N2 Adsorption Measurement

The Brunauer-Emmett-Teller (BET) adsorption model [32] is adopted to determine the specific surface of shale samples when 0.05 < *p*/*ps* < 0.35. The pressure is too small to achieve multilayer adsorption when *p*/*ps* < 0.05, and capillary condensation may happen when *p*/*ps* > 0.40. Some studies (e.g., [33]) pointed out that capillary condensation could not happen in shale gas reservoirs, since the common shale gas reservoir temperature is much higher than the critical temperature of shale gas (mainly methane). The two-parameter BET equation can be expressed as follows [32]:

$$\frac{p/p\_s}{V(1-p/p\_s)} = \frac{1}{V\_m b} + \frac{b-1}{V\_m b} \frac{p}{p\_s} \tag{1}$$

where *V* is the adsorbed gas volume, mL; *Vm* is the saturated adsorption volume of monolayer, mL; *p* is pressure, Pa; *ps* is saturated vapor pressure, Pa; and *b* is a dimensionless constant related to the adsorption capacity.

After measuring the adsorbed gas amount *G*, a linear relationship between *p*/[*V*(*ps* − *p*)] and *p*/*ps* (0.05 < *p*/*ps* < 0.35) can be found. According to the slope and intercept of the straight line, the saturated adsorption amount *Vm* can be calculated, by which the specific surface of samples can be obtained:

$$S\_{\mathcal{S}} = \frac{V\_m A\_m N\_A}{22400W} \times 10^{-18} \,\text{,}\tag{2}$$

where *NA* is the Avogadro constant; *Am* is the cross-section area of *N2* (0.162 nm2); *W* is the weight of the samples, g; and *Sg* is the specific surface of samples, m<sup>2</sup>/g.

The Barrett-Joyner-Halenda (BJH) equation [34] is used to calculate PSD when *p*/*ps* > 0.40:

$$r = -2\gamma V\_m / \left[ \text{RT} \ln(p/p\_\circ) \right] + 0.354 \left[ -5 / \ln(p/p\_\circ) \right]^{1/3},\tag{3}$$

where γ is the surface tension, N/m; *R* is the mole heat capacity, J/(mol·K); *T* is the environmental temperature, K; and *r* is the pore radius, m.

Mercury Injection Capillary Pressure

A mercury intrusion porosimeter is widely adopted to determine PSD in conventional sandstone reservoirs, where the pressure of mercury and pore radius *r* satisfy the Washburn equation [35]:

$$
\sigma = \frac{2\sigma\cos\xi}{p},
\tag{4}
$$

where ξ is the contact angle between mercury and shale surface; σ is surface tension of mercury, 10−<sup>3</sup> N/m; and *p* is the injection pressure, Pa.

The smallest pore radius that can be tested is determined by the highest pressure that mercury porosimetry can hold. In our study, a PoreMaster 60 mercury porosimeter is employed and its measurement range of pore size lies between 3.6 nm and 950 μm, but values near the lower limit can hardly be detected. This is because it is difficult to inject mercury into micro/nanopores due to the

high capillary pressure. Meanwhile, high pressure may create artificial crack and stress sensitivity, which reduces the credibility of the measurement. Therefore, MICP is mainly used to analyze mesopores and macropores in shale samples.

#### Nuclear Magnetic Resonance (NMR)

The relaxation characteristic of a hydrogen nucleus under an external magnetic field is used to obtain the PSD by the NMR method, which causes no harm to the shale samples. The speed of relaxation is characterized by the longitudinal relaxation time *T*1 and transverse relaxation time *T*2. The relaxation characteristics of fluid in different-sized pores are different, based on which PSD can be calculated. The transverse relaxation time *T*2 is composed of bulk phase relaxation *T2B*, surface relaxation *T2S*, and diffusion relaxation *T2D*, which is expressed as follows:

$$\frac{1}{T\_{\!2}} = \frac{1}{T\_{\!2B}} + \frac{1}{T\_{\!2D}} + \frac{1}{T\_{\!2S}}.\tag{5}$$

The diffusion relaxation speed can be ignored compared to the surface relaxation speed in a uniform magnetic field, and the reciprocal of diffusion relaxation time *T*2*D* is almost 0. Meanwhile, the bulk phase relaxation time *T*2*B* is much bigger than the surface relaxation time *T*2*S*. Therefore, 1/*T*2*D* and 1/*T*2*B* in Equation (5) can be ignored, and we have

$$\frac{1}{T\_2} \approx \frac{1}{T\_{2S}} = \rho\_2 \frac{F\_s}{r}.\tag{6}$$

Letting *C* = *Fs* · ρ2, we obtain the relationship between relaxation time *T*2 and pore radius *r* via

$$r = \mathbb{C}T\_2. \tag{7}$$

Note that the transformation coefficient *C* in Equation (7) is an empirical parameter varying from one area to another, which can be determined by experiments [36]. In order to obtain the value of *C*, the *T*2 spectrum need to be measured for specific shale samples first, and a N2 adsorption test needs to be conducted on exactly the same samples (or samples from the same formation) afterwards [36]. Since core plugs are used in NMR and crushed rock samples are needed for the N2 adsorption test, it is essential to perform the NMR test prior to N2 adsorption. Comparing the two PSD results, the transformation coefficient *C* can be fitted. Accurate determination of *C* is a key part of determining the PSD of shale samples by NMR.

#### 2.4.2. Pore Size Distribution

## N2 Adsorption Results

According to the principle of N2 adsorption on measuring PSD, the measurable pore-throat size range is on the magnitude of nanometers, mainly micropores (<2 nm) and mesopores (2–50 nm). N2 adsorption results (Figure 9) show that PSD displays a high single peak at the pore size range of 2 to 5 nm, implying that nanopores ranging from 2 nm to 5 nm are very developed in shale formations, which is advantageous for the storage of adsorbed gas. Meanwhile, we see that pores larger than 10 nm are not very developed. In a PSD frequency histogram (Figure 10), mesopores account for the largest percentage of all pores, followed by micropores and macropores. Micropores and mesopores accounted for more than 90% of the total pore volume.

**Figure 9.** PSD of samples from Longmaxi formation based on low-temperature N2 adsorption.

**Figure 10.** PSD histogram of samples from the Longmaxi Formation in Sichuan Basin based on N2 adsorption.

## Mercury Intrusion Results

Two peaks can be found on the MICP measurement results of PSD, as shown in Figure 11. The left peak is relatively small and smooth, corresponding to macropores of 10 nm to 1000 nm in organic matter and clay minerals. The right peak is very high, corresponding to a pore size of 40–200 μm. The highly developed lamellation in shale formations generates micro fractures, which may happen during sample preparation or mercury injection tests. Therefore, there is a high probability that the right peak corresponds to artificial fractures. Considering the fact that large pores (>5 μm) correspond to mercury injection pressure less than 0.14 MPa, these artificial fractures are more likely to be induced during sample preparation. Figure 12 shows that macropores account for the largest percentage (73.17%), followed by mesopores (26.83%). Due to the limitations of the instrument, no micropores are detected by MICP. Whether the tested macropores are primitive or induced needs to be determined by combining with other techniques, such as NMR.

**Figure 11.** PSD of samples from the Longmaxi Formation based on mercury intrusion.

**Figure 12.** PSD histogram of samples from the Longmaxi Formation in Sichuan Basin based on mercury intrusion.

#### Nuclear Magnetic Resonance Results

Two or three peaks can be found on PSD, measured by NMR (Figure 13). The left peak, corresponding to pores smaller than 10 nm, has the largest percentage, while the other two peaks correspond to larger pore sizes of 800 nm and 7000 nm, respectively. The NMR results indicate that small pores are very developed in shale formations, while large pores account for a small but non-negligible percentage (Figure 14). Generally, the left two peaks correspond to micro-, meso-, and macro-pores in matrix, while the third peak corresponds to micro fractures. The PSD histogram measured by the NMR is similar to that of N2 adsorption in terms of the small pore size range, while large pores could not be detected by N2 adsorption, but by NMR.

**Figure13.**PSDofsamplesfromtheLongmaxiFormationbasedonNMR.

**Figure 14.** PSD histogram of samples from the Longmaxi Formation in the Sichuan Basin based on NMR.

2.4.3. Comprehensive Analysis of Pore Size Distribution

N2 adsorption, MICP, and NMR can all measure PSD and reflect the heterogeneity of shale samples, with different test ranges. The lowest limit of N2 adsorption is 0.35 nm, while the MICP test range is 3.6 nm–950 μm, and the NMR test range is 1 nm–5 mm. Comparing the results from the three methods, we find that the N2 adsorption results mainly reflect the micropore and mesopore size distribution, while the NMR results reflect all pore size range and MICP results mainly test the development of macropores and micro fractures. Although the N2 adsorption and NMR results display similar PSD trends of small pore size ranges, the peak of N2 adsorption results (3–4 nm) is slightly smaller than that of NMR (4–5 nm). This is because samples are saturated by plant oil in the NMR test, and they struggle to enter micropores due to their large diameter compared to nitrogen molecules. Therefore, the micropore size determined by NMR is larger than that measured by N2 adsorption. The nitrogen molecule is much smaller, so it enters micropores more easily than oil molecules. Therefore, the N2 adsorption results are closer to the real data compared to NMR results.

N2 adsorption can measure micropores and mesopores accurately, while MICP mainly tests macropores. Consequently, combining the two methods can better characterize PSD in shale formations. Figures 15 and 16 show the PSD of the Longmaxi shale samples, tested comprehensively by N2 adsorption and MICP, where pores smaller than 50 nm are measured by N2 adsorption and pores larger than 50 nm are measured by MICP. Pore volume in the Longmaxi Shale Formation is mainly mesopores and macropores (including artificial fractures).

**Figure 15.** PSD of samples from the Longmaxi Formation based on N2 adsorption and MICP.

**Figure 16.** PSD histogram of samples from the Longmaxi Formation in the Sichuan Basin based on N2 adsorption and MICP.

#### *2.5. Gas Composition and Origin*

Milkov et al. [37] studied gas composition and origins based on around 2600 shale gas samples from 76 geological formations in 38 sedimentary basins located in eleven countries. It is found that methane is the predominated hydrocarbon component, with more than 80% in volume concentration, followed by ethane with around 6% in volume concentration, and propane with around 2% in volume concentration. Nitrogen and carbon dioxide are two main non-hydrocarbon components in shale gas samples, with average volume concentration around 6% and 2%, respectively. For most shale plays in the USA, China and Argentina, it is found that the most productive and commercially successful shale

plays have pure thermogenic origin. This is very different from the study of Curtis [19], where it is found that shale gas has predominantly microbial origin.

#### *2.6. Shale Gas Occurrence Types*

The types of natural gas in shale formations are determined by diverse formation physics and pore characteristics. In accordance with the classification of pore structures in shale formations (Section 2.3), free gas, adsorbed gas, and dissolved gas are three possible gas occurrence states underground [38,39]. Generally, free gas is stored not only in fractures, but also in pore systems, including organic pores and inorganic pores. Adsorbed gas is mostly stored on the surface of organic matter in equilibrium state with free gas. Dissolved gas is usually stored in liquid hydrocarbons, formation water, but most importantly in solid kerogen. Organic kerogen serves as the source rock and generates shale gas continuously [40].

The percentage of different gas types varies from one reservoir to another, since it is significantly influenced by pressure, temperature, organic matter types, organic matter content, organic matter maturity, the development of micro fractures, and liquid hydrocarbon content. The different gas types and gas flow mechanisms in organic shale nanopores can be seen in Figure 17.

**Figure 17.** The storage form and flow mechanism of shale gas in organic nanopores [38,41].

#### 2.6.1. Free Gas Characterization

Free gas is stored in organic or inorganic pores, micro fractures, and hydraulic fractures. The content of free gas is determined by adsorbed gas and dissolved gas. Only when the total gas amount is larger than the sum of adsorbed and dissolved gas amount does a free gas state exist. Under high-pressure or high-temperature reservoir conditions, gas behaviors do not satisfy the ideal gas equation of state (EOS), so the real gas EOS needs to be adopted to describe its behaviors [42,43].
