The crystal size of the carbonate minerals can be divided into micritic (<50 µm), very fine (50–100 µm), fine (100–250 µm), medium (250–500 µm), and coarse (>500 µm) (Bissell and Chilingar, 1967). All of the limestone samples collected from the XBX outcrop are bioclastic limestone, the cement between the bioclastics is micritic calcite with crystal sizes of <10 μm, and no obvious crystallization was observed in the bioclastics and calcite cement (Figure 2A). The limestone samples collected from the Puguang gas field include bioclastic limestone (Figure 2B) and micritic limestone (Figure 2C). The crystal sizes of the calcite are <10 μm, and no obvious crystallization occurred in these limestone samples. The dolostone samples collected from the Puguang gas field include micritic dolostone (Figures 2D,E), very fine crystallized dolostone (Figure 2F), and fine crystallized dolostone (Figure 2G). The crystal size of the two micritic dolostone samples is about 10 µm (average of 12 μm for D87 and 10 µm for D90), and intercrystal pores were hardly observed in the two micritic dolostone samples. The average crystal size of the very fine crystallized dolostone (D89) is about 70 μm, with very limited dolomite recrystallization, and some pores are developed between the subhedral dolomite crystals (Figure 2F). The crystal sizes of the fine crystallized dolostone (D99) are 150–200 µm (average of 194 µm), with obvious dolomite recrystallization, and black solid bitumen was observed in the pores between the subhedral dolomite crystals (Figure 2G). The calcite cement samples (crystal sizes of 0.3–1.0 cm) collected from the Puguang gas field are mainly developed in vugs in dolostone, and it is generally associated with black solid bitumen (Figures 2H,I).

The δ ¹³C, δ ¹⁸O, Δ ₄₇, and T_Δ47 values of all of the carbonate samples collected from the XBX outcrop and the Puguang gas field are presented in Table 1. The δ ¹³C, δ ¹⁸O, and Δ ₄₇ values of the three limestone samples from the XBX outcrop range from 3.451 to 3.788‰, −6.336‰ to −4.793‰, and 0.499–0.514‰. For the limestone, dolostone, and calcite cement samples collected from then Puguang gas field, the δ ¹³C values range from 2.505 to 4.014‰, 2.478–3.903‰, and −1.108‰ to −0.227‰, respectively; the δ ¹⁸O values range from −6.943‰ to −6.366‰, −6.300‰ to −4.044‰, and −7.732‰ to −4.722‰, respectively; and the Δ ₄₇ values range from 0.333 to 0.347‰, 0.391–0.481‰, and 0.355–0.368‰, respectively. The δ ¹³C values of the limestone and dolostone samples from the Puguang gas field are basically similar (2.505–4.014‰), while the δ ¹³C values of the calcite cement (−1.108‰ to −0.227‰) are significantly lower than those of the limestone and dolostone samples.

T_Δ47 of all of the carbonate samples exhibit a relatively large variation (Table 1). T_Δ47 of the limestone from the XBX outcrop are 57.6–65.6°C (average of 61.9°C); while T_Δ47 of the calcite cement and limestone samples from the Puguang gas field are 145–156.5°C (average of 151.4°C) and 163.9–179.1°C (average of 173.8°C), respectively. There is a large difference in T_Δ47 of the four dolostone samples from the Puguang gas field. T_Δ47 of the two micritic dolostone samples are 71.7 ± 8.9°C (D90) and 72.5 ± 4.5°C (D83), that of the very fine crystallized dolostone is 88.5 ± 5.4°C, and that of the fine crystallized dolostone is 126.3 ± 7.6°C (D99).

The R_o values of the Permian shales from the XBX outcrop and the Puguang gas field are presented in Table 2. The R_o values of the two P₂d shale samples from the XBX outcrop are 0.92 and 0.96%, while the R_o values of the P₂w shales from the Puguang gas field are 2.39–3.11% (average of 2.80%).

The maturity of organic matter, which is usually characterized by R_o and/or equivalent R_o (such as the solid bitumen reflectance or graptolite reflectance), is a commonly used method for paleotemperature reconstruction (Mukhopadhyay, 1994; Hackley et al., 2015; Luo et al., 2020b). The maturity evolution of organic matter is an irreversible process and can be characterized by a first-order chemical kinetics reaction. According to the Arrhenius equation, the maturity of organic matter has an exponential relationship with temperature and a linear relationship with time. As a result, temperature is the most important parameter affecting the maturity evolution of organic matter (Hunt, 1996). Theoretically, the MBT can be obtained based on a model of the evolution of the organic matter’s maturity with temperature (such as the EASY%R_o model; Sweeney and Burnham, 1990).

The EASY%R_o model is a widely accepted model for the evolution of the maturity of organic matter, and the organic matter maturity (R_o) can be calculated for a given heating rate (Sweeney and Burnham, 1990). According to apatite fission track analysis (Deng et al., 2013), the Permian and Triassic strata in the XBX outcrop and the Puguang gas field reached their maximum burial depths at about 80 and 120 Ma, respectively (Figure 3). The area of the XBX outcrop was uplifted in the Late Indosinian (Burchfiel et al., 1995), and the R_o of the Permian shale near the XBX outcrop in the NW Sichuan Basin is <1.3% (Fu et al., 2010), so the MBT of the Permian shale should be less than 160°C (Figure 4). A lot of solid bitumen with a relatively high maturity (R_o>1.7%) is commonly present in the Permian and Triassic gas reservoir in the Puguang gas field, suggesting that large scale oil-cracking occurred in this gas field, and the maximum burial temperature may have exceeded 200°C (Hao et al., 2008). In addition, the heat flow has decreased gradually since the Late Permian (Zhu et al., 2016). Thus, the burial temperature of the Permian and Triassic strata in the XBX outcrop and the Puguang gas field should have reached the maximum values when the burial depths reached the maximum values at about 80 and 120 Ma (Figure 3), respectively. As a result, the heating rates should be about 1.0°C/Ma (150°C/(260–80 Ma) = 0.83°C/Ma) and 2.0°C/Ma (220°C/(250–120 Ma) = 1.7°C/Ma) for the XBX outcrop and the Puguang gas field, respectively.

The evolution of R_o with temperature based on the EASY%R_o model for heating rates of 1.0 and 2.0°C/Ma is shown in Figure 4. According to this model, R_o of the P₂d shale in the XBX outcrop is 0.92–0.96%, so the MBT of the P₂d should be 132–140°C, while R_o of the P₂w shale in the Puguang gas field is 2.39–3.11%, so the MBT of the P₂w should be 207–232°C (Figure 4). The thicknesses of the intervals between the P₁q limestone and the P₂d shale in the XBX outcrop and between the P₂c-T₁f dolostone and the P₂w shale in the Puguang gas field are about 300 and 200 m (Figure 3), respectively. In addition, the paleotemperature gradient in the Late Cretaceous was about 25°C/km (Zhu et al., 2016). As a result, the MBTs of the P₁q limestone in the XBX outcrop and the P₂c-T₁f dolostone in the Puguang gas field should be 139.5–147.5 and 202–227°C, respectively. The MBT determined using the EASY%R_o model supplies a basic constraint on the MBT determined using the solid-state reordering model of carbonate clumped isotopes.

Carbonate clumped isotopes (Δ₄₇) can be used to directly determine the formation temperature or the equilibrium temperature of carbonate minerals, and they are independent of the δ ¹⁸O of the fluid from which the carbonate minerals were deposited. This is called the clumped isotope thermometer (Ghosh et al., 2006; Eiler, 2007). The clumped isotope thermometer is mainly based on the exchange reactions of the ¹³C and ¹⁸O in carbonate minerals, and the abundance of ¹³C-¹⁸O in carbonate minerals is a function of temperature (Eiler, 2007). However, the clumped isotope temperature (T_Δ47) may be altered by high temperatures and/or recrystallization during the late burial process and can be completely different from the original formation temperature (Passey and Henkes, 2012). Ancient carbonate minerals have usually experienced relatively high temperatures during late burial, which resulted in solid-state exchange (reordering) of the ¹³C-¹⁸O in the carbonate minerals. Consequently, the abundances of ¹³C-¹⁸O in carbonate minerals will differ from the original abundances when the carbonate minerals were formed, and the T_Δ47 values should also be different from the original formation temperature of the carbonate minerals. In addition, recrystallization after mineral formation can also change the abundance of ¹³C-¹⁸O and T_Δ47 of the carbonate minerals (Ryb and Eiler, 2018). Therefore, for ancient carbonate minerals, the present-day T_Δ47 is often the result of the combined effect of recrystallization and solid-state reordering. The solid-state reordering of Δ₄₇ can be characterized using a kinetic model, and the MBT of the carbonate minerals can be reconstructed if the carbonate minerals experienced no or limited recrystallization.

There are two main kinetic models for characterizing the solid-state reordering of carbonate minerals: the transient defect/equilibrium defect model (Henkes et al., 2014) and the exchange-diffusion model (Stolper and Eiler, 2015). The best agreement between model predictions and natural dolomite marbles was found when using the exchange-diffusion model (Lloyd et al., 2018). Therefore, the exchange-diffusion model was used to in this study. According to the exchange-diffusion model, the variation of T_Δ47 was shown in Figure 5, if the Permian-Triassic limestone was formed at about 30°C and reached a maximum temperature of about 220°C at 120 Ma. When the burial temperature was <100°C, no solid-state reordering occurred and T_Δ47 of the calcite would be stable. When the burial temperature was between 100 and 200°C, partial solid-state reordering occurred and T_Δ47 of the calcite increased as the burial temperature increased. When the burial temperature was >200°C, full solid-state reordering occurred and T_Δ47 of the calcite reached equilibrium with the burial temperature. When the burial temperature was <200°C during the late uplift and exhumation, partial solid-state reordering occurred again and T_Δ47 of the calcite decreased as the burial temperature decreased. If the burial temperature was decreased from above 200°C to below 150°C during the uplift, T_Δ47 of the calcite would have decreased to a blocking temperature (final apparent temperature) of about 175–200°C (Henkes et al., 2014), and it did not decrease as the burial temperature decreased (Figure 5). The solid-state reordering of dolomite is similar to that of calcite, but T_Δ47 of dolomite is stable when the burial temperature is <150°C, and it does not reach equilibrium with the burial temperature when the burial temperature is <250–300°C (Lloyd et al., 2018).

T_Δ47 of the limestone from the XBX outcrop is 62°C on average, which is significantly higher than the seawater temperature (20–30°C) during the deposition of P₁q (Henkes et al., 2018), but is far lower than the blocking temperature after reaching the equilibrium temperature. According to the kinetic model of the solid-state reordering of calcite, it can be inferred that the limestone only underwent partial solid-state reordering, and it did not reach equilibrium. The petrological characteristics of the three bioclastic limestone samples (D1–D3) from the XBX outcrop show that the bioclastics were cemented with micritic calcite, and no obvious recrystallization was observed. Therefore, the T_Δ47 values of the present-day limestone samples were mainly affected by the solid-state reordering process. As a result, the solid-state reordering model can be used to reconstruct the MBT of these limestone samples. Based on the solid-state reordering model for the calcite in the XBX outcrop, the relationship between T_Δ47 and MBT is shown in Figure 6. T_Δ47 of the present-day limestone is 62°C, and the corresponding MBT of the XBX limestone is about 139–147°C (Figure 6), which is basically consistent with the MBT constrained by the EASY%R_o model (139.5–147.5°C).

The MBT determined using the EASY%R_o model is >200°C (202–227°C; Figure 4), which supports the fact that widespread oil cracking occurred in the Puguang gas field (Hao et al., 2008), while the present-day burial temperature of the P₂c-T₁f is 100–135°C. According to the solid-state reordering model of calcite (Figure 5) and the temperature history of the Puguang gas field, the limestone or early-formed calcite cements should have experienced complete solid-state reordering, and the final apparent temperature of the limestone and calcite cement should be similar to the blocking temperature (150–160°C) because the present-day burial temperature is 100–135°C due to the late uplift and exhumation. T_Δ47 of the micritic limestone and bioclastic limestone is 150–170°C, which is consistent with the blocking temperature predicted by the solid-state reordering model for calcite. The coarse calcite cements, associated with the solid bitumen and having more negative δ ¹³C values (−1.108‰ to −0.227‰) than that of its bulk rock (dolostone), are considered to be the product of oil cracking and thermochemical sulfate reduction (TSR) processes (Hao et al., 2008), and they were deposited during the early burial process not during the late uplift and exhumation. T_Δ47 of the calcite cements in the Puguang gas field are 145–156.5°C (average of 151.4°C), which is also very close to the blocking temperature of calcite predicted by the model. The small differences in the final apparent temperatures of the limestone and the coarse calcite cements in the Puguang gas field according to the uniform solid-state reordering model may be due to the different kinetic parameters used in the solid-state reordering models of the coarse calcite and micritic limestone, especially during the cooling process. However, no published paper has discussed this problem, and it is not discussed in detail in this paper. However, it is certain that the relatively high temperature (>200°C) in the Puguang gas field resulted in the complete solid-state reordering of the micritic limestone and the coarse calcite cements. Therefore, the micritic limestone and coarse calcite cements cannot be used to reconstruct the MBT in the Puguang gas field.

However, the temperature of the onset of the partial reordering of dolomite is much higher than that of calcite, and the complete solid-state reordering temperature of dolomite can be as high as 250–300°C (Lloyd et al., 2018). As a result, the solid-state reordering of the dolostone samples can be used to reconstruct the MBT in the Puguang gas field. The T_Δ47 values of the dolostone with different dolomite crystal sizes from the Puguang gas field are significantly different (Table 1). T_Δ47 of the micritic dolostone (71.7–72.5°C) is the lowest, followed by T_Δ47 of the very finely crystallized dolostone (88.5 ± 5.4°C), but T_Δ47 of the two types of dolostone are very close to each other. T_Δ47 of the finely crystallized dolostone (126.3 ± 7.6°C) is significantly higher than that of the micritic dolostone and the very finely crystallized dolostone, suggesting that T_Δ47 of the finely crystallized dolostone was also affected by relatively strong recrystallization, while the very finely crystallized dolostone only experienced very limited recrystallization.

It is widely accepted that the micritic and very finely crystallized dolostones were caused by penecontemporaneous dolomitization, which occurred under near surface conditions or quite shallow burial conditions. As a result, the initial formation temperatures of the micritic and very finely crystallized dolostones should be similar to the temperature of the coeval seawater. The temperature (30–40°C) in Southern China was lethally hot during the Late Permian-Early Triassic (Sun et al., 2012), so the initial formation temperature of the micritic and very finely crystallized dolostones can be assumed to be 30–40°C. Assuming that the MBT reached 180°C, 200°C, 220°C, and 240°C, the corresponding T_Δ47 evolution of the dolostone can be predicted using the solid-state reordering model for dolomite (Figure 7). If the MBT reached 180°C, only T_Δ47 of the micritic dolostone (D83) and the very finely crystallized dolostone (D89) are within the predicted range (1.0 σ error included; Figure 7A), while T_Δ47 of the finely crystallized dolostone (D99) is significantly higher than the predicted range. If the MBT reached 200°C or 220°C, only T_Δ47 of the very finely crystallized dolostone (D89) is within the predicted range, and T_Δ47 of the micritic dolostone and the finely crystallized dolostone (D99) are slightly lower and significantly higher than the predicted range, respectively (Figures 7B,C). If the MBT reached 240°C, only T_Δ47 of the finely crystallized dolostone (D99) is within the predicted range, and T_Δ47 of the micritic dolostone and the very finely crystallized dolostone are lower than the predicted range (Figure 7D). As was discussed above, T_Δ47 of the limestone and calcite cements were similar to the blocking temperature during the late cooling process, suggesting that the calcite experienced complete solid-state reordering, and the MBT should be >200°C. Combined with the T_Δ47 evolution shown in Figure 6, the MBT of the P₂c-T₁f in the PG gas field should be 200–220°C, which is similar to the MBT determined using the EASY%R_o model (202–227°C).

Based on the model of the relationship between the final apparent temperature (present-day T_Δ47) and the MBT (Figure 8), the MBTs determined using the present-day T_Δ47 of the micritic dolostone (D83 and D90), the very finely crystallized dolostone (D89), and the finely crystallized dolostone (D99) are 162–174, 171–220, and 245–252°C, respectively. Only the MBT determined using the finely crystallized dolostone falls within the temperature range determined using the EASY%R_o model. The MBT determined using the micritic dolostone is slightly lower than the temperature range determined using the EASY%R_o model. This may be due to the kinetic parameter of the solid-state reordering model for dolomite was constructed based on dolomite with some recrystallization. While the MBT determined using the finely crystallized dolostone is significantly higher than the temperature range determined using the EASY%R_o model, which is most likely due to the occurrence of significant recrystallization. However, the time and temperature at which the recrystallization reached final equilibrium is unknown. Consequently, the present-day T_Δ47 of the finely crystallized dolostone cannot be used to determine the MBT. Perhaps U-Pb dating of carbonate can be used to accurately determine the final equilibrium age of the dolostone (Pan et al., 2020), and combined with the general burial and thermal gradient information, it can be used to reconstruct the MBT based on the solid-state reordering model, which is a valuable research direction for future studies.