Silica controls on hydration kinetics during serpentinization of olivine: Insights from hydrothermal experiments and a reactive transport model

Journal Pre-proofs Silica controls on hydration kinetics during serpentinization of olivine: Insights from hydrothermal experiments and a reactive transport model Ryosuke Oyanagi, Atsushi Okamoto, Noriyoshi Tsuchiya PII: DOI: Reference:

S0016-7037(19)30725-2 https://doi.org/10.1016/j.gca.2019.11.017 GCA 11529

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Geochimica et Cosmochimica Acta

Received Date: Revised Date: Accepted Date:

5 July 2019 9 November 2019 12 November 2019

Please cite this article as: Oyanagi, R., Okamoto, A., Tsuchiya, N., Silica controls on hydration kinetics during serpentinization of olivine: Insights from hydrothermal experiments and a reactive transport model, Geochimica et Cosmochimica Acta (2019), doi: https://doi.org/10.1016/j.gca.2019.11.017

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Silica controls on hydration kinetics during serpentinization of olivine: Insights from hydrothermal experiments and a reactive transport model Ryosuke Oyanagia,b,*, Atsushi Okamotoa, Noriyoshi Tsuchiyaa a

Department of Environmental Studies for Advanced Society, Graduate School of Environmental Studies, Tohoku University, Sendai 980-8579, Japan

b

Solid Earth Geochemistry Research Group, Volcanoes and Earth's interior Research

Center, Research Institute for Marine Geodynamics, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Yokosuka 237-0061, Japan *Corresponding author: Tel.: +81-46-867-9667 E-mail address: [email protected] E-mail address Atsushi Okamoto [email protected] Noriyoshi Tsuchiya [email protected]

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Abstract Silica activity in fluids is a key factor that controls reaction pathways during the hydrothermal alteration of olivine in the oceanic lithosphere. In this study, we conducted hydrothermal experiments (300°C, 8.58 MPa) on the olivine (Ol)–quartz (Qtz)–H2O system to understand the coupling between silica transport and olivine alteration. Mineral powders were reacted with 0.5 mol kg–1 NaCl solution in a tube-intube type vessel, and the spatial distribution of reactant and product minerals was investigated after the experiments. Alteration zones formed in the Ol-hosted region after 2055 hours of reaction. With increasing distance from the Ol–Qtz boundary these were: talc; talc + serpentine; and serpentine + magnetite + brucite. Talc formed 0–2.3 mm from the Ol–Qtz boundary in the Ol-hosted region, and brucite formed >5 mm from the Ol–Qtz boundary in the Ol-hosted region. No secondary minerals formed in the Qtzhosted region. The observed mineral distribution was modeled using a reactive transport model that simulated the coupling between SiO2(aq) diffusion and seven silicacontrolling reactions. An inverse modeling framework, which combines a reactive transport model with an exchange Monte Carlo method, was used to parameterize the diffusivity of SiO2(aq) and the rate constants of the seven overall reactions. Our model shows that the rate of hydration in the serpentine + metastable talc zone with intermediate silica activity was higher than in the serpentine, serpentine + brucite, and talc zones, suggesting that the silica activity of the reacting fluid has a significant control on the rate of hydrothermal alteration of mantle peridotite by crustal fluids. Moreover, the model suggests that the rate-control process changed from being surfaceto transport-controlled over the course of the experiments. We suggest that dynamic changes in rate control process are important contributors to the formation of metasomatic zoning and heterogeneous hydration patterns within the oceanic lithosphere.

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1. INTRODUCTION Hydration of the oceanic lithospheric peridotite occurs at slow-spreading ridges (Bach et al., 2004, 2006; Beard et al., 2009; Klein et al., 2009; Früh-Green et al., 2018), in faults as the slab bends prior to subduction (Ranero et al., 2003; Shillington et al., 2015), and strongly controls rheology (Escartín et al., 2003; Hirauchi et al., 2016) and microbial habitability of the oceanic lithosphere (Sleep et al., 2004; Boetius, 2005). The amounts and distribution of serpentinized peridotite in the oceanic lithosphere are also critical to constraining the global cycles of water and other elements (Deschamps et al., 2013), volcanic and seismic activity at subduction zones (Boudier et al., 2010). Despite the influence of serpentinized peridotite on various processes from the oceanic lithosphere to subduction zone, it is difficult to understand the extent of serpentinization within the oceanic lithosphere, because serpentinization is a complicated process involving surface reactions, mass transfer, and deformation. Serpentinization reactions via the interaction of ultramafic rocks and fluids have been extensively investigated by hydrothermal experiments. The most-studied reaction is the hydration of olivine, simply written in the MgO–SiO2–H2O system as follows: 2 Mg2SiO4 + 3 H2O → Mg3Si2O5(OH)4 + Mg(OH)2. Olivine

Serpentine

(1)

Brucite

The reaction kinetics of this “isochemical” serpentinization have been estimated experimentally (e.g., Martin and Fyfe, 1970; Wegner and Ernst, 1983; Macdonald and Fyfe, 1985; Okamoto et al., 2011; Lafay et al., 2012; Malvoisin et al., 2012; McCollom et al., 2016; Lamadrid et al., 2017). However, reaction (1) is idealized and does not involve mass transport, except for H2O. In the oceanic lithosphere, silica-rich fluids are thought to infiltrate peridotites at mid-ocean ridges and at the outer-rise fault, where hydrothermal fluids pass through crustal to mantle lithologies (Bach et al., 2013; Seyfried et al., 2015; Klein et al., 2017). An input of silica significantly affects the reaction paths during the hydrothermal alteration of peridotites, which cause talc formation (Escartín et al., 2003; Boschi et al., 2006; Bonnemains et al., 2017; FrühGreen et al., 2018; Rouméjon et al., 2019) and brucite breakdown (Klein et al., 2009; Tutolo et al., 2018) in hydrated peridotite, and controls the magnetite formation and hydrogen generation during serpentinization (Frost and Beard, 2007; Beard et al., 2009; Syverson et al., 2017; Oyanagi et al., 2018a). Therefore, a realistic understanding of the

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extent and rate of serpentinization in the oceanic lithosphere requires the effect of mass transport, especially of silica, during serpentinization. Despite the large number of experimental studies on the rate of serpentinization, few have considered the effects of mass transport on the kinetics of hydrothermal peridotite alteration. Andreani et al. (2012) and Huang et al. (2017) suggested that the presence of elements such as Al and Cr accelerates the hydrothermal alteration of olivine. However, the solution chemistry was not taken into consideration in the rate equations derived in these studies, so their reaction rates cannot be extrapolated to systems different from those of their experiments. A small number of studies have investigated the effect of solution chemistry on kinetic rate laws during serpentinization. Ogasawara et al. (2013) conducted hydrothermal experiments on the Olivine (Ol)– orthopyroxene (Opx)–H2O system at 250°C, and found that the rate of olivine serpentinization was increased by the elevated SiO2(aq) produced by serpentinization of Opx. They proposed a serpentinization rate law as a function of silica concentration in the solution. However, in their experiments, the reaction product was serpentine without brucite or talc, so the relationships between fluid silica activity and reaction kinetics are still unclear in cases where the hydrothermal alteration of olivine involving the dissolution-precipitation reaction of talc, serpentine, and brucite occur. In this study, we performed hydrothermal experiments on the Ol– quartz (Qtz)– H2O system. Olivine powder in contact with Qtz powder was reacted with an aqueous solution containing 0.5 mol kg−1 of NaCl. We used a tube-tube experimental apparatus similar to that used by Oyanagi et al. (2015), who have performed experiments of Ol– Qtz–H2O system to investigate hydrothermal alteration of olivine involving the dissolution-precipitation reaction of smectite, serpentine, and brucite. In contrast to Oyanagi et al. (2015) who used a 1 mol kg−1 NaOH solution to impose a highly alkaline pH, in the present study the pH was controlled by the solid reactants as expected in natural systems. Qtz was used to provide a source of aqueous silica because: (1) SiO2 is the main constituent of the crust; (2) Qtz dissolves to provide aqueous SiO2 faster than other minerals (e.g., pyroxenes); (3) the presence of Qtz buffers silica activity to values higher than that of talc–serpentine equilibrium; and (4) silica is the only component of quartz, so the effects of silica on hydrothermal alteration are easily recognized. Tube-intube experiments and detailed image analysis were used to reveal the characteristic spatial variation of minerals and porosity produced by hydrothermal alteration and silica 4

transport around an Ol-Qtz boundary. We modeled silica diffusion and olivine hydrothermal alteration using a reactive transport model, and constrained multiple kinetic parameters (e.g., reaction rate constants and the aqueous diffusion coefficient), using the results of the spatial analysis. The significance of aqueous silica for reaction pathways and the overall hydration rate of the oceanic lithosphere is discussed, based on the calculated kinetic parameters. 2. EXPERIMENTAL METHODS AND ANALYTICAL TECHNIQUES 2.1. Hydrothermal experiments We conducted batch-type hydrothermal experiments in the Ol–Qtz–H2O system at 300°C at a vapor-saturated pressure (Psat) of 8.58 MPa. (Fig. EA1a, b). Natural olivine from China and quartz sand were crushed, wet sieved to a size of 25–53 μm, and repeatedly washed with deionized water. The olivine had an XMg [Mg/(Mg + ΣFe)] value of 0.91 (Table 1). Tube-in-tube vessels were used for the experiments; these consisted of a main vessel (Fig. EA1a) and inner tubes (Fig. EA1b) made of grade-two titanium. All titanium surfaces available for contact with the solution were oxidized in air at 400°C prior to the experiments. Four inner tubes were placed in the main vessel (23 cm3), with 12 mL of 0.5 mol NaCl kg–1 solution (Fig. EA1a). Nitrogen gas was bubbled through the NaCl solution for at least 3 h before it was added to the autoclaves. Each inner tube contained 50 mg of Qtz powder (25–53 μm) at the bottom and 170 mg of Ol powder (25–53 μm) on top of the Qtz layer (Fig. EA1b). The bases of the inner tubes were sealed and the tops were left open. The fluid:rock mass ratio was ~14. The Qtz and Ol layers were ~10 mm and ~30 mm thick, respectively (Fig. EA1b). The porosity prior to the experiments was ~37%, based on the initial amount of olivine powder and the volume of the inner tubes. The main vessel was sealed under an N2 atmosphere to minimize the effects of O2 and CO2 contamination (Fig. EA1a). The main vessel was placed in an oven and maintained at 300°C. Experiments were performed for 168, 336, 566, 2055, 3258, 6000, and 8055 h. 2.2. Solid sample analysis After each experiment, the reaction vessel was cooled to room temperature (~25°C) within 1 h and the solutions and the four inner tubes that contained the solid materials (products + unreacted reactants) were removed from the vessel. The solid 5

material was dried for >24 h at 90°C inside the four inner tubes. One of the inner tubes was cut parallel to its long axis, encased in epoxy resin, and polished to provide a polished section. The chemical compositions of the minerals in the polished thin section were analyzed by an electron probe micro-analyzer (EPMA; JEOL JXA-8200) at Tohoku University, Japan, with an accelerating voltage of 15 kV, a beam current of 12 nA, and beam diameter of 1–2 µm. The textures of primary- and secondary-minerals in the polished thin section were investigated with a field-emission scanning electron microscope (FESEM; JEOL JSM-7001F) at Tohoku University. The serpentine mineral species were identified using micro-Raman spectroscopy (HORIBA XploRA PLUS equipped with a 532 nm laser and a 2400 groove mm–1 grating) at Tohoku University. A second inner tube was used for thermogravimetry (TG; Rigaku Thermo Plus EVOII TG8120) at Tohoku University to analyze the H2O content of the solid samples. The inner tube was cut manually into eight segments of ~5 mm length. Segments 1 and 2 represent the original Qtz layer (Qtz-hosted region) and segments 3–8 represent the original Ol layer (Ol-hosted region). During the TG measurements, temperatures were increased from room temperature to 1100°C at 10°C min–1. The loss on ignition (LOI) was calculated for each segment, based on measurements in the temperature range of 120–1100°C. Measurements below 120°C were omitted to exclude weight loss associated with molecular water within the solid samples. Backscattered-electron (BSE) images (100 × 385 µm) of the polished section were used to determine the proportion, by area, of olivine (ArOl), porosity (Arφ), magnetite (ArMag), and the total area of hydrous secondary minerals (ArTlc + Srp + Brc), as a function of the distance from the Ol–Qtz boundary. The total area of secondary minerals was used because it was difficult to identify the secondary minerals (talc (Tlc), serpentine (Srp), and brucite (Brc)) with confidence because of their similar brightness in the BSE images. The resolution of the images used in the analyses was ~1 μm2 per pixel. 2.3. Solution sample analysis The pH of the solution at room temperature was measured immediately after sampling and exposure to atmospheric conditions using a HORIBA 9618S-10D Micro ToupH electrode. Then, the solutions were diluted with 5% nitric acid and the concentrations of Si, Mg, Fe, and Na measured using inductively coupled plasma– 6

optical emission spectrometry (ICP–OES; ThermoFisher, iCE3500) at Tohoku University. The solution chemistry results are summarized in Table EA1 in the Electronic Annex. 3. RESULTS OF HYDROTHERMAL EXPERIMENTS 3.1. Reaction products in the olivine-hosted regions Optical photographs of thin sections showing products of the experiments with run-times of 566, 2055, 3258, 6000, and 8055 h were inspected (Fig. 1a). The position of an observation within the inner tube is described relative to the Ol–Qtz boundary (x = 0); the Qtz-hosted region was from x = –10 to 0 mm, and the Ol-hosted region was from x = 0 to ~30 mm (Fig. 1a). The entire Qtz-hosted region was white to gray in color from 566 h to 8055 h (Fig. 1a). In contrast, the color of the Ol-hosted region varied as a function of the distance from the Ol–Qtz boundary. For example, at 2055 h, the Ol-hosted region was white at x = 0–1.5 mm, yellow at x = 1.5–2.0 mm, dark green at x = 2.0–5.0 mm, and light green at x > ~5.0 mm (Fig. 1a). The white area near the Ol–Qtz boundary in the Ol-hosted region was largest at 566 h (x = 0–7 mm; Fig. 1a), decreased at 2055 h (x = 0–2 mm; Fig. 1a), increased at 3258 h (x = 0–3 mm), remained constant to 6000 h (x = 0–3 mm), and decreased at 8055 h (x = 0–2 mm); the appearance of a gray–white zone at x = 3–5 mm was noted in the 8055 h experiment. No new product minerals were observed in the Qtz-hosted region after the experiments (Fig. 1b), but talc, serpentine, magnetite, and brucite formed in the Olhosted region. The results of Raman spectroscopy indicate that the serpentine mineral is lizardite. Chrysotile, rather than lizardite, is reported in some previous studies. This is probably attributed to the highly alkaline solutions utilized in the experiments (Yada and Iishi, 1977; Lafay et al., 2012), and solutions that were highly supersaturated with serpentine (Normand et al., 2002). However, the factors that determine the stable serpentine polymorph are poorly known. The chemical compositions of the reaction products and the SEM observations document systematic changes in the reaction product mineralogy with distance from the Ol–Qtz boundary, with zones of talc, talc + serpentine, and serpentine ± magnetite ± brucite. In the talc zone, the atomic (Mg + Fe)/Si ratio in the product is ~0.75 (Fig. 2a), consistent with the composition of talc (Mg3Si4O10(OH)2). Talc occurs as fiber-shaped 7

aggregates that surround the olivine grains (Fig. 1c). Olivine grains show irregular surfaces rather than rounded shapes (Fig. 1c). The XMg value of talc is 0.91, which is similar to XMg of olivine (Table 1). The size of the talc zone was 0–2.0 mm at 566 h, 0– 1.1 mm at 2055 h, 0–2.1 mm at 3258 h, and 0–1.8 mm at 6000 h. In the talc + serpentine zone (x = 1.5–2.0 mm at 2055 h), the chemical composition of the product minerals is a mixture between the compositions of talc ((Mg + Fe)/Si = 0.75; Fig. 2a) and serpentine ((Mg + Fe)/Si = 1.50). This suggests the presence of aggregates of talc and serpentine with grain sizes less than the EPMA beam spot size. The talc and serpentine in this zone cannot be distinguished in the SEM images. The end of the talc + serpentine zone, (i.e., the point of talc disappearance) was at 6.0 mm at 566 h, 2.3 mm at 2055 h, 3.8 mm at 3258 h, 3.9 mm at 6000 h, and 2.2 mm at 8055 h, based on (Mg + Fe)/Si atomic ratios (Fig. 2b). With increasing x within the serpentine ± magnetite ± brucite zone, the mineralogy changes from serpentine + magnetite to serpentine + magnetite + brucite (Fig. 1d, e). The length of the fibrous serpentine grains is <10 μm, and the size of the planar brucite and rounded magnetite grains are up to ~100 and ~10 μm, respectively (Fig. 1d, e). Magnetite appears at x = 6.5 mm at 566 h, 2.2 mm at 2055 h, 3.8 mm at 3258 h, 3.8 mm at 6000 h, and 2.3 mm at 8055 h (Fig. 1b); these x values are similar to those of talc disappearance (Fig. 2b). Brucite appearance, defined as the location where discrete brucite grains were first observed, is slightly offset from talc disappearance (x = 5.0 mm at 2055 h, 5.8 mm at 3258 h, 7.8 mm at 6000 h, and 4.5 mm at 8055 h) (Fig. 2b). We were unable to identify the brucite appearance front at 566 h because no brucite formed in this experiment. The migration of these fronts is discussed in detail in section 6.1. 3.2. Extent of hydration evaluated from the thermogravimetry results The total H2O content of the solid was measured for the eight segments, and plotted against temperature (Fig. 3a). The total H2O content of the Qtz-hosted region was below 2 wt.% for all experiments. In contrast, the total H2O content of the Olhosted region increased with time for nearly all of the segments; the average weight loss of segments 3–8 increased from ~3 wt.% at 566 h to ‫׽‬12–14 wt.% at 6000 h (Fig. 3b).

At 2055 h, the H2O content of the segment closest to the Ol–Qtz boundary (6.0 wt.%;

segment 3) was higher than that of the other segments (Fig. 3b). After 3258 h, the total 8

H2O content of segment 3 was lower than that of segments 4–8 (Fig. 3b). At 6000 h, the difference in the H2O content between segments 3 and 4–8 was large (Fig. 3a), and the H2O content in segment 3 was less than that in segment 3 at 3258 h. 3.3. Image analysis results The values of ArTlc + Srp + Brc, ArOl, and Arφ after 2055 h were plotted as a function of the distance from the Ol–Qtz boundary (Fig. 4a). The value of ArTlc + Srp + Brc varied with x; it decreased from 60% to 45% as x varied from 0 to 1.8 mm, increased from 45% to 85% as x increased from 1.8 to 2.4 mm, decreased from 85% to 40% as x increased from 2.4 to 4.2 mm, and finally stabilized at 40% as x increased from 4.2 to 10 mm (Fig. 4a). At 2055 h, the ArOl values were low at x values between 1.8 and 4.0 mm (7%–27%) relative to ArOl values from 0–2 mm (~35%) and 5–10 mm (~36%) (Fig. 4a). The average value of Arφ for the whole inner tube was ~16% (Fig. 4b). The porosities at x = 0–1.0 mm (~7%) and x = 2.5 mm (~5%) were lower than those elsewhere (Arφ = 20%–26% at x > 3.2 mm; Fig. 5a). A small amount of magnetite (average = ~0.5%) was observed at x > 2.3 mm (Fig. 4b). 4. ESTIMATION OF KINETIC PARAMETERS USING AN INVERSION ANALYSIS METHOD 4.1. Description of dataset The amount of each mineral in a reference bulk volume consisting of the volume of the solids plus the volume of the pores, in the unit of mol cm–3 bulk, was calculated after 2055 h of reaction at each position in the inner tube, based on the ArOl and ArTlc + Srp + Brc

values. Initially, we assumed that the proportion of the area occupied by each

phase (Ari; Fig. 4a and b) was the same as the volume proportion (Vi). We calculated theoretical TG values, based on the measured Vi values, to check the consistency between the BSE observations and the TG values. However, the TG values calculated were higher than the measured values. We attribute the differences to: (1) small differences in signal amongst the secondary phases in the BSE images, which caused uncertainties in the calculated mineral modes; and (2) the very small crystals and porous aggregates of serpentine and talc. These factors mean that it is difficult to estimate the accurate precise proportions of secondary minerals from the image analysis alone. While the spatial resolution of the image analyses is superior to that of the TG analyses, 9

the latter provide the most accurate values of Vi. To optimize the use of the two data sources, the total volumes of secondary minerals (VTlc+Srp+Brc) and porosity were taken from the image analysis and normalized such that they were consistent with the measured TG values. This method is similar to the method described by Oyanagi et al. (2015), and is described in detail in the Electronic Annex. The amount of olivine decreased during the experiment and the average mode was ~7.0 mmol cm–3 bulk (Fig. 5a). The amount of olivine at x = 2.4–3.1 mm was lower (~2 mmol cm–3 bulk; Fig. 5a) than in other segments of the inner tube (e.g., x = 0–2.3 and 3.2–7 mm; Fig. 5a). There was a large amount of talc close to the Ol–Qtz boundary (~4.2 mmol cm–3 bulk at x = 0.1 mm), which decreased with increasing x to zero at x = 2.0 mm (Fig. 5b). There was no serpentine close to the Ol–Qtz boundary (x = 0–1.0 mm), but the serpentine mode increased to ~8.0 mmol cm–3 bulk at x = 2.5 mm (Fig. 5c). The amount of serpentine at x = 2.7–4.9 mm could not be estimated. The amount of serpentine at x > 5.0 mm was nearly constant at 3.5 mmol cm–3 bulk (Fig. 5c). There was no brucite close to the Ol–Qtz boundary (x = 0–2.7 mm), and the brucite mode increased with increasing x (e.g., ~2.2 mmol cm–3 bulk at x = 5.0–7.0 mm) (Fig. 5d). The amount of brucite could not be estimated at x = 2.7–4.9 mm. The average porosity was ~16% (Fig. 6e), and the porosity showed some spatial variability. Porosities close to the Ol–Qtz boundary were lower (~7% at x = 0–1.0 mm and ~5% at x = 2.5 mm) than the porosity in the other segments (20%–26% at x > 3.2 mm; Fig. 5e). 4.2. Simplified overall reaction Reaction in the Ol-hosted region was characterized by coupling between olivine dissolution and the precipitation of secondary talc, serpentine, and brucite. Representative reactions in the MgO–SiO2–H2O system can be written as, for example, Mg2SiO4 + 4 H+ ® 2 Mg2+ + SiO2(aq) + 2 H2O

(2)

(olivine dissolution), 3 Mg2+ + 2 SiO2(aq) + 5 H2O ® Mg3Si2O5(OH)4 + 6 H+ (serpentine precipitation), Mg2+ + 2 H2O ® Mg(OH)2 + 2 H+

(3) (4)

(brucite precipitation), and 3 Mg2+ + 4 SiO2(aq) + 4 H2O ® Mg3Si4O10(OH)2 + 6 H+

10

(5)

(talc precipitation). These reactions involve three aqueous species (SiO2(aq), Mg2+, and H+). We did not observe reaction products in the Qtz-hosted region (Fig. 1b), which indicates that the Mg2+ flux from the Ol-hosted region to the Qtz-hosted region was effectively zero. The mass-balance calculations show that changes in the Mg content were smaller than changes in the Si content during the first 2055 h of the experiment (Fig. 5f), which indicates that the concentration of aqueous silica was the most important control on the reactions. To quantify this control, we considered five idealized reactions constructed on the assumption that Mg was immobile (Table 2). We considered only the forward reactions involving olivine (R1 (talc after olivine), R2 (serpentine after olivine), and R3 (brucite after olivine)) because forsteritic olivine is not thermodynamically stable at the pressure–temperature (P–T) conditions of the experiment (Fig. 6b; Table 2; e.g., Klein et al., 2013). We considered the forward and backward directions of the reactions between serpentine and talc (R4+ and R4−), and brucite and serpentine (R5+ and R5-) (Fig. 6b; Table 2). 4.3. Development of the reactive transport model The following one-dimensional equation describes surface reactions and the diffusion of aqueous species (e.g., Lasaga, 1998): ሺ

ሻ

ൌ

൬

൰൅

chem ǡ

ሺ6ሻ

where Ci, and Rchem represent, the concentration of i (mol cm–3 solution), and the rate of gain or loss of chemical species i due to surface reactions (mol cm–3 solution s–1),

respectively. We assumed that pores are filled with solution. The porosity is represented by φ (cm3 solution cm–3 bulk), which is defined as the volume of solution in the reference bulk volume. The molecular diffusion coefficient of aqueous species i in solution is represented by Di (cm2 s–1). The m parameter is the cementation exponent, which represents the relationship between the effective diffusivity of ions in the rock and the porosity (Oelkers, 1997; Seigneur et al., 2019). The term Di φm is derived from the expression for effective diffusivity in a porous medium using Archie’s law (Archie, 1942). In heterogeneous water–rock systems, molal units (moles of solutes per solution mass) are commonly used to describe solution chemistry and reaction kinetics (Rimstidt, 2013). However, in reactive transport models the molar unit (moles of solutes 11

per solution volume) is traditionally used (Lichtner, 1985; Lichtner et al., 1986; Steefel and Lasaga, 1994; Oelkers, 1997; Seigneur et al., 2019). This is because: (1) Fick’s first law of diffusion uses molar concentrations (e.g., Cussler, 2009; Rimstidt, 2013); and (2) it is more convenient and practical to normalize the amount of solutes to the volume of the fluid-filled porosity, which is defined as the volume of pores normalized to the volume of rock. The first-order equations for the Ol-hosted region are as follows: chem

ൌ෍

SiO2 ሺaqሻ

ቆ1 െ

SiO2 ሺaqሻǡeq

ቇǡ

ሺ7ሻ

where kn, Ai, and CnSiO2(aq),eq are the reaction rate constant (mol SiO2(aq) cm–2 mineral s–1) for reaction n, the bulk surface area (cm2 mineral cm–3 bulk) of the rate-limiting mineral i, and the equilibrium silica concentration (mol SiO2(aq) cm–3 solution) for the overall reaction n, respectively (Table 2). The parameter Ai/φ (cm2 mineral cm–3 solution) is the surface-area-to-volume ratio (SA:V). The CnSiO2(aq),eq values for R1–R5 were plotted on an activity diagram (stars on Fig. 6a) and calculated as follows: (1) the equilibrium silica molalities (mol kg–1 solution) for the overall reactions R1–R5 were calculated

from log K values from SUPCRTBL (Zimmer et al., 2016), assuming that the activity of the water and minerals was one; and (2) the molal units were converted to molar units (mol cm–3 solution). The relationship between molal and molar units is not a simple function of the solution density, because the mass and volume of a solution change with concentration (Rimstidt, 2013). In this study, molarities were calculated by using the partial molar volume of SiO2(aq) (–9.1 cm3 mol–1; Walther and Helgeson, 1977) and the density of H2O at 300 °C and Psat (0.712 g cm–3; Zimmer et al., 2016). The bulk surface area of olivine was updated at each time step using a shrinking-sphere model (e.g., Lichtner, 1988; Navarre-Sitchler et al., 2011):

Ol  ൌ  Olǡ0 ൬

2 3

2 3

0

൰ ቆ

Ol Olǡ0

ቇ Ǥ

The bulk surface area of secondary mineral i was calculated from ൌ

ǡ0 ൬

2 3

ǡ0

൰ Ǥ

ሺ8ሻ ሺ9ሻ

where Ai,0 is the initial bulk surface area of mineral i (cm2 mineral cm–3 bulk), and the

parameters φ and φ0 are the instantaneous and initial porosity, respectively. The φi and φi,0 parameters represent the instantaneous and initial volume fractions of mineral i, 12

respectively. The φ0 and φOl,0 parameters were set to 0.37 and 0.63, respectively, based on the initial mass of olivine and the volume of the inner tube. The values of φSrp,0, φTlc,0, and φBrc,0 were set to 1.0 × 10–9, to simulate the presence of seed material for the secondary phases. Different models were used to represent the bulk surface area of the primary and secondary minerals; because it was necessary to simulate the reduction in the surface area of the primary mineral (olivine) in response to armoring by the secondary minerals (serpentine, brucite, and talc). The initial bulk surface area of the primary and secondary minerals was calculated from ǡ0

ǡ0

ൌ

ത

ሺ10ሻ

ǡ

where ܸത௜ (cm3 mol–1) is the molar volume (Holland and Powell, 2011), Si (cm2 g–1) is

the specific surface area, and Mi (g mol–1) is the molar weight of mineral i. The value of SOl (3.82 × 103 cm2 g–1) was obtained from the empirical relationship between the

Brunauer–Emmett–Teller (BET) specific surface area and grain size proposed by (geo)

Brantley and Mellott (2000). The geometric surface area of olivine (SOl ) is 4.88 × 102 cm2 g–1, based on the assumption that the grains were spherical. The surface roughness (geo)

factor (SOl/SOl ) of olivine is approximately 8, which is similar to previously reported values (White and Peterson, 1990; Brantley and Mellott, 2000; Rimstidt et al., 2012). The specific surface area of brucite (SBrc = 6.60 × 103 cm2 g–1) was taken from Tutolo et al. (2018). The specific surface areas of talc (STlc = 1.54 × 106 cm2 g–1) and serpentine (SSrp = 1.54 × 106 cm2 g–1) were calculated geometrically, assuming that the minerals were present as 10 μm-long fibers (Fig. 1c–e). The calculated values of SSrp and STlc are similar to the BET specific surface areas of synthetic serpentine and talc produced under hydrothermal conditions (1.85 × 106 cm2 g–1; Lafay et al., (2014), and 1.26–5.44 × 106 cm2 g–1; Chabrol et al., (2010), respectively). 1െ൫

The porosity was calculated from the sum of the mineral volume fractions (  ൌ Ol

൅

Tlc

൅

Srp

൅

Brc ൯)

and was updated at each time step. Combining the

previous equations, a reactive-diffusive transport model for the Ol-hosted region is as follows (Fig. 6b): ቀ

SiO2ሺaqሻ ቁ

ൌ

ቆ

SiO2ሺaqሻ SiO2ሺaqሻ

ቇ൅ ෍

13

൭1 െ

SiO2ሺaqሻ SiO2ሺaqሻ ǡ

൱Ǥ

ሺ11ሻ

This partial differential equation was solved numerically using an implicit-difference method from x = 0 to 7.0 mm and between 0 and 2055 h. To prevent numerical instability, we set the time step to 0.1–0.01 second and the space step to values of 0.01– 0.001 cm; the optimum value of the space step was determined by trial and error. The boundary condition at the inlet (x = 0) was set to CSiO2(aq) = 7.41× 10–6 mol cm–3 solution, consistent with silica saturation in the fluid at the experimental conditions. The boundary condition at the outlet (x = 7.0 mm) was ∂CSiO2(aq)/∂x = 0. The initial condition for CSiO2(aq) at t = 0 was set to 7.12 × 10–8 mol cm–3 (equal to 0.100 mmol kg–1 solution) elsewhere in the inner tube; this value is similar to the value of CSiO2(aq) in the 168 h run (0.135 mmol kg–1; Table EA1). 4.4. Estimation of kinetic parameters A set of unknown parameters, Θ, consists of the following nine parameters: ൌሼ

2ሺ ሻ

ǡ

1ǡ

2ǡ

3ǡ

4ା ǡ

4ି ǡ

5ା ǡ

5ି ǡ

ሽǤ

ሺ12ሻ

The discrepancy between the observed experimental value and the value calculated by the model, E(Θ), is evaluated from

E(Θ) =

1 M×N

෍

෍ቀ

ǡ

െ

ǡ

ሺ ሻቁ ǡ

ሺ

ሻ

where i represents a mineral or the porosity, and M is the number of minerals plus one, to account for the porosity (talc, serpentine, brucite, olivine, and porosity: M = 5). The parameters yi,j, yi,j(Θ), and σi represent the experimentally observed abundance of i at the j-th distance at 2055 h (observed data, Fig. 5a–e), the calculated abundance of mineral i at the j-th distance at 2055 h, and the standard deviation of the observed data for i, respectively. The number of observations in each dataset is Nobs. In some cases, estimation of the multiple kinetic parameters (Θ) by minimization of E(Θ) becomes complicated by convergence of the solution to a local minimum rather than the global minimum. In this study, we used the exchange Monte Carlo method (EMC; Hukushima and Nemoto, 1996; Earl and Deem, 2005) to find the global minimum of E(Θ) and avoid local minima; this method is an improvement over the Markov chain Monte Carlo method (Metropolis et al., 1953). Oyanagi et al. (2018b) conducted a benchmark test of the EMC using artificial parameters. The results indicate that the EMC method can be used to estimate the true values of multiple kinetic 14

parameters in a reactive transport model. Using EMC, a probability distribution was derived for each parameter in Θ, and the uncertainties associated with the parameters were determined from the characteristics of the probability distributions. 4.5. Model selection via a cross-validation technique The overall reaction simulated by the model consists of a combination of elementary reactions associated with primary mineral dissolution and secondary mineral precipitation. The Ai value in the equation 7 is the surface area of the rate-limiting mineral, which may be a reactant or a product (Lasaga, 1986; Lasaga and Rye, 1993; Lüttge et al., 2004). With five reactions, and with minerals able to play the role of reactant or product in each, there are 25 = 32 possible combinations of Ai values. To select the most appropriate combination of surface-area values, we calculated the value of E(Θ) for each combination of surface areas using a cross-validation (CV) method, which is a versatile and simple evaluation technique used in machine learning to avoid overfitting (Bishop, 2006; Goodfellow et al., 2016). The two-hold CV method was used in this study; in this method, the available dataset is divided into two subsets. One subset is used to train the model and the other subset is used to evaluate the classification capability of the trained model. Cycles of training and evaluation are repeated for two combinations and the generalization ability (CV error) is calculated from the mean of the two combinations. 5. RESULTS OF KINETIC PARAMETER ESTIMATION The CV error calculations produced highly variable results for the different choices of rate-limiting surface area in the reactive transport model (Fig. 7a). The CV error for the majority of models was greater than 2, and only two models had a CV error lower than 1 (Fig. 7a). When the surface area of the reactants was selected in each of the reactions R1–R5, the CV error was 3.5 (Rank 25 in Fig. 7a) and the observed mineral distributions were not reproduced well by the model (Fig. 7b–f). Similarly, if the surface area of the products was specified to be rate-limiting in each of reactions R1– R5, the CV error was 3.2 (Rank 17 in Fig. 7a) and the observed mineral distributions were not reproduced well (Fig. 7b–f). The best fit (Rank 1 in Fig. 7a) was obtained when the rate-controlling Ai was: olivine for reaction R1 (talc after olivine); serpentine for R2 (serpentine after olivine); olivine for R3 (brucite after olivine); serpentine for 15

R4± (talc after serpentine and serpentine after talc); and serpentine for R5± (serpentine after brucite and brucite after serpentine) (Fig. 7a). The best-fit model based on this Ai combination satisfactorily reproduced the observed mineral distribution and porosity after 2055 h (Fig. 7b–f). The kinetic parameters estimated from the best-fit model, and uncertainties derived from the probability distributions (Fig. EA2), are listed in Table 3. The distribution of log10[DSiO2(aq)] was approximately normal with a mean of –4.20 ± 0.03 (Fig. EA2; Table 3). This value is similar to the value of the diffusivity of H4SiO4 in pure water extrapolated from 25°C to 300°C (log10DH4SiO4 = –3.65; Rimstidt, 2013). The estimated value of m is 1.13 ± 0.07 (log10(m) = 0.03 ± 0.02; Table 3), which is lower than values of m obtained empirically from natural rocks (1.3–4.0; Oelkers, 1997). The probability distributions of the calculated rate constants for the overall reactions (log10(kR1), log10(kR2), log10(kR3), log10(kR4−), and log10(kR5+)) show a sharp single peak with 1σ uncertainties of 0.02, 0.02, 0.10, 0.13, and 0.22, respectively (Fig. EA2; Table 3). In contrast, the probability distributions of log10(kR4+) and log10(kR5-) show a broad single or bimodal peak with much larger uncertainties (1σ values of 2.12 and 1.09, respectively) (Fig. EA2; Table 3). 6. DISCUSSION 6.1. Migration of the metasomatic front The model predicts that the talc disappearance front, defined as the distance at which the molar fraction of talc/(talc + serpentine + brucite) equals 0.05, occurs at x = 6.5 mm at 566 h and x = 2.3 mm at 2055 h (Fig. 8). These values are similar to those of the observed talc disappearance fronts (6.0 mm at 566 h and 2.3 mm at 2055 h: Fig. 2b). Of note, the mineral distribution at 566 h was not used to parameterize the reactive transport model. The good agreement between the observations and the model output indicates that the reactions at <2055 h are represented by the model. The validity of the model further would be supported by consistencies on hydration flux with previous studies, as discussed in section 6.3. After 2055 h, the model predicts that the talc disappearance front ceases to migrate (Fig. 8). However, the observed position of the front moved to slightly higher, then lower, values of x during this time (Fig. 8). One explanation for the discrepancy is that the expansion of the solid volume during the reaction changed the position of the 16

front. At the talc disappearance front (x = 2.2 mm), the ratio of the total solid volume after 2055 h (VSolid = 1 – φ)to the initial solid volume (VSolid,0 = φOl,0) was 1.45 (Fig. 9a). Lower values were observed at x = 7.0 mm (VSolid/VSolid,0 = 1.20; Fig. 9a) and higher values were observed at x = 0 mm (VSolid/VSolid,0 = 1.58; Fig. 9a). The increase in solid volume at the talc disappearance front (VSolid/VSolid,0 = 1.45 at x = 2.2 mm; Fig. 9a) at 2055 h can be attributed to R1 (talc after olivine) and R2 (serpentine after olivine), which caused increases in the solid volume of +21% and +31%, respectively, and R4− (serpentine after talc), which caused a decrease in the solid volume of –7% (Fig. 9b). In low-porosity rocks, increases in the solid volume cause reaction-driven fracturing (Iyer et al., 2008; Plümper et al., 2012; Malvoisin et al., 2017). However, reaction-driven fracturing is unlikely in our experiments because of the high porosity of the experimental system (Ulven et al., 2014). Instead, the solid volume increase might have affected the observed position of the reaction front by altering the position of the minerals within the inner tube. The preferred explanation for the discrepancy is that subtle differences in the initial porosity between tubes. The TG values of two tubes at 2055 h differed by ~0.3 wt.% (Table. EA2), which is not enough to explain the discrepancy. However, after longer reaction times, the small initial differences between the tubes might have been magnified by differences in factors such as the reaction rates to produce the discrepancy between the observed and calculated position of the talc-disappearance front (Fig. 2b). Therefore, we conclude that the position of talc-disappearance observed in the experiments cannot be reliably used to quantify the discrepancy between the model and experiments. 6.2. Spatio-temporal reaction variation Multiple reactions occur in parallel during the hydrothermal alteration of olivine. The relative rates and extents of the reactions are a function of CSiO2(aq), Ai, and φwhich vary in time and space. Due to complex relationships among these parameters, only the total SiO2(aq) and H2O consumed during experiments have been estimated (Oyanagi et al., 2015); however, the instantaneous rates of SiO2(aq) and H2O production and consumption (rSiO2(aq): mol SiO2(aq) cm–3 bulk s–1; rH2O: mol H2O cm–3 bulk s–1) at each time step have not been calculated, and the relative contributions of R1–R5 to rSiO2(aq) and rH2O are unknown. 17

The best-fit reactive-transport model was used to quantify spatio-temporal changes in reaction progress. The temporal evolution of silica activity (Figs. 10a–c), rSiO2(aq) (Figs. 10d–f), and rH2O (Figs. 10g–i) was calculated at selected distances (x = 1.0, 3.0, and 5.0 mm). The value of log10[aSiO2(aq)] increased from 0 h (log10[aSiO2(aq)] = −4.0) to 1 h (−2.3 at x = 1.0 mm (Fig. 10a); −2.7 at x = 3.0 mm (Fig. 10b); and −3.1 at x = 5.0 mm (Fig. 10c)). These increases in aSiO2(aq) indicate that SiO2(aq) was transported from the Qtzhosted region to distances as high as x > 5.0 mm in the Ol-hosted region within 1 h of the start of the experiment. At x = 1.0 mm, log10[aSiO2(aq)] decreased with time from −2.3 at 1 h to −2.7 at 2000 h (Fig. 10a). This period coincided with the duration of predicted talc stability 0– 2000 h (Fig. 10a). The value of rSiO2(aq) was <0 for R1 (talc after olivine) from 0 to 2000 h, and zero for the other overall reactions (R2–R5), so the total rSiO2(aq) was equal to that of R1 (Fig. 10d). Similarly, the value of rH2O was <0 for R1 (talc after olivine) and zero for the other overall reactions (R2–R5), so the total rH2O was identical to that of R1 (Fig. 10g). These results indicate that the total values of rSiO2(aq) and rH2O were controlled by the progress of R1 (talc after olivine) at x = 1.0 mm from 0–2000 h. At x = 3.0 mm, log10[aSiO2(aq)] decreased from −2.7 at 1 h to −3.8 at 2000 h (Fig. 10b). This change was associated with a change in the stable mineralogy, from talc at 0– 150 h to serpentine at 150–2000 h (Fig. 10b). The total rSiO2(aq) was negative between 0 and 2000 h (−0.27 to −0.98 × 10–9 mol SiO2(aq) cm–3 bulk s–1; Fig. 10e), and the overall reaction that controlled the total rSiO2(aq) changed over this time period. Between 0 and 700 h, the values of rSiO2(aq) for R1 (talc after olivine) and R2 (serpentine after olivine) were <0, while that of R4 (talc after serpentine and vice versa) was >0, and the total rSiO2(aq) was similar to the value of rSiO2(aq) for R1(talc after olivine)(Fig. 10e). This suggests that the changes in rSiO2(aq) associated with R4− (serpentine after talc) and R2 (serpentine after olivine) were balanced, and that the total rSiO2(aq) was controlled by the progress of R1 (talc after olivine). A similar approach can be used to show that the total rSiO2(aq) was controlled by R1, R2, and R4 from 700 to 1800 h and by R2 (serpentine after olivine) from 1800 to 2000 h (Fig. 10e). In contrast, the total rH2O was similar to the rH2O for R2 (serpentine after olivine) from 0–2000 h, suggesting that R2 controlled total rH2O from 0–2000 h (Fig. 10h). At x = 5.0 mm, log10[aSiO2(aq)] value decreased from −3.1 at 1 h to −4.8 at 2000 h (Fig. 10c). Over this time period, the stable mineralogy changed from serpentine (0– 18

1600 h) to serpentine + brucite (1600–2000 h) (Fig. 10c). From 0–1000 h, R1 (talc after olivine), R2 (serpentine after olivine), and R4− (serpentine after talc) contributed to the total rSiO2(aq) (Fig. 10f). After 1000 h, the total rSiO2(aq) was controlled by the progress of R2 (serpentine after olivine: 1000–1600 h) (Fig. 10f). From 1600–2000 h, the rSiO2(aq) value of R3 (brucite after olivine) was >0, that of R5 (serpentine after brucite) was <0, and consumption and release of SiO2(aq) by reactions R3 and R5, respectively, were balanced (Fig. 10f). Thus, the overall reaction at this time was 2 Ol + 3 H2O → Srp + Brc (reaction (1)). The total rH2O was controlled mainly by R2 (serpentine after olivine) from 0–1600 h, and a combination of R3 (brucite after olivine) and R5+ (serpentine after brucite) from 1600–2000 h (Fig. 10i). Oyanagi et al. (2015) conducted hydrothermal experiments on the Ol–Qtz–H2O system at 250°C using a highly alkaline solution (pH = 13.8 at 25°C). They used mass balance calculations to show that the total SiO2(aq) and H2O consumed during 0–600 h of reaction were 2.0–7.0 ×10−3 and 2.0–15 ×10−3 mol cm–3 bulk, respectively. These values are higher than those of the present study, which was performed at 300°C using solutions that contain 0.5 mol kg−1 of NaCl (pH = ~7 at 25°C). In the present study, the total SiO2(aq) and H2O consumed between 0 and 600 h was 0.06−8.0 ×10−3 and 0.4−3.2 ×10−3 mol cm–3, respectively, based on the integrals of rSiO2(aq) and rH2O. The differences are attributed to differences in solution pH, fluid salinity, product mineralogy, and temperature between the experiments of Oyanagi et al (2015) and the present study. 6.3. Effects of silica activity on hydration kinetics and alternation zone The flux of H2O from the fluid phase into the solid phases (JH2O) is defined as the rate of H2O consumption per unit surface area of olivine (mol H2O cm–2 olivine s–1), which was calculated by normalizing the bulk hydration rate to the initial bulk surface area of olivine. The value of log10(JH2O) changed in time and space over the course of the experiment (−15.6 to −12.9: Fig. 11a). The location of the maximum JH2O changed from x = 0.1 mm at 0–500 h (talc formation only), to x = 2.2–3.1 mm from 500–2000 h (talc + serpentine formation) (Fig. 11a). The maximum value of log10[JH2O] was attained at 2000 h (log10[JH2O] = −12.9), when log10[aSiO2(aq)] was −3.1 (Fig. 11b); this high value is attributed to progress of R1, R2, and R4−. The lowest value of log10(JH2O) at 2000 h (log10(JH2O) = −14.6), was attained at the boundary between the serpentine and talc zones, where log10[aSiO2(aq)] = −2.9 (Fig. 11b). 19

The values of JH2O calculated in the present study for serpentine–brucite coexistence (log10(JH2O) = −13.2; Fig. 11b) are comparable with previous estimates based on hydrothermal experiments in the Ol–H2O system (see summary in Lamadrid et al. (2017)). For example, McCollom et al. (2016) reported a value for log10(JH2O) of −13.0 at 300°C, and Malvoisin et al. (2012) reported a value of −12.6. However, the JH2O calculated in the present study is ~2 orders of magnitude lower than some estimates of JH2O at 300°C; Martin and Fyfe (1970) and Wegner and Ernst (1983) estimated values of log10(JH2O) of −10.8 and −11.4, respectively. The consistency of our results with the conclusions of Malvoisin et al. (2012) indicates that the rate of olivine serpentinization in natural systems is lower than the rates suggested in the earlier studies (Martin and Fyfe, 1970; Wegner and Ernst, 1983). In the present study, experiments were performed in a fixed volume reactor at saturated vapor pressure. While this likely caused H2 to escape into the headspace (McCollom, 2016), JH2O is consistent with values from previous studies at 300°C and 35–50 MPa (Malvoisin et al., 2012; McCollom et al., 2016), which indicates that the H2 escape had a minor effect on JH2O. Ogasawara et al. (2013) used observations of the Ol–Opx system in hydrothermal experiments at 250°C to investigate silica transport during serpentinization; these workers showed that the extent of hydration due to R2 (serpentine after olivine) was enhanced at the elevated SiO2(aq) associated with Opx serpentinization. In our model, JH2O increases with silica activity in the serpentine stability field (Fig. 11b), consistent with the results of Ogasawara et al. (2013). Furthermore, the results of our calculations indicate that JH2O is lower in the talc stability field than in the serpentine stability field (Fig. 11b), which suggests that the SiO2(aq)-induced increase in the rate of R2 is limited to the serpentine stability field. These complexities emphasize that constraints on the aqueous silica activity are necessary for accurate estimation of the rate of olivine hydration in natural hydrothermal systems. Differences in the alteration zones as a function of CSiO2(aq) at the inlet were investigated in another reactive–transport simulation. This simulation used parameters similar to those used for the Ol–Qtz system, except that the boundary condition at the inlet (x = 0) was set to CSiO2(aq) = CR4 SiO2(aq) ,eq (Table 2). This model system is an analogue for hydrothermal alteration of olivine in equilibrium with Opx (enstatite), because pyroxene hydration buffers CSiO2(aq) to the talc–serpentine equilibrium (Allen 20

and Seyfried, 2003; Okamoto et al., 2011; Klein et al., 2013; Ogasawara et al., 2013). After 2000 h, the predicted alteration zones (Fig. 12a) are different from the alteration zones in the Ol–Qtz simulation at 2000 h (Fig. 12b). The calculated amount of serpentine around the inlet (x = 0–1 mm) was greater than that in the original model (Fig. 12a), which is consistent with experimental observations of the Ol–Opx boundary at 250°C (Ogasawara et al., 2013). However, the model predicts formation of talc around the inlet (Fig. 12a), which was not observed by Ogasawara et al. (2013). This inconsistency might reflect differences in the boundary conditions of our model and the initial conditions of the experimental study, such as temperature and the initial porosity. Oyanagi et al. (2015) investigated the effects of silica transport on serpentinization by conducting hydrothermal experiments on the Ol–Qtz–H2O system at 250°C under highly alkaline conditions (pH = 13.8 and 10.5 at 25 and 250°C, respectively), using a similar experimental apparatus to the present study (Fig. EA1). The mineralogy of the alteration zones is different in the two studies. In the study of Oyanagi et al. (2015), the alteration zones, with increasing distance from the Ol–Qtz boundary, were smectite–serpentine and serpentine–brucite–magnetite. In the present study, we documented zones of talc–serpentine and serpentine–brucite–magnetite (Fig. 1a–e). We attribute the formation of smectite, rather than talc, to differences in pH between the two studies. Furthermore, the position of the metasomatic zones differed between the two studies. Oyanagi et al. (2015) reported that the smectite disappearance front was at x = 16.0 mm after 1104 h. In contrast, in the present study the talc disappearance front was at x = 2.2 mm after 2055 h (Fig. 2b). This is attributed to the presence of the HSiO3–(aq) species in highly alkaline solutions, which increases the quartz solubility. At 250°C and Psat (3.98 MPa), the quartz solubilities at pH = 7.0 and pH = 10.5 are 6.28 and 187.7 mmol kg–1, respectively. Therefore, solution pH is likely to provide a first-order control on the widths of metasomatic zones. 6.4. Rate-limiting processes Relative rates of silica transport and surface reactions The saturation index of a mineral is a useful way to determine the rate-controlling process of a heterogeneous reaction. However, it is impossible to calculate the

21

saturation index of the minerals using our reactive transport model, because the model outputs do not include the concentrations of Mg2+ and H+. Therefore, the second Damkőhler number (DaII), which describes the rate of consumption (or production) of a chemical species by surface reaction relative to the rate of diffusive transport, was used to elucidate the rate-controlling processes. Values of DaII were calculated from the bestfit model output using the following equation: II

ൌ

ʹ

2 ǡSiO2ሺaqሻ

ǡ

ሺ14ሻ

(Steefel, 2008), where l (cm) is the characteristic length, and De,SiO2(aq) (cm2 s–1) is the

effective diffusivity of SiO2(aq) in the porous media, which was calculated by De,SiO2(aq) = φmDSiO2(aq) (Archie’s law (Archie, 1942)). The k’n (s–1) is an effective rate coefficient for overall reaction n, defined as: k'n =

ሺ‫ܣ‬௜ Ȁ߮ሻkn Ǥሺͳͷሻ n CSiO 2 ሺaqሻ,eq

When log10(DaII) > 1.0, the rate of diffusion controls the overall rate of reaction and

reaction is transport-controlled. In contrast, when log10(DaII) < −1.0, surface processes control the overall reaction rate, and the rate of reaction is surface-controlled. When 1.0 > log10(DaII) > –1.0, a combination of diffusive and surface-controlled processes control the overall reaction rate (mixed kinetics) (Rimstidt, 2013). The values of Ai and φ change in time and space, so the values of k’n and De,SiO2(aq) also change in time and space. Therefore, DaII was calculated from the best-fit model as a function of time (0– 2000 h) and distance (x = 0–7 mm) for the representative reactions, assuming l = 0.01 cm. The log10(DaII) of R1 (talc after olivine) was less than −1 from 0–2000 h and for x = 0–7 mm (Fig. 13a), which indicates that the rate of R1 (talc after olivine) is surfacecontrolled. The log10(DaII) for R3 (brucite after olivine) was between −0.18 and 0.1 for 0–2000 h and x = 0–7 mm (Fig. 13c), which indicates that the rate of R3 was controlled by mixed kinetics. In contrast, the rate-controlling process of R2 (serpentine after olivine), R4− (serpentine after talc), and R5+ (serpentine after brucite) changed in time and space. For example, the log10(DaII) of R2 at 0 h and x = 0–7 mm was less than −1, suggesting that the rate of this reaction was surface-controlled (Fig. 13b). At 1300 h, log10(DaII) of R2 at x = 2.6 mm was greater than −1, although it was less than −1 in other parts of the Ol22

hosted region at this time (e.g., at x = 0–2.5 and 2.7–7.0 mm; Fig. 13b); this result indicates that the rate-controlling process at 1300 h was locally variable, with mixed kinetics at x = 2.6 mm and surface-controlled kinetics at x = 0–2.5 and 2.7–7.0 mm (Fig. 13b). With increasing reaction time, the region where R2 was controlled by mixed kinetics increased in size (x = 1.8–3.3 mm at 2000 h; Fig. 13b). Similarly, the rate of R4− (serpentine after talc) was surface-controlled at 0 h, shifted to mixed kinetics at x = 2.1 mm and 800 h, was controlled by mixed kinetics at x =1.5–2.5 mm, and surfacecontrolled at x = 2.6–2.8 mm at 2000 hours (Fig. 13d). The rate of R5+ (serpentine after brucite), was controlled by mixed kinetics at 0 h, but shifted to transport-controlled after ~400 h (Fig. 13e). The increase in DaII, which implies a shift in the rate-controlling process, might reflect: (1) an increase in k’n and/or (2) a decrease in De,SiO2(aq) (equation 14 and 15). The former reflects the coupled effects of an increase in Ai and a decrease in φ with increasing time (equation 14). The ratio of DaII at the time of interest (t*) to DaII at 0 h is (k’n(t*)/k’n(0)) × (De,SiO2(aq)(t*)/De,SiO2(aq)(0))–1, where k’n(t*)/k’n(0) is the ratio of the effective rate constant of overall reaction n at t* to the same parameter at 0 h, and De,SiO2(aq)(t*)/De,SiO2(aq)(0) is the ratio of the effective diffusivity of SiO2(aq) at t* to the same parameter at 0 h. The relative contributions of the two parameters can be evaluated from relative values of k’n(t*)/k’n(0) and the inverse of De,SiO2(aq)(t*)/De,SiO2(aq)(0). For R2 (serpentine after olivine) and R5+ (serpentine after brucite), the shift in rate-controlling process occurred at 1500 h and x = 3.0 mm. At this time and position, the values of k’n(t*)/k’n(0) for R2 and R5+ are both ~105 (Fig. EA3). These values are orders of magnitude higher than the inverse of De,SiO2(aq)(t*)/De,SiO2(aq)(0), which is ~100.5 at 1500 h and x = 3.0 mm (Fig. EA3). These results indicate that the shift in the rate-controlling process of R2 and R5+ was attributed to an increase in k’n, which was mainly caused by increases in Ai; the decrease in φ had a minor effect. For R4− (serpentine after talc), the shift in rate-controlling process occurred at 700 h and x = 3.0 mm. At this time and position, the k’n(t*)/k’n(0) value for R4− was ~101 (Fig. EA3), which is similar to the value of the inverse of De,SiO2(aq)(t*)/De,SiO2(aq)(0) (100.5; Fig. EA3). These results indicate that the process controlling the rate of R4− was affected by increases in k’n and decreases in De,SiO2(aq). In summary: (1) R1 was surface-controlled; (2) R2 shifted from surface-controlled to mixed kinetics; (3) R3 was controlled by mixed kinetics; (4) R4− shifted from 23

surface-controlled to mixed kinetics; and (5) R5+ shifted from mixed kinetics to transport-controlled. The changes are attributed to increases in the effective rate constant for R2 and R5+, and a combination of the effects of an increase in the effective rate constant and a decrease in effective diffusivity for R4−.

Dissolution- versus precipitation-limited reactions To simplify our model, we assumed that the dissolution of a reactant was coupled to the precipitation of a product. In fact, either dissolution or precipitation can limit the rate of overall reactions. The rate-limiting process (dissolution or precipitation) can be determined if the mineral surface area that controls the overall reaction rate can be identified (Lasaga, 1986; Schramke et al., 1987; Dachs and Metz, 1988; Milke and Metz, 2002). The CV identified the rate-limiting minerals in our experiments (Fig. 7a). For example, the olivine surface area controlled the rate of R1 (talc after olivine) (Fig. 7a), suggesting that the olivine dissolution rate limits the overall rate of R1. Similarly, serpentine precipitation limited the rate of R2 (serpentine after olivine), olivine dissolution limited the rate of R3 (brucite after olivine), and talc dissolution limited the rate of R4− (serpentine after talc). Xia et al. (2009) discussed differences between the replacement textures formed by dissolution- and precipitation-limited reactions during coupled dissolution– precipitation. When reaction is dissolution-limited, a high degree of pseudomorphism is observed and the shape of parent minerals is preserved by the replacement reaction. In contrast, the shape of the parent mineral is not preserved by precipitation-limited reactions. In our experiments, talc precipitated after olivine preserves the shape of the olivine, consistent with a dissolution-limited mechanism for R1 (talc after olivine) (Fig. 1c). In contrast, serpentine after olivine does not preserve the shape of the parent mineral, indicating that R2 (serpentine after olivine) is precipitation-limited (Fig. 1e). Malvoisin et al. (2012) examined the rate of serpentinization as a function of the initial olivine grain size using Ol–H2O experiments on mineral powders, and concluded that olivine dissolution was the rate-limiting step for the reaction 2 Ol + 3 H2O = Srp + Brc (reaction (1)). The results of our reactive transport model indicate that olivine hydration associated with formation of serpentine and brucite (reaction (1)) can be expressed by a coupling between R3 (brucite after olivine) and R5+ (serpentine after

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brucite; Fig. 10f, i). The rate of R3 (brucite after olivine) depends on the surface area of olivine (Fig. 7a), so the overall reaction (1) increases with an increase in the olivine surface area. The rate of elemental dissolution/precipitation reactions changes with temperature, so the rate-limiting process might also change with temperature. The ratelimiting process (dissolution- or precipitation-limited) is determined by the relative rates of the dissolution and precipitation reactions. The Arrhenius relationship can be used to evaluate the temperature dependence of reaction rates, but previous workers found that reaction rates calculated with the Arrhenius relationship are inconsistent with experimentally determined rate constants (Malvoisin et al., 2012; Fritz et al., 2018), so it is unlikely that extrapolation would provide accurate values at ~300°C. Therefore, additional quantitative kinetic data are required to determine whether the rate-limiting process changes with temperature. 6.5. Implications for the hydrothermal alteration of peridotite in the oceanic lithosphere Our experiments and modeling indicate that the rate-controlling process can change as hydration progresses in the presence of silica. These changes are attributed to an increase in the surface area of the secondary minerals and a decrease in porosity with increasing reaction progress. This result is consistent with previous suggestions that reactions might shift from surface- to transport-controlled as metamorphic reactions progress (Fisher, 1978; Thompson, 1986; Lüttge and Metz, 1993). One of the biggest differences between the conditions of our experiment and those of natural hydrothermal systems is the ratio of the mineral surface area to porosity (i.e., SA:V). In our experiments, the initial porosity was ~40%, which decreased to 6%–26% after 2055 h. These porosities are higher than those of natural unaltered and altered peridotites, so the rate-controlling processes in the experiments are not directly equivalent to those of natural hydrothermal systems. However, it is the relative values of the effective rate constants and the effective diffusivity (equations 14 and 15) that determine the rate-controlling process for each reaction, so DaII can be used to predict the processes that control alteration in a natural hydrothermal system. In low-porosity rocks, the values of De,SiO2(aq) and SA:V are lower and higher, respectively, than their values in our high-porosity experiments, so DaII is 25

higher for hydrothermal alteration of peridotites with low porosity than for our experiments. However, the porosity is increased by deformation processes, such as reaction-induced fracturing (Iyer et al., 2008; Plümper et al., 2012; Shimizu and Okamoto, 2016; Malvoisin et al., 2017) and hydrofracturing (Nishiyama, 1989; Miller et al., 2003; Oyanagi et al., 2015; Okamoto et al., 2017). Increases in the porosity would increase the value of De,SiO2(aq) and decrease the value of SA:V, so the value of DaII in deforming rock systems would be lower than for hydrothermal alteration of unfractured peridotite. Therefore, dynamic switching between surface- and transport-controlled reactions probably occurs during hydrothermal alteration of peridotite in the oceanic lithosphere. However, the values of SA:V are not well known for most rocks, so the rate-controlling mechanisms in natural hydrothermal systems cannot be determined quantitatively from the results of the present study. In this study, the physical surface area (i.e., BET, specific, or geometric surface area) was used for normalizing to estimate intrinsic rate constants (mol cm–2 s–1; Table 3), and uncertainty and error of Ai were incorporated into the estimated rate constant. Therefore, errors in Ai are offset by corresponding changes in kn, so the calculated spatial distribution of minerals and porosity are independent of the errors in Ai. Previous studies have modeled zones of forsterite–serpentine–talc–quartz as a consequence of diffusive mass transport processes coupled with multiple precipitation– dissolution reactions (Korzhinskii, 1968; Lichtner et al., 1986). These models predict that: (1) two different minerals (e.g., olivine and serpentine), coexist only at zone boundaries; and (2) the talc and serpentine zones grow as a function of the square root of time. These findings were based on the assumption of local equilibria between solution and minerals and constant porosity in time and space. In our experiments, the individual reaction zones were not monomineralic (e.g., unreacted olivine grains remained throughout the inner tube; Fig. 5a) and the talc zone did not grow as a function of the square root of time (Fig. 2b). These observations suggest that local equilibrium was not attained in our high porosity experiments; this conclusion is supported by the results of our calculations, which indicate that R1–R5 were not always transport-controlled (Fig. 13a–d). The results of kinetic reaction path modeling indicate that the formation of talc by reaction between crust-equilibrated fluids and peridotite requires fluid:rock mass ratios of >102 (Malvoisin, 2015). In our experiments, the fluid:rock mass ratio was ~14, an 26

order of magnitude lower than the value required for the talc formation by reaction path modeling. Since reaction occurs at mineral surfaces, the effective fluid:rock mass ratio in our experiments might have been much higher than 14. In this study, we have shown that the reaction rates of multiple simultaneous reactions can be extracted from the spatial distribution of minerals using machine learning techniques. This approach could be used to estimate in situ reaction rates from a natural hydrothermal system, and produce improved model predictions of the physical and chemical responses during hydrothermal alteration of peridotite. Numerical simulations of hydrothermal systems on the oceanic seafloor consider heat budgets, fluid transport, deformation, and reaction (Emmanuel and Berkowitz, 2006; Iyer et al., 2010; Evans et al., 2018). However, in these studies the reaction rates are based on simplified representations of reactions (e.g., reaction (1), using values based on the reaction progress in Ol–H2O experiments). Our model shows that the rate of hydration is higher in the serpentine + talc zone, where silica activity is intermediate, than in the talc zone, serpentine zone, and serpentine + brucite zone. Therefore, the silica activity in the reacting fluid is a first-order control on the rate of hydrothermal alteration of mantle peridotite, and the products of peridotite hydration are heterogeneously distributed. Realistic models of hydrothermal alteration in the oceanic lithosphere and of the global crustal water cycle from mid-ocean ridge to subduction zone require quantitative descriptions of the relationships between reaction rates and silica activity over a wide range of temperatures. 7. CONCLUSIONS A combination of hydrothermal experiments on the Ol–Qtz–H2O system at 300°C and Psat (8.58 MPa) with reactive transport modeling were used to investigate the role of silica transport in olivine hydration. 1. Metasomatic zoning in the Ol-hosted region consisted of zones of talc, talc + serpentine, and serpentine ± brucite ± magnetite with increasing distance from the Ol–Qtz boundary. The talc disappearance position moved away from, and slightly towards, the original Ol–Qtz boundary in the early and late stages of the experiments, respectively. 2. The complex relationships among olivine, talc, serpentine, and brucite were represented by five overall reactions, and the SiO2(aq) diffusivity and rate 27

constants for the overall reactions were obtained through a comparison of the spatial distribution of the experimental products with the results of the reactive transport model. 3. The flux of H2O from the fluid phase into the solid phases (JH2O; mol H2O cm–2 s–1) varied significantly as a function of silica activity; log10(JH2O) varied from −15.6 to −12.9 during our experiments. The JH2O were higher in the serpentine + metastable talc zone with intermediate silica activity than in the serpentine, serpentine + brucite, and talc zones. 4. Production of talc after olivine (R1) was surface-controlled from 0–2000 h, whereas the rate of production of brucite after olivine (R3) was controlled by a combination of diffusion and surface reactions (mixed kinetics). The ratecontrolling process of the overall reactions serpentine after olivine (R2), serpentine after talc (R4−), and serpentine after brucite (R5+), varied in space and time. The rate-controlling process shifted from surface-controlled to mixed kinetics for R2 and R4−, and from mixed kinetics to transportcontrolled for R5+. 5. Identification of the rate-limiting mineral for the overall reactions suggests that, in our experiments, the talc after olivine (R1), brucite after olivine (R3), and serpentine after talc (R4−) reactions were dissolution-limited, whereas the serpentine after olivine (R2) reaction was precipitation-limited. 6. Reactions could shift from surface- to transport-controlled during hydrothermal alteration in the oceanic lithosphere, and reaction-induced fracturing and hydrofracturing might trigger additional switches from transport- to surface-controlled reactions. These temporal and spatial changes in the rate-controlling process are important contributors to the formation of metasomatic zoning and heterogeneous hydration patterns within the oceanic lithosphere. ACKNOWLEDGMENTS We are grateful to Koji Hukushima, Tatsu Kuwatani, and Toshiaki Omori for helpful advice on the exchange Monte Carlo method and cross-validation method. We thank Michihiko Nakamura, Takeshi Komai, Kenichi Hoshino, Masaoki Uno, Takayoshi Nagaya, Fumiko Higashino, and Otgonbayar Dandar for valuable 28

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Sleep N. H., Meibom A., Fridriksson T., Coleman R. G. and Bird D. K. (2004) H2-rich fluids from serpentinization: Geochemical and biotic implications. Proc. Natl. Acad. Sci. 101, 12818–12823. Steefel C. I. (2008) Geochemical Kinetics and Transport. In Kinetics of Water-Rock Interaction Springer New York, New York, NY. pp. 545–589. Steefel C. I. and Lasaga A. C. (1994) A coupled model for transport of multiple chemical-species and kinetic precipitation dissolution reactions with application to reactive flow in single-phase hydrothermal systems. Am. J. Sci. 294, 529–592. Syverson D. D., Tutolo B. M., Borrok D. M. and Seyfried W. E. (2017) Serpentinization of olivine at 300 °C and 500 bars: An experimental study examining the role of silica on the reaction path and oxidation state of iron. Chem. Geol. 475, 122–134. Thompson A. B. (1986) The Role of Mineral Kinetics in the Development of Metamorphic Microtextures. In Fluid-Rock Interactions during Metamorphism (eds. J. V Walther and B. J. Wood). Springer New York, New York, NY. pp. 154– 193. Tutolo B. M., Luhmann A. J., Tosca N. J. and Seyfried W. E. (2018) Serpentinization as a reactive transport process: The brucite silicification reaction. Earth Planet. Sci. Lett. 484, 385–395. Ulven O. I., Jamtveit B. and Malthe-Sørenssen A. (2014) Reaction-driven fracturing of porous rock. J. Geophys. Res. Solid Earth 119, 7473–7486. Walther J. V. and Helgeson H. C. (1977) Calculation of the thermodynamic properties of aqueous silica and the solubility of quartz and its polymorphs at high pressures and temperatures. Am. J. Sci. 277, 1315–1351. Wegner W. W. and Ernst W. G. (1983) Experimentally determined hydration and dehydration reaction rates in the system MgO-SiO2-H2O. Am. J. Sci. 283 A, 151– 180. White A. F. and Peterson M. L. (1990) Role of Reactive-Surface-Area Characterization in Geochemical Kinetic Models. In Chemical Modeling of Aqueous Systems II pp. 461–475. Xia F., Brugger J., Chen G., Ngothai Y., O’Neill B., Putnis A. and Pring A. (2009) Mechanism and kinetics of pseudomorphic mineral replacement reactions: A case

36

study of the replacement of pentlandite by violarite. Geochim. Cosmochim. Acta 73, 1945–1969. Yada K. and Iishi K. (1977) Growth and microstructure of synthetic chrysotile. Am. Mineral. 62, 958–965. Zimmer K., Zhang Y., Lu P., Chen Y., Zhang G., Dalkilic M. and Zhu C. (2016) SUPCRTBL: A revised and extended thermodynamic dataset and software package of SUPCRT92. Comput. Geosci. 90, 97–111.

37

Captions for Figures and Tables Fig. 1 (a) Photomicrographs of the experimental products of Ol–Qtz–H2O experiments run for 566, 2055, 3258, 6000, and 8055 h. (b–e) Back-scattered electron images of reaction products and unaltered reactant minerals after 2055 h. The areas shown in the SEM images are indicated in Fig. 2a. (b) Contact between the Ol- and Qtz-hosted regions. No secondary minerals formed around the Qtz grains, whereas Ol is surrounded by secondary talc. (c) Talc replacing olivine near the Ol–Qtz boundary. (d and e) Reaction products in the serpentine + brucite + magnetite zone. Ol = olivine; Srp = serpentine; Brc = brucite; Mag = magnetite; Tlc = talc; Qtz = quartz. Fig. 2 (a) Spatio-temporal evolution of the atomic (Mg + Fe)/Si ratio in the serpentine–talc mixtures. (b) Temporal evolution of appearance/disappearance fronts for talc, magnetite, and brucite. The talc disappearance front was constrained using the (Mg + Fe)/Si ratio, and the Brc and Mag appearance fronts were constrained from SEM observations. Fig. 3 (a) Representative TG profiles of water loss with temperature in samples from segments 3 and 7 (6000 h experiment). (b) Water content as a function of distance from the Ol– Qtz boundary, measured by TG. Fig. 4 Area proportions of (a) pores (Arφ), olivine (ArOl), hydrous minerals (ArTlc + Srp + Brc), and (b) magnetite (ArMag), as measured from BSE images. Fig. 5 Amount of (a) olivine, (b) talc, (c) serpentine, (d) brucite, and (e) porosity in the products of the 2055 h experiment as a function of distance from the Ol–Qtz boundary. The black dashed lines in (a) and (e) represent initial values. Data for serpentine and

38

brucite were not estimated at x = 2.7–4.9. (f) Changes in the bulk rock contents of Mg, Si, and H2O between 0 h (before the experiments) and 2055 h. Fig. 6 (a) Activity–activity diagram of the MgO–SiO2–H2O system at 300°C and Psat, assuming unit activities of all minerals and water (c.f. Klein and McCollom, 2013). The Fe component was not included in the stability diagram because the positions of the boundaries between the MgO–SiO2–H2O minerals are not sensitive to the Fe content of the phases. The stars labeled R1–R5 indicate the equilibrium values for R1–R5 (Table 2). (b) Schematic illustration of the conceptual reactive transport model used to simulate coupled reaction and diffusion. Aqueous SiO2(aq) is transported within a porous forsterite medium, with a source at x = 0. Arrows indicate the directions of the reactions. The parameters kn (mol SiO2(aq) cm–2 s–1) are the reaction rate constants for the overall reaction n. Modified after Oyanagi et al. (2018b). Fig. 7 (a) Summary of the results of cross-validation (CV) error calculations for different choices of surface areas. Dark gray and light gray indicate that the reactant and product mineral were assumed to provide the rate-limiting surface area, respectively. (b–e) Bestfit model (bold red curve) to the observed amount of: (b) olivine; (c) talc; (d) serpentine; (e) brucite; and (f) porosity after 2055 h reaction. The green and blue dotted lines show the best-fit results when all Ai in R1–R5 were assumed to be reactant and product, respectively. Fig. 8. Comparison of the modeled and observed location of the talc disappearance front. The predicted position is consistent with the observed position at 566 and 2055 h, despite the fact that data at 566 h were not used for model calibration. Fig. 9 (a) Spatial variations in the ratio of total solid volume after 2055 h (VSolid) to the initial total solid volume (VSolid,0) calculated from the reactive–transport model. (b) Spatial variations in the volume change from 0 to 2055 h for each reaction. The dotted line in 39

(a) and (b) indicates the position of the talc disappearance front at 2055 h (Figs. 2b and 8). Fig. 10 Temporal evolution of solution chemistry and reaction rate derived from the best-fit model. (a–c) Temporal evolution of aqueous silica activity (pink line) at (a) x = 1.0, (b) x = 3.0, and (c) x = 5.0 mm, superimposed on the stability fields of brucite, serpentine, and talc at 300°C and Psat. The white dashed lines represent the metastable boundaries of mineral stability fields. (d–f) Temporal evolution of the rate of production of SiO2(aq) by R1–R5 at (d) x = 1.0, (e) x = 3.0, and (f) x = 5.0 mm. Positive and negative values of rSiO2(aq) indicate release and consumption of SiO2(aq) from solution, respectively. The black dashed line represents the sum of rSiO2(aq) of R1–R5. (g–i) Temporal evolution of the rate of production of H2O by R1–R5 at (g) x = 1.0, (h) x = 3.0, and (i) x = 5.0 mm. Positive and negative values of rH2O indicate release (dehydration) and consumption (hydration) of H2O, respectively. In (g–i) the dashed line shows the sum of rH2O values of R1–R5. In (d–i), the lines are superimposed in the following order: black (front), green, yellow, purple, red, blue (back). Fig. 11 (a) Relationship between temporal and spatial changes in the calculated changes in JH2O and the mineralogy. The gray line shows the maximum JH2O for each hour of the experiment. (b) Relationship between SiO2(aq) activity in the solution and the best-fit calculated hydration flux normalized to the initial surface area of olivine. The white dotted lines indicate metastable phase boundaries. Ol = olivine; Srp = serpentine; Brc = brucite; Tlc = talc; Qtz = quartz. Fig. 12 Calculated spatial distribution of minerals at 2000 h. The boundary condition at the inlet (CSiO2(aq) at x = 0) is set to (a) talc–serpentine equilibrium, and (b) Qtz–SiO2(aq) equilibrium. Fig. 13

40

Spatial and temporal variations in the second Damkőhler number (DaII) during the Ol– Qtz–H2O experiments: (a) R1; (b) R2; (c) R3; (d) R4−; and (e) R5+. The characteristic length (l) was set to 0.01 cm. The contours are labeled with Log10[DaII]. Ol = olivine; Srp = serpentine; Brc = brucite; Tlc = talc; Qtz = quartz

Table 1. Representative chemical compositions of the experimental reactant and product minerals. Table 2. Summary of the overall reactions used in the reactive transport model and the equilibrium constants at 300°C and Psat. Table 3. Summary of the estimated kinetic parameters and uncertainties (1s)

41

Figure 1

(a) Ol-hosted region

Qtz-hosted region 504 h (b)

(c)

(d)

(e)

2055 h 3258 h 6000 h 8055 h Seg. 1

Seg. 2

Seg. 3

Seg. 4

0

-10

Seg. 5

Seg. 6

10

Seg. 7

Seg. 8

20

Distance from Ol–Qtz boundary, x (mm)

(b)

(c)

Qtz

Ol

Ol Epoxy

Tlc

Tlc 20 µm

(d)

10 µm

(e)

Srp

Ol Mag Srp

Brc Mag

Srp

Brc 20 µm

40 µm

Figure 2

(a)

(b) Distance from Ol–Qtz boundary (mm)

(Mg + Fetotal)/Si (atomic ratio)

2.0

Serpentine

1.5

504 hour 2055 hour 3258 hour 6000 hour

1.0 Talc

0.5 0

2

4

6

8

Distance from Ol–Qtz boundary (mm)

10

10 Brc appearance front 8

6

Mag appearance front

4

2

0 0

Tlc disappearance front

2000

4000

6000

Time (hours)

8000

(a)

Figure 3

Weight loss (wt%)

0 -2 Seg. 3 Brucite breakdown

-4

Talc breakdown

-6 -8 Serpentine breakdown

-10 Seg. 7

-12 -14 0

200

400

600

800

1000

Temperature (°C)

(b)

1

15

Segment number 3 4 5 6

2

Ol-hosted region

Qtz-hosted region

Weight loss (wt%)

8

7

6000 h

10

3258 h

5 2055 h 504 h

0 -10

-5

0

5

10

15

20

25

30

Distance from Ol–Qtz boundary (mm)

(a)

Figure 4

Area proportion (%)

100 ArTlc + Srp + Brc ArOl

80

Arφ 60 40 20 0 0

(b)

2 4 6 8 Distance from Ol–Qtz boundary (mm)

2 Magnetite free

Area proportion (%)

10

ArMag

1

0 0

2 4 6 8 Distance from Ol–Qtz boundary (mm)

10

Figure 5

16

4

0

0

Amount (mmol/cm3 bulk)

Serpentine

6 4 2 0

0

2

30

Brucite

6 4 2 0

0

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

20

Initial

Pores

20

10

0

-10

10 0 0

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

8

(f) 40

0

10

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

(e)

Porosity [%]

4

0

(d)

8

Talc

6

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

10

(c)

Amount (mmol/cm3 bulk)

8

8

Amount (mmol/cm3 bulk)

Amount (mmol/cm3 bulk)

Olivine

12

10

(b)

Initial

Δmi (mmol/cm3 bulk)

(a)

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

-20 0

Gain Loss mΣMg mΣSi mH2O 1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

(a)

Figure 6

Quartz

-2

ivi Ol

Tal c

ne

R4

R1 en rp Se

-4

e tin

Log10[aSiO2(aq)]

-3

R3

R5

-5

Brucite

Solution

-6 5

6

7

R2 8

Log10[(aMg2+)/(aH+)2]

(b) 0

Distance (x)

SiO2(aq)

Olivine

DSiO2(aq) Porosity = ~37% kR1 kR2

Talc kR4+

kR3

kR4-

kR5-

Brucite kR5+

Serpentine

(a)

R1 (Ol→Tlc) R2 (Ol→Srp) R3 (Ol→Brc) R4± (Srp↔Tlc) R5± (Brc↔Srp)

CV error

Figure 7

5 4 3 2 1 0 1

5

10

15

20

25

30

Ranking 16

10

(b)

12

Olivine

8

4

0

0

Amount (mmol/cm3 bulk)

Amount (mmol/cm3 bulk)

Initial

(d)

8

Serpentine

6 4 2 0

0

40 30 Porosity [%]

4 2

0

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

10

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

Initial

(f)

Pores

20 10 0 0

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

Amount (mmol/cm3 bulk)

Amount (mmol/cm3 bulk)

10

Talc

6

0

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

(c)

8

(e) Brucite

8 6 4 2 0

0

1 2 3 4 5 6 7 Distance from Ol–Qtz boundary [mm]

Distance from Ol–Qtz boundary (mm

Figure 8

10

8 Model 6 Talc disappearance front

4

2

0 0

2000

4000

6000

Time (hours)

8000

(a)

Figure 9

1.6

VSolid / VSolid, 0

Talc disappearance front at 2055 h

1.4

1.2

1.0

0

1

2

3

4

5

6

7

Distance from Ol–Qtz boundary (mm)

(b)

60 Talc disappearance front at 2055 h

ΔVSolid (%)

40

R1 (Ol→Tlc) R2 (Ol→Srp) R3 (Ol→Brc) R4± (Srp↔Tlc) R5± (Brc↔Srp)

20

0 -10 0

1

2

3

4

5

6

Distance from Ol–Qtz boundary (mm)

7

Qtz SiO2(aq)

Log10[aSiO2(aq)]

-2 Tlc

-3 Srp

-5

Brc

[×10 mol cm-³ bulk s-1] -9

rSiO(aq)

(d) 4 2

2.0

-4

Srp

-5

Brc

0

rSiO(aq) > 0 (SiO(aq) release)

-4

4

Tlc

Ol Brc

1.0 Time [×103 hours]

-4

Srp

-5

Brc

2.0 0

(f)

4

4

2

2

Tlc Ol Ol Brc

1.0 Time [×103 hours]

2.0

x = 5.0 mm

0 -2 rSiO(aq) < 0 (SiO(aq) consumption) 1.0 Time [×103 hours] x = 1.0 mm

-2

-4

2.0

0

-4 1.0 Time [×103 hours]

(h) x = 3.0 mm

2.0 0

(i)

4

4

2

2

0

0

0

-2

-2

-2

-4

-4

-4

-6

-6

-8

-8

-10

-10

rHO > 0 (dehydration)

0.3 0.2 0.1 0 -0.1 -0.2 -0.3

0

0.5

1.0

1.0 2.0 Time [×103 hours] x = 5.0 mm

-9

rHO

-

2

Qtz SiO2(aq)

-2 -3

Tlc Ol

(e) x = 3.0 mm

x = 1.0 mm

-2

(g) [×10 mol cm ³ bulk s ]

-3

0

0

-1

Qtz SiO2(aq)

Tlc

Ol Brc

1.0 Time [×103 hours]

(c) x = 5.0 mm

-2

Tlc Ol

-4

0

(b) x = 3.0 mm

x = 1.0 mm

-6 -8

rHO < 0 (hydration)

-10 0

Figure 10

(a)

1.0 Time [×103 hours]

2.0 0

1.0 2.0 0 3 Time [×10 hours]

1.0 2.0 3 Time [×10 hours]

Total R1 (Ol→Tlc) R2 (Ol→Srp) R3 (Ol→Brc) R4± (Srp↔Tlc) R5± (Brc↔Srp)

Figure 11 (a)

Distance from Ol–Qtz boundary [mm]

7

Srp

6

Srp + Brc

5

Tlc + Srp 4 3 2 1 0

Tlc 0

400

800

1600

1200

2000

Time [hours] JH2O (Log10 [mol/cm2 olivine/s]) -15

-15.5

-14.5

-14

-13

-13.5

–12

Srp

Tlc h h 10 0

h

50 0

–14

10 00

h 15 00

20 00

h

Brc

Qtz SiO2(aq)

–13

Tlc Ol

Ol Brc

JH2O (Log [mol/cm2 olivine/s]) 10

(b)

–15

-5

-4

-3

Log10[aSiO2(aq)]

-2

Figure 12

(a) 50

100 Brucite

80 䢲䢰䢺

60 䢲䢰䢸

40 30

Serpentine Talc

20

40 䢲䢰䢶

Porosity 20

10

䢲䢰䢴

0 0

Olivine

䢲

䢲

1 䢳

2 䢴

3 䢵

4 䢶

5 䢷

6 䢸

Porosity (%)

Mol% Minerals

䢳

0 7 䢹

Distance (mm)

(b) 50

䢳

䢲䢰䢺

80

Brucite Talc

40

Serpentine

30

䢲䢰䢸

60 Porosity

䢲䢰䢶

40 䢲䢰䢴

10

Olivine

20 䢲

0 0 䢲

20

䢳

1

䢴

2

䢵

3

䢶

4

Distance (mm)

䢷

5

䢸

6

0 7 䢹

Porosity (%)

Mol% Minerals

100

Figure 13

(a) R1

(b) R2

(c) R3 (Ol + 2 HO → 2 Brc + SiO(aq) )

(3 Ol + SiO(aq) + 4 HO → 2 Srp)

(3 Ol + 5 SiO(aq) + 2 HO → 2 Tlc)

6

6

6

Distance from Ol–Qtz boundary (mm)

-2 -3

4

4

4 -1

0

2

2

2 -2

0 0

1.0

2.0

0

0

3

3

Time [×10 hours]

(d) R4-

0 2.0 0

1.0

2.0

3

Time [×10 hours]

Time [×10 hours]

(e) R5+

(Tlc + HO → Srp+ 2 SiO(aq))

(3 Brc + 2 SiO(aq) → 2 Srp + HO)

6

Surface controlled

6 0 1

-2

4

-4

4

2 3

-1

2

0 0

1.0

2

1.0

Time [×103 hours]

2.0

0

0

1.0

Time [×103 hours]

2.0

-2

Mixed Transport controlled 0 2 Log10(DaII)

4

Table 1 

Olivine

Talc

Lizardite

Brucite

Magnetite











wt.%

SiO2

40.94

48.94

40.66

0.15

4.13

TiO2

0.00

0.00

0.00

0.00

0.00

Al2O3

0.02

0.51

0.00

0.12

0.00

Cr2O3

0.00

0.00

0.00

0.00

0.00

FeO

8.49

4.02

2.44

11.67

84.54

MgO

50.65

21.78

39.66

60.72

1.51

MnO

0.15

0.03

0.07

0.25

0.24

CaO

0.08

0.03

0.05

0.00

0.00

Na2O

0.03

0.42

0.10

0.07

0.05

K2O

0.00

0.00

0.00

0.04

0.00

100.36

75.73

82.98

73.02

90.49

Total

cations per formula unit Oxygen

4.00

11.00

7.00

7.00

7.00

Si

0.99

3.99

1.99

0.01

0.36

Ti

0.00

0.00

0.00

0.00

0.00

Al

0.00

0.05

0.00

0.01

0.00

Cr

0.00

0.00

0.00

0.00

0.00

Fe

0.17

0.27

0.10

0.68

6.07

Mg

1.83

2.64

2.90

6.27

0.19

Mn

0.00

0.00

0.00

0.01

0.02

Ca

0.00

0.00

0.00

0.00

0.00

Na

0.00

0.07

0.01

0.01

0.01

42

K

0.00

0.00

0.00

0.00

0.00

Total

2.99

7.02

5.01

6.99

6.65

0.91

0.91

0.97

0.90



atomic Mg/(Mg + Fetotal)

43

Table 2

Overall reaction

n

㻌㻌

Equilibrium silica concentration for reaction n



Log10Keq§ (CnSiO2(aq), eq ; mol cm–3 solution)

R1

3 Mg2SiO4 + 5 SiO2(aq) + 2 H2O

ˢ

2 Mg3Si4O10(OH)2

17.148

2.649 × 10–7

R2

3 Mg2SiO4 + SiO2(aq) + 4 H2O

ˢ

2 Mg3Si2O5(OH)4

6.263

3.887 × 10–10

2 Mg(OH)2 + SiO2(aq)

–4.395

2.868 × 10–8

R3

Mg2SiO4 + 2 H2O

ˢ

R4+

Mg3Si2O5(OH)4 + 2 SiO2(aq)

ˢ

Mg3Si4O10(OH)2 + H2O

5.442

1.354 × 10–6

R4-

Mg3Si2O5(OH)4 + 2 SiO2(aq)

ˣ

Mg3Si4O10(OH)2 + H2O

5.442

1.354 × 10–6

R5+

3 Mg(OH)2 + 2 SiO2(aq)

ˢ

Mg3Si2O5(OH)4 + H2O

9.724

9.787 × 10–9

R5-

3 Mg(OH)2 + 2 SiO2(aq)

ˣ

Mg3Si2O5(OH)4 + H2O

9.724

9.787 × 10–9

§

Value at 300°C and Psat obtained from SUPCRTBL (Zimmer et al., 2016)

$

Calculated from Keq.

44





Table 3

Parameter

Symbol

Value

Diffusion coefficient of SiO2(aq) in water

Log10(DSiO2(aq))

Rate constant of reaction R1

Log10(kR1)

–13.51 ± 0.02

Rate constant of reaction R2

Log10(kR2)

–15.75 ± 0.02

Rate constant of reaction R3

Log10(kR3)

–11.76 ± 0.10

Rate constant of reaction R4 (forward)

Log10(kR4+)

–7.65 ± 2.12

Rate constant of reaction R4 (backward)

Log10(kR4-)

–11.56 ± 0.13

Rate constant of reaction R5 (forward)

Log10(kR5+)

–10.74 ± 0.22

Rate constant of reaction R5 (backward)

Log10(kR5-)

–19.00 ± 1.09

Cementation exponent

Log10(m)

0.036 ± 0.019

–4.20 ± 0.03

Diffusivity in cm2 s–1 and rate constants in mol SiO2(aq) cm–2 mineral s–1

45