The critical degassing pressure during magma decompression

The decompression of fresh magma results in the selective release of dissolved volatiles depending on their solubilities28. This means that while barely soluble CO 2 dominates deep degassing3,29,30, more-soluble H 2 O prevails at shallower depths31. Given this selective release of volatiles from magma and the different capacities of these two species to carry thermal energy, the pattern of heat transfer to overlying rocks and hydrothermal systems will be complex and will vary as the unrest progresses.

Several saturation models have been reported in the literature25,28,32,33,34,35,36 that can be used to investigate magma degassing in an H 2 O–CO 2 system. Whereas most of them predict the H 2 O and CO 2 solubilities over narrow ranges of silicate melt composition, one of the models25 can be extended to any silicate melt composition. Here we use that model to predict H 2 O–CO 2 partitioning during magma decompression; however, the use of alternative models would lead to similar results and conclusions.

Model calculations were initialized at conditions relevant to CFc, where the marked variations in the compositions of fumarole emissions37 observed over the last 30 years have been attributed14,21 to decompression-driven open-system degassing of trachybasalt magma. A good match21 between model-calculated solubilities25 and experimentally derived solubilities for CFc or CFc-like magmas has also been demonstrated.

Figure 1a shows the total quantities of H 2 O and CO 2 released at equilibrium conditions by 1 kg of magma during open-system depressurization. We assumed isothermal conditions (temperature=1,425 K) and that the CO 2 –H 2 O mixture is initially saturated at 200 MPa. This pressure corresponds to a depth of ∼8 km, where a large magma reservoir below CFc has been detected by seismic tomography38.

Figure 1: Open-system magma-degassing models for CFc. The different curves refer to different initial H 2 O and CO 2 contents and describe the evolution of the fluids released during magma depressurization in an open-system Rayleigh-type degassing process (where at each infinitesimal decompression step, an infinitesimal parcel of gas phase in excess of the permissible saturation is distilled from the well-mixed magma). Theoretical degassing curves were calculated for the most-primitive magma compositions of CFc (trachybasalt) and show the pressure dependence of (a) the moles of H 2 O and CO 2 released by one kilogram of magma for each 1-MPa decrease in pressure; (b) the energy associated with fluid release (enthalpy of the separated H 2 O–CO 2 mixture at the specific temperature and pressure, computed using MUFITS63); (c) the residual gas in the melt, as a percentage of the original content; and (d) the CO 2 /H 2 O ratio of the released fluids. The blue circle and orange line indicate the conditions used in the corresponding TOUGH2 (ref. 26) simulations. Full size image

A range of total volatile contents was explored, but all of the simulations converged to indicate different degassing behaviours of CO 2 and H 2 O. Figure 1a shows that, during deep (pressure >150 MPa) degassing stages, less than 0.001 moles per kilogram of magma of CO 2 -dominated magmatic gas are separated for each 1-MPa decrease in pressure. H 2 O degassing becomes effective only at lower pressures (Fig. 1a,c), and when this happens there is a narrow pressure interval over which the total amount of separated fluid increases steeply (by more than one order of magnitude). This stage is marked by abrupt variations (Fig. 1a) and it leads to the complete exhaustion of CO 2 in the magma, leaving only H 2 O available for subsequent low-pressure degassing (Fig. 1c). A particularly important feature at this stage is that each model curve shows an inflection point (Fig. 1a) at a specific pressure, which we refer to as the CDP. In each of the model curves of Figs 1 and 2, we set the CDP as the pressure value at which the second derivative of separated gas content with respect to pressure reaches its maximum. This condition marks an abrupt increase in the amount of thermal energy released through fluid expulsion, from <50 J to >1,000 J per kilogram of magma and for each 1-MPa decrease in pressure (Fig. 1b).

Figure 2: Results of magma degassing models. The different curves refer to different initial H 2 O and CO 2 contents, reported as couple of values on each and describe the evolution of the fluids released during magma depressurization in various conditions. (a) Theoretical degassing curves were calculated for rhyolitic magma compositions and show the pressure dependence of the moles of H 2 O and CO 2 released during open-system degassing by one kilogram of magma for each 1-MPa pressure decrease. (b) Theoretical degassing curves were calculated for the most-primitive magma compositions of CFc and refer to open and closed degassing (trachybasalt). Full size image

We found similar nonlinear degassing behaviour over a range of magma compositions and volatile contents. For any magma type (for example, rhyolitic magma; Fig. 2a), complete CO 2 exhaustion in the melt marks a critical condition at which the amount of separated fluids and the energy transfer to the hosting rocks both increase dramatically. It is important to stress that most of the H 2 O (∼95% of the original content) is still dissolved in the magma at the CDP (Fig. 1c) and is therefore available for further subterraneous gas–magma separation, heating, and (eventually) sustaining an eruption39.

Our calculations were performed under open-system conditions since the long-lasting variations in the fumarole-gas composition at CFc cannot be reproduced in a closed system, instead requiring efficient separation of gas from the magma21. The large amount of magmatic fluids released by CFc manifestations40 also supports an ongoing open (rather than closed) magma-degassing behaviour. Our open-system Rayleigh-type degassing model assumes that volatiles are continuously separated from magma at each decompression step. However, the release of magmatic fluid from CFc surface manifestations actually shows a pulsed (noncontinuous) behaviour (Supplementary Figs 1 and 2), which suggests a mechanism in which periods of closed-system decompression alternate with episodes of system opening and gas release (that is, a multistep degassing process) over timescales of years.

Tests show that such multistep degassing can be adequately reproduced as an open-system degassing process provided that there are numerous and recurrent system-opening events, as is likely to be the case.

Open-system, unsteady degassing is not only observed at CFc41,42. During extrusive volcanic eruptions, pulsed degassing behaviour can occur even at shorter timescales, and is thought to derive from multiphase flow dynamics within the conduit43. At CFc, we argue that such degassing behaviour can ultimately result from the complex geometry of crustal volcano plumbing systems, whose intricate networks of fractures, dikes, sills and small reservoirs44,45,46,47 facilitate the segregation of gas from melt, and the loss of volatiles from a foam layer48. Foam growth in low-viscosity mafic melts takes place over timescales of months to a few years48,49, which is faster than the observed decennial trends in gas composition. While we therefore favour an open-system scenario, we also show examples of model degassing simulations in closed-system conditions (Fig. 2b) to demonstrate that a CDP can be reached even in that type of system, despite the mass of released volatiles varying less markedly than in open-system conditions. We conclude that the concept of the CDP applies over a wide range of magmatic conditions. We also find that CDP conditions are reached independently on the solubility model used, for example, VolatileCalc36 (Supplementary Fig. 3).

The thermal regime of hydrothermal systems can be strongly impacted if the underlying magma approaches the CDP. Within the typical temperature and pressure hydrothermal range, CO 2 behaves as an incondensable species, while H 2 O can condense and therefore heat the rocks very efficiently. Our models of fluid flow in porous media26 that describe the injection of fluids enriched in either CO 2 or H 2 O into a virtual hydrothermal system confirm the different heating capacities of the two volatiles. The ability of ascending magmas to heat any overlying hydrothermal system will therefore be greatly enhanced as the CDP is approached. We use below the CFc example to further illustrate this aspect.

The case of Campi Flegrei caldera

Of the several quiescent calderas worldwide, CFc has recently shown among the clearest signs of unrest. At CFc, several ktons of hydrothermal fluids are emitted daily by the Solfatara-Pisciarelli fumarolic field40 (Fig. 3a,b). Stable isotopes of fumarolic steam concur to indicate that such fluids are, at least partially, sourced by magma degassing50.

Figure 3: The hydrothermal system of CFc and its signals. (a) Locations of CFc and the main hydrothermal sites: Solfatara and Pisciarelli. (b) Conceptual model of the hydrothermal system feeding the two manifestations: a 4-km-deep zone of magmatic gas accumulation that supplies fluids to a shallower part where they vaporize liquid of meteoric origin to form a 2-km-deep vertical plume of gas14. Previous geochemical investigations based on the stable isotopes of water revealed the presence of typical magmatic waters in the Solfatara fumarole vents50. (c) Temporal evolution of the N 2 /He ratio at the Solfatara fumaroles. (d) Time series of the CO content in the Solfatara fumaroles. The increasing trend indicates heating of the system, and matches the TOUGH2 (ref. 26) model-derived temperatures (magenta line) exceptionally well. Full size image

The large variations in the fumarole emissions of N 2 –He–CO 2 –Ar (ref. 21), including the 25-year-long decreasing trend of the N 2 /He fumarole ratio (Fig. 3c), fully support the idea that a primitive magma degassing in open-system conditions at increasingly lower pressures is sustaining the unrest. A particularly important observation is that the ground deflation and N 2 /He gas ratios followed exponential-like trends from 1985 to 2005, with very similar characteristic times, implying common source processes14. The presence of magma depressurization is also supported by modelling of the ground uplift in 2012–2013, which has been interpreted as the effect of a magma intrusion at a depth of 3 km (ref. 22). At the same time, a generalized heating up of the CFc hydrothermal system is indicated by the 15-year-long exponential increase in CO emissions from the fumaroles (Fig. 3d); note that CO is the fumarole gas most sensitive to temperature changes51.

Based on these observations, we argue that the CFc magmatic system may be approaching the CDP; that is, that depressurizing magma may release fluids progressively richer in H 2 O so as to affect the thermal structure of the hydrothermal system. We tested this hypothesis by using TOUGH2 (ref. 26; see Methods) to model the injection of magmatic fluids (IMF) into a hydrothermal system under physical conditions appropriate for CFc13 (Fig. 4).

Figure 4: Computational domain of the TOUGH2 simulations. The rock physical properties were homogeneous (porosity=0.2; thermal capacity=1,000 J kg−1 °C−1; density=2,000 kg m−3; horizontal permeability=10−14 m2; vertical permeability=1.5 × 10−14 m2; and thermal conductivity=2.8 W m−1 °C−1). The temperature and the volumetric gas fraction Xg (different shades of gray) refer to steady-state conditions. The ‘checkpoint for gas composition’ is the zone where the simulated CO 2 /H 2 O is compared with the measured one (see Methods). The ‘Temperature box’ (yellow rectangle above the injection zone) is the region where the average temperature is calculated during the simulations (see Figs 5 and 6 and Supplementary Fig. 1c). Full size image

Our new model simulations refine previous ones13 that first identified the magmatic gas trigger of the unrest. The model involves injecting H 2 O–CO 2 magmatic gas mixtures into a virtual hydrothermal system at subcritical temperature and pressure conditions. The composition (CO 2 /H 2 O ratio) of the injected magmatic gas phase is based on the results of our magma-degassing models (see Methods and Fig. 1d). We highlight that these modelled magmatic CO 2 /H 2 O ratios can only approximate the composition of fluids entering the real hydrothermal system, since the model does not account for secondary processes potentially occurring along the magma-to-hydrothermal gas cooling path.

We simulated 14 IMF events occurring between 1983 and 2014, whose timing and intensity were constrained based on measured geochemical anomalies only (see Methods and Supplementary Fig. 1a,b). Ground deformation pulses and clustered earthquakes support the timing of the IMF events, which were independently fixed based on geochemical anomalies (Supplementary Fig. 2). Previous simulations13 considered injections of hot fluids with a constant CO 2 /H 2 O ratio. Here we update these previous calculations to the current CFc state (Simulation 1), but also consider a new scenario (Simulation 2) in which magmatic fluids that are increasingly rich in H 2 O are injected. The first scenario corresponds to degassing of a stationary source at 200 MPa and with original H 2 O and CO 2 contents of 3.89 wt% and 0.079 wt%, respectively (blue circle in Fig. 1a,d). The second scenario describes the depressurization of the same source down to 130 MPa (orange line in Fig. 1a,d). The CO 2 /H 2 O ratio used in each IMF event was inferred from the measured N 2 /He ratios and the results obtained in simulations of open-system magma-degassing models (Supplementary Figs 4 and 5).

We found that each modelled IMF episode involves the injection of 0.1–25 Mt of magmatic fluids, which is within the range of the gas mass associated with small to moderate-size volcanic eruptions13. The modelled cumulative trends of injected magmatic fluid masses exhibit clear exponential acceleration since the 2000s (Supplementary Fig. 1d). The acceleration trend is steeper in Simulation 2 (in which the gas compositions varied during the simulation) than in Simulation 1. Simulation 2 also predicts an average temperature increase of 60 °C in the deep-central part of the hydrothermal system (Figs 3d, 5 and 6). One interesting outcome of Simulation 2 is that, while the CO 2 /H 2 O ratio of the injected magmatic fluids decreases over time, the simulated gas composition at the ‘checkpoint for gas composition’ (Fig. 4) becomes increasingly rich in CO 2 (Supplementary Fig. 1b). This apparent paradox results from H 2 O condensation in the hydrothermal system, which is the same process heating the rocks. Condensation of a mixed magmatic-meteoric vapor, followed by H 2 O–CO 2 oxygen isotope exchange in the fumaroles’ feeding conduits50, also well account for the observed hydrogen and oxygen isotope composition of fumarolic steam (Supplementary Fig. 6).

Figure 5: Observations and modelled data for the current period of unrest of CFc. (a) Average temperature obtained by the model (in Simulation 2) for the central deeper zone of the computational domain. (b) Temperatures computed using the CO-CO 2 geothermometer at Solfatara fumaroles14 compared with modelled temperatures (gray line). The modelled temperatures, which refer to the central deeper zone of the computational domain (‘Temperature box’ in Fig. 4), have the same temporal evolution but are systematically higher than the CO–CO 2 temperatures, which reflect the thermal state of the upper part of the hydrothermal system14. (c) Vertical displacements measured at the RITE CGPS station (black line) and modelled volume increases in the computational domain due to thermal expansion (magenta line). We used a coefficient of volumetric thermal expansion of 3 × 10−5 °C−1. Full size image

Figure 6: Discharge temperature at the Pisciarelli fumarole compared with the modelled temperature. The temperature at the Pisciarelli fumarole (gray dots) increased from the boiling temperature (95 °C) in 2005–2006 to 115–120 °C in 2015. During the same time interval, temperature increased of only 3–4 °C at the highest temperature fumarole BG, implying clustering of hydrothermal influx on the eastern outer slope of Solfatara crater, where Pisciarelli is sited (Fig. 3). At Pisciarelli, localized low-magnitude seismic swarms20, a weak phreatic activity (mud emission, opening of boiling pools and new vents), and a strong increase in the fumarole flow rate accompanied the temperature increase. The variation occurs concurrently with the increasing temperature of the CFc hydrothermal system modelled in Simulation 2 (magenta line; that is, average temperature inside the yellow box in Fig. 4). Full size image

Our model predicts that the injection of increasingly H 2 O-rich volatiles released by magma approaching the CDP leads to significant heating of the hydrothermal system (Fig. 5a) with obvious implications for volume expansion of the rocks (Fig. 5c).