地质学中一些比较常用的水的状态方程的评价

<正>本文以水的高精度热力学模型IAPWS-95与Zhang and Duan[1]通过分子动力学模拟所得到的高精度压力-体积-温度(PVT)数据为参考,对一些比较常用的可用于高温、高压的水的状态方程进行了检验、分析和评价。这些方程包括:Holloway[2],Kerrick and Jacobs[3],Halbach and Chatterjee[4],Bowers and Helgeson[5],     

H2O-CH4-H2-CO2-CO-O2在高温、高压和高密度条件下的状态方程

为了计算高温，高压和高密度流体的热力学性质，提出了一个具有19个参数的维里型状态方程，其中参数与温度间的函数关系采用由Sutherland位能函数导出的维里系数近似式。除临界点附近以外，在已报道的pVT数据所覆盖的大部分超临界区域内，该方程均可适用。用该方程对H2O，CH4，H2，CO2，CO和O2等流体pVT关系的计算结果令人满意，其中pVT上限分别为：91-610GPa,1.6-11.0cm^3/mol,4000-5000K。计算体积的平均偏 小于0．8％，最大偏差小于5．4％。     

宽广温压范围内纯流体pVT性质的预测

一个具有 1 9个参数的半经验状态方程 ,可以很容易地转化为关于体积的多项式方程 ,应用起来十分方便。对于气体和超临界流体 ,该方程可以在很宽的温压范围内保持较高的精度。用该方程计算 H2 O、CO2 、CH4、H2 、CO、O2 等流体的 p VT关系 ,结果令人满意。在从常温常压直到 4 0 0 0～ 50 0 0 K和 90～ 60 0 GPa的范围内 ,预测的体积误差为 :平均偏差小于 1 % ,最大偏差小于 6% ,标准偏差小于 1 .5%。     

温度和压强对花岗岩中矿物微观物理力学特性的影响

岩石工程性质取决于岩石中不同矿物的微观特征,本次研究将从微观角度计算北山花岗岩中主要矿物（石英、黑云母和钠长石）的物理性质和力学性质。矿物的微观物理性质使用体积和密度来表征,矿物的微观力学性质使用杨氏模量和泊松比来表征;矿物的初始晶体结构、初始晶胞参数、单晶胞模型和超晶胞模型使用公开数据库获得;矿物晶胞的稳定构象由几何优化方法来实现;使用分子力学模拟,得到了不同矿物稳定构象的微观物理性质参数和微观力学性质参数;使用分子动力学模拟,分析了温度和压强对这些微观物理力学性质参数的影响。结果表明,花岗岩的3种主要矿物中,晶胞体积大小顺序是钠长石、黑云母、石英,晶胞密度大小顺序是黑云母、石英、钠长石;石英的杨氏模量为161.70~168.78GPa、泊松比为0.25,黑云母的杨氏模量为164.85~579.93GPa、泊松比为0.16~0.31,钠长石的杨氏模量为110.72~112.49GPa、泊松比为0.27;压强为0.0001GPa、温度从300K变化到500K时,石英晶胞体积增大0.17%、密度减小0.15%、杨氏模量和泊松比没有明显变化,黑云母晶胞体积增大0.24%、密度减小0.26%、杨氏模量增大140.55%、泊松比减小26.92%,钠长石晶胞体积减小3.76%、密度增大3.91%、杨氏模量增大319.71%、泊松比减小7.41%;温度为298K、压强从0.010GPa变化到0.020GPa时,石英晶胞体积、密度、杨氏模量和泊松比没有明显变化,黑云母晶胞体积和密度没有明显变化、杨氏模量增大53.79%、泊松比减小23.81%,钠长石晶胞体积和密度没有明显变化、杨氏模量减小36.24%、泊松比增大29.41%。研究结果对分析岩石宏观物理力学特性的微观机制具有一定的参考价值。     

非饱和土热力学参数确定的探讨

研究非饱和土热力学的力学性质,必须建立能量守恒方程,表征能量的两个基本物理力学参数（体积比热系数和热传导系数）的确定是求解能量守恒方程的重要因素。对于不同颗粒组成的土体,对其干燥颗粒有效热力学参数进行了分析,对固体、液体和气体三相共存的热力学参数进行了研究,并对计算结果进行了对比分析,在此基础上,提出了较适合计算热传导系数的方法,并将此方法和体积平均法、自洽法及Hashin-Strikman方法进行了比较。经与试验结果对比表明：提出的方法能较好地描述非饱和土的热力学参数特性。     

台湾中西部沉积盆地三维密度结构及其重力异常

台湾中西部沉积盆地是台湾省海陆油气勘探的重点区域。本文利用石油钻井资料和重力观测数据,依据Kriging插值及台湾中国石油公司深度-密度经验公式,计算了该地区沉积地层三维密度及剩余密度结构,并依据三维有限元解泊松方程方法,通过求解重力位计算出三维剩余密度体产生的剩余重力异常。密度结构显示,在0~6km深度范围,自更新统到先中新统的沉积地层大致分为2.0~2.30g/cm3、2.30~2.45g/cm3、2.45~2.60g/cm3、2.60~2.70g/cm3等4个密度层。其中,台中盆地陆缘区中下部2~4km深度存在较大沉积凹陷,凹陷区密度比周围低0.05~0.10g/cm3.重力计算结果表明,本区沉积地层产生的剩余重力异常在-20~+15mGal之间,深部凹陷对应负异常低值圈闭,其形态和量值与实测重力异常一致。      

简化Bishop法的剩余下滑推力计算方法研究

简化Bishop法是评价圆弧形滑动面滑坡稳定性的"严格"方法,计算方法简便、精确,已有相关学者研究了其严格性,但却没有与之相适应的滑坡剩余下滑推力解析法,给滑坡（边坡）的综合治理带来了一定困难。本文从简化Bishop法计算原理出发,考虑坡体自重、外力、水平地震力、滑动面处的孔隙水压力等,利用力多边形法则,得到了两类简化Bishop法剩余下滑推力分析模型,即:Ⅰ型（T_i ≥ 0）和Ⅱ型（T_i < 0）;针对两类模型推导出了第i-1条块的下滑推力,然后,使F_i-1参与到第i条块的力多边形受力模型中,从上往下逐条块计算下滑推力,进而推导出条块i的剩余下滑推力解析计算公式。该解析法与传递系数法隐式解所计算的剩余下滑推力进行比较,总体上呈现出简化Bishop法剩余下滑推力高于传递系数法隐式解,两者的剩余下滑推力差值随着安全储备的增大而减小,且该解析法适用于安全储备要求较高的滑坡（边坡）,该解析法为圆弧形滑动面滑坡（边坡）治理设计提供了一定的理论依据。     

基于Pitzer模型预测Na-K-Ca-Mg-Cl-H2O溶液的密度

天然水体系的体积性质与压力、温度、组成的相关性(PVTx性质)研究在地球化学、盐湖化工等领域有广泛的应用。密度是卤水最基本的体积性质,不仅可以通过实验测定,还可以用理论模型进行预测。建立富钾卤水密度与组成、温度的关联模型有助于认识钾在复杂卤水中的富集、迁移规律。为了构建基于Pitzer离子相互作用模型的卤水密度预测方法,本文用高精度振荡管密度计测定了常压下KCl、CaCl₂纯盐溶液以及最高离子强度为11.8 mol·kg^-1的混合溶液在283~323 K下的密度,用所测得的密度通过Pitzer离子相互作用模型拟合得到多温下Pitzer单电解质参数和Pitzer混合参数。用Pitzer模型参数计算了Na-K-Ca-Mg-Cl-H₂O体系293~313 K的密度,计算密度值与实验值的相对偏差在±0.25%以内,计算的结果整体上要优于文献值,文献在计算中均未考虑Pitzer混合参数项。结果表明,K、Ca、Cl离子间的相互作用对于Na-K-Ca-Mg-Cl-H₂O溶液的密度有显著的影响,本文获得的Pitzer参数反映了这些离子间的相互作用,可用于计算含有K、Ca、Cl离子的复杂卤水密度的预测。     

基于非充分掺混模式的流域来水组成模型

针对如何减小数值求解对流输运方程耗散误差的问题,引进断面计算浓度的概念来计算河段平均浓度,提出了非充分掺混模式的有限控制体积法离散对流输运方程的新算法,据此构建了模拟流域内的水源组成以及不同水源在流域内的时空变化情况的流域来水组成模型。通过数值试验与具体实例验证,结果表明所提出的非充分掺混模式的新算法可有效地提高流域来水模型的计算精度。     

太古宙变化的热力学状态

自太古宙以来,这段时间内再现了40％的地球早期历史。在此期间地球在热力学和岩石学方面正处于演化阶段。该阶段不是以简单的热力学体系为特征。在特定的时间内,因为大洋岩石圈可能组成的地球表层,所以人们可以确立“平均”地球热力学体系用以清楚地反映大洋热力学体系。在整个太古宙,地球平均热力学体系的演化包括:平均地幔温度降低了200K,地表热则降低了2倍,且岩石圈的年龄和厚度(热边界层)增加了1/2。从太古宙末期到现在为止,以上的变化及平均地热体系的变化同时进行,且与平均地热体系之间的偏差总是存在,在地幔对流作用过程中这种偏差和上升流体及下降流体有关,从深部热边界层和岩石圈陆块开始,热柱呈现不稳定上升的趋势。     

http://www.sciencedirect.com/science/article/pii/S1674987111000831

The IAPWS-95 formulation explicit in Helmholtz free energy proposed by Wagner and Proβ(2002) is the best equation of state of water,from which all thermodynamic properties can be obtained over a wide T—p range from 273.16 to 1273 K and from 0 to 1000 MPa with experimental accuracy.This paper reports the applications of the IAPWS-95 formulation in fluid inclusion and mineral-water phase equilibria. A reliable and highly efficient calculation method is presented for the saturated properties of water so that the formulation can be conveniently applied in the study of fluid inclusion,such as calculating homogenization pressures,homogenization densities(or molar volumes),volume fractions and isochores.Meanwhile,the univariant curves of some mineral-dehydration reactions are calculated based on the IAPWS-95 formulation.The computer code of the IAPWS-95 formulation can be obtained from the corresponding author.     

A new cubic equation of state and its applications to the modeling of vapor-liquid equilibria and volumetric properties of natural fluids

A cubic equation of state was developed for both pure systems and mixtures in this study. It has only one empirical constant to be evaluated for each component and two constants for each binary. To test its validity, the saturated properties of 22 pure fluids were calculated with the new equation, as compared with the most frequently used or the most recently published cubic equations. The results indicate that the new equation is superior to the previous cubic equations in the overall performance in vapor pressures and saturated volumes. Its overall average deviation of the saturation pressures from experiments is 0.46%, and the maximum deviation is 3.6%. Its average deviation of the liquid volumes from experiments at the reduced temperatures T_r≤0.95 is 2.80%, and that of vapor volumes is 2.2%. Because of the high accuracy of the new equation for saturation pressures, it can be easily extended to binary mixtures for the prediction of vapor-liquid equilibria (both densities and compositions) with a simple mixing rule, as demonstrated by eight binary systems, including an aqueous mixture.     

A high-pressure neutron diffraction study of the ferroelastic phase transition in RbCaF3

The fluoroperovskite phase RbCaF₃ has been investigated using high-pressure neutron powder diffraction in the pressure range ~0–7.9 GPa at room temperature. It has been found to undergo a first-order high-pressure structural phase transition at ~2.8 GPa from the cubic aristotype phase to a hettotype phase in the tetragonal space group I4/mcm. This transition, which also occurs at ~200 K at ambient pressure, is characterised by a linear phase boundary and a Clapeyron slope of 2.96 × 10^?5 GPa K^?1, which is in excellent agreement with earlier, low-pressure EPR investigations. The bulk modulus of the high-pressure phase (49.1 GPa) is very close to that determined for the low-pressure phase (50.0 GPa), and both are comparable with those determined for the aristotype phases of CsCdF₃, TlCdF₃, RbCdF₃, and KCaF₃. The evolution of the order parameter with pressure is consistent with recent modifications to Landau theory and, in conjunction with polynomial approximations to the pressure dependence of the lattice parameters, permits the pressure variation of the bond lengths and angles to be predicted. On entering the high-pressure phase, the Rb–F bond lengths decrease from their extrapolated values based on a third-order Birch–Murnaghan fit to the aristotype equation of state. By contrast, the Ca–F bond lengths behave atypically by exhibiting an increase from their extrapolated magnitudes, resulting in the volume and the effective bulk modulus of the CaF₆ octahedron being larger than the cubic phase. The bulk moduli for the two component polyhedra in the tetragonal phase are comparable with those determined for the constituent binary fluorides, RbF and CaF₂.     

Hydrostatic compression of γ-Mg2SiO4 to mantle pressures and 700 K: Thermal equation of state and related thermoelastic properties

P-V-T equations of state for the γ phase of Mg₂SiO₄ have been fitted to unit cell volumes measured under simultaneous high pressure (up 30 GPa) and high temperature (up to 700 K) conditions. The measurements were conducted in an externally heated diamond anvil cell using synchrotron x-ray diffraction. Neon was used as a pressure medium to provide a more hydrostatic pressure environment. The P-V-T data include 300 K-isothermal compression to 30 GPa, 700 K-compression to 25 GPa and some additional data in P-T space in the region 15 to 30 GPa and 300 to 700 K. The isothermal bulk modulus and its pressure derivative, determined from the isothermal compression data, are 182(3) GPa and 4.2(0.3) at T=300 K, and 171(4) GPa and 4.4(0.5) at T=700 K. Fitting all the P-V-T data to a high-temperature Murnaghan equation of state yields: K _TO=182(3.0) GPa, K _TO=4.0(0.3), ?K _T /?T)₀=?2.7(0.5)×10^?2 GPa/K and (?² K _T /?P?T)₀=5.5(5.2)×10^?4/K at the ambient condition.     

Equations of state of CaSiO3 Perovskite: a molecular dynamics study

The molar volumes and bulk moduli of CaSiO₃ perovskite are calculated in the temperature range from 300 to 2,800 K and the pressure range from 0 to 143 GPa using molecular dynamics simulations that employ the breathing shell model for oxygen and the quantum correction in addition to the conventional pairwise interatomic potential models. The performance of five equations of state, i.e., the Keane, the generalized-Rydberg, the Holzapfel, the Stacey–Rydberg, and the third-order Birch–Murnaghan equations of state are examined using these data. The third-order Birch–Murnaghan equation of state is found to have a clear tendency to overestimate the bulk modulus at very high pressures. The Stacey–Rydberg equation of state degrades slightly at very high pressures along the low-temperature isotherms. In comparison, the Keane and the Holzapfel equations of state remain accurate in the whole temperature and pressure range considered in the present study. K ₀′ derived from the Holzapfel equation of state also agrees best with that calculated independently from molecular dynamics simulations. The adiabatic bulk moduli of CaSiO₃ perovskite along lower mantle geotherms are further calculated using the Keane and the Mie-Grüneisen–Debye equations of state. They are found to be constantly higher than those of the PREM by ~5%, and also very similar to those of the MgSiO₃ perovskite. Our results support the view that CaSiO₃ perovskite remains invisible in the Earth’s lower mantle.     

Molecular dynamics simulation of the CH4 and CH4-H2O systems up to 10 GPa and 2573 K

Based on our previous study of the intermolecular potential for pure H₂O and the strict evaluation of the competitive potential models for pure CH₄ and the ab initio fitting potential surface across CH₄-H₂O molecules in this study, we carried out more than two thousand molecular dynamics simulations for the PVTx properties of pure CH₄ and the CH₄-H₂O mixtures up to 2573 K and 10 GPa. Comparison of 1941 simulations with experimental PVT data for pure CH₄ shows an average deviation of 0.96% and a maximum deviation of 2.82%. The comparison of the results of 519 simulations of the mixtures with the experimental measurements reveals that the PVTx properties of the CH₄-H₂O mixtures generally agree with the extensive experimental data with an average deviation of 0.83% and 4% in maximum, which is equivalent to the experimental uncertainty. Moreover, the maximum deviation between the experimental data and the simulation results decreases to about 2% as temperature and pressure increase, indicating that the high accuracy of the simulation is well retained in the high temperature and pressure region.After the validation of the simulation method and the intermolecular potential models, we systematically simulated the PVTx properties of this binary system from 673 K and 0.05 GPa to 2573 K and 10 GPa. In order to integrate all the simulation results and the experimental data for the calculation of thermodynamic properties, an equation of state (EOS) is developed for the CH₄-H₂O system covering 673-2573 K and 0.01-10 GPa. Isochores for compositions <4 mol% CH₄ up to 773 K and 600 MPa are also determined in this paper. The program for the EOS can be downloaded from www.geochem-model.org/programs.htm.     

Fluid-bearing and fluid-absent invariant points in the system CaO-MgO-Al2O3-SiO2-CO2-H2O for a greenschist facies assemblage

An outline for a metamorphic grid involving a greenschist facies assemblage is presented in Watts (1973). This grid is derived from a theoretical determination of all possible P-T dependent (solid-solid) reactions and invariant points as well as those in which a fluid, containing CO₂, H₂O and other unspecified components, takes part. The thermodynamic data in Watts (1973) were accidentally calculated at 425° K and not at 425° C. Since 425° K is an unreasonably low temperature for greenschist facies equilibria, these data have been recalculated at 700° K (427° C) and a new topology of fluid-absent (solid-solid) reactions and invariant points in P-T space results, since the slopes of such reactions change under conditions at the higher temperature. The slopes of the fluid-bearing reactions are independent of P, T and remain unchanged. However, for each different P-T grid of solid-solid reactions, a new set of chemographic arrangements is valid for the fluidbearing invariant points. A set of μ_H2O-μ_CO2 diagrams consistent with, and dependent on the new P-T grid is presented.     

Equation of state and pressure-induced structural changes in mirabilite (Na2SO4·10H2O) determined from ab initio density functional theory calculations

We have carried out ab initio calculations using density functional theory to determine the bulk elastic properties of mirabilite, Na₂SO₄·10H₂O, and to obtain information on structural trends caused by the application of high pressure up to ~60 GPa. We have found that there are substantial isosymmetric discontinuous structural re-organisations at ~7.7 and ~20 GPa caused by changes in the manner in which the sodium cations are coordinated by water molecules. The low-pressure and intermediate-pressure phases both have sodium in sixfold coordination but in the high-pressure phase the coordination changes from sixfold to sevenfold. These coordination changes force a re-arrangement of the hydrogen-bond network in the crystal. The trend is towards a reduction in the number of hydrogen bonds donated to the sulphate group (from twelve down to six over the range 0–60 GPa) and an increase in hydrogen bonding amongst the Na-coordinated water molecules and the two interstitial water molecules. Ultimately, we observe proton transfers from the interstitial waters (forming OH^? ions) to two of the Na-coordinated waters (forming a pair of H₃O⁺ ions). The equation of state in the athermal limit of the low-pressure phase of mirabilite, parameterised by fitting an integrated form of the third-order Birch-Murnaghan expression to the calculated energy as a function of unit-cell volume, yields the zero-pressure unit-cell volume, V ₀ = 1468.6(9) ų, the incompressibility, K ₀ = 22.21(9) GPa, and the first pressure derivative K ₀′ = (?K/?P)₀ = 5.6(1).