生态地理建模中的多尺度问题

本文在分析生态地理建模内涵的基础上,讨论了生态地理建模中的尺度转换问题、跨尺度相互作用问题、空间尺度与时间尺度的关联问题和多尺度数据处理问题.由于生态地理问题的非线性、生态环境的异质性和随机事件,简单的线性尺度转换方法远不能满足生态地理建模的要求.为了从根本上解决生态地理建模中的时空尺度问题,除需要运用微分几何学和等级理论等经典方法外,还需要引入格点生成法和网格计算等现代理论和技术手段.     

Calculating the effective permeability of sandstone with multiscale lattice Boltzmann/finite element simulations

The lattice Boltzmann (LB) method is an efficient technique for simulating fluid flow through individual pores of complex porous media. The ease with which the LB method handles complex boundary conditions, combined with the algorithm’s inherent parallelism, makes it an elegant approach to solving flow problems at the sub-continuum scale. However, the realities of current computational resources can limit the size and resolution of these simulations. A major research focus is developing methodologies for upscaling microscale techniques for use in macroscale problems of engineering interest. In this paper, we propose a hybrid, multiscale framework for simulating diffusion through porous media. We use the finite element (FE) method to solve the continuum boundary-value problem at the macroscale. Each finite element is treated as a sub-cell and assigned permeabilities calculated from subcontinuum simulations using the LB method. This framework allows us to efficiently find a macroscale solution while still maintaining information about microscale heterogeneities. As input to these simulations, we use synchrotron-computed 3D microtomographic images of a sandstone, with sample resolution of 3.34 μm. We discuss the predictive ability of these simulations, as well as implementation issues. We also quantify the lower limit of the continuum (Darcy) scale, as well as identify the optimal representative elementary volume for the hybrid LB–FE simulations.     

CFD-based modelling of bubble-particle collision efficiency with mobile bubble surface in a turbulent environment

Flotation modelling to date has concentrated either on macroscale processes or on ideal microscale processes — there has been no attempt to integrate detailed models at different scales. In this paper, bubble-particle collision efficiency with mobile bubble surfaces in a turbulent flow is investigated from a multiscale modelling viewpoint and a general methodology for modelling is present. Comparisons are carried out to illustrate the method. Turbulence effects on bubble-particle collision efficiency are systematically studied using a 3D k–ε turbulence model.     

Carbon isotopic fractionation by the marine diatom Phaeodactylum tricornutum under nutrient- and light-limited growth conditions

A theoretical model was developed to explain the characteristics of carbon isotopic fractionation (ε_P) by the marine diatom Phaeodactylum tricornutum under nutrient- and light-limited growth conditions. The model takes into consideration active transport and diffusion of inorganic carbon through the cell membrane and chloroplast membrane and the energetic tradeoff between production of Rubisco and operation of a carbon-concentrating mechanism to achieve a given growth rate. The model is able to explain 88% of the variance in experimental ε_p data reported in this study and in previous work and is able to account for the observed pattern of Rubisco activity in nitrate-limited chemostats. Two important implications of the model include the fact that ε_p is not a unique function of the ratio of growth rate to external CO₂ concentration (as opposed to the predictions of several previous models) and that changes in light-limited and nutrient-limited growth rates have opposite effects on the fraction of CO₂ taken up by the chloroplast that is lost to diffusion and hence on certain patterns of carbon isotopic fractionation.     

Optimal choice of the softening length and time step in <Emphasis Type="Italic">N</Emphasis>-body simulations

A criterion for the choice of optimal softening length ε for the potential and the choice of time step dt for N-body simulations of a collisionless stellar system is analyzed. Plummer and Hernquist spheres are used as models to analyze how changes in various parameters of an initially equilibrium stable model depend on ε and dt. These dependences are used to derive a criterion for choosing ε and dt. The resulting criterion is compared to Merritt’s criterion for choosing the softening length, which is based on minimizing the mean irregular force acting on a particle with unit mass. Our criterion for choosing ε and dt indicate that ε must be a factor of 1.5–2 smaller than the mean distance between particles in the densest regions to be resolved. The time step must always be adjusted to the chosen ε (the particle must, on average, travel a distance smaller than 0.5 ε during one time step). An algorithm for solving N-body problems with adaptive variations of the softening length is discussed in connection with the task of choosing ε, but is found not to be promising.     

Hierarchical multiscale numerical modelling of internal erosion with discrete and finite elements

This paper presents a coupled finite and discrete-element model (FEM and DEM) to simulate internal erosion. The model is based on ICY, an interface between COMSOL, an FEM engine, and YADE, a DEM code. With this model, smaller DEM subdomains are generated to simulate particle displacements at the grain scale. Particles in these small subdomains are subjected to buoyancy, gravity, drag and contact forces for short time steps (0.1 s). The DEM subdomains provide the macroscale (continuum) model with a particle flux distribution. Through a mass conservation equation, the flux distribution allows changes in porosity, hydraulic conductivity and hydraulic gradient to be evaluated for the same time steps at a larger, continuum scale. The updated hydraulic gradients from the continuum model provide the DEM subdomains with updated hydrodynamic forces based on a coarse-grid method. The number of particles in the DEM subdomains is also updated based on the new porosity distribution. The hierarchical multiscale model (HMM) was validated with the simulation of suffusion. Results for the proposed HMM algorithm are consistent with results based on a DEM model incorporating the full sample and simulation duration. The proposed HMM algorithm could enable the modelling of internal erosion for soil volumes that are too large to be modelled with a single DEM subdomain.

     

Multiscale Habitat Selection of Wetland Birds in the Northern Gulf Coast

The spatial scale of habitat selection has become a prominent concept in ecology, but has received less attention in coastal ecology. In coastal marshes, broad-scale marsh types are defined by vegetation composition over thousands of hectares, water-level management is applied over hundreds of hectares, and fine-scale habitat is depicted by tens of meters. Individually, these scales are known to affect wetland fauna, but studies have not examined all three spatial scales simultaneously. We investigated wetland bird habitat selection at the three scales and compared single- and multiscale models. From 2009 to 2011, we surveyed marsh birds (i.e., Rallidae, bitterns, grebes), shorebirds, and wading birds in fresh and intermediate (oligohaline) coastal marsh in Louisiana and Texas, USA. Within each year, six repeated surveys of wintering, resident, and migratory breeding birds were conducted at >100 points (n?=?304). The results revealed fine-scale factors, primarily water depth, were consistently better predictors than marsh type or management. However, 10 of 11 species had improved models with the three scales combined. Birds with a linear association with water depth were, correspondingly, most abundant with deeper fresh marsh and permanently impounded water. Conversely, intermediate marsh had a greater abundance of shallow water species, such as king rail Rallus elegans, least bittern Ixobrychus exilis, and sora Porzana carolina. These birds had quadratic relationships with water depth or no relationship. Overall, coastal birds were influenced by multiple scales corresponding with hydrological characteristics. The effects suggest the timing of drawdowns and interannual variability in spring water levels can greatly affect wetland bird abundance.     

Spectral element analysis to evaluate the stability of long and steep slopes

This paper evaluates the stability of long and steep slopes examining the effect of the critical length/depth ratio, L/H, and critical slope angle, β _cr, by comparing the results of infinite slope equation with the spectral element method. In addition, the influence of uphill and downhill boundaries on stability of long and steep slopes is also evaluated in theoretical domains. As an example, this paper presents a stability analysis of long and steep vegetated and barren slopes in saturated and seismic conditions, and also evaluates the effectiveness of the infinite slope equation for those slopes. In the vegetated slopes, the root zone may not extend to the whole depth of slope, which may lead to overestimating the factor of safety by infinite slope equation. This paper examines the applicability of the infinite slope equation for infinitely long, steep, and shallow slope model by comparing the results of the spectral element method.     

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.     

Analysis of the solid phase stress tensor in multiphase porous media

Conservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three‐phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

脆性颗粒材料的动态多尺度模型研究

脆性颗粒材料的多尺度模型一般包含微观尺度的基本粒子、细观尺度的颗粒和宏观尺度的颗粒堆积体3个尺度。基于离散元方法（DEM）构建多尺度模型,并将该模型应用于动态加载。首先,对多尺度模型所涉及的两种接触模型和两种黏结模型的参数进行分析,详细讨论微细观模型参数与宏观材料常数之间的联系。然后,选用Hertz-Mindlin接触模型[1]和平行键黏结模型,建造石英砂的动态多尺度模型。通过选择合适的强度和局部阻尼参数发现,模型宏细观尺度上的动态压缩响应与对石英砂的相关试验结果吻合很好。利用多尺度模型和选定的参数,探讨与动态加载密切相关的局部阻尼机制对多尺度模型各个尺度上力学响应的影响。结果表明,阻尼越大则颗粒材料对波的衰减能力越强,但过高的阻尼会使团簇强度和模型的宏观压缩曲线都表现出异常的加载速度效应（后者实际是阻尼引起的微惯性效应）。另外,高阻尼会过度衰减颗粒破碎过程产生的应力波,从而阻碍颗粒破碎。最后,应用改进的动态多尺度模型,对脆性颗粒材料的动态破碎特性进行研究,发现该模型不但能给出与试验相吻合的颗粒级配曲线,还能揭示出颗粒破碎过程中微裂纹分布的空间不均匀性,即颗粒破碎过程中波的产生机制和衰减机制相互作用导致的微裂纹聚团分布的现象。     

A new model for flow in shale-gas reservoirs including natural and hydraulic fractures

In this work, we construct a new coupled Multiscale/Discrete Fracture Model for compressible flow in a multiporosity shale gas reservoir containing networks of natural and hydraulic fractures. The geological formation is characterized by four distinct length scales and levels of porosity. The window of observation of the finest (nanoscale) portraits the nanopores within organic matter containing adsorbed gas. At the microscale, the medium is formed by two solid phases: organic, composed by kerogen aggregates, and inorganic (clay, quartz, calcite). Such phases are separated by the network of partially-saturated interparticle pores where microscopic free gas flow influenced by Knudsen effects along with gas diffusion in the immobile water phase occur simultaneously. The upscaling of the local flow to the mesoscale gives rise to a nonlinear homogenized pressure equation in the shale matrix which lies adjacent to the system of natural fractures. Homogenization of the coupled matrix/preexisting fractures to the macroscale leads to a microstructural model of dual porosity type. Such homogenized model is subsequently coupled with the hydrodynamics in the network of induced fractures which, in the context of the discrete fracture modeling, are treated as (n ? 1), (n = 2, 3) lower dimensional objects. In order to handle numerically the nonlinear interaction between the different flow equations, we adopt a superposition argument, firstly proposed by Arbogast (1996), in each iteration of a fixed-point algorithm. The resultant governing equations are discretized by the finite element method and numerical simulations of gas production in stratified arrangements of the fracture networks are presented to illustrate the potential of the multiscale approach.     

Kriging with strings of data

The concept of a random function and, consequently, the application of kriging cells for the implicit assumption that the data locations are embedded within an infinite domain. An implication of this assumption is that, all else being equal, outlying data locations will receive greater weight because they are seen as less redundant, hence, more informative of the infinite domain. A two- step kriging procedure is proposed for correcting this siring effect. The first step is to establish the total kriging weight attributable to each string. The distribution of that total weight to the samples in the string is accomplished by a second stage of kriging. In the second stage, a spatial redundancy measure r_(n) is used in place of the covariance measure in the data-data kriging matrix. This measure is constructed such that each datum has the same redundancy with the (n)data of the string to which it belongs. This paper documents the problem of kriging with strings of data, develops the redundancy measure r_(n),and presents a number of examples.     

The distribution of nitrate N/N in marine sediments and the impact of benthic nitrogen loss on the isotopic composition of oceanic nitrate

We report ¹⁵N/¹⁴N ratios of porewater nitrate in sediments from the Bering Sea basin, where microbial nitrate reduction has been identified as a significant sink for fixed nitrogen (N). Strong ¹⁵N enrichment in porewater nitrate is observed as one goes deeper in the sediments and nitrate concentration decreases (δ¹⁵N generally reaches 25-35‰). Analysis of profiles with a one-dimensional diffusion-reaction model yields organism-scale isotope effects for dissimilatory nitrate reduction (ε_cell) of 11‰ to 30‰, in the same range as measured in previous studies of cultures and the marine and lacustrine water column. Estimates of ε_cell, while uncertain, show a negative correlation with bottom water [O₂]; we propose that this relates to the at the depth of denitrification. The N isotope effect at the scale of nitrate sediment-water exchange (ε_app) is ∼0‰ in two unreactive deep sites and is typically <3‰ at more reactive sites at various depths. ε_app is much lower than ε_cell because nitrate consumption is nearly complete at the sediment depth of denitrification, minimizing the escape of ¹⁵N-enriched nitrate from the sediments. In reactive sediments, this is due to rapid denitrification, while in less reactive sediments, it is due to greater diffusive distances for nitrate to the depth of denitrification. The data suggest that low bottom water [O₂] tends to yield more complete expression of ε_cell at the sediment-water scale, due to higher at the depth of denitrification. While porewater ammonium-N isotopes were not measured, our porewater model suggests that, in sediments with high organic matter supply and/or low-[O₂] bottom waters, the efflux and subsequent oxidation of ammonium enriched in ¹⁵N by incomplete nitrification can significantly enhance the total net isotope effect of sedimentary N loss (ε_sed, equivalent to ε_app but including ammonium fluxes). Model analysis of representative sedimentary environments suggests a global mean ε_sed of ∼4‰ (∼2‰ if restricted to seafloor below 1 km depth).     

Adsorption of methyl tert-butyl ether using granular activated carbon: Equilibrium and kinetic analysis

The adsorption of methyl tert-butyl ether by granular activated carbon was investigated. The experimental data were analyzed using the Freundlich isotherm and the Langmuir isotherm. Although equilibrium data were found to follow Freundlich isotherm model, it were fitted better by the Langmuir model with a maximum adsorption capacity of 204.1 mg/g. The kinetic data obtained at different concentrations were analyzed to predict the constant rate of adsorption using three common kinetic models: pseudo-first-order, pseudo-second-order equation and intraparticle diffusion equation. The pseudo-second-order model was suitable for describing the adsorption kinetics for the removal of methyl tert-butyl ether from aqueous solution onto granular activated carbon. Both the Lagergren first-order rate constant k ₁ and pseudo-second-order rate constant k ₂ decrease with increasing initial concentrations of methyl tert-butyl ether and the intraparticle diffusion rate constant k _p shows the reverse characteristic. Analysis of sorption data using a boyd plot confirmed that external mass transfer is the main rate-limiting step at the initial stage of adsorption. Results illustrate that granular activated carbon is an effective adsorbent for methyl tert-butyl ether and also provide specific guidance into adsorption of methyl tert-butyl ether on granular activated carbon in contaminated groundwater.     

复杂储层多尺度数字岩石评价

复杂储层岩石矿物组成非均质性强,孔喉结构细小.储集空间有效性评价、岩石结构精细评价及流体赋存状态与运移规律评价是决定复杂储层油气勘探成效的关键.针对复杂储层的储集空间（孔喉、裂缝）、岩石结构（矿物、有机质）、流体特征3方面,建立了复杂储层多尺度数字岩石评价技术及工作流程.储集空间表征方面:二维大面积分析技术可建立跨越6~7个数量级的多尺度选取及非均质性评价;多尺度CT及FIB-SEM联用可精确刻画孔喉和裂缝的三维空间分布;电化学和显影剂技术可以有效地帮助分析微观孔隙连通性.固体组分分析方面:XRF及Qemscan联用可定量评价矿物组成与分布;三维FIB-SEM技术可以实现有机质形态和分布的定量分析.流体特性方面:荷电效应可用于微量残留有机流体的识别与表征;通过合成孔径、润湿性、表面微结构均可调控的纳米材料,开展地层条件下页岩油赋存及流动物理模拟研究,确定了单一因素对页岩油赋存及可动孔径下限的影响;利用分子模拟研究油气在无机、有机质纳米孔隙中的聚集机理与扩散潜力.复杂储层多尺度数字岩石评价技术体系和一系列具体应用可以有效地填补常规储层分析手段的不足,为页岩油气、致密砂岩油气储层以及深部油气储层等复杂储层有效性评价和含油气性定量评价提供技术支撑.      

Oxygen diffusion in three silicate melts along the join diopside-anorthite

The self-diffusion of oxygen has been measured for three silicate melts along the join diopsideanorthite. The experiments were done by isotope exchange between an “infinite” reservoir of oxygen gas and spheres of melt. The oxygen self-diffusion coefficients for the three melts are given as: C-1(diopside): D = 1.64 × 10¹ exp(?(63.2 ± 20)(kcal/mole)/RT) cm²/sec C-2(Di₅₈An₄₂): D = 1.35 × 10^?1 exp(?(46.8 ± 9)(kcal/mole)/RT) cm²/sec C-3(Di₄₀An₆₀): D = 1.29 × 10^?2 exp(?(44.2 ± 6)(kcal/mole)/RT) cm²/secThe self-diffusion coefficients do not agree with the Eyring equation unless mean ionic jump distances (λ) considerably larger than the diameter of oxygen anion are assumed. However, the sense of variation of the actual diffusivities is as the Eyring equation predicts.Consideration of the results of this study and the bulk of previous work shows that oxygen appears to conform to the compensation law for cationic diffusion in silicate melts and glasses. The range of oxygen diffusivities was also found to encompass the field of divalent cation diffusivities in silicate melts.Those results imply that the diffusion of oxygen in silicate melts may involve a contribution from a cation-like diffusion mechanism (discrete O^2? anions) as well as contributions from the diffusion of larger structural units.     

Extension of the specific interaction model to include gas solubilities in high temperature brines

A semi-empirical model for gas solubilities in high temperature brines was developed by modification of the Pitzer interaction model (Pitzer, 1973) and evaluated by least-squares fitting to available P-T-X data for carbon dioxide, hydrogen sulfide, and methane in pure water and in aqueous sodium chloride solutions. Over the range of experimental data used (25°–350°C, NaCl concentration 0–6 m, P_CO2 1–150 atm. P_CH4 1–30 atm, P_CH4 1–1700 atm), standard deviations of fit in the natural logarithm of the Henry's law ratio were 0.096 for CO₂, 0.093 for H₂S and 0.116 for CH₄.The model has several advantages. First, it has a theoretical basis which can easily be extended for the inclusion of more than one salt or gas. Second, the equations simplify to the empirically derived equation of Setschenow, in the limit of infinite dilution. Finally, the model is easily integrated into a framework of equations which can yield all of the thermodynamic properties of the system.An example in which values of the model parameters for interaction of gas with salt may be used to estimate the effect of dissolved gas or salt solubility is given.