In situ desorption gas measurement can be used to evaluate shale gas potential, sweet spot prediction, and production strategy optimization. However, gas contents and carbon isotope compositions of in situ desorption gas and the relationship to reservoir properties and shale compositions are not systematically studied from the actual production situation. In this study, 63 core shales of Wufeng-Longmaxi formation from the YY1 well in the eastern Sichuan Basin were subjected to TOC (total organic carbon), solid bitumen reflectance (Rb), maceral fractions of kerogen analysis, and X-ray diffraction (XRD) analysis to obtain shale compositions, and 10 selected samples were conducted on low-pressure N2/CO2 (N2/CO2GA), mercury injection capillary pressure (MICP), and field emission scanning electron microscopy (FE-SEM) tests to acquire reservoir properties. Meanwhile, 60 samples were also subjected to in situ desorption tests to obtain shale gas content, and 5 selected samples were used to investigate variations in shale gas compositions and carbon isotopes during the desorption process. Results indicated that transient rates of shale gas during desorption process are significantly controlled by desorption time and temperature. In terms of in situ desorption process, total gas is divided into desorbed gas and lost gas. Desorbed gas is mainly comprised of CH4, N2, CO2, and C2H6, with desorption priorities of N2 > CH4 > CO2 ≈ C2H6, which are consistent with their adsorption capacities. The δ13CH4 values tend to become heavier during desorption process, varying from -37.7‰ to -16.5‰, with a maximum increase amplitude of 18.8‰, whereas the change of δ13C2H6 value, from -38.2‰ to -34.8‰, is minor. Desorbed gas shows carbon isotope reversals, due to that preferential desorption of 12C-CH4 during desorption process results in δ13C value less negative in CH4. The tested desorbed gas, lost gas, and total gas ranged 0.088 to 1.63 cm3/g, 0.15 to 3.64 cm3/g, and 0.23 to 5.20 cm3/g, respectively. Shale gas content, i.e., desorbed gas and lost gas, is controlled primarily by TOC content and organic matter (OM)-hosted nanometer-size pores. Clay mineral content is negatively correlated with shale gas content, due to that, clay mineral pores are more easily compacted during burial and occupied by water molecules. Compared with shale gas reservoirs in North America, the studied shale reservoir has high brittle mineral content and permeability, which is considered to have great potential of shale gas resource and to be the next commercial development zone in south China.
Shale gas, as a type of unconventional natural gas, has been exploited in several countries and attracted great concern worldwide due to its enormous potential [1–4]. The successful development of shale gas in North America enabled great enthusiasm of shale gas investigation around the world, particularly in China [5–10]. The recoverable shale gas is estimated to in China and to approximately in the Sichuan Basin . The evaluation of geological sweet spots in shale gas reservoirs is an important part of shale gas reservoir evaluation . To estimate or predict gas-in-place (GIP), measuring gas content is an essential step [13–15]. And therefore, the quantity, quality, and desorption behavior of in situ gas must be understood , which has been adopted to estimate recoverable reserves and predict gas production [13–15]. Exploration practices have indicated that shale gas content is primarily controlled by reservoir properties, e.g., total organic carbon (TOC) content, thermal maturity, water saturation, porosity, formation pressure, and preservation condition. Though remarkable progress has been made in gas adsorption/desorption experiments and molecular simulation in shale gas content. However, detailed and reliable informations on actual gas desorption process remain stagnated, which is still a challenging issue of shale gas efficient development and production [17–20].
Shale gas is consisted mainly of free gas and adsorbed gas, however, it is difficult to distinguish them apart completely [21–23]. Generally, shale gas content evaluation is primarily obtained via laboratory simulation and in situ desorption measurement. Adsorbed gas is obtained by methane sorption experiment on representative core shales in the laboratory, and free gas is determined based on effective porosity and gas pressure-volume-temperature (PVT) properties under reservoir conditions . However, shale gas content obtained by this approach represents the maximum value, which is probably not well consistent with actual shale gas content. Canister desorption, a more direct, quick, and reliable approach, plays an important role in determining gas contents and compositions in favorable area [1, 16, 24], which is based on onsite desorption data to estimate total gas content . This method was firstly applied to coalbed methane reservoir, and was gradually used to measure shale gas contents, variations of shale gas components and carbon isotopes in recent years [19, 26–28]. According to desorption process, in situ desorption gas is divided into lost gas, desorbed gas, and residual gas [1, 24]. Lost gas refers to the gas lost during the drilling process, and it is generally obtained using the USBM method . Desorbed gas is the gas directly measured from cores by using an inverted graduated cylinder. Residual gas refers to the gas retained in shale that is not easily released during desorption process . Laboratory simulation is easy to operate and realize, and therefore, it has been widely adopted by scholars. However, in situ desorption measurement has obvious defects, e.g., harsh work condition and high cost. More and more scholars have concerned variations in gas component and carbon isotopes, as well as their controlling factors [1, 30, 31]. Variations in isotopic compositions during desorption process were also used to predict shale gas production in the late stage [27, 32]. However, the characteristics of desorption gas are still less studied and poorly understood, thus, its application to reliable evaluation of shale gas reservoir deserves a more in-depth investigation.
Gas geochemical indicators, e.g., molecular compositions and carbon isotopes, are generally used to evaluate natural gas source, predict gas content, and reconstruct physiochemical process . The carbon isotopes have become an important index for shale gas exploration . Stable isotopic compositions are generally used to differentiate biogenic gas and thermogenic gas origins, as well as coal and mudstone source rocks [33, 34]. Thermogenic methane is characterized by a δ13C1 value of -20‰ to -50‰, whereas δ13C1 value of biogenic methane with acetate fermentation/methyl utilization route is less than -50‰ and with carbon dioxide reduction route is less than -60‰ [33, 35, 36]. Carbon isotopes of shale gas has significant variability during shale gas desorption process [27, 37], probably due to the free gas and adsorbed gas have different isotope with different desorption degrees. For instance, δ13CH4 value can become heavier by an extent of 4.8–31‰ and 9.1–10.2‰ for the Longmaxi and Shuijintuo shales, respectively, in south China [27, 32], but δ13C2H6 generally increases with a relatively smaller range . Variation in δ13 CH4 value can indicate shale gas desorption stage. Carbon isotope value has an inverse correlation with shale gas production, due to that carbon isotope becomes heavier with decreased production of shale gas . Moreover, desorbed gas is generally characterized by isotopic reversal and the extent of isotopic reversal increased as desorption increased , which is also closely related to the high-production rates of shale gas [31, 39]. However, which factors control variations in shale gas compositions and carbon isotopes are still unclear.
In this study, a total of 63 shales of Wufeng-Longmaxi formation from YY1 well in eastern Sichuan Basin were collected and subjected to organic geochemistry and mineral composition analysis. Moreover, 60 selected samples were used to proceed in situ desorption measurement at mud circulation temperature (49–54°C) and reservoir temperature (110°C), respectively, in order to release natural gas from cores as much as possible, and 5 samples were selected to measure variations in gas compositions and carbon isotopes. Finally, the influences of shale compositions and physical properties on shale gas content were discussed, and shale gas reservoir features were also compared with those in adjacent areas and in North America.
2. Geological Setting
The studied area is located in eastern Sichuan Basin (Figure 1), which is composed of high and steep anticlinal belts and fault belts in NE and NNE directions. The basement is shallow metamorphic rock of Presinian Banxi group. The Devonian stratum was partially missed, and Carboniferous, Cretaceous, and Paleogene strata were all corroded. During the Late Ordovician-Early Silurian, affected by multistage tectonic movements, a north-opening continental shelf sandwiched by middle Guizhou, central Sichuan, and Xuefeng ancient uplifts was formed. In the early-middle Ordovician, the paleo-sea was expanded and transformed into a limited sea by uplifts. In the Late Ordovician-Early Silurian, sea level raised globally, forming the deep-water shelf facies and organic-rich shales were developed in the Sichuan Basin. The Wufeng-Longmaxi shale, the most important significant stratum for shale gas development in the Sichuan Basin, is characterized by its larger thickness, abundant organic matter (OM), high maturity, and favorable brittleness . In eastern Sichuan Basin, the depth of the Wufeng-Longmaxi shales ranges from 3700 to 4200 m, with pressure coefficient of 1.7–2.1, and 8 horizontal wells indicated that shale gas production in the studied area varies from to [40, 41], indicating huge potential of shale gas resource in studied area.
3. Samples and Experimental Methods
In this study, 63 core shales were collected from YY1 well, with depth of 3770–3864 m, to analyze organic geochemistry, mineral component, and rock petrophysical property. Moreover, 60 samples were selected to perform in situ desorption test to measure shale gas content, and 5 selected samples were conducted to investigate variations in compositions and carbon isotopes of shale gas.
3.2.1. Geochemical Measurements
Shale sample was first ground into 150 μm, and then divided into several portions to conduct different tests. TOC content was measured by a LECO CS230 carbon/sulfur instrument, with error below 0.5%. Before the experiment, the sample was dealt with HCl to reduce the influence of carbonate minerals, and then the HCl was washed with distilled water. The sample was compared to a standard value of the Chinese standard GB/T19145-2003 to compute TOC content [42, 43]. Mineral compositions were measured using a Bruker D8 advance X-ray diffractometer (XRD), operated using a Cu X-ray tube at 40 kV and 30 mA. Counts were collected from 3o to 90o with a step size of 0.02o and a speed of 3o/min. The prepared sample was placed on the test instrument, and the appropriate parameters were adjusted to obtain the mineral compositions by a semiquantitative method with XPower software . Due to the lack of vitrinite grain, solid bitumen reflectance (Rb) was determined by a MPV-SP microscope. Rb value would be converted into equivalent vitrinite reflectance (eqvRo) in terms of  (). Maceral compositions were performed on powdered kerogens, referred by coal petrology , using Polarizing fluorescence microscope, and the percent fraction of each component was determined according to the Chinese standard SY/T5125-1996.
3.2.2. Field Emission Scanning Electron Microscopy (FE-SEM)
A FEI Helios 650 Dual Beam Scanning Electron Microscopy was adopted to observe shale pore type, morphology, distribution, and connectivity. This instrument, with an accelerate voltage of 4 kv, can produce a series of images of shale pores with resolution of 0.8 nm. Prior to the test, shale blocks were burnished with fine grit sand paper and polished by an IM4000 argon ion beam milling, with an acceleration of 3 kv, to prepare a flat surface. An energy dispersive spectroscopy (EDS) microprobe was used to measure in situ elemental composition precisely, and it can help understand which factor controls nanometer-scale pore development.
3.2.3. Low Pressure Nitrogen/Carbon Dioxide Gas Adsorption (N2GA/CO2GA) Test
Low pressure N2GA and CO2GA measurements are common means to characterize shale pore size distribution, pore volume, and surface area [47–49]. These experiments were performed on a Micromeritics ASAP 2020 analyzer. Shale pores are divided into micropores (), mesopores (), and macropores (), in terms of the International Union of Pure and Applied Chemistry (IUPAC) scheme. Micropore is primarily measured by CO2GA analysis, and micro- to mesopore is determined by N2GA test. Prior to the tests, shale samples were ground into 150 μm, and then dried at 110°C to remove volatile materials and free moisture. N2GA test was conducted at a low temperature of 77.35 K with a relative pressure of 0.001–0.0995. The Brunauer-Emmett-Teller (BET) method was used to obtain specific surface area, and the Barrett-Johner-Halenda (BJH) method was adopted to obtain pore size distribution and pore volume, respectively. CO2GA experiment was conducted at 273.1 K with a relative pressure of 0.00001-0.032. Volume, surface area, and size distribution of micropores were obtained by the Density Function Theory (DFT) model, which is considered to gain a more reliable quantification of the pore structure information .
3.2.4. Mercury Injection Capillary Pressure (MICP) Analysis
MICP analysis was performed on small block samples with size of and weight of 10–20 g by a Micromertics Autopore IV 9510 apparatus. Hg pressure was increased continuously from 0.43 to 60, 000 psia in this experiment, and pores with sizes of 3 nm–350 μm were determined in terms of the Washburn equation in the case of cylindrical pores . The accuracy of the mercury intrusion volume was 0.1 ml. This method can obtain pores within meso- to macropore range, as well as porosity, from Hg intrusion data.
3.2.5. In Situ Gas Desorption Test
In situ desorption gas was quantified since the core shale was put into a desorption canister. During the process, the sample was placed as soon as possible into a hermetically sealed canister that was immersed in a water bath with temperature of 49–54°C (Figure 2). This temperature refers to mud circulation temperature. Natural gas would be released inside the canister, and was periodically tested by a graduated cylinder. However, natural gas cannot be completely released from cores at this stage. To accelerate shale gas release, a high temperature of 110°C, referring to reservoir temperature, was adopted. When gas volume is less than 2.5 ml/h, the in situ desorption process is considered to be finished. Generally, in situ desorption test would last 3–4 days and no more than a week. Released gas would be converted into a value under standard conditions (STP, 273.15 K and 101.325 kPa) . Gas obtained by in situ desorption measurement is divided into three parts: lost gas, desorbed gas, and residual gas. Desorbed gas refers to the measured gas during the desorption process. Lost gas is estimated in terms of initial desorbed data using the USBM method, as shown in Figure 3. Residual gas is very limited, and it is not detected in this study.
3.2.6. Chemical and Isotopic Analyses
5 selected samples were subjected to collect desorbed gas every 0.5 h interval at the exhaust port through drainage gas collection method. Desorbed gas was sealed within 250 ml salt bottle and then taken it back to the laboratory, with the purpose of measuring variations in compositions and carbon isotopes. Chemical compositions of desorbed gas were analyzed by an Agilent 7890A gas chromatograph. The gas chromatograph was first set at 30°C for 10 min, then raised to 180°C at a rate of 10°C/min, and finally maintained at this temperature for 20–30 min. All the gas compositions had been made oxygen-free correction . Carbon isotope was measured by a mass spectrometer (MS; Thermo Delta V Advantage). The initial temperature was set at 30°C, followed was raised to 80°C, and lastly was increased from 80°C to 250°C at a rate of 5°C/min and maintained for 10 min. The analytical precision was ±0.3%, and stable carbon isotope data were recorded in δ-notation (δ13C, ‰) relative to V-PDB standards.
4.1. Geochemistry Characteristics
Organic geochemical data, e.g., TOC content, eqvRo value, and kerogen type of the Wufeng-Longmaxi shales were plotted in Figure 4, and thin section and organic petrology photographs were displayed in Figure 5. TOC contents are in the range of 0.11–5.54%, averaged 1.99%, and they exhibit an increased trend with increased depth. Shales formed in deep-water shelf facies have higher TOC contents than those formed in shallow-water shelf facies. For shallow-water shelf facies, shales are primarily argillaceous shale lithofacies and siliceous argillaceous shale facies, primarily dominated by clay minerals, followed by quartz. Flocculated clay minerals are widely distributed in these shales and silt-sized quartz laminae are distributed among clay-rich laminas (Figures 5(a) and 5(b)). For deep-water shelf facies, shales are dominated by argillaceous siliceous shale facies and siliceous shale facies, among which pyrite aggregates, graptolite, and radiolarian are widely developed (Figures 5(c) and 5(d)). EqvRo value varies from 2.54% to 2.67%, suggesting that these shales have entered overmature stage. Kerogen maceral compositions of the Wufeng-Longmaxi shales are consisted mainly of planktonic algae, amorphous formed by benthic algae, and amorphous body (Figures 5(e)–5(h)). And therefore, the kerogen is oil-prone, and it is classified as type I-II1 kerogen .
Mineral compositions of the studied shales are listed in Table 1 and summarized in a ternary diagram of Figure 6. Quartz and clay mineral contents, in the range of 18–58% and 17–58%, averaged 35.11% and 47.28%, respectively, are dominated components. Quartz content shows an increased trend and clay mineral content has a decreased trend with increased depth. Feldspar and pyrite both have minor contents, with values of 1–7% and 1–14%, respectively. Carbonate content varies between 1% and 30%, averaged 7.78%. As shown in Figure 6(a), most samples are located within the quartz-feldspar-pyrite member, suggesting that the Wufeng-Longmaxi shales have a high brittleness index and are more easily to be fractured. Illite, chlorite, and I/S mixed layer are dominated clay minerals (Figure 6(b)). I/S mixed layer has the highest content, with value of 47–70% in clay minerals. Illite and chlorite have contents of 22–40% and 1–21%, respectively, and kaolinite content is quite low, only accounting for 1–4%.
The relationship of quartz content with TOC content can reflect depositional environment of organic-rich shales, due to that quartz is generally evolved from aquatic organism, e.g., radiolarian and sponge spicule, in strongly reductive environment . Quartz content exhibits a positive correlation with TOC content if quartz is biogenic origin; otherwise, it is negatively correlated with TOC in the case of quartz derived from terrigenous detrial origin . As seen in Figure 7(a), quartz content has a positive correlation with TOC content only when for the studied shales, indicating that quartz in organic-rich shales is mainly contributed by biogenic origin. On the contrary, quartz is primarily from terrigenous detrital input in organic-poor shales with . This is well consistent with previous studies for the Wufeng-Longmaxi shales in southern Sichuan Basin [56, 57]. Also, a negative relationship exists between clay mineral content and TOC content for shales with (Figure 7(b)), which confirms that clay minerals were dominated by terrigenous detrital inputs.
4.2. Pore Types
FE-SEM technique is an effective method to characterize pore structure in unconventional reservoir . FE-SEM observations show that OM pores, with shapes of ellipsoid and irregular polygon, are the dominated pore type in the studied shales (Figures 8(a)–8(c)). OM pore diameters span from several nanometers to hundreds of nanometers, similar to those in the Barnett shales [59, 60]. OM nanometer-scale pores are well-connected with coarse mesopores or macropores related to minerals, and therefore, they can store not only adsorbed gas but also free gas. Previous studies have demonstrated that OM porosity can account for more than 50% of total porosity in organic-rich shales . However, not all OM particles contain numerous pores, due to the differences in OM compositions. InterP pores with larger sizes generally occur between mineral grains, e.g., soft and rigid minerals (Figures 8(d) and 8(e)), which have better connectivity than OM pores. These interP pores, with no obvious preferential orientation, are scattered along brittle minerals. They are mainly residual pores suffered by compaction and cementation, and therefore, the number of these pores is not numerous. Pores with linear and flocculent shapes are developed within clay minerals (Figure 8(d)). Linear pores are formed due to the shrinkage of clay minerals after dehydration during diagenesis process, and flocculate pores are primarily developed within flocculent clay mineral aggregates. As seen in Figure 8(d), flocculent clay minerals have suffered strong compaction and pores are displayed better orientations. Flocculent clay minerals indicate that detrital materials had experienced a long-distance suspended deposition in marine environment. Unlike OM pores and interP pores, intraP pores exist primarily within mineral grains, e.g., pyrite framboids and unstable brittle minerals (Figures 8(f) and 8(g)). Pyrite framboids are composed of a great deal of pyrite crystals, among which, intraP pores are well developed. IntraP pores related to brittle minerals are mainly dissolved pores, due to that unstable minerals, e.g., carbonate and feldspar, were invaded by organic acids during hydrocarbon generation process. IntraP pores are generally poor-connected, resulting to limited contribution to shale gas accumulation. Microfractures, with several micrometer length and nanometer width, are well-developed in the studied shales, which can contribute partial shale porosity. Affected by compaction, microfractures display as zigzag shape (Figure 8(h)), due to late tectonic activity. A portion of mircofractures were cemented by secondary calcites. Partial microfractures like cleavage (Figure 8(i)), often filled by solid bitumen. Microfractures are generally well-connected OM pores and interP pores, and play an important role in shale gas storage and migration.
4.3. Low-Pressure CO2GA/N2GA Curves and Mercury Intrusion Curves
As discussed by , CO2 adsorption at 273.15 K can be used to characterize micropore volume and N2 adsorption at 77 K can be used to measure pore volume in the larger micropore to mesopore range.
CO2 adsorption curves (Figure 9(a)) are type I, indicative of micropore adsorption and reversible adsorption . All samples show similar shapes. Sample YY1-57 with the highest TOC exhibits by far the highest adsorption, and samples YY1-10 and YY 1-18 with the lowest TOC display limited adsorption. Overall, adsorbed CO2 volume in the samples increased with increased TOC values.
Low-pressure N2 adsorption/desorption curves together with their hysteretic patterns can be used to characterize pore shape and pore structure across from micro- to macropore range. The adsorption/desorption curves for the ten samples are shown in Figure 9(b). According to the IUPAC classification, all the samples exhibit H3 type hysteresis loop, suggesting that the process of capillary condensation and evaporation are within the mesopores and these mesopores are primarily slit-shaped pores. The sudden closure of the adsorption and desorption branches at a P/P0 of 0.45–0.50, referred to as the “Tensile Strength Effect” , which is attributed to the collapse of the hemispherical meniscus during capillary evaporation in pores with sizes of approximately 4 nm. Similar to low-pressure CO2 adsorption curves, quantity adsorbed volume of N2 increases with increased TOC content, suggesting that shales with higher TOC contain more nanometer pores.
Mercury intrusion was used to quantify the mesopore to macropore characteristics. The liquid pressure required to intrude into the pores is inversely proportional to the size of the pores . The mercury intrusion and extrusion curves of the ten Wufeng-Longmaxi shales are depicted in Figure 9(c). These samples have similar intrusion and extrusion features. The mercury intrusions have sharp increases when liquid pressures are less than 10 psia, suggesting that microfractures, possible beddings, are well developed in the studied shales. Different samples have different intrusions, which are probably related to TOC contents, as high TOC shales would results in more microfractures . However, with increased pressure, mercury intrusions are limited, suggesting that macropores are limited in these shales. Mercury extrusions from shales samples are very limited due to the limited intrusions at high pressures.
4.4. Pore Size Distribution
Different techniques can obtain different sizes of shale pores due to the limitations of their measured pore range, and comprehensive analyses of pore size distributions are very necessary. Pore size distributions of the Wufeng-Longmaxi shales determined jointly by low-pressure CO2GA, N2GA, and MICP methods are shown in Figure 9(d). Micropores with were obtained from low-pressure CO2GA experiment, and mesropores with diameters of 2–50 nm were determined by low-pressure N2GA test. Macropores (>50 nm) were provided by MICP data. As shown in Figure 9(d), the studied shales have similar pore size distributions, which are exhibited by multiple peaks with peaks at approximately 0.50 nm, 1.78 nm, 48.48 nm, and 145.35 μm. Pores within diameters of 60 nm–30 μm are poorly developed for all the studied samples. Pores with are primarily related to OM pores, and pores with diameters of approximately 145 nm are mainly microfractures. It follows that organic-rich Wufeng-Longmaxi shale is a dual porous rock composed of OM pores and microfractures, and mineral-related pores are not well developed. It should be noted that, pore size distribution is closely related to TOC content. Samples with high TOC contain more micropores and mesopores, suggesting that OM nanometer-sized pores are main contributor to total porosity in organic-rich shales. However, microfractures also have a certain relationship with TOC content, the higher TOC content, the more microcracks are developed. This is due to that shales with higher TOC contain higher quartz content and can result in more microfractures.
4.5. Pore Structure Parameters
10 selected samples were subjected to low-pressure N2GA, CO2GA, and MICP measurements, respectively, which can obtain different pore structure parameters. The pore structure parameters, including porosity, pore volume, and surface area, are shown in Table 2. Total porosity and macropore volume of 0.05–10 μm were determined by MICP test, which are in the range of 1.62–5.62% and 0.0004–0.0012 cm3/g, averaged 3.64% and 0.00072 cm3/g, respectively. BET surface area, volume, and surface area of mesopores were determined by low-pressure N2GA experiment. BET surface area varies from 9.43 to 41.98 m2/g, with mean value of 19.32 m2/g. Volume and surface area of mesopores are in the range of 0.0051–0.0126 cm3/g and 4.02–11.28 m2/g, respectively. Volume and surface area of micropores were measured by low-pressure CO2GA tests, which are in the range of 0.0032–0.0097 cm3/g and 7.95–26.36 m2/g, respectively. Overall, shale pore volume is mainly contributed by mesopores, followed by micropores. Macropores with diameters of 0.05–10 μm have the least contribution to total pore volume. This suggests that macropores, excluding microfractures, are poorly developed in organic-rich shales. Therefore, shale porosity is dominated by OM nanometer-sized pores rather than macropores. As a contrast, surface area is mainly contributed by micropores, followed by mesopores, implying that micropores are the main space for adsorbed gas accumulation.
4.6. In Situ Desorption Gas Content
In situ desorption measurement was performed on 60 samples with depth of 3772.2–3869.24 m from YY1 well. Desorbed gas, the direct measured gas, is the sum of gas released at mud circulation temperature (49–54°C) and reservoir temperature (110°C). Lost gas was determined using the USBM method, and residual gas was not detected in this study. Hence, the total gas content is the sum of desorbed gas and lost gas. Shale gas content, including total gas, desorbed gas, and lost gas, is plotted in Figure 10. Desorbed gas content ranges from 0.088 to 1.63 cm3/g. It is quite low for samples shallower than 3804.53 m in depth. However, desorbed gas content is generally higher than 0.5 cm3/g in samples with depth of 3805.77–3869.24 m, with a maximum value of 1.63 cm3/g at 3865.82 m, which is similar to the desorbed gas content (0.65 to 1.21 cm3/g) in Fuling shale gas field  and higher than that in X5 well in southeastern Chongqing . Lost gas content ranges from 0.15 to 3.64 cm3/g, which is higher than desorbed gas content. Lost gas accounts for 58.53% to 75.68% of total gas, suggesting that a large portion of shale gas had escaped before desorption test. This case indicates that porous shale reservoir is favorable for free gas storage, and free gas is the main proportion of shale gas. Total gas content is in the range of 0.23–5.20 cm3/g, higher than that in Changning shale gas field with content of 0.42–3.88 cm3/g . By contrast, total gas content is very low for shales formed in shallow-water shelf facies, and with increased depth, total gas content gradually increases for shales deposited in deep-water shelf facies.
5.1. The Influence of Desorption Time and Temperature on Desorption Process
Unlike coalbed methane, shale gas commonly reached a higher recovery in a shorter time . In this study, in situ desorption process was divided into two stages, as desorption at mud circulation temperature 49–54°C and at reservoir temperature 110°C, to reveal shale gas desorption characteristics. The first stage lasted for about 3.5–4 h and the second stage was generally finished within 8–10 h. The entire desorption process would be accomplished within 14 h. As shown in Figure 11, at the beginning of the first stage, the transient desorption rate is high, however, it declines rapidly with increased desorption time. At the second stage, the transient desorption rate starts to increase dramatically due to the enhanced temperature, and followed by a sharp decline due to shale gas depletion. Shale gas occurrence state during the two stages is different. At the first stage, desorption gas is rapidly released from shale cores, which is probably dominated by free gas. During this process, free gas can be rapidly released from macropores and microcracks, whereas sorbed gas is difficult to be liberated from shale cores. However, in the second phase, a sharp increase in transient desorption rate is due to that adsorbed gas is converted into free gas at a high temperature of 110°C. During this process, the rate of adsorbed gas converted into free gas is far slower than free gas escaped from shale core. And therefore, transient desorption rate exhibits a significant decrease with increased desorption time. It can be seen that desorption time and temperature are two main factors controlling shale gas desorption rate for a specific shale. In addition to the external factors, TOC content is the factor controlling shale gas desorption rate. Samples with higher TOC contents have higher transient desorption rates, implying that higher TOC contents can contain more nanometer-sized pores as well as higher free gas and adsorbed gas contents . Overall, shale gas desorption rate is comprehensively controlled by external factors, e.g., desorption temperature and time, and internal factors, e.g., TOC contents. It is worth suggesting that shale gas content is ultimately controlled by geological conditions and shale compositions.
5.2. Variations of Shale Gas Components during Desorption Process
5 selected shales were subjected to measure natural gas component variations during desorption process. As seen in Figure 12 and Table 3, desorbed gas is mainly consisted of CH4, with volume percentage of 41.11–97.05%, followed by a small amount of N2, CO2, and C2H6, with their volume percentages of 1.08–52.34%, 0.89–7.75%, and 0.05–1.27%, respectively. This is well consistent with the Wufeng-Longmaxi shales in adjacent areas in inner Sichuan Basin and in west Hubei, China [28, 68]. However, desorbed gas compositions have significant variations during desorption process. N2 has a high volume at initial stage and then decreases rapidly to a low volume at the end of the first stage, and has no obvious significant change at the second stage (Figure 12(a)), slightly higher than that in Changning and Fuling areas [69, 70]. CO2 displays a rapid decrease trend at the first stage, but has a slight increase at the second stage (Figure 12(b)), slightly different with the Shanxi Formation in Ordos Basin . CH4 exhibits an obvious increase trend at first 2 hours, and then shows a slighter decrease in the later stage (Figure 12(c)), suggesting CH4 still accounts for a large proportion of residue gas after desorption. Unlike CH4, C2H6 has a slow increase at the first stage, and exhibits a significant increase at the second stage (Figure 12(d)), implying that C2H6 occurs mainly in adsorbed state .
The reasons for the variations in desorbed gas components are significantly controlled by their adsorption capacities. Shale gas adsorption is an exothermic process, and the gas with a high supercritical temperature has a stronger sorption capacity . As shown in Figure 13, the order of adsorption capacity of shale to different gases is C2H6 ≈ CO2 > CH4 > N2 [72, 73], which results in the different gas composition in various stages of gas desorption. N2 in all samples is almost completely desorbed at the first stage, and hence, it has very low content at the second stage. This can be explained by the larger diffusion coefficient and low sorption capacity of N2 among N2, C2H6, CO2, and CH4 . During the desorption process, both C2H6 and CO2 increase at the second stage, due to that, more CO2 and C2H6 were released from adsorbed state. However, the increase of CO2 is not obviously compared with C2H6. C2H6 has greater adsorption force and shale adsorbs more energy at the second stage, resulting in more release of C2H6 . However, CH4 has slight changes after 2 h of desorption, because CH4 is more easily to escape from shale pore network at the first stage. Different gas components have different adsorption capacities, and they probably have synergistic changes with each other. C2H6 exhibits a negative correlation with N2 (Figure 14(a)), but has a positive correlation with CO2 when C2H6 content is higher than 0.2% (Figure 14(b)). This suggests that C2H6 content is not affected by the first stage of desorption, during which, desorbed gas is comprised mainly of free gas. As C2H6 content is higher than 0.2%, adsorbed gas contributes more to desorbed gas, and more C2H6 and CO2 were released from shale cores. This case further indicates that desorbed gas at first stage is dominated by free gas and at second stage is primarily contributed by adsorbed gas.
5.3. Variations in Carbon Isotope during Desorption Process
A number of researchers have found that there are significant carbon isotope fractionation effects in the process of adsorption-desorption and diffusion of shale gas . As reported, both δ13CH4 and δ13C2H6 became heavier during desorption process, but the increased degree was more significant for δ13CH4 [75, 76]. As shown in Figure 15 and Table 4, carbon isotopes of alkanes in desorbed gas have different features at different desorption stages. With increased desorption time, δ13CH4 and δ13C2H6 values both become heavier, with their values in the range of -37.7‰ to -16.5‰ (Figure 15(a)) and -38.9‰ to -34.8‰ (Figure 15(b)), respectively. δ13C2H6 becomes slightly heavier with a jagged shape throughout the entire desorption process, due to that, C2H6 exists primarily in adsorbed state and the desorption of C2H6 is still in the early stage. As a contrast, δ13CH4 value has significant changes from the first stage to the second stage. It tends to become slightly heavier at the first stage with desorption temperature of 49–54°C, and becomes significantly heavier at the second stage with desorption temperature of 110°C. δ13CH4 value is much heavier at the second stage, due to that, desorption of CH4 is in its late stage. Overall, δ13CH4 value has a significant increment, changing from 4.1‰ to 18.8‰, and δ13C2H6 value has a minor change with increment of 0.5‰ to 2.9‰. Therefore, we can conclude that δ13CH4 value changed more significantly than δ13C2H6 is mainly due to different desorption stages of CH4 and C2H6, i.e., C2H6 was possibly in its early desorption stage while CH4 was possibly in its later desorption stage . This is similar to the results that δ13CH4 had maximum positive variations of 5.41–25.93‰ and δ13C2H6 had maximum positive variations of 0.8–2.3‰ for Wufeng-Longmaxi Formation in Fuling shale gas fields in eastern Sichuan Basin and EFD1 well in west Hubei [28, 67]. Diffusion and adsorption/desorption are considered to be the main factors controlling carbon isotope fractionation during shale gas desorption process [67, 77]. The heavy isotopes have a larger molecular radius and a smaller diffusion coefficient than the light isotopes for alkanes, and therefore, the light isotopes generally have the priority of diffusion and transport. In terms of dynamics theory, 13C molecules released from shale cores need more energy than 12C. Therefore, 12C is more easily to release from shale core during desorption, and therefore, 13C molecules would increase with increased desorption time and temperature, resulting in that desorbed gas becomes heavier with proceeded desorption. Scholars have considered that the fractionation of carbon isotopes in shale gas was primarily controlled by adsorption, due to that, shale was characterized as low permeability and strong sorption capacity [77, 78]. During shale gas “adsorption-desorption-diffusion” process, heavy hydrocarbon and 13C alkane gas have preferential adsorption and delayed desorption orders. Alkane gas molecules with 12C are more easily escaped during the diffusion process, which gives rise to that shale gas in the early stage has a lighter isotope composition . Therefore, we could conclude that (1) at the first stage, CH4 has lighter δ13C value due to that methane exists mainly in free gas state, and (2) at the second stage, δ13C values of CH4 and C2H6 become heavier, due to that, desorbed gas is primarily contributed by adsorbed methane.
Carbon isotope reversal has become a hot topic in shale gas research due to gas wells with isotopic reversal trends to have high production in recent years . δ13CH4 and δ13C2H6 values of desorbed gas from the Wufeng-Longmaxi shale reservoir in YY1 well are plotted in Figure 16, and meanwhile, they are compared with typical marine shales, e.g., Barnett shale and Wufeng-Longmaxi shale in Changning, Jiaoshiba, and Weiyuan areas. Line AB means the relationship of . Low-mature Barnett shale-G1 is located above the line AB, which is characterized by . With increased thermal maturity, δ13CH4 becomes heavier and δ13C2H6 becomes lighter in high-mature Barnett shale-G2. However, highly mature shales of Wufeng-Longmaxi Formation are located below the line AB, suggesting . At initial stage, δ13CH4 in desorbed shale gas in YY1 well is similar to that in Weiyuan, Jiaoshiba, and Changning fields, and with increased desorption time, it becomes heavier. In Figure 16, the first turning point corresponds to the beginning of secondary cracking, comprised of primary and secondary cracking gas. The second turning point is a “postreversal” stage for high- to overmature shale gas. Isotope reversal in high- to overmature shale is based on differential rates of molecular and isotope fractionation due to variations in adsorption and diffusivity properties of molecules [39, 80]. As illustrated above, CH4 enriched in 12C are released from shales more readily than that enriched in 13C, and meanwhile, CH4 is more easily released from shales than C2H6 during desorption process. The residual CH4 becomes enriched in 13C more rapidly than residual C2H6, which leads to isotope reversal of alkanes in shales that experienced significant uplift and depressurization . Hence, carbon isotope reversal of shale gas in overmature shale reservoir is likely to be caused mainly by strong adsorption. Furthermore, carbon isotopic fractionation/reversal degree was regarded to correlate shale gas content, and was used to evaluate in situ gas content, adsorbed/free gas ratio, and predict production status of shale gas wells [28, 31, 67, 76, 82].
5.4. Shale Gas Content Relevant to Shale Compositions and Pore Structures
For marine shale gas reservoirs, TOC is considered to be the main factor of shale gas content . As shown in Figure 17(a), TOC content exhibits good relationships with the contents of desorbed gas, lost gas, and total gas, with correlation coefficients of 0.91, 0.86, and 0.90, respectively. This case indicates that OMs contain a great deal of nanometer-sized pores which accumulate not only adsorbed gas but also free gas, and therefore, the level of TOC determines shale gas content for the studied shale in this study, similar to other marine shale reservoirs around the world. In addition to TOC, brittle minerals, e.g., quartz and carbonate, are also favorable for shale gas accumulation. Quartz and carbonate both exhibits weakly positive correlations with shale gas content (Figures 17(b) and 17(c)). Quartz and carbonate rigid grains can resist strata pressure and protect OM pores from compaction, which effectively supports the development degree of OM pores during burial. And therefore, the increase of quartz and carbonate can provide more protected OM pores for adsorbed gas and free gas accumulation. Moreover, quartz/carbonate related pores, e.g., interP pores, dissolution pores, and microcracks can also contribute partial pore space for free gas storage. Overall, quartz and carbonate have directly and indirectly positive effect on shale gas storage. However, feldspar content is negatively correlated with shale gas content (Figure 17(d)); due to that, feldspar related pores are not well-developed and contribute limited to shale pore space. As illustrated above, pyrite framboids generally occur with OMs and form OM/pyrite complexes, in which, a great many of OM pores and intraP pores are developed. Pyrite framboids, an indicator mineral of anoxic environment, are favorable for OM preservation as well as OM pore development. Therefore, pyrite content shows a slightly positive correlation with shale gas content in Figure 17(e). Unlike brittle minerals, clay mineral content has negative relationships with desorbed gas, lost gas, and total gas (Figure 17(f)). The increase of clay minerals would dilute TOC content, and therefore, clay minerals inhibit the development of OM nanometer-sized pores as well as shale gas storage in the studied shales. Among clay minerals, illite and I/S mixed layer have slight inhibitions on shale gas content (Figures 17(g) and 17(i)), due to that illite and I/S mixed layer contain a certain amount of flocculated nanometer-sized pores. Chlorite content plays a significantly negative role on desorbed gas, lost gas, and total gas, with correlation coefficients of 0.75, 0.66, and 0.70, respectively (Figure 17(h)). This is due to that chlorite is characterized by large-sized lamellar pores, which can be easily compressed and is not favorable for adsorbed gas storage. Overall, clay mineral-related pores are easily to be compacted, resulting in the decrease of the effective pore space. Moreover, clay minerals are hydrophilic and can retain water molecules in internal pores and adsorbed on the surfaces, and the water molecules can form competitive adsorption with methane molecules in clay mineral pores, thus, it further reduce the storage capacity of shale gas.
Shale gas content and its occurrence state are closely related to pore structures, and investigation of shale pore structures and their controlling factors are essential. Previous studies have indicated that TOC is the decisive factor of shale pore development in marine shale reservoirs, e.g., the Marcellus , Horn River , Niutitang , and Longmaxi shales . In this study, there is a highly positive correlation between TOC content and micropore volume, with correlation coefficient of 0.75 (Figure 18(a)), implying that shale micropores are primarily contributed by OMs. Mesopore volume exhibits a moderate correlation with TOC content, with correlation coefficient of 0.31 (Figure 18(a)), suggesting that mesopores are partially contributed by OMs. However, there is no significant correlation between macropore volume and TOC content (Figure 18(a)), suggesting that OMs contribute limited to macropores. Overall, OMs provide primarily micropores, followed mesopores, which have been verified by FE-SEM images of Figure 8. FE-SEM observations show that OM pores are mainly located within several nanometers to several hundreds of nanometsers, concentrated in tens of nanometers. Both carbonate and pyrite contents have positive correlations with volumes of micropores and mesopores, but they exhibit no correlations with macropore volume (Figures 18(a) and 18(b)). This case indicates that carbonate and pyrite grains can enhance volumes of micro- to and mesopore, due to that, these minerals can protect OM micropores and mesopores rather than macropores. This is also the reason why carbonate and pyrite contents are positively correlated with shale gas content, especially desorbed gas content, in Figure 18(c). Predictably, clay mineral content, illite + chlorite content and I/S mixed layer content, all show negative correlations with micropore volume (Figures 18(d)–18(f)), implying that increased clay minerals dilutes TOC content and therefore reduces micropore volumes. However, volumes of mesopores and macropores have no obvious correlations with total clay mineral content, as well as contents of illite + chlorite and I/S mixed layer. It can be obtained that clay minerals have limited contribution to shale pore space, as well as gas content. The unfavorable effect of clay minerals on shale pore structure and gas content has been explained by many researchers, which is consistent with this study. And therefore, high content of clay minerals are not a favorable condition for shale gas exploration and exploitation for the Wufeng-Longmaxi shales.
Total porosity is a crucial factor that is used to evaluate free gas content under actual geological conditions , and it is necessary to investigate shale porosity. As shown in Figure 19(a), TOC exhibits a linear relationship with Hg-porosity, with correlation coefficient of 0.72, suggesting that OM pores are the main provider to shale porosity. This is consistent with , who concluded that OM porosity can account for 31.3%-70% of the total porosity in the Wufeng-Longmaxi shales. There are positive correlations of Hg-porosity with carbonate and pyrite contents (Figures 19(b) and 19(c)), which also suggests that carbonate and pyrite grains can enhance shale porosity via protecting OM pores and providing intraP pores and dissolution pores. Similar to pore volume, Hg-porosity is negatively correlated with contents of total clay mineral, illite + chlorite, and I/S mixed layer, with correlation coefficients of 0.29, 0.29, and 0.18, respectively (Figures 19(d)–19(f)). The influences of clay minerals on shale porosity still remain controversial. Previous studies considered that clay minerals exhibited positive correlations of clay mineral content with pore structures for the Niutitang shales and the Longmaxi shales in southern Sichuan Basin [88, 89]. However, some researchers thought that clay minerals are more easily to be compacted and as well as adsorbed in water, which result in the reduction of clay mineral pores in shale. FE-SEM images in Figure 8 show few pores developed in clay minerals, probably due to that, pores related to clay minerals substantially compacted by compaction or due to clay mineral transformation . Different kinds of clay minerals, with different crystal structures, play different roles in shale pore evolution . Hence, the specific compositions of clay minerals should be taken into consideration. I/S mixed-layer and smectite are interstratified and possess larger surface areas , which are more easily occupied by water molecules . Illite and chlorite contain few micropores and contribute limited to shale porosity. For the studied shales, clay minerals are dominated by illite, chlorite, and I/S mixed layer. Based on this situation, clay minerals have limited contribution to the effective porosity.
Pores with different sizes have different roles on shale gas accumulation and occurrence state. As shown in Figure 20(a), desorbed gas, lost gas, and total gas have positive correlations with micropore volume, with correlation coefficients of 0.65, 0.62, and 0.63, respectively. This suggests that micropores primarily accumulate shale gas storage, including most adsorbed gas and partial free gas. Mesopore volume displays weak correlations with desorbed gas, lost gas, and total gas, with correlation coefficients of 0.37, 0.22, and 0.26, respectively (Figure 20(b)), implying that mesopores are also the main space for shale gas accumulation but are not saturated by free gas. As a contrast, macropore volume is not relevant with shale gas content (Figure 20(c)), indicating that macropores are not primary space for shale gas storage. Porosity is primarily contributed by OM pores, and it is also positively correlated with shale gas content (Figure 20(d)). Overall, shale gas is mainly stored in OM micropores and mesopores, and macropores related to minerals are not saturated by shale gas. Previous studies pointed out that shale gas is primarily adsorbed gas in small pores, and pores larger than 50 nm contribute limited to shale gas content in Shuijingtuo Formation . Therefore, we could conclude that macropores are not favorable for free gas storage, because free gas is more easily to be escaped during burial process.
Water content is another factor that controls shale gas content, especially free gas. Hydrophilic pores tend to adsorb water molecules, and then reduce shale porosity and gas capacity to some extent . However, which factor controls water content in shale reservoir is still in dispute. Water content is regarded to be determined by TOC content , due to that, water molecules are primarily attracted to OM functional groups even OM nanometer pore surfaces. This case implies that kerogen probably contains a certain number of hydrophilic pores. Researchers pointed out that kerogen is hydrophobic at high maturity stage, neutral wettability at moderate maturity stage, and hydrophilic at a low maturity stage [96, 97]. However, more and more scholars considered that water molecules are primarily adsorbed on pore surfaces of clay minerals rather than OMs. Ross and Bustin  considered that hydrophilic nature of clay minerals determines water content, and it can significantly reduce shale gas content. As shown in Figure 21(a), water saturation exhibits a negative correlation with TOC content. High TOC and OM porosity with hydrophobic property, are not favorable for water molecules existence at high- to overmature stage. A positive correlation is exhibited by water saturation and clay mineral content (Figure 21(b)), because clay minerals can adsorb water through inner- and outerlayers . Therefore, water molecules are more easily to sorb by specific hydrophilic sites related to clay minerals rather than hydrophobic pores related to OMs. Since shale porosity is primarily contributed by OM-hosted pores, porosity has a negative relationship with water saturation (Figure 21(c)). Water saturation can also affect shale gas content via reducing shale pore space. As shown in Figure 21(d), desorbed gas, lost gas, and total gas show negative correlations with water saturation, with correlation coefficients of 0.78, 0.75, and 0.77, respectively. To sum up, TOC is the decisive factor of shale gas content, including adsorbed gas and free gas, and the increase of clay minerals and water saturation can significantly reduce shale gas content.
5.5. Comparisons of Reservoir Quality with Marine Shale Gas Reservoir in North America and Sichuan Basin
With the success of shale gas production in North America, shale gas development in the Sichuan Basin is flourishing as never before. As displayed in Table 5, shale gas production of the Marcellus Formation in Appalachian Basin and of the Haynesville Formation in Louisianan salt Basin are of and , respectively, in 2020, due to abundant drilling wells, which are far higher than that of the Sichuan Basin in China . To get clear, the features and prospects of shale gas reservoir in the Sichuan Basin are of vital importance. In the Sichuan Basin, shale gas production is mainly from Wufeng-Longmaxi Formations, which are mainly distributed in the Fuling, Changning, and Weiyuan areas, with their productions are , , and , respectively, in 2020. Other areas, e.g., Taiyang and Luzhou, have minor production due to late development and limited drilling wells. Presently, there is no accurate data of shale gas production in Yongchuan area.
Comparisons of reservoir qualities and controlling factors were conducted on shales from Yongchuan area with other marine shale reservoirs, to elaborate its shale gas potential and prospect. Exploration practices have proved that high TOC content, moderate maturity, and favorable kerogen type are decisive factors of shale gas generation and accumulation. The TOC content of the studied shales in YY1 well is high, slightly less than that in Changning, Weiyuan, and Fuling areas. Other parameters, e.g., kerogen type and thermal maturity, are similar to those in shale gas fields. Total gas content of YY1 well is higher than that of Taiyang area, but is slightly lower than that in Fuling, Weiyuan, and Changning areas. Overall, Yangchuan area is a promised target for Wufeng-Longmaxi shale gas exploration. Permeability and brittle mineral content in the studied shales are higher than those in North America, and therefore, shale gas reservoirs in Yongchuan area can be easily fractured and shale gas are easily liberated during explotation. Overall, the discrepancies are small between shale gas reservoir and other reservoirs in the Sichuan Basin. And therefore, it is considered to be an important target for shale gas exploration, in terms of accumulation condition, gas-bearing capacity, and flow capacity. Further work should be concerned on shale gas recovery evaluation by seepage simulation and actual mining work.
In this study, variations in content, composition, and carbon isotope of Wufeng-Longmaxi Formation shale gas in eastern Sichuan Basin were investigated, and the relationship to pore structures and shale compositions were also discussed. Preliminary conclusions are as follows:
During desorption gas process, transient desorption gas rate is controlled by both desorption temperature and desorption time. At the initial periods of the first stage and second stage, transient desorption gas rate is high, and with increased desorption time, it decreases rapidly. With elevated temperature, more shale gas can accelerate desorption from core samples
Desorbed gas from in situ desorption measurement contains both hydrocarbon gases and nonhydrocarbon gases, primarily dominated by CH4, followed N2, CO2, and C2H6. Based on the variation trends of gas components in the process of desorption, CH4 showed a rapid increase at initial stage, and then remains stable. C2H6 and CO2 were significantly increased with increased desorption time, whereas, N2 volume were displayed an adverse trend. It can thus be seen that the orders of adsorption capacities of different components are to be C2H6 ≈ CO2 > CH4 > N2
The carbon isotopes of shale gas became heavier during desorption. In detail, δ13C value of CH4 becomes noticeably heavier, increased by 4.1‰ to 18.8‰, and that of C2H6 increased by a small range. Variations of δ13C2H6 with δ13CH4 also showed a reversal at high- to overmature stage. The carbon isotope fractionation during desorption process is mainly influenced by diffusion and adsorption/desorption behaviors. Compared to CH4, C2H6 was preferred to be adsorbed and delayed to be desorbed, resulting in that, more obviously, the carbon isotope of C2H6 in desorbed gas would become lighter at the same time of a desorption process
Desorbed gas content obtained by in situ desorption measurement ranges from 0.088 to 1.63 cm3/g, and lost gas determined by the USBM method varies from 0.15 to 3.64 cm3/g, respectively. Total gas includes desorbed gas and lost gas, with contents of 0.23–5.20 cm3/g. Shale gas content is primarily determined by TOC content and OM-hosted porosity. Clay mineral content and water saturation are adverse factor for shale gas accumulation, due to that, clay mineral pores are more easily compacted during burial and also occupied by water molecules
By comparing with other marine shale reservoirs in North America and Sichuan Basin, the Wufeng-Longmaxi shales have good gas generation capacity, physical property, gas content, and fractured ability, and are similar to shale reservoirs in Changning-Weiyuan region. And therefore, it has great good prospects for shale gas exploration and exploitation
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Conflicts of Interest
There are no conflicts of interest with respect to the results of this paper.
This study was supported by the National Natural Science Foundation of China (Grant Nos. 41802163 and 42002136), Hunan Provincial Natural Science Foundation of China (Grant Nos. 2021JJ30240 and 2020JJ4020), and Scientific Research Project of Hunan Education Department (21B0448).