Experiments on the heat discharge at the dynamic magma-water-interface



[1] Compared to “dry” atmospheric eruption of magma or “dry” magma/rock contact, intensity and time scale of heat discharge from magma to the surroundings is strongly modified by an effective coolant: water or water-sediment mixes. In the case of subaqueous or subglacial eruptions magma-water contact must take place and can result in phreatomagmatic explosions. Even if no explosions occur, rapid cooling results in the formation of pyroclasts by thermal granulation. To study this process in detail, a short-term calorimeter was built for the direct measurement of the heat-flux from a magmatic melt to a coolant. Volcanic rocks from recent eruptions in Iceland were remelted and used to produce jets of melt poured into a coolant-filled container. Particles could be produced in a non-explosive process, that are practical identical to those from natural hyaloclastites. The process' fragmentation energy is about 10% of the total heat transferred from melt to coolant.

[2] The impact of volcanic eruptions on the environment depends on the rate of magma discharge and on the coupling parameters. Most important among the latter is the thermal coupling, i.e., the heat discharge per unit time from a unit magma mass to the surroundings. The “surroundings” may be considered as a coolant, and when magma is surrounded by liquid water it is this water that acts as the coolant. Thermal coupling is governed by material properties of magma and coolant, and by the interfacial conditions. The presence of a magma-water interface shortens the time scale of heat discharge dramatically, whether the type of interaction is explosive (MFCI [e.g., Zimanowski, 1998; Zimanowski and Büttner, 2003]) or non-explosive [Clague et al., 2009; Helo et al., 2008; Schipper and White, 2010; White and Houghton, 2006; Wohletz, 2003, 2002]. Due to volume contraction silicate melts are affected by cooling crack formation once a critical cooling rate is exceeded. The process of fragmentation due to crack formation caused by rapid cooling of melt (surrounded by a coolant/water) is one possible mechanism of magma-water interaction. In powerplant engineering and metallurgy this process is commonly referred to as “thermal granulation” [e.g., Schreiner, 1972], now also introduced into volcanology [Büttner et al., 1999; Zimanowski, 1998]. The well known thermo-physical properties of water, especially its high specific heat (about 4181 JK1 kg−1 at atmospheric conditions, [Wagner and Pruß, 2002]) can be used to quantify the time scale of the thermal granulation effect and the amounts of the energies converted. While there is research investigating many qualitative aspects of thermal granulation [e.g., Mastin et al., 2009] explicit numbers, especially concerning calorimetric data, i.e., the transferred amounts of heat, need to be determined experimentally. The following experimental setup aims and enables the quantitative measurement of calorimetric data describing this process. The energy conversion from heat initially contained in the melt to the heat content of the coolant and the residual energy consumed by production of new surface and other events, e.g., acoustic emission, can be determined accurately. It is possible to quantify the efficiency of the thermal granulation process, which turns out to be constant for the considered material.

[3] To observe the thermal granulation process and the participating heat quantities, a natural volcanic sample was remelted and poured into a coolant reservoir. Its heat content can be measured accurately if the coolant is contained in an insulating tank with a known, small heat capacity—a calorimeter. The dimensions of this tank were chosen so that 100 g of melt, which is a reasonable amount to produce in the laboratory, would induce a temperature step of about 10K in the water. The melt was produced in an induction furnace [e.g., Zimanowski et al., 1995], which consists of a coil in a tuned circuit heating a crucible which contained the melt. The furnace was mounted on a tilting device directly above the water reservoir. This way it is possible to pour the melt directly from the heated crucible into the coolant in a continuous jet with a minimum of heat loss. The calorimeter was mounted on a balance to record the amount of melt in the water.

[4] The material selected for the experiments was sampled in 2006 from deposits of the basaltic 2004 Grímsvötn eruption (documented online by the University of Iceland (http://www.earthice.hi.is/page/ies_grimsvotn2004)). About 150 kg of fresh bombs were crushed and homogenized to get a good representation of the average source magma of the eruption. The heat content of this material is given by its temperature T and the temperature dependent specific heat capacity cp. The amount of heat participating in the thermal granulation is

equation image

where T0 and T are the initial melt-, and the final melt/water mixture temperatures, respectively, and m denotes the melt's mass. Since cp strongly depends on structures formed by the sample's temperature history, a part of the sample was quenched, and cp was measured using this sample at a heating rate of 20 Kmin−1. The measured heat capacity during the first heating is shown in Figure 1. It shows a significant undershoot around 1150 K due to recrystallization and an overshoot around 1375 K due to the structural reorganization from the solid to the fluid state. The values of the specific enthalpies corresponding to this two peaks are almost identical but of opposite sign. Since the original cooling rate was much higher than the heating rate during measurement of cp, the effective amount of heat contained in the ingoing melt can be calculated from a linear interpolation of the measured cp-data between 1075 K and 1425 K. Figure 1 shows the measured specific heat as well as the dependency assumed to calculate the melt's heat content.

Figure 1.

Specific heat of Grímsvötn basalt.

[5] The calorimeter is made of stainless steel and insulated on the outer surface. The total volume is roughly 12 liters, the water volume used in the experiments was between 3 liters and 4.5 liters. The calorimeter's heat capacity is 0.76 kJ−1K, and much smaller compared to the heat capacity of liquid water (18.8 kJ−1K using 4.5 liters at room temperature and ambient pressure). The relative heat loss due to the calorimeter's non-perfect insulation is less than 0.01%. To observe the water temperature 8 thermocouples (NiCr-Ni, type K) were symmetrically built into the container. A calibration between freezing point and boiling temperature of water improved the accuracy of each thermocouple to a maximum error of ±0.3 K. A sketch of the complete experimental setup is shown in Figure 2. Heat loss due to radiation of the ingoing melt jet to the atmosphere can be neglected, since experiments from different drop heights (which were varied between 63 cm and 114 cm) did not show any significant variations of the ingoing heat content. Optical measurements (pyrometer) used to observe the surface temperatures of the melt jets also displayed only negligible variations.

Figure 2.

(left) Sketch of the experimental setup. (right) Frame of a high speed record of a submerging melt jet of about 1 cm in diameter (transparent test container).

[6] The melt is poured in roughly 10 s into the water. In test runs the diameter of the melt jet was varied between few mm and some cm. Above a critical diameter of about 5 mm the granulation process leads to comparable results. Below the critical value the surface/volume ratio becomes so large that granulation is overridden and only cylindrical chunks are produced. At sub millimetre jet diameters, long pieces of pele's hair occur, which form curly aggregates shaped by thermally induced strain [Mastin et al., 2009]. Consequently we used a melt jet diameter of about one cm for the experiments. Before, during, and after the granulation run the water temperature and the mass contained in the calorimeter were recorded. Figure 3 shows the results of a typical granulation experiment. During the main melt-water interaction the measured water temperatures distribute over a quite large interval due to the melt-induced water convection. Figure 3, however shows, that the average temperature is a good measure for the transient of total heat in the calorimeter. From these raw data an energy balance can be derived by calculating the change of heat in the melt reservoir ΔQm(t) and the water ΔQw(t) at given time t during the experiment. ΔQm is given by the melt's specific heat cp(T) (as described above)

equation image

Here T and T0 denote the asymptotic water/melt temperature for large t, and the initial melt temperature, respectively. mm(t) is the mass of melt in the water, and m0 the total melt mass. Figure 4 shows the time dependency of these two energies. The graph shows also clearly that there is a significant difference ΔE between ΔQm,0, the total amount of heat “spent” by the melt, and ΔQw,, the total amount of heat “received” by the water. This energy difference is consumed by the granulation process to produce new surface in brittle and hydrodynamic processes. ΔQw, was found to depend linearly on ΔQm,0. This implies that ΔE is characteristic for the granulation process of this material. Hence the efficiency defined by

equation image

is a constant material property. Figure 5 shows ΔQw, for various ΔQm,0. The slope of the fitted line results in η = (90.7 ± 2.5)%. The variations in the melt's initial heat contents Qm,0 can be achieved in different ways: by variation of T0, or by variation of m0. Figure 5 shows results of both types of variations. It was not possible to identify significant dependencies on either of the two mechanisms.

Figure 3.

Raw data of a granulation run. Thin dotted lines show temperatures at each thermo couple, which produce the average temperature T shown as the solid line. Cumulating melt mass is represented by the dashed line.

Figure 4.

Thermal energy transfer during granulation process.

Figure 5.

Efficiency of the granulation process.

[7] The thermal granulation experiment introduced here is able to produce particles identical to pyroclasts formed in natural subaqueous and subglacial volcanic eruptions [Sohn et al., 2008; D. A. Clague and J. D. L. White, personal communication, 2009]. The constant efficiency η and the minor influence of the initial melt temperature T0 imply that the boundary conditions necessary to start the thermal granulation process are satisfied in many situations of natural magma-water interaction. The independence of η on T0 and m0 further shows that the calorimetric results can be applied to heat transfer models and scaled to sizes of natural volcanic activity. Determination of the thermal efficiency η provides information on the maximum fragmentation energy consumed in non-explosive magma-water interaction. If the release of heat during a subglacial/subaqueous eruption can be measured (e.g., by monitoring of ice melting) the mass of erupted magma can be estimated. Next steps will incorporate measurements of the surface area of the granulated material and influences due to variation on the coolant side. Different temperatures of the coolant need to be investigated, since this can influence the stability and size of vapor films. Also impure coolants, like wet sediments [Wohletz, 2002; White, 1996; Hooten and Ort, 2002], are of interest, as differences in the coolant's heat capacity, thermal conductivity, and viscosity could change the heat transfer characteristics dramatically.


[8] This work was funded by the German Science Foundation DFG (Zi 481/14-1)). We would like to thank Greg Valentine and an anonymous reviewer for their constructive remarks which greatly improved the quality of this article.