Reaction path model of the formation of abiotic immiscible hydrocarbon fluids in subducted carbonated serpentinites, Lanzo Massif (Western Italian Alps)

Abstract Fluids generated from subducted slabs participate in the cycling of deep carbon in the crust and upper mantle. In these fluids, aqueous carbon species vary in oxidation state between +IV and -IV depending on whether the fluids are oxidizing or reducing, respectively. Most studies of subduction-zone fluids have focused on oxidized carbon species. However, recent studies of natural samples have demonstrated the occurrence of deep, reducing fluids, generated in both subducted oceanic upper mantle and crustal rocks. 𝐶𝐻4-𝐻2-rich fluid inclusions in subducted carbonated serpentinites have demonstrated the existence of abiotic, immiscible, hydrocarbon fluids at upper mantle conditions. To investigate the formation of such immiscible hydrocarbon fluids during the evolution of subducted carbonated serpentinites, we used equilibrium constants from the Deep Earth Water model to carry out predictive chemical mass transfer modeling to simulate the alteration reactions. A novel feature of the models was the inclusion of an immiscible hydrocarbon fluid containing six components ( 𝐶𝐻4,𝑓,𝐶2𝐻6,𝑓, 𝐶3𝐻8,𝑓, 𝑖𝑠𝑜𝐶4𝐻10,𝑓,𝐶𝑂2,𝑓,𝐻2,𝑓 ). This feature enabled prediction of the formation of a separate immiscible fluid in equilibrium with aqueous species and minerals. We developed a predictive reaction path model of invasive 𝐻2,𝑓 reacting with carbonated serpentinites and interstitial aqueous fluids for comparison with the natural samples from the Lanzo Massif, western Italian Alps. Over a range of temperatures and pressures, immiscible hydrocarbon fluids formed in association with altered mineral assemblages. Reaction progress caused the transformation of carbonated serpentinites and the formation of clinopyroxene, brucite, graphite, and hydrocarbon fluids, along with changes of 𝑝𝐻, 𝑙𝑜𝑔𝑓 𝑂2, and aqueous species. 𝐶𝐻4,𝑓 was the most abundant hydrocarbon species in all the models. The overall results at 2.0 GPa and Abstract Click here to access/download;Abstract;Abstract.docx 400 to 450 °C were consistent with the natural samples from the Lanzo Massif. Interestingly, large amounts of 𝐻2𝑂 formed due to oxidation of 𝐻2. More hydrocarbons and 𝐻2𝑂 formed in models with lower fluid/rock mass ratios or with more reactant 𝐻2. Models at different pressure and temperature conditions showed similar results with some variation in the relative stabilities of aragonite, graphite and olivine solid solution, and associated differences in mineral sequences, hydrocarbon fluids, values of aqueous species, and the final 𝑙𝑜𝑔𝑓 𝑂2 and 𝑝𝐻. Our models strongly support the laboratory and field evidence that reduction of carbonated serpentinites by infiltrating 𝐻2 fluids can cause the formation of immiscible, abiotic hydrocarbon fluids in subduction zones. Key words: Abiotic hydrocarbon; Carbonated serpentinites; DEW model; Thermodynamic modeling; Deep carbon fluids Highlights ● Novel reaction path model for invasive H2 fluids interacting with carbonated serpentinites ● Use of the Deep Earth Water model for predictive chemical mass transfer modeling ● Significant immiscible CH4 fluid and H2O formed under high pressure and temperature ● Serpentinite and aragonite destroyed with brucite, graphite, and clinopyroxene formed ● Model results agree with natural samples from Lanzo Massif, western Italian Alps Highlights (for review) 1. Introduction 1 It has long been proposed that hydrocarbon fluids could exist in the deep Earth (Mendeleev 2 1877, Kudryavtsev 1959, Kolesnikov et al. 2009, 2017, Kutcherov and Krayushkin 2010). 3 Although controversial (McCollom 2013, Sephton and Hazen 2013), a deep, abiotic theory for the 4 origin of hydrocarbons received support in the late 20th century from the hypothesis of a deep hot 5 biosphere feed by ascending abiotic fluid hydrocarbons from the deep Earth (Kudryavtsev 1951, 6 Gold 1992, 2001). However, the amounts of abiotic hydrocarbons that could be produced in the 7 upper mantle were never quantified and remain highly speculative. 8 Recent studies have suggested evidence of possible abiotic hydrocarbon-𝐻2-bearing fluids 9 in association with ultramafic or mafic rocks and serpentinization in mid-ocean ridge settings 10 where the hydrocarbons are present in minor quantities dissolved in the circulating aqueous fluids 11 (Proskurowski et al. 2008, Alt et al. 2013, McDermott et al. 2015, Klein et al. 2019). However, it 12 is doubtful that the 𝐶𝐻4 formed recently in the present hydrothermal circulation systems 13 (McDermott et al. 2015, Reeves and Fiebig 2020). For example, Klein et al. (2019) suggested that 14 𝐻2 and 𝐶𝐻4 can be formed inside olivine-hosted aqueous fluids as a result of host-inclusion 15 interactions during cooling and subsequently released into the mid-ocean ridge hydrothermal 16 circulation system. 17 Many fewer studies have been concerned with hydrocarbon production during high18 pressure metamorphism in subduction zones, where most studies have typically focused on 19 oxidized carbon species dissolved in the fluid phases (Hacker et al. 2003, Dasgupta and 20 Hirschmann 2010, Scambelluri et al. 2019). Subduction zone serpentinization has been proposed 21 to produce large amounts of 𝐻2 and 𝐶𝐻4 (Vitale Brovarone et al. 2020). Additionally, 𝐶𝐻4 has 22 Manuscript Click here to access/download;Manuscript;MS_AVB.docx Click here to view linked References 1 been found in high-pressure and ultra-high-pressure metabasic rocks (Tao et al. 2018, Zhu et al. 23 2020). Experimental and theoretical studies have demonstrated that 𝐻2 and light hydrocarbons can 24 be immiscible at subduction zone conditions (Huang et al., 2017; Huang et al., 2023; Li, 2017; 25 Pruteanu et al., 2017). However, the generation of reduced-carbon species in subduction zone 26 fluids or as immiscible phases has not received much attention. Nevertheless, natural confirmation 27 of immiscible, 𝐶𝐻4-𝐻2-bearing fluids related to serpentinization in subduction zones have now 28 been found world-wide. For example, coexisting aqueous and 𝐻2-𝐶𝐻4-rich gaseous fluid 29 inclusions in the Lanzo massif, western Italian Alps (Pelletier and Müntener 2006, Vitale 30 Brovarone et al. 2017, 2020, Giuntoli et al. 2020, Sverjensky et al. 2020) have been suggested to 31 document immiscibility of reduced fluids in metamorphic fluids. In these rocks, 𝐶𝐻4 formed by 32 𝐻2-mediated reduction of carbonate in carbonated serpentinites. The reaction also resulted in the 33 formation of diopside, brucite, graphite, ±Ca-rich garnet (Vitale Brovarone et al. 2017, Giuntoli et 34 al. 2020). A recent geochronological study indicates that the event of 𝐶𝐻4 formation happened at 35 peak metamorphic conditions (Piccoli et al. 2023), corresponding to about 500 °C and depths up 36 to 80 km, or ~2.5 GPa (Vitale Brovarone et al., 2017 and references therein). 37 In addition to natural examples of abiotic hydrocarbons, numerous experimental studies of 38 abiotic hydrocarbon formation at elevated temperatures and pressures have been reported 39 (Foustoukos and Stern 2012, Manning et al. 2013, McCollom 2013). Under crustal conditions, the 40 formation of hydrocarbons in serpentinization experiments has been widely studied with and 41 without catalysts such as metallic iron (Barbier et al. 2020). At higher, upper mantle pressures, 42 experimental studies have focused on fluids without minerals present. For example, immiscible 43 𝐶𝐻4-𝐶2𝐻6-𝐻2 fluid inclusions were recorded in quartz at 1.5 - 2.5 GPa and 600 - 700 °C (Li 2017), 44 and immiscible hydrocarbon droplets containing isobutane and other hydrocarbons were observed 45 2 with in situ Raman spectroscopy at 1.6 – 4.6 GPa and 300° C (Huang et al., 2017; Huang et al., 46 2023). 47 Overall, natural examples and experiments at upper mantle temperatures and pressures 48 indicate that the formation of immiscible abiotic hydrocarbons does occur. However, quantitative, 49 predictive models of the formation of immiscible abiotic hydrocarbon fluids in geologic settings 50 at depth have been lacking. In this study, we conducted predictive, irreversible chemical mass 51 transfer modeling to simulate the formation of hydrocarbon fluids in a well-documented natural 52 setting. We chose to model the reduction of carbonated serpentinites and the associated production 53 of an immiscible 𝐶𝐻4-rich fluid in the Lanzo Massif previously described in detail by Vitale 54 Brovarone et al. (2017). Following the genetic model by Vitale Brovarone et al. (2017), we 55 modeled the interaction between 𝐻2-rich fluids and carbonated serpentinites in the pressure and 56 temperature range of 1.0 - 2.0 GPa and 400 - 500 °C which is consistent with reported subduction 57 zone conditions (Van Keken et al. 2002, Syracuse et al. 2010, Penniston-Dorland et al. 2015, Holt 58 and Condit 2021). Our models provide a test of our ability to predict the formation of immiscible 59 hydrocarbon fluids in a chemically and mineralogically complex system at elevated pressure60 temperature conditions for comparison with the observed mineral assemblages and fluid inclusion 61 compositions previously described for the reduced carbonated serpentinites from the Lanzo Massif. 62 2. Geologic setting of the Lanzo Massif and abiotic methanogenesis during the 63 reduction of carbonated serpentinites 64 The ultramafic rocks of the Lanzo Massif in the western Italian Alps underwent Cenozoic 65 eclogite-facies peak metamorphic conditions to about 500-550 °C and 2 GPa (Rubatto and 66 Hermann 2001, Pelletier and Müntener 2006). The massif includes carbonated serpentinites, 67 3 including carbonated serpentinites, regarded as the products of sub-seafloor hydrothermal 68 reactions (Lagabrielle et al. 1990, Rubatto and Hermann 2001, Pelletier and Müntener 2006, Vitale 69 Brovarone et al. 2017). The carbonated serpentinites are located in the pervasive serpentinized 70 shell outside the peridotite core of the massif. The shell surrounds mostly the north and west sides 71 of the peridotite core. For the purposes of the present study, the detailed petrographic, fluid 72 inclusion, isotopic, modeling, and geochronological results reported by Vitale Brovarone et al. 73 (2017), Giuntoli et al. (2020), and Piccoli et al. (2023) can be summarized by the following key 74 points relevant to our reaction path modeling: 75  The samples of carbonated serpentinite consist of clasts of serpentinite embedded in a Ca76 carbonate matrix. 77  Pristine serpentinite clasts consist mainly of antigorite – the serpentine mineral stable at 78 high temperature and pressure conditions – and small amounts of chlorite and magnetite. 79  The reacted serpentinite clasts are coated by ubiquitous graphite rims. Other product 80 minerals include diopside ± brucite ± Ca-rich garnet ± perovskite (CaTiO3). 81  The reacted rocks are found along discrete layers within the carbonated serpentinite, which 82 were interpreted as fluid pathways and shear zones (Giuntoli et al. 2020). Overall, the 83 degree of alteration of the serpentinite clasts is highly variable on a spatial scale of meters. 84  Petrographic relations indicate that graphite formation occurred at high-pressure conditions 85 in the antigorite stability field. Dating of syn-reduction perovskite including 𝐶𝐻4 and 86 graphite inclusions provided an age of 49.6 ± 1 Ma (Piccoli et al. 2023), which is consistent 87 with previous constraints on the peak metamorphic age of the Lanzo massif (Rubatto and 88 Hermann, 2001). 89 4  Two types of structurally coexisting fluid inclusion populations were found in the 90 carbonate matrix adjacent to serpentinite clasts and the reacted rims of serpentinite: a 𝐶𝐻491 𝐻2-rich population and a 𝐻2𝑂-rich population. These two populations were interpreted to 92 represent coexisting immiscible fluids (Vitale Brovarone et al. 2017, Sverjensky et al. 93 2020). 94  The 𝛿 𝐶 13 values of the residual, reacted carbonate samples are up to about 8 per mil 95 heavier than the least reacted samples which have typical marine carbonate values of about 96 2 - 3 per mil relative to the PeeDee Belemnite standard (Vitale Brovarone et al. 2017). 97 These values are consistent with the partial transformation of carbonate into 𝐶𝐻4. 98  The 𝐶𝐻4 genesis was interpreted as the result of 𝐻2-carbonate interactions along 99 channelized fluid pathways inside the carbonated seprentinite. The process was 100 summarized according to the following overall reaction: 101 𝑎𝑛𝑡𝑖𝑔𝑜𝑟𝑖𝑡𝑒 +17𝐶𝑎-𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒+68𝐻2 = 17𝑑𝑖𝑜𝑝𝑠𝑖𝑑𝑒 +31𝑏𝑟𝑢𝑐𝑖𝑡𝑒 102 +17𝐶𝐻4+34𝐻2𝑂 (1) 103 𝑀𝑔48𝑆𝑖34𝑂85(𝑂𝐻)62 +17𝐶𝑎𝐶𝑂3+68𝐻2 = 17𝐶𝑎𝑀𝑔𝑆𝑖2𝑂6+31𝑀𝑔(𝑂𝐻)2 104 +17𝐶𝐻4+34𝐻2𝑂 (2) 105  Overall, the mineral assemblages and fluid inclusions suggest the reduction of carbon in 106 Ca-carbonate by the 𝐻2-fluids to form 𝐶𝐻4 and graphite. Reaction between the external 𝐻2 107 and the newly formed graphite was also proposed to generate additional 𝐶𝐻4. 108  The pressure and temperature conditions of the reactions were determined by the presence 109 of graphite and aragonite inclusions in magnetite, and syn-reduction antigorite, and 110 modeled in a simplified 𝐶𝑎-𝑀𝑔-𝑆𝑖-𝐶-𝑂-𝐻 thermodynamic system. The minimum 111 condition was inferred to be 1.0 GPa and 370 °C (i.e., 370 °𝐶 𝐺𝑃𝑎−1 of gradient, same as 112 5 below) constrained by graphite-aragonite coexistence along the exhumation path of the 113 Lanzo massif. The maximum condition was predicted to be about 2.5 GPa and 500 °C (200 114 °𝐶 𝐺𝑃𝑎−1) constrained by the peak metamorphic condition of the Lanzo Massif. 115  The oxygen fugacities during the reactions were estimated to range from log𝑓𝑂2 -29 to -37 116 (QFM -3 to -6), assuming graphite saturation and the co-occurrence of magnetite in the 117 carbonated serpentinites. 118 3. Methods 119 3.1 Thermodynamic data for aqueous species and minerals 120 We have used the geochemical Deep Earth Water (DEW) model which was built to address 121 the predictive geochemical modeling challenge of a huge range of temperatures, pressures, and 122 chemically complex systems (Sverjensky et al. 2014, Huang and Sverjensky 2019, 123 Sverjensky 2019). The DEW model is based on predictive geochemical theory resting on 124 decades of theoretical and experimental studies of the thermodynamic properties of electrolytes, 125 neutral aqueous solutes, metal-complexes, and organic species. The DEW model enables 126 prediction of equilibrium constants involving aqueous species of all types to be incorporated into 127 the data files for aqueous speciation, solubility, and chemical mass transfer codes. Here we use the 128 codes EQ3 & EQ6 (Wolery 1992) modified to operate at elevated temperatures and pressures. The 129 standard Gibbs free energies of formation of the end-member mineral components were calculated 130 with the modified Berman thermodynamic database (Berman 1988, Sverjensky et al. 1991, 131 Sverjensky 2019). 132 133 12 of 𝐶𝐻4,𝑎𝑞 0 and 𝐶𝐻4,𝑓 will be reached, followed by the stability field of 𝐶𝐻4-rich hydrocarbon 266 fluid. 267 It should be noted here that although graphite appears as a phase in Figs. 2A - D, these 268 figures refer to a chemical system without the component 𝐶𝑎𝑂, an important component in the 269 natural carbonated serpentinites. When 𝐶𝑎𝑂 is included, the stability of graphite is limited by the 270 appearance of aragonite or calcite solid solution, depending on the value of the 271 𝑙𝑜𝑔(𝑎𝐶𝑎2+ (𝑎𝐻+)2 ⁄) in the aqueous phase. For the conditions we modeled below, the stability field 272 of graphite is replaced by aragonite or calcite solid solution at 1.0 GPa and 400°C. 273 274 4.2 Fluid hydrocarbon formation during the destruction of carbonated serpentinites in the 275 Lanzo Massif 276 Chemical mass transfer models of the transformation of carbonated serpentinites by 𝐻2 277 fluids were conducted at 1.0 - 2.0 GPa and 400 °C - 500 °C consistent with the conditions proposed 278 for the Lanzo Massif (Vitale Brovarone et al. 2017). The initial aqueous fluids were predicted at 279 each pressure and temperature condition (Table 1, S-1, S-2, S-3, S-4) using an aqueous speciation 280 solubility model as described above (section 3.3). The initial total concentrations of the aqueous 281 carbon were 0.01, 0.05, or 0.1 molal, which were the lowest values usable given our assumptions 282 about equilibrium with the minerals and with initial 𝑙𝑜𝑔𝑓𝑂2 values between QFM -1.6 to +1.2. The 283 saturation activity of 𝐶𝐻4,𝑎𝑞 0 increased with temperature at the same pressure. The carbon 284 speciation in the initial fluids was controlled by 𝑙𝑜𝑔𝑓𝑂2 relative to the QFM buffer and the total 285 aqueous carbon concentrations. For example, at 1.5 GPa and 400 °C, two oxidation states could 286 be considered: at 𝑙𝑜𝑔𝑓𝑂2 of QFM+1.0, 𝐶𝐻4,𝑎𝑞 is 0.03% of the total carbon of 0.01 m, whereas at 287 13 𝑙𝑜𝑔𝑓𝑂2 of QFM-1.4, 𝐶𝐻4,𝑎𝑞 is 91.4% of the total carbon of 0.1 m. Importantly, the different 288 oxidation states of these two fluids did not affect the major results of the mass transfer reactions. 289 Therefore, either fluid could be used at each pressure and temperature. In other words, the initial 290 values of 𝑙𝑜𝑔𝑓𝑂2 in the fluid were not important variables. The main reason being that in all cases 291 the total initial carbon in the fluid was low. 292 4.2.1 The standard model at 2.0 GPa and 400.0 °C and 𝐹/𝑅 equal to 0.1 293 Here we present a mass transfer model at 2.0 GPa and 400 °C and 𝐹/𝑅 equal to 1.0 that 294 can serve as a representative example of our modeling (Table 1, Fig. 3). At this temperature and 295 pressure, the activity of 𝐶𝐻4,𝑎𝑞 0 in equilibrium with pure methane fluid was 2.4 (see Fig. 1A). 296 Therefore, as the aqueous activity coefficient in our model for neutral species was assumed to be 297 unity, at least 2.4 m 𝐶𝐻4,𝑎𝑞 0 would need to accumulate in the fluid during the mass transfer 298 reactions for an immiscible pure methane fluid to form. In our models, a hydrocarbon fluid with 299 variable composition could form. Such a fluid was more stable than a pure methane fluid; therefore, 300 it could form at concentrations of C less than 2.4 m. The initial mineral reactants were 16.45 moles 301 of aragonite, 3.53 moles of antigorite, 0.71 moles of magnetite, and 1.88 moles of chlorite(ss) per 302 1,000 g of 𝐻2𝑂. The initial aqueous fluid/rock (𝐹/𝑅) mass ratio was 0.10. This ratio was the lowest 303 value tested and corresponded to 10.0 kg of rock and of a dilute initial aqueous fluid containing 304 1.0 kg of 𝐻2𝑂. The endpoint of the model was determined by the initial amount of 𝐻2 with a value 305 of 66.5 moles per 1000 g of 𝐻2𝑂 (Table 2). This value of 𝐻2 resulted in the formation of 306 hydrocarbon fluids without secondary olivine(ss) appearance due to the reduction of magnetite. 307 The initial and final aqueous fluid compositions and mineral assemblages are shown in 308 Table 1 and the detailed mass transfer results are shown as a function of the logarithm of the 309 14 reaction progress (𝑙𝑜𝑔 𝜉) in Figs. 3A - E. Here, 𝜉 represents the number of moles of 𝐻2 added. The 310 full reaction path output file is given in Appendix A. It can be seen in Fig. 3A that the reactant 311 minerals, aragonite, antigorite, and magnetite were stable in the beginning, as these were used in 312 the EQ3 code to develop the initial aqueous fluid chemistry, while chlorite(ss) increased with 𝑙𝑜𝑔 𝜉. 313 At a 𝑙𝑜𝑔 𝜉 value of -1.37, clinopyroxene(ss) appeared consisting of almost pure diopside (95%) 314 and miner hedenbergite (5%). The mole fraction of diopside decreased slightly to 90% until the 315 end of the reaction (Table 1). Chlorite(ss) reached a plateau after 𝑙𝑜𝑔 𝜉 of 0.28. Shortly after, 316 brucite started to form, then antigorite and aragonite decreased strongly. Graphite then formed and 317 increased until aragonite was totally destroyed; meanwhile, antigorite stopped decreasing. The 318 graphitization could be expressed as the following reaction: 319 𝑎𝑛𝑡𝑖𝑔𝑜𝑟𝑖𝑡𝑒 +17𝐶𝑎-𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒 +34𝐻2 = 17𝑑𝑖𝑜𝑝𝑠𝑖𝑑𝑒 +31𝑏𝑟𝑢𝑐𝑖𝑡𝑒 +17𝑔𝑟𝑎𝑝ℎ𝑖𝑡𝑒 320 (7) 321 𝑀𝑔48𝑆𝑖34𝑂85(𝑂𝐻)62 +17𝐶𝑎𝐶𝑂3+34𝐻2 = 17𝐶𝑎𝑀𝑔𝑆𝑖2𝑂6+31𝑀𝑔(𝑂𝐻)2+17𝐶 +34𝐻2𝑂 322 (8) 323 Finally, hydrocarbon fluid formed and completed replaced graphite. This reaction could be 324 expressed as the reaction below: 325 𝑔𝑟𝑎𝑝ℎ𝑖𝑡𝑒+2𝐻2,𝑓 → 𝐶𝐻4,𝑓 (9) 326 The overall reaction of methane genesis was presented in Eqs. (1 and 2). The hydrocarbon 327 fluid contained almost pure 𝐶𝐻4,𝑓 (99.7%), as well as 𝐶2𝐻6,𝑓 (0.1%), 𝐻2,𝑓 (0.2%). Only trace 328 amounts of 𝐶3𝐻8,𝑓 and 𝑖𝑠𝑜𝐶4𝐻10,𝑓 were produced. The amount of hydrocarbon fluid increased 329 mainly during the final period of reaction progress (∆𝑙𝑜𝑔 𝜉 0.21). 330 The change of mineral volumes can be seen in Fig. 3B. The volumes shown refer to 25°C 331 and 0.1 MPa but these differ by less than about 3% from the volumes at 400°C and 2.0 GPa. For 332 15 the model system volume of in a 4,600 𝑐𝑚3 (3,800 𝑐𝑚3 of reactant rock and 800 𝑐𝑚3 of initial 333 aqueous fluid), the volumes show a dramatic destruction of antigorite and aragonite by about 1,680 334 𝑐𝑚3 and 560 𝑐𝑚3, respectively, while the other two reactants (magnetite and chlorite) were just 335 accessory minerals. In terms of product minerals, about ~1,090 𝑐𝑚3 of clinopyroxene(ss) and 336 ~770 𝑐𝑚3of brucite were generated. Despite the significant number of moles of graphite formed, 337 the volume of graphite is small. The total volume of product minerals was about ~380 𝑐𝑚3 less 338 than the destroyed reactants. However, in addition to the mineral products, about 32.3 moles of 339 𝐻2𝑂 and 12.7 moles of fluid 𝐶𝐻4 were also produced (Table 2), which corresponded to about 487 340 𝑐𝑚3 of 𝐻2𝑂 and 332 𝑐𝑚3 of fluid 𝐶𝐻4, respectively (see also Fig. 4B below). Overall, the volume 341 of the system expanded by around 440 𝑐𝑚3. The reactions are self-promoting because more fluid 342 𝐶𝐻4 formed at 2.0 GPa and 400 °C than lower pressures (Fig. 6A, see section 4.2.3). 343 The molalities of most dissolved elements showed only small changes as a function of 344 𝑙𝑜𝑔 𝜉 (Fig. 3C). Ca increased slowly and then decreased a little in the end. Fe decreased because 345 of the formation of clinopyroxene(ss). Then after clinopyroxene(ss) reached a peak, the reduction 346 of magnetite caused the decrease of Fe. Na, Cl, and Al did not participate significantly in any 347 reactions. However, the total dissolved C increased strongly with 𝑙𝑜𝑔 𝜉 as aragonite progressively 348 dissolved. The molality of C reached a plateau when graphite formed, and the system was buffered. 349 Major changes in 𝑙𝑜𝑔𝑓𝑂2 and 𝑝𝐻 can be seen in Fig. 3D. The values of 𝑙𝑜𝑔𝑓𝑂2 decreased 350 gradually then strongly, corresponding to the continuous addition of 𝐻2 as a function of 𝑙𝑜𝑔 𝜉. A 351 plateau was reached when graphite appeared, which buffered the 𝑙𝑜𝑔𝑓𝑂2 co-existing with aragonite. 352 After all the aragonite was destroyed, the 𝑙𝑜𝑔𝑓𝑂2 dropped quickly to the value where graphite and 353 hydrocarbon fluids (almost pure 𝐶𝐻4,𝑓) could co-exist. The final 𝑙𝑜𝑔𝑓𝑂2 was -30.2 (QFM -4.1). 354 16 The initial 𝑝𝐻 was very alkaline with significant amounts of Ca and Mg (Table 1). Overall, it was 355 a 𝑀𝑔(𝑂𝐻)2 and 𝐶𝑎(𝑂𝐻)2 solution. Interestingly, the 𝑝𝐻 became even more alkaline with 𝑙𝑜𝑔 𝜉 356 as more Ca was added to the fluid by dissolution of aragonite (Fig. 3D). The rate of increase slowed 357 when clinopyroxene(ss) appeared, and then reached a peak after brucite appeared, resulting in 358 buffering of the 𝑝𝐻 at 5.80. The pH decreased a little to 5.77 corresponding to the formation of 359 the hydrocarbon fluids. 360 The change of concentrations of individual aqueous species mirrors the above changes in 361 the 𝑙𝑜𝑔𝑓𝑂2, 𝑝𝐻, and mineral products (Fig. 3E). It can be seen that 𝐶𝐻4,𝑎𝑞 0 was the most abundant 362 aqueous C-species and increased until graphite formed after which it increased again. These 363 changes correspond to the conversion of the carbonate in aragonite to graphite and then to methane. 364 The trends of the other aqueous hydrocarbon species were similar. Carbonate species decreased 365 all the way because of the drop of 𝑙𝑜𝑔𝑓𝑂2. The molality of 𝐻2,𝑎𝑞 0 did not increase much until the 366 last stage of the reaction progress where it only reached about 10 millimolal, which means that 367 almost all the reactant 𝐻2 were consumed by incorporation into hydrocarbons as well as oxidation 368 to 𝐻2𝑂 and 𝑂𝐻-groups in brucite. 369 4.2.2 Models at 2.0 GPa and 400 °C with different initial 𝐹/𝑅 mass ratios 370 The standard model discussed above referred to an initial 𝐹/𝑅 ratio of 0.10 by weight. In 371 that model, the initial mass of rock was 10.0 kg and the initial fluid contained 1.0 kg 𝐻2𝑂 (55.51 372 moles). We also investigated models with higher initial 𝐹/𝑅 for two reasons. First, the 𝐹/𝑅 of 373 natural samples are variable, and we could test differences in the model results if the decarbonation 374 reactions were extended. Second, higher 𝐹/𝑅 ratios might represent initial carbonated 375 serpentinites with a higher porosity. Third, higher 𝐹/𝑅 ratios imply less amounts of initial 376 17 aragonite relative to 1.0 kg 𝐻2𝑂, which in turn requires less 𝐻2 to destroy the aragonite and 377 facilitate the formation of hydrocarbon fluids. 378 Models of four additional initial 𝐹/𝑅 ratios were calculated ranging from 0.10 to 0.63 and 379 corresponding initial amounts of reactant 𝐻2 from 66.5 moles to 10.6 moles, respectively (Table 2 380 and Figs. 4A and B). All the models finished before the formation of olivine(ss). The mass ratios 381 of 𝐻2 and rock were very similar for all the runs, around 0.0133 (Table 2 and Fig. 4A). 382 Interestingly, even with a wide range of 𝐹/𝑅 ratios, the predicted mineral sequences, solid solution 383 compositions, hydrocarbon fluid compositions, 𝑙𝑜𝑔𝑓𝑂2, 𝑝𝐻, trends of dissolved elements and 384 aqueous species were all very similar to the standard run described above. The absolute amounts 385 of minerals and hydrocarbon fluids decreased with higher 𝐹/𝑅 ratios. Less 𝐻2𝑂 formed during the 386 reactions (from 32.3 to 5.57 moles) so the concentration of elements and aqueous species were 387 lower than the standard run (Fig. 4B). 388 The formation of hydrocarbon fluids decreased by 2 log units corresponding to the rise in 389 𝐹/𝑅 from 0.10 to 0.63 (Table 2, Fig. 4B). The mass of rock after reaction decreased in every run. 390 In the standard run, the mass of rock decreased by 7.30%. The percentage of decrease was slightly 391 greater in runs with higher 𝐹/𝑅 (8.18%). Taking into account the final amounts of 𝐻2𝑂, the final 392 values of 𝐹/𝑅 could be calculated, and they were higher than the initial 𝐹/𝑅 ratio because of the 393 significant number of moles of excess 𝐻2𝑂 created during the mass transfer. The percentage of 394 increase was 10% for the initial 𝐹/𝑅 ratio of 0.63, but reached 59% for the initial 𝐹/𝑅 ratio of 395 0.10. To conclude, lowering the 𝐹/𝑅 increased the formation of the immiscible hydrocarbon fluids 396 significantly because of the reduction of large amounts of aragonite. Because of the extra 𝐻2𝑂 397 formed, the aqueous fluids were diluted by the oxidation of 𝐻2 fluids and 𝐶𝐻4,𝑎𝑞 0 was the only 398 major aqueous carbon species. 399 18 4.2.3 Models at different temperature-pressure conditions 400 To investigate the roles of temperature and pressure during the formation of hydrocarbons 401 from the reduction of carbonated serpentinite, we expanded our conceptual model at pressure and 402 temperature conditions along the metamorphic path of the Lanzo Massif (Vitale Brovarone et al. 403 2017, Giuntoli et al. 2020). The pressure and temperature conditions run with the mass transfer 404 model were 1.0 GPa and 400 °C, 1.5 GPa and 400 °C, 2.0 GPa and 450 °C, and 2.0 GPa and 500 °C 405 (Figs. 5, 6, & 7, Table S-1 to S-4) with a 𝐹/𝑅 mass ratio of 0.1. The rock reactants were the same 406 for each run: 16.45 moles of aragonite, 3.53 moles of antigorite, 0.71 moles of magnetite, and 1.88 407 moles of chlorite(ss). However, the numbers of moles of 𝐻2 needed were 68.4, 66.4, 53.9, and 408 76.8, respectively, depending on the reaction conditions. At 1.5 GPa and 400 °C, the amount of 409 𝐻2 corresponds to the point just before olivine(ss) formation, the same as the standard run at 2.0 410 GPa and 400 °C. However, at 1.0 GPa and 400 °C, 2.0 GPa and 450 °C, and 2.0 GPa and 500 °C, 411 the number of moles of 𝐻2 corresponds to the point when 1.0 mole of hydrocarbon fluids formed 412 because olivine(ss) formed before hydrocarbon fluids. 413 The lowest pressure considered, 1.0 GPa and 400 °C, was on the exhumation path, other 414 conditions were on the prograde path of the Lanzo massif (Vitale Brovarone et al. 2017). Figure 5 415 presents the amounts of minerals, both reactants and products, as a function of 𝑙𝑜𝑔 𝜉. Antigorite 416 was stable in the beginning and then decreased at all conditions. Because of the large molecular 417 formula of antigorite, the destroyed volume of antigorite reached about 1,800 𝑐𝑚3 (37% of the 418 total volume in the system). Clinopyroxene(ss) was the first product mineral with almost pure 419 diopside and then brucite formed in all the runs. Chlorite(ss) with more than 95 mol% clinochlore 420 did not react and stayed until the end of the runs, except for a slight decrease at 1.0 GPa and 400 °C. 421 Hydrocarbon fluids formed during a late interval of reaction progress and increased quickly. 422 19 At 1.0 GPa and 400 °C, calcite(ss) was more stable than aragonite (Fig. 5A, Table S-1). 423 Interestingly, this, the retrograde path model, was the only model without graphite formation. 424 Hydrocarbon fluids formed directly from calcite(ss). As mentioned above, graphite is not stable 425 relative to aragonite for certain levels of the ratio 𝑎𝐶𝑎2+/𝑎𝐻+ 2 in the aqueous phase. At this pressure 426 and temperature, graphite cannot be stable when the aqueous fluid has a log(𝑎𝐶𝑎2+ /𝑎𝐻+ 2) value 427 less than 9.50. In the run shown in Fig. 5A, the value of log(𝑎𝐶𝑎2+ /𝑎𝐻+ 2) changed from an initial 428 value of 9.29 to a final value of 9.46. Fe-rich olivine(ss) with XFayalite 0.29 formed near the endpoint 429 and increased rapidly to 3.8 moles before hydrocarbons appeared. 430 The model at 1.5 GPa and 400 °C (Fig. 5B, Table S-2) was similar to the standard model 431 at 2.0 GPa and 400 °C in terms of the mineral sequence, the relative amounts of minerals, and the 432 amount of 𝐻2 reactant. However, the model at 2.0 GPa and 450 °C (Fig. 5C, Table S-3) showed 433 the same mineral sequence as the standard model until magnetite was totally consumed and then 434 olivine(ss) formed before the formation of hydrocarbon fluids. The olivine was Fe-rich (XFayalite 435 0.26), representing a metasomatic composition. It appeared that the breakdown of magnetite 436 caused by the addition of 𝐻2 provided 𝐹𝑒2+ that stabilized olivine. If more 𝐻2 was added, olivine 437 became unstable and was reduced to metallic iron. The amount of 𝐻2 (53.9 moles) used here 438 represents the value when 1.0 mole of hydrocarbon formed co-existing with graphite. Graphite 439 was completely destroyed for values of 𝐻2 equal to or more than 66.5 moles. 440 Interestingly, our model at 2.0 GPa and 500 °C (Fig. 5D, Table S-4) contained olivine with 441 antigorite throughout the reaction progress. As magnetite started to decrease sooner in this model, 442 the formation of olivine(ss) was even more strongly favored, and it became the most abundant 443 mineral quickly. When magnetite was destroyed, the iron content of the olivine reached a peak at 444 Fa 21, but then the rate of olivine increase slowed. Forsterite started to increase and finally reached 445 20 the upper mantle composition (Fo 93). If more 𝐻2 was added, even up to 90.0 moles, no metallic 446 iron formed and the hydrocarbon fluids ended up very 𝐻2-rich. Calcite(ss) was more favored than 447 aragonite at this condition and was reduced to form graphite and then hydrocarbon fluids. Graphite 448 formed only slightly before brucite. 449 In order to investigate the effect of magnetite destruction on the formation of olivine(ss), 450 we tested models without magnetite as a reactant. At 2.0 GPa and 450 °C, without reactant 451 magnetite in the initial rock, we found that only a very small amount of magnetite formed and then 452 disappeared during the run (Fig. 5E). The log number of moles of magnetite was -5.7 to -5.0 during 453 𝑙𝑜𝑔 𝜉 from -3.8 to -2.6. This small amount of magnetite simply reflected the (low) amount of Fe 454 in the initial fluid. No olivine formed. However, for the model at 2.0 GPa and 500 °C also without 455 magnetite, a very small and transient amount of olivine(ss) appeared (Fig. 5F), but at a much later 456 stage of reaction progress than in Fig. 5D at the same pressure and temperature. Only 0.056 moles 457 of olivine(ss) formed from 𝑙𝑜𝑔 𝜉 at 0.20 - 0.28 and then disappeared. No extra olivine(ss) formed 458 even if more 𝐻2 was added. The excess 𝐻2 stayed in the hydrocarbon fluids at 2.0 GPa and 500 °C 459 and the hydrocarbon fluids became 𝐻2-rich. Clearly, the absence of magnetite as a reactant had a 460 strong effect in inhibiting olivine(ss) formation at both 450 and 500 °C. We note that in the natural 461 samples, no preserved olivine was observed. The reason for this discrepancy may lie in the highly 462 heterogeneous nature of the Lanzo carbonated serpentinite or to retrograde hydration. If 𝐻2 fluid 463 pathways did not encounter magnetite, or the amount of magnetite encountered was very low, our 464 models show that olivine would not be expected to form to a significant extent. 465 Hydrocarbon fluids formed at the end of the reactions at each pressure and temperature 466 condition are presented in Figs. 5A - F. The final amounts and compositions of the hydrocarbon 467 fluids can be seen in Fig. 6 over the range of 1.0 - 2.0 GPa and 350 - 500 °C. At the higher pressures 468 21 and lower temperatures, if olivine(ss) did not form, hydrocarbon fluid formation was favored (Fig. 469 6A). The reason is simply that the saturation activity of 𝐶𝐻4,𝑎𝑞 was smaller at higher pressure and 470 lower temperature. In models without magnetite, more hydrocarbons formed, and the degree of 471 increase is greater at higher temperature. Except for the models at 2.0 GPa, 450 °C and 500 °C, 472 the amounts of 𝐻2 were about 66.0 moles. If the saturation activity of 𝐶𝐻4,𝑎𝑞 0 were smaller (i.e. the 473 solubility was lower), more 𝐶𝐻4,𝑓 could equilibrate in hydrocarbons. 474 The fluid compositions shown in Fig. 6B indicate that 𝐶𝐻4,𝑓 was the most abundant 475 endmember of the immiscible fluids over the temperature range considered. Except at 2.0 GPa and 476 500 °C, the hydrocarbon was almost pure 𝐶𝐻4,𝑓 with a mole fraction larger than 0.90. At 2.0 GPa, 477 from 450 °C to 500 °C, the mole fraction of 𝐶𝐻4,𝑓 dropped from 0.99 to 0.65 as the 𝐻2,𝑓 478 component increased up to 0.35. However, other hydrocarbons were negligible. At 1.0 GPa, the 479 mole fraction of 𝐻2,𝑓 was much greater than at higher pressures at 400 °C. No significant effect on 480 the composition of fluids by pressure was observed. Overall, the fluids were methane-rich without 481 olivine. If more initial 𝐻2 were added, the curves would move towards more 𝐻2-rich compositions. 482 After all the carbon was reduced by the reactant 𝐻2, the 𝐻2,𝑓 became unreactive and built up as a 483 component in the hydrocarbon fluid. 484 The final 𝑙𝑜𝑔𝑓𝑂2 at each condition with an 𝐹/𝑅 equal to 0.1 is given relative to the QFM 485 buffer in Fig 7A. The highest 𝑙𝑜𝑔𝑓𝑂2 was at 2.0 GPa and 450 °C because hydrocarbon fluids 486 formed coexisting with graphite with the lowest initial number of 𝐻2 moles. The 𝑙𝑜𝑔𝑓𝑂2 at 400 °C 487 of both 1.5 and 2.0 GPa were very close, as were the other results for minerals, aqueous species, 488 and hydrocarbon compositions at these conditions. At 2.0 GPa and 350 °C, the 𝑙𝑜𝑔𝑓𝑂2 was lower 489 probably because olivine(ss) was not favored at low temperature and only formed at temperatures 490 28 We found the following principal results from this modeling study: 624  Chemical mass transfer models predicted minerals and hydrocarbon fluids consistent with 625 field and laboratory observations in Vitale Brovarone et al. (2017) and Giuntoli et al. 626 (2020): 627 a) Serpentinite (antigorite, magnetite, and chlorite) and aragonite were destroyed. 628 b) Brucite, clinopyroxene(ss), graphite, and immiscible hydrocarbon fluids were formed at 629 1.5 and 2.0 GPa and 400 - 500 °C. 630 c) For high initial carbonate/serpentinite ratios, Ca-Fe-rich garnet was formed at 400°C and 631 2.0 GPa. 632 d) Methane was the main constituent of the immiscible hydrocarbon fluids and also reached 633 molal concentrations in the coexisting aqueous fluids. 634  As an example, the reaction progress during our standard run at 2.0 GPa and 400 °C with 635 𝐹/𝑅 mass ratio of 0.10 revealed the sequence of mineral formation, the number of moles 636 and volumes of each mineral, the aqueous fluid composition and speciation, and the 637 evolution of the 𝑙𝑜𝑔𝑓𝑂2 and 𝑝𝐻. During the reactions, aragonite was reduced by 𝐻2 to form 638 graphite and then graphite was reduced to hydrocarbon fluid (almost pure 𝐶𝐻4,𝑓) associated 639 with an almost continuous drop of 𝑙𝑜𝑔𝑓𝑂2. 640  The reaction of 𝐻2 with carbonated serpentinite generated significant amounts of 𝐻2𝑂. 641  Lower 𝐹/𝑅 (aqueous fluid/rock) ratios imply more 𝐻2 fluids, which resulted in greater 642 amounts of 𝐻2𝑂 and hydrocarbon fluids formed. 643  At 1.0 GPa and 400 °C, graphite was not stable due to the log(𝑎𝐶𝑎2+ /𝑎𝐻+ 2) of the system 644 being too low. 645 29  Even small amounts of magnetite in the initial rock caused olivine(ss) to appear before 646 hydrocarbon formation in models at 1.0 GPa and 400 °C, 2.0 GPa and 450 °C, and 2.0 GPa 647 and 500 °C. Olivine was not stable if the reactant carbonated serpentinite did not contain 648 magnetite. 649  Carbon and hydrogen budgets trace the transfer and redistribution of these elements during 650 the redox reactions. 651  Overall, the combined results of the modeling study and the natural samples strongly 652 support the concept that 𝐶𝐻4-rich immiscible hydrocarbon fluids have formed at eclogite 653 facies conditions in subduction zones. How widespread this phenomenon is (at the present 654 and in the geologic past) remains to be seen. 655 656 Data Availability: 657 The files of the model results are available on Johns Hopkins Research Data Repository 658 using the DOI given below. The data can be referred to using the citation below. 659 Huang, Jingyi; Sverjensky, Dimitri A.; Daniel, Isabelle; Brovarone, Alberto Vitale, 2022, 660 "Data associated with: Reaction path model of the formation of abiotic immiscible hydrocarbon 661 fluids in subducted carbonated serpentinites, Lanzo Massif (Western Italian Alps)", 662 https://doi.org/10.7281/T1/NLHSKE, Johns Hopkins Research Data Repository. 663 Acknowledgements: 664 This research was supported by a Johns Hopkins Graduate Fellowship, the NSF Grant 665 #2032039, and DOE Grant #DE-SC0019830. This work is part of a project that has received 666 30 funding from the European Research Council (ERC) under the European Union’s Horizon 2020 667 research and innovation programme (Grant agreement No. 864045). This work also received 668 support by the Richard Lounsbery foundation. We would like to thank Daniel Viete for reading a 669 version of this manuscript. We gratefully acknowledge the help and support of the Johns Hopkins 670 University. We thank Fang Huang and Zhigang Zhang for discussions. 671 Appendix A. Supplementary Material 672 The supplementary material contains the description of model files and tables about the 673 summary of the initial and final fluid compositions and mineral assemblages. The files contain 674 model results of 𝐻2 fluid reacting with carbonated serpentinites with 15 vol% of aragonite and 85 675 vol% of serpentinite at 2.0 GPa and 400 °C, 1.0 GPa and 400 °C, 1.5 GPa and 400 °C, 2.0 GPa 676 and 450 °C, and 2.0 GPa and 500 °C; with 30 vol% of aragonite and 70 vol% of serpentinite at 677 400°C and 2.0 GPa; and with 50 vol% of aragonite and 50 vol% of serpentinite at 400°C and 2.0 678 GPa. 679 680 31 References: 681 Alt, J.C., Schwarzenbach, E.M., Früh-Green, G.L., Shanks, W.C., Bernasconi, S.M., Garrido, 682 C.J., Crispini, L., Gaggero, L., Padrón-Navarta, J.A., and Marchesi, C., 2013. 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(A) 𝐶𝐻4, (B) 𝐶2𝐻6, (C) 𝐶𝑂2, 5 and (D) 𝐻2. 6 7 -5 -4 -3 -2 -1 0 1 2 3 300 400 500 600 700 0.5 GPa 1.0 GPa 1.5 GPa 2.0 GPa 2.5 GPa 3.0 GPa 3.5 GPa 4.0 GPa 4.5 GPa 5.0 GPa log K T (°C) CH4,f = CH40,aq -5 -4 -3 -2 -1 0 1 2 3 300 400 500 600 700 0.5 GPa 1.0 GPa 1.5 GPa 2.0 GPa 2.5 GPa 3.0 GPa 3.5 GPa 4.0 GPa 4.5 GPa 5.0 GPa log K T (°C) C2H6,f = C2H60,aq -1 0 1 2 3 300 400 500 600 700 0.5 GPa 1.0 GPa 1.5 GPa 2.0 GPa 2.5 GPa 3.0 GPa 3.5 GPa 4.0 GPa 4.5 GPa 5.0 GPa log K T (°C) CO2,f = CO20,aq -3 -2 -1 0 1 2 300 400 500 600 700 0.5 GPa 1.0 GPa 1.5 GPa 2.0 GPa 2.5 GPa 3.0 GPa 3.5 GPa 4.0 GPa 4.5 GPa 5.0 GPa log K T (°C) H2,f = H20,aq Figure Click here to access/download;Figure;Figures_AVB.docx 2 A. B. 8 9 C. D. 10 11 Figure 2. 𝐿𝑜𝑔𝑓 𝑂2 vs. 𝑙𝑜𝑔𝑎𝐶𝐻4,𝑎𝑞 0 diagrams of the stability field among graphite, 𝐶𝐻4,𝑎𝑞 0 , and 12 𝐶𝐻4,𝑓 at (A) 1.0 GPa & 400 °C, (B) 1.5 GPa & 400 °C, (C) 2.0 GPa & 400 °C, and (D) 2.0 GPa 13 & 500 °C. 14 15 -40 -35 -30 -25 -20 -15 -0.5 0 0.5 1 1.5 log fO2 log a CH40,aq CH4,f Graphite QFM Magnetite/a-Fe H2O/H2(f) a=1.0 H2O/H2(f) a=0.1 1.0 GPa & 400 °C CH40,aq -40 -35 -30 -25 -20 -15 -0.5 0 0.5 1 1.5 log fO2 log a CH40,aq 1.5 GPa & 400 °C CH4,f Graphite CH40,aq QFM Magnetite/a-Fe H2O/H2(f) a=1.0 H2O/H2(f) a=0.1 -40 -35 -30 -25 -20 -15 -0.5 0 0.5 1 1.5 log fO2 log a CH40,aq CH4,f Graphite QFM Magnetite/a-Fe H2O/H2(f) a=1.0 H2O/H2(f) a=0.1 2.0 GPa & 400 °C CH40,aq -40 -35 -30 -25 -20 -15 -0.5 0 0.5 1 1.5 log fO2 log a CH40,aq CH4,f Graphite QFM Magnetite/a-Fe H2O/H2(f) a=1.0 H2O/H2(f) a=0.1 2.0 GPa & 500 °C CH40,aq 3 A. B. 16 C. D. 17 E. 18 19 Figure 3. Reaction path model of the reduction of carbonated serpentinite by 𝐻2 at 2.0 GPa and 20 400.0 °C with 𝐹/𝑅 equal to 0.1 (by weight) as a function of the logarithm of the reaction progress 21 (𝑙𝑜𝑔 𝜉): (A) minerals and hydrocarbon fluid, (B) volumes of minerals, (C) dissolved elements, (D) 22 𝑙𝑜𝑔𝑓 𝑂2 and 𝑝𝐻, and (E) aqueous species. 23 -4 -3 -2 -1 0 1 2 -3 -2 -1 0 1 2 log moles log ξ chlorite (SS) clinopyroxene(SS) HC(LL) graphite aragonite brucite antigorite magnetite F/R = 0.1 0.1 1 10 100 1000 10000 -3 -2 -1 0 1 2 Volume (cm3) log ξ brucite (product) antigorite (reactant) clinopyroxene(SS) (product) graphite (product) magnetite (reactant) chlorite(SS) (reactant) aragonite (reactant) F/R = 0.1 -5 -4 -3 -2 -1 0 -3 -2 -1 0 1 2 log molality of dissolved elements log ξ Al C Fe Mg Si Cl Ca Na F/R = 0.1 -30.5 -30 -29.5 -29 -28.5 -28 -27.5 -27 5.6 5.65 5.7 5.75 5.8 5.85 -3 -2 -1 0 1 2 log fO2 pH log ξ log fO2 pH F/R = 0.1 -6 -5 -4 -3 -2 -1 0 -3 -2 -1 0 1 2 log molality of aqueous species log ξ CH4,aq H2,aq propane,aq CO32H2CO3,aq ethane,aq HCO3isobutane,aq F/R = 0.1