**7. 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.

**Author Contributions:** Conceptualization, W.L., X.L. (Xiangjun Liu), and L.L.; methodology, W.L., X.L.(Xiangjun Liu), and L.L.; software, W.L. and Y.Z.; lab measurement, X.L. (Xiansheng Li), and J.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **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.



#### **Table A1.** *Cont*.
