The behavior of noble gases in silicate liquids: Solution,diffusion, bubbles and surface effects,with applications to natural samples

Solubilities of noble gases in five natural silicate liquids as a function of temperature and partial pressure at 1 atm total pressure were determined and diffusion coefficients of the noble gases were measured in a tholeiite basalt at 1350°C. Solubilities of noble gases in silicate liquids obey Henry's law and are a strong function of composition and/or physical properties of the liquids. Solubility is greatest in less dense, more silica-rich liquids. Solubility is highest for the light gases and is related to the radius of the gas atom according to K_i = aexp (−br²_i). Temperature dependence of solubility is weak, but in general solubility increases with increasing temperature yielding positive enthalpies of solution. Diffusion coefficients in a basalt liquid at 1350°C show more or less the same linear relationship with r² as solubility and are larger than what would be expected from extrapolation of values determined at lower temperatures. A large percentage of samples of andesite composition had bubbles that contained gas which was fractionated from the gas of the experiment. Concentrations of noble gases in samples equilibrated on Pt wire loops correlate with the surface/volume ratio, suggesting that surfaces of silicate liquids can accommodate more noble gases than the liquid proper. Solubility fractionation is a valid process to account for certain patterns in marine basalts. The density of silicate liquids appears to be a good predictor of noble gas solubility in these liquids.     

A first-principles study of helium diffusion in quartz and coesite under high pressure up to 12GPa

Helium diffusion in mantle minerals is crucial for understanding mantle structure and the dynamic processes of Earth's degassing.In this paper,we report helium incorporation and the mechanism of its diffusion in perfect crystals of quartz and coesite.The diffusion pathways,activation energies(Ea),and frequency factors of helium under ambient and high pressure conditions were calculated using Density Functional Theory(DFT)and the climbing image nudged elastic band(CI-NEB)method.The calculated diffusive coefficients of He in the quartz in different orientations are:D[100]=1.24×10^?6exp.(?26.83 kJ/mol/RT)m²/s D[010]=1.11×10^?6exp.(?31.60 kJ/mol/RT)m²/s.and in the coesite:D[100]=3.00×10^?7exp.(?33.79 kJ/mol/RT)m²/s D[001]=2.21×10^?6exp.(?18.33 kJ/mol/RT)m²/s.The calculated results indicate that diffusivity of helium is anisotropic in both quartz and coesite and that the degree of anisotropy is much more pronounced in coesite.Helium diffusion behavior in coesite under high pressures was investigated.The activation energies increased with pressure:Ea[100]increased from 33.79 kJ/mol to 58.36 kJ/mol,and Ea[001]increased from 18.33 kJ/mol to 48.87 kJ/mol as pressure increased from0 GPa to 12 GPa.Our calculations showed that helium is not be quantitatively retained in silica at typical surface temperatures on Earth,which is consistent with the findings from previous studies.These results have implications for discussion of the Earth's mantle evolution and for recognition thermal histories of ultra-high pressure(UHP)metamorphic terranes.     

复杂3D瞬变电磁场FDTD模拟中需要解决的问题

为了实现缓变瞬态电磁场的时域有限差分(FDTD)模拟,引入了虚拟位移电流,使FDTD随时间步的递推能够进行。在以往较简单模型的计算中,利用时域瞬变场传播需要时间的性质,可将激励源化为初始条件代入,但是对于复杂3D模型,原有的方法不再适用,应当重新考虑源和边界条件的处理方法。由于实际源带有“斜坡”,故可采取将激励源模拟注入的方式;地下边界根据电磁波在导电媒质中快速衰减的特性设定,将改进的完全匹配层用于空中边界。分析表明,对于由空中和地下区域非均匀网格离散引起的时间稳定性问题,交替方向隐式FDTD是可行的解决办法。      

Rare earth element diffusion in diopside: influence of temperature, pressure, and ionic radius, and an elastic model for diffusion in silicates

Volume diffusion rates for five rare earth elements (La, Ce, Nd, Dy, and Yb) have been measured in single crystals of natural diopside at pressures of 0.1 MPa to 2.5 GPa and temperatures of 1,050 to1,450 °C. Polished, pre-annealed crystals were coated with a thin film of rare earth element oxides, then held at constant temperature and pressure for times ranging from 20 to 882 h. Diffusion profiles in quenched samples were measured by SIMS (secondary ion mass spectrometry) depth profiling. At 1 atm pressure, with the oxygen fugacity controlled near the quartz-fayalite-magnetite buffer, the following Arrhenius relations were obtained for diffusion normal to (001) (diffusion coefficient D in m²/s): log₁₀D_Yb=(-4.64ǂ.42)-(411ᆠ kJ/mol/2.303RT); log₁₀D_Dy=(-3.31ǃ.44)-(461ᆽ kJ/mol/2.303RT); log₁₀D_Nd=(-2.95DŽ.64)-(496ᇡ kJ/mol/2.303RT); log₁₀D_Ce=(-4.10ǃ.08)-(463ᆳ kJ/mol/2.303RT); log₁₀D_Lu=(-4.22DŽ.66)-(466ᇢ kJ/mol/2.303RT). Diffusion rates decrease significantly with increasing ionic radius, with La a factor of ~35 slower than Yb. The relationship between diffusivity and ionic radius is consistent with a model in which elastic strain plays a critical role in governing the motion of an ion through the crystal lattice. Activation volumes for Yb and Ce diffusion, at constant temperature and oxygen fugacity, are 9.0DŽ.0 cm³/mol and 8.9Dž.2 cm³/mol, respectively, corresponding to an order of magnitude decrease in diffusivity as pressure is increased from 0 to 3 GPa at 1,200 °C. Diffusion of Nd is such that grain-scale isotopic equilibrium in the mantle can be achieved in ~1 My under conditions near the peridotite solidus (~1,450 °C at 2.5 GPa). The equilibration time is much longer under P, T conditions of the lithospheric mantle or at the eclogite solidus (~1 Gy at 1.5 GPa and 1,150 °C). Because of the relatively strong decrease in diffusivity with pressure (two orders of magnitude between 2.5 and 15 GPa along an adiabatic temperature gradient), Nd transport in clinopyroxene will be effectively frozen at pressures approaching the transition zone, on time scales less than 100 My. Rare earth element diffusion rates are slow enough that significant disequilibrium uptake of REE by growing clinopyroxene phenocrysts may be preserved under natural conditions of basalt crystallization. The relative abundances and spatial distributions of REE in such crystals may provide a sensitive record of the cooling and crystallization history of the host lava.     

软煤夹层水射流层状卸压增透抽采瓦斯数值模拟及试验

水力冲孔是煤层瓦斯增透抽采的主要技术措施,其主要以出煤量考察卸压效果,但是也存在出煤量大、卸压不均一、应力易集中等问题。因此,提出软煤夹层水射流层状卸压增透抽采瓦斯技术,考虑瓦斯压力压缩和煤基质吸附瓦斯膨胀对本体变形的影响,建立应力场、裂隙场、渗流场耦合条件下的多物理场理论模型,并结合COMSOL数值模拟软件对软煤夹层水射流分支数、卸压影响范围内煤体的瓦斯压力和瓦斯含量变化规律进行了研究。研究表明：当水射流分支长半轴为2 m,短半轴为0.22 m时,水射流分支数为6个时较为合理;在相同出煤率情况下,相同时间内瓦斯压力和含量均随着与钻孔距离的增加而减小,抽采180 d,水射流层状卸压有效抽采半径约为常规水力冲孔有效抽采半径的2.14倍,且在有效影响范围2 m时,水射流层状卸压瓦斯含量降低量为7 m³/t,而常规水力冲孔瓦斯含量降低量为4.1 m³/t,水射流层状卸压瓦斯降低量为常规水力冲孔的1.71倍;在新义煤矿现场试验中发现,当水射流层状卸压出煤率为常规冲孔出煤率的0.29~0.71倍,抽采较高浓度瓦斯时长仍是常规水力冲孔的2倍。软煤夹层水射流层状卸压增透抽采瓦斯技术的提出,对未来煤矿井下软煤夹层水力冲孔技术的发展有着重要的意义,为井下瓦斯的治理提供了新的方法和方向。     

Extreme pressure due to expanded cylindrical and spherical cavity in a limitless medium: applications in soil mechanics

The extreme net pressure resulting from an expansion in a cylindrical or spherical cavity within a limitless medium is studied. Performing the static and kinematic approaches of yield design theory, analytical solutions of the extreme net pressure are established for cohesive–frictional as well as for purely cohesive medium. In the case of a cylindrical cavity, the identification between the analytical extreme net pressure and limit net pressure leads to the prediction of shear strength characteristics of soil. As useful result, in soil mechanics, the assessment of correlations using pressuremeter data has been discussed. Also, some assumptions for designing foundations, from pressuremeter data, have been highlighted.     

A scalable multistage linear solver for reservoir models with multisegment wells

Wellbore flow and interactions between wells and the reservoir can be complex. Accurate modeling of these behaviors is especially important for multilateral and other advanced wells. This paper describes a new scalable linear solver for flow simulation of detailed reservoir models with advanced wells and well groups. A general purpose research simulator serves as the computational platform, in which a multisegment well (MsWell) model is used to describe wellbore flow. In the MsWell model, the wellbore is discretized into a number of segments. Hence, the MsWell model adds a large number of equations and unknowns, which are fully coupled to the reservoir model. Operating constraints on groups of wells add one more level of complexity to the system. The new linear solver is a generalized two-stage constrained pressure residual preconditioner. A global pressure system is obtained algebraically in the first stage. The system represents the pressure coupling between the reservoir and wells accurately. The well groups are disaggregated into individual multisegment wells, which then are further reduced to a standard well-like form. The two-stage scheme serves as the inner loop of a generalized minimum residual solver. Algebraic multigrid is used to compute the first-stage pressure solution; a special block-based incomplete lower–upper preconditioner is used for the second stage. We demonstrate the superior performance of this new solver compared with state-of-the-art methods using a variety of highly detailed reservoir models with complex wells and well groups.     

Neodymium diffusion in orthopyroxene: Experimental studies and applications to geological and planetary problems

We have determined the Nd³⁺ diffusion kinetics in natural enstatite crystals as a function of temperature, f(O₂) and crystallographic direction at 1 bar pressure and applied these data to several terrestrial and planetary problems. The diffusion is found to be anisotropic with the diffusion parallel to the c-axial direction being significantly greater than that parallel to a- and b-axis. Also, D(//a) is likely to be somewhat greater than D(//b). Diffusion experiments parallel to the b-axial direction as a function of f(O₂) do not show a significant dependence of D(Nd³⁺) on f(O₂) within the range defined by the IW buffer and 1.5 log unit above the WM buffer. The observed diffusion anisotropy and weak f(O₂) effect on D(Nd³⁺) may be understood by considering the crystal structure of enstatite and the likely diffusion pathways. Using the experimental data for D(Nd³⁺), we calculated the closure temperature of the Sm-Nd geochronological system in enstatite during cooling as a function of cooling rate, grain size and geometry, initial (peak) temperature and diffusion direction. We have also evaluated the approximate domain of validity of closure temperatures calculated on the basis of an infinite plane sheet model for finite plane sheets showing anisotropic diffusion. These results provide a quantitative framework for the interpretation of Sm-Nd mineral ages of orthopyroxene in planetary samples. We discuss the implications of our experimental data to the problems of melting and subsolidus cooling of mantle rocks, and the resetting of Sm-Nd mineral ages in mesosiderites. It is found that a cooling model proposed earlier [Ganguly J., Yang H., Ghose S., 1994. Thermal history of mesosiderites: Quantitative constraints from compositional zoning and Fe-Mg ordering in orthopyroxene. Geochim. Cosmochim. Acta 58, 2711-2723] could lead to the observed ∼90 Ma difference between the U-Pb age and Sm-Nd mineral age for mesosiderites, thus obviating the need for a model of resetting of the Sm-Nd mineral age by an “impulsive disturbance” [Prinzhoffer A, Papanastassiou D.A, Wasserburg G.J., 1992. Samarium-neodymium evolution of meteorites. Geochim. Cosmochim. Acta 56, 797-815].     

An analytical model for chemical diffusion in layered contaminated sediment systems with bioreactive caps

An analytical model for contaminant transport in multilayered capped contaminated sediments including the degradation of organic contaminant is presented. The effect of benthic boundary layer was treated as a Robin-type boundary condition. The results of the proposed analytical model agree well with experimental data. The biodegradation of contaminant in bioturbation layer shows a significant influence on the flux at the surface of system. The maximum flux for the case with t_1/2,bio = 0.07 year can be 4.5 times less than that of the case without considering the effect of biodegradation. The thickness of bioturbation layer has a significant effect on the performance of the capped contaminated sediment. The maximum flux for the case with l_bio = 15 cm can be 17 times larger than that of the case without bioturbation layer. This may be because the effective diffusion coefficient of sand cap can be 28 times lower than D_bio. The mass transfer coefficient should be considered for the design of the capping system as the contaminant concentration at the top of system for the case with k_bl = 2.5 × 10⁻⁵ cm/s can be 13 times greater than that of the case with k_bl = 10⁻⁴ cm/s. The proposed analytical model can be used for verification of complicated numerical methods, evaluation of experimental data, and design of the capping contaminated sediment systems with reactive cap layers.     

A model for gas pressure in layered landfills with horizontal gas collection systems

The recovery and emission of landfill gas (LFG) is an important topic in landfill management. To produce an effective engineering design for an LFG collection system, designers must understand the migration of gas from the waste body to horizontal extraction wells. This paper develops a two-dimensional analytical solution to enable the study of the gas pressure distribution, well pressure and recovery efficiency in layered landfills with horizontal wells. A horizontal layered structure is used to accommodate the non-homogeneity of various municipal solid waste (MSW) aspects with respect to depth, including gas generation, permeability and temperature. The governing equations, subject to boundary and continuity conditions, are solved by using separation of variables and double finite integral transforms. The solution was verified against another analytical solution and a numerical simulation. Subsequently, a sensitivity analysis of single-well model parameters is performed to optimize a double-well system. The results show that a landfill with horizontal collection systems cannot be assumed to be one dimensional with increasing well spacing. Additionally, both the operational vacuum and maximum gas pressure can be reduced through the design of a double- or multiple-well system. Therefore, the proposed solution can be used for the verification of more complex models and the preliminary design of a horizontal well system.     

Anisotropic diffusion in a finite cylinder, with geochemical applications

Atomic diffusion in minerals may not be well represented by solutions to the diffusion equation for a sphere with a single-valued diffusivity, either because they have platy or elongated habits or because the energetics of diffusion is sensitive to crystallographic direction. In many cases, a cylinder having characteristic radial and axial diffusivities is arguably a better model, but rigorous solutions to the anisotropic diffusion equation for a finite cylinder have not been available. Here we develop general analytical solutions that capture both the internal distribution of diffusant as a function of time, C(r, z, t), and the fraction, F, of diffusant lost during a specified thermal history. These solutions are shown to conform with existing analytical expressions for limiting cases of diffusion in a slab or infinite cylinder. We present, in addition, a simple numerical (finite difference) approach that not only reproduces the results of our analytical expressions but also enables us to move beyond some of the limitations of the equations to simulate complex natural scenarios involving non-zero and time-dependent boundary conditions, arbitrary initial distribution of diffusant within the cylinder and simultaneous diffusion and radiogenic ingrowth. The complementary nature of the two approaches is emphasized and several illustrative applications to ‘real-world’ problems are described, including noble-gas thermochronometry and halogen-hydroxyl interdiffusion in apatite.     

A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains

Numerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical solutions for one‐dimensional axisymmetric diffusion problems. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global ABCs are simplified to local ABCs to significantly enhance the computational efficiency. The proposed local ABCs are implemented in a finite element computer program so that the solutions to various seepage problems can be calculated. The proposed approach is first verified by the computation of a one‐dimensional radial flow problem and then tentatively applied to more general two‐dimensional cylindrical problems and planar problems. The solutions obtained using the local ABCs are compared with those obtained using a large element mesh and using a previously proposed local boundary. This comparison demonstrates the satisfactory performance and obvious superiority of the newly established boundary to the other local boundary. Copyright © 2017 John Wiley & Sons, Ltd.     

Large deformation dynamic analysis of saturated porous media with applications to penetration problems

This paper outlines the development as well as implementation of a numerical procedure for coupled finite element analysis of dynamic problems in geomechanics, particularly those involving large deformations and soil-structure interaction. The procedure is based on Biot’s theory for the dynamic behaviour of saturated porous media. The nonlinear behaviour of the solid phase of the soil is represented by either the Mohr Coulomb or Modified Cam Clay material model. The interface between soil and structure is modelled by the so-called node-to-segment contact method. The contact algorithm uses a penalty approach to enforce constraints and to prevent rigid body interpenetration. Moreover, the contact algorithm utilises a smooth discretisation of the contact surfaces to decrease numerical oscillations. An Arbitrary Lagrangian–Eulerian (ALE) scheme preserves the quality and topology of the finite element mesh throughout the numerical simulation. The generalised-α method is used to integrate the governing equations of motion in the time domain. Some aspects of the numerical procedure are validated by solving two benchmark problems. Subsequently, dynamic soil behaviour including the development of excess pore-water pressure due to the fast installation of a single pile and the penetration of a free falling torpedo anchor are studied. The numerical results indicate the robustness and applicability of the proposed method. Typical distributions of the predicted excess pore-water pressures generated due to the dynamic penetration of an object into a saturated soil are presented, revealing higher magnitudes of pore pressure at the face of the penetrometer and lower values along the shaft. A smooth discretisation of the contact interface between soil and structure is found to be a crucial factor to avoid severe oscillations in the predicted dynamic response of the soil.     

Preconditioned IDR(s) iterative solver for non‐symmetric linear system associated with FEM analysis of shallow foundation

Non‐associated flow rule is essential when the popular Mohr–Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes non‐symmetric when this non‐associated flow rule is applied. Efficient solution of this large‐scale non‐symmetric linear system is of practical importance. The standard Krylov solver for a non‐symmetric solver is Bi‐CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s = 6) is more efficient than Bi‐CGSTAB when the preconditioner is the incomplete factorization with zero fill‐in of global stiffness matrix K_ep (ILU(0)‐K_ep). Iteration time is reduced by 40% by using IDR(s = 6) with ILU(0)‐K_ep. To further reduce computational cost, the global stiffness matrix K_ep is divided into two parts. The first part is the linear elastic stiffness matrix K_e, which is formed only once at the beginning of solution step. The second part is a low‐rank matrix Δ, which is re‐formed at each Newton–Raphson iteration. Numerical studies show that IDR(s = 6) with this ILU(0)‐K_e preconditioner is more time effective than IDR(s = 6) with ILU(0)‐K_ep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used. Copyright © 2013 John Wiley & Sons, Ltd.     

Coupled CaAl-NaSi diffusion in plagioclase feldspar: Experiments and applications to cooling rate speedometry

The rate of CaAl-NaSi interdiffusion in plagioclase feldspar was determined under 1 atm anhydrous conditions over the temperature range 1400° to 1000°C in calcic plagioclase (An_80?81) by homogenizing coherent exsolution lamellae. The dependence of the average interdiffusion coefficient on temperature is given by the expression: $\text{D}\text{?}\text{= 10.99 (}\text{cm}{}^2\text{/sec) exp}\text{(?123.4(}\text{kcal/mol}\text{)/RT), (T}$ in °K). This value is for diffusion perpendicular to the (03 1?) interface of the lamellae. CaAl-NaSi interdiffusion is 4 to 5 orders of magnitude slower than oxygen diffusion in the temperature range 1400° to 1200°C and possibly 10 orders of magnitude slower at subsolidus temperatures.The large differences in diffusion rates explain the apparent contradiction posed by the plagioclases of large layered intrusions (e.g., the Skaergaard), which retain delicate Ca, Na compositional zoning profiles on the micron scale, but have undergone complete oxygen isotopic exchange with heated meteoric groundwater from the surrounding wall rocks. CaAl-NaSi diffusion is slow, the closure temperature is high (within the solidus-liquidus interval), and Ca-Na zoning is preserved. Oxygen diffusion is faster, the closure temperature is lower (350°-400°C) and the feldspars exchange oxygen with the low-temperature hydrothermal fluids.The complex micron-scale oscillatory zones in plagioclase can also be used as cooling rate speedometers for volcanic and plutonic plagioclase. Cooling histories typical of large mafic intrusions (e.g. the Stillwater) are slow, begin at high initial temperatures (1200°C) and result in homogenization of oscillatory zones on the scale of 10 microns. The oscillatory zones found in the plagioclase of granodioritic plutons are preserved because cooling is initiated at a lower temperature (1000°C) limiting diffusion to submicron length scales despite the slow cooling rate of the intrusion.     

Effects of pressure on aqueous chemical equilibria at subzero temperatures with applications to Europa

Pressure plays a critical role in controlling aqueous geochemical processes in deep oceans and deep ice. The putative ocean of Europa could have pressures of 1200 bars or higher on the seafloor, a pressure not dissimilar to the deepest ocean basin on Earth (the Mariana Trench at 1100 bars of pressure). At such high pressures, chemical thermodynamic relations need to explicitly consider pressure. A number of papers have addressed the role of pressure on equilibrium constants, activity coefficients, and the activity of water. None of these models deal, however, with processes at subzero temperatures, which may be important in cold environments on Earth and other planetary bodies. The objectives of this work were to (1) incorporate a pressure dependence into an existing geochemical model parameterized for subzero temperatures (FREZCHEM), (2) validate the model, and (3) simulate pressure-dependent processes on Europa. As part of objective 1, we examined two models for quantifying the volumetric properties of liquid water at subzero temperatures: one model is based on the measured properties of supercooled water, and the other model is based on the properties of liquid water in equilibrium with ice.The relative effect of pressure on solution properties falls in the order: equilibrium constants(K) > activity coefficients (γ) > activity of water (a_w). The errors (%) in our model associated with these properties, however, fall in the order: γ > K > a_w. The transposition between K and γ is due to a more accurate model for estimating K than for estimating γ. Only activity coefficients are likely to be significantly in error. However, even in this case, the errors are likely to be only in the range of 2 to 5% up to 1000 bars of pressure. Evidence based on the pressure/temperature melting of ice and salt solution densities argue in favor of the equilibrium water model, which depends on extrapolations, for characterizing the properties of liquid water in electrolyte solutions at subzero temperatures, rather than the supercooled water model. Model-derived estimates of mixed salt solution densities and chemical equilibria as a function of pressure are in reasonably good agreement with experimental measurements.To demonstrate the usefulness of this low-temperature, high-pressure model, we examined two hypothetical cases for Europa. Case 1 dealt with the ice cover of Europa, where we asked the question: How far above the putative ocean in the ice layer could we expect to find thermodynamically stable brine pockets that could serve as habitats for life? For a hypothetical nonconvecting 20 km icy shell, this potential life zone only extends 2.8 km into the icy shell before the eutectic is reached. For the case of a nonconvecting icy shell, the cold surface of Europa precludes stable aqueous phases (habitats for life) anywhere near the surface. Case 2 compared chemical equilibria at 1 bar (based on previous work) with a more realistic 1460 bars of pressure at the base of a 100 km Europan ocean. A pressure of 1460 bars, compared to 1 bar, caused a 12 K decrease in the temperature at which ice first formed and a 11 K increase in the temperature at which MgSO₄·12H₂O first formed. Remarkably, there was only a 1.2 K decrease in the eutectic temperatures between 1 and 1460 bars of pressure. Chemical systems and their response to pressure depend, ultimately, on the volumetric properties of individual constituents, which makes every system response highly individualistic.     

Experimental effects of pressure and fluorine on apatite saturation in mafic magmas, with reference to layered intrusions and massif anorthosites

Apatite is a cumulate phase in the upper parts of some mafic layered intrusions and anorthositic complexes. We investigated the effect of pressure and fluorine on apatite saturation in mafic magmas to better understand under which conditions this mineral crystallizes. Apatite saturation gives information about the formation of silicate rocks, and is of interest in explaining the formation of apatite–oxide-rich rocks (e.g. nelsonites comprising approximately, one-third apatite and two-third Fe–Ti oxide). Two models of formation are proposed for this rock type: crystal fractionation followed by accumulation of apatite and Fe–Ti oxides and liquid immiscibility. New experiments carried out with mafic compositions at 500 MPa confirm that the most important variables on phosphate saturation are SiO₂ and CaO. Fluorine addition leads to apatite saturation at lower SiO₂ and higher CaO concentrations. Comparison of our results with those of previous experimental studies on liquid–liquid immiscibility at upper-to-mid-crustal conditions allows us to investigate the relative importance of apatite saturation versus liquid–liquid immiscibility in the petrogenesis of nelsonites and similar rocks. The liquid line of descent of three natural examples studied (the Sept-Îles intrusive suite, the anorthositic Complex of the Lac-St-Jean and the Skaergaard layered intrusion) do not cross the liquid–liquid immiscibility field before they reach apatite saturation. Thus, the apatite–oxide-rich rock associated with these three intrusive suites are best explained by crystal fractionation followed by accumulation of apatite and Fe–Ti oxides.     

A parallel global-implicit 2-D solver for reactive transport problems in porous media based on a reduction scheme and its application to the MoMaS benchmark problem

In this article, an approach for the efficient numerical solution of multi-species reactive transport problems in porous media is described. The objective of this approach is to reformulate the given system of partial and ordinary differential equations (PDEs, ODEs) and algebraic equations (AEs), describing local equilibrium, in such a way that the couplings and nonlinearities are concentrated in a rather small number of equations, leading to the decoupling of some linear partial differential equations from the nonlinear system. Thus, the system is handled in the spirit of a global implicit approach (one step method) avoiding operator splitting techniques, solved by Newton’s method as the basic algorithmic ingredient. The reduction of the problem size helps to limit the large computational costs of numerical simulations of such problems. If the model contains equilibrium precipitation-dissolution reactions of minerals, then these are considered as complementarity conditions and rewritten as semismooth equations, and the whole nonlinear system is solved by the semismooth Newton method.     

土力学的现状及其数值分析方法中某些问题的讨论

概括性地论述了土力学目前的状况,指出土力学仍然处于半理论、半经验的发展水平。论述了土力学数值分析方法在工程应用中存在的问题,并对如何正确地使用土力学的数值分析方法和改变土力学数值分析在工程应用中的不利状况进行了讨论。另外,就如何改善这种状况提出了一些措施。从这些讨论可以得到以下结论,土力学还处于发展的初期阶段,随着土力学的理论及其数值分析方法的不断发展,以及其使用经验的不断积累,计算土力学在工程实践中将会得到越来越多的应用,它必将成为岩土工程分析中的有力工具。     

H2O diffusion models in rhyolitic melt with new high pressure data

Water diffusion in silicate melts is important for understanding bubble growth in magma, magma degassing and eruption dynamics of volcanos. Previous studies have made significant progress on water diffusion in silicate melts, especially rhyolitic melt. However, the pressure dependence of H₂O diffusion is not constrained satisfactorily. We investigated H₂O diffusion in rhyolitic melt at 0.95–1.9 GPa and 407–1629 °C, and 0.2–5.2 wt.% total water (H₂O_t) content with the diffusion-couple method in a piston-cylinder apparatus. Compared to previous data at 0.1–500 MPa, H₂O diffusivity is smaller at higher pressures, indicating a negative pressure effect. This pressure effect is more pronounced at low temperatures. Assuming H₂O diffusion in rhyolitic melt is controlled by the mobility of molecular H₂O (H₂O_m), the diffusivity of H₂O_m (D_H2Om) at H₂O_t ≤ 7.7 wt.%, 403–1629 °C, and ≤ 1.9 GPa is given by

D_H2Om=D₀exp(aX),