**7. Conclusions**

This study uses rock-physics templates to estimate the total and microcrack porosities of tight sandstone gas reservoirs. The models are based on the poroelasticity theory to obtain the elastic attributes at different frequency bands, namely, how Poisson's ratio, velocity, and other relevant attributes are affected by those porosities. Ultrasonic experiments are performed under full water and gas saturations, showing that the wave velocities increase with effective pressure. When the rock is fully saturated with gas, the ratio between the Pand S-wave velocities increases with effective pressure, while for water, an opposite trend is observed.

A sensitivity analysis shows that P-wave impedance and Poisson's ratio are most sensitive to both porosities. The attributes are considered to build the templates which are calibrated with experimental and log data. Finally, the templates are applied to seismic data to estimate the porosities, indicating that the predictions are consistent with the gas production reports.

At present, the tight sandstone gas reservoirs of Sichuan Basin have contributed to the major proportion of the total gas production output of the petroleum industries in China. However, the tight sandstone reservoirs generally exhibit the characteristics of low porosity, low permeability, high heterogeneity, and deep burial. There are difficulties in the precise prediction and detailed description of high-quality reservoirs based on the traditional geophysical exploration methods. In this work, we propose a multiscale rock physics modeling method by incorporating the effects of microcrack porosity on rock physics attributes. A workflow is presented to establish the relationships between rock physical properties and seismic wave responses, based on which the prediction of microcrack porosity is achieved in the 3D seismic survey work area. The application of the method is effective as a case study.

The proposed method can be applied in rock physics modeling based on the elastic/seismic responses of reservoir rock. It may be affected by the problem of multiplicity of solutions in the parameter inversion and reservoir prediction. Further studies may incorporate the wave attenuation in rock physics modeling, so that more attributes will be available for validating and calibrating the templates, and the influence by the multiplicity of solutions can be alleviated. Furthermore, this paper is focused on the studies on tight gas sandstone reservoirs, and for the different types of complex reservoirs, the approach should be extended and adjusted to achieve effective applications. Specifically, for those tight/shale oil reservoirs, the viscoelasticity characteristics of fluid have to be analyzed and incorporated in rock physics modeling, so that some reasonable results can be obtained.

For future studies, the different sensitivity analysis methods should be included to analyze the interactions between different attributes with respect to rock basic properties. Furthermore, the multi-phases of different types of microcracks, mesopores and fractures need be considered to establish a more realistic rock model, with which the in situ reservoirs can be better described and simulated, in combination with the latest techniques of digital rock physics.

**Author Contributions:** Conceptualization, J.B. and R.H.; Data curation, T.C.; Formal analysis, C.R., J.B., J.M.C. and R.H.; Funding acquisition, J.B.; Investigation, J.B., J.M.C., T.C. and R.H.; Methodology, C.R., J.B. and J.M.C.; Project administration, J.B. and T.C.; Resources, T.C.; Supervision, J.B.; Validation, C.R. and J.M.C.; Writing—original draft, C.R. and J.B.; Writing—review & editing, J.B., J.M.C. and R.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 41974123, Jiangsu Province Outstanding Youth Fund Project, grant number BK20200021, and Strategic Priority Research Program of the Chinese Academy of Sciences, grant number XDA14010303.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data relevant with this study can be accessed by contacting the corresponding author.

**Acknowledgments:** The authors are grateful to the National Natural Science Foundation of China (Grant no. 41974123), the Jiangsu Province Outstanding Youth Fund Project (Grant no. BK20200021), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant no. XDA14010303).

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

#### **Abbreviations**


#### **Appendix A**
