Natural Fluctuation of Sulfur Species in Volcanic

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fluctuations of the sulfur species caused by the presence of the dissipative struc- ... non-equilibrium chemical structures whose persistence in natural systems re- ...... zero and first-order terms are able to describe the dissipative structure phe-.
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J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · pp. 75–102

Natural Fluctuation of Sulfur Species in Volcanic Fumaroles 

Giordano Montegrossi1, , Franco Tassi2 , Angelo A. Minissale1 , Orlando Vaselli1,2 , and Antonella Buccianti2 1 National Research Council of Italy (C.N.R), Institute of Geosciences and Earth Resources, Via G. La Pira 4, 50121 Florence, Italy 2 Department of Earth Sciences, University of Florence, Via G. La Pira 4, 50121 Florence, Italy 

Corresponding author ([email protected])

Communicated by E.E. Michaelides, Denton, USA, and B. Zimanowski, Würzburg, Germany

Abstract We describe and discuss the origin of short-term (hours) variations in the concentration of sulfur species (SO2, H2 S, and S8 0) of crater fumaroles discharging at different temperatures (up to 410 ◦ C) from five volcanic systems. Sulfur species can be investigated as an independent subsystem within the whole composition characterizing the fumarolic fluids, their chemical behavior being governed by similar laws in volcanic systems. The measured data are time dependent and show regular oscillations whose amplitude is by far larger than the analytical error. The agreement between the theoretical and the measured concentrations of SO2, H2S, and S8 0 suggests that the formation of dissipative structures can explain the observed oscillations. Accordingly, the periodicity and the amplitude of the compositional oscillations were found to be in strong relation with the entropy excess of the non-equilibrium systems under investigation. The results of our study suggest that the amplitude and magnitude of short-term natural (self-induced) fluctuations of the sulfur species caused by the presence of the dissipative structures, and their comparison with the compositional variations of other subsystems, should be taken into serious account for geochemical monitoring purposes.

1. Introduction Dissipative structures, firstly recognized in biological processes [1–3], are non-equilibrium chemical structures whose persistence in natural systems reJ. Non-Equilib. Thermodyn. · 2008 · Vol. 33 · No. 1 © 2008 Walter de Gruyter · Berlin · New York. DOI 10.1515/JNETDY.2008.005

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quires a continuous interchange of matter and energy between the system under consideration and the environment. One of the first discovered dissipative structures is related to the process of energy transfer during the photosynthesis process, from methylenetetrahydrofolatereductase (NADPH2 ) to CO2 , to obtain hexose-phosphate (C6 H13O9 P), which is converted to disaccharide (C12H22 O11) and triggered by the sunlight at a rate proportional to the concentration of triose-phosphate ion [H(OH)C=C(OH)-CH2 O(PO2 )−3 ] [2]. Dissipative structures have been described for both inorganic chemical reactions and physical processes [4–6]. Statistical and non-equilibrium thermodynamic models have been developed for generic systems [3]. An important consequence of the formation of dissipative structures is that, as a chemical– physical process proceeds in an open system under steady-state conditions, both the concentration of the participating components and the associated entropy follow oscillations within dynamic equilibrium conditions [2, 3, 7]. In active volcanic environments, fumarolic gas discharges are dynamic systems where energy (heat) and chemical species (H2 O, CO2 , SO2 , H2 S, HCl, HF, CH4, etc.) are transferred from a deep source (magma chamber) to the atmosphere. Long-period (months or years) variations in energy (manifested through fumarolic outlet temperatures) and in the concentration of gas components are considered possible precursors of eruptive activity, since they can be caused by (i) new magma inputs from depth into shallower magma chambers, (ii) changes in the path and/or geometry of the volcanic conduit from the magma chamber to the surface, (iii) changes in the boundary conditions, such as seismic activity or salt deposition (sealing processes) in fractures and ducts, and (iv) changes in the local shallow hydrology as a consequence of permeability variations (caused by sealing processes). However, variations of the chemical and isotopic compositions of fumarolic gases, although partly affected by analytical error, were also observed even at a very shorter time scale (minutes) (e.g., Satsuma-Iwojima and Kuju volcanoes [8]). Such rapid compositional changes on volcanic fluids, which cannot be ascribed to macroscopic modifications of the volcanic systems, were interpreted by the authors as the result of a mixing process at different degrees among at least three end-members (i.e., magmatic water, air, and hydrothermally derived fluids), an explication that seems to be not completely exhaustive for the observed phenomena. In the present work, the short-term temporal changes in the concentration of SO2 , H2 S, and S8 0, which can be considered an independent subsystem within the whole fumarolic composition, observed in nine crater fumaroles, Solfatara volcano and Vulcano Island (Italy), Poas and Turrialba volcanoes (Costa Rica), and El Chichon volcano (Mexico), are interpreted as related to the formation of non-equilibrium dissipative structures. J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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2. Fluido-dynamic effects on the composition of a fumarolic fluid and sampling strategies The fluid discharging from a fumarole can be considered a mixture of steam, gas components, and solid particles such as dust, crystals, aerosols, and elemental sulfur. The fluid is rapidly transported to the surface at temperatures ranging from about 80 to more than 1100 ◦ C [9]. Several methods to collect fumarolic gases exist, each adopting different sampling times, which are mainly based on the personal experience of the individuals [8, 10–14]. The fluid-dynamic conditions existing inside a fumarolic duct are of primary importance in evaluating the dependence of the chemical composition of fumaroles on sampling time. Fluid motion in a fumarolic conduit consists of (i) a laminar regime that transfers the heterogeneous fluid to the surface at a regular speed and (ii) a turbulent regime that generates vortices and locally increases the solids/(gas+steam) ratio [15–17]. Thus, portions of different motion regimes can be related to segments of the moving fluids, where the variation in concentration of solid material depends on (a) a random frequency component (frequency noise oscillation), caused by the fortuitous formation of vortices in maximum turbulence zones; (b) a random concentration component (amplitude noise oscillation), caused by local accumulation of particulate material; (c) a concentration component with a fixed frequency and regularly variable amplitude (periodic or well-ordered oscillation), caused by the alternation of laminar and turbulent motion regimes; (d) a concentration component with fixed amplitude and regularly variable frequency, caused by re-mobilization of particulate from the walls of the fumarolic conduit. The random variations of frequency (a) and concentration component (b) have oscillation periods of generally less than 1 s [18]. Thus, such variations do not affect the average solid/fluid ratio for observation periods longer than 1 min. Regularly variable amplitude concentrations (c) and frequency concentrations (d) are caused by the alternation of laminar and turbulent phases, depending on (i) fluid speed, (ii) conduit shape, and (iii) size of particulate material carried on by the fluid. Periods of type (c) and (d) range up to 100 s [18–23]. Experimental studies carried out at Stromboli (Italy) [24, 25], where a persistent degassing condition is acting, report outlet speed of about 10 m/s and pressure and thermal waves having a mean frequency of 2 s and an amplitude up to 20 Pa and 30 ◦ C, respectively.According to the fluid-dynamic model proposed J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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by [26], for Poas (Costa Rica) and Vulcano Island (Aeolian Islands) fumarolic discharges, near turbulent flow conditions can be assumed.Turbulent fluid motion is an irregular condition in which the various quantities have a random variation with time and space coordinates, so that statistically distinct average values can be discerned. According to the main theory [27–29], the turbulence time scale can be described by pressure and thermal waves. Such time scale confirms our working hypothesis providing a rough estimation of the fluiddynamic effects. This suggests that, to avoid the effects of fluid-dynamic turbulence during sampling of a fumarolic fluid, a >15-min sampling time must be adopted, i.e., one order of magnitude longer than the (c) and (d) periods. Owing to the fluid-dynamic considerations discussed above and laboratory analytical optimizations [14], a 30-min sampling time has been adopted. A 6 h and 30 min measurement time, with 5 samples, each lasting 30 min, was used. To better constrain the behavior of the sulfur species, variations to this sampling strategy were adopted, as follows: 1. Repeated “random” sampling experiment at Solfatara volcano (Bocca Grande fumarole): 10 gas samples were taken in 8 h; 2. Six samples were taken in 8 h at the Central fumarole at Turrialba volcano; 3. Synchronous sampling of two fumaroles (F48 and F54) at La Fossa crater (Vulcano Island), collecting 4 samples in 5 h and 30 min; 4. Synchronous sampling of two fumaroles (F5 and F202) at La Fossa crater (Vulcano Island) with quite different temperature outlets (233 and 410 ◦ C, respectively); 5. Eighteen gas samples collected over 26 h at the FNA fumarole at La Fossa crater (Vulcano Island).

3. Sampling and laboratory procedures The nine fumaroles considered in the present study (F5, F48, F54, F202, FNA at Vulcano Island; Bocca Grande at Solfatara; Central at Turrialba; Norte at Poas; F1 at El Chichon), for a total of eleven time-series profiles, were sampled according to the newest method proposed [14]. Any external (meteorological) effect could be neglected. The sampling procedure involves the use of a titanium tube inserted at the depth of 50 cm in the fumarolic vent. The fluid is channeled in a specific apparatus consisting of a 60-cm titanium tube (3/4 inch internal diameter), a 30-cm Dewar quartz pipe, and a splitting Dewar device that collects about one-tenth of the gas, once it has attained thermal equilibrium. This sampling system minimizes the J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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perturbation effects of the gas sampling. Due to the high thermal capacity and insulation of the sampling apparatus, external variations such as wind, air humidity, and temperature can be neglected. Moreover, sampling refers to short-term (hours) period sampling series, during which meteorological conditions have not significantly changed. Pre-evacuated and pre-weighted one-way tapped 60-mL glass vials [12] connected to the splitting device, were used. The vials contained 25 mL of a 4N NaOH and 0.15 M Cd(OH)2 suspension. During sampling, any reaction among the sulfur species was prevented by precipitating H2 S as CdS after reacting with Cd2+ ions in the vials solutions, while SO2 remained dissolved in the alkaline solution and S80 remained as a stable precipitate. The solution and the solid precipitate were transferred to a Teflon tube and centrifuged at 15,000 rpm at 25 ◦ C for 15 min to separate the two phases. The supernatant was then oxidized with H2 O2 to convert SO3 2− to SO4 2− , and CdS in the solid phase was oxidized to highly soluble CdSO4 with H2 O2 . S8 0 was extracted from the residual precipitate with CCl4 and oxidized to S2I2 with the addition of KI. Then, sulfur in S2I2 was oxidized to SO4 2− by using KBrO3 . The three SO4 2− bearing aliquots were analyzed by a Dionex DX100 ion chromatograph. The average errors for the determination of SO2 , H2 S, and S80 contents were about 5.0%, 5.0%, and 10.0%, respectively [14].

4. Results Nine fumaroles from five volcanoes, characterized by different compositions of main sulfur gas species (SO2 , H2 S and S8 0 ), were selected for this study. Geochemical features and conceptual models of circulation of the fluids discharging from the different volcanic edifices are discussed elsewhere, e.g., La Fossa Crater (Vulcano Island) [30], Solfatara (Phlegrean Fields) [31], Poas [32], Turrialba [33], Chichon [34]. Outlet temperature of the fumaroles ranges from 90 ◦ C at F1 and Central fumaroles at El Chichon and Turrialba volcanoes, respectively, to 410 ◦ C at the F202 fumarole of Vulcano Island (Table 1). The lowest SO2 concentrations reported were measured at the F1 fumarole of El Chichon (1.0–4.5 μmol/mol; Table 1) and at the Bocca Grande fumarole in the Solfatara volcano (from below the detection limit to 1 μmol/mol; Table 1). The highest SO2 content was found at the Central fumarole in the Turrialba volcano (36,232 μmol/mol; Table 1). H2 S content ranges from 172 at the Norte fumarole of Poas volcano up to 4,000 μmol/mol at the F5 at Vulcano (Table 1). Finally, S8 0 content varies from 0.073 μmol/mol at the Bocca Grande to 15.0 μmol/mol at the J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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Table 1 Average values of SO2, H2 S and S8 measured concentrations (in μmol/mol); standard deviation (%) for the measured data (SO2 , H2 S and S8 0 concentrations) of each sampling series; amplitude A (in μmol/mol) period of oscillation P (in seconds), phase shift of oscillations φ (in radians), life time τ , (in seconds) of the calculated theoretical oscillations; squared Pearson coefficient R2 between the theoretical curves calculated from eqs. (34-36; Appendix 1) and the measured concentrations of SO2 , H2 S and S8 0 . Vulcano F5 November 2000 T = 270 ◦ C SO2 H2 S S Std. Dev. % 40.3 37.4 37.7 φ 2.72 1.78 2.50 τ (sec) 3412 2674 3308 R2 0.99 0.96 0.88 A (μmol/mol) 559 2499 0.39 P (sec) 18884 18308 14789 Av. (μmol/mol) 858 4078 0.98 Vulcano F5 September 2001 T = 233 ◦ C H2 S S SO2 Std. Dev. % 29.5 33.1 45.8 φ 2.55 2.65 2.59 τ (sec) 2493 2491 2555 R2 0.81 0.81 0.63 A (μmol/mol) 939 1416 2.46 P (sec) 15656 15643 16045 Av. (μmol/mol) 2697 4076 6.73 Bocca Grande T = 161 ◦ C SO2 H2 S S Std. Dev. % 107.2 14.4 69.0 φ 0.78 2.78 5.66 τ (sec) 2042 1100 2074 R2 0.14 0.42 0.23 A (μmol/mol) 0.01 83 0.07 P (sec) 12824 6908 13025 Av. (μmol/mol) 0.03 1226 0.29 Vulcano F48 T = 299 ◦ C H2 S S SO2

Vulcano F5 May 2001 T = 230 ◦ C SO2 H2 S Std. Dev. % 47.3 36.0 φ 5.35 5.41 τ (sec) 3383 3332 R2 0.99 0.90 A (μmol/mol) 1171 1621 P (sec) 18724 18441 Av. (μmol/mol) 1827 2608 Vulcano 202 T = 410 ◦ C SO2 H2 S Std. Dev. % 27.1 39.4 φ 3.52 3.80 τ (sec) 2715 2843 R2 0.86 0.84 A (μmol/mol) 1863 1089 P (sec) 994 704 Av. (μmol/mol) 17050 17854 El Chichon F1 T = 90 ◦ C SO2 H2 S Std. Dev. % 53.8 28.7 φ 4.93 4.84 τ (sec) 1928 1987 R2 0.56 0.84 A (μmol/mol) 0.56 450 P (sec) 12108 12478 Av. (μmol/mol) 2.70 2034 Vulcano F54 T = 342 ◦ C SO2 H2 S

Std. Dev. % φ τ (sec) R2 A (μmol/mol) P (sec) Av. (μmol/mol)

Std. Dev. % φ τ (sec) R2 A (μmol/mol) P (sec) Av. (μmol/mol)

11.1 1.89 1914 0.98 488 12020 2379

8.2 2.08 1918 0.96 277 12045 1346

8.2 2.17 1951 0.93 0.08 12252 0.39

18.4 3.87 1850 0.99 1067 11618 5567

22.8 4.25 2005 0.98 789 12591 3506

S 46.9 1.22 3702 0.99 1.54 20489 2.01 S 19.3 3.40 2673 0.16 1500 4.76 16786 S 34.7 5.15 1987 0.77 0.63 12478 2.84 S 26.0 5.06 2242 0.99 0.26 14080 0.91

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Table 1 (continued) Poas Norte T = 101 ◦ C SO2 Std. Dev. % 9.9 φ 2.72 τ (sec) 1493 R2 0.95 A (μmol/mol) 765 P (sec) 9376 Av. (μmol/mol) 6125 Vulcano FNA T = 290 ◦ C SO2 Std. Dev. % 31.6 φ 5.74 τ (sec) 3019 R2 0.85 A (μmol/mol) 2336 P (sec) 18959 Av. (μmol/mol) 4578

H2 S 9.9 3.25 1509 0.83 25 9477 193

S 40.8 3.05 1530 0.69 0.23 9608 1.77

H2 S 29.2 5.71 3018 0.81 868 18953 1702

S 30.5 5.70 3016 0.83 0.63 18940 1.23

Tirrialba Central T = 90 ◦ C SO2 H2 S Std. Dev. % 24.2 28.4 φ 4.72 5.02 τ (sec) 2307 2429 R2 0.95 0.97 A (μmol/mol) 8013 339 P (sec) 14488 15254 Av. (μmol/mol) 26888 1026

S 50.3 4.71 2432 0.24 0.99 15273 2.98

F202 fumarole at Vulcano (Table 1). The full set of data is available by request from the senior author. The suitability of the selected fumaroles at different contents of sulfur species can be envisaged in terms of average SO2 /H2 S; the lowest SO2 /H2S ratio pertaining to the Phlegrean Fields (SO2 /H2 S = 2 · 10−5 ) and tends to increase at El Chichon (SO2 /H2S = 1.3 · 10−3 ), Vulcano (SO2 /H2 S = 0.2 ÷ 2.7), and Turrialba and Poas (SO2 /H2 S = 26.2 and 31.7, respectively). A relatively large variability is also observed when considering the S8 0 /SO2 and S8 0 /H2S ratios. The former ranges between 1.1 · 10−4 (Turrialba) and 9.7 (Phlegrean Fields), whereas the S80 /H2 S ratios are from 2.4·10−4 (Phlegrean Fields) to 9.2·10−3 (Poas Norte).

5. Discussion 5.1. Theoretical thermodynamic and statistical basis In the last decades several conventional fluctuation theorems (CFTs) have been derived for systems with deterministic or stochastic dynamics in nonequilibrium stationary states [35]. Here, CFTs describe the ratio of probability between a given value of entropy production and its opposite. Once the physical-chemical boundary conditions are constrained non-equilibrium J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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processes can be described as a function of time, using internal variables, such as concentration of involved components, temperature, pressure and so forth. Through this thermodynamic statistical approach, it is possible to model the behavior of the entropy excess in complex natural systems. Accordingly, chemical processes proceed through self-organized steady states called dissipative structures [3]. Regarding the behavior of gas components in volcanic vents, the thermodynamic models proposed [36–38] were not adequately developed to take into account the random or stochastic nature of the compositional data in the appropriate sample space [39]. Compositional data consist of vectors whose components are the proportion or percentages of some whole. Their sum is constrained to be some constant. Following [40, 41], the log-ratio transformation, yi = log (xi /xD ) = log xi − log xD , for i = 1, . . . , D, with D being the number of components of the whole composition (CO2 , HCl, HF, SO2 , H2 S, S80 , H2 O, N2 , CH4 , Ar, O2 , Ne, H2 , He, and CO), has been applied to overcome the closure problems. The descriptive analysis of compositional data in the correct sample space can be performed through the total variation matrix of the whole that characterizes a volcanic gas. Here, the  composition  detection of the E log xj /xi ≈ 0 quantities (E is the expected value, i and j components of the composition) indicates that a clear subcomposition given by SO2 , H2 S, and S8 0 can be extracted; consequently, the sulfur species show in each volcanic fumarolic discharge similar simple reciprocal ratio relationships, independently from the other components of the composition, revealing the presence of an auto-organized sulfur system. The statistical modeling of chemical changes in sulfur species subcomposition can be made by using a log-contrast (principal component) analysis. A log contrast is a linear combination of the logarithms of the components a1 log x1 + . . . + aD log xD , with the constraint a1 + . . . + aD = 0 to ensure that the linear form can be expressed as a function of component ratios. Following [42],

 i1 j





ai log xi /xj =

D  i=1

ai log xi =

D 

ai log (xi /g (x)),

(1)

i=1

where g (x) = (x1 . . . xD )1/D is the geometric mean of the D components of the composition. Applied to each sulfur subcomposition, this technique produces eigenvalues λ1 and λ2 and the corresponding first and second log contrasts (Tables 2 and 3), with a form similar to the mass action law used in geochemistry. In each fumarolic system, the first log contrast k 1 is able to explain more J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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Table 2 Results of the log-contrast analysis applied on sulfur species; the first log-contrast equation, which explains the λ1 /(λ1 + λ2 ) of the total data variability. λ1 and λ2 are the eigenvalues of the variance-covariance matrix of each dataset. Sample place

λ1

λ2

First log-contrast (S0.82 )/(SO2 0.48 × H2 S0.34 ) = exp(k1 ) (S0.82 )/(SO2 0.39 × H2 S0.43 ) = exp(k1 ) (S0.81 )/(SO2 0.30 × H2 S0.514 ) = exp(k1 ) (S0.81 )/(SO2 0.21 × H2 S0.60 ) = exp(k1 ) (S0.81 )/(SO2 0.51 × H2 S0.30 ) = exp(k1 ) (S0.82 )/(SO2 0.44 × H2 S0.38 ) = exp(k1 ) (S0.81 )/(SO2 0.38 × H2 S0.43 ) = exp(k1 ) (S0.82 )/(SO2 0.38 × H2 S0.44 ) = exp(k1 ) (S0.78 )/(SO2 0.58 × H2 S0.20 ) = exp(k1 ) (S0.81 )/(SO2 0.41 × H2 S0.40 ) = exp(k1 )

Explained data variability

Vulcano F5/1

0.816

0.0060

Vulcano F5/2

0.578

0.0008

Vulcano F202

0.189

0.0034

Vulcano F54

0.203

0.0008

Vulcano F48

0.029

0.0001

Vulcano FNA

0.311

0.0013

Poas Norte

0.180

0.0011

Turrialba central

0.352

0.0015

El Chichon F1

0.559

0.0050

Pozzuoli B.G.

0.299

0.0110

99.3% 99.8% 98.2% 99.6% 99.6% 99.7% 99.4% 99.4% 99.1% 96.8%

Table 3 Results of the log-contrast analysis applied on sulfur species; the second log-contrast equation. λ1 and λ2 are those in Table 2. Sample place

λ1

λ2

Second log-contrast (k 2 ≈ constant)

Vulcano F5/1

0.816

0.006

(SO2 0.66 × S0.08 )/(H2 S0.74 ) = exp(k2 ) = 0.42

Vulcano F5/2

0.578

0.0008

(SO2 0.72 )/(S0.03 × H2 S0.69 ) = exp(k2 ) = 0.90

Vulcano F202

0.189

0.0034

Vulcano F54

0.203

0.0008

(SO2 0.76 )/(S0.12 × H2 S0.64 ) = exp(k2 ) = 0.02 (SO2 0.80 )/(S0.20 × H2 S0.60 ) = exp(k2 ) = 8.6

Vulcano F48

0.029

0.0001

(SO2 0.64 × S0.12 )/(H2 S0.76 ) = exp(k2 ) = 0.55

Vulcano FNA

0.311

0.0013

(SO2 0.69 × S0.03 )/(H2 S0.72 ) = exp(k2 ) = 1.55

Poas Norte

0.180

0.0011

(SO2 0.72 )/(S0.030 × H2 S0.69 ) = exp(k2 ) = 0.10

Turrialba central

0.352

0.0015

El Chichon F1

0.559

0.005

(SO2 0.73 )/(S0.03 × H2 S0.70 ) = exp(k2 ) = 13.7 (SO2 0.57 × S0.22 )/(H2 S0.79 ) = exp(k2 ) = 0.005

Pozzuoli B.G.

0.299

0.011

(SO2 0.70 )/(S0.005 × H2 S0.70 ) = exp(k2 ) = 0.0003

than 96.5% of the data variability and consequently it represents the most important process working in the different systems. The near zero eigenvalue associated with the second log contrast k 2 implies that the latter is almost constant, particularly when the S8 0 exponent is near to zero, being related to the constancy of the SO2 /H2 S ratio. For each gas sample k 1 and k 2, values can be determined by substituting the values of the single variables in the logcontrast equations (Tables 2 and 3). To evaluate whether the arithmetic mean of k 1 for each time series data set can be used as a synthesis parameter, the Kolmogorov–Smirnov test for normality has been applied.The null hypothesis J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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of normal distribution of k 1 , considered as a random variable with parameters given by sampling mean and variance, can be accepted with α > 0.05 for all fumaroles. The practical and very important consequence of this result is that the arithmetic mean of k 1 for each data set is a parameter around which values decrease and/or increase with equal probability, following the Gaussian model. Moreover, if k 1 values are analyzed as a function of time, random fluctuations around the mean values appear to be the dominant feature (run test, α > 0.05) for each temporal series. According to the theoretical thermodynamic and the statistical results, all possible reactions among sulfur species in fumaroles can be summed up by the following reaction: SO2 + 2H2 S



3/8 S8 0 + 2H2 O.

(2)

This reaction proceeds to the right or to the left as a function of energy loss or gain, respectively [43]. Therefore, reaction (2) could proceed through nonequilibrium states, with oscillations from one side to the other of reactants and products and energy variations related to the formation of stationary dissipative structures. The whole theoretical description of the model for the sulfur species with the assumed boundary conditions is reported in the appendix. What is useful to summarize here are the parameters used in the theoretical calculations of sulfur species concentrations as a function of time (Table 1 and Figures 1–9), as follows: 1. The average concentrations (SO2av , H2 Sav , S8av ) obtained from measured data; 2. The characteristic time of dissipative structures (τ , related to the period of the oscillation p by the relation p = 2πτ ); 3. The phase shift (φ) of the first sample with respect to the beginning of the oscillation. 5.2. Comparison between theoretically calculated and measured data In order to verify the presence of dissipative structures able to govern the temporal behavior of sulfur species in volcanic gases, the theoretical concentrations of SO2 , H2 S, and S8 0, obtained from Eqs. (34)–(36) (appendix), were compared with those analytically measured. The average values of SO2 , H2 S, and S80 measured concentrations (in μmol/ mol), the amplitude A (in μmol/mol) and the calculated period of oscillation P (in seconds) are reported in Table 1, where the calculated relative phase shift of oscillations φ (in radians) for each fumarole and the life time τ (in J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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seconds) of the dissipative structures related to reaction (2) are also shown.All measured values of SO2 , H2S, and S8 0 and the relative time series curves for all the fumaroles considered are plotted in Figures 1 to 8. Agreement between the theoretical curves calculated from Eqs. (34)–(36) and the measured concentrations of SO2 , H2 S, and S8 0 was evaluated through the squared Pearson coefficient R2, reported in Table 1. Measured data for the three sulfur species have an average analytical error ranging from 5% to 10% [14], significantly lower than the values of the standard deviation for the measured data of each sampling series (Table 1). Therefore, the measured compositional variations cannot be ascribed to the analytical and/or sampling error. R2 values are higher than 80%, thus the correspondence between measured and calculated values can be considered highly significant. Moreover, five main experimental tests were performed on Italian fumaroles in order to check 1. the possible seasonal influence on the sulfur species concentrations; 2. the simultaneous behavior of SO2 , H2 S, and S8 0 in fumaroles characterized by different composition and temperature; 3. the behavior of sulfur species in fumaroles characterized by similar composition and similar outlet temperature; 4. the possible dependence of the correlation between the calculated and the measured contents of sulfur species on the periodicity of the sampling interval; 5. the medium-term (days) behavior of the average contents of sulfur species. To verify point 1, the F5 fumarole at the Vulcano was sampled in November 2000 (during the dry season) and in May 2001 (during the wet season). Both outlet temperatures (270 ◦ C in September and 230 ◦ C in May) and SO2 , H2 S, and S8 0 averages were quite different. Although the outlet temperature was lower in May, SO2 was more than twice the concentration of that measured in November (1,827 and 858 μmol/mol, respectively), which is not compatible with a cooling caused by increased rainfall entering the system.The calculated period of oscillation was 19,500 s in September and 21,000 s in May 2001, suggesting a minor seasonal effect (Figure 1). The simultaneous behavior of SO2 , H2 S, and S8 0 in fumaroles with different composition and quite different outlet temperature (point 2), was analyzed J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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Figure 1 Computed and measured variation patterns in time of H2 S, S8 0 , and SO2 concentrations at the F5 fumarole at Vulcano Island (Italy), sampled in November 2000 (top) and May 2001 (bottom).

by sampling in parallel the F5 (233 ◦ C) and the F202 (410 ◦ C) fumaroles of Vulcano (Figure 2) in September 2001. As shown in Table 1, the τ value constraining the harmonic oscillation of sulfur compounds in F5 fumarole was significantly shorter (2,400 s) than that calculated for F202 fumarole (2,700 s). To compare the behavior of sulfur species in fumaroles characterized by similar composition and similar outlet temperature (point 3), the F48 (300 ◦ C) and F54 (350 ◦ C) fumaroles of Vulcano Island, were sampled contemporaneously (Figure 3). In this case, the τ values describing the time series of these two fumaroles were similar (≈ 1,900–2,000 s), whereas the initial phase shift φ, despite the contemporaneous sampling, was different (Table 1). This suggests that fumaroles characterized by similar physical-chemical features at the same volcano have comparable entropy excess and, as a consequence, dissipative structures. J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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Figure 2 Computed and measured variation patterns in time of H2 S, S8 0 , and SO2 concentrations at the F5 fumarole (top) and F202 (bottom) fumaroles, both sampled contemporaneously at Vulcano Island (Italy) in September 2001.

To verify that the correlation between the calculated and the measured contents of sulfur species were not dependent on the periodicity of the sampling interval (point 4), a variable interval sampling was performed at the Bocca Grande (Solfatara) fumarole (Figure 4). Although sometimes SO2 and S8 0 contents were only slightly above the minimum detection limits (0.05 μmol/mol), H2 S periodic oscillations, with P = 6,908 s and R2 = 0.42, were observed as expected (since only H2 S is representative of thermodynamic non-equilibrium structure, i.e., not quenched). To evaluate the medium-term (days) behavior of the average contents of sulfur species (point 5), a long (26 hours) time-series sampling was generated at FNA fumarole at Vulcano. The average concentrations of SO2 , H2 S, and S8 0 show periodic oscillations, with P = 18,953 s, and this did not change significantly during the observation time (Figure 5). J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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Figure 3 Computed and measured variation patterns in time of H2 S, S8 0 , and SO2 concentrations at the F48 Fumarole (top) and F54 Fumarole (bottom) at Vulcano Island, sampled in November 2002.

Oscillations in sulfur species concentrations were also observed at volcanoes in the Latin American countries. The comparison between theoretical and measured gas concentrations in fumaroles sampled at Turrialba, Poas (Costarica) and El Chichon (Mexico) are shown in Figures 6, 7, and 8, respectively. All three volcanoes are characterized by fumaroles with an outlet temperature near the boiling point for water at atmospheric pressure. Considering the high elevation of the fumaroles (1,400 and 2,400 m a.s.l. at El Chichon and Poas volcanoes, respectively) and the fact that all the three fumaroles have SO2 , sometimes in substantial amounts (e.g., Turrialba: 26,888 μmol/mol) a slight superheating of the steam is evidently maintained along the volcanic ducts. It is reasonable to suppose that, at least at El Chichon, most SO2 (where SO2 concentration is as low as 2.7 μmol/mol) is removed by partial condensation of steam along the conduit. This is the likely reason for the low Pearson square correlation (R2) values for S8 0 at Turrialba and J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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Figure 4 Computed and measured variation patterns in time of H2 S, S8 0 , and SO2 concentrations at the Bocca Grande fumarole in the Solfatara volcano (Italy), sampled in October 2001.

Figure 5 Computed and measured variation patterns in time of H2 S, S8 0 , and SO2 concentrations at the FNA fumarole at Vulcano Island, sampled in September 2003.

Poas and for SO2 at El Chichon: 0.24, 0.69, and 0.56, respectively. Moreover, deposition of sulfur either around the volcanic vents and/or along the fumarolic conduits, because of condensation of steam, may affect the temporal patterns. However, in spite of the low temperature of the fumaroles, temporal oscillations in the concentration of the sulfur species are still evident (Figures 6–8). J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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Figure 6 Computed and measured variation patterns in time of H2 S, S8 0 , and SO2 concentrations at the main Central fumarole sampled at the west summit crater of the Turrialba volcano (Costa Rica) in April 2002.

Figure 7 Computed and measured variation patterns in time of H2 S, S8 0 , and SO2 concentrations of the Norte fumarole sampled at Poas volcano (Costa Rica) in February 2001.

The theoretical concentrations of sulfur species obtained by the thermodynamic approach proposed in the appendix agree with the analytical data more closely if the duration of the temporal series covers the entire oscillation period. This is clearly evidenced in Figure 9 where the relative oscillation amplitude A (equal to τ 2/ξ ) and the relative variation amplitude of measured concentrations (i.e., (Cmax–Cmin )/2Caverage ) are positively correlated. J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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Figure 8 Computed and measured variation patterns in time of H2 S, S8 0 , and SO2 concentrations at a fumarole sampled at El Chichon volcano (Mexico) in October 2000.

This correlation is particularly evident for H2 S, SO2 , and, though at a minor extent, for S8 0, the latter being more affected by analytical problems caused by its generally low concentrations.

6. Conclusions The results described above suggest that the temporal variation in fumarolic gases for SO2 , H2 S, and S8 0 concentrations, with different temperature and chemical composition sampled from different volcanoes, is controlled by nonequilibrium dissipative structures formed during energy transfer and fluid motion. The main evidence is the harmonic behavior of sulfur compounds shown by the 26-h sampling at the FNA fumarole of Vulcano (Figure 5). Furthermore, during FNA sampling series, diurnal or semi-diurnal effects were not observed, and the contemporaneous sampling carried out at F5 and F202 fumaroles (September 2001, Vulcano Island, Table 1) clearly show different oscillation periods. This implies that tidal influence should not play a significant role in the observed chemical fluctuations. From the general theory presented in the appendix and according to the measured data, SO2 , H2 S, and S8 0 oscillations have a higher amplitude and longer periods in fumaroles characterized by higher entropy excess, such as the F202 fumarole of Vulcano, which is in agreement with the general theory [44]. This suggests that high energy systems can deviate further from equilibrium (i.e., τ 2/ξ and/or (Cmax –Cmin )/2Cav ). J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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Figure 9 Comparison between calculated τ 2 /β (τ values in Table 1; β=17,859,076 s2 ) and its equivalent experimental half-amplitude variation of concentration of component x divided by average concentration (see text). The ideal correlation lines and linear fitting ones are present.

Our results are also corroborated by the statistical analysis following the log-ratio approach on the experimental data. Results indeed demonstrate that sulfur species are able to constitute a self-organized system, similarly behaving in fumaroles from volcanic centers characterized by different outlet temperatures and concentrations of SO2 , H2 S, and S80 . The structure of the data in each volcano follows a law similar to that of mass action. It can be represented by the average of the log-contrast score values of the first log contrast (Kolmogorov–Smirnov test about normality, α > 0.05), while the behavior in the investigated time spans appears to be stationary (run test, J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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α > 0.05). In the case of the fluctuations of SO2 and H2 S contents observed in the fumaroles sampled in the Satsuma Iwojima and Kuju volcanic systems [8], it is likely that the oscillations of the two sulfur species analyzed were jeopardized by fluid-dynamic variations caused by the relatively short-time gas sampling (few minutes). One of the most important consequences of the results of our study is that the evaluation of the magnitude of the short-term natural fluctuation of sulfur species, by considering that these gas compounds are particularly sensitive to magmatic fluid-induced modifications [45], is highly recommended.This may have strong implications for the geochemical monitoring of active volcanoes. Acknowledgements Many colleagues and Ph.D. students were involved in several sampling campaigns, sometimes under uncomfortable conditions. Among them we want to thank P. Marchev (Institute of Geology, Bulgarian Academy of Sciences), F. Bergamaschi and A. Nencetti (Dept. of Earth Sciences, University of Florence, Italy), E. Duarte Gonzales and E. Fernandez (Volcanologic Observatory of Costarica at Heredia), and M. M. Yalire (Volcanological Observatory of Goma, Democratic Republic of Congo). F. Cuccoli (Dept. of Electronics and Telecommunications, University of Florence, Italy) and R. Carniel (Dept. of Earth Resources and Land Use, University of Udine, Italy) are warmly thanked for useful discussions and comments at early stages of the study. A. T. Caselli (Dept. of Geological Sciences, University of Buenos Aires, Argentina) is gratefully acknowledged for participating to the 26-hour-long gas sampling at Vulcano. A special thanks is due to F. Di Benedetto (Dept. of Earth Sciences, University of Florence, Italy) for his help during the data processing. The Italian Spatial Agency (ASI) has financially supported O.V. for the field work at Vulcano and Costa Rica. Under the scientific cooperation between Italy and Mexico, B. Capaccioni (Institute of Volcanology and Geochemistry, University of Urbino, Italy) is acknowledged for financially supporting the field trip to El Chichon of F.T. and O.V. We wish to thank the managing editor Torsten Krüger, the editor-in-chief Jürgen U. Keller, and three anonymous referees for improving an early draft of the manuscript.

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Appendix: Theoretical thermodynamic model of the SO2 -H2S-S8 0 dissipative structure Ax c Cx d/dt I J K p p P

= = = = = = = = = =

q s t T(K) X τ

= = = = = = =

φ

=

ε σ μ

= = =

(∇ )σ

1/ρ ∇, ∇·

= = = =

entropy variation of reacting component x molar fraction of a component half-amplitude variation of concentration of component x material time-derivative defined as d/dt = d/dt + v. ∇ pressure directors matrix diffusive mass flux Boltzman constant pressure oscillation period statistical-thermodynamic probability to have a positive collision for the formation of products energy flux specific entropy time temperature concentration of component x finite difference between final and initial values characteristic time of dissipative structures, which in our model coincides with the average molar lifetime of reacting species and/or products phase shift for the first sample with respect to the beginning of the oscillation specific internal energy entropy production chemical potential difference in the considered reaction system (μ = μprod. − μreact. ) symmetric part of the velocity gradient symmetric pressure tensor of the fluid mixture specific volume gradient, divergence, directional derivative

In a generic chemical and/or physical process, the entropy excess (EE) of the system depends on several factors. In our system, related to the sulfur species rising in a fumarolic duct, EE depends on (i) the rate of energy exchange between the fluid and the magma source; (ii) the shape (morphology) of the fumarolic duct, and (iii) the mechanism of energy transfer between the fumarolic fluids and their surroundings, such as heat drainage from shallow aquifers. In the theoretical model described here, we have assumed the following boundary conditions of the system: J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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(0) the thermal and chemical fluid–rock interaction along the fumarolic conduit is negligible; (1) the behavior of SO2 , H2 S, and S8 0 is independent with respect to other compounds in the fumarolic fluid, e.g., CO2, HCl, HF, due to higher reaction rate kinetics [43]; (2) owing to the long sampling period (30 min), fluido-dynamic effects on the gas composition are negligible; (3) interaction energies between sulfur species and water (steam) are not relevant for the process under study; (4) steam is the thermal buffer of the system; (5) the high temperature and thermal capacity of the fumarolic conduit at the depth of 50 cm are able to prevent any external influences (see paragraph 3). Some of the reactions involving sulfur species during the uprising of a volcanic fluid from its source are S + (OH) → H + SO,

(3a)

SO + (OH) → H + SO2 ,

(3b)

H + SO → O + SH,

(4a)

(OH) + SH → O + H2 ,

(4b)

. . . . . . etc., and these can be summarized by the cumulative reaction H2 S + SO2



3/8 S80 + 2H2 O.

(5)

Both the oxidation of S8 0 to SO2 and/or its reduction to H2S involves reaction with the hydroxide molecular fragment (OH). Formation enthalpies at 298 K for the sulfur species are −296.8 kJ/mole for SO2 , −20.6 kJ/mole for H2 S, and 432 kJ/mole for S8 0 [43]. As a consequence, the sequence of reactions from H2 S to SO2 and vice versa has two important characteristics: (i) elemental sulfur is produced in case of energy increase of J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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the system (at about 700 K this is reversed) and (ii) the oxidation of H2 S to SO2 , without the contemporary formation of elemental sulfur, is impossible. Therefore, energy absorption by steam will lead to an increase of S80 concentration with respect to H2 S and SO2 , whereas an energy loss will favor a decrease of S8 0 . Owing to this energy dependence, energy variations of reaction (5) are easily governed by dissipative structures and, consequently, reaction (5) can be forced to oscillate from one side to the other, as theoretically described by [6]. From a theoretical point of view, the sine-qua-non condition for asymptotic stability of a chemical system (i.e., for an infinite time) has to satisfy the first and second Liapunov theorems [3] in the framework of a convective process. For an open system, the first Liapunov theorem states that a chemical process can proceed if entropy production is 0. Among all the functions that could satisfy this kind of equation, the wave functions are included. The internal variables for an open system can be constrained by the thermo and fluid-dynamic conditions defined by [35, 46–48] Tds/dt = dε/dt − (p/ρ 2 )dρ/dt − μdc/dt,

(6)

the entropy balance being Tσ = (∇ . TS + μ∗ J - q) − ( − pI)/∇ σ − J. ∇μ∗ − S. ∇T − ρδ( ε/δX)(δX(δt)),

(7)

where the formalism is the one reported in [35, 47, 48]. Equation (7) gives the entropy production as a function of δX/δt, where X is the concentration of a generic chemical component of the system. Then, the function of X vs. t could represent the EE production function. Solutions for Liapunov theorems can be written as concentration functions and used to represent the EE function in Eq. (7). The resulting periodic (or pseudo-periodic) function can be simplified by using the Fourier series expansion, where the zero and first-order terms are able to describe the dissipative structure phenomena ([3, 6, 35, 42, 46–48] and references therein). It can be expressed with the following formalism: X(t) = Xav (1 + sin(t/τ + φ)),

(8)

where the parameter τ is defined as the characteristic time of the dissipative structure [3]; τ is clearly related to the oscillation period, which is an observable. J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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As indicated by the statistical thermodynamics [49], once given the entropy variation ( S) of reaction (5), the probability P to have a positive collision for the formation of products is known. The ratio between the maximum shifting (Pmax ) from the equilibrium and the probability at equilibrium condition (Peq ) is given by Pmax /Peq = e(EE/K) ,

(9)

being (i) τ the average molar life time of reactants, (ii) xav the average concentration of component x, (iii) Cx the half-amplitude variation of concentration of component x [Cx = (Cmax –Cmin )/2], and (iv) φx the starting phase of concentration of the x component at the starting sampling time, the concentrations of the main sulfur species SO2 , H2 S, and S80 are functions of time t, according to the following equations: SO2 = SO2 av + CSO2 sin(t/τ SO2 + φSO2 ),

(10)

H2 S = H2 Sav + CH2 S sin(t/τ H2 S + φH2 S),

(11)

S08 = S8 0av + CS8 0 sin(t/τ S8 0 + φS8 0).

(12)

Value of entropy S for sulfur compounds is obtained by multiplying the relative S ◦ for Eqs. (10)–(12). By substituting S ◦ Cx with Ax, we obtain SSO2 = S ◦ SO2 · SO2av + ASO2 sin(t/τSO2 + φSO2 ), SH2 S = S



H2 S

· H2 Sav + AH2S sin(t/τH2 S + φH2 S ),

SS80 = S ◦ S8 0 · S8 0av + AS8 0 sin(t/τS80 + φS80 ),

(13) (14) (15)

by applying the condition of maximum concentration for each component, as described by the following equations: sin(t/τSO2 + φSO2 ) = 1,

(16)

sin(t/τH2 + φH2 ) = 1,

(17)

sin(t/τS80 + φS8 0 ) = 1,

(18)

the second derivative of Eqs. (13)–(15) with respect to the time t is given by: δ 2SSO2 = −ASO2 /(τSO2 )2 ,

(19)

δ 2SH2 S = −AH2 S /(τH2 S)2 ,

(20)

δ 2 SS80 = −AS8 0 /(τS8 0 )2 .

(21)

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By substituting Eqs. (16)–(18) in Eqs. (13)–(15), solving as a function of EE, and combining the results with Eq. (9), the maximum probability of a positive collision between reactants to form products Pmax , with respect to that at the equilibrium condition Peq for each sulfur component, is obtained. The Pmax /Peq , e.g., for SO2 , is given by the following equation: Pmax /Peq = e(( S

◦ SO

2 SO2av +SSO2 )/K

.

(22)

To calculate τ , the second derivative of Eq. (22) is solved: δ 2 (Pmax /Peq ) = (1/K 2 )e

−((δ2SO2 /K(τ SO2 )2)+( S◦ SO2 SO2av )/K)

,

(23)

which combined with Eq. (19) gives ln(K 2 δ 2(Pmax /Peq )) = − EESO2 /(K (τSO2 )2 ) − ( S ◦ SO2 · SO2av )/K . (24) By combining Eqs. (22) and (24) we obtain   ◦ ln K 2 δ 2 e( S SO2SO2av +SSO2 )/K + S◦ SO2 · SO2av /K = − EESO2 /(K · (τSO2 )2 ). (25) By calculating the derivative and then the logarithm of Eq. (25), the average life time τ of SO2 can be expressed as follows: τSO2 = (−EESO2 /(2 S◦ SO2 · SO2av + SSO2 ))1/2 .

(26)

To simplify Eq. (26), two new variables, r and ξ , can be introduced; r is the relative SO2 oscillation with respect to the average concentration, and ξ is a constant representing the maximum entropy contents of the dissipative structure, defined by the following equations: r = −EESO2 /(2 S◦ SO2 · SO2av ),

(27)

ξ = 2 S◦ SO2 · SO2av /(SSO2 + 2 S◦ SO2 · SO2av ).

(28)

Hence, Eq. (26) can be rewritten, as follows: 2 τSO = r · ξ. 2

(29)

To calculate ξ from Eq. (29) we adopt a logical artifice. At the inversion temperature (about 700 K [43]), small temperature variations reverse the direction of how the reaction (5) would proceed. Thus, the entropy variation J. Non-Equilib. Thermodyn. 2008 · Vol. 33 · No. 1

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ASO2 equals the formation entropy f S ◦ (700), i.e., r = 1, and, consequently, Eq. (29) becomes ξ = τ 2. Since at 700 K τSO2 is 4,226 s [43], ξ is 17,859,076

(30) s2 .

Once ξ and τ are calculated, they can be substituted in Eq. (11) to describe the temporal evolution of SO2 contents as a function of (i) SO2av , (ii) τ SO2 , and (iii) φSO2 : SO2 = SO2av + SO2av (τ 2 SO2 /ξ ) sin(t/τSO2 + φSO2 ).

(31)

By applying the same procedure to obtain Eq. (31), the theoretical harmonic variations in time for H2 S and S8 0are: H2 S = H2 Sav + H2 Sav (τ 2 H2 S/ξ ) sen (t/τH2S + φH2S ]),

(32)

S8 0 = S8 0av + S8 0av (τ 2 S80 /ξ ) sen (t/τS8 0 + (φS8 0 + γ )),

(33)

where τ SO2 ∼ τ H2 S ∼ τ S8 0 ∼ τ . In Eq. (33), γ represents the phase time shift between products and reactants and theoretically is equal to π/2 [44]. Consequently, φSO2 and φH2 S, which are similar, have a π/2 shift with respect to φS8 0 . By substituting φSO2 , φH2 S, and φS8 0 with φ, Eqs. (31)–(33) can be expressed as SO2 = SO2av (1 + (τ 2 /ξ ) sin(t/τ + φ)),

(34)

H2 S = H2 Sav (1 + (τ 2 /ξ ) sin(t/τ + φ)),

(35)

S8 0 = S8 0av (1 + (τ 2 /ξ ) sin(t/τ + φ + π/2)).

(36)

The values of φ, τ, SO2av , H2 Sav , and S80 av obtained from Eqs. (34)–(36) and used to plot the theoretical curves shown in Figures 1 to 9 are listed in Table 2.

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Paper received: 2007-04-24 Paper accepted: 2007-08-24

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