An experimentally-validated numerical model of diffusion and speciation of water in rhyolitic silicate melt

Abstract

The diffusion of water through silicate melts is a key process in volcanic systems. Diffusion controls the growth of the bubbles that drive volcanic eruptions and determines the evolution of the spatial distribution of dissolved water during and after magma mingling, crystal growth, fracturing and fragmentation, and welding of pyroclasts. Accurate models for water diffusion are therefore essential for forward modelling of eruptive behaviour, and for inverse modelling to reconstruct eruptive and post-eruptive history from the spatial distribution of water in eruptive products. Existing models do not include the kinetics of the homogeneous species reaction that interconverts molecular () and hydroxyl () water; reaction kinetics are important because final species distribution depends on cooling history. Here we develop a flexible 1D numerical model for diffusion and speciation of water in silicate melts. We validate the model against FTIR transects of the spatial distribution of molecular, hydroxyl, and total water across diffusion-couple experiments of haplogranite composition, run at 800–1200°C and 5 kbar. We adopt a stepwise approach to analysing and modelling the data. First, we use the analytical Sauer-Freise method to determine the effective diffusivity of total water as a function of dissolved water concentration and temperature for each experiment and find that the dependence of on is linear for wt.% and exponential for wt.%. Second, we develop a 1D numerical forward model, using the method of lines, to determine a piece-wise function for that is globally-minimized against the entire experimental dataset. Third, we extend this numerical model to account for speciation of water and determine globally-minimized functions for diffusivity of molecular water and the equilibrium constant for the speciation reaction. Our approach includes three key novelties: 1) functions for diffusivities of and , and the speciation reaction, are minimized simultaneously against a large experimental dataset, covering a wide range of water concentration ( wt.%) and temperature (), such that the resulting functions are both mutually-consistent and broadly applicable; 2) the minimization allows rigorous and robust analysis of uncertainties such that the accuracy of the functions is quantified; 3) the model can be straightforwardly used to determine functions for diffusivity and speciation for other melt compositions pending suitable diffusion-couple experiments. The modelling approach is suitable for both forward and inverse modelling of diffusion processes in silicate melts; the model is available as a Matlab script from the electronic supplementary material.