Pore-Structural Characteristics of Tight Fractured-Vuggy Carbonates and Its Effects on the P- and S-Wave Velocity: A Micro-CT Study on Full-Diameter Cores

Abstract: Pore structure has been widely observed to affect the seismic wave velocity of rocks. Although taking lab measurements on 1.0-inch core plugs is popular, it is not representative of the fractured-vuggy carbonates because many fractures and vugs are on a scale up to several hundred microns (and greater) and are spatially heterogeneous. To overcome this shortage, we carried out the lab measurements on full-diameter cores (about 6.5–7.5 cm in diameter). The micro-CT (micro computed tomography) scanning technique is used to characterize the pore space of the carbonates and image processing methods are applied to filter the noise and enhance the responses of the fractures so that the constructed pore spaces are reliable. The wave velocities of Pand S-waves are determined then and the effects of the pore structure on the velocity are analyzed. The results show that the proposed image processing method is effective in constructing and quantitatively characterizing the pore space of the full-diameter fractured-vuggy carbonates. The porosity of all the collected tight carbonate samples is less than 4%. Fractures and vugs are well-developed and the spatial distributions of them are heterogeneous causing, even the samples having similar porosity, the pore structure characteristics of the samples being significantly different. The pores and vugs mainly contribute to the porosity of the samples and the fractures contribute to the change in the wave velocities more than pores and vugs.


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 of these deep-buried tight carbonates are different 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][3][4][5][6][7]. This issue becomes further complicated considering the fractures and the vugs developed in the carbonate rocks [8,9]. These challenges aroused

Difficulties 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 Energies 2020, 13, 6148 4 of 17 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). 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). 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 segment the pores and the vugs well but it cannot segment the fractures (Figure 2b), and a high threshold can continuously segment 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). 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 segment the pores and the vugs well but it cannot segment the fractures (Figure 2b), and a high threshold can continuously segment 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. 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.  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  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.

Methods
The method is mainly composed of the acquisition and analysis of the three experimental measurements: the micro-CT, helium porosity, and the pulse transmission measurements. The overall method is shown in Figure 4. First, the collected carbonate samples were sawed into cylindrical plugs and scanned using micro-CT instruments. The obtained 2D images of micro-CT were filtered and enhanced to improve quality. Then, the pore space in each 2D image was acquired and the 3D pore spaces of the samples were constructed using the software AVIZO (manufactured by Visualization Sciences Group, FEI Co., Hillsboro, OR, USA) basing on the 2D pore space. After that, the pore space was divided into pores, vugs, and fractures according to the geometry and the diameter of each individual pore space. Finally, the pore structure parameters were calculated to quantify the characteristics of the pore space and analyze its effect on wave speeds. The density and porosity were measured with helium and the wave speeds were determined using the pulse transmission technique. The following two subsections provide details of pore space acquisition, helium porosity measurements, and the pulse transmission measurements.

Methods
The method is mainly composed of the acquisition and analysis of the three experimental measurements: the micro-CT, helium porosity, and the pulse transmission measurements. The overall method is shown in Figure 4. First, the collected carbonate samples were sawed into cylindrical plugs and scanned using micro-CT instruments. The obtained 2D images of micro-CT were filtered and enhanced to improve quality. Then, the pore space in each 2D image was acquired and the 3D pore spaces of the samples were constructed using the software AVIZO (manufactured by Visualization Sciences Group, FEI Co., Hillsboro, OR, USA) basing on the 2D pore space. After that, the pore space was divided into pores, vugs, and fractures according to the geometry and the diameter of each individual pore space. Finally, the pore structure parameters were calculated to quantify the characteristics of the pore space and analyze its effect on wave speeds. The density and porosity were measured with helium and the wave speeds were determined using the pulse transmission technique. The following two subsections provide details of pore space acquisition, helium porosity measurements, and the pulse transmission measurements. Workflow chat for characterizing the pore space and analyzing its effect on wave speeds. After sawing the samples into cylindrical plugs, the samples are scanned using micro-CT. Then, the quality of each acquired 2D micro-CT image is improved using image filtering and enhancement techniques. The pore spaces of the samples are constructed and divided into pores, fractures, and vugs basing on the geometric characteristics of each individual pore space. Finally, the pore-structural parameters are acquired and related to the density, porosity, and wave velocities to analyze its effect on wave speeds. of each acquired 2D micro-CT image is improved using image filtering and enhancement techniques. The pore spaces of the samples are constructed and divided into pores, fractures, and vugs basing on the geometric characteristics of each individual pore space. Finally, the pore-structural parameters are acquired and related to the density, porosity, and wave velocities to analyze its effect on wave speeds.

Pore Space Construction and Division Method
Median filtering and nonlocal means filtering were applied to the micro-CT images first to remove the speckled random noises and the Gaussian noises. Then, the micro-CT image was enhanced with the top-bottom hat transformation. Finally, the processed image was filtered again to remove the remaining noises that were also enhanced after top-bottom hat transformation.
For the division of the pore space, the total pore space was segmented into individual volumes using the watershed algorithm and then the individual volumes were classified into pores, fractures, and vugs according to its geometry and diameter. Usually, the fracture is identified from the pores and vugs using the ratio of the length and width over thickness and the vugs are separated from the pores by the diameter of the isovolumetric sphere. It should be noted that using only the ratio of length over the thickness may mistakenly classify a throat into a fracture ( Figure 5). Thus, we used both the ratio of length over thickness and the ratio of width over thickness to avoid this issue. According to the standard of the studies area, the volumes having both the ratios of length over thickness and width over thickness higher than 10 were defined as fractures. The remaining volumes having an equivalent diameter longer than 2.0 mm were defined as vugs and those having an equivalent diameter shorter than 2.0 mm were defined as pores. and vugs according to its geometry and diameter. Usually, the fracture is identified from the pores and vugs using the ratio of the length and width over thickness and the vugs are separated from the pores by the diameter of the isovolumetric sphere. It should be noted that using only the ratio of length over the thickness may mistakenly classify a throat into a fracture ( Figure 5). Thus, we used both the ratio of length over thickness and the ratio of width over thickness to avoid this issue.
According to the standard of the studies area, the volumes having both the ratios of length over thickness and width over thickness higher than 10 were defined as fractures. The remaining volumes having an equivalent diameter longer than 2.0 mm were defined as vugs and those having an equivalent diameter shorter than 2.0 mm were defined as pores. Figure 5. Illustration of the difference between a throat and a fracture in geometry. The lengths of a throat and a fracture are both usually significantly longer than their widths and thicknesses. The difference is that the width and the thickness of a throat are close while the width of a fracture is usually significantly longer than the thickness of it. To avoid mistakenly acquire a throat as a fracture, both the ratios of length over thickness and width over thickness should be large.
After dividing the total pore space into pores, vugs, and fractures the pore structural parameters are quantified. The porosity of the whole pore space, the pores, the vugs, and the fractures were calculated by dividing the total amount of the pixels in the whole pore space, the pores, the vugs, and the fractures over that of the whole sample, respectively. The equivalent pore diameter was calculated by averaging the diameters of the isovolumetric spheres of the pores and the vugs. The orientation of a fracture was defined by the normal vector of the fracture surface.

Porosity and Wave Velocity Measurements
The porosity of the samples was determined with the single-cell He-gas filling method to offer a reference for the micro-CT pore-space construction. The pore volume was determined using Boyle's Law under room temperature and a confining pressure of 3 MPa applied to the external surface of the sample jacket. The diameter and the length of the samples are both measured three times for each sample using a caliper and the averaged diameter and length were used to calculate the volume of the cylindrical samples. The porosimeter apparatus was built based on API RP40 (1998) [52] as shown in Figure 6. Before measuring the porosity of the samples, the measurement system was calibrated using a standard sample to calibrate the system dead volume. The total pore volume of the samples  Figure 5. Illustration of the difference between a throat and a fracture in geometry. The lengths of a throat and a fracture are both usually significantly longer than their widths and thicknesses. The difference is that the width and the thickness of a throat are close while the width of a fracture is usually significantly longer than the thickness of it. To avoid mistakenly acquire a throat as a fracture, both the ratios of length over thickness and width over thickness should be large.
After dividing the total pore space into pores, vugs, and fractures the pore structural parameters are quantified. The porosity of the whole pore space, the pores, the vugs, and the fractures were calculated by dividing the total amount of the pixels in the whole pore space, the pores, the vugs, and the fractures over that of the whole sample, respectively. The equivalent pore diameter was calculated by averaging the diameters of the isovolumetric spheres of the pores and the vugs. The orientation of a fracture was defined by the normal vector of the fracture surface.

Porosity and Wave Velocity Measurements
The porosity of the samples was determined with the single-cell He-gas filling method to offer a reference for the micro-CT pore-space construction. The pore volume was determined using Boyle's Law under room temperature and a confining pressure of 3 MPa applied to the external surface of the sample jacket. The diameter and the length of the samples are both measured three times for each sample using a caliper and the averaged diameter and length were used to calculate the volume of the cylindrical samples. The porosimeter apparatus was built based on API RP40 (1998) [52] as shown in Figure 6. Before measuring the porosity of the samples, the measurement system was calibrated using a standard sample to calibrate the system dead volume. The total pore volume of the samples was determined following API RP40 (1998) and the porosity was obtained by dividing the volume of the pore space over that of the sample.
Energies 2020, 13, x FOR PEER REVIEW 9 of 19 an electrical voltage. The voltage was recorded into the computer by an 8-bit digitizer and a digital oscilloscope programmed using LabVIEW software. The sampling rate was 10.0 ns. The averaged receiving signal was stacked over 300 times and then collected. The transit time was picked at the first amplitude peak of the received waveform. The calibration of the transducer delay was determined from the measurements taken on a set of cylindrical aluminum plugs (6061-T6) with different lengths following Melendez-Martinez (2014) [53]. By plotting the transit time against cylinder length, the excitation delay, equaling 16.16 μs for the longitudinal-mode piezoelectric discs or 8.82 μs for the transverse mode piezoelectric plates, was obtained from the non-zero intercept of the fitting line. The measurement was taken under a confining pressure of 70 MPa (the in-situ confining pressure). Figure 6. Scheme of the wave velocity measurement system. The system is mainly composed of three parts that provide confining pressure, porosity measurement, and pulse transmission measurement, respectively.

Pore Structure Characteristics of the Tight Carbonates
After processing each 2D micro-CT image, the processed 2D images were imported into the software AVIZO to construct and divide the pore spaces of the samples. Taking sample Num. 10 as an example, the total pore space ( Figure 7a) was separated into individual volumes using a watershed algorithm ( Figure 7b). The colors used in Figure 7b help identify the individual volumes. These individual volumes were classified into pores (colored in yellow), vugs (in blue), and fractures (in gray) according to the geometry of the individual volumes as shown in Figure 7c. It can be seen in Figure 7 that the proposed method can effectively divide the pore spaces into pores, vugs, and fractures. The pore structure parameters were acquired basing on the characteristics of the constructed spaces of pores, vugs, and fractures. Figure 6. Scheme of the wave velocity measurement system. The system is mainly composed of three parts that provide confining pressure, porosity measurement, and pulse transmission measurement, respectively.
The wave velocities of the P-and S-waves of the collected carbonate samples were determined with the ultrasonic pulse transmission technique. The voltage step was periodically applied to the piezoelectric ceramic to generate a pulse. The generated pulse transmits throughout the sample and encountered the piezoelectric ceramic used to receive the pulse by converting the vibration back to an electrical voltage. The voltage was recorded into the computer by an 8-bit digitizer and a digital oscilloscope programmed using LabVIEW software. The sampling rate was 10.0 ns. The averaged receiving signal was stacked over 300 times and then collected. The transit time was picked at the first amplitude peak of the received waveform. The calibration of the transducer delay was determined from the measurements taken on a set of cylindrical aluminum plugs (6061-T6) with different lengths following Melendez-Martinez (2014) [53]. By plotting the transit time against cylinder length, the excitation delay, equaling 16.16 µs for the longitudinal-mode piezoelectric discs or 8.82 µs for the transverse mode piezoelectric plates, was obtained from the non-zero intercept of the fitting line. The measurement was taken under a confining pressure of 70 MPa (the in-situ confining pressure).

Pore Structure Characteristics of the Tight Carbonates
After processing each 2D micro-CT image, the processed 2D images were imported into the software AVIZO to construct and divide the pore spaces of the samples. Taking sample Num. 10 as an example, the total pore space (Figure 7a) was separated into individual volumes using a watershed algorithm ( Figure 7b). The colors used in Figure 7b help identify the individual volumes. These individual volumes were classified into pores (colored in yellow), vugs (in blue), and fractures (in gray) according to the geometry of the individual volumes as shown in Figure 7c. It can be seen in Figure 7 that the Energies 2020, 13, 6148 9 of 17 proposed method can effectively divide the pore spaces into pores, vugs, and fractures. The pore structure parameters were acquired basing on the characteristics of the constructed spaces of pores, vugs, and fractures.   Table 1.  Table 1.
The acquired pore structural parameters are listed in Table 2. The micro-CT porosity of the collected samples ranges from about 1% to 4%. The averaged equivalent pore diameter ranges from about 100 to 400 µm. The vugs are the main contribution of the large pores. The volumetric fractions of pores, vugs, and fractures vary significantly with the samples be 5.16-57.63%, 0-75.22%, and 1.77-94.01%, respectively. The majority of the samples contain both the vugs and fractures. The orientations of the fractures change a lot from being parallel to intersect with each other. The intersection of the fractures with pores and vugs form the main flow channel of the tight carbonates. Table 2. Pore structural parameters obtained from the constructed pore space. 'VF' represents volume fraction. The VF of pores, vugs, or fractures equals the ratio of the volume of them over that of the total pore space, respectively. The orientation of the fractures parallel or perpendicular to the ends of the core plug is defined as 0 • or 90 • , respectively. The VR of oriented fractures equals the ratio of the volume of the fractures oriented in a certain angle range, for example, 0-30 • , over that of all fractures.

Porosity and Wave Velocities of the Tight Carbonates
The He gas porosity and wave speeds of both the P-and S-waves of the tight carbonate samples are shown in Figures 9 and 10. The samples are collected at a burial depth of over 5000 m and, thus, the porosity of the tight carbonate samples is less than 5%. The porosity acquired from the micro-CT scanning is close to that obtained from He gas filling demonstrating that the acquired pore space from micro-CT is reasonable ( Figure 9). The difference in the acquired porosity between the micro-CT and He gas filling might be caused by the isolated pores or the resolution of the micro-CT that pores less than 40 µm are too small to be detected. The wave speeds are measured under an in-situ confining pressure of about 70 MPa. The P-and S-wave velocities of the collected samples range from about 5.6 to 6.7 km/s and 2.6 to 3.2 km/s, respectively. The ratio of V p over V s ranges from 1.95 to 2.41. The cross plots of the wave velocities of both P-and S-waves against the He gas porosity are scattered ( Figure 10).  . Cross plot of the micro-CT porosity against He gas filling porosity. It can be seen that the porosity acquired from micro-CT is close to that from He gas. . Cross plot of the micro-CT porosity against He gas filling porosity. It can be seen that the porosity acquired from micro-CT is close to that from He gas. Figure 10. Cross plots of (a) P-wave and (b) S-wave speeds against He gas porosity. The data referring to both P-and S-waves are scattered.

Discussion
The pore structure of the tight carbonates is involved to help analyze and explain the relationship between the porosity and the wave speeds of both P-and S-waves. Seen from the constructed pore space of the tight carbonates, the pore spaces of the tight carbonate samples vary significantly and fractures and vugs are well developed causing the relationship between the porosity and the wave speeds to be scattered.
The pores and vugs possess the majority of the pore space for most of the samples, except those fractured tight carbonates. Thus, the porosity of the samples is positively related to the sum of the volume fraction of the vugs and pores (Figure 11). The existence of vugs and pores improves the porosity of the tight carbonate samples. However, considering the wave speeds, the fractures are key compared to the pores and the vugs because the vugs are distributed heterogeneously in the samples, and some of them are on or near the sidewall of the core plugs that might not affect the path of the waves.

Discussion
The pore structure of the tight carbonates is involved to help analyze and explain the relationship between the porosity and the wave speeds of both P-and S-waves. Seen from the constructed pore space of the tight carbonates, the pore spaces of the tight carbonate samples vary significantly and fractures and vugs are well developed causing the relationship between the porosity and the wave speeds to be scattered.
The pores and vugs possess the majority of the pore space for most of the samples, except those fractured tight carbonates. Thus, the porosity of the samples is positively related to the sum of the volume fraction of the vugs and pores (Figure 11). The existence of vugs and pores improves the porosity of the tight carbonate samples. However, considering the wave speeds, the fractures are key compared to the pores and the vugs because the vugs are distributed heterogeneously in the samples, and some of them are on or near the sidewall of the core plugs that might not affect the path of the waves. If a fracture is perpendicular to the wave path, the wave has to transit through the fracture and consequently, its speed is slower. However, a fracture can merely affect the wave speed if it is parallel to the wave path. This kind of fracture adds to the total porosity but will not reduce the wave speed. Thus, the heterogeneity in the spatial distribution of the vugs and the fractures with high orientation angles are the main causes of the scatterings in the porosity and wave velocity relationship. On this consideration, the wave speeds of both the P-and S-waves are related to the porosity of the fractures as shown in Figure 12. Removing the samples with a limited amount of low-oriented fractures (the fractures having their surface perpendicular or nearly perpendicular to the direction of wave propagation), the wave velocity of the remaining samples is negatively related to the fracture porosity indicating that the wave velocity of the tight carbonate samples is more sensitive to the fractures, especially those intersecting its wave path. The Pearson coefficient of S-wave velocity with fracture porosity is about two times that of the P-wave velocity with fracture porosity indicating that the Swave is more sensitive to the fracture porosity compared to the P-wave.  If a fracture is perpendicular to the wave path, the wave has to transit through the fracture and consequently, its speed is slower. However, a fracture can merely affect the wave speed if it is parallel to the wave path. This kind of fracture adds to the total porosity but will not reduce the wave speed. Thus, the heterogeneity in the spatial distribution of the vugs and the fractures with high orientation angles are the main causes of the scatterings in the porosity and wave velocity relationship. On this consideration, the wave speeds of both the P-and S-waves are related to the porosity of the fractures as shown in Figure 12. Removing the samples with a limited amount of low-oriented fractures (the fractures having their surface perpendicular or nearly perpendicular to the direction of wave propagation), the wave velocity of the remaining samples is negatively related to the fracture porosity indicating that the wave velocity of the tight carbonate samples is more sensitive to the fractures, especially those intersecting its wave path. The Pearson coefficient of S-wave velocity with fracture porosity is about two times that of the P-wave velocity with fracture porosity indicating that the S-wave is more sensitive to the fracture porosity compared to the P-wave.
consequently, its speed is slower. However, a fracture can merely affect the wave speed if it is parallel to the wave path. This kind of fracture adds to the total porosity but will not reduce the wave speed. Thus, the heterogeneity in the spatial distribution of the vugs and the fractures with high orientation angles are the main causes of the scatterings in the porosity and wave velocity relationship. On this consideration, the wave speeds of both the P-and S-waves are related to the porosity of the fractures as shown in Figure 12. Removing the samples with a limited amount of low-oriented fractures (the fractures having their surface perpendicular or nearly perpendicular to the direction of wave propagation), the wave velocity of the remaining samples is negatively related to the fracture porosity indicating that the wave velocity of the tight carbonate samples is more sensitive to the fractures, especially those intersecting its wave path. The Pearson coefficient of S-wave velocity with fracture porosity is about two times that of the P-wave velocity with fracture porosity indicating that the Swave is more sensitive to the fracture porosity compared to the P-wave.

Conclusions
Carbonate rocks, buried at depths deeper than 5 km, are usually tight. Characterizing the pore structure characteristics of the tight carbonates are key in evaluating its physical properties. To be representative, micro-CT scanning and pulse transmission measurements were carried out on fulldiameter drilling cores instead of 1.0-inch core plugs. The two main challenges in constructing the The red solid and black empty dots represent the data collected from the samples possessing fractures with low and high orientation angles, respectively. Decreasing trends of the wave speeds with porosity are observed for both P-and S-waves in the samples mainly containing low orientation fractures.

Conclusions
Carbonate rocks, buried at depths deeper than 5 km, are usually tight. Characterizing the pore structure characteristics of the tight carbonates are key in evaluating its physical properties. To be representative, micro-CT scanning and pulse transmission measurements were carried out on full-diameter drilling cores instead of 1.0-inch core plugs. The two main challenges in constructing the pore space of a full-diameter carbonate core sample basing on micro-CT are the noisy image and the low contrast between the fractures and the matrix. The proposed micro-CT workflow can effectively construct the pore space and divide the pore space into pores, vugs, and fractures so that the pore structural parameters can be quantitatively acquired.
Both the micro-CT acquired and He gas-filling measured porosity show that the porosity of the collected tight carbonate samples is less than 5%. Although the values of the porosity of the tight carbonates are similar, the pore structure varies significantly from sample to sample. The majority of the samples possess well-developed fractures and vugs. The spatial distribution of fractures, vugs, and pores is strongly heterogeneous. Both parallel and intersected fractures are observed in the constructed pore space. The porosity of the samples is positively related to the volume fraction of the vugs and pores. Due to the complex pore structure of the tight carbonates, the relationships between the porosity and the wave speeds of both P-and S-waves are scattered. The wave velocity is related to the fracture porosity for the samples having the majority of the fractures aligned perpendicular to the wave path.
The micro-CT scanning taken on full-diameter core plugs do not contain any information about the pores having a diameter of less than 50 microns. A combination of the study on full-diameter core plugs and those on smaller samples or other pore structure measurements, for example, SEM, NMR, and mercury injection, is an interesting further work.

Appendix A. Constructed and Divided Pore Spaces of the Rest Tight Carbonates
The constructed pore spaces and the pores, vugs, and fractures acquired by dividing the pore spaces of six samples are listed in Figure 8. The results referring to the remaining samples are shown in Table A1. Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.

Num.
Type Sample Image

Cross Section
Longitudinal Section Constructed Pore Space Divided Pore Space 1 FV Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.          Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.              Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.  Table A1. Photos, cross and longitudinal sections of the CT scanning image, constructed pore spaces, and divided pore spaces of the remaining carbonate samples. This figure together with Figure 8 provides the constructed and divided pores spaces of all the collected tight carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. In the last column, the fractures, vugs, and pores are colored in gray, blue, and yellow, respectively. The subgraphs are too small that a scale would be hard to see if it is directly marked on the subgraph. Thus, instead of a scale, we provide the physical size including the radius and the length of all the samples in Table 1.