The effect of H2O on the viscosity of K-trachytic melts at magmatic temperatures

Chemical Geology 235 (2006) 124 – 137 www.elsevier.com/locate/chemgeo

The effect of H2O on the viscosity of K-trachytic melts at magmatic temperatures Valeria Misiti a,⁎, Carmela Freda a , Jacopo Taddeucci a , Claudia Romano b , Piergiorgio Scarlato a , Antonella Longo c , Paolo Papale c , Brent T. Poe a,d a

Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Sismologia e Tettonofisica, Via di Vigna Murata 605, Rome, I-00143, Italy b Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, Rome, I-00146, Italy c Istituto Nazionale di Geofisica e Vulcanologia, Via della Faggiola 32 Pisa, I-56100, Italy d Università degli Studi G. D'Annunzio, Via dei Vestini 31, Chieti, I-66013, Italy Received 10 February 2006; received in revised form 26 June 2006; accepted 26 June 2006 Editor: R.L. Rudnick

Abstract Viscosity of hydrous trachytes from the Agnano Monte Spina eruption (Phlegrean Fields, Italy) has been determined at 1.0 GPa and temperatures between 1200 and 1400 °C using the falling sphere method in a piston cylinder apparatus. The H2O content in the melts ranged from 0.18 to 5.81 wt.%. These high-temperature hydrous viscosities, along with previous ones determined at low-temperature (anhydrous and hydrous) and at high-temperature (anhydrous), at 1 atm on the same melt composition, represent the only complete viscosity data set available for K-trachytic melts, from magmatic to volcanic conditions. Viscosity decreases with increasing temperature and water content in the melt. At constant temperature, viscosity appears to significantly decrease when the first wt.% of H2O is added. At H2O content higher than 3 wt.% the effect of temperature on viscosity is slight. Moreover, the deviation from Arrhenian behaviour towards greater “fragility” occurs with increasing water content. We combined low- and high-temperature viscosities (also from literature) and parameterized them by the use of a modified Vogel–Fulcher–Tamman equation, which accommodates the non-Arrhenian temperature dependence of melt viscosity. Moreover, in order to explore the extent to which the improved knowledge of Agnano Monte Spina trachyte viscosity may affect simulation of volcanic eruption at Phlegrean Fields, we included our viscosity models in numerical simulations of magma flow and fragmentation along volcanic conduits. These simulations show that the new parameterizations (and hence the new equations) give stronger predictions in the temperature interval relevant for magmatic and eruptive processes. © 2006 Elsevier B.V. All rights reserved. Keywords: Viscosity; Trachyte; Falling sphere method; Vogel–Fulcher–Tamman equation

1. Introduction Viscosity is an important physical property of silicate melts controlling the kinetics of magmas from magma ⁎ Corresponding author. Tel.: +39 06 51860230; fax: +39 06 51860507. E-mail address: [email protected] (V. Misiti). 0009-2541/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.chemgeo.2006.06.007

chamber to volcanic vent. This property is strongly influenced by temperature, amount of dissolved water, and chemical composition of magma (Pinkerton and Stevenson, 1992; Dingwell et al., 1993), while pressure, at least up to 2.0 GPa, does not influence viscosity significantly (Pinkerton and Stevenson, 1992; Dingwell et al., 1993). Water content, exerting a strong influence on the viscosity of silicate melts, is one of the most important parameters

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controlling the eruptive style of volcanoes (Sparks, 2003 and references therein). Up to now a number of experimental viscosity studies have been published either for anhydrous or hydrous melts. However, viscosity of hydrous melts at high temperature, essential input for the modelling of magma movements, is still difficult to determine. Without an appropriate knowledge of the viscosity of magma depending on the amount of dissolved volatiles, it is not possible to model the processes (i.e., magma ascent, fragmentation, and dispersion) required to predict realistic volcanic scenarios and thus forecast volcanic hazards. In order to model the viscosity of magmas as a function of temperature and water content usually the experimental data are fitted with a modified Vogel–Fulcher–Tamman equation (hereafter VFT; Vogel, 1921; Fulcher, 1925; Tammann and Hesse, 1926; Giordano et al., 2000; Giordano and Dingwell, 2003; Romano et al., 2003; Giordano et al., 2004, and references therein). The viscosity of hydrous melts can be determined experimentally by micropenetration and parallel plate creep (Richet et al., 1996; Romano et al., 2003) at atmospheric pressure and relatively low temperature. In order to prevent water loss, the determination of viscosity of hydrous melts at high temperature needs to be carried out in sealed noble metal capsules under a confining pressure. This can be done by using the falling sphere method either in a piston cylinder apparatus (Kushiro, 1976; Kushiro et al., 1976; Brearley et al., 1986; Scarfe et al., 1987; Brearley and Montana, 1989) or in a multi anvil apparatus (Kanzaki et al., 1987; Terasaki et al., 2001; Suzuki et al., 2002), the latter associated with an X-ray synchrotron monitoring method for in situ measurements. In this paper we investigate the viscosity of natural K-trachytic melts from the Agnano Monte Spina eruption (Phlegrean Fields, Italy; Civetta et al., 1991; de Vita et al., 1999; Di Vito et al., 1999) at 1.0 GPa, over a range of water content from 0.18 to 5.81 wt.%, and temperatures between 1200 and 1400 °C. Despite their potential for large explosive eruptions, the viscosity of K-trachytic melts, as a function of water content, is relatively poorly constrained in comparison to that of haplogranites, rhyolites and basalts (Khitarov et al., 1976; Persikov et al., 1990; Dingwell et al., 1996; Schulze et al., 1996; Zhang et al., 2003). This is the second natural composition that has been studied both at low and high temperature under hydrous conditions (the first was Himalayan leucogranite, measured with falling sphere by Scaillet et al. (1996) and with parallel-plate by Whittington et al. (2004)). Romano et al. (2003) defined a modified VFT equation to be used for the determination of the viscosities of Agnano Monte Spina trachytes using anhydrous high-temperature and

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anhydrous and hydrous low-temperature experimental viscosity data. However, as they pointed out, the extrapolation of the equation for hydrous liquids at high temperatures yields a substantial degree of uncertainty. Thus, combining high-temperature viscosity determinations, obtained experimentally in this work, with the viscosity data of Romano et al. (2003), we attain a new parameterization in the form of new VFT equations as a function of temperature and water content. Numerical simulations of trachytic magma flow and fragmentation in the conduit, performed with the new and old equations, show that the former give stronger predictions in the temperature interval relevant for magmatic and eruptive processes. 2. Methods 2.1. Experimental approach The starting material used for the viscosity determinations was produced by melting the trachytic glassy matrix of pumices of the Agnano Monte Spina eruption (hereafter AMS) deposit at atmospheric pressure and 1400–1650 °C (further details about the synthesis method are in Dingwell et al., 1998). The same glass composition (Table 1) was also used in a recent H2O solubility study (Di Matteo et al., 2004) as well as for H2O diffusion investigations (Freda et al., 2003). Glasses with various H2O content were synthesised at the Institut für Mineralogie in Hannover (IMH) in an internally heated pressure vessel at 0.5 GPa, 1200 °C (24 h duration) in sealed gold–palladium capsules (40 mm long, 8 mm inner diameter) containing the nominally anhydrous AMS glass powder and the desired amount of distilled water (from 0.5 to 6 wt.% H2O added). Argon was used as a pressure medium, while temperature was controlled by three S-type thermocouples, two placed at the top and bottom of the furnace respectively, and the Table 1 Composition (wt.%) of AMS sample by X-ray fluorescence Oxide

wt.%

SiO2 TiO2 Al2O3 FeO MnO MgO CaO Na2O K2O P2O5 LOI Total

59.90 0.39 18.00 3.86 0.12 0.89 2.92 4.05 8.50 0.21 1.31 100.15

Note: data are from Romano et al. (2003).

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third located on the sample capsule. Quench was isobaric with control of pressure to within 25 bar of the nominal pressure. To check for the homogeneity of water distribution within the sample, selected chips of hydrated glasses as well as the nominally anhydrous starting material were analysed by Karl–Fischer-titration (KFT; Holtz et al., 1992; Behrens, 1995) at the IMH. A complete description of the KFT method is reported in Behrens (1995) and the data are summarised in Table 2. It is worth noting from Table 2 that the nominally anhydrous starting material contains small amount of water (0.18 wt.%, accuracy ± 0.1 wt.%). The viscosity determinations were carried out at the HP–HT Laboratory of Experimental Volcanology and Geophysics of Istituto Nazionale di Geofisica e Vulcanologia (INGV) of Rome in a piston cylinder apparatus (intrinsic condition NNO + 2) at 1.0 GPa and temperatures between 1200 and 1400 °C using the falling sphere method. The glasses were ground to powder and dried at 110 °C in an oven. Pt capsules (15 mm long, 3.0 mm outer diameter) were loaded in three stages: first we loaded a small amount of glass powder, then we positioned a Pt sphere (diameter from 90 to 450 μm), and finally we loaded more glass powder up to few millimetres below the top of the capsule. The interaction between Pt spheres and melt that contains 3.86 wt.% of FeO (Table 1), can be considered negligible, as measured by Vetere F. (personal communication). Loaded capsules were stored in an oven at 110 °C overnight to remove humidity and then welded. X-ray radiographs of each capsule were made before the experiments (Fig. 1a) in two different positions (one perpendicular to the other) to check for the initial position of the sphere. Loaded capsules were put into 19.1 mm NaCl-crushable alumina–pyrex (nominally anhydrous samples) or

Fig. 1. X-ray image of samples. (a) Before experiments; (b) after experiments. The arrows indicate the platinum sphere position.

NaCl-crushable alumina–pyrophillite–pyrex (Freda et al., 2001) assemblies. To check for reproducibility, we paired two capsules loaded with the 0.18 wt.% H2O glass and spheres having the same radius in the same assembly. At the end of the experiment we found that the difference in the final position of the spheres was within the measurement error (±20 μm; empty squares in Fig. 2). Moreover, because of the difficulty in preparing spheres with exactly the same radius we have also conducted experiments with spheres whose radius differed by 10 μm and we found that the related viscosity determinations were within error (empty triangles in Fig. 2).

Table 2 Karl Fischer Titration (KFT) analyses performed on AMS glasses before the falling sphere experiments and FTIR water content on AMS glasses after the falling sphere experiments KFT

FTIR −3

H2O (wt.%)

Density (kg m )

OH (wt%)

H2O mol (wt.%)

H2Otot (wt.%)

CO2 mol (ppm)

0.18 (± 0.01) 0.88 (± 0.07) 1.44 (± 0.03) 3.18 (± 0.05) 5.81 (± 0.05)

2475 (±1) 2520 (±4) 2510 (±3) 2490 (±4) 2440 (±2)

bdl 0.658 0.799 1.140 1.220

0.230 0.364 0.632 2.148 4.877

0.23 (± 0.04) 1.02 (± 0.08) 1.43 (± 0.06) 3.28 (± 0.06) 6.09 (± 0.04)

101.97 116.89 65.39 bdl bdl

The amount of water dissolved in the glasses before the experiments is comparable (within the error) with those analysed by FTIR in the same glasses after the experiments. The molar absorptivity (ε) values ε2350 is 975 l mol− 1 cm− 1 (Baker et al., 2005) while ε4500 and ε5200 are 1.359 and 1.1014 l mol− 1 cm− 1 respectively (Romano personal communication). Errors (2σ) in parentheses. bdl: below detection limit.

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In order to calculate the terminal fall velocity (see below), we performed at least three runs with the starting material having the same water content at the same temperature and different experimental duration (Table 3, Fig. 2). Samples were first pressurised to 1.0 GPa (nominal pressure within 25 MPa of the actual pressure) and then heated at a rate of 200 °C/min up to 20 °C below the set point. The last 20 °C were reached with a gradient of 40 °C/min. The temperature was controlled by a W95Re5–W74Re26 thermocouple and held within 3 °C of the experimental temperature. The thermocouple was positioned such that its junction was coincident with the cylindrical axis of the furnace and the midpoint (lengthwise) of the capsules, where the furnace hot spot is estimated to be approximately 8 mm in length. Quench was isobaric with an initial quench rate of 2000 °C/min. X-ray image of capsules were made after the experiments (Fig. 1b) and the sinking distance of sphere was measured (with an error of ± 20 μm) by superimposing pre- and post-experiments images (Fig. 1a and b). From the superimposition of the pre- and post-experiment images, however, (Fig. 1a and b) some shortening of the capsule due to compression can be observed. Because the sphere is likely to have begun its descent before the ramp to experimental temperature was complete, it was necessary to perform more than one experiment at the same P and T conditions but with varying duration. In fact, at least three experiments of varying duration were performed for each P, T condition to ensure that the terminal velocity of the descending sphere was reached, as indicated by a linear relationship between sphere position and duration (time at experimental temperature) among all data points. In order to verify that the shortening occurred during compression at room temperature, i.e. while the sphere was not descending, and also that compression did not affect the initial position of the sphere and the measurement of the sinking distance, we performed a test experiment. We inserted a film of Pt powder close to the

Fig. 2. Time vs. distance diagrams for all water content. The line outfit through the experimental points represent the constant sphere falling velocity (terminal fall velocity) that we used for the viscosity calculation. Symbols: squares, 1200 °C; triangles, 1300 °C; dots, 1400 °C. Empty squares represent the reproducibility of the method: two capsules with the same sphere radius were put in the same run. The difference in the final position of the spheres is within the measurement error (±20 μm). Empty triangles represent experiment conducted with spheres whose radius differ by 10 μm: the related viscosity values are within error. For water contents higher than 3 wt.% the sphere attained the terminal fall velocity before the experiment reached the temperature set point. This can be seen in the last two pictures where t = 0 gives a sphere position N0.

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Table 3 Experimental conditions for hydrous trachytic samples of the Agnano Monte Spina eruption (Phlegrean Field) T (°C)

H2O (wt%)

texa (s)

tefb (s)

d c (mm)

1200 1300 1400 1200 1300 1400 1200 1300 1400 1200 1300 1400 1200 1300 1400

0.18 0.18 0.18 0.88 0.88 0.88 1.44 1.44 1.44 3.18 3.18 3.18 5.81 5.81 5.81

25,200–21,600–19,200–19,200 17,280–17,280–11,520–9000 2400–1800–1800–1200–1200 21,600–14,400–9960 9360–7020–4680 3000–2700–1200 21,600–14,400–9960–9000 9360–7020–4680 3000–2700–1200 150–75–25 40–20–0 100–60–40 150–75–25 40–20–0 100–60–40

25,584–21,984–19,584–19,584 17,694–17,694–11,934–9414 2844–2244–2244–1644–1644 21,984–14,784–10,344 9774–7434–5094 3444–3144–1644 21,984–14,784–10,344–9384 9774–7434–5094 3444–3144–1644 534–459–409 454–434–414 544–504–484 534–459–409 454–434–414 544–504–484

4.2–3.6–3.4–3.2 6.5–5.9–3.9–2.9 5.2–4.9–4.6–1.7–1.4 5.5–3.4–1.8 5.5–3.9–2.4 7.2–5.9–4.2 7.0–4.2–2.2–1.5 6.4–4.9–2.9 7.4–5.1–3.9 2.9–1.0–0.65 2.1–1.4–0.73 5.1–3.8–2.9 4.9–1.83–0.65 3.3–1.9–0.5 6.5–4.6–1.8

a b c

Experimental duration, considering only the dwell time. At least three experiments have been performed for each temperature. Effective experimental duration accounting for heating up and cooling down. Falling distance of the sphere.

sphere to mark its initial position and just compressed the capsules at room temperature. Then we checked the position of the sphere relative to the Pt powder (using X-ray images) to verify that it did not change. After the experiments, to check for homogeneity and possible water leakage during the experiments, the water content of all samples was measured by Fourier Transform Infra-Red Spectroscopy at Università degli Studi Roma Tre (Table 2). A Nicolet 760 FTIR spectrometer has been used with CaF2 and KBr beamsplitter, MCT/A detector and 128 scans with a resolution of 4 cm− 1. The water contents were evaluated using the combination bands at 4500 cm− 1 (proportional to hydroxyl group abundance) and 5200 cm− 1 (proportional to molecular water abundance). In order to calculate the water content the samples were also characterised for density (Table 2) by weighing single glass chip in air and in water using quartz as standard (accuracy ±0.01%). The thickness of each sample was measured with a Mitutoyo digital micrometer with a precision of ±2 μm. We also note that, from the FTIR analyses with KBr beamsplitter small concentrations of CO2 were detected as reported in Table 2. The presence of CO2 can be considered negligible in terms of viscosity because of its small concentration dissolved in the melt and also because Bourgue and Richet (2001) demonstrated that the effects of CO2 in silicates melts becomes weaker with increasing temperature (especially above 1200 °C). Pre-experiment KFT and post-experiment FTIR analyses revealed comparable water contents within error (Table 2).

2.2. Theoretical approach The terminal fall velocity (i.e. the maximum velocity attainable by a particle that falls in a fluid) of the spheres needs to be estimated prior to the experiments, in order to determine the run duration. This velocity can be estimated by using the Stokes' law: g¼

2grs2 ðqs −qm ÞW 9m

ð1Þ

where η is the viscosity (Pa s) of the melt, g is the gravitational acceleration (9.8 m s− 2); rs is the radius (m) of the sphere; ρs and ρm are the densities (kg m− 3) of sphere and melt (Table 2) , respectively; W is the Faxen correction (see Eq. (2)); and v is the terminal fall velocity (m s− 1). In general the Stokes' law expects also the so called “end effect” (E =1 + 3.3 (rs /hc) where hc is the height of the capsule) that we have not considered in this work because the sphere never reached the end of the capsule. The Faxen correction considers the effects of the capsule walls: W ¼ ½1− 2:104ðrs =rc Þ þ 2:09ðrs =rc Þ3 − 0:95ðrs =rc Þ5 

ð2Þ

where rs and rc are the radius (m) of the sphere and capsule, respectively. In this work this correction has been estimated to be comprised between 0.69 and 0.93 (Table 4) and it has been verified to be independent from the position of the

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sphere with respect to the centre of the capsule. We performed a run coupling two capsules (loaded with the 0.18 wt.% H2O glass) in the same assembly: one capsule with the sphere positioned in the centre and the other capsule with the sphere close to the wall. At the end of the experiments the spheres covered the same distance within error. In our experiments we could not measure the falling velocity of the sphere in situ. Instead, for each experimental condition, we performed three to four runs with different durations, measuring, for each run, the sinking distance of the sphere. Combination of these “snapshots” gave a time–distance profile from which we obtained the terminal fall velocity (Fig. 2). The terminal fall velocity thus measured was inserted in the Stoke's law to calculate melt viscosity. We noted discrepancies between estimated and measured viscosities that stem from the extrapolation of VFT parameters of Romano et al. (2003) from low to high temperatures, as discussed below. 3. Results and discussion 3.1. Effect of temperature, pressure, and water content Experimental conditions and results are reported in Tables 3 and 4 (Fig. 2). shows the sphere falling distance versus time for all water contents and temperatures. Since a linear fit is generally consistent to all data points,

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we assume that these linear fits represent the terminal fall velocities and we used their slopes to calculate the viscosities by using Eq. (1). To evaluate the error in the viscosity determinations, all of the experimental data have been fitted assuming an Arrhenian behaviour over the 1200–1400 °C relatively narrow temperature range using the equation: Log g ¼ A þ

Ea RT

ð3Þ

where A is a pre-exponential term and Ea is the activation energy in kJ mol− 1. The addition of water to the melts decreases the activation energy (see Table 4) from 131 kJ mol− 1 (0.18 wt.% H2O) down to 25 kJ mol− 1 (5.81 wt.% H2O). The decrease of activation energy with increasing water content is in good agreement with previous results on albitic melts (Dingwell, 1987; Persikov, 1991) and on albitic and quartzofeldspathic melts (Shelby and McVay, 1976; Schulze et al., 1996; Holtz et al., 1999) and is well demonstrated combining the viscosity data from Romano et al. (2003) and from this paper (Fig. 3). For each composition and temperature we calculated the error using the equation of propagation error. For comparison purposes we also computed the error for the experimental data of Romano et al. (2003; see below). As for several other natural and synthetic melts (cf. Dingwell and Virgo, 1988; Dingwell et al., 1996; Schulze

Table 4 Viscosity data for hydrous trachytic samples of the Agnano Monte Spina eruption (Phlegrean Field) H2O (wt.%)

T (°C)

sr 1) (m)

v (m s− 1)

W 2)

log η 3) (Pa s)

A 4)

Ea5) (kJ mol− 1)

0.18 0.18 0.18 0.186) 0.187) 0.88 0.88 0.88 1.44 1.44 1.44 3.18 3.18 3.18 5.81 5.81 5.81

1200 1300 1400 1400 1400 1200 1300 1400 1200 1300 1400 1200 1300 1400 1200 1300 1400

205 × 10− 6 225 × 10− 6 165 × 10− 6 160 × 10− 6 165 × 10− 6 150 × 10− 6 135 × 10− 6 95 × 10− 6 90 × 10− 6 95 × 10− 6 80 × 10− 6 150 × 10− 6 130 × 10− 6 135 × 10− 6 50 × 10− 6 50 × 10− 6 50 × 10− 6

1.42 × 10− 7 3.94 × 10− 7 3.32 × 10− 6 3.25 × 10− 6 3.29 × 10− 6 3.17 × 10− 7 6.65 × 10− 7 1.51 × 10− 6 4.24 × 10− 7 7.50 × 10− 7 1.56 × 10− 6 1.85 × 10− 5 3.48 × 10− 5 3.69 × 10− 5 3.40 × 10− 5 7.09 × 10− 5 7.40 × 10− 5

0.72 0.69 0.77 0.78 0.77 0.79 0.81 0.87 0.87 0.87 0.89 0.79 0.82 0.81 0.93 0.93 0.93

3.66 (± 0.21) 3.56 (± 0.20) 2.66 (± 0.21) – – 3.41 (± 0.22) 2.96 (± 0.22) 2.38 (± 0.25) 2.85 (± 0.25) 2.64 (± 0.25) 2.17 (± 0.28) 1.57 (± 0.21) 1.23 (± 0.20) 1.19 (± 0.18) 0.35 (± 0.45) 0.21 (± 0.40) 0.11 (±0.41)

− 6.64 − 6.64 − 6.64 – – − 5.14 − 5.14 − 5.14 − 2.74 − 2.74 − 2.74 − 1.78 − 1.78 − 1.78 − 1.66 − 1.66 − 1.66

131 131 131 – – 105 105 105 69 69 69 41 41 41 25 25 25

1)

Radius of the spheres used in the falling sphere experiments. Faxen correction for the wall effects. 3) Error (2σ) log unit, in parentheses. 4) Pre-exponential factor, see Eq. (3) in the text. 5) Activation energy, see Eq. (3) in the text. 6) and 7) run coupling two capsules: one capsule with the sphere positioned in the centre and other capsule with the sphere close to the wall. 2)

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Fig. 3. Measured viscosities vs. the inverse of absolute temperature. Numbers represent water content in wt.%. Data at lower temperature are from Romano et al. (2003).

et al., 1996; Romano et al., 2001), viscosity decreases with both increasing temperature and water content for trachytic melts also, the decrease being more marked at low water contents and temperatures (Fig. 4). Extrapolating to T = ∞ viscosity becomes independent of water content, converging to a common viscosity value of −4.7307

Fig. 4. (a) Measured viscosities vs. the inverse of absolute temperature. Numbers represent water content in wt.%. (b) Measured viscosities vs. wt.% of H2O. In both diagrams is evident the viscosity decrease with increasing temperature and water content.

log Pa s (Glasstone et al., 1941; Myueller, 1955; Frenkel, 1959; Russell et al., 2003). The viscosity–water content relationship shows an upward-concave trend which is more evident at low temperature (Fig. 4b). Some experiments were also performed to gauge the pressure effect on viscosity. The experiments were carried out using the glass with 0.18 wt.% of H2O at 1400 °C, 0.5 and 2.0 GPa, and the same time duration (480 s) of those performed at 1.0 GPa and same temperature (Table 4). The post-run X-ray image of 0.5 and 2.0 GPa experiments demonstrated that the sphere reached the same final position, within the error, of the experiment performed at 1.0 GPa. Therefore, we concluded that the pressure dependence on viscosity is negligible, at least up to 2.0 GPa, as already demonstrated also by Behrens and Schulze (2003) for anhydrous compositions and by Scaillet et al. (1996) and Liebske et al. (2003) for hydrous compositions. 3.2. New Vogel–Fulcher–Tamman parameterization By comparing viscosities calculated by using the modified VFT of Romano et al. (2003) with those experimentally determined in this work, it can be observed that the parameterization of Romano et al. (2003) overestimates the viscosity of hydrous samples at high temperature (Fig. 5). In fact, the only experimental data from this work in good agreement with Romano et al. (2003) are those measured on the sample with 0.18 wt.% of H2O (i.e. very close to the anhydrous condition). The fact that discrepancies between estimated (Romano et al., 2003) and determined (this work) viscosity increase with increasing amount of dissolved water and temperature can be related to the lack of viscosity data

Fig. 5. Comparison between the measured and the calculated viscosities. The dotted lines represent the viscosities calculated by using the VFT from Romano et al. (2003). The numbers in the lines refer to water content in wt.%.

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for hydrous melts at high temperature in Romano et al. (2003). For example the viscosities obtained in this work at 1200 °C and 1.44 and 3.18 wt.% of H2O are 2.85 and 1.57 (log Pa s), respectively; while those calculated from Romano et al. (2003) are 3.58 and 3.16 (log Pa s), respectively. In order to extend the range of applicability of a modified VTF parameterization to high temperature and hydrous conditions, we combined the high-temperature hydrous data from this work with the high-temperature (1150–1496 °C) anhydrous and low-temperature (415–814 °C) anhydrous and hydrous data from Romano et al. (2003). By doing this, we established new parameters a, b, and c (reported in Table 5) to be used in the modified VTF equation (reported below, Eq. (4)): b1 þ b2 w H 2 O Log g ¼ a1 þ a2 ln w H2 O þ T −ðc1 þ c2 ln wH2 O Þ

ð4Þ

where a1 and a2 are the logarithm of viscosity at infinite temperature, b1 and b2 are the ratio between the activation energy Ea and the gas constant R, c1 and c2 are the temperatures (K) at which viscosity becomes infinity, w is the amount of H2O (wt.%), and T is the absolute temperature. However, the above mentioned Eq. (4) cannot be used to estimate viscosity of anhydrous samples. To overcome the limitation that the terms containing a2 and c2 approach zero at the anhydrous condition wH2O = 0, and the term containing b2 approaches 1 we suggest the following: Log g ¼ a1 þ a2 ln ð1 þ w H2 O Þ b1 þ b2 ð1 þ w H2 O Þ þ T −ðc1 þ c2 ln ð1 þ w H2 O ÞÞ

ð5Þ

In Table 5 we report the values of the parameters and the standard error of estimations of the global fit for Eqs. (4) and (5). We also tried to apply the Zhang et al. (2003) model to our data, but the standard error is bigger than that reported in Table 5. Fig. 6 shows the measured vs. calculated viscosity using the two different equations reported above. It is

Fig. 6. Measured vs. calculated viscosity using different VFT equations as discussed in the text. All the values are aligned showing a good correlation between the measured and calculated viscosities.

worthwhile noting that all of the data from the two equations fall close to the zero deviation line. The largest discrepancies between measured and calculated viscosity appear in the low viscosity–high water content range. Despite the general good prediction capabilities of both equations, specific differences do exist. Fig. 7 shows the deviations between the experimentally determined viscosities and those predicted by each of the two equations. 3.3. Application of the new VFT equations In order to explore the extent to which the improved knowledge of AMS trachyte viscosity may affect the volcanic eruption simulations at Phlegrean Fields, we have performed numerical simulations of magma flow and fragmentation along volcanic conduits. The simulations have been done by using the CONDUIT4 code (Papale, 2001), and have been repeated with either the viscosity parameterization of Romano et al. (2003) which does not account for high-T hydrous data, and the new parameterization given in this paper. A range of conditions covering a H2O content in magma of 2–6 wt.%, and a conduit diameter of 30–90 m, has been considered, for a total of 18 numerical simulations. Three additional simulations have

Table 5 Calibrated parameters for TVF equations

Eq. (4) Eq. (5)

a1

a2

b1

b2

c1

c2

Std error⁎

− 4.731 (± 0.581) − 4.764 (± 0.182)

− 0.004 (± 0.024) −1.118 (± 0.137)

10,788.93 (± 1211.55) 11,187.60 (± 1689.36)

− 587.33 (±31.39) 132.08 (±82.10)

173.56 (± 52.67) 241.38 (± 72.37)

− 26.78 (±1.62) − 149.54 (±10.91)

0.221 0.262

Listed values correspond to use of wt.% of H2O, absolute temperature and restitute viscosity in Pa s. Numbers in parentheses represent the standard deviation for each value. ⁎Represents the standard error of estimation of the global fit.

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Fig. 7. Deviation values from measured and calculated viscosities vs. the inverse of absolute temperature. Data from Eqs. (4) and (5) lie within the error in the viscosity measurements.

been done by using the same input data as for those with trachytic composition, H2O content of 4 wt.%, and conduit diameter of 30, 60, and 90 m, but replacing the trachyte with a typical rhyolitic magma (composition reported in Polacci et al., 2004), using the Hess and Dingwell (1996) viscosity parameterization for hydrous rhyolites, and using the Romano et al. (2003) parameters for phonolites. These simulations have been done in order to explore further similarities and differences between trachytic and rhyolitic magma ascent dynamics, in light of the new parameterization of this work. Conduit length (5 km), stagnation pressure (123 MPa), and magma temperature (830 °C), are kept constant in all simulations performed, and are the same as those given in Polacci et al. (2004). Fig. 8 shows the viscosity vs. dissolved H2O content relationships at 830 °C for the cases considered, corres-

Fig. 8. Viscosity vs. dissolved H2O content relationships at 830 °C for the cases considered, corresponding to rhyolite, trachyte with parameterization reported in Romano et al. (2003), trachyte with the parameterization presented in this work, and phonolite [data from Romano et al., 2003].

ponding to rhyolite, trachyte and phonolite using the Romano et al. (2003) parameterization, and trachyte using this work parameterization. For comparison, the trachyte with the old parameterization (Romano et al., 2003) is also included in this figure. It bears repeating that the new parameterization estimates a viscosity lower than that obtained in Romano et al. (2003; e.g. 0.21 log units lower at 2 wt.% H2O, up to 0.9 log units lower at the maximum value of 6 wt.% H2O considered in the figure). The minimum viscosity difference between rhyolite and trachyte is only about 0.2 log units using the Romano et al. (2003) parameterization, while it is more than 0.6 log units with the new one. At 6 wt.% dissolved H2O, the Romano et al. (2003) parameterization corresponds to a viscosity which is 0.6 log units less than that of the rhyolite, while this difference increases to more than 1.5 log units with the new parameterization. Fig. 9 shows how the above viscosity differences translate into different simulated magma ascent dynamics. The plot in the figure shows the calculated magmatic pressure along the volcanic conduit, from its base to the exit, for trachytic magma, 6 wt.% total H2O, old and new viscosity parameterization, and three different conduit diameters of 30, 60, and 90 m. Only the effects of the different viscosity equation adopted in the simulations are discussed here, since the roles of different conduit diameters, water contents, and magma composition are extensively discussed in previous papers (e.g., Papale et al., 1998). Note that the maximum amount of dissolved H2O at the conduit base, calculated with the Papale et al. (2006) model incorporated in the magma ascent modeling, is found to be slightly above 4.4 wt.%. In cases with 4 and 2 wt.% total water content (not shown in the figure), the

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dictated by the elastic properties of magma. Since the rate of strain in the conduit increases with the rate of pressure decrease, and rapid pressure decrease is delayed when the viscosity is lower, the result is delayed fragmentation with lower magma viscosity. The present simulation results show that at equal conduit diameter and total H2O content in magma, the different viscosities predicted by the new parameterization result in a fragmentation level up to 1000 m shallower (Fig. 10a). In contrast, the predicted gas volume fraction at fragmentation does not change appreciably when using either Romano et al. (2003) or new viscosity parameterization, being in both cases confined Fig. 9. Calculated pressure distribution along the volcanic conduit for the trachytic magma erupted during the AMS eruption at Phlegrean Fields. Input data: total water content in magma 6 wt.%, conduit diameters 30, 60, and 90 m, and use of viscosity parameterizations from this work and from Romano et al. (2003). The dashed line corresponds to lithostatic pressure distribution.

ascending magma enters the volcanic conduit at undersaturated conditions, and the exsolution level is placed between 780–1000 m (4 wt.%) and 2400–3500 m (2 wt.%), depending on the specific simulation conditions. The trends in Fig. 9 show that at equal conduit diameter, a lower viscosity of AMS trachyte as resulting from the present investigation produces (i) a larger magmatic pressure distribution all along the volcanic conduit, and (ii) a shallower level of magma fragmentation. The larger pressure is due to the fact that a lower magma viscosity results in less efficient heat loss due to lower friction forces inside the conduit. From the results in the figure, it emerges that the differences in pressure can be very large, resulting in a maximum pressure difference between lithostatic and magmatic from 63 to 28 MPa for conduit diameters from 30 to 90 m when the Romano et al. (2003) viscosity parameterization is adopted, and from 40 to only 8 MPa when the new parameterization is used. Additionally, the new parameterization results in much longer portions of the volcanic conduit where the magmatic pressure exceeds the lithostatic value, and reveals significantly larger positive differences between magmatic and lithostatic pressure at a given level in the conduit. The shallower level of magma fragmentation, which is invariably found in all the simulations performed when adopting the new viscosity parameterization, is also related to the lower efficiency of friction forces in producing a pressure drop inside the conduit. The occurrence of magmatic fragmentation is determined on the basis of the visco-elastic properties of magma, as illustrated in Papale (1999). The resulting criterion implies that fragmentation occurs when the product of viscosity and elongational rate of strain overcomes a critical value

Fig. 10. Calculated fragmentation depth (a), conduit exit pressure (b), and mass flow-rate (c) as a function of the assumed conduit diameter, for three different total water contents of 2, 4, and 6 wt.% (numbers beside lines), and employing the Romano et al. (2003; dashed lines) and present (solid lines) parameterizations for the viscosity of the AMS magma from Phlegrean Fields.

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to a narrow range of 82–86% in the performed simulations. Fig. 10b shows the calculated conduit exit pressure for all the performed simulations corresponding to trachytic magma composition, with Romano et al. (2003; dashed lines and open symbols) and new viscosity parameterizations. Conduit exit conditions are particularly important since they contribute substantially to determine the dynamics of the discharged gas–particle mixture in the atmosphere, and the buoyant versus collapsing style of the volcanic column (Neri et al., 1998). Calculated exit pressures of 1 atm in Fig. 10b for most of the cases with 2 wt.% total water content means that the flow is equilibrated with the atmosphere. In all other cases with exit pressure greater than atmospheric, the flow conditions are sonic and the flow is choked. Choking has important implications in large scale eruption dynamics, since it implies that the depressurization dynamics in the crater region and in general the processes occurring above the conduit exit plane do not affect the dynamics inside the volcanic conduit. The results in the figure show that the new viscosity parameterization extends the range of conditions where the flow is choked. For a total H2O content in magma of 2 wt.% and 90 m conduit diameter, the difference in conduit exit pressure calculated using the new instead of the old Romano et al. (2003) viscosity parameterization is as large as 500%. In all other cases this difference is much less, yet still relevant, in the range 45–65%, with the new parameterization producing greater exit pressure. Fig. 10c shows the calculated mass flow-rate for all the simulations with trachytic composition, using both Romano et al. (2003) and the new viscosity parameterizations. Mass flow-rate is among the most critical quantities characterizing explosive eruptions. An increase in mass flow-rate produces a volcanic column reaching higher levels in the atmosphere (Wilson et al., 1978), therefore affecting wider areas with ash fallout, or pyroclastic flows travelling faster and reaching larger run-out distances (Todesco et al., 2002). As shown in Fig. 10, the lower viscosity associated with the new parameterization produces, at equal conduit diameter and total volatile content, a larger mass flow-rate of the eruption. Maximum differences are found for low volatile content and small conduit diameter. With a conduit diameter of 30 m and 2 wt.% total water in magma, the mass flow-rate predicted by adopting the new viscosity parameterization is nearly twice that obtained with the old parameterization. For all other considered cases, the mass flow rate increases by 30–50%. Fig. 11 shows a comparison between conditions predicted for rhyolitic and trachytic magma ascent, by using both the old and new parameterization for trachyte

Fig. 11. Comparison between magma ascent dynamics for rhyolite and trachyte from AMS, for an assumed conduit diameter of 60 m. (a) Pressure and gas volume fraction distributions for an assumed total water content of 4 wt.%. Simulation names (defined in the text) are placed at the intersection between the corresponding curves. The dashed line represents lithostatic pressure distribution. (b) Calculated mass flow-rate as a function of total water content in magma.

viscosity and a conduit diameter of 60 m. All input conditions for the simulations in Fig. 11 corresponding to equal total water content are the same, except composition (rhyolite vs. trachyte), and adopted viscosity parameterization: Hess and Dingwell (1996) for runs labelled “rhyol”, Romano et al. (2003) for runs labelled “trach_old”, and present work for runs labelled “trach_new”. Fig. 11a shows the gas volume fraction and pressure distribution along the volcanic conduit for the three cases above and total water content of 4 wt.%. The discharge of trachytic magma results in shallower fragmentation and larger magmatic pressure with respect to the rhyolitic case. Fragmentation occurs at a gas volume fraction around 72% for rhyolite, and 82% for trachyte. Qualitatively, the comparison between rhyolitic and trachytic magma ascent dynamics does not change when considering the old and new viscosity parameterization for trachyte, and corresponds to that described in Polacci et al. (2004). Nonetheless, the old parameterization results in a decrease, and the new parameterization in an increase, of the mass flow-rate for the trachytic magma with respect to the rhyolitic magma (Fig. 11b).

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As seen above, the new viscosity parameterization produces a shallower fragmentation and larger pressure with respect to the old one. There is therefore a trend of decreasing fragmentation depth and increasing pressure in the conduit from rhyolite to trachyte, which reflects a parallel trend of progressively decreasing viscosity (Fig. 8). In spite of this monotonic trend, the mass flow-rate displays a minimum in correspondence of the trachyte with old viscosity parameterization. As noted in Polacci et al. (2004), one might expect that any other condition being equal, the discharge of a magma with lower viscosity is associated with a larger mass flow-rate, since a lower viscosity means lower friction forces contrasting the flow. On the other hand, lower mass flow-rate implies delayed fragmentation, therefore longer conduit region where highviscosity bubbly flow conditions are effective. In other words, a low-viscosity magma, which by itself would favour the flow, corresponds to a longer conduit distance over which the flow-contrasting effects of viscosity are effective. The result is a strongly non-linear dependency of mass flow-rate on viscosity. The present numerical simulations show that a complete parameterization of the temperature–viscosity behaviour of hydrous trachytic liquids leads to important differences in mass flow rate with respect to simulations based on earlier viscosity parameterizations constructed with a more limited data set. 4. Conclusions The present work provides a significant improvement in the knowledge of the viscosity–dissolved water content relationships for trachytes from Phlegrean Fields. Previous parameterization obtained by fitting only low temperature hydrous and low- and high-temperature anhydrous viscosity data were not able to reproduce our experimental results. The new modified VFT equations allows us, for the first time, to estimate viscosity in the complete temperature and water content range of volcanic processes without the need of extrapolating values outside the experimental range of measurements. This allows us to model the Newtonian viscosity of K-trachytes from magma chamber to emplacement of volcanic products. Numerical simulations of magma ascent dynamics demonstrate that such an improvement is not trivial, rather, it results in significant differences with previous calculations. Specifically, the lower viscosity found at magmatic temperature results in a shift of magma fragmentation towards higher levels in the conduit by an amount which can be as large as 1 km. This shift is accompanied by a generally higher pressure distribution in the volcanic conduit, easily resulting in magmatic pressures exceeding the corresponding lithostatic values, and in much lower maxi-

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mum underpressures with respect to lithostatic. Mass flowrate is found to be significantly higher, or in other words, the conduit diameter necessary to sustain a given mass flow-rate is smaller than previously calculated. Conduit exit conditions, only partly analysed in this paper, correspond to larger pressure and mixture density, while exit velocities are found to depend scarcely on the assumed magma viscosity for total water contents of 4 and 6 wt.%, and to display more non-linear trends for total water contents of 2 wt.%. All these changes are expected to affect the dynamics of gas–particle dispersion in the atmosphere and of pyroclastic flow generation and propagation. Future numerical simulations of eruption dynamics at Phlegrean Fields taking into account the discharge of a magma with composition similar to the trachyte erupted during the Agnano Monte Spina eruption, should therefore incorporate the new parameterization from the present work. Acknowledgements Many thanks to Alessandro Iarocci for helping us during the set up of the INGV HP–HT laboratory. We gratefully acknowledge Harald Behrens and Francesco Vetere for their assistance in hydrating samples and Federico Falcini for his providential help in the data analysis. Many thanks to Daniele Giordano for his comments. This work has been supported by the Gruppo Nazionale per la Vulcanologia 2000–2003 framework programme, Project n. 17 of Paolo Papale. References Baker, D.R, Freda, C., Brooker, R.A., Scarlato, P., 2005. Volatile diffusion in silicate melts and its effect on melt inclusions. Ann. Geophys. 48, 699–717. Behrens, H., 1995. Determination of water solubilities in high-viscosity melts: an experimental study on NaAlSi3O8 and KAlSi3O8 melts. Eur. J. Mineral. 7, 905–920. Behrens, H., Schulze, F., 2003. Pressure dependence of melt viscosity in the system NaAlSi 3O 8 –CaMgSi2 O6 . Am. Mineral. 88, 1351–1363. Bourgue, E., Richet, P., 2001. The effects of dissolved CO2 on the density and viscosity of silicate melts: a preliminary study. Earth Planet. Sci. Lett. 193, 57–68. Brearley, M., Montana, A., 1989. The effect of CO2 on the viscosity of silicate liquids at high pressure. Geochim. Cosmochim. Acta 53, 2609–2616. Brearley, M., Dickinson Jr., J.E., Scarfe, C.M., 1986. Pressure dependence of melt viscosities on the join diopside–albite. Geochim. Cosmochim. Acta 50, 2563–2570. Civetta, L., Carluccio, E., Innocenti, F., Sbrana, A., Taddeucci, G., 1991. Magma chamber evolution under Phlegrean Fields during the last 10 ka: trace element and isotope data. Eur. J. Mineral. 3, 415–428. de Vita, S., Orsi, G., Civetta, L., Carandente, A., D'Antonio, M., Deino, A., di Cesare, T., Di Vito, M.A., Fisher, R.V., Isaia, R., Marotta, E., Necco, A., Ort, M., Pappalardo, L., Piochi, M., Southon, J., 1999. The

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