**1. Introduction**

During the past 20 years, deep buried carbonate formations have become one of the major sources of natural gas resources in China. Unlike the carbonate formations discovered in the middle-east having a porosity of about 8–25% buried in depths of 2000–4500 m underground, lots of the carbonate gas formations discovered in China are buried over 5000 m in depth and consequently, these formations are usually 'tight' having a porosity of less than 6% [1]. The pore structural characteristics ofthese deep-buried tight carbonates are di fferent from those buried at shallower depths and referred studies are rare. In the seismic exploration, as well as the acoustic-logging evaluation, of the tight fractured-vuggy carbonate formations, a widely-aware challenge is that the seismic and acoustic properties of the carbonate formations depend, not only on the minerals and the porosity, but also the pore structural characteristics, especially for the tight deeply buried carbonates [2–7]. This issue becomes further complicated considering the fractures and the vugs developed in the carbonate rocks [8,9]. These challenges aroused interest in characterizing both the pore-structures and elastic properties of the tight fractured-vuggy carbonates in the lab before field formation evaluations.

Thin section observation, mercury injection, gas absorption, nuclear magnetic resonance (NMR), and micro-CT scanning are the popular methods for characterizing the pore structure in lab [10–18]. Among these methods, micro-CT scanning has a unique advantage in o ffering a visible spatial distribution of the pore space, including both the fractures and vugs. Characterizing the pore space of a rock using micro-CT scanning usually contains three major steps: segmenting the 2D pore space from each CT-scanned 2D image, constructing the 3D pore space with all the 2D images, and extracting pore structural parameters to quantitatively characterize the pore structure [19–22]. Histogram shape, clustering, entropy, object attribute, spatial and local methods are the commonly used threshold segmenting method [23,24]. Parameters widely used to characterize the pore structure are the porosity, tortuosity, connectivity, pore radius distribution, ratio of pore radius over throat radius, fracture orientation, etc. [25–32]. These pore structural parameters along with porosity are then usually used to interpret the behavior of the elastic waves propagating in carbonates [33–35]. It has been shown that the porosity–velocity relationship is related to the pore structure, especially those possessing fractures and vugs [36–38]. Previous studies are usually carried out on 1.0-inch cores that might not be representative for tight fractured-vuggy carbonates. Moving the lab study from 1.0-inch core plugs to full diameter cores could provide more representative results but adds to the di fficulties in acquiring and interpreting the lab data.

One di fficulty is the relatively low quality of the micro-CT scanning images. For the full-diameter cores having a diameter of, for example, 6.5 cm, it is relatively hard for the x-ray to penetrate the rock. This fact causes noised micro-CT images and low contrasts between the fractures and the rock matrix. Consequently, image processing, for example, filtering and enhancement, are necessary before segmenting and constructing the pore space of fractured-vuggy carbonates. Averaging and median filtering are commonly used filtering methods [39–41]. For the filtering of the micro-CT images of the fractured-vuggy carbonates, the challenge involved in denoising the images are that the method should maintain the details of the pore structure or at least avoid blurring the image. In this consideration, filtering methods, for example, nonlocal means and anisotropic di ffusion filtering, that tried to maintain the structural boundaries during filtering might be potentially better [42,43]. For the issue of the low contrasts between the fractures and the matrix, image enhancement techniques are possible solutions [44,45]. One issue involved here is that the 'background energy' of the figure might not be uniform and, in this consideration, the methods that can calibrate the background energy di fference might be potentially better, for example, the top-bottom hat method [46,47].

Another aspect of di fficulties is in linking the wave speeds to the porosity and pore-structural parameters. The pore space of 1.0-inch core plugs contains limited amounts of fractures and vugs while that of the full-diameter cores is usually composed of pores, fractures, and vugs that a ffect the wave speeds of carbonates comprehensively. Thus, the cross plot of wave speeds over porosity might be scattered [38,48]. It is not clear which pore-structural parameter is the key in linking the wave velocity to the porosity, especially for the fractured-vuggy carbonates.

In this paper, we first develop an image-processing method to improve the quality of each the micro-CT scanned image of the full diameter cores, construct the pore space, and extract the pore structural characteristics. Then, these pore structural parameters are related to the wave speeds to analyze the e ffect of pore structure on the wave velocity of fractured-vuggy carbonates.

#### **2. Scanned Micro-CT Images of the Full-Diameter Carbonate Cores**

We collected 18 carbonate samples, having a diameter of 6.5–7.5 cm and a length of 5.0–10.0 cm, from a burial depth of over 5000 m in the DY Group, Sichuan Basin, Southwest China. Fractures and vugs can be observed with naked eyes on the surface of the sample. According to the standard of the study area, the pore spaces having a ratio of length over width higher than 10 are defined as the fractures, the pore spaces having a diameter longer than 2.0 mm are defined as the vugs, and shorter than 2.0 mm are defined as the pores [49]. From the naked-eye observation of the fractures and vugs appearance on the surface of the collected carbonate cores, the samples can be roughly summarized

into three groups: fractured-vuggy carbonates containing relatively developed fractures and vugs, fractural carbonates possessing relatively developed fractures, and vuggy carbonates having relatively developed vugs. The exact classification of the samples was done according to the quantitative analysis of the pore spaces constructed from the micro-CT scanned images.

The samples are scanned using an industrial micro-nano CT instrument—phoenix v|tome|x M manufactured by General Motors Corporation. The High power 300 kV micro-scale X-ray source was used. The micro-CT scanning was taken with an X-ray tube voltage of 200 kV and a tube current of 180 mA. Each sample was scanned for 8 h to achieve the best physical resolution of the instrument. A resolution of 40–50 μm/pixel was achieved and about 1100–1700 slices, depending on the lengths of the scanned samples, having about 1680 × 1695 pixels were obtained for each sample. The resolution and number of slices of the micro-CT scanning of all the samples are listed in Table 1. Some of the obtained micro-CT images are shown in Figure 8. According to the observation of micro-CT scanned images, the length of the fractures varies obviously from partly through the sample (e.g., sample Num. 10) to fully penetrate the sample, e.g., sample Num. 12. The orientations of the fractures are di fferent. Some of the fractures, in the sample, e.g., Num. 16, are parallel while others intersect each other, e.g., Num. 12. The spatial distributions and the sizes of the vugs are significantly heterogeneous. The pores are widely distributed throughout the sample.


**Table 1.** The resolution, pixels per scanned image, and the amount of the scanned images, and the size information of all the samples.

#### **3. Di** ffi**culties in Constructing the Pore Space**

If we zoom in each 2D micro-CT image, it is obvious that the speckled random noise and the Gaussian noise are involved in the image (Figure 1a). To give a relatively straightforward view of the noises, we used the false coloring technique to turn a grayscale image into an RGB color image (Figure 1b,c). After that, the speckled random noise is as shown as the red dots; the Gaussian noise makes the matrix (colored in yellow) into yellow and green messy patterns. It is important to filter the noise before constructing the pore space, especially when image enhancement is necessary, to avoid mistakenly considering the noise as parts of the pore space. The pepper and speckled random noise can be removed by median filtering. However, the most commonly used averaging filtering is not applicable for removing the Gaussian noise because it blurs the image and lowers the contrasts between the pore space and the matrix. To avoid this issue, the Gaussian noise was filtered using nonlocal mean filtering. After filtering, the noise involved in the image is decreased and the image is only slightly blurred that will not affect the acquisition of the pore space (Figure 1d).

**Figure 1.** The application of image filtering method to the micro-CT scanned image: (**a**) the micro-CT scanning image, (**b**) the enlarged image, (**c**) the false-colored image, and (**d**) the filtered image. After the false coloring, the pore space is in sky blue and the matrix is in yellow. The speckled random noises are the red dots and Gaussian noises make the matrix a mix of green and yellow.

After filtering the image, another difficulty is the lower contrast between the fractures and the matrix compared to the contrast between the vugs or pores with the matrix (Figure 2). A consequence of this lower contrast is that, if one uses the commonly used binary thresholding segmentation, a low threshold can segmen<sup>t</sup> the pores and the vugs well but it cannot segmen<sup>t</sup> the fractures (Figure 2b), and a high threshold can continuously segmen<sup>t</sup> the fractures, but the volumes of the acquired pores and vugs are larger than they should be and the shapes of the pores and vugs are partly distorted (Figure 2c).

We applied three methods, including the watershed segmentation [50], histogram equalization enhancement [44], and top-bottom hat algorithm, to enhance and acquire the fractures (Figure 3). The watershed algorithm is self-adaptive thresholding that segments the pore space basing on the local minimum instead of a single threshold. The acquired pore space using watershed is as shown in Figure 3b. Although the acquired pores and vugs are clear, the watershed method cannot acquire the fractures. After enhancing the image with the histogram equalization algorithm (Figure 3c) and filtering the remained noise enhanced by the algorithm (Figure 3d), the acquired pore space is similar to that segmented using a high threshold in that the fractures are acquired but the volume of the pores and vugs are larger compared to the original figure and the shapes of the pores and vugs are distorted to some extent. Compared to the former two methods, the top-bottom hat algorithm is better in that the fracture is acquired and it avoids the 'overflow' of the pores and vugs and maintains the majority of the shape details (Figure 3e,f). Basing on the above studies about the methods of filtering and enhancement applied to the micro-CT images of tight fractured-vuggy carbonates, a workflow is established to acquire and link the pore structural characteristics to the wave velocities.

**Figure 2.** Binary threshold image segmentation: (**a**) the original figure, (**b**) the segmented image using a low threshold, and (**c**) the segmented image using a high threshold. The fractures cannot be segmented as shown in the subgraph (**b**) and the volumes of the pores and the vugs spilled out in the subgraph (**c**).

**Figure 3.** Different methods applied to fracture acquirement: (**a**) the filtered image, (**b**) the segmented pore space by watershed method, (**c**) the segmented pore space after histogram equalization enhancement, (**d**) the filtered image of the subgraph (**c**), (**e**) the segmented pore space after top-bottom hat algorithm, (**f**) the filtered image of the subgraph (**e**).

The image processing methods mentioned above to contour the issue of the low contrast between the pore space and the matrix is convenient to use. However, if the contrast between the pore space and the matrix is too low, physical method might be necessary to enhance the contrast, for example, the difference map method [51]. The difference map method is to scan the sample twice under the conditions of dry and saturated with fluids containing X-ray dense agent, respectively. The pore space then can be highlighted by subtracting the dry image from the saturated image. This method is effective, but the disadvantage is that one has to make sure that the pore space can be fully saturated with the fluid. For the rocks having relatively high porosity, is relatively easier to saturate the pore space. However, for tight rocks, for example, the rocks having a porosity of less than 6%, it is hard to fully saturate the sample. For our samples, the image processing method is enough for extracting the pore space and thus, we did not apply physical method to enhance the contrast between the pores and the matrix.
