Experimental determination of the hydrothermal solubility of ReS2 and the Re–ReO2 buffer assemblage and transport of rhenium under supercritical conditions

To understand the aqueous species important for transport of rhenium under supercritical conditions, we conducted a series of solubility experiments on the Re–ReO2 buffer assemblage and ReS2. In these experiments, pH was buffered by the K–feldspar–muscovite–quartz assemblage; in sulfur-free systems was buffered by the Re–ReO2 assemblage; and and in sulfur-containing systems were buffered by the magnetite–pyrite–pyrrhotite assemblage. Our experimental studies indicate that the species ReCl40 is dominant at 400°C in slightly acidic to near-neutral, and chloride-rich (total chloride concentrations ranging from 0.5 to 1.0 M) environments, and ReCl3+ may predominate at 500°C in a solution with total chloride concentrations ranging from 0.5 to 1.5 M. The results also demonstrate that the solubility of ReS2 is about two orders of magnitude less than that of ReO2. This finding not only suggests that ReS2 (or a ReS2 component in molybdenite) is the solubility-controlling phase in sulfur-containing, reducing environments but also implies that a mixing process involving an oxidized, rhenium-containing solution and a solution with reduced sulfur is one of the most effective mechanisms for deposition of rhenium. In analogy with Re, TcS2 may be the stable Tc-bearing phase in deep geological repositories of radioactive wastes.


Introduction
There has been increasing interest in the aqueous geochemistry of rhenium because of its various important applications as summarized in Xiong and Wood. 1,2 In our previous publications, the dominant oxidation state of rhenium in high-temperature hydrothermal solutions under geologically reasonable oxygen fugacity conditions was determined experimentally to be z4 by measuring the solubility of ReO 2 as a function of oxygen fugacity. 1 In the temperature range from 100 to 200 uC, Xiong and Wood 2 suggest that the neutral species, formulated as Re(OH) 4 0 , is important over a wide range of pH, and is responsible for transport of rhenium leading to the enrichment of rhenium in various environments, including sandstone copper deposits and black shales.
In this communication, we present our experimental data on the solubility of rhenium phases under supercritical conditions. The objective of our study is to assess probable rhenium species important under supercritical conditions (up to 510 uC). Based on findings from these experiments, we hope to provide a better understanding of the possible enrichment and deposition mechanisms for rhenium in various high-temperature environments. In particular, our treatment will focus on possible enrichment mechanisms for Re in porphyry copper-molybdenum and skarn molybdenum-(tungsten) deposits. In addition, our experimental results may also provide guidance to applications of the Re-Os system in high-temperature environments.

Methology
The methodology employed in our experiments under supercritical conditions has been described in detail elsewhere. 1,3 The key components of the methodology employed are briefly summarized here.
In our experiments, self-sealing reaction vessels with a volume of approximately 250 mL, lined with gold, and which permit withdrawal of samples at the temperatures and pressures of interest, were used. The pH and f O 2 were buffered by thermodynamically well-characterized solid-phase assemblages such as K-feldspar z muscovite z quartz and Re-ReO 2 . K-feldspar, quartz, and muscovite were mixed in approximately a 1 : 1 : 1 mass ratio and the total mass was approximately 15 g. The source of these solid phases and their respective purities are given in detail elsewhere. 1,3 Starting materials were metallic rhenium (99.995%, grain size smaller than 149 mm, minimum grain size ¢1.8 mm) and ReO 2 (99.9%, grain size smaller than 44 mm, minimum grain size ¢1.8 mm) from Aldrich Chemical Company. The ReS 2 (99%, minimum grain size w 1.8 mm) employed was from Johnson Matthey Company. Magnetite, pyrite and pyrrhotite (research grade) were natural samples and were from Ward's Natural Science Establishment, Inc. Starting materials were loaded in silver or gold capsules as in previous work. 1 After the reaction vessels were assembled into the furnaces, compressed argon was used to check for leaks in the line. Next, the reaction vessels were purged with compressed argon at least three times to dislodge and remove any residual air in the reaction vessels. The vessels were then heated rapidly to the desired temperature and pressure in nichrome resistance furnaces. The amount of electric power provided to the top and bottom of the furnace could be adjusted separately so that the thermal gradient could be controlled precisely. Details of the temperature control and calibration of type K thermocouples used in our experiments can be found in Xiong and Wood. 1,3 To homogenize the solutions in the vessel, convection was induced by maintaining the bottom of the vessel 2 uC higher than the top.
Pressure was measured to within ¡10 bar using a pressure transducer and a digital pressure meter from Omega Engineering Company. To minimize the exposure of the transducer to corrosion, the vessel was connected with an Ashcroft Inconel 718 tube analogue gauge in some experimental runs, and the pressure was measured to within ¡15 bar. Both the transducer and Ashcroft analogue gauge were calibrated against a Heise analogue gauge.
When sampling, supercritical conditions were assured by setting run temperatures and pressures according to the data of Sourirajan and Kennedy 4 for the analogous NaCl system. Sampling details are similar to those of Xiong and Wood. 1,3 The concentrations of Re were determined by inductively coupled plasma-atomic emission spectrometry (ICP-AES) with an axial-view torch (Perkin Elmer Optima 3000 XL). In order to minimize matrix effects, blanks and standard calibration solutions were precisely matched to the samples with respect to matrix. The correlation coefficients of the calibration curves were better than 0.999. The conservative detection limit for rhenium is estimated to be better than 14 ppb [y7.5 6 10 28 mol (kg H 2 O) 21 ] based upon at least three replicate analyses of matrix-matched blanks. The analytical precision in terms of the relative standard deviation (RSD) of replicate analyses is better than 1.5%.
After each run, the starting phases, and the pH and f O 2 buffer assemblages were examined by X-ray powder diffraction. No components of the buffers were observed to have been exhausted and no new phases appeared during any run, suggesting that buffered conditions were maintained.
In order to facilitate the interpretation of experimental results, the pH values and molar concentrations of major species in the KCl-H 2 O system at different KCl concentrations were calculated according to the following equations using the EQBRM computer code 5 (Table 1). Equilibrium constants for these reactions were obtained from the SUPCRT92 database 6 with updated parameters for relevant species for HKF equations from ref. [7][8][9] Mass-action expressions were: The charge-balance expression employed was: And the mass-balance expression was: Activity coefficients for charged species were calculated using the extended Debye-Hü ckel equation, 10 log c i~2 AZ i where A and B at 400 uC and 0.5 kbar and 500 uC and 1 kbar are from Helgeson and Kirkham, 11 å is from the compilation, 12 and b for the similar NaCl system is from Helgeson et al.. 13 Activity coefficients of neutral species were assumed to be unity.
In those experiments assessing the solubility of rhenium sulfide (ReS 2 , purity 99.5%, Johnson Matthey Co.) in sulfurcontaining environments, f O 2 and f S 2 were buffered by the magnetite(Mt)-pyrite(Py)-pyrrhotite (Po) assemblage, as shown by the following reactions: The pH values fixed by the assemblage KMQ in our experiments range from 4.5 to 5.7 at around 400 uC and from 4.6 to 5.7 at around 500 uC, respectively (Table 1) (for reference, neutral pH at 500 uC and 800 bar is y6.0). The pH of the KMQ buffer in a 0.1 mol KCl solution at 500 uC and 550 bar is calculated to be 5.5 (neutral pH at 500 uC and 550 bar is y6.6) and in 0.1 mol KCl solution at 400 uC and 550 bar is calculated to be 5.0 (neutral pH at 400 uC and 550 bar is y5.6), respectively. Therefore, the experiments are all in the nearneutral to slightly acidic pH range.

Experimental design
The purpose of the present experiments was to determine the solubility of rhenium as a function of chloride concentration and pH. As we have demonstrated that, at geologically reasonable oxygen fugacity the dominant oxidation state of rhenium is z4, 1 the general solubility reactions can be expressed as one of the following, the same as those suggested by Xiong and Wood, 1 using ReO 2 as starting material: Reaction (13) reflects the consideration that some cations with four positive charges such as V z4 and U z4 tend to form oxoaquo-cations before other complexes are formed. 14 Reaction (12) represents the view that there is no structural evidence for cations with four positive charges such as Zr z4 and Hf z4 to form ''yl'' ions like ZrO z2 and HfO z2 . 15 For simplicity, we follow the convention of Baes and Mesmer 15 for cations with four positive charges. In the present solubility studies, it is not possible to resolve the degree of hydration of the complex or the possible existence of the rhenyl cation (ReO z2 ). Other techniques are needed to resolve these issues in future experimental work.
Using reaction (12) as an example, if the equilibrium constant for reaction (12) is expressed in logarithmic form and rearranged when temperature, pressure, and concentrations of chloride are constant, in log SRe versus pH space, the ligand number p for hydroxide can be evaluated according to the slope: (h log SRe/h pH) T,P,mCl2~2 (4 2 p) When temperature, pressure and pH are constant, the ligand number n for chloride can be determined according to the slope in log SRe versus log m Cl 2 space: (h log SRe/h log m Cl 2) T,P,pH~n The above experimental design has been applied successfully in our experimental work under subcritical conditions. 2

Experimental results and interpretations
The results of experiments conducted under supercritical conditions are tabulated in Table 1 and plotted in Fig. 1. The molal concentrations of major species in each system as calculated using EQBRM (see above) are listed in Table 2. From Fig. 1 it is clear that equilibrium was attained after 400 h at 400 uC and 200 h at 500 uC. In comparison, it should be recalled that our experimental results presented elsewhere 2 under subcritical conditions were buffered with respect to oxygen fugacity and pH by a fixed partial pressure of hydrogen and by aqueous pH buffers, respectively. These buffers equilibrate more quickly than solid assemblages adopted both in the present experiments and those involving platinum group elements (PGE) under supercritical conditions presented elsewhere. 3 It can be seen from Fig. 1A and 1C that the concentrations of rhenium in experimental runs using ReS 2 buffered by the Mt-Py-Po assemblage are about two orders of magnitude lower than those using the Re-ReO 2 assemblage at the same temperature and chloride concentration. Experimental results show that there is good agreement of concentrations between filtered and unfiltered samples from experiments involving the Re-ReO 2 assemblage ( Fig. 1A-1C), implying that rhenium is truly in solution. However, there is some scatter between the concentrations from filtered samples and those from unfiltered samples in the experimental run involving ReS 2 buffered by the Mt-Py-Po assemblage (Fig. 1A). This may be due to the fact that experimental runs involving ReS 2 have lower concentrations of rhenium than those using the Re-ReO 2 assemblage, resulting in a larger analytical uncertainty. The average equilibrium concentrations (¡two standard deviations) are listed for each experiment in Table 3. All of the  Interpretation of data. From Table 3, it is apparent that at similar chloride concentrations and pH, the rhenium concentrations from experiments using ReS 2 are about two orders of magnitude lower than those from experiments using the Re-ReO 2 buffer assemblage. This suggests that ReS 2 (or the ReS 2 component in molybdenite or other sulfides) is a solubilitycontrolling phase in high-temperature environments containing sulfur.
Ideally, the chloride-and pH-dependence of the solubility of rhenium is independently evaluated according to eqn. (11) and (12), as we did under subcritical conditions. 2 However, because the KMQ buffer was adopted in our experiments under supercritical conditions, pH and chloride dependence cannot be evaluated independently; i.e., the coefficient p in reaction (12) cannot be evaluated by keeping chloride concentration constant while pH is changed independently. In this communication, we assumed that mixed chloride complexes with hydroxyl suggested in reaction (12) or (13) are not important in the present experiments considering the conditions of the high temperatures, relatively high concentration of chloride, and slightly acidic to near-neutral pHs. This assumption is mainly based on the findings of previous studies which demonstrated increased stability of chloride complexes, simplified speciation, and the unimportance of mixed complexes at high temperatures (i.e., 500 uC). 16,17 Therefore, the interpretation of chloride dependence is based on reaction (11). However, it should be cautioned that this assumption is subject to experimental verification in the future.
To evaluate the chloride-dependence of the solubility of the assemblage Re-ReO 2 , log m SRe is plotted versus log m Cl2 at constant pH in accordance with eqn. (15). For this purpose, the rhenium concentration data from Re-0.5, Re-0.75/4 and Re-1.0S (Table 3) are plotted against log m Cl2 (Fig. 2). Note that the pH is almost constant (from 4.5 to 4.6) in these experimental runs (Table 1), but the measured Re concentrations were corrected for pH differences assuming the pHdependence indicated by reaction (11). As the slope of a straight line fit to the data in Fig. 2 is close to 4 (3.94 ¡ 0.35, R 20 .99), the dominant species appears to be ReCl 4 0 according to reaction (16): It is also possible that small amounts of ReCl 3 z and ReCl 5 It should be mentioned that we attach considerable uncertainty to the interpretation of the chloride dependence of the experimental data at 500 uC because the variation in pH is 0.3 log units for these experiments. The solubility correction introduced by such pH differences should be more than one log unit according to reaction (11), which may result in large uncertainties in the chloride ligand number when determined as described in the preceding paragraph. The slope determined with the pH correction according to reaction (11) is 1.28 ¡ 0.16 (R 2~0 .985) (Fig. 3), whereas the slope determined without the pH correction is 2.99 ¡ 0.016 (R 2~0 .99997) (Fig. 4). Judging from the results at 400 uC and at lower temperatures, 2 a slope of y3 (corresponding to ReCl 3 z ) is more likely than a slope of y1 (corresponding to ReCl z3 ) at 500 uC. This interpretation is also supported by the relatively small variation of calculated equilibrium constants as a function of ionic strength (see below) . However, as the pH differences are relatively large in these experiments, more experiments are certainly needed to refine the interpretations at 500 uC.
It is of interest to note that there is a negative dependence on temperature in the temperature range from 400 to 500 uC in the same solution, implying that there is a retrograde solubility of the Re-ReO 2 buffer assemblage. This can be demonstrated by examining the results from OsO 2 -0.1RRO at 400 uC and Re-0.1RRO at 500 uC. The former has an average equilibrium concentration of 3.0 ¡ 0.4 6 10 24 molal, whereas the latter has an average equilibrium concentration of 2.1 ¡ 1.1 6 10 24 molal. This trend is also suggested by the Re-0.5 runs at 410   and 510 uC, and by the Re-1.0S run (1.0 mol KCl) at 410 uC and the Re/Os-1.0RRO run (1.0 mol KCl) at 500 uC. In addition to higher calculated pH at 500 than at 400 uC, this may be due to the combination of decreasing free chloride concentration with decreasing chloride ligand number with temperature. For example, in a 1.0 mol KCl solution, the concentration of free chloride decreases from about 20.096 log units at 410 uC to about 20.59 log units at 500 uC (Table 1), i.e., a decrease of y0.6 log units. This decrease in the concentration of free chloride with increasing temperature may also be responsible for the apparent decrease in chloride ligand number as temperature increases from 400 to 500 uC (see the preceding paragraph). On the other hand, the solubility of ReS 2 shows a slight increase in solubility between 400 and 500 uC (cf., Re-0.1MPP at 400 uC and Re-0.1MPP/2 at 500 uC).
Derivation of equilibrium constants. In order to calculate thermodynamic equilibrium constants according to reaction (16), the activity coefficient of the neutral species, ReCl 4 0 , is assumed to be unity. As mentioned before, the activities of other species were calculated by using the extended Debye-Hü ckel equation and EQBRM code. The thermodynamic equilibrium constants for reaction (16) at 400 uC at different ionic strengths are listed in Table 4. At 500 uC, the species ReCl 3 z was identified tentatively as the predominant species. The thermodynamic equilibrium constant for reaction (17) at 500 uC (17) was estimated. In these calculations, the extended Debye-Hü ckel equation 10 is used to estimate the activity coefficient for ReCl 3 z ; å is assumed to be the same as other z4-charged ions, and is taken from the compilation. 12 It is apparent from Table 4 that there is relatively little variation in the calculated thermodynamic equilibrium constants for both reactions (16) and (17) as a function of ionic strength, lending support to our assignment of the stoichiometry of the Re-chloride complexes.

Implications
The above results indicate that, in high-temperature environments, appreciable amounts of rhenium can be dissolved in chloride-containing (log m Cl 2~20.4 to 20.1) aqueous fluids as the neutral chloride species, ReCl 4 0 . It is also of importance to note that ReS 2 is much less soluble than ReO 2 (about two orders of magnitude lower). These conclusions have bearing on the transport and deposition of rhenium in various environments and our data are the first step in the quantitative elucidation of origins of rhenium deposits in these environments. In the following, we apply our results to various environments and explore their implications.
As mentioned above, the solubility of ReS 2 is about two orders of magnitude lower than that of ReO 2 . This has important implications. First of all, it is apparent that rhenium will be stabilized as a sulfide phase(s) in environments where reduced sulfur is present. This explains why rhenium sulfides occur in a wide range of environments including mafic and ultramafic complexes such as the Stillwater Complex 18 and fumarolic deposits from volcanoes, 19 whereas sulfur-free rhenium phases have limited occurrences. Second, it can be inferred that samples which have been subject to alteration by oxidizing fluids are likely to have experienced rhenium remobilization, and therefore they are not good candidates for Re-Os radiogenic investigations. Third, it can be deduced that reducing fluids containing sulfur have much less capacity for transporting rhenium, and therefore environments dominated by reducing fluids are not favorable to formation of rhenium deposits of importance. To form rhenium deposits of significance, oxidizing fluids must be operative at some stage(s) of ore formation. On the other hand, reducing fluids have the least ability to disturb the Re-Os system. In the following, transport of rhenium by hydrothermal fluids is addressed quantitatively.
Quantitative assessment of potential size of rhenium mineralization in porphyry copper-molybdenum and skarn tungsten-molybdenum systems Molybdenite in porphyry copper-molybdenum and skarn tungsten-molybdenum systems has been observed to be enriched in Re. [20][21][22][23][24][25][26][27][28] It is of special interest to note that existing reserves of rhenium indicate that porphyry copper-molybdenum systems are very important. 23 In the following, we first present field observations on rhenium mineralization in skarn tungsten-molybdenum and porphyry copper-molybdenum systems and then compare these observations with our quantitative predictions based on our experimental data.
Field observations: The Little Boulder Creek skarn molybdenum deposit in Idaho can be used as an example to estimate the size of skarn Mo-(W) systems and the amount of rhenium mineralization. The reserves of ores with a grade of 0.15 wt% of MoS 2 are 167 million tons. 29 Although the rhenium concentration in molybdenite in this deposit is not available, we may assume that the rhenium concentration in molybdenite in this deposit is similar to the rhenium concentration in other skarn Mo-(W) deposits. For example, Stein et al. 29 determined that the rhenium concentration in molybdenite in the Schwartz, Klee and Meyer skarn Mo-W deposits in the Pitkaranta district, Russia, ranges from 130 to 479 ppm with an average of 224 ppm. Assuming the rhenium concentration in molybdenite in the Little Boulder Creek deposit is of the order of 100 to 200 ppm, the mass of rhenium in this deposit is estimated to be from y2.5 6 10 7 to y5 6 10 7 grams (Table 5).
In the El Teniente porphyry Cu-Mo mine, the grade of rhenium in ores is 10 ppm (10 grams tonne 21 ). 23 As ore reserves are estimated to be about 3.5 billion tonnes, the total mass of rhenium in the ore reserves is about 3.5 6 10 10 grams. 23 In addition, this deposit has about 4 6 10 8 tonnes of tailings in its waste dumps with a grade of 9 grams tonne 21 of rhenium. 23 Therefore, the total rhenium in this deposit is y4 6 10 10 grams (Table 5).
Predictions: In order to determine, from our experimental solubility data, the total amount of Re that can be transported in porphyry Cu-Mo and skarn Mo-W deposit-forming systems, the total amount of fluid involved in these systems must be estimated. The total amount of Re predicted based on our experimental results can then be compared to the amounts calculated in the preceding section from grade and tonnage data.
The amount of fluid involved in a typical porphyry Cu-(Mo) system has been estimated to be y10 15 grams using the average tonnage of copper (y1 million tonnes) and the copper concentrations in ore-forming fluids (1000 ppm). 3 In giant porphyry Cu-Mo systems such as El Teniente porphyry Cu-Mo mine, the total mass of fluid involved may be one to two orders of magnitude higher than that in a typical porphyry Cu-Mo system. For example, the tonnage of copper in El Teniente porphyry Cu-Mo mine is at least 31.5 million tonnes. 24 Therefore, a total mass of fluids of y10 17 grams may be reasonable. The pH of porphyry Cu-(Mo) systems is likely to be buffered by the KMQ assemblage. 3 Other thermodynamic parameters in porphyry Cu-(Mo) systems employed in the present predictions have been described in Xiong and Wood. 3 In order to estimate the total mass of fluids involved in the formation of a typical skarn tungsten-molybdenum system, the calculated scheelite solubility (39 ppm) in 1.0 mol NaCl solution at 600 uC and 2000 bar of Wood and Samson 31 is used. This calculated value has been demonstrated to be in excellent agreement with an experimentally measured value. 31 The Molyhill skarn W-Mo deposit in the Northwestern Territory, Australia, has reserves of 1.5 million tons of ores with a WO 3 grade of 1.0 wt%. 32 Apparently, the mass of tungsten in the Molyhill deposit is 1.2 6 10 10 grams. The total mass of fluid involved should be y3.0 6 10 14 grams according to the solubility of scheelite cited above, assuming that all the tungsten in the fluid is deposited. The Osgood Mountains W-Mo skarns in Humbolt County, Nevada, USA, have reserves of 1.4 million tons of ores with a WO 3 grade of 0.45 wt%. 32 The mass of tungsten in this deposit is 5 6 10 9 grams. Therefore, the estimated total mass of fluid involved should be y1.3 6 10 14 grams. Consequently, based on the estimated total mass of fluids involved in these two deposits, we assume that the total mass of fluid involved in the formation of a typical W-Mo skarn system should be in the neighborhood of y2 6 10 14 grams.
The pH of skarn W-Mo systems is likely to be buffered by various assemblages such as the wollastonite-quartz assemblage, which is common in the distal zone of W-Mo skarns: Although the wollastonite-quartz assemblage has not been deliberately calibrated as a pH buffer, it has been reasoned that this assemblage should buffer pH values in the near-neutral range, 33 which is close to our experimental pH values. In the endoskarn zone, where major W-Sn mineralization occurs, the pH of initial mineralizing fluids exsolved from crystallizing (granitoid) magmas should be buffered by mineral assemblages of granitoid rocks such as quartz z K-feldspar z muscovite. For example, in the endoskarn of the Sangdong deposit, Korea, biotite skarn and muscovite skarn are dominant. 32 As the quartz z K-feldspar z muscovite assemblage was employed as a pH buffer in our experiments, the pH values in our experiments should be most likely to resemble those in the early stages of mineralizing fluids. It has been documented that fluids responsible for proximal skarns with which W-Mo mineralization is generally associated have salinities ranging from w60 wt% NaCl eq. to y8 wt% NaCl eq., 32 which correspond to concentrations of NaCl ranging from y1.5 M to higher than y26 M. Fluids res-ponsible for distal skarns commonly have lower salinities ranging from y12.5 to y1.25 wt% NaCl eq., 32 corresponding to concentrations of NaCl from y0.2 to y2.5 M. Obviously, wt% NaCl eq. to y8 wt% NaCl eq. g As log m FeSO4 , King Island.
these salinities, especially those in fluids responsible for proximal skarns, are generally higher than those in our experiments. In this respect, our solubility data yield minimum estimates of the amount of Re that can be transported by these hydrothermal systems (but see comments below regarding the occurrence of ReS 2 in solid solution). Assuming the solubility-controlling phase is pure ReS 2 and using the estimated total masses of fluids in typical porphyry Cu-(Mo) and skarn W-Mo systems mentioned above, when we apply our solubility data solutions with total chloride concentration of 0.1 M (Table 3) at 400 uC (1.2 6 10 26 mol kg 21 H 2 O) and at 500 uC (3.2 6 10 26 mol kg 21 H 2 O) to the above systems, the rhenium that can be transported by typical porphyry Cu-Mo and skarn W-Mo systems ranges from y2 6 10 8 to y6 6 10 8 and from y4 6 10 7 to y1.2 6 10 8 grams, respectively (Table 5). It should be emphasized that the experimental conditions are comparable to those conditions prevailing in porphyry Cu-Mo and skarn W-Mo systems ( Table 5), except that the salinities in our experiments are somewhat lower. Therefore, direct application of our experimental results using ReS 2 as the starting material and magnetite-pyrite-pyrrhotite assemblage to buffer f O 2 and f S 2 is well justified. However, the ReS 2 used in our experiments is a pure end-member. In the natural systems, it is likely that a solid solution between MoS 2 and ReS 2 would control the solubility of rhenium as suggested in Table 5. It is well known that the solubility of a component in solid solution is generally less than that of the pure end-member phase because the activity of the solid solution is less than unity. 34 Although the concentrations of rhenium in molybdenite (MoS 2 ) have been determined in several deposits as mentioned above, the activity coefficients of ReS 2 in MoS 2 -ReS 2 solid solution system are not known. Therefore, the activity of ReS 2 in such solid solutions cannot be quantitatively evaluated at present. However, it can be expected that pure ReS 2 should have higher solubility than the solid solution between MoS 2 and ReS 2 . Notice that our predicted tonnage of rhenium mineralization for skarn W-Mo systems is on the same order of magnitude as the observed tonnage in a typical skarn W-Mo systems (Table 5). Our predicted tonnage of rhenium mineralization for porphyry Cu-Mo systems is about one order of magnitude higher than the observed tonnage in typical porphyry systems (such as La Disputada, Chile), but is on the same order of magnitude as the tonnage observed in the giant porphyry Cu-Mo systems (e.g., El Teniente, Chile) (Table 5). Therefore, when the fact that solid solution of MoS 2 and ReS 2 controls solubility is taken into account, our experimental results are in excellent agreement with field observations and our results for giant porphyry Cu-Mo systems (Table 5) predict that the El Teniente depositforming fluid was probably close to saturation with the ReS 2 component in solid solution with molybdenite.
In the Chenmanshan skarn and porphyry deposit (where molybdenite is observed) in Juijiang, Jiangxi Province, China, the grade of rhenium is 6 6 10 25 %. 35 The reserves of Cu in this deposit were 2.1 6 10 6 tons 36 and the grade of Cu was 0.75%. 35 Therefore, the total amount of ore is estimated to be y2.8 6 10 14 grams. Hence, the amount of Re that had been transported is computed to be y10 8 grams. In comparison with the above minimum mass of Re that can be transported (y2 6 10 8 to y6 6 10 8 grams) in a typical porphyry system, the Chenmanshan porphyry deposit-forming fluid may have also been saturated with ReS 2 or its solid solution with other sulfides.

Deposition of rhenium
As the stabilities of the predominant rhenium complexes deduced from our experiments, i.e., ReCl 4 0 and ReCl 3 z , have strong dependences on chloride concentration, we can infer that dilution owing to mixing of high-concentration chloride fluids with low-chloride fluids is one of most effective mechanisms for the deposition of rhenium from porphyry systems. It also needs to be realized that, according to reactions (16), (17), (19) and (20) ReS 2 z 4H z z nCl 2 < ReCl n 4 2 n z 2H 2 S 0 (19) ReS 2 z 2H z z nCl 2 < ReCl n 4 2 n z 2HS 2 (20) the solubility of ReO 2 or ReS 2 should decrease strongly with increasing pH. Therefore, an increase in pH could induce precipitation of rhenium in chloride-rich fluids. However, hydroxy complexes of rhenium may become important at higher pH ranges in chloride-poor fluids, in which case an increase in pH might possibly cause an increase in rhenium solubility. In addition, from the fact that ReS 2 has much lower solubility than Re or ReO 2 , we can conclude that mixing processes involving an oxidizing fluid transporting rhenium and a fluid containing reduced sulfur should be an effective depositional mechanism for rhenium. The slight prograde solubility of ReS 2 in the temperature range from 400 to 500 uC means that more rhenium sulfide is dissolved at higher temperatures. This is different from the Re-ReO 2 assemblage in sulfur-free environments, which shows a slight retrograde solubility in the temperature range from 400 to 510 uC. The slight prograde solubility of ReS 2 might explain the puzzling observation that molybdenite deposited at higher temperatures has lower rhenium concentration (i.e., lower content of ReS 2 ). 20,37 This explanation is contingent upon a weak or retrograde temperature dependence of molybdenite solubility over the above temperature range. However, regarding the solubility of molybdenite in hydrothermal solutions, a consistent picture has not emerged. 38 The much lower solubility of ReS 2 compared to that of the Re-ReO 2 assemblage also has implications to disposal of fissiogenic 99 Tc, for which Re is a good analogue. 39 As ReS 2 is the stable phase in most subsurface geological environments, TcS 2 should be the preferred phase in deep geological repositories for radioactive wastes. This can ensure that even if radioactive wastes in deep geological repositories interact with solution at elevated temperatures in the worst-case scenario, release of 99 Tc would be at a minimum. To achieve this goal, radioactive wastes containing 99 Tc should be sequestered as TcS 2 .