Fluorite dissolution at acidic pH: In situ AFM and ex situ VSI experiments and Monte Carlo simulations

Dissolution of the fluorite (1 1 1) cleavage surface was investigated by means of in situ atomic force microscopy (AFM) and ex situ vertical scanning interferometry (VSI) experiments at pH range 1-3 in HCl solutions. Surface retreat was quantified at different pH values, yielding dissolution rates that were used to derive an empirical rate law for fluorite dissolution:

     

蒙特卡罗模拟在区域地震滑坡灾害评价中应用

2004年10月23日,日本新泻中越地区发生史上最强地震之一,震级达到Mw6.6。这次地震诱发上千个规模大小不一、形式各样的滑坡,造成一定的灾害损失和人员伤亡。因此,为了有效地避免和减轻这方面的灾害,有必要有效地、科学地预测和评价地震诱发滑坡的空间发生规律。为此以一定的地区作为研究对象,提出了蒙特卡罗随机模拟和Newmark滑动体位移分析法在区域地震斜坡失稳概率分析中的应用。该法充分考虑到岩土参数和相关地震参数空间变异性,结合地理信息系统空间分析的优势,以网格模型为基础,分析该区斜坡滑动体位移分布规律,并以2cm为失稳临界值探讨网格斜坡破坏的概率。实例证明,所提出的模型有效地预测了滑坡发生的空间分布规律。     

Probabilistic modeling of seismically triggered landslides using Monte Carlo simulations

The 2004 Chuetsu earthquakes of Niigata (Japan) triggered numerous landslides, and the most widespread types of landslides were highly disrupted, relatively shallow slides and soil (debris) flows. This paper presented a method to evaluate slope instability using Newmark displacement on a pixel-by-pixel basis in a given area. The proposed method was able to integrate Newmark displacement modeling and Monte Carlo simulations within geographical information systems. In the modeling, an empirical attenuation relationship was utilized to calculate Arias intensity over this study area, and the variability of geotechnical parameters was taken into account to calculate coseismic landslide displacement. Before deriving the displacement from related inputs, the Monte Carlo simulations ran 1,500 times and generated 1,500 displacement values for each grid cell, and then means and standard deviations of displacement were calculated and probabilistic distributions can be obtained. Finally, given 10 cm as a threshold value of displacement, estimated probabilities of displacement exceeding 10 cm were shown as a map of seismic landslide hazards. The resulting hazard map was classified into four categories from very low to high level.     

A reduced-order model for Monte Carlo simulations of stochastic groundwater flow

We explore the ability of the greedy algorithm to serve as an effective tool for the construction of reduced-order models for the solution of fully saturated groundwater flow in the presence of randomly distributed transmissivities. The use of a reduced model is particularly appealing in the context of numerical Monte Carlo (MC) simulations that are typically performed, e.g., within environmental risk assessment protocols. In this context, model order reduction techniques enable one to construct a surrogate model to reduce the computational burden associated with the solution of the partial differential equation governing the evolution of the system. These techniques approximate the model solution with a linear combination of spatially distributed basis functions calculated from a small set of full model simulations. The number and the spatial behavior of these basis functions determine the computational efficiency of the reduced model and the accuracy of the approximated solution. The greedy algorithm provides a deterministic procedure to select the basis functions and build the reduced-order model. Starting from a single basis function, the algorithm enriches the set of basis functions until the largest error between the full and the reduced model solutions is lower than a predefined tolerance. The comparison between the standard MC and the reduced-order approach is performed through a two-dimensional steady-state groundwater flow scenario in the presence of a uniform (in the mean) hydraulic head gradient. The natural logarithm of the aquifer transmissivity is modeled as a second-order stationary Gaussian random field. The accuracy of the reduced basis model is assessed as a function of the correlation scale and variance of the log-transmissivity. We explore the performance of the reduced model in terms of the number of iterations of the greedy algorithm and selected metrics quantifying the discrepancy between the sample distributions of hydraulic heads computed with the full and the reduced model. Our results show that the reduced model is accurate and is highly efficient in the presence of a small variance and/or a large correlation length of the log-transmissivity field. The flow scenarios associated with large variances and small correlation lengths require an increased number of basis functions to accurately describe the collection of the MC solutions, thus reducing significantly the computational advantages associated with the reduced model.     

Determining optimum number of geotechnical testing samples using Monte Carlo simulations

Knowing how many samples to test to adequately characterize soil and rock units is always challenging. A large number of tests decrease the uncertainty and increase the confidence in the resulting values of design parameters. Unfortunately, this large value also adds to project costs. This paper presents a method to determine the number of samples as a function of the coefficient of variation. If, as in the case of a reliability-based design, the resistance factors are a function of the coefficient of variation of the measurements, then lowering the coefficient of variation (COV) can result in lowering of the resistance factor resulting in a less conservative design. In this study, laboratory samples were isolated by specific unified soil classification system soil type and general site location. A distribution was fitted for each of the geotechnical parameters measured. For each scenario, groups of 2, 3, 4, 5, 10, 15, 20, 30, 50, and 100 random samples were generated by using Monte Carlo simulations from the fitted distributions. For each group, the variability was calculated in terms of the COV. In all cases, the COV decreased as the sample size increased. However, the rate of decrease for the COV was the greatest at a low number of samples; it becomes increasingly smaller at a higher number of samples.     

Adsorption of molybdenum on to anatase from dilute aqueous solutions

Adsorption of Mo on to hydrous TiO₂ (anatase) particles was investigated. Batch experiments were conducted at 19 and 90 °C over a pH range of 2 to 12 and Mo concentrations ranging from approximately 10⁻⁶ to 10⁻⁴ M. The extent of sorption was strongly dependent on pH and surface loading. Maximum sorption was observed in the acidic pH range at low surface loading. Adsorption behavior was described using the empirical Langmuir adsorption model. A constant capacitance surface complexation model was also used to fit the adsorption isotherms using a ligand exchange reaction for a hydroxyl surface site on anatase. Comparison of experimental data at two different temperatures (19 and 90 °C) indicates that Mo sorption in the acidic pH range decreases with increasing temperature.     

Polymerization of silicate and aluminate tetrahedra in glasses,melts, and aqueous solutions—IV. Aluminum coordination in glasses and aqueous solutions and comments on the aluminum avoidance principle

The coordination of aluminum with oxygen in crystalline and amorphous alumina, aluminates, and aluminosilicates has been determined with magic angle spinning ²⁷Al nuclear magnetic resonance. The ²⁷Al NMR spectra of crystalline materials show that ^VIAl and ^IVAl can readily be distinguished. The same is not the case for amorphous aluminosilicates due to the superposition of a narrow peak, characteristic of ^IVAl, on a broad band. Our spectroscopic results indicate that Al coordination is not the determining factor in explaining differences in devitrification behavior of albite and anorthite glasses. The coordination of Al in aqueous solutions seems to prevent precipitation of the three common Al(OH)₃ polymorphs (^VIAl) at pH above 10. There is clear evidence to suggest that, in solutions containing Si as well as Al, aluminum coordination is related to the type of precipitate formed in acid (clays, ^VIAl, ^IVAl), and basic (zeolites, ^IVAl) environments. Zeolites can be precipitated in near neutral pH environments at higher temperatures, reflecting an increase in ^IVAl under these conditions. The Al avoidance principle for aluminosilicates does not seem to be a hard principle. It is likely that the validity of this principle depends on the type of modifying cation present in the aluminosilicate framework.     

Analyzing reproduction of correlations in Monte Carlo simulations: application to mine project valuation

Monte Carlo (MC) simulations are extensively used to assess risk in mining ventures; however, the correlation between the inputs used to build the models is often overlooked. We observed how value-at-risk (VaR) of a mining venture was affected by running MC simulations, using two different input correlation methods: Spearman's rank correlation and copulas using Kendall's tau. The goal was to compare different correlation approaches on risk analysis associated with uncertain parameters of mining ventures and uncover which one would yield the most accurate result. Three case studies were carried out to compare correlation structures. Modelling the input variable correlations was better achieved using copulas since they were able to capture a wider range of correlations that did not make any linearity assumptions. In the case study based on MC simulations, the impact of the input correlation choice on the VaR was rather severe with an approximate 9% difference between the results obtained with Spearman's correlations and the Normal copula correlations.     

Microsommite: crystal chemistry, phase transitions, Ising model and Monte Carlo simulations

Microsommite, ideal formula [Na₄K₂(SO₄)] [Ca₂Cl₂][Si₆Al₆O₂₄], is a rare feldspathoid that occurs in volcanic products of Vesuvius. It belongs to the cancrinite–davyne group of minerals, presenting an ABAB… stacking sequence of layers that contain six-membered rings of tetrahedra, with Si and Al cations regularly alternating in the tetrahedral sites. The structure was refined in space group P6₃ to R=0.053 by means of single-crystal X-ray diffraction data. The cell parameters are a=22.161?Å=√3a _dav, c=5.358?Å=c _dav; Z=3. The superstructure arises due to the long-range ordering of extra-framework ions within the channels of the structure. This ordering progressively decreases with rising temperature until it is completely lost and microsommite transforms into davyne. The order–disorder transformation has been monitored in several crystals by means of X-ray superstructure reflections and the critical parameters T _c?≈?750?°C and β?≈?0.12 were obtained. The kinetics of the ordering process were followed at different temperatures and the activation energy was determined to be about 125?kJ?mol^?1. The continuous order–disorder phase transition in microsommite has been discussed on the basis of a two-dimensional Ising model in a triangular lattice with nn (nearest neighbours) and nnn (next-nearest neighbours) interactions. Such a model was simulated using a Monte Carlo technique. The theoretical model well matches the experimental data; two phase transitions were indicated by the simulated runs: at low temperature only one of the three sublattices begins to disorder, whereas the second transition involves all three sublattices.     

Octahedral cation ordering of illite and smectite. Theoretical exchange potential determination and Monte Carlo simulations

The distributions of Al ³⁺/Mg ²⁺ and Al ³⁺/ Fe ³⁺ were studied in the octahedral sheet of illites and smectites. Cation exchange interaction parameters J _i, as first, second, third and fourth neighbours were calculated by means of empirical interatomic potentials. Several compositions with different interlayer cations and tetrahedral charge were studied in both Al/Mg and Al/Fe systems. The values of J _i parameters were similar in all Al/Mg samples. From these J _i values, a strong trend to form AlMg pairs was observed in the Al/Mg system. In the Al/Fe system, the values of J _i are very small, indicating no preference for Al/Fe mixing. From these J _i parameters, Monte Carlo simulations of octahedral cation ordering were performed. In the Al/Mg system, an order/disorder phase transition was observed obtaining a fully ordered distribution without presence of an MgMg pair, according to experimental data. Similar phase transitions were observed for the octahedral compositions Al/Mg 1/1 and 3/1. In the Al/Fe system an order/disorder phase transition was also detected but at very low temperature for illite and smectite. Complete Al/Fe mixing is observed in the most stable ordered distribution. This is consistent with experimental results for synthetic Fe/Al smectites.     

Multilevel Monte Carlo methods using ensemble level mixed MsFEM for two-phase flow and transport simulations

In this paper, we propose multilevel Monte Carlo (MLMC) methods that use ensemble level mixed multiscale methods in the simulations of multiphase flow and transport. The contribution of this paper is twofold: (1) a design of ensemble level mixed multiscale finite element methods and (2) a novel use of mixed multiscale finite element methods within multilevel Monte Carlo techniques to speed up the computations. The main idea of ensemble level multiscale methods is to construct local multiscale basis functions that can be used for any member of the ensemble. In this paper, we consider two ensemble level mixed multiscale finite element methods: (1) the no-local-solve-online ensemble level method (NLSO); and (2) the local-solve-online ensemble level method (LSO). The first approach was proposed in Aarnes and Efendiev (SIAM J. Sci. Comput. 30(5):2319-2339, 2008) while the second approach is new. Both mixed multiscale methods use a number of snapshots of the permeability media in generating multiscale basis functions. As a result, in the off-line stage, we construct multiple basis functions for each coarse region where basis functions correspond to different realizations. In the no-local-solve-online ensemble level method, one uses the whole set of precomputed basis functions to approximate the solution for an arbitrary realization. In the local-solve-online ensemble level method, one uses the precomputed functions to construct a multiscale basis for a particular realization. With this basis, the solution corresponding to this particular realization is approximated in LSO mixed multiscale finite element method (MsFEM). In both approaches, the accuracy of the method is related to the number of snapshots computed based on different realizations that one uses to precompute a multiscale basis. In this paper, ensemble level multiscale methods are used in multilevel Monte Carlo methods (Giles 2008a, Oper.Res. 56(3):607-617, b). In multilevel Monte Carlo methods, more accurate (and expensive) forward simulations are run with fewer samples, while less accurate (and inexpensive) forward simulations are run with a larger number of samples. Selecting the number of expensive and inexpensive simulations based on the number of coarse degrees of freedom, one can show that MLMC methods can provide better accuracy at the same cost as Monte Carlo (MC) methods. The main objective of the paper is twofold. First, we would like to compare NLSO and LSO mixed MsFEMs. Further, we use both approaches in the context of MLMC to speedup MC calculations.     

不同有机酸对矿物溶解的动力学实验研究

用石英、微斜长石和方解石混合颗粒模拟碎屑组分分别与不同有机酸水溶液进行溶蚀实验,以比较储集层内不同矿物在含低分子量有机酸地层水中溶解的速率,并试图探讨矿物溶蚀的微观机理。结果表明：①所有矿物颗粒都发生了不同程度的溶解,表现为颗粒失重,溶液中SiO2和金属阳离子含量增加,pH值上升。②优先溶解的是方解石,其次是硅酸盐矿物。③温度增加,硅酸盐矿物在水中的溶解度明显增加,而方解石的溶解度基本不变。④由于不同有机酸与二氧化硅和金属阳离子生成的络合物稳定性不同,因此,在不同有机酸水溶液中,矿物的溶蚀速率有较大差别。多官能团有机酸的水溶液中,不同矿物有更大的溶解;但在含有丰富Ca2＋的草酸水溶液中,由于矿物颗粒表面难溶草酸钙的沉淀,方解石的溶解变得更加困难。⑤多官能团有机酸与SiO2形成的多环螯合物由于完全取代了硅氧四面体的氧原子,在水中具有高度稳定性,可能有助于(铝)硅酸盐的溶蚀和硅元素的迁移     

Energetics of water dissolution in trachyte glasses and liquids

Enthalpies of dissolution in HF solutions have been measured at 323 K for a series of hydrous trachyte glasses. Enthalpies of mixing between water and molten trachyte have then been calculated from heat capacity data for the same set of samples and available enthalpy for pure water. The moderately negative enthalpies of mixing suggested at 1 bar by the measurements made on glasses almost disappear when trachyte liquids and water are referred to the same temperature, and particularly so when enthalpies of mixing are calculated for a few kbars pressure. As found for albite and phonolite liquids, trachyte melts thus appear to mix nearly ideally as far as enthalpy is concerned. These results imply that the enthalpy of exsolution of water from magmas is very small or negligible under the P-T-X conditions relevant to trachytic volcanism, even for complete degassing of up to 5 wt% H₂O. Furthermore, the viscosity increase associated with exsolution-driven cooling is negligible compared to the decrease caused directly by water exsolution.     

The structure of sodium tetrasilicate glass from neutron diffraction, reverse Monte Carlo simulations and Raman spectroscopy

The reverse Monte Carlo (RMC) method was used for modelling the three-dimensional structure of sodium tetrasilicate glass (Na₂Si₄O₉, NS4). Neutron diffraction data over a large momentum transfer range and nuclear magnetic resonance results (Q-species distribution) as well as chemical bonding considerations have been used to constrain the RMC simulations. Very good agreement with the experimental structure factor was achieved. The three-dimensional model is analysed in terms of partial pair distribution functions, bond-angle distributions, short-range order (SRO) clusters and ring statistics. The average Si–O–Si bridging angle is different for the different Qⁱ–Q^j units. The effect of different Q species on the network connectivity is analysed by comparison with statistical SRO distributions. While the Q² species are randomly distributed, a high preference for the formation of Q⁴–Q⁴ units in three-membered rings is found. This explains why during the initial stages of hydration of NS4 glass, Si–OH groups are preferentially formed by breaking Q⁴–Q⁴ linkages. The RMC model also provides an independent test for the assignment of bands in the Si–O stretching region of the Raman spectrum. It is shown that the bands at about 1050 and 1100 cm⁻¹ are probably due to Q³ units surrounded by different numbers of Q⁴ units. Received: 7 April 1997 / Revised, accepted: 5 July 1997     

Experimental study of brucite dissolution and precipitation in aqueous solutions: surface speciation and chemical affinity control

Dissolution and precipitation rates of brucite (Mg(OH)₂) were measured at 25°C in a mixed-flow reactor as a function of pH (2.5 to 12), ionic strength (10⁻⁴ to 3 M), saturation index (−12 < log Ω < 0.4) and aqueous magnesium concentrations (10⁻⁶ to 5·10⁻⁴ M). Brucite surface charge and isoelectric point (pH_IEP) were determined by surface titrations in a limited residence time reactor and electrophoretic measurements, respectively. The pH of zero charge and pH_IEP were close to 11. A two-pK, one site surface speciation model which assumes a constant capacitance of the electric double layer (5 F/m²) and lack of dependence on ionic strength predicts the dominance of >MgOH₂⁺ species at pH < 8 and their progressive replacement by >MgOH° and >MgO⁻ as pH increases to 10-12. Rates are proportional to the square of >MgOH₂⁺ surface concentration at pH from 2.5 to 12. In accord with surface speciation predictions, dissolution rates do not depend on ionic strength at pH 6.5 to 11. Brucite dissolution and precipitation rates at close to equilibrium conditions obeyed TST-derived rate laws. At constant saturation indices, brucite precipitation rates were proportional to the square of >MgOH₂⁺ concentration. The following rate equation, consistent with transition state theory, describes brucite dissolution and precipitation kinetics over a wide range of solution composition and chemical affinity:

     

Modeling radon time series on the North Anatolian Fault Zone,Turkiye: Fourier transforms and Monte Carlo simulations

Natural Hazards - Time series studies depend mostly on stochastic models for radon seasonal, annual or temporal variability explanations. Others solve radon transport steady state equation...     

Improvement of cadmium ion electrochemical removal from dilute aqueous solutions by application of multi-stage electrolysis

Improvement of cadmium ion electrochemical removal from dilute aqueous solutions in a spouted bed reactor was investigated. Enlargement of cathode surface area from 1,000 to 1,500 cm² resulted in a decrease of nearly 30 % in both of the process time and the specific energy consumption. Application of a three-stage electrolysis process for a solution containing initial concentration of 270 ppm cadmium ion, resulted in the removal of 99.9 % cadmium ion in 135 min with the specific energy consumption of 2.29 kWh/kg, 23 % less than the value of a single-stage process. For a solution with cadmium ion initial concentration of 180 ppm, 99.9 % of cadmium ion was removed in 135.5 min by application of a two-stage electrolysis process, while the specific energy consumption was 2.82 kWh/kg, 30 % less than that of a single-stage process. For a solution with cadmium ion initial concentration of 90 ppm, 99.5 % of cadmium ion was removed in 100.2 min with the specific energy consumption of 3.78 kWh/kg in a single-stage electrolysis process.     

A theoretical interpretation of the chemical shift of Si NMR peaks in alkali borosilicate glasses

In ²⁹Si-NMR, it has so far been accepted that the chemical shifts of Qⁿ species (SiO₄ units containing n bridging oxygens) were equivalent between alkali borosilicate and boron-free alkali silicate glasses. In the sodium borosilicate glasses with low sodium content, however, a contradiction was confirmed in the estimation of alkali distribution; ¹¹B NMR suggested that Na ions were entirely distributed to borate groups to form BO₄ units, whereas a −90 ppm component was also observed in ²⁹Si-NMR spectra, which has been attributed to Q³ species associated with a nonbridging oxygen (NBO). Then, cluster molecular orbital calculations were performed to interpret the −90 ppm component in the borosilicate glasses. It was found that a silicon atom which had two tetrahedral borons (B4) as its second nearest neighbors was similar in atomic charge and Si2p energy to the Q³ species in boron-free alkali silicates. Unequal distribution of electrons in Si-O-B4 bridging bonds was also found, where much electrons were localized on the Si-O bonds. It was finally concluded that the Si-O-B4 bridges with narrow bond angle were responsible for the −90 ppm ²⁹Si component in the borosilicate glasses. There still remained another interpretation; the Q³ species were actually present in the glasses, and NBOs in the Q³ species were derived from the tricluster groups, such as (O₃Si)O(BO₃)₂. In the glasses with low sodium content, however, it was concluded that the tricluster groups were not so abundant to contribute to the −90 ppm component.     

Polymerization of silicate and aluminate tetrahedra in glasses,melts, and aqueous solutions—III. Local silicon environments and internal nucleation in silicate glasses

The local, up to second nearest neighbor, around Si atoms in alkali and alkaline earth-silicate glasses has been characterized by SiKβ X-ray emission spectroscopy. Principally two types of Si atoms can be distinguished. These are Si atoms with only other Si atoms as second nearest neighbours, and those with one or more alkali or alkaline earth atoms in their second coordination sphere. The spectroscopic results indicate that the lower molecular weight alkali and alkaline earth-silicate glasses tend towards a bimodal distribution of local Si environments, which is designated Q₄-Q₀ following the assignment by Engelhardtet al. (1975) for silica species in aqueous solutions. From a different perspective the outcome of these experiments suggests that, though the concentration of bridging oxygens (O(br)) and non-bridging oxygens (O(nbr)) is fixed by the stoichiometry of the glass, the distribution of O(nbr) in the glass varies according to the kind of alkali or alkaline earth atom present. From observed nucleation data on R₂O-SiO₂ (R = Li, Na, K) glasses it is inferred that a bimodal Q distribution and in particular the presence of Q₀ species dominates the internal nucleation process in the alkali and alkaline earth-silicate glasses studied. Using this inference rationalizations can readily be found to explain the observed resistance to thermal shock and devitrification rates of these glasses.