An experimentally-validated numerical model of diffusion and speciation of water in rhyolitic silicate melt
An experimentally-validated numerical model of diffusion and speciation of water in rhyolitic silicate melt
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DOI：
10.1016/j.gca.2020.02.026
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发表时间：
2020-05
影响因子：
5
通讯作者：
J. Coumans;E. Llewellin;M. Humphreys;M. Nowak;R. Brooker;S. Mathias;I. McIntosh
中科院分区：
文献类型：
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作者：
J. Coumans;E. Llewellin;M. Humphreys;M. Nowak;R. Brooker;S. Mathias;I. McIntosh
水通过硅酸盐熔体的扩散是火山系统中的一个关键过程。扩散控制着驱动火山爆发的气泡的生长，并决定了岩浆混合、晶体生长、断裂和破碎以及火山碎屑焊接期间和之后溶解水空间分布的演变。因此，准确的水扩散模型是必不可少的喷发行为的正向建模，并为逆建模重建喷发和喷发后的历史，从空间分布的水在喷发产品。现有的模型不包括动力学的均相物种反应，相互转化分子（H 2 O m）和羟基（OH）水;反应动力学是重要的，因为最终物种分布取决于冷却的历史。在这里，我们开发了一个灵活的一维数值模型的扩散和形态的水在硅酸盐熔体。我们验证了该模型对FTIR断面的分子，羟基，和总水的空间分布在整个扩散耦合实验的单花岗岩组成，在800-1200° C和5千巴。我们采用逐步的方法来分析和建模的数据。首先，我们用分析Sauer-Freise方法确定了每个实验中总水的有效扩散系数DH 2 O t作为溶解水浓度CH 2 O t和温度T的函数，并发现DH 2 O t对CH 2 O t的依赖性在CH 2 O t ≥ 1.8wt.%时是线性的对CH 2 O的反应为指数反应，t = 1.8wt.%。其次，我们开发了一个一维数值正演模型，使用线的方法，以确定一个分段函数DH 2 O t CH 2 O t，T是全球最小化对整个实验数据集。第三，我们扩展这个数值模型，以考虑水的形态和确定全球最小化的功能，分子水扩散系数D H 2 O m C H 2 O t，T和平衡常数K的形态反应。我们的方法包括三个关键的新颖性：（1）对一个大的实验数据集，覆盖了广泛的水浓度范围（0.25≤ CH 2 O t≤ 7 wt.%），同时最小化了H2O t和H2O m的扩散系数和形态反应的函数和温度（800° C≤ T≤ 1200° C），使得所得函数既相互一致又广泛适用;（2）最小化允许对不确定性进行严格和稳健的分析，使得函数的准确性被量化;（3）该模型可以直接用于确定其他熔体组合物的扩散率和形态的函数，等待合适的扩散偶实验。该建模方法适用于硅酸盐熔体中扩散过程的正向和反向建模;该模型可作为电子补充材料的MATLAB脚本提供。
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 (H 2 O m) and hydroxyl (OH) 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 D H 2 O t as a function of dissolved water concentration C H 2 O t and temperature T for each experiment and find that the dependence of D H 2 O t on C H 2 O t is linear for C H 2 O t≲ 1.8 wt.% and exponential for C H 2 O t≳ 1.8 wt.%. Second, we develop a 1D numerical forward model, using the method of lines, to determine a piece-wise function for D H 2 O t C H 2 O t, T 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 D H 2 O m C H 2 O t, T and the equilibrium constant K for the speciation reaction. Our approach includes three key novelties:(1) functions for diffusivities of H 2 O t and H 2 O m, and the speciation reaction, are minimized simultaneously against a large experimental dataset, covering a wide range of water concentration (0.25≤ C H 2 O t≤ 7 wt.%) and temperature (800° C≤ T≤ 1200° C), 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.