How do volatiles escape their shallow magmatic hearth?

Abstract

Only a small fraction (approx. 1–20%) of magmas generated in the mantle erupt at the surface. While volcanic eruptions are typically considered as the main exhaust pipes for volatile elements to escape into the atmosphere, the contribution of magma reservoirs crystallizing in the crust is likely to dominate the volatile transfer from depth to the surface. Here, we use multiscale physical modelling to identify and quantify the main mechanisms of gas escape from crystallizing magma bodies. We show that most of the outgassing occurs at intermediate to high crystal fraction, when the system has reached a mature mush state. It is particularly true for shallow volatile-rich systems that tend to exsolve volatiles through second boiling, leading to efficient construction of gas channels as soon as the crystallinity reaches approximately 40–50 vol.%. We, therefore, argue that estimates of volatile budgets based on volcanic activity may be misleading because they tend to significantly underestimate the magmatic volatile flux and can provide biased volatile compositions. Recognition of the compositional signature and volumetric dominance of intrusive outgassing is, therefore, necessary to build robust models of volatile recycling between the mantle and the surface.

This article is part of the Theo Murphy meeting issue ‘Magma reservoir architecture and dynamics’.

1. Introduction

Volatile elements (which can be either dissolved or exsolved in magmas, see definitions below) have a fundamental control over igneous processes in our planet. They play a role in the temperatures at which rocks melt (or magmas crystallize), affect the mechanical response and rheological properties of magmas (in particular viscosities and densities) in reservoirs and conduits, influence eruptive styles, and carry economically important elements (e.g. S, Cu, Mo, Au, Ag), environmentally critical gases (CO₂, HCl, SO₂) and pollutants (Hg, F, …) towards the surface of the Earth [1]. Their composition and transport to the surface can also provide information about the state of the magma reservoir during volcanic unrests (e.g. [2,3]).

Volatile elements are dissolved in silicate melts at high pressure. They come out of solution (exsolve) as magmas decompress while they ascend to shallower depths (first boiling) or crystallize while they cool during storage, which concentrates the volatiles in the melt to the point of saturation (second boiling, e.g. [4]). Hence, silicic subvolcanic magma reservoirs that are typically crystal-rich [5–7] and located in the upper 10 km of the crust will ultimately saturate and develop an exsolved gas phase [8–11]. Once a low-density, low-viscosity magmatic volatile phase (hereafter shortened to MVP) is formed, it can potentially leave its magmatic hearth and rise towards the surface. In this paper, we explore the underlying mechanisms and their efficiency as magma evolves from storage conditions to solidification.

As silicic volcanic rocks are generally volatile-rich, while their plutonic counterparts are volatile-poor [12], a significant amount of MVP should escape into the atmosphere during crustal storage before magmas reach full solidification. Some of the volatiles are entrained by volcanic eruptions (e.g. unexpectedly high sulfur contents in volcanic plumes betrays the presence of excess volatiles in melt-rich portions of magma reservoirs [12–17]. However, as most magmatic rocks never reach the surface (intrusive/extrusive ratios are greater than 10 : 1 for continental settings [18–22] and volcanic eruptions are rare in the lifetime of magmatic provinces, passive degassing during non-erupting periods must volumetrically dominate magma outgassing, as shown by decadal sulfur output into the atmosphere [23]. This paper discusses potential mechanisms to feed this passive degassing.

The separation of an MVP from its host magma reservoir is controlled by a balance between three forces: buoyancy of the MVP caused by its density difference with the melt and crystal phases (gravity), viscous drag between phases and capillary forces (because of interfacial tension between the MVP and the melt). Inertia plays a negligible role on MVP-mush separation under magma reservoir conditions. One can therefore parametrize the relative importance of each force by three dimensionless numbers, the Reynolds number (inertia/viscous forces) which is ≪1, the Archimedes number (buoyancy/viscous forces) which identically is ≪1 given the high viscosity of the melt. The Bond number (buoyancy/capillary forces) is defined by

$$Bo=\frac{\mathrm{\Delta }\rho g{D}^2}{\sigma },$$ 1.1

with Δρ the density difference between the melt and the MVP, g the gravitational acceleration, D the bubble diameter and σ the interfacial tension. For magma reservoir conditions, Δρ ≈ 2000 kg m⁻³, g = 9.81 m s⁻², σ ≈ 0.07 N m⁻¹, and we estimate the average crystal size to be between 0.5 and 5 mm, generating bubble diameters D of similar sizes. This results in a Bond number that spans a range between 0.07 and 7 (see [12]).

Three possible mechanisms for MVP segregation in the magma reservoir have been identified in the literature (figure 1):

• (1)bubble flow at high melt fraction (either as discrete bubbles, or as bubbly plumes; [12,25]),
• (2)channel flow in a permeable crystal network at intermediate melt fraction [26,27], and
• (3)capillary trapping at low melt fraction, where large overpressures and crystal repacking or brittle/ductile deformation of the crystal mush are required for the MVP to move [12,24,28].

Figure 1.

Ternary diagram showing the three possible regimes for outgassing in shallow, silicic magma reservoirs: (1) bubble (and crystal) suspension, (2) MVP channels and (3) capillary fracturing. The white region where the gas phase is dominant is possible during syn-eruptive outgassing, but is not a mechanism that will operate within the magma reservoir. Modified from [24].

(a). Regime 1: high melt fraction—bubbly flow

At high melt fraction, bubbles in magmas tend not to be crowded by crystals, as exsolved fluids are dominantly non-wetting with respect to silicate minerals. Considering a closed-system (no input of MVP from surrounding areas), they are also typically in low abundance (less than 10 vol.%), as significant second boiling has not yet been contributing much. Hence, exsolved volatiles are expected to form relatively spherical bubbles and dominantly ascend either as individual bubbles or as bubble plumes/trains under the effect of their buoyancy. As the fraction of bubbles becomes higher than a few per cent, a hindering effect of neighbouring bubbles starts to kick in (see [29]) and the ascent rate decreases because of hydrodynamic bubble–bubble interactions. Although bubble coalescence can enhance phase separation, it is likely to be inefficient because of the low volume fraction of bubbles and high melt viscosity. Moreover, convective motion within the magma entrains bubbles, which can slow down the outgassing process (e.g. [30,31]).

(b). Regime 2: intermediate melt fraction—channel flow

At intermediate melt fraction, one can expect a higher fraction of exsolved MVP through second boiling, which, coupled to the increasing fraction of crystals, favours coalescence and channelization of the MVP. As vertical MVP channels of significant lengths form by viscous fingering, outgassing can become much faster [12,26,27,32]. The transport efficiency of the MVP is modulated by the effective permeability of the MVP phase in the three-phase mush. In essence, intermediate crystallinity provides conditions that are optimal for outgassing because the intrinsic permeability of the crystal mush remains high, and the relative permeability of the MVP, which increases with its pore volume fraction, is intermediate to high as well.

(c). Regime 3: Low melt fraction—capillary fracturing

At low melt fraction, the volume fraction of MVP exsolved in the pore space is likely to be high. At the same time, the sizes of pores and pore throats tend to be significantly smaller at high crystallinity so that the intrinsic permeability decreases significantly from approximately 10⁻⁷ m² to 10⁻¹⁰ m² with crystal content increasing from approximately 40–75 vol.% (assuming an average crystal size on the order of millimetres; see [24]; figure 2). The overall effect of the phase proportions is such that the effective permeability of the MVP drops to zero (i.e. bubbles are capillary trapped). Hence, outgassing will happen only after some overpressurization of the system, leading to repacking or deformation (elastic, plastic or brittle) of the crystalline framework [27,33].

Figure 2.

Three different snapshots of the LB numerical simulations. The left panel shows the initial condition. A high melt fraction region overlies a low melt fraction region with the crystal network shown in grey. The dark red colour indicates the surface of the MVP. MVP is injected into the bottom of the computational domain. The middle and right panels show the MVP migration over time where the crystal network has been made transparent to be able to visualize the MVP in detail. The velocity field (in lattice units) is also visualized on top of the MVP surfaces with blue indicating low velocity, and red showing high velocity. Once the channels become connected in the low melt fraction region, the velocity of the MVP becomes markedly higher than that in the high melt fraction region, which is dominated by bubble rise.

2. Method

In this study, we use numerical simulations at the pore-scale (lattice Boltzmann or LB calculations; see full method description in [24]) focusing on the stress balance that regulates MVP mobility in a crystalline environment at average crystal volume fraction (0.39–0.75; characteristic of mushy environment, see [34]). In particular, we emphasize the role of buoyancy versus capillary stresses in a porous medium (made out of a crystalline framework) containing a low-density non-wetting phase (the MVP) and a higher density, wetting phase (the silicate melt). The main goal of our pore-scale calculations is to determine in which conditions the modes of MVP transport switch from bubble flow to channel flow (regime 1 to regime 2) and ultimately to capillary clogging (regime 3).

The outcome of these multiphase porous flow simulations is strongly controlled by the initial spatial and size distribution of bubbles in the porous domain. The proportion of bubbles that are poorly connected to the most efficient flow pathways in the medium dictates, to a large extent, the critical volume fraction of bubbles required to form connected MVP pathways and the relative permeability of the mush to MVP outgassing. In a previous set of simulations [24], the initial distribution of bubbles, and their respective size, was set randomly, which limited the validity of the results. For instance, larger pores contain prior to exsolution more dissolved volatiles and offer less resistance to bubble growth than smaller pores. In the present study, we build on the model of [24], but treat the initial spatial and size distribution of MVP bubbles with a more physically consistent approach using spinodal decomposition.

Spinodal decomposition is a well-studied mechanism in statistical mechanics whereby two phases unmix under the principle of mass conservation and capillary stresses. In this study, it is the melt and MVP that repel each other. The size and position of MVP bubbles derived by the unmixing process results in a spatial and size distribution of bubbles that satisfy mass balance locally, i.e. larger bubbles form where they are the most probably to form. This leads to a more consistent and therefore more accurate initial condition, which translates in improved estimation of critical MVP volume fraction for the formation of connected MVP pathways and relative mush permeability for the MVP.

In detail, the initial condition works as follows. The respective mass fraction of the two phases considered in the spinodal decomposition (i.e. melt and MVP) is a priori defined for each run. Both phases are, initially, homogeneously distributed all around the pore space and locally (i.e. at each grid node of the computational domain) obey a pre-determined mass fraction. We start the simulation by adding a relative fluctuation (or disequilibrium) on the order of 0.1% on the mass fraction of volatiles. This small disequilibrium initiates spontaneous phase separation so that non-wetting MVP bubbles start to grow in the pore space. The growth of these bubbles ceases when the two phases are fully separated, such that the final MVP volume fraction is determined by the initial mass fraction (figure 3). In this study, we use a fixed Bond number of 0.5 (see equation (2.1)), which provides a good approximation for magmatic systems with intermediate crystal size and volume fraction (see [12,24]).

Figure 3.

The top panels show the modelled crystal networks used for the LB numerical simulations at three different crystal volume fractions varying from 0.49 to 0.75. The crystals are colour coded dark blue, turquoise and yellow as a visual aid. The six panels on the middle and bottom row show different snapshots of simulations showing the potential spatial distribution of the MVP (in dark red) at different volume fraction (from 2.7 to 11%) in partially crystallized porous media (the corresponding crystal network shown in the same column is made transparent in these panels to be able to visualize the MVP). Second row: at lower crystal volume fraction values (0.49 and 0.59), MVP concentrations higher than 6% allow MVP channels to form. At higher crystal volume fraction (0.75) the lower degree of connectivity prevents MVP channels to form even at MVP concentration as high as 11%. Third row: bubble distribution for lower MVP volume fractions. MVP volume fraction is too low for MVP channels to form.

In order to assess the efficiency of outgassing on the volatile budget at the scale associated with a magma reservoir, we parametrize the results of the pore-scale LB simulations and implement them in a macro-scale reservoir model [24]. We use the reservoir model of [35], expanded to include outgassing (see the detailed implementation in [24]) as it allows us to directly couple thermal and mechanical evolution of the magma reservoir. The original model assumes a magma chamber that evolves due to magma injection, magma withdrawal, exsolution and crystallization. The magma chamber loses heat to its surroundings (crystalline mush transitioning to crustal wall-rocks), which responds visco-elastically to volume changes of the chamber. For simplicity, we will not consider magma injection or withdrawal, except for the loss of magmatic volatiles by outgassing, which influences the enthalpy budget of the magma body and therefore the cooling rate of the magma chamber.

As in [24], we initialize the magma chamber at a lithostatic pressure of 200 MPa, a temperature of 850°C and a volume of 50 km³. The initial density of the melt and crystals are 2400 kg m⁻³ and 2750 kg m⁻³, respectively, and they vary less than 1% during a calculation. The heat loss is calculated through an analytical solution of a sphere (magma chamber) at the centre of a larger sphere (mush and crustal surroundings) that takes into account the time-dependent temperature variations in the chamber. We assume the following thermal properties for the surroundings, a thermal diffusivity of 10⁻⁶ m² s⁻¹, a specific heat capacity of 1200 J kg⁻¹ K⁻¹ and a density of 2500 kg m⁻³. We explore the difference between a colder and hotter crust, by setting the temperature of the outer shell at 250°C and 300°C, respectively. The magma solidifies according to a parametrized melt fraction–temperature curve for a dacitic composition [7] with a solidus and liquidus temperature of 700°C and 1020°C, respectively.

For these conditions, we track the outgassing efficiency during the thermo-mechanical evolution of the chamber. We start from a total water content of 5.5 wt%. The water exsolves according to a parametrized solubility model for water in rhyolitic melt [36]. We use new closure relationships for outgassing based on the results of the pore-scale LB model that includes spinodal decomposition. The nature of the reservoir model requires a volume-averaged parametrization of the results from the pore-scale model. We determine (i) the critical MVP volume fraction ${\epsilon }_g^{cr}$ at which channels can form, (ii) the intrinsic permeability of the crystal network k, and (iii) the relative permeability k_r of the MVP as a function of the crystallinity ε_X of the mush.

The critical MVP volume fraction in the LB calculations is determined by the minimum MVP volume fraction at which channels are able to form for a given crystal volume fraction. For Bo = 0.5 and crystal volume fraction between 0.39 and 0.7, our pore-scale simulations yield a critical MVP volume fraction for the formation of percolating MVP pathways that can be fitted as follows (figure 4a):

$${\epsilon }_g^{cr}=0.7495{\epsilon }_X^3-0.4268{\epsilon }_X^2-0.1626{\epsilon }_X+\mathrm{0.1478.}$$ 3.1

Below a crystal volume fraction of 0.39, no channels form as the crystals do no longer form a rigid network and are held in suspension. Above a crystal volume fraction of 0.7, no channels form as the pore space becomes too small and poorly connected. These boundaries are indicated in figure 1 by the red curves and define the region for MVP loss by channels. The intrinsic permeability of the crystal network is found from single-phase fluid flow simulations through the crystal matrices. It is identical to that of [24], as we are using the same porous media and we can use the same equation to describe it:

$$k={10}^{-4}(-0.0534{\epsilon }_X^3+0.1083{\epsilon }_X^2-0.0747{\epsilon }_X+0.0176)\hspace{0.17em}{\text{m}}^2.$$ 3.2

The relative permeability is determined from the LB calculations at the onset of channel formation. The parametrization is then calculated from linear interpolation of the minimum values with respect to critical volume fraction found with the pore-scale simulation, with the additional constraint of zero relative permeability at a crystal volume fraction below and equal to 0.39 (where bubbly flow is assumed to prevail; figure 4b). The latter is to avoid a sharp transition between different outgassing regimes. There is also a dependence of the relative permeability on the MVP volume fraction, but this has a negligible effect on the results. As outgassing is generally able to keep pace with exsolution, the MVP volume fraction remains close to the critical MVP volume fraction up to the point of capillary trapping. This set of closure relationships allow us to estimate the mass flow rate out of the chamber that results from outgassing. This enters into the model description as sink terms in the conservation of mass, water and enthalpy [24].

Figure 4.

Critical MVP volume fraction (a) and relative permeability (b) for gas channels to form based on lattice Boltzmann simulations (points) of [24] in black and the current study in blue. The dashed lines show the respective parametrization of these results, which were implemented in the reservoir model. (Online version in colour.)

3. Results

Our results show that the MVP volume fraction needed to form channels is lower taking into account our improved initial bubble distributions (figure 4a). Owing to the fact that the formation of large bubbles is favoured in the best-connected areas of the porous medium, more of the MVP will be able to participate in the formation of channels. Larger pore spaces contain initially a higher integrated mass of volatiles accessible for bubble growth than small pores. Larger and more mobile bubbles are therefore predominantly formed in large and better-connected pore space leading to a greater efficiency at forming MVP percolating pathways (see figures 2 and 3) than expected from a random initial distribution of bubbles. Hence, well-connected pores collect more MVP mass, and stabilize channels at lower MVP volume fraction than found in Parmigiani et al. [24]. However, the general behaviour remains similar; the most efficient outgassing regime in terms of rate is still at intermediate crystallinity, in which channels can efficiently form due to the effect of crystal confinement (focusing the MVP into the pore space) but are not easily clogged by capillary forces when the MVP volume fraction and porous medium constrictions become too important at very high crystallinities.

The results from the magma reservoir model suggest that although more MVP can be lost earlier (lower crystal content) than what was predicted by Parmigiani et al. [24], the relative contribution of each outgassing regime (bubble migration, MVP channel formation and capillary fracturing) remains roughly similar (figure 5). We estimate the mass fraction of MVP that is released in each regime to be:

• —up to 0.05 wt% of MVP or about 1% of the total MVP available is lost through migration of bubbles at low crystallinity
• —up to approximately 2.7 wt% of MVP or about 50% of the total MVP available is lost by channels at intermediate to high crystallinity
• —a minimum of approximately 2.8 wt% of MVP or about 50% of the total MVP either remains trapped or potentially leaves the chamber through capillary fracturing at high crystallinity.

Figure 5.

Example of a reservoir scale simulation showing the total amount of MVP loss for the different regimes with different viscosities (and therefore response timescales) for the wall rocks. At high melt fraction, MVP mass loss is negligible, while it is significant in the lower melt fraction regime (total volatile mass fraction goes from about 5.5 to less than 3 wt% in this particular case).

The elastic response of the surrounding crust will act to hinder outgassing (figure 5). When the crust responds elastically, outgassing creates an underpressure in the chamber up to a point where the lithostatic pressure of the surroundings will oppose the buoyancy that drives the MVP upward [24]. This underpressure is avoided if the crust responds viscously. Thus, the most efficient outgassing takes place in a large reservoir that sits in a thermally mature crust. Those values are very similar to those proposed by Parmigiani et al. [24], where the results indicated a minimum of 3.25 wt% of MVP was left behind at high crystallinity. Thus, MVP loss by channels is slightly more efficient when incorporating spinodal decomposition. The minimum amount of H₂O that is left behind (approx. 2.8 wt% H₂O) is independent of the initial total MVP mass fraction as the saturation limit is entirely determined by the critical MVP volume fraction. Hence, systems that are more water-rich than what we started with (5.5 wt% H₂O) can outgas even more at intermediate crystallinities.

4. Discussion/outlook

The loss of MVP from shallow maturing magma reservoirs has deep implications for the subsequent thermal evolution of the system as well as the potential and magnitude of forthcoming eruptions. More specifically, because the MVP has a low viscosity, low density and high compressibility, it can deeply influence the mechanical behaviour of magma reservoirs [37,38]. As such the rate of outgassing of magma reservoirs influences the response of magma reservoirs to magma recharges, because the compressibility of the MVP can dampen the pressurization and help such reservoirs to grow rather than blow (e.g. [37,39]). Dampening pressurization by enhanced compressibility can also foster more efficient reheating in the reservoir, potentially leading to a less explosive eruptive style if the system does erupt [40]. Moreover, the fact that melt-rich pockets tend to outgas more slowly than crystal-rich areas leads to MVP accumulation in such melt-rich pockets, fostering larger eruptions due to the increase in compressibility [12,37,40].

Apart from those mechanical effects on magma reservoir dynamics and volcanic behaviour, the presence of an MVP, and the dynamics of outgassing, controls the rates and compositions of gases that escape magmatic systems. As the composition of gases emitted during and in between eruptive events are key to monitor active volcanic areas [41–45], and feed into global volatile cycles on Earth [10,46–48], it is of paramount importance to determine how such rates and compositions might evolve as outgassing proceeds in crystallizing magma bodies

• 1.Rates. In the light of our results and assuming a intrusive:extrusive mass ratio of about 10:1 to greater than 50:1 in continental acs [18–20,22], we expect that volcanic eruptions contribute only a small fraction (a few per cent, even assuming some MVP accumulation in eruptible pockets of magmas) of the volatile flux from the mantle to the surface at present. The rest of the flux is divided between channel outgassing at intermediate crystallinity (i.e. 0.4 ≤ ε_x ≤ 0.7) and capillary fracturing during the last gasps of the crystallization of plutons (potentially leading to the formation of aplite and pegmatites). Hence, the background volatile flux released at subduction zones is likely dominated by passive outgassing from shallow reservoirs with intermediate to high crystallinities (greater than 40 vol.% crystals) with a superimposed lower amplitude perturbation associated with volcanic eruptions (e.g. [23]).
• 2.Composition. The differences between ‘low-crystallinity' and ‘high-crystallinity’ outgassing will influence the chemistry of the gases released. For instance, volatile species that have low solubility in silicate melts, or are compatible with the MVP (sulfur species, CO2, Ar, N₂, Cl,…) are likely to partition early into the MVP and outgas predominantly during spikes of volcanic activity. By contrast, less MVP-compatible species (e.g. F, Br, and potentially He and Li) are expected to be dominantly released passively from high-crystallinity bodies. This suggests that constraining the mass and composition of volatile species from eruptive episodes at subduction zones can be misleading not only in terms of the magnitude of the flux but also the composition of the volatile species involved. For example, CO₂ degasses early (low crystal content), whereas He, which tends to be more soluble than other inert gases [49], may be enriched during degassing at higher crystal content. In consequence, we expect gases emitted during volcanic eruptions to record a bias towards lower He/X (where X=CO₂, N₂, other noble gases) compared to the more abundant high-crystallinity outgassing. The poorly recognized role of intrusive magmas on volatile cycles begs to reassess our understanding of volatile recycling fluxes at subduction zones, both in terms of magnitude and volatile composition. Gas compositions emitted during volcanic eruptions, which are commonly used as a proxy for the Earth's degassing patterns, may not provide an accurate chemical signature for and/or magnitude of the volatiles exchanged between mantle and surface.

Data accessibility

This article has no additional data.

Competing interests

We declare we have no competing interests.

Funding

During the course of the writing of this paper, O.B. was supported by Swiss NSF grant nos 200020_165501 and 200021_178928, and C.H. was supported by an NSF CAREER grant.