Fe–Mg diffusion in olivine II: point defect chemistry,change of diffusion mechanisms and a model for calculation of diffusion coefficients in natural olivine

Analysis of existing data and models on point defects in pure (Fe,Mg)-olivine (Phys Chem Miner 10:27–37,1983; Phys Chem Miner 29:680–694, 2002) shows that it is necessary to consider thermodynamic non-ideality of mixing to adequately describe the concentration of point defects over the range of measurement. In spite of different sources of uncertainties, the concentrations of vacancies in octahedral sites in (Fe,Mg)-olivine are on the order of 10⁻⁴ per atomic formula unit at 1,000–1,200 °C according to both the studies. We provide the first explicit plots of vacancy concentrations in olivine as a function of temperature and oxygen fugacity according to the two models. It is found that in contrast to absolute concentrations at ∼1,100 °C and dependence on fO₂, there is considerable uncertainty in our knowledge of temperature dependence of vacancy concentrations. This needs to be considered in discussing the transport properties such as diffusion coefficients. Moreover, these defect models in pure (Fe,Mg)-olivine need to be extended by considering aliovalent impurities such as Al, Cr to describe the behavior of natural olivine. We have developed such a formulation, and used it to analyze the considerable database of diffusion coefficients in olivine from Dohmen et al. (Phys Chem Miner this volume, 2007) (Part - I) and older data in the literature. The analysis documents unequivocally for the first time a change of diffusion mechanism in a silicate mineral—from the transition metal extrinsic (TaMED) to the purely extrinsic (PED) domain, at fO₂ below 10⁻¹⁰  Pa, and consequently, temperatures below 900 °C. The change of diffusion mechanism manifests itself in a change in fO₂ dependence of diffusivity and a slight change in activation energy of diffusion—the activation energy increases at lower temperatures. These are consistent with the predictions of Chakraborty (J Geophys Res 102(B6):12317–12331, 1997). Defect formation enthalpies in the TaMED regime (distinct from intrinsic defect formation) lie between −66 and + 15 kJ/mol and migration energies of octahedral cations in olivine are most likely ∼ 260 kJ/mol, consistent with previous inferences (Phys Chem 207:147–162, 1998). Plots are shown for diffusion at various constant fO₂ as well as along fO₂ buffers, to highlight the difference in behavior between the two. Considering all the diffusion data and constraints from the point defect models, (Fe–Mg) diffusion in olivine along [001] is best described by the Master equations: (1) At oxygen fugacities greater than 10⁻¹⁰ Pa:

Identification of diffusion parameters in a nonlinear convection–diffusion equation using the augmented Lagrangian method

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments are presented and discussed. This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431.     

Application of Vegetation Geosynthetic Technique to Slope Stability in the Three Gorges Reservoir

INTRODUCTIONThe Three Gorges Project is the largest waterconservation and hydropower project in the world.The dam began to impound in June 2003. The initialimpounded level is 135 m and the normal level will be175 m. During normal operation…     

Experimental measurements of the diffusion parameters of light hydrocarbons in water-saturated sedimentary rocks—I. A new experimental procedure

An automatic experimental set-up has been developed for the determination of diffusion parameters of hydrocarbon gases through water-saturated rock samples. Diffusive flow of hydrocarbons through rock slices is monitored by gas chromatography. Experiments are carried out according to the time lag method yielding diffusion coefficients, solubility coefficients, and diffusion permeabilities. Diffusion coefficients down to 10⁻¹² m² s⁻¹ (10⁻⁸ cm⁻² s⁻¹) may be determined routinely on rock samples of 2–10 mm thickness. Maximum errors in diffusion coefficients are estimated around 20% and reproducibility was found to range between 10 and 20%. Specific features of this set-up are automatic sampling and data acquistion, high sampling frequency, and maintenance of water-saturation of the rock samples throughout the experiment.     

Sobol’ sensitivity analysis of parameters in the common land model for simulation of water and energy fluxes

The water and energy transfer of land surface is complex due to its large spatial and temporal variability. The modeling and simulation is an important means to study land water and energy transfer, but most selection and analysis of model parameters are empirical and qualitative. This paper has proposed a method of quantitatively identifying the most influential parameters of Common Land Model through Sobol?? sensitivity analysis. Considering sensible heat flux as the model output, the first order and total sensitivity indices of 25 model input parameters are estimated using an improved Sobol?? method. The simulated results are resampled using a bootstrapping method and the corresponding sensitivity indices are calculated. Confidence intervals for the bootstrapping sensitivity indices are estimated by using a percentile method. The results show that the parameters phi0 and porsl are the most important parameters, followed by ref(2,1), tran(2,1) and bsw. Five out of 25 parameters need to have an accurate evaluation, while the other parameters are fixed to a certain value. The sensitivity indices of parameters phi0 and porsl are decreasing after precipitation, while the sensitivity indices of parameters tran(2, 1) and ref(2, 1) are increasing after precipitation.     

Phlogopite Formation in the Orthopyroxene–Garnet System in the Presence of H2O–KCl Fluid in Application to the Processes of Mantle Metasomatism

Doklady Earth Sciences - The results of experimental studies are presented for reactions in the orthopyroxene–garnet–phlogopite system in the presence of H2O–KCl fluid at...     

Application of the geochemical prospecting to improve oilfield structure models

Background： Complicated structure of surveyed area has minor efficiency of seismic surveys-the main method for petroleum and gas prospecting and interpretation of subsurface structure of the Earth. This paper gives an example that in certain cases geochemical surveys can be used as additional tool to establish suitable geological model of the trap. This paper presents geochemical studies in the southeastern part of European territory of Russia-Nagumanovskoe oilfield. Complicated geological structure causes difficulties to create suitable geological model of the trap itself. There are two models of geological structure for the Nagumanovskoe oilfield： Variant A： Researchers assume the presence of gas condensate accumulation and perspective for exploration traps. Variant B： Researchers assume presence of 2 local structures. Method and results： Geochemical data came from over than 2000 shallow probes （2 meters, 6.6 feet） of soil gas samples collected every 200 meters over more than 7 different long profiles. The adsorbed soil gases were analyzed for hydrocarbones. All samples were decomposed into geochemical populations. According to geochemical data the Nagumanovskoe oilfield was well defined on all geochemical profiles. Examination and comparison of hydrocarbon ratio plots and magnitude graphs for each of the two models indicate that the more anomalous magnitude sites agree with the disposition of structures according to model B. The geochemical oil/gas data exhibit clearly defined compositional sub-populations which match the composition of the underlying reservoirs, difference in standard deviation of hydrocarbon values at background and Cretaceous structure （model B） leads to the deduction that variant B is more suitable geological structure model of the Nagumanovskoe oilfield.     

Review of the use of Péclet numbers to determine the relative importance of advection and diffusion in low permeability environments

In low permeability environments, transport by advection is often neglected based on a Péclet number criterion. Such a criterion usually states that if the Péclet number (Pe) is much smaller than 1, diffusion dominates over advection and transport may be modeled considering diffusion only. Unfortunately, up to 10 different Péclet number definitions exist and for a particular case these different definitions lead to very diverse Péclet number values, differing several orders of magnitude from each other. In this paper, the different Péclet number definitions are therefore evaluated on their ability to determine the relative importance of transport by advection and by diffusion in low permeability environments. This is done by comparing the results of the analytical solution for pure diffusion with the analytical solution for diffusion, advection and dispersion for a large number of different input parameter values. The relation between the different Péclet numbers and the difference between the calculated concentration considering diffusion only and the calculated concentration considering both diffusion and advection is studied. These calculations show that some Péclet number definitions are not well suited to decide whether advection may be neglected in low permeability media.

---

Resumen Frecuentemente se descuida el transporte por avección en ambientes de baja permeabilidad sobre la base del criterio del número de Péclet. Dicho criterio usualmente sostiene que si el número de Péclet (Pe) es mucho menor a 1, la difusión domina sobre la avección y es posible modelar el transporte considerando la difusión únicamente. Desafortunadamente existen 10 definiciones diferentes del número de Péclet y para un caso en particular estas diferentes definiciones conducen a valores de número de Péclet muy diversos los cuales difieren entre sí en varias magnitudes. Por lo tanto, en este artículo se evalúan las diferentes definiciones en base a su habilidad para determinar la importancia relativa del transporte por avección y difusión en ambientes de baja permeabilidad. Esto se lleva a cabo mediante la comparación de los resultados de la solución analítica para difusión pura con los de la solución analítica por difusión, avección y dispersión para un número amplio de diferentes valores como parámetro. Se ha estudiado la relación entre los diferentes números de Péclet y las diferencias entre la concentración calculada considerando difusión únicamente y considerando tanto difusión como avección. Estos cálculos muestran que algunas de las definiciones de los números de Péclet no son muy apropiadas par decidir si se puede descuidar la avección en medios de baja permeabilidad.

---

Résumé Dans les milieux à faible perméabilité, le transport par advection est souvent négligeable lorsquon se base sur le critère du nombre de Péclet. Un tel critère suggère habituellement que pour un nombre de Péclet beaucoup plus petit que 1, la diffusion domine sur ladvection et que le transport peut être modélisé par diffusion seulement. Malheureusement, il existe jusquà environ dix définitions du nombre de Péclet et pour un cas spécifique, ces différentes définitions mènent à des valeurs du nombre de Péclet très différentes, et qui varient entre elles de plusieurs ordres de grandeur. Dans cet article, les différentes définitions du nombre de Péclet sont évaluées en fonction de leur habileté à déterminer limportance relative du transport par advection et par diffusion dans les milieux à faible perméabilité. Ceci est fait en comparant les résultats de la solution analytique pour la diffusion pure à la solution analytique pour la diffusion, ladvection et la dispersion, et ce, pour un grand nombre de valeurs différentes comme paramètre dentrée. La relation entre les différents nombres de Péclet et la différence entre la concentration calculée en considérant la diffusion seulement et la concentration calculée considérant simultanément la diffusion et ladvection est étudiée. Ces calculs prouvent que certaines définitions de nombre de Péclet ne sont pas appropriées afin de décider si ladvection peut être négligée dans les milieux à faible perméabilité.

     

Water Resource Development in the Quaternary Ryukyu Limestone Regions of Japan:Application of the GIS to the Site Selection of Underground Dams

Based on the natural and social conditions as well as hydrogeological characteristics of the Ryukyu limestone, a major aquifer in the Ryukyu Islands, a conception of underground dam, was proposed in the early 1970s in order to develop ground water resources in the Quaternary Ryukyu limestone regions of Japan. The practice of nearly thirty years has shown that the underground dam is an environment-friendly and effective way for developing ground water in these regions.To further improve the technology associated with underground dam, the authors introduced related analytic methods. The application of the geographical information system technology to site selection of the underground dam is reported in this paper.     

The Application of Computerized Pattern Recognition to the Prediction of Mineral Resources

The technique of mineral prediction by pattern recognition has been developed through the applicationof computerized pattern recognition to geological exploration. The principles and computing method of thistechnique as well as some characteristics of its application in geological exploration are expounded in thispaper. Some of the study results gained by the authors in this aspect are also given. which include classifica-tion of oil-field waters. evaluation of gossans of main ore deposits in China, prediction of ore resources inthe Dachang Sn-polymetallic field. and appraisal of Pb and Sn anomalies and prediction of mineral re-sources in southern Hunan. Some of the prediction results have been proved correct.     

The Kovdor-2015 experiment: study of the parameters of a conductive layer of dilatancy–diffusion nature (DD Layer) in the Archaean crystalline basement of the Baltic Shield

This paper addresses the Kovdor-2015 Experiment involving frequency electromagnetic soundings of the Archaean basement of the Earth’s crust in the southwestern part of the Kola Peninsula. Eleven soundings were carried out using two transmitting arrangements, 85 km apart. Each arrangement consisted of two mutually orthogonal grounded electric dipoles of 1.5 km long. The distances between the source and the receiver were 25 and 50 km. Interpretation of the results took into account the influence of displacement currents and static distortions. It is found that there is an intermediate conductive layer of the dilatancy–diffusion nature (DD layer) with a longitudinal conductivity of about one siemens at depths ranging from 1.5–2 to 5–7 km. The results are interpreted in the terms of geodynamics.     

A surrogate-based simulation–optimization approach application to parameters’ identification for the HydroGeoSphere model

A systematic approach is needed to use water more productively, because water shortages limit socio-economic development in many parts of the world. The aim of this paper is to establish a surrogate-based simulation–optimization approach to identify parameter values for a fully integrated surface water and groundwater flow coupling simulation. A surface water and groundwater flow coupling simulation model was implemented using HydroGeoSphere (HGS) model and the parameter sensitivities in the model were analyzed using local sensitivity analysis method. The parameters that exerted a large influence on the output results of the HGS model were then selected as stochastic variables, and the stochastic variable data sets were generated using the latin hypercube sampling (LHS) method, which, thereby, were used as inputs in HGS model to obtain the corresponding outputs. On the basis of input and output data sets, a kriging surrogate model of the HGS model was then established and verified, and parameter values of HGS model were identified using a surrogate-based simulation–optimization approach. The results of this study show that parameters that exert a large influence on the simulation output results include hydraulic conductivity, porosity, the van genuchten parameter (\(\alpha\)), and channel manning coefficient. The established kriging surrogate model is an ideal alternative to the HGS model for simulating and predicting, while optimal parameter values can be identified effectively and accurately using the established approach. The results of this research reveal that huge computational loads can be mitigated while using the kriging surrogate as an alternative for a simulation model in the solution process of optimization model.     

Application of a 3D photorealistic model for the geological analysis of the Permian carbonates (Khuff Formation) in Saudi Arabia

Three dimensional (3D) photorealistic models of geological outcrops have the potential to enhance the teaching of earth sciences by providing scale models in a virtual reality environment. These models can be run on low-cost desktop computers. Photorealistic models for geological outcrops are a digital illustration of outcrop photographs with either a point cloud representation or Triangular Irregular Network (TIN) mesh of the outcrop surface. The level of detail for these models is dependent on the target resolutions (physical and optical) that were used during data acquisition. In addition, the technique in which the data is rendered as a digital model affects the level of detail that can be observed by the geologists. A colored point cloud representation is suitable for large-scale features, but fine details are lost when the geologist zooms in to view the model close up. In contrast, a photorealistic model that is constructed from photographs draped onto a triangle mesh surface derived from Light Detection and Ranging (LiDAR) point clouds provides a level of detail that is restricted only by the resolution of the photographs.     

Calibration of the parameters for a hardening–softening constitutive model using genetic algorithms

The present paper introduces a genetic algorithm-based optimization technique to calibrate a nonlinear strain hardening–softening constitutive model for soils using five material parameters. The efficiency of the proposed technique is analyzed through the use of different GA techniques. The effects of elitism, crossover, and mutation, as well as population size, on the performance of the conventional GAs for this problem are investigated. Micro-genetic algorithms (mGAs) are chosen and tested for different population sizes. The mGAs with a population size of five yields the optimal parameter values after fewer function evaluations and capture the overall simulated or experimental behavior at every point in stress–strain and strain paths in triaxial compression. The proposed calibration technique is validated through comparison with the traditional calibration technique.     

Application of “panel-data” modeling to predict groundwater levels in the Neishaboor Plain, Iran

The aim of this research was to predict groundwater levels in the Neishaboor plain, Iran, using a ??panel-data?? model. Panel-data analysis endows regression analysis with both spatial and temporal dimensions. The spatial dimension pertains to a set of cross-sectional units of observation. The temporal dimension pertains to periodic observations of a set of variables characterizing these cross-sectional units over a particular time span. Firstly, the available observation wells in the Neishaboor plain were clustered according to their fluctuation behavior using the ??Ward?? method, which resulted in six areal zones. Then, for each cluster, an observation well was selected as its representative, and for each zone, values of monthly precipitation and temperature, as independent variables, were estimated by the inverse-distance method. Finally, the performance of different panel-data regression models such as fixed-effects and random-effects models were investigated. The results showed that the two-way fixed-effects model was superior. The performance indicators for this model (R ²?=?0.97, RMSE?=?0.05?m and ME?=?0.81?m) reveal the effectiveness of the method. In addition, the results were compared with the results of an artificial-neural-network (ANN) model, which demonstrated the superiority of the panel-data model over the ANN model.