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[SVC32-09] Estimation of the dissolution heat of water in the rhyolitic melt
Keywords:rhyolitic melt, water, dissolution heat, solubility, decompression-induced vesiculation, temperature drop
[Introduction]
To understand the volcanic eruption dynamics in detail, it is important to know the temperature (T) change of magma as it rises the conduit. Among multiple causes, the contribution of vesiculation (vesi.) and crystallization (cryst.) seems to be significant in the central part of the conduit. The latent heat of vesi. and the mechanical work of bubble expansion cool the system, while the latent heat of cryst. heats the system, thus they work to cancel each other out. This is why many previous studies assumed that the magma is isothermal during decompression. However, there is no evidence that each amount is equivalent.
[Thermodynamic estimation of the water dissolution heat into rhyolitic melt]
Sahagian and Proussevitch (1996) [SP96] estimated the total dissolution heat thermodynamically from the water solubility in albite melt, but the calculation process was incorrect (Zhang, 1999 [Z99]). Z99 proposed a method to estimate the dissolution heat of the first reaction from the Gibbs-Helmholtz equation, but he gave up the practical calculation due to the lack of solubility data at low-P and the unreliability of the equilibrium constant of the second reaction at high-P.
In this study, we assumed that these problems were solved by Liu et al. (2005) and by Nowak and Behrens (2001), respectively, and the dissolution heat of the first reaction was determined using the method of Z99 in the range of 700-1200°C, 100-300 MPa for the Wada Pass obsidian glass composition (Fig. 1). Due to the combination of two dissolution reactions, the T-dependence of the total dissolution heat is reversed between low and high-P. The total dissolution heat approaches zero at higher T and P, which can be interpreted as silicate and water approaching the supercritical state where they mix with zero dissolution heat.
[Numerical calculations on temperature drop of rhyolitic melt by decompression vesiculation]
Next, the differential equation describing the T drop due to equilibrium decompression vesi. of rhyolitic melt, modified from SP96, was calculated numerically. Adiabatic reversible process and the closed system degassing were assumed. The calculations were terminated when the volume fraction of vapor reaches 80%. In Fig. 2, the left, middle, and right columns show the total T drop, in it the effects of latent heat and expansion, respectively. In SP96, the initial T-dependence of the T drop was not taken into account because the value of the exsolution heat at the initial T was assumed to be maintained during decompression. In contrast, in this study, the final T drop has a slight dependence on the initial T because the value of the exsolution heat was calculated sequentially with the T-P change. Compared with SP96, the effect of expansion was not so different, but the effect of latent heat was more than twice as large, and the total T drop could be up to 80°C or more.
[Implications for natural systems]
These calculations suggest that the increase of melt viscosity during decompression vesi. of rhyolitic melts may be due not only to a decrease of water content in melt but also to the decrease of melt T. This may lead to a faster increase in viscosity of magma ascending the conduit than the conventional case where the magma is isothermal, also to a deeper disruption depth or a smaller strain rate for disruption of magma. The temperature drop due to vesi. may also be responsible for part of the effective undercooling required for the microlite cryst. mechanism (Cashman and Blundy, 2000). In order to evaluate the contribution of vesi. to the temperature change in a cryst.-prone melt, such as andesitic melt, where it has already been pointed out that the latent heat of cryst. can increase the temperature by about 100°C (Blandy and Cashman, 2006), it is necessary to solve for the temperature change due to vesi. and cryst. simultaneously.
This work was supported by JSPS KAKENHI Grant Number JP20J20188.
To understand the volcanic eruption dynamics in detail, it is important to know the temperature (T) change of magma as it rises the conduit. Among multiple causes, the contribution of vesiculation (vesi.) and crystallization (cryst.) seems to be significant in the central part of the conduit. The latent heat of vesi. and the mechanical work of bubble expansion cool the system, while the latent heat of cryst. heats the system, thus they work to cancel each other out. This is why many previous studies assumed that the magma is isothermal during decompression. However, there is no evidence that each amount is equivalent.
[Thermodynamic estimation of the water dissolution heat into rhyolitic melt]
Sahagian and Proussevitch (1996) [SP96] estimated the total dissolution heat thermodynamically from the water solubility in albite melt, but the calculation process was incorrect (Zhang, 1999 [Z99]). Z99 proposed a method to estimate the dissolution heat of the first reaction from the Gibbs-Helmholtz equation, but he gave up the practical calculation due to the lack of solubility data at low-P and the unreliability of the equilibrium constant of the second reaction at high-P.
In this study, we assumed that these problems were solved by Liu et al. (2005) and by Nowak and Behrens (2001), respectively, and the dissolution heat of the first reaction was determined using the method of Z99 in the range of 700-1200°C, 100-300 MPa for the Wada Pass obsidian glass composition (Fig. 1). Due to the combination of two dissolution reactions, the T-dependence of the total dissolution heat is reversed between low and high-P. The total dissolution heat approaches zero at higher T and P, which can be interpreted as silicate and water approaching the supercritical state where they mix with zero dissolution heat.
[Numerical calculations on temperature drop of rhyolitic melt by decompression vesiculation]
Next, the differential equation describing the T drop due to equilibrium decompression vesi. of rhyolitic melt, modified from SP96, was calculated numerically. Adiabatic reversible process and the closed system degassing were assumed. The calculations were terminated when the volume fraction of vapor reaches 80%. In Fig. 2, the left, middle, and right columns show the total T drop, in it the effects of latent heat and expansion, respectively. In SP96, the initial T-dependence of the T drop was not taken into account because the value of the exsolution heat at the initial T was assumed to be maintained during decompression. In contrast, in this study, the final T drop has a slight dependence on the initial T because the value of the exsolution heat was calculated sequentially with the T-P change. Compared with SP96, the effect of expansion was not so different, but the effect of latent heat was more than twice as large, and the total T drop could be up to 80°C or more.
[Implications for natural systems]
These calculations suggest that the increase of melt viscosity during decompression vesi. of rhyolitic melts may be due not only to a decrease of water content in melt but also to the decrease of melt T. This may lead to a faster increase in viscosity of magma ascending the conduit than the conventional case where the magma is isothermal, also to a deeper disruption depth or a smaller strain rate for disruption of magma. The temperature drop due to vesi. may also be responsible for part of the effective undercooling required for the microlite cryst. mechanism (Cashman and Blundy, 2000). In order to evaluate the contribution of vesi. to the temperature change in a cryst.-prone melt, such as andesitic melt, where it has already been pointed out that the latent heat of cryst. can increase the temperature by about 100°C (Blandy and Cashman, 2006), it is necessary to solve for the temperature change due to vesi. and cryst. simultaneously.
This work was supported by JSPS KAKENHI Grant Number JP20J20188.