Distribution function of comminution kinetics — Modelling and experimental study

A mathematical model for distribution function is developed considering the distribution of the number of fractures that can occur in a particle. It is shown as a consequence of the model that selection and distribution functions are intimately related through a single parameter — expected number of fractures per unit original size. This parameter can be comparatively easily obtained from batch experiments and can later be used to simulate industrial-scale grinding mills. Predictions of the model are amply confirmed by preliminary experimental results and other published observations. A correlation is developed to predict the parameter of the model from known equipment and operating variables for the particles used in the present study.     

Application of geological benchmarks for determining groundwater residence time in the aquifer based on uranium isotope data: Evidence from the Severnaya Dvina Basin

Using the Severnaya Dvina Basin as an example, it is shown that information on the distribution of natural U isotopes in aquifers can be applied for practical estimation of the duration of interaction between groundwater and host rocks (age of groundwater). The proposed calculation method includes preliminary determination of the generalized calculated parameter (probability of the transfer of ²³⁴U excess to water) based on geological benchmarks, hydrodynamic calculations, and paleohydrogeological reconstructions. It is assumed that this probability is constant for aquifers composed of homogeneous rocks with certain lithological composition and oxidizing conditions for U. The obtained correlations are valid for a model, where water entering the aquifer lacks U. If it contains such U, the “transport” time, which is equivalent to the timing of respective concentrations and isotopic ratios in the aquifer unit, is determined and estimates of the “water-rock” interaction in the aquifer unit are corrected.     

非均匀多孔介质等效渗透率的普适表达式

多孔介质渗流是普遍的物理过程,涉及地下工程、地热开采、环境工程等各行各业,尤其是工程建设,常面临防渗问题。由于地质条件的复杂性,工程区域地层受到成岩、压实、风化、生物作用等各种影响,故渗流性质复杂,常需要对建设区域的渗流状况进行数值模拟,从而为工程的设计施工提供决策依据。数值仿真结果依赖于对地层介质关键参数的选取,但目前工程多将其视为均匀介质处理,对于介质的非均匀特性考虑较少。文章旨在研究非均质多孔介质渗透率空间分布与等效渗透率的关系。基于连续介质假定、达西定律以及非均匀多孔介质渗透率空间分布函数,建立一维到三维的达西渗流问题模型,通过求解偏微分方程和理论推导,得到基于渗透率空间分布函数的等效渗透率理论表达式,并与有限元计算的数值解进行对比分析,结果表明理论值和数值解误差很小,证明等效渗透率的表达式的合理性。利用该成果可通过多点局部渗透率的测定构建渗透率空间分布函数,从而对整体渗流区域的渗透性质进行快速计算和评估,从而简化异常复杂的工程地质模型以减少计算量需求,对于工程仿真的快速计算和结果评估有重要意义。     

Scale up of lifters in ball mills

Liner design and lifter geometry in tumbling mills are very important in comminution kinetics and energy consumption. In terms of the parameters of the batch grinding model, the breakage rate function decreases as lifter size increases while the breakage distribution function is independent of the lifter size. However, the specific energy consumption is not a function of lifter size. Reducing the lifter height from 2.54 cm to 0.32 cm increases the production from this mill by 37%. When the mill is operated without any lifters, the charge apparently slips inside the shell resulting in lower breakage kinetics and higher energy consumption.     

Distribution surfaces in solvent extraction systems

In the solvent extraction of metals, the distribution of the metal is usually dependent on the concentrations of several different species in the two phases. Despite this fact, distribution isotherms are usually presented as plots of C_o as a function of C_aq and these are used for a McCabe-Thiele type evaluation of a number of stages and flow rates, etc., each individual isotherm being valid only for one set of initial conditions; this treatment limits the possibilities of optimizing the system. In the present paper an extension of three-dimensional plots is suggested with special reference to the Cu/LIX64N extraction system. The distribution surface is defined and the general properties of the plots are outlined.A procedure is outlined whereby the surface can be represented on a two dimensional plot and a theoretical model for the surface can be superimposed.The paper also shows how distribution ratios (D values) are related to the surface.     

固结试验的数学描述

固结试验的一般数学描述是建立在主次固结人为的分开的基础上的.而本文根据固结试验所得到的沉降与时间关系曲线的特点,建立了一个简单实用且连续的函数来描述固结试验,并分析了该模型的特点.历时18个月的香港软土固结试验,验证了该方法的正确性,并对模型的参数进行了讨论.     

Application of distribution functions to partition curves

The regular Tromp curve is a log-normal probability (K—Kolmogoroff) function; it is, however, also a modified RRS (Rosin-Rammler-Sperling) or GGS (Gates-Gaudin-Schuhmann) function. The exponent m (distribution modulus) is a measure of the slope of the functions, i.e. Tromp curves and can be used instead of the indices E_p or I to characterize the efficiency of the various separating (sorting or classifying or sizing) equipments. The relationship $\text{Im ?}\text{constant}$ is valid.     

Modelling mineral size reduction in the closed-circuit ball mill at the Pine Point Mines concentrator

Using plug flow material transport and a cumulative-basis rate-of-breakage parameter, overall size reduction through the closed-circuit ball mills at the Pine Point and Gibraltar concentrators was simulated over a wide range of operating conditions. The rate-of-brakage parameter was related to particle size by a power law, the exponent (n) being: Pine Point, n = 1.043 ± 0.026, and Gibraltar, n = 0.747 ± 0.020. The success of this approach probably stems from the high (> 1.5) circulating load ratios encountered.By analogy individual mineral size reduction at Pine Point was examined. A similar rate-of-breakage parameter versus size relationship was found. Pyrite was the hardest mineral, but fine galena was equally resistant. However, the approximation that mineral and overall rates of breakage were the same gave an adequate fit to the mineral size reduction. This was emphasized by combining with a cyclone model to simulate cyclone overflow mineral size distribution. A more accurate cyclone model is shown to be more important in simulating mineral deportment at Pine Point.Complementary laboratory batch grinding tests were conducted on rod mill discharge and ball mill feed samples. Sufficient agreement with the first-order hypothesis was observed to analyse the rate-of-breakage parameter. The kinetics was similar for both samples and in turn similar to the plant-derived kinetics in terms of relative mineral rates-of-breakage and the relationship of the rate-of-breakage parameter with particle size.     

非一致性水文频率分析的研究进展

水文频率分析计算需满足独立随机同分布假设,其中同分布是指水文样本在过去、现在和未来均服从同一总体分布,即样本应具有一致性。然而,由于气候变化及人类活动的影响,使得一致性的假设受到挑战,因此变化环境下传统频率计算方法获得的设计结果,其可靠性受到质疑。为此,探索适应非一致性极值系列的频率分析方法已显得非常重要。总结介绍国内外关于非一致性水文频率分析的一些代表性研究成果,主要集中在以下两方面:一是基于还原/还现途径;二是基于非一致性极值系列直接进行水文频率分析途径。最后对进一步值得研究的问题进行了展望。     

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.     

Peut-on évaluer le rôle de la sédimentation sur l'effet de serre à l'échelle de temps des cycles orbitaux ?Can the role of sedimentation in the greenhouse effect at the time scale of orbital cycles be evaluated?

The evolution of the atmospheric CO₂ content is partly a response to the lack of balance between oceanic sedimentation and continental weathering, because the oceanic C reservoir tends to balance net inputs or losses from slow processes by rapid exchanges with the atmospheric reservoir. This response strongly depends on both amplitudes and time scales of the related processes. At Milankovitch or lower time scales, global models generally do neglect organic matter fossilisation, but such an assumption is only valid for oligotrophic systems. In eutrophic or mesotrophic systems, organic matter is not negligible and should be considered relatively to the carbonate sedimentation in order to know whether the impact of the sedimentation was a source or a sink for atmospheric CO₂. To cite this article: P. Bertrand, C. R. Geoscience 334 (2002) 521–528.     

Pressure dependence of the elastic constants of nonmetamict zircon

The single crystal elastic constants of nonmetamict zircons have been measured as a function of pressure to 12 kb at room temperature and also as a function of temperature between 25 and 300° C at atmospheric pressure. The pressure derivatives of the elastic constants are: C ₁₁=10.78, C ₃₃=5.88, C ₄₄=0.99, C ₆₆=?0.31, C ₁₂=3.24, C ₁₃=6.20. The anomalous negative behaviour of C ₆₆ versus pressure could be associated with a high pressure phase transition. The pressure and temperature derivatives of the isotropic elastic wave velocities and elastic moduli for nonmetamict zircon are calculated from the present single crystal data by the Voigt, Ruess, and Hill approximations and compared with the values of some other oxides and silicates. The pressure derivative of the isotropic adiabatic bulk modulus is relatively high (dK _S/dP=6.50), and the pressure derivative of the shear modulus is relatively low, (dG/dP=0.78), compared to the corresponding values for some other oxides and silicates. The Debye temperature, ?_D, and the high temperature limit of the Grüneisen parameter, γ_Ht, calculated from the elastic constants and their pressure derivatives, agrees well with the Debye temperature and the thermal Grüneisen parameter, γ_th, calculated from the thermal expansion, heat capacity, and compressibility data.     

Empirical assessment of the critical time increment in explicit particulate discrete element method simulations

This contribution considers the critical time increment (Δt_crit) to achieve stable simulations using particulate discrete element method (DEM) codes that adopt a Verlet-type time integration scheme. The Δt_crit is determined by considering the maximum vibration frequency of the system. Based on a series of parametric studies, Δt_crit is shown to depend on the particle mass (m), the maximum contact stiffness (K_max), and the maximum particle coordination number (C_N,max). Empirical expressions relating Δt_crit to m, K_max, and C_N,max are presented; while strictly only valid within the range of simulation scenarios considered here, these can inform DEM analysts selecting appropriate Δt_crit values.     

An iterative method for the construction of equilibrium N-body models for stellar disks

One widely used technique for the construction of equilibrium models of stellar disks is based on the Jeans equations and the moments of velocity distribution functions computed using these equations. Stellar disks constructed using this technique are shown to be “not entirely” in equilibrium. Our attempt to abandon the epicyclic approximation and the approximation of infinite isothermal layers, which are commonly adopted in this technique, failed to improve the situation substantially. We conclude that the main drawback of techniques based on the Jeans equations is that the system of equations employed is not closed and, therefore, requires adopting an essentially ad hoc additional closure condition. A new iterative approach to constructing equilibrium N-body models with a given density distribution is proposed. The main idea behind this approach is that a model is first constructed using some approximation method, and is then allowed to adjust to an equilibrium state with the specified density distribution—if necessary, with the required parameters of the velocity distribution remaining fixed in the process. This iterative approach was used to construct isotropic, spherically symmetric models and models of stellar disks embedded in an external potential. The numerical models constructed prove to be close to equilibrium. It is shown that the commonly adopted assumption that the profile of the radial-velocity dispersion is exponential may be wrong. The technique proposed can be applied to a wide range of problems involving the construction of models of stellar systems with various geometries.     

损伤条件下深部岩体巷道光面爆破参数研究

岩体条件复杂多变,为了提高光面爆破的适应性、改善光面爆破效果,对损伤条件下深部岩体巷道光面爆破参数进行研究。通过对深部岩体巷道光爆层原岩应力场、光面爆破机制和振动损伤特征进行分析,基于爆炸应力波和爆生气体综合作用理论,考虑高原岩应力和岩石损伤影响,提出了损伤条件下深部岩体巷道光面爆破参数确定的计算方法。研究表明, （1）高原岩应力相当于提高了岩石的抗拉强度,不利于炮孔初始裂纹的形成及贯通,宜减小周边眼间距;（2）岩石损伤后,其他条件不变,光面爆破的炮孔间距和抵抗线值可适当加大;（3）高原岩应力和损伤条件下,光面爆破的炮孔间距较小时,容易造成爆后围岩损伤,降低围岩的稳定性能,因此,提高爆破效果的同时应及时加强支护,以确保施工安全和围岩稳定;（4）本文提出的光面爆破参数计算公式,经现场爆破验证效果良好,适用于复杂多变的岩体环境。     

Sources and occurrence of C12C22n-alkane distributions with even carbon-number preference in sedimentary environments

The occurrence of C₁₂C₂₂n-alkanes with a strong even carbon-number preference is reported in recent and Miocene sediments, encompassing marine and freshwater systems, deposited under oxic and anoxic conditions. It is therefore shown that these n-alkanes can be found in a wider type of sedimentary environment than those previously described. The occurrence in some cases of a parallel distribution of C₁₄C₂₀n-alk-1-enes is also illustrated. A variety of biological sources, including both marine and freshwater bacteria as well as fungi and yeast species is suggested to account for such distributions.     

Reconstructing the Green's function through iteration of correlations

Correlations of ambient seismic noise are now widely used to retrieve the Earth response between two points. In this study, we reconstruct the surface-wave Green's function by iterating the correlation process over the tail of the noise-based correlation function. It has been demonstrated that the so-called C³ function shows the surface-wave part of the Green's function. Using data from 150 continuously recording stations in Europe, the C³ results help in the extraction of the travel-times from noise-based measurements, especially through the suppression of effects caused by non-isotropic source distributions. We present the results of the next iterative step (i.e. C⁵), which show that some coherent signal is still present in the coda of the C³ function, and we investigate the evolution of the reconstruction of the Green's function throughout the iteration process. Finally, we discuss the interest of combining information from the different correlation functions to improve noise-based tomography analysis.     

Steady-state vertical distribution of cohesive sediments in a flow

Settling velocity of diluted suspended aggregates is examined under steady-state conditions. It is shown that if the local settling velocity of the suspended mass of sediments at the bottom is gamma distributed, then, the vertical variation of the local mean settling velocity $\overline{W}$ is proportional to a power $1/r$ of the local concentration C, where r is the gamma distribution parameter. That is a consequence of the suspended-sediment sorting produced by the vertical dynamics. The parameter r characterizes the range of settling velocity values for all the aggregates simultaneously in suspension. To cite this article: M. Sánchez et al., C. R. Geoscience 337 (2005).     

Mathematical models for petroleum-forming processes: carbon isotope fractionation

A mathematical model has been developed in which carbon isotope fractionation during thermal cracking of n-paraffins can be simulated. The model has been calibrated based on data from laboratory cracking experiments carried out on n-octadecane. Relative rate constants for cleavage of C¹²-C¹², C¹²-C¹³ and C¹³-C¹³ bonds agree with the experimental values obtained by other workers.Application of this model to the process of petroleum formation gives good agreement with some existing experimental data, but suggests that a review of our understanding of isotope fractionation during thermal cracking may be necessary. The relative importance of the degree to which the organic material has been cracked and of the type of the organic material in influencing δC¹³ values is discussed.The present model predicts that cracking of n-paraffin distributions having initial odd or even carbon number predominances can induce isotopic inhomogeneity among the homologs of the resulting distribution. The model exhibits some deficiencies in explaining or predicting the δC¹³ values of ethane and propane in relation to methane in gases and of oils and associated methane. Explanations for these discrepancies may lie in the simplicity of our mathematical model, in our assumption of initial isotopic homogeneity within molecules and in our use of only n-paraffins as the source molecules for the cracking reactions.