**5. Results**

#### *5.1. 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 7.** Illustration of (**a**) the acquired pore space, (**b**) segmented individual volumes with watershed method, and (**c**) divided pores, vugs, and fractures according to the geometry of individual volumes.

The structural characteristics of the tight carbonate samples vary significantly, although the values of the porosity of the samples are close being less than 4%. The results of six samples are shown in the 6th and 7th columns of Figure 8 and the rest are shown in Appendix A. Inside the pore space, bubble-like pores and vugs and sheet-like fractures are observed. The pores are separately distributed, and the fractures are intersected and widely distributed inside the core. Fractured-vuggy, fractured, and vuggy carbonates are observed. For the fractured-vuggy carbonates, both the fractures and the vugs are well developed inside the sample. Although, the fractional volumes of the fractures are relatively low compared to the sum of those of the vugs and pores, the fractures penetrating the samples and each other connecting the pore spaces. For the fractured carbonates of the collected samples, the pore space is mainly composed of the fractures and the total porosity of them are all less than 2%.


**Figure 8.** Examples of the sample, cross section, and longitudinal section of the CT scanning image, constructed pore space, and divided pore space of the carbonate samples. 'FV', 'F', and 'V' represent fractured-vuggy carbonate, fractured carbonate, and vuggy carbonate, respectively. The total pore spaces of the carbonate samples are in blue as shown in the sixth column. The pore space after division is shown in the seventh column with the fractures colored in gray, vugs in blue, and pores in yellow. The rest of the constructed and divided pore spaces of the samples are provided in the supplementary file. 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.

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.

#### *5.2. 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 *Vp* over *Vs* 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).

**Figure 9.** 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.
