# Experimental determination of H 2 O and CO 2 solubilities of mafic alkaline magmas from Canary Islands

María Jiménez-Mejías, Joan Andújar, Bruno Scaillet, Ramón Casillas

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María Jiménez-Mejías, Joan Andújar, Bruno Scaillet, Ramón Casillas. Experimental determination of H 2 O and CO 2 solubilities of mafic alkaline magmas from Canary Islands. Comptes Rendus. Géoscience, 2021, 353 (S2), pp.1-26. 10.5802/crgeos.84. insu-03429189

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# Comptes Rendus
## Géoscience
### Sciences de la Planète

María Jiménez-Mejías, Joan Andújar, Bruno Scaillet and Ramón Casillas

**Experimental determination of H₂O and CO₂ solubilities of mafic alkaline magmas from Canary Islands**

Online first, 5th November 2021

<https://doi.org/10.5802/crgeos.84>

**Part of the Special Issue:** Perspectives on alcaline magmas

**Guest editor:** Bruno Scaillet (Institut des Sciences de la Terre d'Orléans, CNRS, France)

© Académie des sciences, Paris and the authors, 2021.

Some rights reserved.

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This article is licensed under the

CREATIVE COMMONS ATTRIBUTION 4.0 INTERNATIONAL LICENSE.

http://creativecommons.org/licenses/by/4.0/
# Experimental determination of H₂O and CO₂ solubilities of mafic alkaline magmas from Canary Islands

María Jiménez-Mejías*®, a, b, c, d, Joan Andújar® a, Bruno Scaillet® a
and Ramón Casillas® d

E-mails: maria.jimenez@cnrs-orleans.fr (M. Jiménez-Mejías), juan.andujar@cnrs-orleans.fr (J. Andújar), bruno.scaillet@cnrs-orleans.fr (B. Scaillet), rcasilla@ull.es (R. Casillas)

**Abstract.** We present new H₂O and CO₂ solubility data in mafic to intermediate alkaline magmas from Fasnia and Garachico volcanoes, Tenerife. H₂O- and CO₂-saturated experiments were conducted at ~50–400 MPa, 1200 °C, and fO₂ from 2 log units below the NiNiO solid buffer to 3.2 log units above it. Although existing solubility models for alkali-rich mafic magmas broadly describe H₂O and CO₂ behaviour, associated errors are worthy of consideration since they usually exceed 15–20%. For this reason, we have determined the specific solubility laws of basanitic and phonotephritic melts from the Canary Islands. Results show similar H₂O solubilities for both compositions, whereas the basanite can dissolve an average of ~45% more CO₂ than the phonotephrite. By combining these data, we have established a simple empirical model that allows us to calculate melt inclusion entrapment pressures accurately and, therefore, better understand the inner workings of volcanic oceanic islands. Application to El Hierro 2011–2012 and young (<20 ka) basanites from this location shows that previous barometric estimates were, on average, overestimated by 15–28%. Our results suggest that magmas rising from depth experienced a first but short episode of equilibration at 8–10 km, whereas the bulk of the crystallization occurred during the subsequent dyke injection, ascent, and degassing at P ⇐ 200 MPa (6–1.5 km).

**Keywords.** H₂O, CO₂, Solubility, Canary Islands, Alkaline magmas, Melt inclusions, El Hierro.
Online first, 5th November 2021

<footnote>a Institut des Sciences de la Terre d'Orléans (ISTO), UMR 7327, Université d'Orléans, CNRS, BRGM, 1A rue de la Férollerie, F-45071 Orléans, France</footnote>

<footnote>b Geosciences Barcelona (GEO3BCN-CSIC), C/Lluis Solé i Sabarís s/n, 08028, Barcelona, Spain</footnote>

<footnote>c Instituto Geográfico Nacional, Centro Geofísico de Canarias, C/ La Marina 20, 2º,
38001 Santa Cruz de Tenerife, Spain</footnote>

<footnote>d Departamento de Biología Animal, Edafología y Geología. Facultad de Ciencias.
Universidad de La Laguna. C/Astrofísico Francisco Sánchez S/N. 38206. La Laguna,
Santa Cruz de Tenerife, Spain</footnote>

<footnote>* Corresponding author.</footnote>
# 1. Introduction

Understanding magmatic volatiles behaviour in terms of the maximum amount that can be dissolved in a silicate melt under a given set of conditions (pressure, temperature, melt composition, and redox state) is crucial for improving the knowledge of magmatic processes and degassing mechanisms involved in volcanic eruptions [Moore, 2008, Moore and Carmichael, 1998, Oppenheimer et al., 2014].

Among other species (CO₂, S, F, and Cl), water is the most abundant volatile phase in magmas on Earth, exerting an important control on their physical and rheological properties [i.e., density, viscosity; Andújar and Scaillet, 2012a, Giordano et al., 2008, Stolper, 1982a] and phase equilibria [Andújar et al., 2015, 2017, Scaillet and Evans, 1999, Scaillet et al., 2008]. The amount of volatiles along with the level, rate, and efficiency of the exsolution process (especially for H₂O) during magma ascent, largely control the explosive–effusive style of an eruption [Andújar and Scaillet, 2012b, Burnham, 1979, Sparks, 1978]. Therefore, understanding the mechanisms that control the solubility of the different volatile species dissolved in magmas is crucial to decipher surface gas signals, changes in the eruptive dynamic, and correctly interpretate melt inclusion (MI) data.

For this reason, the solubility of H₂O and CO₂ and their speciation in melts have been the focus of numerous experimental studies, which have explored the dissolution behaviour of pure H₂O [e.g., Carroll and Blank, 1997, Lesne et al., 2011a, Moore et al., 1998, Mysen and Cody, 2004, Schmidt and Behrens, 2008, Stolper, 1982a,b], pure CO₂ [e.g., Brooker et al., 2001a,b, Dixon and Pan, 1995, Jendrzejewski et al., 1997, Lesne et al., 2011b, Moore et al., 2000, Mysen et al., 1975, Pan et al., 1991], and mixed H₂O–CO₂ fluids [e.g., Allison et al., 2019, Botcharnikov et al., 2005, Dixon et al., 1995, Dixon and Stolper, 1995, Iacono-Marziano et al., 2012, Iacovino et al., 2013, Moussallam et al., 2016, Newman and Lowenstern, 2002, Schanofski et al., 2019, Shishkina et al., 2010, 2014, Tamic et al., 2001, Vetere et al., 2014] over a large range of melt compositions and experimental P–T conditions.

Pioneering works [e.g., Burnham and Jahns, 1962, Goranson, 1931, 1936] already pointed out the strong dependence of water solubility on pressure, melt composition, and to a lesser degree, temperature.

Theoretical considerations and spectroscopic studies show that water dissolves in silicate melts either as hydroxyl (–OH) groups [e.g., Burnham, 1975, Burnham and Davis, 1971, 1974] or H₂O molecules [e.g., Carroll and Blank, 1997, McMillan and Remmele, 1986, Mysen and Virgo, 1986a,b, Newman et al., 1986, Stolper, 1982a,b], and their relative proportion varying significantly with total water content. At low H₂O concentrations (<1 wt%), the hydroxyl species predominates while at high H₂O*total*, molecular water dominates [e.g., Silver et al., 1990, Stolper, 1982a,b]. The CO₂ solubility is also highly dependent on pressure and composition but compared to H₂O, magmas can incorporate relatively low amounts of carbon under the same P–T conditions. The difference in solubility gives rise to the exsolution of a CO₂-rich fluid at very initial stages of magma ascent, which gets enriched in water as decompression proceeds, in particular during the very last steps of ascent [e.g., Dixon et al., 1995, Dixon and Stolper, 1995, Edmonds and Wallace, 2017]. Consequently, CO₂ plays an important role in generating vapour-saturation conditions at crustal pressures with strong implications on eruption triggers and changes in the eruptive dynamic [e.g., Anderson, 1975, Newman and Lowenstern, 2002, Pichavant et al., 2013].

The dependence of CO₂ solubility with magma composition is commonly described as a function of the NBO/T parameter (average number of nonbridging oxygens per tetrahedrally coordinated cation), which is considered as a proxy for the degree of (de)polymerization of a silicate melt [e.g., Mysen et al., 1982, Mysen, 1990, 1991]. The increase of NBO/T species in the melt enhances CO₂ solubility [e.g., Brooker et al., 2001a,b, Iacono-Marziano et al., 2012]. However, this parameter alone cannot fully capture the details of CO₂ solubility behaviour observed in magmas of broadly similar compositions. In particular, CaO and K₂O contents also play an important role in enhancing CO₂ solubility in magmas [e.g., Behrens et al., 2009, Dixon, 1997, Lesne et al., 2011b, Moore, 2008, Scaillet and Pichavant, 2005, Vetere et al., 2014].

Despite all the existing H₂O and/or CO₂ solubility models, associated errors generally exceed 15–20%, translating into differences of ±1–2 wt% H₂O and ±1000–2000 CO₂ ppm at ≥300 MPa, namely up to ±6 km in depth. Such uncertainties have a significant impact on the estimates of the saturation and entrap-
<figure><img src="image_3.png" /></figure>

**Figure 1.** (a) Geographic location of Canary Islands. Digital elevation model of Tenerife, showing the location of the two historical monogenetic eruptions of Fasnia (in green) and Garachico (in orange) and their sampling points (green square and orange circle, respectively). (b) Classification of the starting experimental glasses based on the total alkalis versus silica diagram [TAS, Le Bas et al., 1986]. *The large dark green square and orange circle* represent the starting compositions of Fasnia (basanite) and Garachico (phonotephrite), respectively. *The smaller light green squares (Fasnia) and orange circles (Garachico) correspond* to experimental run products. Each symbol represents the average of 10–15 single EPMA analyses.

ment pressures of magmas and melt inclusions, and consequently, on the interpretation of storage conditions and degassing processes. Thus, in order to obtain the most accurate barometric information on magmas and related degassing processes, it is imperative to determine solubility laws for the most abundant species (H₂O–CO₂) adapted to the magma composition emitted by each volcanic system.

Here we report the results of water and carbon dioxide solubility experiments performed on basanitic and phonotephritic magmas from Tenerife (Canary Islands, Figure 1) at 1200 °C and pressures ranging from 50 to 400 MPa. Concentrations of molecular water (H₂O), hydroxyl groups (–OH), and carbonate ion complexes (CO⁻³) of quenched glasses were measured by Fourier Transform Infrared Spectroscopy (FTIR) on glasses drop-quenched at high pressures. Two other complementary and independent techniques, Nanoscale Secondary Ion Mass

Spectrometry (NanoSIMS) and Elemental Analyzer (EA) were used, when possible, to complement FTIR results.

These concentrations were subsequently used to establish empirical H₂O and CO₂ solubility models specifically calibrated for the mafic–intermediate alkaline compositions from the Canary Islands, allowing us to calculate, first, the H₂O and CO₂ fugacities and partial pressures and, second, to re-evaluate volatile entrapment conditions recorded by melt inclusions from different eruptions of El Hierro, including the 2011–2012 event [Longpré et al., 2014, 2017, Taracsák et al., 2019].

## 2. Experimental and analytical techniques

Solubility experiments and the characterization of run products were performed using established procedures which are detailed in Supplementary
Material. In short, experiments were performed in internally heated pressure vessels equipped with a drop quench set-up and allowing redox conditions to be controlled. Run products were characterized by EPMA (Electron Probe Micro-Analysis), SEM (Scanning Electron Microscopy), FTIR, NanoSIMS (Nanoscale Secondary Ion Mass Spectrometry), and EA (Elemental Analyzer) techniques.

# 3. Results

## 3.1. Major element compositions and Fe-loss in experimental charges

The major element compositions of our experimental glasses are presented in Table S1 after recalculation to a 100% anhydrous basis. Almost all of our supra-liquidus melts are crystal-free and compositionally homogeneous, as indicated by the low standard deviations obtained (often ≤0.4 wt%), closely matching (within analytical errors) the starting material composition (Table 1). It should be noted that some samples (e.g., F3a, F4a and G3a) show slightly higher silica and lower iron contents than the starting composition (Table 1) due to some iron-loss towards the capsule [e.g., Grove, 1982, Hall et al., 2004, Kawamoto and Hirose, 1994] or the crystallization of small Fe-oxides. The apparent loss or gain of FeO (all iron as FeO) was calculated as follows: for crystal-free charges and those containing a low amount of quench crystals (Table 2), the Fe-loss was estimated considering the iron content of experimental glasses (FeO<sub>gl</sub>) relative to such the starting material (FeO<sub>st</sub>) following the expression: 100*FeO<sub>gl</sub>/FeO<sub>st</sub>; for the three oxide-bearing charges G3a, F3a, and F4a, we performed least-square mass balance calculations to retrieve the phase proportions and iron-loss, considering the corresponding oxide and residual glass compositions. Overall, in CO<sub>2</sub> and H<sub>2</sub>O-saturated experiments, approximately 80 to 100% of the iron was kept in the melt, except for FC4b, GC05, GC3b, and GC4b, in which the loss reaches 22–25%. Despite that the SEM inspection of these four charges did not reveal the presence of mineral phases within the glasses, we cannot rule out the possibility of an occasional crystallization of Fe–Ti oxides non-detectable by SEM (<0.5 µm in size), which could explain such slightly higher iron-loss. Glasses from G3a, F3a, and F4a charges have lower iron contents compared to the starting material, owing to the crystallization of

different proportions of Fe–Ti oxides which depleted the residual melt in FeO (Table 2).

## 3.2. H₂O concentrations

As stated above, the water contents of our experimental glasses were analysed by FTIR and EA whenever possible. The comparison of the results shows that the retrieved H₂O concentrations agree to less than 0.3 wt% H₂O, even considering the associated analytical errors (Table 2) and are consistent with the measured ¹⁶OH⁻/²⁸Si⁻ ratio by the NanoSIMS. Given the similarities between the data, in the following we use the H₂O contents obtained with FTIR.

For both compositions, the general trend is to increase the amount of dissolved water with pressure, from ~2.3 wt% at 50 MPa up to 7.6 wt% at 400 MPa (Figure 2). In this case, the differences in composition of the studied materials (2–3.5 wt% in major oxides; Table 1) or imposed fO₂ do not have any significant effects on water solubility. Based on the observed relationships, we have mathematically regressed the H₂O content-P dependence according to expressions of the form H₂O<sub>melt</sub> (wt%) = a * P<sup>b</sup> (P in MPa) obtaining the equations shown in Figure 2. These expressions back-calculate analysed water contents to within ~2%.

### 3.2.1. Determination of H₂O fugacities

For any volatile species dissolved in a silicate melt that is fluid-saturated, the condition of equilibrium requires that the fugacity (f) of each species (i) in the melt equals that of the fluid, i.e., for water: fH₂O<sub>melt</sub> = fH₂O<sub>fluid</sub>. At very low pressures (1 bar) and high temperatures (>600 °C), the fugacity of a pure gas is well described by the ideal gas law. However, as pressure increases, departure from ideality occurs, which is described by the fugacity coefficient, Φᵢ. For a pure fluid (i.e., one species i), the relationship is

$$ \Phi_i = f_i / P_{tot}, \qquad (1) $$

where P<sub>tot</sub> is total pressure (in bars).

In mixed fluids, the total pressure is replaced by the partial pressure (Pᵢ):

$$ P_i = f_i / \Phi_i \qquad (2) $$

With the constraint that:

$$ P_{tot} = \sum P_i $$

So, assuming that H₂O and CO₂ are the main volatile species present in the melt, we obtain the
<table><caption>**Table 1.** Starting compositions (wt%)</caption><thead><tr><th>Composition<br>Sample</th><th>Basanite<br>FAS<sup>a</sup></th><th>Phonotephrite<br>GCH<sup>a</sup></th><th>Basanite<br>Fasnia<sup>b</sup></th><th>Phonotephrite<br>Garachico<sup>b</sup></th></tr></thead><tbody><tr><td>SiO<sub>2</sub></td><td>45.08<br>0.14</td><td>48.06<br>0.37</td><td>44.46</td><td>48.56</td></tr><tr><td>TiO<sub>2</sub></td><td>3.82<br>0.13</td><td>3.15<br>0.15</td><td>3.71</td><td>3.09</td></tr><tr><td>Al<sub>2</sub>O<sub>3</sub></td><td>14.45<br>0.17</td><td>17.77<br>0.20</td><td>15.01</td><td>17.47</td></tr><tr><td>FeO<sup>c</sup></td><td>12.51<br>0.27</td><td>9.43<br>0.37</td><td>12.12</td><td>9.32</td></tr><tr><td>MnO</td><td>0.28<br>0.05</td><td>0.19<br>0.07</td><td>0.19</td><td>0.20</td></tr><tr><td>MgO</td><td>7.16<br>0.22</td><td>3.98<br>0.09</td><td>7.71</td><td>4.05</td></tr><tr><td>CaO</td><td>10.82<br>0.17</td><td>8.42<br>0.14</td><td>10.68</td><td>8.80</td></tr><tr><td>Na<sub>2</sub>O</td><td>3.60<br>0.10</td><td>5.34<br>0.09</td><td>3.83</td><td>5.40</td></tr><tr><td>K<sub>2</sub>O</td><td>1.57<br>0.07</td><td>2.19<br>0.10</td><td>1.54</td><td>2.21</td></tr><tr><td>P<sub>2</sub>O<sub>5</sub></td><td>0.71<br>0.07</td><td>1.25<br>0.16</td><td>0.76</td><td>1.25</td></tr><tr><td>Na<sub>2</sub>O + K<sub>2</sub>O</td><td>5.17</td><td>7.53</td><td>5.37</td><td>7.61</td></tr><tr><td>LOI</td><td></td><td></td><td>-0.55</td><td>-0.34</td></tr><tr><td>Total</td><td>100</td><td>100</td><td>100</td><td>100</td></tr></tbody></table>

Compositions normalized to 100% anhydrous melt.

<sup>a</sup>Oxide concentrations were measured by EPMA at ISTO-CNRS.

Standard deviations are italicized.

<sup>b</sup>Oxide concentrations determined by XRF analyses at CRPG-Nancy, France, for comparison.

<sup>c</sup>Total iron expressed as FeO.

following equations:

$$P_{\text{H}_2\text{O}} = f_{\text{H}_2\text{O}}/\Phi_{\text{H}_2\text{O}} \quad (3)$$

$$P_{\text{CO}_2} = f_{\text{CO}_2}/\Phi_{\text{CO}_2} \quad (4)$$

Therefore, since according to our FTIR, NanoSIMS and EA results, all charges devoted to study water solubility in melts are CO₂-free (Table 2), the fugacity coefficient of pure H₂O can be calculated at the corresponding *P* and *T* using the modified Redlich-Kwong equation of state [Holloway, 1977]. Then, the *f*H₂O at given *P*–*T* of each charge is computed using

the expression

$$f_{\text{H}_2\text{O}} = \Phi_{\text{H}_2\text{O}} * X_{\text{H}_2\text{O}} * P_{\text{tot}}, \quad (5)$$

where X<sub>H₂O</sub> is the mole fraction of water in the fluid. Since in H₂O-saturated experiments, the X<sub>H₂O</sub> is equal to one, the previous relationship can be transformed to

$$X_{\text{H}_2\text{O}} = \frac{f_{\text{H}_2\text{O}}}{\Phi_{\text{H}_2\text{O}} * P_{\text{tot}}} \rightarrow X_{\text{H}_2\text{O}} = 1 \rightarrow f_{\text{H}_2\text{O}} = \Phi_{\text{H}_2\text{O}} * P_{\text{tot}} \quad (6)$$

$P_{\text{tot}}$ (in bars).
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Dissolved water contents in experimental glasses plotted as a function of pressure for (a) Fasnia basanite (green squares) and (b) Garachico phonotephrite (orange circles). The filled and empty symbols represent experiments performed at NNO + 1.4 and NNO + 3.2, respectively.</figcaption></figure>

The calculated fugacities and the determined water contents were then regressed using power-law equations that allowed a close fit between both parameters ($R^2 = 0.99$) (Figure 3), yielding for each case the following equations:

$$ 
\begin{aligned}
f_{\text{H}_2\text{O}}^{1200 \,^{\circ}\text{C}} &= 10.6616 * (\text{wt}\% \text{H}_2\text{O})^{1.8774} \\
R^2 &= 0.99 \quad \text{for Fasnia at NNO} + 3.2 \quad (7)
\end{aligned}
 $$

$$ 
\begin{aligned}
f_{\text{H}_2\text{O}}^{1200 \,^{\circ}\text{C}} &= 11.5813 * (\text{wt}\% \text{H}_2\text{O})^{1.8407} \\
R^2 &= 0.99 \quad \text{for Fasnia at NNO} + 1.4 \quad (8)
\end{aligned}
 $$

$$ 
\begin{aligned}
f_{\text{H}_2\text{O}}^{1200 \,^{\circ}\text{C}} &= 10.3418 * (\text{wt}\% \text{H}_2\text{O})^{1.8693} \\
R^2 &= 0.99 \quad \text{for Garachico at NNO} + 3.2 \quad (9)
\end{aligned}
 $$

$$ 
\begin{aligned}
f_{\text{H}_2\text{O}}^{1200 \,^{\circ}\text{C}} &= 9.9808 * (\text{wt}\% \text{H}_2\text{O})^{1.8725} \\
R^2 &= 0.99 \quad \text{for Garachico at NNO} + 1.4 \quad (10)
\end{aligned}
 $$

These empirical relationships allow us to calculate the water fugacities of basanitic and phonotephritic melts from Tenerife at different oxidation states considering the dissolved water contents in residual glasses or melt inclusions with an accuracy of 95%.

### 3.3. CO₂

The dissolved CO₂ contents that we present here correspond to those determined using the absorbances of the carbonate doublet (~1430 cm⁻¹ and ~1520 cm⁻¹) in the mid-infrared (MIR) since no molecular CO₂ was detected in our experimental glasses [Blank and Brooker, 1994, Botcharnikov et al., 2005, Dixon et al., 1995].

CO₂ dissolved content gradually increases with pressure from 278–484 ppm at 50 MPa up to 3400–5800 ppm at 400 MPa for the phonotephrite and the basanite, respectively (Figure 4). Contrary to H₂O, our results define a negative relationship between CO₂ solubility and alkalinity since at a given P, the basanite dissolves up to 40–49% more CO₂ than its phonotephritic counterpart (Figure 5).

Even if no water was initially added to the CO₂-bearing charges (Table 3), all the run products contain variable amounts of H₂O, as evidenced in FTIR spectra (Figure S2c). H₂O contents of CO₂-bearing charges range from 0.18 up to 1.84 wt%, indicating that, despite our efforts, the experiments are not strictly CO₂ pure. The presence of water can be related to the following factors [e.g., Behrens et al., 2009, Gaillard et al., 2003, Holloway et al., 1992, Lesne et al., 2011b]:

(1) The starting glass was synthesized at relatively oxidizing conditions compared to those imposed during experiments. The re-equilibration to the new fO₂ conditions generates H₂O following the bulk reaction Fe₂O₃ + H₂ ↔ 2FeO + H₂O. The H₂ source comes from the Ar + H₂ gas used to pressurize the vessel.

(2) To a lesser extent, during capsule preparation, both the silver oxalate used as a CO₂ source and the starting glass can adsorb small but finite amounts of atmospheric water.
<table><caption>Table 2. Experimental results</caption><thead><tr><th>Sample</th><th>P (MPa)</th><th>T<sup>a</sup> (°C)</th><th>Density (g/l)<sup>a</sup></th><th>%FeO loss<sup>b</sup></th><th>% Oxides<sup>c</sup></th><th>fH<sub>2</sub>O (MPa)<sup>d</sup></th><th>fCO<sub>2</sub> (MPa)<sup>d</sup></th><th>XH<sub>2</sub>O<sup>e</sup> XCO<sub>2</sub><sup>e</sup></th><th>ΦH<sub>2</sub>O<sup>f</sup></th><th>ΦCO<sub>2</sub><sup>f</sup></th><th>ΔNNO<sup>g</sup></th><th>Calculated log(fO<sub>2</sub>)<sup>g</sup></th><th>wt% H<sub>2</sub>O E.A<sup>h</sup></th><th>wt% H<sub>2</sub>O A3500<sup>i</sup></th><th>wt% H<sub>2</sub>O A4500<sup>i</sup></th><th>wt% H<sub>2</sub>O A5200<sup>i</sup></th><th>wt% H<sub>2</sub>O 4300 + 5200<sup>i</sup></th><th>CO<sub>2</sub> (ppm) A1430<sup>i</sup></th><th>Comments for run products</th></tr></thead><tbody><tr><td>F05</td><td>52</td><td>1200</td><td>2748</td><td>0.93</td><td></td><td>52</td><td></td><td>1</td><td></td><td>0.99</td><td>1.13</td><td>1.40</td><td>-6.32</td><td>2.54</td><td><strong>2.29</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>F1a</td><td>100</td><td>1200</td><td>2669</td><td>14.34</td><td></td><td>99</td><td></td><td>1</td><td></td><td>0.99</td><td>1.26</td><td>3.18</td><td>-4.53</td><td>0.07</td><td></td><td>0.19</td><td></td><td></td><td></td><td></td></tr><tr><td>F1c</td><td>108</td><td>1200</td><td>2750</td><td>1.24</td><td></td><td>107</td><td></td><td>1</td><td></td><td>0.99</td><td>1.29</td><td>1.44</td><td>-6.28</td><td></td><td>3.32</td><td>1.65</td><td>1.72</td><td><strong>3.37</strong></td><td></td><td></td></tr><tr><td>F2a</td><td>210</td><td>1200</td><td>2626</td><td>14.68</td><td></td><td>213</td><td></td><td>1</td><td></td><td>1.02</td><td>1.70</td><td>3.25</td><td>-4.45</td><td>0.26</td><td>3.24</td><td>1.62</td><td>1.63</td><td><strong>3.25</strong></td><td></td><td></td></tr><tr><td>F2b</td><td>210</td><td>1200</td><td>2720</td><td>5.19</td><td></td><td>213</td><td></td><td>1</td><td></td><td>1.02</td><td>1.70</td><td>1.38</td><td>-6.32</td><td></td><td>0.60</td><td>0.60</td><td>2.25</td><td>2.58</td><td><strong>4.82</strong></td><td></td><td></td></tr><tr><td>F3a</td><td>292</td><td>1200</td><td>2785</td><td>4.47*</td><td>6.6</td><td>308</td><td></td><td>1</td><td></td><td>1.05</td><td>2.27</td><td>3.18</td><td>-4.51</td><td>5.66</td><td>6.10</td><td>2.39</td><td>3.75</td><td>0.59</td><td>0.27</td><td></td></tr><tr><td>F3c2</td><td>319</td><td>1200</td><td>2727</td><td>4.88</td><td></td><td>341</td><td></td><td>1</td><td></td><td>1.07</td><td>2.51</td><td>1.34</td><td>-6.35</td><td></td><td>6.03</td><td>1.14</td><td>5.03</td><td><strong>6.14</strong></td><td></td><td></td></tr><tr><td>F4a</td><td>411</td><td>1200</td><td>2690</td><td>4.53*</td><td>7.3</td><td>464</td><td></td><td>1</td><td></td><td>1.13</td><td>3.62</td><td>3.22</td><td>-4.44</td><td>6.90</td><td>7.20</td><td>1.28</td><td>6.06</td><td><strong>7.35</strong></td><td></td><td></td></tr><tr><td>F4b</td><td>397</td><td>1200</td><td>2737</td><td>5.50</td><td></td><td>444</td><td></td><td>1</td><td></td><td>1.12</td><td>3.42</td><td>1.20</td><td>-6.48</td><td>0.29</td><td>0.88</td><td></td><td></td><td>0.48</td><td></td><td></td></tr><tr><td>G05</td><td>52</td><td>1200</td><td>2661</td><td>-0.39</td><td></td><td>52</td><td></td><td>1</td><td></td><td>0.99</td><td>1.13</td><td>1.40</td><td>-6.32</td><td></td><td><strong>2.35</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>G1a</td><td>100</td><td>1200</td><td>2523</td><td>6.73</td><td></td><td>99</td><td></td><td>1</td><td></td><td>0.99</td><td>1.26</td><td>3.18</td><td>-4.53</td><td>3.48</td><td>0.25</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>G1b</td><td>108</td><td>1200</td><td>2543</td><td>1.32</td><td></td><td>107</td><td></td><td>1</td><td></td><td>0.99</td><td>1.29</td><td>1.44</td><td>-6.28</td><td>0.60</td><td>3.45</td><td>1.71</td><td>1.65</td><td><strong>3.36</strong></td><td></td><td></td></tr><tr><td>G2a</td><td>210</td><td>1200</td><td>2533</td><td>5.71</td><td></td><td>213</td><td></td><td>1</td><td></td><td>1.02</td><td>1.70</td><td>3.25</td><td>-4.45</td><td>5.15</td><td>0.40</td><td>3.71</td><td>1.98</td><td>1.69</td><td><strong>3.67</strong></td><td></td><td></td></tr><tr><td>G2b</td><td>207</td><td>1200</td><td>2632</td><td>0.19</td><td></td><td>210</td><td></td><td>1</td><td></td><td>1.01</td><td>1.69</td><td>1.38</td><td>-6.32</td><td></td><td>0.47</td><td>0.47</td><td>2.57</td><td>2.55</td><td><strong>5.12</strong></td><td></td><td></td></tr><tr><td>G3a</td><td>292</td><td>1200</td><td>2642</td><td>3.17*</td><td>3.9</td><td>308</td><td></td><td>1</td><td></td><td>1.05</td><td>2.27</td><td>3.18</td><td>-4.51</td><td>6.20</td><td>0.61</td><td>0.61</td><td>2.55</td><td>3.77</td><td><strong>6.32</strong></td><td></td><td></td></tr><tr><td>G4a</td><td>411</td><td>1200</td><td>2567</td><td>6.07</td><td></td><td>464</td><td></td><td>1</td><td></td><td>1.13</td><td>3.62</td><td>3.22</td><td>-4.44</td><td>7.45</td><td>0.19</td><td>0.83</td><td>2.75</td><td>4.64</td><td><strong>7.38</strong></td><td></td><td></td></tr><tr><td>G4b</td><td>413</td><td>1200</td><td>2551</td><td>-1.13</td><td></td><td>468</td><td></td><td>1</td><td></td><td>1.13</td><td>3.66</td><td>1.20</td><td>-6.48</td><td>0.08</td><td>0.35</td><td>0.35</td><td>1.38</td><td>6.18</td><td>0.90</td><td>0.40</td><td></td></tr><tr><td>FC05</td><td>60</td><td>1200</td><td>2746</td><td>12.63</td><td></td><td>16</td><td></td><td>51</td><td>0.266</td><td>0.734</td><td>0.99</td><td>1.13</td><td>0.37</td><td>-7.35</td><td>0.19</td><td>0.10</td><td></td><td></td><td>0.10</td><td>4.84</td><td></td></tr><tr><td>FC1c</td><td>113</td><td>1200</td><td>2787</td><td>15.93</td><td></td><td>24</td><td></td><td>116</td><td>0.214</td><td>0.786</td><td>0.99</td><td>1.26</td><td>0.14</td><td>-7.58</td><td>0.12</td><td>1.49</td><td></td><td></td><td>0.12</td><td>35</td><td>1205</td></tr><tr><td></td><td></td><td></td><td>33</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>55</td></tr></tbody></table>

(continued on next page)
<table><caption>**Table 2. (continued)**</caption><thead><tr><th>Sample</th><th>P<br>(MPa)</th><th>T<sup>a</sup><br>(°C)</th><th>Density<br>(g/l)<sup>a</sup></th><th>%FeO<br>loss<sup>b</sup></th><th>%<br>Oxides<sup>c</sup></th><th>fH<sub>2</sub>O<br>(MPa)<sup>d</sup></th><th>fCO<sub>2</sub><br>(MPa)<sup>d</sup></th><th>XH<sub>2</sub>O<sup>e</sup></th><th>XCO<sub>2</sub><sup>e</sup></th><th>ΦH<sub>2</sub>O<sup>f</sup></th><th>ΦCO<sub>2</sub><sup>f</sup></th><th>ΔNNO<sup>g</sup></th><th>Calculated<br>log(fO<sub>2</sub>)<sup>g</sup></th><th>wt%<br>H<sub>2</sub>O<br>E.A<sup>n</sup></th><th>wt%<br>H<sub>2</sub>O<br>A3500<sup>i</sup></th><th>wt%<br>H<sub>2</sub>O<br>A4500<sup>i</sup></th><th>wt%<br>H<sub>2</sub>O<br>A5200<sup>i</sup></th><th>wt%<br>H<sub>2</sub>O<br>4500+<br>5200<sup>i</sup></th><th>CO<sub>2</sub><br>A1430<sup>i</sup></th><th>ppm</th><th>Comments<br>for run<br>products</th></tr></thead><tbody><tr><td>FC2b</td><td>210</td><td>1200</td><td>2748</td><td>20.33</td><td></td><td>31</td><td>306</td><td>0.145</td><td>0.855</td><td>1.02</td><td>1.70</td><td>-0.30</td><td>-8.00</td><td><strong>1.70</strong></td><td><strong>0.14</strong></td><td></td><td></td><td><strong>2713</strong></td><td></td><td></td></tr><tr><td>FC3b</td><td>294</td><td>1200</td><td>2771</td><td>16.02</td><td></td><td>32</td><td>600</td><td>0.102</td><td>0.898</td><td>1.05</td><td>2.27</td><td>-0.73</td><td>-8.42</td><td><strong>1.72</strong></td><td><strong>0.11</strong></td><td></td><td></td><td><strong>4209</strong></td><td></td><td></td></tr><tr><td>FC4b</td><td>397</td><td>1200</td><td>2779</td><td>22.55</td><td></td><td>35</td><td>1247</td><td>0.080</td><td>0.920</td><td>1.13</td><td>3.62</td><td>-1.00</td><td>-8.67</td><td><strong>1.84</strong></td><td><strong>0.13</strong></td><td></td><td></td><td><strong>5748</strong></td><td>few oxides</td><td></td></tr><tr><td>GC05</td><td>60</td><td>1200</td><td>2651</td><td>24.91</td><td></td><td>13</td><td>54</td><td>0.224</td><td>0.776</td><td>0.99</td><td>1.15</td><td>0.22</td><td>-7.50</td><td><strong>1.17</strong></td><td><strong>0.10</strong></td><td></td><td></td><td><strong>278</strong></td><td>287</td><td></td></tr><tr><td>GC1a</td><td>102</td><td>1200</td><td>2669</td><td>-1.06</td><td></td><td>1</td><td>129</td><td>0.011</td><td>0.989</td><td>0.99</td><td>1.27</td><td>-0.52</td><td>-8.24</td><td><strong>0.30</strong></td><td><strong>0.03</strong></td><td></td><td></td><td><strong>620</strong></td><td>49</td><td></td></tr><tr><td>GC2a</td><td>194</td><td>1200</td><td>2654</td><td>2.75</td><td></td><td>0</td><td>314</td><td>0.002</td><td>0.998</td><td>1.01</td><td>1.62</td><td>-1.89</td><td>-9.59</td><td><strong>0.19</strong></td><td><strong>0.02</strong></td><td></td><td></td><td><strong>1291</strong></td><td>few oxides</td><td></td></tr><tr><td>GC2b</td><td>207</td><td>1200</td><td>2638</td><td>13.51</td><td></td><td>16</td><td>324</td><td>0.074</td><td>0.926</td><td>1.01</td><td>1.69</td><td>-0.89</td><td>-8.59</td><td><strong>1.27</strong></td><td><strong>0.11</strong></td><td></td><td></td><td><strong>1419</strong></td><td>146</td><td></td></tr><tr><td>GC3b</td><td>294</td><td>1200</td><td>2548</td><td>2.06</td><td></td><td>18</td><td>630</td><td>0.057</td><td>0.943</td><td>1.05</td><td>2.28</td><td>-1.24</td><td>-8.92</td><td><strong>1.35</strong></td><td><strong>0.12</strong></td><td></td><td></td><td><strong>2166</strong></td><td>93</td><td></td></tr><tr><td>GC4a</td><td>399</td><td>1200</td><td>2586</td><td>13.20</td><td></td><td>1</td><td>1373</td><td>0.002</td><td>0.998</td><td>1.12</td><td>3.45</td><td>-2.16</td><td>-9.83</td><td><strong>0.25</strong></td><td><strong>0.03</strong></td><td></td><td></td><td><strong>3046</strong></td><td>few oxides</td><td></td></tr><tr><td>GC4b</td><td>413</td><td>1200</td><td>2555</td><td>24.46</td><td></td><td>22</td><td>1438</td><td>0.048</td><td>0.952</td><td>1.13</td><td>3.66</td><td>-1.40</td><td>-9.07</td><td><strong>1.54</strong></td><td><strong>0.13</strong></td><td></td><td></td><td><strong>3356</strong></td><td>249</td><td></td></tr><tr><td></td><td></td><td></td><td>27</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>235</td><td></td><td></td></tr></tbody></table>

Volatile concentrations used to determine the solubility equations are listed in bold type. Numbers in italic: standard deviations.

<sup>a</sup>Density measured using Archimedes' method.

<sup>b</sup>Fe-loss estimated considering the iron content of experimental glasses (FeO<sub>g</sub>) relative to such the starting material (FeO<sub>st</sub>) following the expression: 100*FeO<sub>g</sub>/FeO<sub>st</sub>.

<sup>c</sup>Proportion of oxides calculated from least squares mass balance.

<sup>d</sup>Fugacities of pure water were calculated using a modified Redlich-Kwong equation of state [Holloway, 1977], assuming that P<sub>tot</sub> = P<sub>tot</sub>, Fugacities at given P-T calculated following the expression: fH<sub>2</sub>O = eH<sub>2</sub>O * XH<sub>2</sub>O * P<sub>tot</sub>. In CO<sub>2</sub> experiments, fugacities were calculated using (7)–(10). See Sections 3.2 and 3.3 for explanation.

<sup>e</sup>Molar fraction of H<sub>2</sub>O and CO<sub>2</sub> in fluid phase. See Section 3.2.1 for details.

<sup>f</sup>Fugacity coefficients of H<sub>2</sub>O and CO<sub>2</sub> used for each experiment.

<sup>g</sup>Oxygen fugacity calculated from NiO-NiPd metallic sensors.

<sup>h</sup>Elemental analyzer measurements in H<sub>2</sub>O-saturated experiments.

<sup>i</sup>FTIR measurements.

*Fe-loss estimated after performing least-square mass balance calculations to retrieve the phase proportions and iron-loss considering the corresponding oxide and residual glass composition.
<figure><img src="image_5.png" /></figure>

**Figure 3.** Relationship between water fugacity [calculated with the modified Redlich-Kwong equation of state, Holloway, 1977] and dissolved water in the basanitic (a) and phonotephritic (b) melts (in wt%). Curves represent power regressions of the data ($R^2$ = 0.99). The filled and empty symbols represent experiments performed at NNO + 1.4 and NNO + 3.2, respectively.

<figure><img src="image_6.png" /></figure>

**Figure 4.** Dissolved CO₂ measured in the experimental glasses of the Fasnia basanite at NNO – 0.3 (green squares) and the Garachico phonotephrite at NNO – 0.8 (filled orange circles), and NNO – 1.5 (empty orange circles); for which obtained power regression laws are $CO_2 = 2.2202 * P^{1.3233}$, $CO_2 = 1.3733 * P^{1.2969}$ and $CO_2 = 2.7332 * P^{1.1709}$, respectively.

The combination of these factors explains the higher water contents analysed in moderately reduced experiments ($fO_2$ ~ NNO + 1.4) compared to their oxidized counterparts (e.g., 1.54 wt% H₂O in GC4b and 0.24 wt% H₂O in GC4a, Table 2).

### 3.3.1. Determination of CO₂ fugacities

The presence of dissolved water in all the CO₂ experiments have allowed us to calculate their water fugacity

<figure><img src="image_7.png" /></figure>

**Figure 5.** CO₂ solubility plotted as a function of the melt alkalinity showing a negative correlation for our compositions. Squares correspond to the basanitic melt and circles to the phonotephritic melt. Experimental pressures are represented with different colours: light blue (50 MPa), dark blue (100 MPa), orange (200 MPa), grey (300 MPa), and yellow (400 MPa).

using the power-law regressions defined above for both compositions (7)–(10). To achieve this goal, we assume that the low CO₂ concentrations measured in our melts do not affect the thermodynamics of H₂O dissolution [e.g., Lesne et al., 2011b].
<table><caption>**Table 3.** Details of experimental capsules</caption><thead><tr><th>Name</th><th>P (MPa)</th><th>Mass H<sub>2</sub>O (mg)</th><th>Mass Ag<sub>2</sub>C<sub>2</sub>O<sub>4</sub> (mg)</th><th>Mass rock (mg)</th><th>Final mass of CO<sub>2</sub> (mg)</th><th>X<sub>H<sub>2</sub>O</sub></th><th>wt% H<sub>2</sub>O<sup>a</sup> added</th><th>wt% CO<sub>2</sub><sup>b</sup> added</th></tr></thead><tbody><tr><td>F1a</td><td>100</td><td>4.20</td><td>—</td><td>60.10</td><td>—</td><td>1.00</td><td>6.53</td><td>—</td></tr><tr><td>F2a</td><td>210</td><td>5.90</td><td>—</td><td>60.30</td><td>—</td><td>1.00</td><td>8.91</td><td>—</td></tr><tr><td>F3a</td><td>292</td><td>5.60</td><td>—</td><td>60.60</td><td>—</td><td>1.00</td><td>8.46</td><td>—</td></tr><tr><td>F4a</td><td>411</td><td>6.00</td><td>—</td><td>60.10</td><td>—</td><td>1.00</td><td>9.08</td><td>—</td></tr><tr><td>F05b</td><td>52</td><td>3.61</td><td>—</td><td>80.01</td><td>—</td><td>1.00</td><td>4.32</td><td>—</td></tr><tr><td>F1c</td><td>108</td><td>7.11</td><td>—</td><td>79.80</td><td>—</td><td>1.00</td><td>8.18</td><td>—</td></tr><tr><td>F2b</td><td>210</td><td>8.00</td><td>—</td><td>80.00</td><td>—</td><td>1.00</td><td>9.09</td><td>—</td></tr><tr><td>F3c2</td><td>319</td><td>5.60</td><td>—</td><td>79.90</td><td>—</td><td>1.00</td><td>6.55</td><td>—</td></tr><tr><td>F4b</td><td>397</td><td>8.20</td><td>—</td><td>80.10</td><td>—</td><td>1.00</td><td>9.29</td><td>—</td></tr><tr><td>G1a</td><td>100</td><td>4.20</td><td>—</td><td>60.00</td><td>—</td><td>1.00</td><td>6.54</td><td>—</td></tr><tr><td>G2a</td><td>210</td><td>6.00</td><td>—</td><td>60.10</td><td>—</td><td>1.00</td><td>9.08</td><td>—</td></tr><tr><td>G3a</td><td>292</td><td>6.00</td><td>—</td><td>60.00</td><td>—</td><td>1.00</td><td>9.09</td><td>—</td></tr><tr><td>G4a</td><td>411</td><td>6.00</td><td>—</td><td>60.00</td><td>—</td><td>1.00</td><td>9.09</td><td>—</td></tr><tr><td>G05</td><td>52</td><td>3.70</td><td>—</td><td>80.00</td><td>—</td><td>1.00</td><td>4.42</td><td>—</td></tr><tr><td>G1b</td><td>108</td><td>7.00</td><td>—</td><td>80.00</td><td>—</td><td>1.00</td><td>8.05</td><td>—</td></tr><tr><td>G2b</td><td>207</td><td>8.00</td><td>—</td><td>80.00</td><td>—</td><td>1.00</td><td>9.09</td><td>—</td></tr><tr><td>G4b</td><td>413</td><td>8.00</td><td>—</td><td>80.00</td><td>—</td><td>1.00</td><td>9.09</td><td>—</td></tr><tr><td>FC05</td><td>60</td><td>—</td><td>0.82</td><td>80.01</td><td>0.87</td><td>—</td><td>—</td><td>1.08</td></tr><tr><td>FC1</td><td>113</td><td>—</td><td>6.00</td><td>80.00</td><td>1.74</td><td>—</td><td>—</td><td>2.13</td></tr><tr><td>FC2</td><td>210</td><td>—</td><td>6.10</td><td>80.00</td><td>1.77</td><td>—</td><td>—</td><td>2.16</td></tr><tr><td>FC3</td><td>294</td><td>—</td><td>9.00</td><td>80.00</td><td>2.61</td><td>—</td><td>—</td><td>3.16</td></tr><tr><td>FC4</td><td>397</td><td>—</td><td>9.10</td><td>80.00</td><td>2.64</td><td>—</td><td>—</td><td>3.19</td></tr><tr><td>GC1a</td><td>102</td><td>—</td><td>5.00</td><td>60.00</td><td>1.45</td><td>—</td><td>—</td><td>2.36</td></tr><tr><td>GC2a</td><td>194</td><td>—</td><td>5.00</td><td>60.00</td><td>1.45</td><td>—</td><td>—</td><td>2.36</td></tr><tr><td>GC4a</td><td>399</td><td>—</td><td>8.10</td><td>60.00</td><td>2.35</td><td>—</td><td>—</td><td>3.76</td></tr><tr><td>GC05b</td><td>60</td><td>—</td><td>3.00</td><td>80.00</td><td>0.87</td><td>—</td><td>—</td><td>1.07</td></tr><tr><td>GC2b</td><td>207</td><td>—</td><td>6.00</td><td>80.00</td><td>1.74</td><td>—</td><td>—</td><td>2.13</td></tr><tr><td>GC3b</td><td>294</td><td>—</td><td>9.00</td><td>80.00</td><td>2.61</td><td>—</td><td>—</td><td>3.16</td></tr><tr><td>GC4b</td><td>413</td><td>—</td><td>8.10</td><td>60.00</td><td>2.35</td><td>—</td><td>—</td><td>3.76</td></tr></tbody></table>

All represent amounts of starting material, liquid H<sub>2</sub>O, and silver oxalate (Ag<sub>2</sub>C<sub>2</sub>O<sub>4</sub>) loaded into the capsule before experimental run.

Dashes indicate that no fluid was added to the capsule.

<footnote><sup>a</sup>H<sub>2</sub>O wt.% calculated as 100*(mass H<sub>2</sub>O (mg)/mass H<sub>2</sub>O (mg) + mass rock (mg) + Final mass CO<sub>2</sub> (mg)).</footnote>

<footnote><sup>b</sup>CO<sub>2</sub> wt.% calculated as 100*(final mass CO<sub>2</sub>(mg)/mass H<sub>2</sub>O (mg) + mass rock (mg) + final mass CO<sub>2</sub> (mg)).</footnote>
So, once the f<sub>H₂O</sub> of each charge and the fugacity coefficients derived from the Redlich-Kwong equation of state are obtained [Holloway, 1977], the corresponding water molar fraction (X<sub>H₂O</sub>) can be determined by reorganizing (5):

$$X_{\text{H}_2\text{O}} = \frac{f_{\text{H}_2\text{O}}}{\Phi_{\text{H}_2\text{O}} * P_{\text{tot}}} \quad (11)$$

We assume an ideal mixing between real fluids (Lewis and Randall rule) rather than a real mixing since the latter has a minor effect on computed fugacity coefficients at our experimental conditions [≤400 MPa and 1200 °C; Holloway, 1977]. To calculate the molar fraction of CO₂, we further assume that H₂O and CO₂ are the sole species present in the fluid phase [Holloway and Blank, 1994, Pawley et al., 1992], so in this case

$$X_{\text{H}_2\text{O}} + X_{\text{CO}_2} = 1 \rightarrow X_{\text{CO}_2} = 1 - X_{\text{H}_2\text{O}} \quad (12)$$

Therefore, the CO₂ fugacity of each experiment at the given P-T conditions was determined as

$$f_{\text{CO}_2} = \Phi_{\text{CO}_2} * X_{\text{CO}_2} * P_{\text{tot}} \quad (13)$$

The CO₂-contents-fCO₂ data base (up to 400 MPa) was used to derive third-order polynomial equations which provided the closest fit for the entire dataset (R² = 0.99; Figure 6):

$$\begin{align*} f_{\text{CO}_2}^{1200 \,^{\circ}\text{C}} &= 7.2170794265 \times 10^{-9} * \text{CO}_2 \, (\text{ppm})^3 \\ &\quad - 2.5187981515 \times 10^{-5} * \text{CO}_2 \, (\text{ppm})^2 \\ &\quad + 0.122917162244295 * \text{CO}_2 \, (\text{ppm}) \\ R^2 &= 0.99 \quad \text{for Fasnia at NNO} - 0.3 \quad (14) \end{align*}$$

$$\begin{align*} f_{\text{CO}_2}^{1200 \,^{\circ}\text{C}} &= 1.8778812876 \times 10^{-8} * \text{CO}_2 \, (\text{ppm})^3 \\ &\quad + 1.2729586197 \times 10^{-5} * \text{CO}_2 \, (\text{ppm})^2 \\ &\quad + 0.1744557037290380 * \text{CO}_2 \, (\text{ppm}) \\ R^2 &= 0.99 \quad \text{for Garachico at NNO} - 0.8 \quad (15) \end{align*}$$

$$\begin{align*} f_{\text{CO}_2}^{1200 \,^{\circ}\text{C}} &= 2.7077368969 \times 10^{-8} * \text{CO}_2 \, (\text{ppm})^3 \\ &\quad + 1.0456281240 \times 10^{-6} * \text{CO}_2 \, (\text{ppm})^2 \\ &\quad + 0.1963801023546240 * \text{CO}_2 \, (\text{ppm}) \\ R^2 &= 0.99 \quad \text{for Garachico at NNO} - 1.5 \quad (16) \end{align*}$$

It is important to note that the application of these equations (14)–(16) is restricted to melt compositions, water contents (0.18–2 wt%), and pressures (50–400 MPa) similar to those investigated here.

## 4. Discussion

Despite the frequent occurrence of alkaline magmas in specific volcanic settings (i.e., oceanic islands, in-

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Relationship between the CO₂ fugacity of the Fasnia basanite at NNO – 0.3 (green squares) and the Garachico phonotephrite at NNO – 0.8 (empty orange circles) and NNO – 1.5 (filled orange circles), calculated with an MRK equation of state [Holloway, 1977], and the amount of CO₂ dissolved in the melts (in ppm). Curves represent third-order polynomial regressions of the data (R² = 0.99). See Section 3.3 for explanation.</figcaption></figure>

traplate settings), H₂O solubility data of basanitic-phonotephritic melts are still scarce. Their alkaline to mid-alkaline counterparts have been the focus of extensive research concerning volatile solubilities, from which various models allowing H₂O–CO₂ melt content to be calculated have been derived [e.g., Dixon, 1997, Iacono-Marziano et al., 2012, Lesne et al., 2011a,b, Papale et al., 2006, Shishkina et al., 2014, among others]. Whereas these works highlighted the relatively minor control exerted by composition on H₂O solubility in mafic melts at given P–T, this is not the case of CO₂, for which variations in alkalinity, Fe-content, and oxidation state impact to various extents the solubilities of C-bearing species. For this reason, each model incorporates different compositional [i.e., Π, Π*; Dixon, 1997, Shishkina et al., 2014 respectively] or structural parameters [i.e., NBO/O, NBO/T; Iacono-Marziano et al., 2012, Vetere et al., 2014 respectively] to take into account the compositional effect on their calculations. However, despite their seemingly universal character, the application of existing models to a given set of H₂O–CO₂ melt inclusion contents results in a non-negligible difference in the calculated
vapour-saturation conditions, differences between model outputs reaching in some cases ±200–400 MPa [equivalent to 6–12 km of depth, i.e., Longpré et al., 2017]. Obviously, such an uncertainty strongly impacts our understanding of the architecture of the plumbing system of the volcano, hence the interpretation of related degassing processes. Below, the aforementioned models are applied to our experimental charges and calculated H₂O–CO₂ contents are compared to our measurements. Our aim is not to carry out an exhaustive comparison with all existing experimental works or solubility models since this has been already performed elsewhere [i.e., Iacono-Marziano et al., 2012, Iacovino et al., 2013, Ni and Keppler, 2013, Shishkina et al., 2014] but merely to evaluate the applicability of available models in the Canarian context.

## 4.1. *Comparison with H₂O experimental data*

Overall, the water concentrations measured in this work are in good agreement (within errors) with those obtained on similar basanitic, alkali basalts or even mid-ocean ridge basalt (MORB) compositions at equivalent P–T conditions (Figure 7). For example, Shishkina et al. [2014] and Holloway and Blank [1994] [this last reporting data from Cocheo, 1993] present H₂O-saturated experiments performed on two basanites at 100 MPa and 1250 °C and 1200 °C, respectively, both containing ~3.2 wt% H₂O, an amount that closely matches those measured on our 100 MPa equivalent basanitic charges (3.3–3.4 wt% H₂O at 1200 °C; Table 2). Similarly, the study of Dixon et al. [1995] performed on a MORB at 50 MPa and 1200 °C reports water contents (2.2 wt% H₂O, experiment 21H) comparable to those from Fasnia basanite under the same P–T conditions (2.3 wt% H₂O).

Regarding our phonotephritic composition, Figure 7 shows that up to 300 MPa it displays a similar H₂O solubility compared to the K-rich phonotephritic lava from Mt. Mellone (Alban Hills, Italy) studied by Behrens et al. [2009] at 1200–1250 °C, and the alkali basalts from Lesne et al. [2011a] at 1200 °C. In contrast, our sample dissolves between 0.5 to 1 wt% less water above this pressure (>300 MPa) than the other two compositions. At first sight, the higher solubility displayed by the Behrens et al. [2009] phonotephrite above

<figure><img src="image_9.png" /></figure>

**Figure 7.** Comparison between the water contents measured in this study versus results of various other mafic to intermediate compositions at pressures from 50 MPa to 400 MPa (see Section 4.1 for explanation). Data at 500 MPa are shown for visualization. The *filled* and *empty orange circles* represent our Garachico experiments performed at NNO + 1.4 and NNO + 3.2, respectively. The *filled* and *empty green squares* correspond to Fasnia experiments performed under different f'O₂ conditions (NNO + 1.4 and NNO + 3.2, respectively). The solubility curves of Fasnia (*green line*) and Garachico (*orange line*) at NNO + 3.2 are shown. H₂O-pure experimental results from other studies are represented as *violet diamonds* [Alb-1, Behrens et al., 2009], *grey cross-square* [Etna, Iacono-Marziano et al., 2012], *yellow triangles* [VES-9, ETN-1 and PST-9, Lesne et al., 2011a], *green triangles* [A2549-basanite, OB93-alkali basalt, Etna and MORB, Shishkina et al., 2014]. The wide range of the data comes from the different compositions used, or the H₂O/CO₂ ratios added initially in each study.
300 MPa can be explained by its alkali-rich character (9.5 wt% K₂O + Na₂O) compared to the Garachico phonotephrite (7.5 wt% K₂O + Na₂O), as suggested by Lesne et al. [2011a]. However, Lesne et al. [2011a] determined approximately the same water content as Behrens et al. [2009] (~8.3 wt%) at an almost equivalent pressure (384 MPa) for a tephrite which is compositionally equivalent (in terms of Na₂O + K₂O) to Garachico. Thus, in this case, the variations in the total alkali content of a melt cannot alone explain the different solubility trends observed above 300 MPa. In detail, the Tenerife and Vesuvius samples mostly differ by their K/Na ratios (3.1 for Ves-9 and 0.4 for Garachico), which suggests that the K-rich character of the Vesuvius compositions may be responsible for their enhanced water solubility above 300 MPa. We conclude that the total alkali content is not the sole parameter controlling water solubility, the K/Na ratio likely playing an important role on the amount of H₂O that can be incorporated into alkaline mafic melts. In summary, the lack of significant differences (>1 wt% H₂O) between the water contents measured on mafic to intermediate alkaline compositions, in this and equivalent studies, confirms the minor effect of magma composition on their H₂O solubility at crustal *P* (up to 300 MPa), in particular for a given magma family [i.e., basalts sensu stricto; Lesne et al., 2011a, Shishkina et al., 2014]. We cannot rule out the possibility that at higher pressures (≥400–500 MPa), the effect of composition on water solubility is more significant [as in Benne and Behrens, 2003], but exploring volatile solubility at these conditions was beyond the scope of this study.

## 4.2. Application of available water-solubility models

Predicted H₂O contents by the aforementioned models are listed in Table S2. Overall, for the basanitic composition, there is a good concordance (considering associated errors) between predicted and measured water contents in the pressure range 50–100 MPa. Above these pressures, we observe a slight overestimate of ~10–15% at 200 MPa, rising to 20% as pressure increases from 300 MPa to 400 MPa.

Whereas for the previous composition, the predictions made by the three considered models progressively deviated from the experimental values, this

is not the case of the phonotephrite, where back-calculated H₂O contents and foretold solubility behaviour are strongly model-dependent. As for the basanite, the contents returned by the models of Lesne et al. [2011a] and Shishkina et al. [2014] at 50–100 MPa are in reasonable agreement with our measurements (Table S2). However, above these pressures, the two empirical equations proposed by these authors overestimate the measured values in our experimental melts; the maximum observed differences (1–2 wt%) were obtained at 300–400 MPa.

Conversely, the Iacono-Marziano et al. [2012] empirical equation systematically underestimates measured water contents by 0.5–1.2 wt% for the phonotephritic melt. In general, the three models better predict the solubility of water in basanitic melts (±1 wt%) compared to phonotephritic compositions at conditions up to 300 MPa.

## 4.3. Comparison with other CO₂ or H₂O–CO₂ experimental studies

Only a few studies have explored in some detail the CO₂ solubility behaviour of basanites and phonotephrites at crustal *P*–*T* conditions [Behrens et al., 2009, Holloway and Blank, 1994, Shishkina et al., 2014, Allison et al., 2019].

As previously mentioned, our results define a negative relationship between CO₂ solubility and alkalinity (Figure 5). This trend is in contrast with the results obtained in similar works, in which a positive relationship between alkalinity and dissolved CO₂ was observed [Lesne et al., 2011b, Shishkina et al., 2014]. A similar (but less apparent) relationship is observed between CO₂ content and the aluminium saturation and agpaitic index, or NBO/O but, based on the poor correlation existing between the different parameters (R² = 0.6 in the first case and R² < 0.5 in the last two), we do not recommend their use for describing the CO₂ solubility in this type of magmas.

To a first order, the difference between previous works and our results can be related to the compositional variations of the starting materials used in each study, which in some cases exceeds 20% relative [i.e., Na₂O + K₂O, FeO; CaO; Behrens et al., 2009, Dixon, 1997, Lesne et al., 2011b, Moore, 2008, Vetere et al., 2014]. These differences highlight again the strong control that magma composition exerts on CO₂ solubility, a factor that should be carefully considered
when applying H₂O–CO₂ solubility laws that were not specifically calibrated for the target composition.

From a more general perspective, we observe a good correspondence between the CO₂ contents measured in our basanite and that of Shishkina et al. [2014]; however, at 300 MPa, the basanite of Shishkina et al. [2014] incorporates up to 1300 ppm more than our starting material (Figure 8). In contrast, the basanite of Holloway and Blank [1994], systematically dissolves lower contents (~807 ppm CO₂ at 1200 °C and 100 MPa) compared to the two other basanites. The most significant difference between the three compositions is their CaO content: a positive relationship is indeed observed between CaO and the glass CO₂ contents.

The effect of magma composition in controlling CO₂ solubility is also seen for the phonotephrite: Behrens et al. [2009] identified K as an element that enhances CO₂ solubility [see also Scaillet and Pichavant, 2005]. At 200 MPa and 1200–1250 °C, their phonotephrite (with 5 wt% more K₂O) dissolves 2870 ppm CO₂ compared to 1291 ppm for Garachico (Table 2). However, the compositional difference between both phonotephrites is also due to CaO which, in the melt of Behrens et al. [2009], is ~3 wt% higher than in our sample. Thus, the combined effects of CaO and K₂O likely explain the differences in the CO₂ solubilities as already pointed out by previous studies [e.g., Behrens et al., 2009, Botcharnikov et al., 2006, Lesne et al., 2011b, Liu et al., 2005, Moore, 2008].

### 4.4. Application of available CO₂ or H₂O–CO₂ solubility models

For CO₂, we have tested three different models to verify their ability to reproduce the CO₂ contents of our experimental runs and hence, their applicability to the Canary Islands magmas (Table S2). The first model we checked is that of Dixon [1997], who, to calculate the CO₂ solubility in alkaline magmas, proposed an empirical equation that incorporates a compositional parameter (Π) to account for both the ability of the different network modifier elements to form carbonate species and the degree of melt depolymerization.

In Figure 9, we plot the factor Π of Dixon [1997] against the CO₂ concentrations analysed in our two compositions at the P–T conditions considered by

<figure><img src="image_10.png" /></figure>

**Figure 8.** Comparison between the CO₂ contents measured in this study and the experimental results from other mafic to intermediate melts with no water added. The empty orange circles represent our phonotephritic composition at NNO – 0.8 and its solubility curve (orange line). The empty green squares correspond to the basanitic composition at NNO – 1.5 and its solubility curve (green line). Results from other studies correspond to violet diamonds [Alb-1, Behrens et al., 2009], grey cross-square [Etna, Iacono-Marziano et al., 2012], yellow triangles [VES-9, ETN-1 and PST-9, Lesne et al., 2011a], green triangles (A2549-basanite, OB93-alkali basalt, Etna and MORB, Shishkina et al., 2014) and blue square [basanite from Holloway and Blank, 1994]. The wide range of certain data comes from the different compositions used in those studies. See Sections 4.3 and 4.4 for more explanations.
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Correlation of the Π parameter [Dixon, 1997] with (a) the dissolved CO₂ contents measured in Fasnia, Garachico, and other mafic melts [MORB, Kilauea, basanite, and leucitite from Dixon, 1997] at 100 MPa and 1200°; and (b) the silica content of each composition.</figcaption></figure>

this author, and we obtained a similar linear relation-
ship between both parameters. However, this trend
cannot explain the difference in the CO₂ concentra-
tions calculated by Dixon's model for our basanitic
and phonotephritic melts. Whereas for the former,
the parameterization yields a content that closely
matches the one measured here (1222 and 1205 ppm
CO₂, respectively), for Garachico phonotephrite,
Dixon's model predicts a CO₂ content twice less the
measured value (332 ppm CO₂ instead of 620 ppm
CO₂ measured). To explain such a difference, we
hypothesize that in our samples, the order of in-
creasing ability of a cation to enhance CO₂ solubility
may be different from that assumed by Dixon [1997]
[Ca²⁺ > K⁺ > Na⁺ ≫ Mg²⁺ ≈ Fe²⁺, according to Spera
and Bergman, 1980]. Therefore, the role played by
the different cations may vary depending on magma
composition and P-T-fO₂ conditions. The other
possibility is that the model of Dixon [1997] was cal-
ibrated using the data obtained on the basanite of
Holloway and Blank [1994], which as stated before,
dissolves less CO₂ than Fasnia basanite at the same
P-T conditions (see above). However, the detailed
study of cation effects on CO₂ solubility is beyond
the scope of this work.

The second model considered here is the one of
Shishkina et al. [2014], who explored the solubility of
this gas species over a large range of magmatic com-
positions (42–51 SiO₂ wt%) and P–T conditions be-
tween 50–500 MPa and 1200 to 1250 °C. These au-
thors derived a new equation to calculate the CO₂
content in magmatic melts (see this work for further

details), which incorporates an updated parameter-
ization of the Π factor of Dixon [1997] termed Π*
since the former is derived from a narrower range of
magma compositions (40–49 SiO₂ wt%) and requires
normalization at 100 MPa. Therefore, Shishkina et al.
[2014] fitted an exponential equation in terms of ln
(CO₂) as a function of Π (or Π*) and ln P to pre-
dict the CO₂ solubility over the explored range of
compositions. Overall, this model predicts lower than
observed CO₂ contents for the Fasnia basanite and
Garachico phonotephrite, with differences achieving
>20% above P ≥ at 200 MPa (Table S2).

Third, we have tested three variants of the Iacono-
Marziano et al. [2012] model for our compositions at
1200 °C and pressures from 50 to 400 MPa: (1) CO₂
solubility model as a function of pressure (H₂O-free
system), (2) H₂O–CO₂ solubility model that consid-
ers the composition of the fluid phase (X_H₂O), and
(3) equilibrium pressures at 1200 °C for given H₂O
and CO₂ contents in the melt. Model predictions
were calculated using the web application of Iacono-
Marziano et al. [2012] under the mentioned P–T con-
ditions. Input uncertainties were: ±5 °C, ±20 bars
and the standard deviation associated with the EPMA
analysis of each major element oxides.

In the first case, the model underestimates the
CO₂ solubility in the basanitic melt by 15–20%, the
higher differences arising at 400 MPa. Contrarily, for
the phonotephrite, the first variant of the model
highly overestimates the CO₂ contents, exceeding
50% in some cases (Table S2). Similar variations are
also observed in CO₂ contents calculated for the
<figure><img src="image_12.png" /></figure>

**Figure 10.** H₂O and CO₂ solubility data from the experiments of (a) the Fasnia basanite (green squares) at NNO-0.3 and (b) the Garachico phonotephrite (orange circles) at NNO+0.8, compared with the predicted solubility curves (lighter coloured lines) calculated with the H₂O-CO₂ model of Iacono-Marziano et al. [2012] at 1200 °C, pressures between 50 and 400 MPa, different water molar fractions (from X~H₂O~ = 0 to X~H₂O~ = 1) and the starting compositions (in Table 1). Lighter coloured error bars represent the uncertainties associated with the Iacono-Marziano's model at 400 MPa (in blue), 300 MPa (in yellow), and 200 MPa (in grey) for water molar fractions of 0.1, 0.2, and 0.3, respectively, and are shown at the right side of the diagram. Diamonds represent H₂O-CO₂ contents measured in the Etna experimental glasses by Iacono-Marziano et al. [2012] and the different colours correspond to different pressures as described below. Thick and darker coloured lines correspond to isobars obtained in this study for different pressures 50 MPa (in light blue), 100 MPa (in orange), 200 MPa (in grey), 300 MPa (in yellow), and 400 MPa (in dark blue). Symbol error bars indicate the uncertainty of FTIR measurements (propagated errors). There is a significant overestimation of the H₂O solubility at X~H₂O~ = 1 in the basanitic melt and the CO₂ solubility in the phonotephritic melt (see Section 4.4 for details).

Garachico phonotephrite using the mixed H₂O-CO₂ model. Comparatively, as for the first variant, the mixed model slightly underestimates the CO₂ solubility by 10–20% for our basanitic charges.

The solubility curves were computed with the H₂O-CO₂ model for water molar fractions varying

from X~H₂O~ = 0 to X~H₂O~ = 1. As shown in Figure 10 and Table S2, the model yields contrasted results depending on the composition and the volatile species considered in the calculations. Surprisingly, the mixed solubility calculations return H₂O and CO₂ contents for our experiments that differ considerably from
those predicted by the pure-volatile solubility vari-
ant s, but in better agreement (10–20%) with our re-
sults (see above).

For the Fasnia basanite, the H₂O–CO₂ model pre-
dicts extremely high solubilities and saturation pres-
sures for pure H₂O and mixed-volatile runs, increas-
ing the differences in the back-calculated contents
by up to 30–50% as the pressure rises (i.e., 16 wt%
H₂O at 400 MPa; Figure 10a). Comparatively, the dif-
ferences with the experimental values are relatively
lower when the phonotephritic composition is used
in the calculations, since saturation pressures and
volatile contents differ by 10–40%. However, for these
samples, results from the CO₂ solubility model are
doubled compared to experiments (Figure 10b). This
is not a trivial difference, since the isobars predicted
by the Iacono-Marziano's model clearly differ from
those determined in our CO₂-saturated experiments.

Another important issue that needs to be con-
sidered when using the mixed equation of Iacono-
Marziano et al. [2012] is the errors associated with the
calculated CO2 contents, which at pressures above
100 MPa, exceed 1000–2000 ppm (Figure 10, Table
S2). If these errors are projected on the mixed H2O–
CO2 solubility isobars (see error bars associated with
the solubility curves for a given pressure and water
molar fraction in Figure 10a, b), the uncertainty in
the location of a given isobar over the H2O–CO2 dia-
gram proportionally increases with pressure and H2O
content. This results in an important overlapping of
the curves at P ≥ 200 MPa. Neglecting the associated
CO2 errors will have important consequences, not
only when applying the H2O–CO2 model to calculate
the saturation and entrapment pressures of melt in-
clusions having basanitic–phonotephritic composi-
tions but also for the interpretation of storage con-
ditions and associated degassing processes: errors of
±1000 or 2000 ppm translate into depth differences
of up to 6 km (see Figure 10). For this reason, we do
not recommend the use of this model to calculate
H2O–CO2 solubilities of mafic to intermediate mag-
mas from Canary Islands, since these compositions
are outside the range considered by Iacono-Marziano
et al. [2012], as also pointed out by Shishkina et al.
[2014].

Finally, we tested the equilibrium pressure model
of Iacono-Marziano et al. [2012] to back-calculate
the equilibration or entrapment pressure of a given
melt (i.e., MI) when H₂O and CO₂ contents are

known. Results obtained for our H₂O-saturated ex-
periments are underestimated by 20-50% for the
basanitic melts (at 50-400 MPa) and overestimated
by ~10-40% in the phonotephrite at 50-300 MPa,
whereas at 400 MPa, the model underestimates it. For
the CO₂-saturated experiments, model predictions
yield similar pressures for our basanite (within 10-
20%) but underestimate by ~30% the phonotephritic
melt (Table S2).

4.5. Application of the empirical power laws to
melt inclusions data from El Hierro, Canary
Islands

The Canary Islands are an important alkaline group
of oceanic volcanoes which have been the focus
of a large number of volcanological studies. Up to
recently there was limited knowledge of the mag-
matic volatile budget associated with this system
[e.g., Gurenko and Schmincke, 2000, Hansteen et al.,
1991, 1998, Wallace, 1998]. Yet, the recent eruption of
El Hierro in 2011–2012 has provided a unique oppor-
tunity to fill this gap [e.g., Longpré et al., 2017].

Our experimental results allow us to revisit sam-
ples of the 2011–2012 submarine eruption at El Hi-
erro, Canary Islands [Longpré et al., 2017], and those
from young (<20 ka) tephra collected at different lo-
cations in El Hierro [Taracsák et al., 2019], owing
to the compositional similarities between the bulk-
rock, MI, and our starting materials. As a first step,
we have used the amounts of CO₂ + H₂O dissolved
in the MI which give minimum entrapment pressures
[e.g., Esposito et al., 2011, 2014, Gennaro et al., 2019,
Steele-Macinnis et al., 2011]. However, MIs often
have vapour bubbles containing a substantial por-
tion of bulk volatiles [e.g., Moore et al., 2015, Rose-
Koga et al., 2021], so, whenever possible, the restored
CO₂ concentrations (dissolved + exsolved) were con-
sidered in our calculations. We note that even if the
investigated MI contained detectable amounts of S,
Cl [Longpré et al., 2017, Taracsák et al., 2019], these
volatiles are considered to have a minor effect on cal-
culated pressures [e.g., Lesne et al., 2011c], though
their consideration would inevitably increase calcu-
lated P values [e.g., Lesne et al., 2015].

4.5.1. *The 2011–2012 submarine eruption at El Hierro*

This is the most recent eruption of the Canary
archipelago and the first to be fully monitored in
real time [López et al., 2012]. Magma products emitted during this eruption were petrologically characterized by different authors [Martí et al., 2013b, Meletlidis et al., 2015, among others] but only Longpré et al. [2014, 2017] analysed the melt inclusions (MIs) trapped in phenocrysts (mainly olivines). MIs are basanitic-phonotephritic in composition [42–50 wt% SiO₂; Longpré et al., 2014], contain remarkably high concentrations of dissolved volatiles, with up to 3420 ppm CO₂, 3 wt% H₂O, and 5080 ppm S [Longpré et al., 2017]. Saturation pressures were previously calculated in this study using the models of Iacono-Marziano et al. [2012], Newman and Lowenstern [2002], Papale et al. [2006] and Shishkina et al. [2014]. Depending on the model, the retrieved pressures vary from 260 to 630 MPa; however, for consistency with the applied degassing software [D-compress, Burgisser et al., 2015] Longpré et al. [2017] considered only the results given by the Iacono-Marziano et al. [2012] model, since this was already implemented in the above software. This gave a more restricted entrapment pressure range between 7 to 260 MPa for olivine hosted MIs, corresponding to depths ≤10 km beneath El Hierro. Additionally, Longpré et al. [2017] calculated H₂O–CO₂ solubilities as a function of pressure at 1150 °C for the 2011–2012 average matrix glass composition.

In order to compare these data with our results, we assume that the possible variations in the H₂O–CO₂ solubility for a temperature difference of 50 °C are within the associated error [Holloway and Blank, 1994].

The application of our basanitic empirical solubility laws to the 2011–2012 El Hierro melt inclusions yields entrapment pressures between 11 and 280 MPa, with a maximum difference of +33 MPa (~1.5 km) compared to those determined by Longpré et al. [2017]. In both cases, the distribution of H₂O–CO₂ suggests that these magmas experienced a continuous degassing from 260–280 MPa down to 50–100 MPa (Figure 11). Although Longpré et al. [2017] have not analysed the inclusion-hosted bubbles, they have obtained a theoretical estimate of how much CO₂ may be sequestered in the bubble using the method of Shaw et al. [2008]. From 29 theoretically reconstructed MI, we can apply our model to 15 MI with ≤6153 ppm CO₂ (which fall within our calibrated range), resulting in very similar entrapment pressures. Only two of them give P > 280 MPa, corresponding to 337 and 432 MPa (Figure 11). These new pressures are in full agreement with petrological and seismic data, which indicate a storage/re-equilibration level at 10–15 km [López et al., 2012, Martí et al., 2013b].

The other set of 14 MI yields reconstructed CO₂ contents between 0.8–1.3 wt% to up to 2.3 wt%, which prompted the authors to estimate entrapment pressures ≥1 GPa, equivalent to depths ≥30 km. Whereas those MI containing 0.8–1.1 wt% CO₂ would represent magmas rising from deep levels (600–800 MPa or 20–25 km), in line with information gained from fluid inclusions, cpx–melt geobarometry and volcano-tectonic seismicity [Hansteen et al., 1991, 1998, Klügel et al., 2015, Longpré et al., 2014, 2017, López et al., 2012], those with CO₂ concentrations between 1.3–2.3 wt% are more problematic to interpret since they point to entrapment levels amid 1–2 GPa (≥30–40 km) using the solubility data of Holloway and Blank [1994] for basanitic compositions. Such pressures–depths clearly exceed those recorded by other methods during the unrest episode [Domínguez Cerdeña et al., 2013, López et al., 2012].

### 4.5.2. Information gained on young (<20 ka) basanites from El Hierro

To test if the previous 2011–2012 volatile contents are representative of the recent (<20 ka) mafic volcanism of El Hierro, Taracsák et al. [2019] analysed the composition and volatile contents of MIs from tephra samples collected at different locations on El Hierro island. Most of the analysed MIs have H₂O and CO₂ contents comparable to those analysed in the recent 2011–2012 eruption (Figures 11–12), varying mainly between 0.1–2 wt% and <2500 ppm, respectively. The relatively high MI volatile contents (i.e., CO₂ up to 3600 ppm and S up to 4290 ppm) along with the occasional presence of large bubbles (>10 vol.%) within MI suggest that the different magmas were volatile-saturated at the time of entrapment. However, independently of their volatile endowment, almost all the considered magmas experienced a similar degassing during their ascent towards the surface (Figure 12). Taracsák et al. [2019] also used D-compress [Burgisser et al., 2015] to calculate both the mixed H₂O–CO₂ solubility isobars and melt inclusion volatile saturation pressures at 1200 °C. In this case, the highest volatile saturation
<figure><img src="image_13.png" /></figure>

**Figure 11.** H₂O and CO₂ solubility curves determined in basanitic experimental glasses (*thick lines*) at 50 MPa (in *light blue*), 100 MPa (in *red*), 200 MPa (in *grey*), 300 MPa (in *yellow*), and 400 MPa (in *dark blue*), compared to solubility curves calculated by Longpré et al. [2017] with the model of Iacono-Marziano et al. [2012] (*dashed grey lines*). Green squares represent the basanitic glasses from this study. Green, orange, and blue circles correspond to olivine-hosted MI glass phases, reconstructed MI (bubble + glass), and averaged matrix glass composition from El Hierro 2011–2012 eruption, respectively (Figure 4a in Longpré et al. [2017]). Solubility curves from Longpré et al. [2017] are moderately overestimated compared to the isobars of this study. Melt inclusions distribution suggests a continuous degassing from pressures of 260–280 MPa down to 50–100 MPa.

pressures calculated for their MI fall between 150–355 MPa (6–13 km) or 350–700 MPa (13–24) km, depending on whether the CO₂ dissolved in the MI glass is only considered or that stored in bubbles is also into account.

Similar to the recent 2011–2012 eruption, we applied our empirical laws to determine MIs entrapment pressures. For the <20 ka eruptions, our calculations (using only dissolved H₂O and CO₂ contents of MI) yield somewhat lower *P*-saturation values, from 16 to 258 MPa (Figure 12), most of the data falling between the 100–200 MPa isobars. This implies a difference in the equilibration conditions for the MI glass of ~100 MPa, or equivalent to 3–4 km depth. Regarding the restored volatile contents

of melt inclusions (i.e., glass + bubble CO₂), Taracsák et al. [2019] have studied 47 inclusion-hosted bubbles, 25 of which contained detectable CO₂. Of these, 8 MI glass phases were also analysed, and the entrapment pressures for the 6 MIs with CO₂ falling within the calibrated range of the empirical equations, vary between 262 and 443 MPa (or 8–13 km depth). Two MIs have CO₂ contents (0.9–1.2 wt%) outside model calibration range. Using the data of Holloway and Blank [1994], these high CO₂ contents suggest deeper entrapment levels at ~1 GPa (~30 km).

In summary, our results suggest that the last, but also recent (<20 ka), magmas erupted at El Hierro record a main episode of crystallization-entrapment at 250–443 MPa followed by a second one at *P* <
<figure><img src="image_14.png" /></figure>

**Figure 12.** Comparison between H₂O–CO₂ contents from olivine- and clinopyroxene-hosted basanite melt inclusions from El Hierro, Canary Islands [Taracsák et al., 2019] and the H₂O–CO₂ solubility curves (dashed lines) determined for our basanitic melt (green squares) at pressures from 50 MPa to 400 MPa. Light blue circles represent MI glass phases and orange circles correspond to reconstructed melt inclusions (bubble + glass). Coloured borders indicate pairs of unreconstructed and reconstructed MI. Most melt inclusions (glass phases) are located between the 100–200 MPa isobars (equivalent to 3–6 km), whereas the restored MI gives higher pressures (280–440 MPa).

200 MPa–50 MPa, corresponding to depths of 8–13 km and 6–1.5 km, respectively (Figures 11 and 12).

Over the range of pressures proposed, our deeper estimates coincide with the location of the crust-mantle discontinuity at El Hierro, which according to previous authors [e.g., González et al., 2013, Klügel et al., 2015, Martí et al., 2013a,b], operated as the main level of crystallization for the magmas erupted in the 2011–2012 event (i.e., at 10–15 km). These observations are consistent with the upper depths of the seismic swarm observed during the unrest period of the 2011–2012 submarine eruption [Domínguez Cerdeña et al., 2013, López et al., 2012], those estimated using length–thickness ratios of feeder dykes at El Hierro [11–13 km; Becerril et al., 2013], and the

low-pressure equilibration recorded by some cpx-hosted fluid inclusions [280–450 MPa, Longpré et al., 2014]. Compared to the above, our crystallization-entrapment depths ≤6 km are consistent with the interpretation of geodetic data associated with the 2011–2012 event [González et al., 2013] and the presence of high-density bodies (i.e., possibly representing cumulates) at shallow depths beneath the island, both suggesting the low-pressure equilibration conditions experienced by these magmas prior to their eruption [1–6 km; Montesinos et al., 2006]. This last episode may explain the formation of volatile-poor melt inclusions and, thus, the lower calculated entrapment pressures for these magmas.

Altogether, the distribution of volatile contents from El Hierro MIs, the dominant population composition of the host olivines (Fo 78–80), their crystal shape, and the new range of MI entrapment conditions inferred in our work, allow us to provide a robust scenario for the plumbing system feeding basanitic eruptions at El Hierro. Magmas rising from the deep mantle [>20–25 km; López et al., 2012, Martí et al., 2013a,b] experience a first but “short” (1–2 months, according to olivine diffusion modelling and the scarce occurrence of Fo > 84–88 olivines recording these conditions [Longpré et al., 2014, Martí et al., 2013b]; Figure 11–12) crystallization episode at 8–13 km. The subsequent fast injection of dykes from this first level of magma ponding towards the surface [Becerril et al., 2013] produces the isothermal (?) syneruptive crystallization (characterized by Fo₇₈–₈₀) accompanied by progressive H₂O–CO₂ degassing of the magma. This dynamic scenario promotes the rapid growth of crystals, as witnessed by disequilibrium textures [e.g., incomplete, resorbed, skeletal; see Martí et al., 2013b, Welsch et al., 2012] along with the entrapment of melt aliquots having different compositions and variable volatile contents, recording their journey towards the surface.

**5. Conclusions**

We report new H₂O and CO₂ solubility data in basanitic and phonotephritic melts representative of the Canary Islands magmas, from which empirical solubility laws have been derived. Whereas H₂O displays broadly similar behaviour in both compositions, this is not the case of CO₂, for which the role of cations such as Ca²⁺, K⁺, Na⁺, Fe²⁺, and Mg⁺ signif-
icantly impact CO₂ solubility [e.g., Dixon, 1997], in a manner still not well accounted for by existing models. Our study suggests that for compositions having similar total alkali contents, differences in CaO, MgO, and FeO* may play an important role in enhancing or decreasing the CO₂ solubility.

The application of existing H₂O–CO₂ empiri-
cal models yields reasonable water contents for
our compositions at low pressures (50–200 MPa),
whereas the difference increases up to 1–2 wt% at
300–400 MPa. For CO₂, the amounts calculated by
the models differ compared to those measured by
at least 10–20% and up to 85%. As stated above, the
observed differences reflect the incomplete compo-
sitional coverage of available models.

Application of our results at El Hierro suggests a
simple scenario in which magmas rising from the
deep mantle (>25 km) experience a first transient
episode of crystallization at 8–13 km, followed by the
crystallization occurred during the subsequent dyke
injection, ascent, and degassing at P <= 200 MPa (6–
1.5 km).

Acknowledgements

This work was supported by (1) the Institut des Sci-
ences de la Terre d'Orléans (ISTO-CNRS), the LABEX
VOLTAIRE (ANR-10-LABX-100-01), and the PLANEX
projects (11-EQPX-0036); (2) the European Volcano
Early Warning System (EVE) project grant agreement:
826292 through the Group of Volcanology of Geo-
ciencias Barcelona (GEO3BCN-CSIC), and (3) the Na-
tional Geographic Institute of Spain (IGN, Canary Is-
lands). We thank L. Remusat from the MNHN in Paris
for his support with NanoSIMS analysis; Ida Di Carlo
and Aneta Slodczyk from ISTO-CNRS for their assis-
tance in EPMA and FTIR analysis, respectively; and
Ma J. Blanco, Francisco Quirós and Stavros Melet-
lidis from IGN, and Michel Pichavant, for their help in
field tasks, as well as Joan Martí from GEO3BCN-CSIC
for discussions and field support. We kindly thank the
constructive comments of two anonymous review-
ers and the editorial handling of the Editor François
Chabaux.

Supplementary data

Supporting information for this article is available on
the journal's website under https://doi.org/10.5802/
crgeos.84 or from the author.

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