Geographically, the Sichuan Basin, located in Southwest China with an area of approximately 260,000 km² is composed of a low and gentle uplift, a southern folded area, a highly folded southeast area, and a western depression area (Figures 1A, B), which is situated southwest of the West Sichuan Depression. The regional structure is the frontal hidden structural belt within the Longmenshan thrust belt in western Sichuan, adjacent to the Chengdu Depression in the southeast, the Wuzhongshan structural belt in the northwest, the Yazihe structure in the north obliquely, and the Qiongxi structure in the south (Figure 1C). The Dayi structure is a northwest-dipping monocline with traps controlled by local structures, faults, and trough faults as the main developed faults (Chen et al., 2013; Liu et al., 2014; Chen et al., 2016). Based on regional geological data, the Dayi structure of the Xujiahe Formation is a mega-thick continental coal-bearing clastic rock series, deposited in the Xu 2, 3, 4, and 5 members from the bottom up (Figure 1D); the sandstone reservoir of the Xu 3 member is one of the main gas-producing reservoirs.

Research has indicated that the tight sandstone in the Xu 3 Member underwent three stages of evolution. In the early diagenetic stage, because of the large burial depth, the porosity decreased significantly under compaction, and the primary porosity decreased from 30% to nearly 10%. In the middle diagenetic stage, the Anxian orogenic movement provided abundant carbonate cement for the Xujiahe Formation, leading to a further decrease in porosity, and tight reservoirs exhibited ultralow porosity, which dropped below 2%. In the late diagenetic period, the porosity of tight reservoirs increased under dissolution, but was still below 5% (Zhang, 2009; Luo, 2015; Liu et al., 2018; Liu et al., 2020).

The results of the core physical property experiments indicated that the reservoir in the study area was highly dense, and the values of core porosity and permeability were small (Table 1). The porosity is between 2% and 4%, with an average value of 3.16%; permeability ranges from 0.01 × 10⁻³ to 0.1 × 10⁻³ μm², with an average value of 0.0235 × 10⁻³ μm². Porosity and permeability are positively correlated. With similar porosity values, the relative difference in permeability values was significant, implying strong heterogeneity of the reservoir pore structure (Figure 2).

Whole-rock X-ray diffraction analysis of the core revealed that the mineral composition of the reservoir cores was mainly quartz (average value: 66.4%), followed by feldspar (average value: 20.77%) and clay minerals (average value: 8.24%), with minor amounts of dolomite and calcite (Table 1).

The HPMI curves of the ten core samples with different porosities and permeability are shown in Figure 3A. The mercury intrusion curves indicate that the maximum mercury intrusion saturations for all core samples are less than 65%, that is, mercury cannot enter most of the pore systems when the injection pressure reaches 200 MPa. Moreover, the maximum relaxation time of the saturated T₂ spectrum exceeds 20,000 ms and presented a bimodal distribution, indicating strong core heterogeneity (Figure 3B).

Based on the HPMI curves and NMR T₂ spectra aforementioned displayed, quantitative pore structure parameters, such as maximum pore radius (R_a), average pore radius (R_p), median pore radius (R₅₀), structure coefficient (Ф), relative sorting coefficient (D), characteristic structural parameters (C), homogeneity coefficient (ɑ), maximum mercury intrusion saturations (Shg_max), displacement pressure (Pd), median pressure (P₅₀), and saturated T₂ mean value (T_2LM), are calculated and shown in Table 2. The data show that the average pore radius of the reservoir core was between 22 and 96 nm, and the displacement pressure mainly ranged from 1.354 to 8.263 MPa. The maximum throat radius of the corresponding core was between 89 and 543 nm, indicating that the reservoirs of the Xu 3 Member in the study area were developed with nanoscale pore throats with a large difference in size.

Twenty-five cores from the Xu 3 Member in the study area were selected as experimental samples, with porosity ranging from 2.298% to 4.153% and permeability ranging from 0.0071 × 10⁻³ to 0.0591 × 10⁻³  μ m 2 . Figure 2 shows the results of the rock resistivity experiment, indicating that the relationship between core formation factors and porosity in the study area is relatively concentrated, and when proportionality coefficient a=1, the distribution range of cementation exponent (m) is 1.4–1.7 (Figure 4A). For proportionality coefficient b=1, the distribution range of the saturation exponent (n) was 3–8, and the relationship between the resistivity index and water saturation was relatively scattered, which is non-linear when the water saturation is less than 40%, typical of the “non-Archie phenomenon” (Figure 4B).

Although the absolute contents of both quartz and feldspar have no significant correlation with the rock–electrical parameters (Figures 5A, B), the clay content has a good negative correlation with the cementation exponent (Figure 5C), that is, the higher the clay content, the smaller the value of m. The analysis suggests that owing to the adsorption of clay minerals on water, a water film is easily formed on the surface of the particles, increasing the conductivity of the core and reducing the value of the formation factor. This results in a decrease in the fitted m value. Figure 5D shows that there was no significant correlation between the clay content and the saturation exponent.

The cross-plot of the cementation exponent and physical property parameters shows that the value of m increases with an increase in porosity and permeability and is more correlated with porosity, indicating that the cementation index is more affected by porosity (Figures 5E, F). Similarly, the cross-plot of the saturation exponent and physical parameters indicated that the saturation exponent was negatively correlated with the porosity and permeability (Figures 5G, H). Further analysis revealed that the fitting trend between the saturation exponent and permeability exhibited two patterns. (1) When n > 5.4, n decreases rapidly with increasing permeability and (2) when n < 5.4, n decreases slowly with increasing permeability. In theory, the saturation exponent reflects the degree of uniformity of the fluid distribution in the core; the larger the n value, the more uneven the fluid distribution. The relationship between the saturation index and permeability reveals that, in an extremely complex fluid distribution, if there are preferential seepage channels, the fluid is distributed quickly and evenly, whereas when the fluid distribution is uniform, the change in permeability has no obvious effect (Gao, 2012; Cong and Hu, 2016; Zhang et al., 2017).

The pore structure of the cores can be characterized quantitatively by HPMI experiments, but with limited pressure in the laboratory mercury intrusion apparatus, it is difficult to inject mercury into every pore of the cores; therefore, the capillary pressure curve cannot reflect the total pore system (Yakov V and Win L S, 2001; Liu et al., 2008; Li et al., 2015). However, the NMR experiment can measure the attenuation signal of all hydrogen nuclei of water-saturated core pores; therefore, the pore structure of tight sandstone cores was evaluated using pseudo-capillary pressure curves constructed through NMR (Figure 6A). Yudan et al. (2005) suggested that the relationship between the capillary pressure (Pc) and relaxation time (T ₂) can be expressed as follows (He et al., 2005): P c = 2 σ ⁡ cos ⁡ θ ρ 2 × F s × 1 T 2 , (1) where σ represents the fluid interface tension, θ is the wetting contact angle, ρ ₂ is the transverse surface relaxation time, and Fs is a geometry factor. The value of Fs was 2 for the cylindrical throat and 3 for the spherical throat. After non-linear interpolation of the T ₂ spectrum, the relationship between the capillary pressure and pore radius (Rc) was fitted, and the results showed that a piecewise fitting relationship exists between the two variables, implying that the pore system can be divided into two parts (Figure 6B).

Finally, the characteristic pore structure parameters of the cores in the study area were extracted based on the construction of a pseudo-capillary pressure curve (Table 3).

The cross-plot of the cementation exponent and mercury intrusion characteristic parameters shows that, overall, the cementation exponent decreases with the increase of the relative sorting and homogenization coefficients, indicating that the stronger the throat homogeneity, the smaller the value of m (Figures 7A, B). The cross-plot of saturation exponent and mercury injection characteristic parameters shows that, in the overall trend, the saturation exponent has a strong negative correlation with the median radius and the average radius, suggesting that the larger the radius of the pore and throat, the more uniform the fluid saturation distribution (Figures 7C, D). The correlation analysis between the rock–electrical parameters and mercury intrusion characteristic parameters also showed that, compared with the cementation exponent, the correlation coefficient between the saturation exponent and mercury intrusion characteristic parameters was greater, indicating that the saturation exponent was more influenced by the pore structure.

A diagram of the saturation exponent and pseudo-capillary pressure curve characteristic parameters revealed that the index was controlled by the core–pore structure. Therefore, the influence of the pore structure on the index was further analyzed by combining it with the data from casting thin section identification, physical property analysis, and NMR experiments.

Four cores (D4-1, D7-1, D9-1, and D9-2) with similar porosities and different saturation exponents were selected for comparative analysis of the water-saturated NMR T₂ spectrum (Figure 8A).The saturation exponent is related to the signal amplitude at 100 ms of the T₂ spectrum, and the larger the signal amplitude at 100 ms, the smaller the value of n (Figure 8B), and a comparison of the casting thin sections from the four cores shows that, in general, the larger the maximum pore size and main pore size distribution interval, the smaller the saturation exponent (Figure 9). Therefore, in tight sandstone reservoirs, the saturation exponent is controlled by the pore structure, particularly by the development of large-size reservoir pores, that is, the more developed the large-size pores, the more uniform the core fluid saturation distribution and the smaller the saturation exponent. To describe the development of large-sized pores, the fractal dimension theory of pore throats was used to quantitatively evaluate the pore structure.

Based on the basic theory of the Archie model, the relationships between porosity and formation factors as well as water saturation and electrical resistivity increase coefficients were fitted, and the fixed rock–electrical parameter values were obtained as a ₁=1.0686, b ₁=1.1939, m ₁=1.56, and n ₁=4.895.

An analysis of the factors influencing the cementation exponent showed that m was controlled by the porosity and clay content. Therefore, the porosity and clay content were selected as independent variables, and linear multiple regression was used to construct the variable cementation index calculation model with a correlation coefficient R ² of 0.7591. The variable cementation exponent is denoted as m ₂, and the calculation model is as follows: m 2 = 0.03 × φ − 0.006 × V c l a y + 1.502 , (5) where m ₂ is the variable cementation exponent and V _clay is the clay content in percentage.

Previous studies have shown that the saturation exponent is primarily controlled by the proportion of large pores in the core relative to the total pore system. The distribution of the core fluid saturation presented different rules, with a threshold proportion of large pores of 5%. Hence, the proportion-dependent variable saturation index model was constructed and denoted as n ₂. The calculation model was n 2 = 9.3547 × e − 0.274 × P , P < 5 % n 2 = 8.6183 × P − 0.321 , P ≥ 5 % . (6)

Based on Archie’s model with variable parameters, the reservoir saturation of the Xu 3 Member in Well X of the Dayi structure in the West Sichuan Depression was quantitatively evaluated. The green curve in the nine sections (Sw₁) represents the saturation calculation results for the fixed rock electrical parameters, and the red curve represents the saturation calculation results for the variable Archie parameter model (Sw₂).

Analysis of the comprehensive evaluation result map of the well logging data obtained from 4750 to 4775 m of this well suggests that this interval is an industrial gas reservoir, as determined by the gas testing results. The conventional logging curve shows that the natural gamma rays in the perforated interval are low, the well diameter is relatively stable, and the spontaneous potential curve presents an overall negative anomaly, indicating the good permeability of this interval. All three porosity curves show that the values of acoustics and neutrons increase, whereas the density value decreases, and the deep and shallow lateral resistivity has a slight positive difference. A comparison of the saturation calculation results in the perforated interval suggests that (1) the calculated water saturation from the fixed rock-electric parameter model is large and overlaps the bound water saturation, indicating that there is a large amount of mobile water, and the calculation is inconsistent with the gas testing result and (2) the calculated water saturation from the variable Archie’s model ranges from 40% to 70%, which is consistent with the bound water saturation. The overlapping results indicate the presence of gas in the interval, which is consistent with the gas test results (Figure 12A).

Based on the analysis of the comprehensive evaluation result map of well-logging data obtained from 4580 to 4605 m in this well, the calculated bound water saturation from the fixed rock–electric parameter model overlaps with the water saturation in the interval, indicating a large amount of mobile water, which is inconsistent with the gas testing result. However, the water saturation calculated from Archie’s model was similar to the bound water saturation, which was consistent with the gas testing results, further proving the effectiveness of Archie’s model with variable parameters in the application (Figure 12B).