**1. Introduction**

The development of society has led to a significant increase in the demand of oil and gas resources, and the depletion of conventional petroleum resources made the exploration and extraction of unconventional hydrocarbon resources necessary [1,2]. Tight sandstone reservoirs are widely distributed and account for a high production of China's total natural gas [3,4]. Large-scale gas fields with great potential have been discovered in more than ten basins, including Sichuan, Ordos, Songliao, Tuha, and Junggar [5].

Deep burial generally leads to high mechanical compaction and cementation of a sandstone reservoir, so that tight and heterogeneous reservoir rocks are generated, where microcracks are developed [6]. These microcracks affect the rock elastic properties and control the fluid flow, providing channels for hydrocarbon migration [7–9]. Their identification is a key factor for evaluating reservoir quality [10,11].

The study of microcracks in tight sandstones has become an important topic of rockphysics studies [12]. Hudson [13] established a relation between microcrack density and rock elastic properties, while Smith [14] stated that in low porosity rocks, the effect of cracks on seismic velocity can be important as mineral composition, total porosity, and fluid type. Yoon [15] established a relation between aspect ratio and microcrack density. Cheng [16] studied the effect of effective pressure and fluids. Zhang et al. [17,18] proposed a differential poroelastic model to describe wave propagation and dissipation in fluid-saturated rocks which contain inclusions at multiple scales.

The use of RPT (rock physics template; the list of abbreviations is given in Abbreviations) is widespread: Avseth and Ødegaard [19] linked the reservoir characteristics with elastic attributes, whereas Avseth et al. [20] used the Biot–Gassmann theory to discriminate

**Citation:** Ruan, C.; Ba, J.; Carcione, J.M.; Chen, T.; He, R. Microcrack Porosity Estimation Based on Rock Physics Templates: A Case Study in Sichuan Basin, China. *Energies* **2021**, *14*, 7225. https://doi.org/10.3390/ en14217225

Academic Editors: Joel Sarout and Manoj Khandelwal

Received: 23 August 2021 Accepted: 27 October 2021 Published: 2 November 2021

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between oil and gas in reservoirs. RPT was also used by Xin and Han [21] to estimate reservoir lithology and fluids. Michel [22] predicted porosity and oil saturation in shales, based on RPTs built with P-wave impedance (*I*P) and the ratio between the P- and S-wave velocities (*V*P/*V*S). Gupta et al. [23] identified thin sandy layers saturated with oil, and Ba et al. [24] estimated porosity and gas saturation. Carcione and Avseth [25] evaluated organic content, hydrocarbon saturation, and in-situ pressure in source rocks, and Liu et al. [26] proposed a combination of fluid indicators. Pang et al. [27] predicted microcrack properties in tight sandstone reservoirs, based on P-wave impedance and attenuation.

The Biot–Rayleigh (BR) theory was introduced by Ba et al. [28,29] for describing wave propagation characteristics in rocks with multi-phase pore structures. This work is mainly based on BR theory. We consider ten wells in the proposed area and perform a sensitivity analysis by using the ultrasonic and well-log data. On the basis of Poisson's ratio (*ν*) and P-wave impedance, we establish multi-scale RPTs for tight sandstone gas reservoirs, which relate the total and microcrack porosities to the seismic properties, which are obtained by means of seismic inversion.

#### **2. Overview of the Work Area**
