Solubility behavior of alkali aluminosilicate components in aqueous fluids and silicate melts at high pressure and temperature

The solubility behavior of K₂O, Na₂O, Al₂O₃, and SiO₂ in silicate-saturated aqueous fluid and coexisting H₂O-saturated silicate melts in the systems K₂O-Al₂O₃-SiO₂-H₂O and Na₂O-Al₂O₃-SiO₂-H₂O has been examined in the 1- to 2-GPa pressure range at 1100°C. Glasses of Na- and K-tetrasilicate compositions with 0, 3, and 6 mol% Al₂O₃ were used as starting materials. In both systems, the oxides dissolve incongruently in aqueous fluid and silicate melt. When recalculated to an anhydrous basis, the aqueous fluids are enriched in alkalis and depleted in silica and alumina relative to their proportions in the starting materials. The extent of incongruency is more pronounced in the Na₂O-Al₂O₃-SiO₂-H₂O system than in the K₂O-Al₂O₃-SiO₂-H₂O system.The partition coefficients of the oxides, D_oxide^fluid/melt, are linear and positive functions of the oxide concentration in the fluid for each composition. There is a slight dependence of the partition coefficients on bulk composition. No effect of pressure could be discerned. For alkali metals, the fluid/melt partition coefficients range from 0.06 to 0.8. For Al₂O₃ this range is 0.01 to 0.2, and for SiO₂, it is 0.01 to 0.32. For all compositions, D_K2O^fluid/melt∼D_Na2O^fluid/melt>D_SiO2^fluid/melt>D_Al2O3^fluid/melt for the same oxide concentration in the fluid. D_K2O^fluid/melt, D_Na2O^fluid/melt, and D_SiO2^fluid/melt correlate negatively with the Al₂O₃ content of the systems. This correlation is consistent with a solubility model of alkalis that involve associated KOH°, NaOH°, silicate, and aluminate complexes.     

A possible effect of melt structure on the Mg-Fe partitioning between olivine and melt

Partitioning of Mg and Fe²⁺ between olivine and mafic melts has been determined experimentally for eight different synthetic compositions in the temperature range between 1335 and 1425°C at 0.1 MPa pressure and at fo₂ ∼1 log unit below the quartz-fayalite-magnetite buffer. The partition coefficient [K_D = (Fe²⁺/Mg)^ol/(Fe²⁺/Mg)^melt] increases from 0.25 to 0.34 with increasing depolymerization of melt (NBO/T of melt from 0.25-1.2), and then decreases with further depolymerization of melt (NBO/T from 1.2-2.8). These variations are similar to those observed in natural basalt-peridotite systems. In particular, the variation in NBO/T ranges for basaltic-picritic melts (0.4-1.5) is nearly identical to that obtained in the present experiments. Because the present experiments were carried out at constant pressure (0.1 MPa) and in a relatively small temperature range (90°C), the observed variations of Mg and Fe²⁺ partitioning between olivine and melt must depend primarily on the composition or structure of melt. Such variations of K_D may depend on the relative proportions of four-, five-, and six-coordinated Mg²⁺ and Fe²⁺ in melt as a function of degree of NBO/T.     

Non-hydrostatic pressure in σ-coordinate ocean models

Numerical ocean modelling is computationally very demanding. Traditionally, the hydrostatic approximation has been applied to reduce the computational burden. This approximation is valid in large scale studies with coarse grid resolution. With faster computers and gradually smaller grid sizes, we may expect that more studies will be performed with non-hydrostatic ocean models. In recent papers several methods for including non-hydrostatic pressure in σ-coordinate models have been suggested. In this paper the sensitivity of the non-hydrostatic pressure field, the velocity fields, and the density fields to changes in the method for computing non-hydrostatic pressure in σ-coordinate ocean models is addressed.The first test case used involves the propagation and breaking of an internal wave at an incline in a tank. The other test case concerns tidally driven flow over a sill in a stratified fjord. The results from our numerical exercises suggest that the velocity and density fields are very robust to the model choices investigated here. The differences between the model results are of the same order as the uncertainty due to the internal pressure gradient error, and they are smaller than an estimate of the uncertainty due to subgrid scale closure.     

On the computation of reliable formal uncertainties in the densification of GPS-levelling networks by least-squares collocation

A realization of a height system covering the south of Norway has been performed, based on least-squares collocation applied to differences between geometric and gravimetric quasigeoid heights, inhomogeneous and isotropic covariance modelling, and without prior information on the error sources of the involved data types. As a result, the derived normal heights were biased by the systematic errors of the GPS-levelling network. The important covariance properties were determined at every location from spatially differenced observations, and made it straightforward to evaluate the uncertainties of the biased height reference. The distribution of predictions followed a Gaussian shape, but extreme realizations were overrepresented.     

Solubility and solution mechanisms of C-O-H volatiles in silicate melt with variable redox conditions and melt composition at upper mantle temperatures and pressures

Solubility and solution mechanisms in silicate melts of oxidized and reduced C-bearing species in the C-O-H system have been determined experimentally at 1.5 GPa and 1400 °C with mass spectrometric, NMR, and Raman spectroscopic methods. The hydrogen fugacity, f_H2, was controlled in the range between that of the iron-wüstite-H₂O (IW) and the magnetite-hematite-H₂O (MH) buffers. The melt polymerization varied between those typical of tholeiitic and andesitic melts.The solubility of oxidized (on the order of 1-2 wt% as C) and reduced carbon (on the order of 0.15-0.35 wt% as C) is positively correlated with the NBO/Si (nonbridging oxygen per silicon) of the melt. At given NBO/Si-value, the solubility of oxidized carbon is 2-4 times greater than under reducing conditions. Oxidized carbon dioxide is dissolved as complexes, whereas the dominant reduced species in melts are CH₃-groups forming bonds with Si⁴⁺ together with molecular CH₄. Formation of complexes results in silicate melt polymerization (decreasing NBO/Si), whereas solution of reduced carbon results in depolymerization of melts (increasing NBO/Si).Redox melting in the Earth’s interior has been explained with the aid of the different solution mechanisms of oxidized and reduced carbon in silicate melts. Further, effects of oxidized and reduced carbon on melt viscosity and on element partitioning between melts and minerals have been evaluated from relationships between melt polymerization and dissolved carbon combined with existing experimental data that link melt properties and melt polymerization. With total carbon contents in the melts on the order of several mol%, mineral/melt element partition coefficients and melt viscosity can change by several tens to several hundred percent with variable redox conditions in the range of the Earth’s deep crust and upper mantle.     

Monotonicity for MPFA methods on triangular grids

Flow in a porous medium can be described by a set of non-linear partial differential equations. The pressure variable satisfies a maximum principle, which guarantees that the solution will have no oscillations. A discretisation of the pressure equation should preserve this monotonicity property. Whether a numerical method is monotone will depend both on the medium and on the grid. We study monotonicity of Multi-point Flux Approximation methods on triangular grids. We derive necessary conditions for monotonicity on uniform grids. Further, we study the robustness of the methods on rough grids, and quantify the violations of the maximum principle. These investigations are done for single phase flow, however, they are supported by two-phase simulations.     

Heterogeneity preserving upscaling for heat transport in fractured geothermal reservoirs

In simulation of fluid injection in fractured geothermal reservoirs, the characteristics of the physical processes are severely affected by the local occurence of connected fractures. To resolve these structurally dominated processes, there is a need to develop discretization strategies that also limit computational effort. In this paper, we present an upscaling methodology for geothermal heat transport with fractures represented explicitly in the computational grid. The heat transport is modeled by an advection-conduction equation for the temperature, and solved on a highly irregular coarse grid that preserves the fracture heterogeneity. The upscaling is based on different strategies for the advective term and the conductive term. The coarse scale advective term is constructed from sums of fine scale fluxes, whereas the coarse scale conductive term is constructed based on numerically computed basis functions. The method naturally incorporates the coupling between solution variables in the matrix and in the fractures, respectively, via the discretization. In this way, explicit transfer terms that couple fracture and matrix solution variables are avoided. Numerical results show that the upscaling methodology performs well, in particular for large upscaling ratios, and that it is applicable also to highly complex fracture networks.     

Solution behavior of reduced COH volatiles in silicate melts at high pressure and temperature

The solubility and solution mechanisms of reduced COH volatiles in Na₂OSiO₂ melts in equilibrium with a (H₂ + CH₄) fluid at the hydrogen fugacity defined by the iron-wüstite + H₂O buffer [f_H2(IW)] have been determined as a function of pressure (1-2.5 GPa) and silicate melt polymerization (NBO/Si: nonbridging oxygen per silicon) at 1400 °C. The solubility, calculated as CH₄, increases from ∼0.2 wt% to ∼0.5 wt% in the melt NBO/Si-range ∼0.4 to ∼1.0. The solubility is not significantly pressure-dependent, probably because f_H2(IW) in the 1-2.5 GPa range does not vary greatly with pressure. Carbon isotope fractionation between methane-saturated melts and (H₂ + CH₄) fluid varied by ∼14‰ in the NBO/Si-range of these melts.The (C..H) and (O..H) speciation in the quenched melts was determined with Raman and ¹H MAS NMR spectroscopy. The dominant (C..H)-bearing complexes are molecular methane, CH₄, and a complex or functional group that includes entities with CCH bonding. Minor abundance of complexes that include SiOCH₃ bonding is tentatively identified in some melts. There is no spectroscopic evidence for SiC or SiCH₃. Raman spectra indicate silicate melt depolymerization (increasing NBO/Si). The [CH₄/CCH]^melt abundance ratio is positively correlated with NBO/Si, which is interpreted to suggest that the (CCH)-containing structural entity is bonded to the silicate melt network structure via its nonbridging oxygen. The ∼14‰ carbon isotope fractionation change between fluid and melt is because of the speciation changes of carbon in the melt.