Diamondoids and thiadiamondoids generated from hydrothermal pyrolysis of crude oil and TSR experiments

Diamondoid compounds are widely used to reflect thermal maturation of high mature source rocks or oils and oil cracking extents. However, diamondoids and thiadiamondoids were demonstrated to have newly been generated and decomposed in our hydrothermal pyrolysis of crude oil and TSR experiments. Our results show that adamantanes and diamantanes are generated primarily within the maturity range 0.48–2.1% and 1.2–3.0% EasyRo, respectively. Their formation is enhanced and the decomposition of diamantanes obviously lags at elevated temperatures compared with anhydrous experiments. MDI, EAI, DMAI-1, DMDI-2 may serve as reliable maturity proxies at > ca.1.0% EasyRo, and other isomerization indices (TMAI-1, TMAI-2 and DMAI-2) are effective for the highly mature organic matter at EasyRo > 2.0%. The extent of oil cracking (EOC) calculated from the broadly used (3- + 4-) MD method (Dahl et al. in Nature 399:54–56, 1999) is proven to overestimate, especially for highly cracked samples due to the new generation of (3- + 4-) MD. Still, it can be corrected using a new formula at < 3.0% EasyRo. Other diamondoid-related indices (e.g., EAI, DMDI-2, As/Ds, MAs/MDs, DMAs/DMDs, and DMAs/MDs) can also be used to estimate EOC. However, these indices cannot be applied to TSR-altered petroleum. TSR is experimentally confirmed to generate diamantanes and thiaadmantanes at 1.81% EasyRo likely via direct reactions of reduced S species with hydrocarbons and accelerate the decomposition of diamantanes at > 2.62% EasyRo compared with thermal chemical alteration (TCA). More studies are needed to assess specific mechanisms for the formation of thiadiamondoids under natural conditions.

On the other hand, diamondoid has been proposed to create by thermochemical sulfate reduction 25 (TSR), a process whereby aqueous sulfate and petroleum compounds react at high temperatures (≥ 120 °C) to result in elevated H 2 S concentrations in many carbonate reservoirs [26][27][28][29] . This is based on the evidence that TSR-altered oils and condensates in the Cambrian and Ordovician in the Tarim basin and Smackover Formation in the US Gulf Coast have much higher concentrations of diamondoids than non-or minor TSR-altered oils which experienced higher heating. The diamondoid isomerization ratios are used to assess the thermal maturity of crude oils and source rocks 30-32 based on the more stable thermodynamic properties of bridge carbon substitution in isomers 4,10,33 9,10,13,16,30,32,34 . However, the maturity scopes for the application of each index are still controversial. Also, the isomerization of diamondoids is proposed to enhance due to TSR. As a result, diamondoid-based proxies cannot be used to reflect maturity and lithology in the TSR active areas 25 . However, these proposals have not been confirmed from simulation experiments and the mechanisms for the generation of diamondoids from TSR remain confused.
Thiadiamondoids are diamond-like compounds with a sulfide bond located within the cage structure. Hanin et al. 35 found that alkylated 2-thiaadamantanes were present only in TSR-altered oils and thus proposed that alkylated 2-thiaadamantanes might have been formed by acid-catalyzed rearrangement of tricyclic sulfide. Wei et al. 36 showed a linear correlation between the concentrations of thiadiamondoids and diamondoids in support of their diamondoids origin. Some laboratory experiments were carried out to address the origins of the thiadiamondoids. There may be at least two distinct mechanisms for the formation of thiadiamondoids, one under relatively low temperatures and the other at high temperatures. Wei et al. 37 found that trace amounts of dimethyl-2-thiaadamantanes were produced by montmorillonite K10-catalyzed rearrangement of thiocholesterol at 200 °C. Such an origin of dimethyl-2-thiaadamantanes may have occurred in extractable organic matter or been bound in kerogen of source rocks during early diagenesis. Thiadiamondoids are also shown to form from reactions between diamondoids or diamondoidthiols and sulfate or sulfur species at ≥ 350°C 37,38 . However, no detectable thiadiamondoids were generated from the experiments of a diamondoid-enriched condensate with CaSO 4 or S 0 at 360 °C for 20 h or 40h 38 , suggesting that no thiadiamondoids have been generated under a lab condition similar to natural geologic environments.
In the present study, hydrothermal pyrolysis and TSR experiments were carried out under the same experimental conditions as those of anhydrous pyrolysis of Fang et al. 13 . The objectives of this study are to: (1) clarify the effect of water on yields of diamondoids; (2) ascertain whether TSR will lead to the new generation of diamondoids and thiadiamondoids; (3) calibrate the reliable EasyRo maturity range of isomerization-related diamondoid proxies; (4) develop diamondoid-related indices to reflect oil cracking extents (EOCs). This study will have a broad application in petroleum evaluation and thus exploration.
To eliminate the effect of original diamondoids on the quantification of the diamondoid generated during oil cracking, both HD23 oil and ZS1-L oil were evaporated in a fume hood for 120 h before the pyrolysis experiment to remove the original adamantanes according to the method described by Fang et al. 13 . GC-MS-MS and GC-MS showed that no adamantanes and thiaadmantanes have remained in the evaporated oil. That means both thiaadmantanes and admantanes had been volatilized before experiments. Inorganic reagents, including MgSO 4 with δ 34 S of + 3.75‰, elemental S with δ 34 S of − 6.3‰, CaSO 4 ·2H 2 O with δ 34 S of + 21.3‰, sodium chloride (NaCl) and magnesium chloride (MgCl 2 ), were purchased from Sigma-Aldrich (St. Louis, MO) and are analytical grade (> 99.9% purity). www.nature.com/scientificreports/ separation of thiadiamondoids needs to recover sufficient pyrolysates (pyrolysis products). Hence, gold tubes were used for hydrothermal experiments and quartz tubes were used for TSR experiments. The thermal maturation of samples was calculated using the Easy%Ro approach developed by Sweeney and Burnham 39 . The pyrolysates were collected and analyzed using GC-MS and GC-MS-MS.

Confined pyrolysis experiments.
Quartz tube pyrolysis experiments. 110 mm-long quartz tubes with 20 mm internal diameter, 1 mm thick wall, giving a total reactor volume of approximately 25 mL, were used for the TSR Experiments. Before loading the tubes, each tube was cleaned using distilled milli-Q water and heated to 450 °C. The solid or liquid reactants were accurately loaded or injected into tubes by a small funnel with an outside diameter slightly smaller than the inner diameter of the quartz tubes. After that, the other end of the tubes was sealed under vacuum conditions. Finally, the tubes with samples loaded were put into autoclaves and desired temperature programs were carried out. After the desired temperature or time was reached, each autoclave was quenched to room temperature before being opened. We used the Mg 2+ -talc-silica system as a mineral buffer at elevated temperatures to keep the in-situ pH in a narrow range (pH ~ 3) 40 . Thus, each quartz tube was loaded with 30 mg talc, 30 mg silica, 100 mL distilled milli-Q water solution with 5.6 wt.% MgCl 2 , 10 wt.% NaCl and 0.56 wt.% MgSO 4 . The approach used to regulate in situ chemical conditions for our study relies on chemical reactions known to proceed rapidly at the temperature and pressure conditions of the experiments 41,42 . More details related to the mineral buffer approach are given by Zhang et al. 40,43 . Subsequently, 100 mg of ZS1-L oil sample, 25 mg elemental S and 100 mg MgSO 4 were accurately weighed and transferred to the tubes by a small funnel with an outside diameter slightly smaller than the inner diameter of the quartz tubes (Group 1). Blank experiments (TCA experiments) with 100 mg of ZS1-L oil sample and 100 mL solution (5.6 wt.% MgCl 2 , 10 wt.% NaCl) were performed in parallel. After being sealed under vacuum conditions, the quartz tubes were placed in stainless steel autoclaves and heated from 336 °C to 600 °C at constant heating rates (20 °C /h). The error of the recorded temperatures is < ± 1 °C. When the desired temperature or time was reached, each autoclave was quenched to room temperature before being opened.
After pyrolysis, the tubes were placed in a vacuum glass system connected to the GC inlet and then pulled out. After cracking the quartz tube, gaseous hydrocarbons were released and introduced into the GC system. Part of the gas collected at each temperature was bubbled through a basic 5% AgNO 3 solution to convert H 2 S to Ag 2 S for isotopic analysis, as discussed in Sect. 2.4. The individual gaseous hydrocarbons were quantified using an Agilent Technologies 6890 N gas chromatograph and the pyrolysates (pyrolysis products) were recovered by repeated sonication with dichloromethane. The organic fraction then LC separated to saturate, aromatic and sulfidic fractions using silver nitrate impregnated silica gel column as described below.
Gold tube pyrolysis experiments. Oil pyrolysis in hydrothermal conditions was conducted in sealed gold tubes with an internal diameter of 5 mm and wall thickness of 0.5 mm after the method of Fang et al. 13 . Each tube was between 40 and 50 mm long, giving a total reactor volume of approximately 0.5 mL. One end of each tube was crimped and sealed using an argon arc welder. Before loading the samples, the open-ended tubes were heated to 600 ℃ to remove any residual organic material. Then, specific amounts of samples (i.e., oil and water with the weight ratio of 1:1) were loaded into the gold tubes, which were subsequently flushed with argon for 5 min and sealed under an argon atmosphere. Individual sealed gold tubes were later placed in separate stainless-steel autoclaves and inserted into a pyrolysis oven. The ovens were heated from 336 to 600 ℃ at two constant rates of 20 °C/h and 2 °C/h, respectively, under the constant pressure of 50 MPa. After reaching desired reaction temperature and the pressure was released, the tubes were taken out from autoclaves.
Two parallel gold tubes were positioned in each autoclave to quantify diamondoid hydrocarbons and the extent of oil cracking (EOC) in pyrolysates. To remove any potential organic contaminants from the exterior of the gold tubes, they were cleaned in dichloromethane and allowed to air dry. Tubes were cooled for 25-30 min using liquid nitrogen following this cleaning procedure. Upon removing the liquid nitrogen, the first cleaned gold tube for diamondoid analysis was rapidly cut in half and placed in a 4 ml sample vial filled with isooctane to minimize loss of volatile components. The parallel gold tube for EOC analysis was first cut off welded ends and then rapidly cut into four equal pieces. The four tube pieces were quickly placed into a 10 ml sample vial filled with dichloromethane and allowed to soak overnight (12-20 h). The vials containing the gold tube pieces were then sonicated repeatedly to recover the pyrolysates. The vials were then opened for a minimal amount of time to remove the pieces of gold tubing and their transfer to 4 mL sample vial containing dichloromethane. Asphaltenes were then precipitated from the products by adding 50-fold (volume ratio for n-hexane/bitumen) cold n-hexane and removed by centrifugation. Then the absolute amount of liquid hydrocarbon was weighed on residual liquid hydrocarbons.
TSR control-experiments. Although anhydrite appears to be the reactive oxidant and is replaced by calcite and dolomite in natural TSR reservoirs [26][27][28][44][45][46][47][48] , it is generally not used in laboratory TSR studies due to its low solubility 17,[49][50][51] . Magnesium (Mg 2+ ) is always present in natural TSR reservoirs and may play a catalytic role in natural TSR processes. To ensure that the sulfate will be involved in TSR experiments, rather than just elemental S, another group of TSR control-experiments using elemental S and CaSO 4 ·2H 2 O was conducted (Group 2). Therefore, there are two sulfates with large different sulfur isotope values (MgSO 4  standards isooctane with n-dodecane-d 26 and n-hexadecane-d 34 were injected into the sample vial. The vial was ultrasonically treated for 10 min to improve the dissolution of pyrolysates. Leaving the vial for 12 h to precipitate asphaltenes, a volume of the supernatant was transferred into a 2 ml auto-sampler vial for GC-MS-MS. The identification and measurement of diamondoids using the GC-MS-MS method was described in detail elsewhere 52 . The liquid chromatographic (LC) separation of thiadiamondoids was done according to the method of Wei et al. 36 : LC on silver nitrate-impregnated silica gel was used to fractionate samples into saturate, aromatic, and sulfidic fractions by sequential elution using hexane, dichloromethane, and acetone, respectively. Care was taken to avoid drying the sulfidic fractions during evaporation and concentration to smaller volumes down to 50-150 μl and analyzed for thiaadamantanes using GC-MS method as detailed in Cai et al. 25 .
Sulfur isotope analysis. For analysis of δ 34 S of the H 2 S (converted to Ag 2 S) was conducted at the Institute of Geology and Geophysics, Chinese Academy of Sciences. The dried Ag 2 S and Cu 2 O were generally mixed in a proportion of 1:10 and then combusted at 1100 °C under vacuum to produce SO 2 . The resulting SO 2 was sealed within pyrex tubing and analyzed on a Thermo Delta S mass spectrometer. Sulfur isotope values are expressed as per mil (‰) deviations from the sulfur isotope composition of the Vienna Canyon Diablo Troilite (VCDT) using the conventional delta (δ 34 S) notation. Isotopic results were generally reproducible within ± 0.3‰.

Results
The yield of the individual diamondoid compounds is used to characterize the variation in the absolute amount of diamondoids during the experiments and expresses as the mass of diamondoids generated at each temperature point relative to the initial weight of the oil in each gold tube or quartz tube, according to where Y i is the yield of the particular diamondoids (e.g., an individual diamondoid compound, a group of compounds, or the total diamondoids); M i is the mass (µg) of the relevant diamondoids; M 0 is the initial mass (g) of the diamondoid-generating substance (original oil mass loaded in the tube).
In this study, 32 diamondoid compounds, including 22 adamantanes and 10 diamantanes were identified by GC-MS-MS, and their concentrations were quantified as in Table 1. Meanwhile, several homologous series of alkylated 2-thiaadamantanes were identified by GC-MS, the tentative peak assignments of alkylated 2-thiaadamantanes were given in Fig. 1.
As for individual compounds, the amounts of generated Adamantane (A), Methyladamantane (MA), Ethyladamantane (EA), Dimethyladamantane (DMA) and Trimethyladamantane (TMA) are shown to increase with EasyRo in the range of 0.48-2.1% and rapid decrease in the EasyRo range 2.1-2.5%. The yields of Tetramethyladamantane (TeMA) increase in the EasyRo range 0.48-2.5% and a reversal occurs above the 2.5% EasyRo ( Fig. 3 and Supplementary Table S1). Similarly, the yields of different types of diamantanes keep nearly constant in the oil samples from experiments at EasyRo < 1.5% (Fig. 3c,f,i). Subsequently, the yields of Methyldiamantane (MD), Dimethyldiamantane (DMD) and Trimethyldiamantane (TMD) increase in the EasyRo range 1.5-3.0% and a reversal occur above the 3.0% EasyRo (Fig. 3). In addition, adamantanes generated during oil cracking are dominated by DMA, followed by TMA, MA, TMA, EA and A, while diamantanes are dominated by MD, DMD, TMD and Diamantane (D).
TSR experiments with ZS1-L oil. H 2 S and sulfur isotope data. The yields of hydrogen sulfide (H 2 S) generated in hydrothermal experiments with MgSO 4 apparently are higher than those with CaSO 4 ·2H 2 O (Table 2). For group1, the H 2 S yields increases from 9.57 mmol/g at EasyRo of 0.57 to 17.43 mmol/g at EasyRo of 2.5%, and then decreases slightly to 14.62 mmol/g at EasyRo of 3.87% (Table 2). For group 2, the H 2 S yields rise from 8.92 mmol/g to 11.47 mmol/g at EasyRo = 1.13-1.69% (Table 2). Moreover, the evolution trends for δ 34 S H2S in two groups of experiments are totally different (Table 2 and Fig. 4). The δ 34 S values of group 1 H 2 S range from − 5.00‰ to − 2.45‰ with EasyRo from 0.57% to 3.87% and show a positive correlation with EasyRo ( Table 2).In contrast, the δ 34 S of H 2 S generated in group 2 ranged from − 5.79‰ to − 6.79‰, within ± 1‰ of elemental S (− 6.3‰) ( Table 2 and Fig. 4).
Diamondoids and thiadiamondoids data. For the yields of diamondoids, only diamantanes from the TSR experiments in group 1 are discussed in this study. See "Hydrothermal experiments of HD23 oil" section for details. Adamantanes were evaporatively lost during sample working up, the collected samples show elevated diamantanes yields, and thus only results of diamantanes are listed ( Table 3). The yields of total diamantanes and (3-+ 4-) MD progressively rises from 129.58 µg/g and 49.11 µg/g before the heating to a maximum of 249.15 µg/g and 79.45 µg/g at EasyRo 1.81%, respectively (Fig. 5d,e). At EasyRo > 1.81%, both (3-+ 4-) MD and (1) www.nature.com/scientificreports/ diamantanes show a decrease. Diamantanes generated during TSR are dominated by MD, followed by DMD, TMD and D (Fig. 5a-c). Interestingly, thiadiamondoids including thiaadmantane and methyl thiaadmantanes isomers were detected from the oil after TSR pyrolysis in the 480 °C experiments (1.81% EasyRo) with the maximum yield of diamantanes (Fig. 1).
In the non-TSR or TCA experiments (blank experiments), the maximum yields of total diamantanes and (3-+ 4-) MD were 184.95 µg/g and 67.88 µg/g, which are significantly lower than those from TSR experiments, respectively (Fig. 5d,e). In addition, an obvious lag in reversals (2.62% EasyRo) occurred for non-TSR experiments compared to TSR (1.81% EasyRo). Similar to the TSR experiments, diamantanes generated during TCA are dominated by MD, followed by DMD, TMD and D (Fig. 5a-c).

Discussion
Formation and decomposition of diamondoids during hydrothermal pyrolysis of an HD23 oil. Hydrothermal pyrolysis of the HD23 oil shows that both adamantanes and diamantanes were newly generated and decomposed. Still, their yield curves are partially different from the anhydrous 13 : First, diamondoids were generated in a broader range of EasyRo with higher yields at < 1.7% EasyRo during the hydrothermal experiments than the anhydrous (Fig. 6), indicating that water promoted the yields of diamondoids at low EasyRo (< ~ 2.0%). With increasing EasyRo, the differences in the yields of diamondoids between the two became smaller. Among diamondoids, adamantanes show an increase in their yields from 0.48% to 2.1% EasyRo (Fig. 6a), and the range is wider than the range of 1.0-2.1% for the anhydrous experiments. Similarly, diamantanes began to be generated at 0.79% EasyRo from hydrothermal pyrolysis experiments, much lower than 1.7% EasyRo for the anhydrous pyrolysis experiments (Fig. 6b). Second, the decomposition of diamantanes      www.nature.com/scientificreports/ Larger yields of diamondoids from hydrothermal pyrolysis than the anhydrous (Fig. 6) can be explained as follow. As the result of ionic reactions, hydrothermal pyrolysis of organic matter generates more considerable amounts of intermediate olefinic and isomeric hydrocarbons than the anhydrous pyrolysis 53 . In turn, the olefins and isomeric hydrocarbons will be hydrogenated by rapid free radical reactions, raising the yields of diamondoids during hydrothermal pyrolysis. That is, combining ionic and free radical reactions can accelerate isomerization and cyclization of these olefinic hydrocarbons to generate the relatively high yields of diamondoids under hydrothermal pyrolysis.
It is necessary to discuss which one, hydrothermal or anhydrous pyrolysis, has the products representing maturation of natural samples, considering the more significant differences in EasyRo for decomposition of diamantanes and yields of diamondoids between the two. The EasyRo for the generation and decomposition of the (3-+ 4-) MD in this study are close to that of natural samples from both coals and rocks, that is, ca. 1.2% EasyRo vs 1.1% Ro for the generation and 3.0% EasyRo vs ca. 4.0% Ro for the decomposition 7 . In contrast, EasyRo obtained from anhydrous pyrolysis are deviated more from the natural samples, 1.5% for the generation and 2.5% for the decomposition 13,54,55 . Ro values are approximately equal to the calculated EasyRo values at EasyRo < 1.5 ~ 2.0%. The differences between Ro and calculated EasyRo are slightly more significant at EasyRo > 1.5 ~ 2.0%, likely due to the change in the chemical composition of solid kerogen with higher maturity levels 56 . This result suggests that hydrothermal pyrolysis has the products closer to the cracking of natural samples, which is supported by the gas produced from the hydrothermal pyrolysis more similar to the natural gas than anhydrous pyrolysis 23 . Moreover, water is ubiquitous in petroleum reservoirs and may provide H and O involved in petroleum generation and evolution 42,57 , suggesting hydrothermal pyrolysis may represent the maturation of natural samples better than the anhydrous. Diamondoids as proxies for thermal maturity. It is widely accepted those isomerization ratios such as MAI. MDI, EAI, DMAI-1, TMAI-1, TMAI-2, DMDI-1 and DMDI-2 can be used to determine the thermal maturity of highly mature crude oils (Ro > 1.1%) 9,10,30,32,34 , and they can be applied for different maturity ranges 16 . Isomerization-related diamondoid ratios are unaffected by thermal maturity levels with EasyRo < 2.0% in anhydrous pyrolysates and used as proxies of thermal maturity at > 2.0% EasyRo 16 . In this study, MDI, EAI, DMAI-1 and DMDI-2 can be applied to reflect maturity at much lower EasyRo from hydrothermal pyrolysis: 1.47-3.5% EasyRo for MDI with R 2 of 0.8717 (Fig. 7b), 0.86-2.5% EasyRo for EAI with R 2 of 0.8412 (Fig. 7c), 1.08-3.5% EasyRo for DMAI-1 with R 2 of 0.8502 (Fig. 7e) and 1.08-3.5% EasyRo for DMDI-2 with R 2 of 0.9304 (Fig. 7d). This supports that MDI is an effective proxy of maturity at > 1.3% Ro for either source rock extracts 9 or hydro-   13 , MAI in this study seems not related to EasyRo (Fig. 7a), and thus cannot be used as a proxy to assess the thermal maturity of oils. MDI, EAI, DMAI-1, DMDI-2 can serve as reliable maturity indicators with broad EasyRo ranges mainly > 1.0%. In contrast, at EasyRo < 1.0%, diamondoid-related proxies including MDI, EAI, DMAI-1, DMDI-2 show no correlations with EasyRo, suggesting that they cannot be used to determine the maturity of oils and thus source rocks. The previous observation supports this proposal that diamondoid concentrations and distributions are dependent on the source rocks instead of maturity within the oil window 58 . Other isomerization ratios (e.g., DMAI-2, TMAI-2 and TMAI-1) show good correlations with thermal maturity in the higher EasyRo ranges of 2.08-3.5% with R 2 of 0.9617, 0.9752 and 0.8581 (Fig. 7g-i). These ratios seem controlled by the parent organic matter during the generation stage of diamondoids (EasyRo < 2.0%), and thus may reflect the source feature rather than maturity 16 . They can be used to reflect maturity only at higher maturity levels (> 2.0% EasyRo) as found in Fang et al. 16 and this study. However, unlike other studies, DMDI-1 does not correlate well with EasyRo values in this study (Fig. 7f), probably due to the relatively sizeable analytical error associated with low concentrations of dimethyldiamantanes in the pyrolysates.  of heavy hydrocarbons to smaller ones, or the process of ultimately converting oil to hydrogen-rich gas and carbon-rich pyrobitumen 59 . In our hydrothermal pyrolysis, we found that the extent of oil cracking (EOC; i.e., the percentage of liquid hydrocarbon converted to gas and pyrobitumen, or EOC = (1-M c /M 0 ) × 100, M c and M o are residual and initial liquid hydrocarbons, respectively) can rapidly increase to 90% with the rise in EasyRo from 0.48% to 1.81% (Fig. 8a). Oil cracking occurs at slower rates with further increasing maturation as reflected in the increase in EasyRo from 1.81% (480 °C) to 3.5% (600 °C) and relatively stable EOC around 90% to 95%. However, at the high maturity (above 500 °C) almost all of the liquid hydrocarbons have been consumed, so the error is around ± 5% from 2.19% (504 °C) to 3.5% (600 °C) in the oil pyrolysis experiments. EOC can also be calculated as (1 − C 0 /C c ) × 100 5 , in which (3-+ 4-) MD is assumed not to have newly been generated or decomposed during oil cracking (C 0 and C c are concentrations of (3-+ 4-) MD before and after oil cracking). However, an increase in the (3-+ 4-) MD occurs at ca. 1.2% EasyRo. The decrease in the (3-+ 4-) MD yield is observed at 3.0% EasyRo during oil thermal cracking experiments (Fig. 9a), suggesting the assumption does not apply (Fig. 9b). This finding is supported by other pyrolysis experiments 8,13,16 , lending usage of (1-C 0 /C c ) × 100% is suspect. Based on our results, Dahl's formula for EOC is only applicable to a very narrow range of maturity (EasyRo < 1.2%), and gives higher values than those obtained from our hydrothermal experiments (Fig. 8a). The differences between the two results become progressively smaller with the increasing extent of oil cracking with the values from 6 to 21% at EasyRo from 0.48% to 1.81% and from 2.5% to 6% at EasyRo from 1.81 to 3.0%. Obviously, the (1-C 0 /C c ) × 100% should be changed to [1-C 0 /(C c -C new gener )] × 100% at 1.2% < EasyRo < 3.0%, but the C new gener is difficult to obtain. Fortunately, we find that the calculative EOC (EOC1 = [1 − C 0 /C c ] × 100) shows a good positive linear correlation with the actual EOC (EOC2 = [1-M c /M 0 ] × 100) with equation of EOC2 = 1.2402 × EOC1 − 28.952 and R 2 value of 0.9593 at EasyRo < 3.0% (Fig. 8b). This reveals that although Dahl's method may overestimate the extent of oil cracking, especially in highly cracked samples due to the new generation of 3-+ 4-MD, the method can be corrected and new calculation formula can be used to reflect actual EOC.
The bridgehead-methylated diamondoids are thermodynamically more stable than other methylated diamondoid species 33 . On this basis, some diamondoid isomerization ratios (MAI, MDI, DMAI-1, DMAI-2, TMAI-1, TMAI-2, EAI, DMDI-1, DMDI-2) are used as maturity indicators. Figure 10a,b shows that there is a good positive correlation between diamondoid isomerization ratios (EAI and DMDI-2) and EOC2 with regressive equations as follow, where EAI is applicable in the range of EasyRo < 1.81% (Fig. 10a). Table 3. The yields (µg/g oil) of individual diamantane compounds identified in Table 1    www.nature.com/scientificreports/ This implies that these parameters might help assess the extent of oil cracking (EOC2). Note that the isomerization ratio of DMDI-2 has a good correlation with EOC2 throughout the EasyRo range examined, indicating that it may be a reliable proxy for a wide range of maturity.
On the other hand, the concentration ratios of diamondoid pairs are expected to eliminate the effect of matrix changes during the thermal cracking of oil. Some diamondoid concentration ratios (As/Ds, MAs/MDs, DMAs/ DMDs, and DMAs/MDs) appear positively correlated with EOC2 at EasyRo from 0.48% to 2.1% (Fig. 10c-f) with regressive equations as follow.
(2) EAI = 0.0015 EOC2 + 0.2635 r 2 = 0.6355 EasyRo < 1.81% (3) DMDI-2 = 0.0024 EOC2 + 0.3177 r 2 = 0.7271 (4) As/Ds = 0.0115 EOC2 + 1.7478 r 2 = 0.6052 EasyRo < 2.1%  www.nature.com/scientificreports/ However, the above diamondoid isomerization ratios negatively correlate with EasyRo values of > 2.1% when admantanesadamantanes enter the decomposition stage. The above equations established from hydrothermal pyrolysis are proposed to be used as proxies of the extent of oil cracking during 0.48-2.1% EasyRo for natural petroleum reservoirs.  An alternative production pathway for the exceptionally high yields of H 2 S was via the classical aqueous reaction of elemental S and hydrocarbon shown in Eq. (9) 17,26 : The H 2 S/S 0 molar ratio can be used to determine the amount of H 2 S from the conversion of elemental S (Table 2), and thus will approach 0.75 and 1 for Eqs. (8) and (9), respectively.
The results from group 1 experiment at the lowest temperature of 336 °C (0.57% EasyRo) has H 2 S/S 0 molar ratio of around 0.71 and δ 34 S H2S value of − 5‰ (Table 2), being close to that of elemental S (-6.3‰),indicating that nearly all H 2 S was derived from elemental S. Furthermore, the increasing production of CO 2 did not start until above 408 °C, when the H 2 S/S 0 molar ratio began to be greater than 0.75. This inconsistency in the product implies H 2 S was not produced by elemental sulfur via Eq. (8) from 336-384 °C (0.57-0.79% EasyRo) in group 1. Thus, MgSO 4 source has to be considered with an Eq. (10).
It can be expected that with an increase in temperature, more MgSO 4 is involved in TSR reaction, or TSR proceeds to higher degrees. Suppose all H 2 S was generated from reactions of S 0 with hydrocarbons without generation of SO 4 2− (Eq. 9). In that case, the H 2 S is expected to have the molarity of elemental S of about 12.79 mmol (26.8 mg), which is lower than H 2 S from experiments at 504 °C to 600 °C. Hence, the conversion of elemental S   62,63 , thus free H 2 S amount is expected to be lower than that of decrease in reactants MgSO 4 and elemental sulfur and more incorporation may have occurred and thus shows a decreasing trend at EasyRo = 2.5-3.87% (Table 2).
In contrast, no TSR may have occurred in group 2 experiments but reactions between elemental S and hydrocarbons with no CaSO 4 ·2H 2 O involved. Firstly, the maximum value of the H 2 S/S 0 molar ratio in Group 2 is around 0.9 at the first EasyRo = 1.13 and then slightly decreases from 0.93 to 0.65 with EasyRo from 1.13% to 1.69%. Secondly, the δ 34 S of H 2 S generated in Group 2 ranged from − 5.79‰ to − 6.79‰, within ± 1‰ of elemental S (-6.3‰). Finally, Group 2 produced a very high amount of CO 2 (1.71 mmol/g at 1.13% EasyRo) at the first desired time compared to the meager yields produced by Group 1 above 360 °C ( Table 2). This indicates H 2 S was generated via the classical aqueous reaction of elemental S and hydrocarbon shown in Eq. (9).
Therefore, it can be concluded that TSR has occurred in the group 1 experiments as reflected by the positive shift in δ 34 S value of H 2 S due to reactant MgSO 4 as the most 34 S-enriched sulfur species in this study,the increase of CO 2 and H 2 S/S 0 molar ratio, and shows higher degrees with increasing temperatures. In contrast, the non-TSR reactions between hydrocarbons and H 2 S or elemental sulfur as shown by group 2 experiments have produced H 2 S/S 0 molar ratio of 0.75 and δ 34 S value of H 2 S close to the elemental sulfur.
Generation of diamondoids during TSR. Group 1 experiments show the presence of TSR reaction significantly accelerates the generation and increases the yield of diamantanes relative to the blank non-TSR experiments (TCA; Fig. 5). Here, diamantanes are shown to be predominantly generated during TSR in the EasyRo range of 0.57-1.81% with maximum yields of 240 μg/g at 1.81% EasyRo. However, peak generation of diamantanes of 184.9 μg/g from TCA on ZS1-L oil occurs at 2.62% EasyRo (Fig. 5d), which is significantly lower than TSR (Fig. 5d). In addition, diamantanes remain stable at up to 528 °C during TCA while the temperature is 480 °C during TSR at the same heating rates of 20 °C /h (Fig. 5f). This result may be due to the catalysis of S radical (i.e., from H 2 S), which can accelerate the decomposition of HC or OM.
Moreover, TSR significantly increases the yield of diamantanes compared with the thermal chemical alteration (TCA; Fig. 5a-e). From 0.57% EasyRo to 1.81% EasyRo, the yield of diamantanes detected in the TSR was higher than that of TCA, indicating that diamantanes must have been newly generated during TSR (Fig. 5d). Elemental S can substantially lower the onset temperature of thermal chemical alteration and appears to reduce the activation energy of low-sulfur oil thermal chemical alteration by approximately 92 kJ mol −164 . Therefore, the observed acceleration of diamantanes generation is possibly due to sulfur-derived radical species or H 2 S formed via TSR or disproportionation reaction that enhances the formation of diamantanes.
The mechanism for generating diamondoids during TSR may be through free radical reactions, a mechanism similar to their generation from high temperature cracking of alkanes during the experiment simulation 65,66 . Consequently, we considered that the sulfur-derived radical species or H 2 S during TSR have a facilitative effect on the cleavage of high molecular-mass fractions, resulting in the new generation of diamondoids from TSR experiments in the present study. Meanwhile, hydrogen exchange between water and organic matter also proceeds via sulfur-derived radical species (i.e., from H 2 S) 53 , leading to demethylation and isomerization of hydrocarbon to form diamondoids. Briefly, TSR can lead to the generation of diamondoids through free radical reactions.
Notably, TSR resulted in the new generation of diamondoids (Fig. 5), and thus had a significant effect on the distribution and concentration of diamondoids. Thus, in TSR-altered oils, diamondoid-related maturity proxies have been altered significantly (Table 3), and thus cannot be used to indicate EOC.
Generation of thiadiamondoids during TSR. Thiaadmantane and methyl thiaadmantanes isomers were detected at 1.81% EasyRo when the yields of diamantanes reached a maximum value during the hydrothermal pyrolysis of ZS1-L oil under TSR condition (Fig. 1). To our knowledge, this is the first successful laboratory synthesis of thiaadmantanes from a petroleum sample via TSR. Although previous laboratory experiments have successfully synthesized thiaadmantanes, thiaadmantanes were only detected from reactions of reduced S or CaSO 4 with pure diamondoids 37,38 . Based on these laboratory experiments, Wei et al. 37 proposed that diamondoids appear to be the only precursors of thiaadmantanes during TSR (Fig. 11a). Our results indicate that diamondoids are formed earlier than thiaadmantanes, thus, thiaadmantanes may have been generated from reactions of diamondoids with sulfur species. However, diamondoids can be formed from alkanes and it is hard to break C-C bonds in cage structure of diamondoids. These facts indicate that thiadiamondoids and diamondoids may have been generated simultaneously, likely not via reactions with diamondoids based on the following aspects (Fig. 11). Firstly, during TSR experiments at EasyRo of 1.81%, both diamantanes and corresponding thiaamantanes were formed, and thiadamantanes show positive correlations with the corresponding diamantanes (2-TA vs D; M-2-TA vs MD; DM-2-TA vs DMD; TM-2-TA vs TMD) from (Fig. 12a,b) with a higher yield of diamantanes during TSR compared with hydrothermal pyrolysis(TCA; Fig. 12a). The experimental results indicate that diamondoids and thiadamantanes may have been formed simultaneously, which is consistent with case studies showing the positive relationships between diamondoids and thiadiamondoids concentrations from oils and condensates from the Tarim Basin and Gulf of Mexico Basin 25,36 . In contrast, if diamondoids are the only precursor of thiaadamantane 37  www.nature.com/scientificreports/ negative correlation between the yields of diamondoids and thiaadmantanes. Secondly, C-C bonds in the cage structure of diamondoids have been proposed to be hard to break up due to their thermal stability [30][31][32] , it is more energy-favorable to form thiaadamantanes from other non-diamondoids compounds. Thus, it is reasonable for thiaadamantanes to have been generated during the formation of diamondoids. Considering that diamondoids can be generated from pyrolysis of all four fractions [13][14][15][16] , a non-diamondoid source of thiaadamantanes is proposed here as shown in Fig. 11b. However, thiaadmantanes were only detected at 1.81% EasyRo (480 °C) not at other TSR experiments at temperatures from 336 °C to 600 °C. It is possible for thiaadamantanes to have been formed in relatively high-temperature conditions and are expected to decompose at higher EasyRo. Xiao et al. 67 proposed that thiaadamantanes  www.nature.com/scientificreports/ show slight to moderate cracking at EasyRo of 1.81%. In contrast, Wei et al. 7 proposed that diamantane is stable up to 550 °C in the laboratory, which is consistent with the stability of adamantane reported by Oya et al. 68

Conclusions
Based on our experiments, we can conclude that: 1. Hydrothermal pyrolysis experiments indicate that water can enhance the yields of diamondoids. Diamondoids may have mainly generated in 0.48% ~ 2.1% EasyRo and decomposed at > 2.1% EasyRo. Especially, diamantanes show decomposition at > 3.0% EasyRo. 2. MDI, EAI, DMAI-1, DMDI-2 are shown to be reliable maturity proxies at maturity over ca.1.0% EasyRo, and TMAI-1, TMAI-2 and DMAI-2 can only be used to reflect the higher maturity at EasyRo > 2.0%. 3. The extents of oil cracking (EOC) calculated from Dahl's (3-+ 4-) MD method are higher than the actual values, especially for highly mature samples due to their new generation, but can be obtained using our correction formula (EOC2 = 1.2402 × EOC1-28.952) at EasyRo < 3.0%. 4. EAI, DMDI-2, As/Ds, MAs/MDs, DMAs/DMDs, and DMAs/MDs can serve as molecular proxies to estimate the extent of oil cracking at EasyRo mainly < 2.1%. 5. TSR is found to newly generate diamantanes at < 1.81% EasyRo followed by their decomposition, while the decomposition of diamantanes by TCA occurs at > 2.62% EasyRo, and thus any diamondoid-related proxy cannot be used to reflect maturity and EOC. 6. Thiaadamantanes were generated from an experiment of TSR by oil at 1.81% EasyRo for the first time, likely via pyrolysis of non-diamondoid structure hydrocarbons.
Our results provide crucial experimental evidence for understanding the evolution of diamondoids during thermal maturity and TSR under natural conditions.