 4. The calibration curve used in this study. The gray-scale values are obtained from the inverted dry image.
2.4. Image upsampling and aperture adjustment algorithm The voxel size of the segmented image is restricted to the voxel size of the miro-CT image. This makes it impossible to assign the correct aperture width where a fracture aperture with a size smaller than image resolution is measured. This issue is resolved by upsampling the images using the Catmull–Rom interpolation [4]. Upsampling is a technique that creates an image with a smaller pixel size by increasing the number of pixels [2,10,19]. This allows for assigning aperture sizes smaller than the image resolution to the fracture network. To locate the mid-points on the fracture network, a medial axis [20] is drawn from the fracture network of the upsampled segmented image (non-calibrated image). Then, gray-scale values along the medial axis are extracted and converted to the aperture values using the equation derived from the calibration curve. This generates a weighted medial axis containing the aperture values. Then the aperture adjustment algorithm goes along the medial axis and opens it according to the corresponding aperture values to generate a new binary image. The result is an SEM-calibrated image in which the fracture network is obtained from the micro-CT images while the aperture sizes are assigned based on the calibration curve obtained from the high-resolution SEM data. 2.5. Connectivity and permeability measurement methods To identify the connected network (cluster), a sample-spanning algorithm is implemented. It initially performs a clusterlabeling algorithm to identify all the connected components of the phase of interest, using a voxel neighborhood connectivity requirement of 6. The algorithm removes the clusters that do not span across the sample from inlet to outlet. The next step
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is simulation of flow in the porous medium using computational fluid dynamics methods to obtain the velocity field [24,25]. Permeability prediction is obtained based on the finite volume solution of the Stokes equation in the connected void space
μ∇ 2 u = ∇ P where u is the velocity vector, P is pressure, and solid surfaces.
(1)
μ is the fluid viscosity. A no-slip boundary condition is applied on the
3. Result and discussion Two subset images (500 × 500) from bright and dull coals are obtained from the micro-CT image of the sample. The chosen bright coal contains a well-developed fracture network. We purposely acquire a subset of dull coal which contains a few fractures. In this way, we can evaluate the impact of the image resolution and segmentation on fracture characterization in the bright and dull coals. The subsets are upsampled by a factor of 4× to create images with a pixel size of ∼4 μm which in turn makes the image size 16× larger. The factor 4× is chosen based on the results presented by Ketcham et al. [14]. Fig. 5a and b shows a registered micro-CT slice and its segmentation result, respectively, using a non-calibrated segmentation technique. This demonstrates the significant error in aperture measurement when a non-calibrated image is used. The weighted medial axis of the same slice is displayed in the Fig. 5c and is compared with the corresponding SEM image taken from a region not used in generation of the original calibration curve (Fig. 5d). This indicates that the presented method can measure apertures with higher accuracy than non-calibrated methods. Fig. 6 shows the distribution of apertures in the bright coal after applying the calibration curve (calibrated image). In this particular case, a bimodal distribution is seen; however, this trend is not universal to coal, i.e. we have observed distinctly different distributions for other coal samples. For Fig. 6, the smaller cleat size distribution mainly represents fracture apertures with a peak size of 12 μm. While the larger cleat size distribution, displays fracture apertures with a peak size of 36 μm. This indicates that most of the aperture sizes are less than the image resolution and would have been neglected if the non-calibrated segmented image was used. To illustrate the significance of precise fracture aperture measurements, the generated calibrated images, in which the calculated apertures are assigned, are used for numerical calculation of permeability (Fig. 7, Fig. 8). The permeability results
Fig. 5. a: A registered slice of the difference image (16.5 μm voxels, dark = fractures and pores, grey = macerals and white = minerals), b: the noncalibrated segmented image of the same slice (16.5 μm voxels, black = fracture, green = solid), c: the weighted medial axis of the same slice, d: the SEM image of the same slice (2 μm/pixel).
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Fig. 6. Normalized distribution of fracture aperture in the calibrated bright coal.
Fig. 7. Image processing of the bright coal. a: A 2D slice of the difference image (dark = fractures and pores, grey = macerals and white = minerals), b: the non-calibrated image (green = fracture network, red = micro-pores, white = macerals, and cyan = minerals), c: the normalized velocity profile of percolating fractures in the calibrated image, the upper right box shows the normalized velocity profile of percolating fractures in non-calibrated image.
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Fig. 8. Image processing of the dull coal. a: A 2D slice of the difference image (dark = fractures and pores, grey = macerals and white = minerals), b: the non-calibrated image (green = fracture network, red = micro-pores, white = macerals), c: the normalized velocity profile of percolating fractures in the calibrated image.
Table 2 The permeability of the bright and dull coal before and after calibration. Segmentation method
Bright coal Non-calibrated
Calibrated
Non-calibrated
Dull coal Calibrated
Permeability (mD)
73
694
0
78
using non-calibrated images and calibrated images for the bright and dull coals are presented in Table 2. The results indicate a significant change in numerical permeability when the fracture network is generated using the calibration method. This occurs because the calibrated images include and adjust the entire fracture network. Some of the fractures are often neglected in the non-calibrated images. 4. Conclusion We developed an image processing workflow that uses micro-CT to image coal samples at dry and contrasting agent saturated (wet) conditions. Dry and wet images are registered and subsequent subtracting of them creates the difference
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image that reveals all of the fluid-accessible structures that are not readily visible with conventional observation techniques. SEM images from the external surface of the sample are acquired and registered into the micro-CT data. At every fracture mid-point for each image, the true aperture (from SEM image) and gray-scale value (from micro-CT image) is obtained. The attenuation values and true apertures are plotted against each other to generate a calibration curve. Two subset images from the bright and dull regions of the imaged sample are acquired. The images are upsampled to provide a smaller voxel size allowing for assigning aperture sizes smaller than the original image resolution. Medial axes of the bright and dull coals are generated using the upsampled images. The medial axes are used to locate the fracture network mid-points for obtaining the gray-scale value from the dry micro-CT image. The equation derived from the calibration curve is applied to the medial axes of gray-scale values to provide weighted medial axes containing true aperture values. Then, an aperture adjustment algorithm goes along the medial axes and generates calibrated binary images by opening the medial axes according to the calculated aperture sizes. Lastly, to demonstrate the importance of precise aperture measurement, permeabilities of the non-calibrated and SEM-calibrated images are calculated using a direct simulation algorithm. Using accurately calibrated images result in significant change in the permeability of dull and bright coals. This indicates that a large amount of information is potentially neglected when determining coal permeability from micro-CT images if the intricacies of image processing and segmentation are not considered. 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Case Studies in Nondestructive Testing and Evaluation www.elsevier.com/locate/csndt
Micro-CT image calibration to improve fracture aperture measurement Hamed Lamei Ramandi ∗ , Ryan T. Armstrong, Peyman Mostaghimi School of Petroleum Engineering, The University of New South Wales, Sydney NSW 2052, Australia
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a b s t r a c t A novel technique for the accurate measurement and adjustment of fracture apertures in digital images of fractured media is presented. We utilize X-ray micro-computed tomography to image a highly fractured coal sample and collect high-resolution scanning electron microscope (SEM) images from the samples surface to facilitate segmentation of coal fractures. The gray-scale micro-CT values at the mid-point of fractures are obtained and correlated to aperture sizes measured with the higher resolution SEM data. Afterwards, the micro-CT images are upsampled to enable assignment of aperture sizes smaller than the image resolution. We initially segment the coal image, upsample the segmented image, and then re-calibrate the fracture aperture sizes. The final calibrated segmented image contains the fracture network acquired from the micro-CT data with precise aperture sizes assigned based on the high-resolution SEM data. To illustrate the importance of accurate aperture measurement, two coal subsets are tested. The permeabilities before and after applying the calibration method are measured. The results show a significant change in numerical permeabilities after applying the calibration method. This indicates that a large amount of information is potentially omitted when utilizing standard image segmentation tools to segment fractured media. © 2016 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/4.0/).
1. Introduction Coal Bed Methane (CBM) is the methane gas (CH4 ) extracted from deeply buried coal seams. Contrary to conventional reservoirs, fluid flow in coal seams is dominated by a highly permeable natural fracture network rather than pores [6, 17]. The characterization of this fracture network is important for choosing commercial CBM reservoirs [42] where there is percolation from one micro-fracture to the next [18]. Fracture aperture size is a key parameter in coal fracture characterization that has received little attention, and there are limited data available on aperture size distribution in the literature [22]. Fracture aperture size refers to the distance between two surfaces of a fracture [7,21]. Several techniques have been used to characterize the fracture geometry and/or aperture distributions, e.g. using digital profiles of the fracture surface [1] or injecting hardening resin or Wood’s metal into a fracture to make a cast [8,27]. Since these methods are destructive, it is important to develop nondestructive techniques for measuring the fracture aperture size distribution. In the last three decades a number of researchers have employed nondestructive techniques for measuring fracture aperture sizes including
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Corresponding author. E-mail addresses: [email protected] (H.L. Ramandi), [email protected] (R.T. Armstrong), [email protected] (P. Mostaghimi). http://dx.doi.org/10.1016/j.csndt.2016.03.001 2214-6571/© 2016 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/4.0/).
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transmitted light [5,30], nuclear magnetic resonance imaging [15,30] and X-ray micro-computed tomography (micro-CT) imaging [13,14,22,31,36,37,40,43]. The key advantage of micro-CT over other techniques is that, for a core-scale sample, it provides higher quality 3D images and allows for digital isolation of favorable sections in the sample. However, when using micro-CT, it is difficult to visualize and even more difficult to accurately measure micrometer-sized fracture apertures. This is because the fracture apertures usually exist near the resolution limit of the micro-CT scanner. This is a significant issue when measuring fracture apertures from segmented data by simply counting the number of pixels that transverse a fracture. Near the image resolution, mislabeling of only a few voxels can create significant error. This can often provide a gross overestimation/underestimation of aperture widths [23]. To accurately represent a fracture network at the core-scale, the sample must be large enough to contain planar fractures and their interconnectivities. However, for this situation, the image resolution in the direction normal to a fracture, is often not enough, i.e. represented by only a few voxels [14]. A few approaches have been proposed where the local gradient in pixel values from the raw and/or filtered images are used to assist fracture aperture measurements [11,14,22,26,37]. Vandersteen et al. [37] explained and compared several parameters, i.e. missing attenuation, peak height, and full width at half maximum for fracture aperture size measurement. They indicated that the advantage of peak height is that it is independent of fracture direction. Mazumder et al. [22] showed that peak height is a better parameter to calculate fracture apertures with lower widths. Using these approaches requires at least two sets of micro-CT images; one for capturing fractures of known dimensions and another for the sample of interest. Using this type of calibration curve can produce uncertainties. This is because attenuation coefficients of each substance can vary with any changes in the imaging conditions. This results in a unique calibration curve for each image obtained that is not comparable for different imaging conditions. This unique calibration curve is not applicable for other images, e.g. images of natural fractures, acquired at different imaging conditions. Another issue with studying coal samples, particularly bright coals, is that coring the sample is difficult. The coring of bright coals that contain a well-developed conductive fracture network usually results in the sample crumpling. This represents a fundamental challenge to subsurface fracture characterization. Herein, we introduce a novel method in which we image coal as a complex fractured porous medium at full core-plug scale, i.e. no additional coring is required. In this technique, we resolve the fracture apertures of the fluid-accessible fracture network. We register high-resolution scanning electron microscope (SEM) images from the samples external surface directly into the micro-CT image to generate a calibration curve. This technique eliminates the need for coring the sample to image with micro-CT at higher resolution as well as the uncertainties caused by acquiring two sets of images at different imaging conditions. We apply the calibration curve to the raw micro-CT image to measure apertures at each point where a fracture exists. Afterward, an algorithm assigns measured apertures to create a calibrated binary image. Lastly, to show the importance of fracture calibration, permeability of the new calibrated image is numerically computed and compared with the results where non-calibrated image segmentation methods are used. 2. Materials and methods 2.1. The sample and data acquisition procedure A cylindrical coal sample, 25 mm in diameter and 37 mm in length, that contains a well-developed fracture network (bright coal) surrounded by less-fractured coal (dull coal) is chosen. The geology of the region and sample specifications are discussed in [29]. A helical scanning micro-CT instrument which is build and developed at Australian National University is used for micro-CT imaging [34]. The instrument routinely acquires images with cone-angles greater than 50◦ [38,39]. Imaging parameters and specification of the instrument are shown in Table 1. In this technique, when performing micro-CT imaging the sample is moved according to a pre-defined helical trajectory, along which a series of radiographs are recorded uniformly around the sample at different viewing angles. The radiographs represent the cumulative attenuation of the X-ray beam through the sample, and are referred to as projections. This method produces a data set with complete information about the sample by collecting projection data along a helical trajectory [39]. To generate a 3D spatial representation of the sample (tomogram), the projections are reconstructed using a reconstruction algorithm based on the Katsevich [12] inversion formula for a helix trajectory. Each data point in the tomogram represents effective X-ray attenuation coefficient which in turn is associated with the density of the sample and expressed by a 16-bit gray-scale image. The micro-CT imaging begins with scanning the sample in as-received (dry) condition. The sample is then saturated with an X-ray attenuating fluid and re-imaged (wet image) to highlight all of the fluid-accessible fractures using the technique described by Golab et al. [9]. The X-ray attenuating fluid is a mixture of 1.5 molar Sodium Iodide (NaI) and 1.0 molar Potassium Chloride (KCl). The sample is initially saturated under vacuum, and then, to ensure that all the fluid-accessible pores and fractures are saturated, the fluid is injected at a high pressure of ∼670 bar. The resolution of acquired images, wet and dry, is 16.5 μm (Fig. 1a and b). In each imaging experiment a 3 mm thick aluminum filter is used to minimize beam-hardening artifacts by attenuating soft X-rays at the source. After micro-CT imaging in order to acquire a higher resolution image, the external surface of the sample is polished for SEM imaging. Secondary Electron and Backscatter Electron SEM techniques are accomplished using a Hitachi S3400 at the Electron Microscope Unit of the Mark Wainwright Analytical Centre at the University of New South Wales. Although SEM is considered as a destructive method, it does not affect the petrophysical properties of sample, i.e. porosity, permeability and aperture distribution, since the data is collected from the
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Table 1 Imaging parameters and specification of the micro-CT instrument used in this study. Scanning parameters
Specifications
Micro-focus X-ray source Radiographic field of vision Number of display voxels Detector pixel size Acquisition time Energy of X-ray Scanning operation X-ray beam form Detector Number of projection per revolution Total number of projections Pitch The angular step The vertical step
GE ns:180 28 mm × 35 mm 3040 × 3040 140 μm 23 h 120 kV (100 mA) Helical system Cone beam Perkin Elmer 2520 10106 25.938 mm 0.002493 Rad 0.010293 mm
Fig. 1. A registered 2D bedding plane section (X-slice) through the sample. a: dry micro-CT image (black = pores and fractures, gray = macerals and white = minerals), b: wet micro-CT image (white = minerals and saturated pores and fractures and black = macerals), c: the same slice from the difference image (inverted difference map, black = pores and fractures, gray = macerals and white = minerals).
external surface of the sample. In addition, the fracture aperture size reconstruction method presented herein can be used with any high-resolution imaging method, such as, region-of-interest micro-CT imaging instead of SEM. The technique developed by Latham et al. [16] is used to register the wet micro-CT image to the dry one. Subtracting the dry and wet images generates the difference image (Fig. 1c). The difference image exposes all of the fluid-accessible structures that are not readily observable with conventional imaging techniques [28,29]. This allows for extracting a more realistic fracture network. The registration technique developed by Latham et al. [16] is employed for registering SEM images to micro-CT images (Fig. 2). This technique enables a direct comparison of the high-resolution SEM image and the corresponding slice from the 3D tomographic image. This technique also assists in selection of appropriate threshold levels and generation of the calibration curve. 2.2. Image enhancement and segmentation Prior to segmentation, for sharpening the image, a nonlinear anisotropic diffusion filter [32,35] followed by the unsharp mask is applied to the difference image [35]. Image segmentation is the process of converting a grey-scale multiphase image into two or more unique well-defined regions. This process is proven to be quite challenging for complex multi-mineral fractured samples such as coal. An advanced method based on a combination of the watershed method [41] and active contour methods [3], called converging active contours (CAC) is used on the filtered difference image to obtain an acceptable segmentation result. CAC employs gradient and local intensity information simultaneously [33,35]. CAC begins by selecting two
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Fig. 2. a: A registered 2D slice of the micro-CT difference image (16.5 μm voxel length) compared to the higher resolution information (5.5 μm/pixel) in the SEM image (b), c: the enlarged portion of the registered micro-CT slice, d: the same region (c) in SEM image (43 nm/pixel).
user-defined lower and upper thresholds. The values less than the lower threshold are labeled as voids and the values above the upper threshold are labeled as solids and the values between the lower and upper thresholds are labeled as unallocated region. The labeled regions grow towards each other, within the unallocated region, to set the boundary at the points where two contours converge. At boundary regions the exact interface between phases is identified by using the image intensity gradient [33,35]. Using CAC the image is segmented into four phases: (1) fracture network (2) micro-pores (3) coal macerals (organic materials) that includes regions of the coal that are not penetrated by contrasting agent, and (4) mineral phase that includes high density regions in the coal (Fig. 3). This creates the non-calibrated segmented image. For a more detailed discussion of segmentation methods, the reader is referred to Sheppard et al. [35] and Schlüter et al. [33]. 2.3. Calibration curve Theoretically, the 2D micro-CT image of a fracture can be considered as the convolution of a box function with a Gaussian Point Spread Function (PSF) [14,37]. The response from this convolution can be matched to the raw image attenuation profile or gray-scale profile that transverses a fracture by adjusting the width of the box function once the PSF is known [14]. We first find the PSF of the micro-CT image using the SEM images as the ground truth fracture aperture measurement. To generate a calibration curve, we correlate the peak height value of numerous aperture profiles acquired from the micro-CT images to the aperture size measured, using the method presented by Ketcham et al. [14]. This provides a direct relationship between the X-ray attenuation coefficient (gray-scale value) at the mid-point of a fracture to the actual fracture aperture (Fig. 4). A distinct calibration curve must be generated for each image since the coefficients, and consequently the gray-scale values, vary with any change in imaging condition and parameters.
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Fig. 3. 2D slice of the difference image and segmented image. a: The difference image (dark = fractures and pores, grey = macerals and white = minerals), b: the non-calibrated segmented image (red = fracture network, green = micro-pores, blue = macerals, and cyan = minerals).
Fig. 4. The calibration curve used in this study. The gray-scale values are obtained from the inverted dry image.
2.4. Image upsampling and aperture adjustment algorithm The voxel size of the segmented image is restricted to the voxel size of the miro-CT image. This makes it impossible to assign the correct aperture width where a fracture aperture with a size smaller than image resolution is measured. This issue is resolved by upsampling the images using the Catmull–Rom interpolation [4]. Upsampling is a technique that creates an image with a smaller pixel size by increasing the number of pixels [2,10,19]. This allows for assigning aperture sizes smaller than the image resolution to the fracture network. To locate the mid-points on the fracture network, a medial axis [20] is drawn from the fracture network of the upsampled segmented image (non-calibrated image). Then, gray-scale values along the medial axis are extracted and converted to the aperture values using the equation derived from the calibration curve. This generates a weighted medial axis containing the aperture values. Then the aperture adjustment algorithm goes along the medial axis and opens it according to the corresponding aperture values to generate a new binary image. The result is an SEM-calibrated image in which the fracture network is obtained from the micro-CT images while the aperture sizes are assigned based on the calibration curve obtained from the high-resolution SEM data. 2.5. Connectivity and permeability measurement methods To identify the connected network (cluster), a sample-spanning algorithm is implemented. It initially performs a clusterlabeling algorithm to identify all the connected components of the phase of interest, using a voxel neighborhood connectivity requirement of 6. The algorithm removes the clusters that do not span across the sample from inlet to outlet. The next step
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is simulation of flow in the porous medium using computational fluid dynamics methods to obtain the velocity field [24,25]. Permeability prediction is obtained based on the finite volume solution of the Stokes equation in the connected void space
μ∇ 2 u = ∇ P where u is the velocity vector, P is pressure, and solid surfaces.
(1)
μ is the fluid viscosity. A no-slip boundary condition is applied on the
3. Result and discussion Two subset images (500 × 500) from bright and dull coals are obtained from the micro-CT image of the sample. The chosen bright coal contains a well-developed fracture network. We purposely acquire a subset of dull coal which contains a few fractures. In this way, we can evaluate the impact of the image resolution and segmentation on fracture characterization in the bright and dull coals. The subsets are upsampled by a factor of 4× to create images with a pixel size of ∼4 μm which in turn makes the image size 16× larger. The factor 4× is chosen based on the results presented by Ketcham et al. [14]. Fig. 5a and b shows a registered micro-CT slice and its segmentation result, respectively, using a non-calibrated segmentation technique. This demonstrates the significant error in aperture measurement when a non-calibrated image is used. The weighted medial axis of the same slice is displayed in the Fig. 5c and is compared with the corresponding SEM image taken from a region not used in generation of the original calibration curve (Fig. 5d). This indicates that the presented method can measure apertures with higher accuracy than non-calibrated methods. Fig. 6 shows the distribution of apertures in the bright coal after applying the calibration curve (calibrated image). In this particular case, a bimodal distribution is seen; however, this trend is not universal to coal, i.e. we have observed distinctly different distributions for other coal samples. For Fig. 6, the smaller cleat size distribution mainly represents fracture apertures with a peak size of 12 μm. While the larger cleat size distribution, displays fracture apertures with a peak size of 36 μm. This indicates that most of the aperture sizes are less than the image resolution and would have been neglected if the non-calibrated segmented image was used. To illustrate the significance of precise fracture aperture measurements, the generated calibrated images, in which the calculated apertures are assigned, are used for numerical calculation of permeability (Fig. 7, Fig. 8). The permeability results
Fig. 5. a: A registered slice of the difference image (16.5 μm voxels, dark = fractures and pores, grey = macerals and white = minerals), b: the noncalibrated segmented image of the same slice (16.5 μm voxels, black = fracture, green = solid), c: the weighted medial axis of the same slice, d: the SEM image of the same slice (2 μm/pixel).
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Fig. 6. Normalized distribution of fracture aperture in the calibrated bright coal.
Fig. 7. Image processing of the bright coal. a: A 2D slice of the difference image (dark = fractures and pores, grey = macerals and white = minerals), b: the non-calibrated image (green = fracture network, red = micro-pores, white = macerals, and cyan = minerals), c: the normalized velocity profile of percolating fractures in the calibrated image, the upper right box shows the normalized velocity profile of percolating fractures in non-calibrated image.
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Fig. 8. Image processing of the dull coal. a: A 2D slice of the difference image (dark = fractures and pores, grey = macerals and white = minerals), b: the non-calibrated image (green = fracture network, red = micro-pores, white = macerals), c: the normalized velocity profile of percolating fractures in the calibrated image.
Table 2 The permeability of the bright and dull coal before and after calibration. Segmentation method
Bright coal Non-calibrated
Calibrated
Non-calibrated
Dull coal Calibrated
Permeability (mD)
73
694
0
78
using non-calibrated images and calibrated images for the bright and dull coals are presented in Table 2. The results indicate a significant change in numerical permeability when the fracture network is generated using the calibration method. This occurs because the calibrated images include and adjust the entire fracture network. Some of the fractures are often neglected in the non-calibrated images. 4. Conclusion We developed an image processing workflow that uses micro-CT to image coal samples at dry and contrasting agent saturated (wet) conditions. Dry and wet images are registered and subsequent subtracting of them creates the difference
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image that reveals all of the fluid-accessible structures that are not readily visible with conventional observation techniques. SEM images from the external surface of the sample are acquired and registered into the micro-CT data. At every fracture mid-point for each image, the true aperture (from SEM image) and gray-scale value (from micro-CT image) is obtained. The attenuation values and true apertures are plotted against each other to generate a calibration curve. Two subset images from the bright and dull regions of the imaged sample are acquired. The images are upsampled to provide a smaller voxel size allowing for assigning aperture sizes smaller than the original image resolution. Medial axes of the bright and dull coals are generated using the upsampled images. The medial axes are used to locate the fracture network mid-points for obtaining the gray-scale value from the dry micro-CT image. The equation derived from the calibration curve is applied to the medial axes of gray-scale values to provide weighted medial axes containing true aperture values. Then, an aperture adjustment algorithm goes along the medial axes and generates calibrated binary images by opening the medial axes according to the calculated aperture sizes. Lastly, to demonstrate the importance of precise aperture measurement, permeabilities of the non-calibrated and SEM-calibrated images are calculated using a direct simulation algorithm. Using accurately calibrated images result in significant change in the permeability of dull and bright coals. This indicates that a large amount of information is potentially neglected when determining coal permeability from micro-CT images if the intricacies of image processing and segmentation are not considered. 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