A recycle flow flotation machine model

Residence time measurements were made on a Denver laboratory flotation machine with and without the DR ring assembly. Soluble and insoluble tracers were used (a dye and fine quartz, respectively), and the variables studied were tank liquid volume, $\text{V}$, water and air volumetric flow rates, Q and Q_A respectively, and some geometric and design variables.By analogy with nominal residence time, $\text{t}{}_{\mathrm{<mtext>N</mtext>}}\text{(=}\text{V}\text{Q}\text{)}$, a term “effective residence time” $\text{t}{}_{\mathrm{<mtext>E</mtext>}}$ is defined by:

$\text{f}\text{(t)=}\text{exp}\text{[?}\text{t}\text{t}{}_{\mathrm{E}}$

where f(t) is the fraction of tracer remaining in the tank at time t. Perfect mixing is indicated if and only if: (i) data satisfies the exponential relationship; and (ii) $\text{t}{}_{\mathrm{<mtext>E</mtext>}}\text{t}{}_{\mathrm{<mtext>N</mtext>}}\text{= 1}$.Using the soluble tracer the machine behaved substantially as a perfect mixer under all operating conditions, except with the DR ring at values of Q_A nearly double the natural aeration capacity of the machine; condition (i) above was satisfied, but $\text{t}{}_{\mathrm{<mtext>E</mtext>}}\text{t}{}_{\mathrm{<mtext>N</mtext>}}\text{～ 1.1}$.With the insoluble tracer the machine behaved as a perfect mixer only without air. As Q_A increased, $\text{t}{}_{\mathrm{<mtext>E</mtext>}}\text{t}{}_{\mathrm{<mtext>N</mtext>}}$ increased from unity to about 1.2, and the effect was emphasized by the DR ring. In all cases condition (i) above was satisfied.A model in which the flow pattern in the tank includes a large component of pulp recirculation through the impeller region is developed. This model can account for the experimental findings but the details remain to be elucidated.     

The air flow number in flotation machine scale-up

The flotation cell is quantified as a mixing device for one, two, and three phase systems using combinations of water, air, and solids. To do this, power consumption was measured as a function of impeller speed, rate of aeration, and solids concentration. Initial suspension of solids and dispersion of suspended solids throughout the water or water/air system were also studied as influenced by impeller speed, particle size and solids concentration. The power number and air flow number were used to correlate the data.Flotation studies with a zinc ore using three sizes of cells of the same design, showed that aeration had to be controlled in the smaller cells to duplicate the results in the cell of commercial size. For optimum results the flow number range in the smallest cell was less than the critical value for suspension of coarse particles. Operating flow numbers for the three cell sizes under optimum conditions were close; commercial cells of the same size operating elsewhere appear to have two to three times higher flow numbers.The general relationships among air flow, impeller speed, particle suspension and flotation are discussed with particular reference to scale-up problems and coarse particle flotation. Both impeller speed and aeration should be considered as variables requiring systematic study and independent adjustment.     

Surrogate-based parameter inference in debris flow model

This work tackles the problem of calibrating the unknown parameters of a debris flow model with the drawback that the information regarding the experimental data treatment and processing is not available. In particular, we focus on the evolution over time of the flow thickness of the debris with dam-break initial conditions. The proposed methodology consists of establishing an approximation of the numerical model using a polynomial chaos expansion that is used in place of the original model, saving computational burden. The values of the parameters are then inferred through a Bayesian approach with a particular focus on inference discrepancies that some of the important features predicted by the model exhibit. We build the model approximation using a preconditioned non-intrusive method and show that a suitable prior parameter distribution is critical to the construction of an accurate surrogate model. The results of the Bayesian inference suggest that utilizing directly the available experimental data could lead to incorrect conclusions, including the over-determination of parameters. To avoid such drawbacks, we propose to base the inference on few significant features extracted from the original data. Our experiments confirm the validity of this approach, and show that it does not lead to significant loss of information. It is further computationally more efficient than the direct approach, and can avoid the construction of an elaborate error model.     

Multiphase models of flotation machine behaviour

Models in which the cell contents are partitioned into distinct pulp and froth phases are reviewed critically. The nature of the mixing within the phases is discussed. Multiphase models describing froth column concentration gradients and pulp residence time effects are mentioned. It is shown that at steady state multiphase models can be reduced to the two-phase case. Deficiencies in the models and topics requiring further development are outlined.     

A modified recycle model for Sr-Nd isotope system

A recycling model in conjunction with the theory of partial melting has been proposed. In contrast to other models, we divided the mantle and crust into the homogeneous recycling systems and the heterogeneous, isolated system, respectively. Inaccourdance with various partition coefficients for Sm, Nd and Rb and Sr, recycling rates and mantle/crust ratios, a series of numerical solutions are presented on the diagrams of f_Rb/Sr, f_Sm/Nd and Nd(t), Sr(t) v. s. time. In the model contrains that the recycling rates must be limited in the range of 1–4 km/yr and a medium-size depleted mantle, i.e., mantle/crust=20–60 can be adopted. The calculated ? Nd- ? Sr correlation curve is quite consistent with the observed values of Nd and Sr isotopes from young volcanic rocks and crustal materials.     

Aeration characteristics of laboratory flotation machine impellers

The aeration characteristics of several laboratory flotation machine impellers have been studied paying special attention to the pressure generated by impeller rotation. Correlations have been established between pressure (or Euler) number and Reynolds number, pressure ratio and air flow number, and these correlations have been compared with the conventional power correlations. Aeration and addition of frother affect both the power and the pressure generated by the rotating impeller; both decrease with increasing frother concentration, although in the low-impeller-speed region at relatively high frother concentrations the decrease in pressure is more pronounced than the decrease in power. Possible applications are mentioned and suggestions for further work are made.     

新安江模型中河网汇流参数Cs的一种计算方法

新安江模型河网汇流参数Cs主要取决于河网形态及地貌特征规律,针对PUB（Prediction in Ungauged Basin）问题,从物理机理分析的角度,构建描述河网汇流动态变化的微分方程并给出适当的定解条件,用解析法得出微分方程的解,从而探索出在无实测水文资料地区适用的Cs计算方法。选取中国湿润地区和半湿润地区25个流域,统计并分析了各流域次洪模型的Cs计算值和率定值。结果表明,从总体来看计算值和率定值基本上相等;不论流域是否分块,提出的Cs计算方法均适用;当其他参数保持不变,虽然Cs取计算值时所得到的次洪模拟结果略逊于取率定值的模拟结果,但误差在可接受的范围之内,也能取得良好的模拟效果;如果令Cs取计算值,再重新率定其余的各项参数,能够使模拟精度得到进一步提高。采用该法可推求无实测资料地区的汇流参数Cs值,使模型在无资料地区的应用成为一种可能。     

Automation of a laboratory flotation machine for improved performance

A commercial laboratory flotation machine (Denver Model D-12) has been automated for ease of operation and reproducibility. The major features of the system include two plexiglass cells of 4- and 2-1 capacity which are interchangeable for rougher and cleaner flotation, respectively, an electronic level controller and an air-flow rate controller. The level controller can be used for either pulp-level or froth-level control by adjusting the threshold setting. Two mechanical paddles on the sides of each flotation cell can be controlled to adjust the rate of froth removal. Test results demonstrate the reproducibility of the data obtained with the equipment.     

A study of a plug-flow model for flotation froth behaviour

The importance of the cleaning action of the froth has been recognised. In order to observe the effect of various mechanisms on the gradients of mineral concentration in the froth, experiments were performed in a flotation cell using a deep froth phase where transverse motion of the froth was reduced to a minimum. The variables chosen for study include gas rate, baffling of the froth and product removal rate. The mineral studied comprised a mixed Cu, Zn and Fe sulphide with a siliceous gangue. A model based on counter-current plug-flow assumptions is advanced to describe some of the effects observed. A number of these effects are simulated using this model, leading to a better understanding of some of the processes occurring in the froth.     

RBFNN模型在渗透系数反演中的应用

针对经典的BP网络存在的一些缺陷,采用了径向基函数神经网络（RBFNN）。在相同的收敛条件下,用RBFNN和经典算法的BP网络进行了比较,表明前者具有优越性。在工程实例中,基于人工神经网络的非线性特点,在三维渗流有限元的基础上,利用RBFNN反演了大坝的渗透系数。并利用反演结果进行渗流场分析,水头预报值也有很高的精度,说明反演结果是正确的,从而,验证了RBFNN应用于反演分析中的可靠性。     

一种新的本构模型及参数标定

在现行本构模型研究的基础上,建立了一种全新本构模型,它可以描述4种行为特征：弹性-弹塑性-软化、弹性-弹塑性-硬化、理想弹塑性、弹脆性;其模型参数只有4个,现行模型只是该模型的特例（如：邓肯-张模型）,介绍了模型参数的决定方法,其决定的依据是：模型所描述的行为特征与实测数据之间相关度最优;分析了岩土体破坏后区特征,提出岩土体破坏后区行为可以定义为视应力-视应变特征。并以实例对该模型进行了说明,结果表明,该模型可以描述岩土体的行为特征,并对虚内键模型、弹簧模型和离散单元法等具有借鉴作用。     

The entrainment factor in froth flotation: Model for particle size and other operating parameter effects

Accurately estimating entrainment is crucial when predicting flotation performance as it is essential for determining the concentrate grade achieved. It has been found previously that the amount of gangue entrained is proportional to the water recovery; this proportionality is referred to as the entrainment factor. Experimentally it has been found that entrainment is a strong function of particle size, as well as being dependent on other cell operating parameters such as froth depth and air rate.A simplified theoretical model for entrainment is developed which includes the effects of liquid motion and content, particle settling and particle dispersion. First, a detailed one-dimensional differential model for the entrainment factor is developed and solved numerically. Thereafter, a simplified analytical expression for the entrainment factor is produced which is a good approximation to the more detailed one-dimensional model. Both these models are shown to predict closely experimental trends for entrainment as a function of particle size and froth depth.     

Impeller/stator interactions in a laboratory flotation machine: The effect of wear on suction

The suction generated by several different combinations of impeller and stator has been measured. An experimental method provides information on the separate contribution of the impeller, while the stator contribution is calculated from an interaction model. The effect of wear as indicated by reversing the direction of rotation is discussed.     

A compartment model for the mass transfer inside a conventional flotation cell

A model is developed by taking into account the simultaneous mechanisms of true flotation and entrainment in a conventional flotation cell. The total volume of the cell is divided into three compartments: pulp collection zone, pulp quiescent zone and froth region, with the mechanisms being modeled as occurring at the same time but originating at different places: true flotation from the collection zone and entrainment from the quiescent one. A particle is referred to as suspended in water or attached to an air bubble, depending upon its original state before crossing the pulp–froth interface (whether or not it remains in that state all the way to the concentrate launder). The model is obtained by solving a set of equations describing the mass conservation of solids and water between adjacent compartments. The principal mass transfer factors are identified as: the flotation rate constant, the mean residence time in the collection zone, the froth recovery of attached particles, the degree of entrainment through the froth and the water recovery from the feed to the concentrate. The development presented here allows the intricate nature of the mass transfer in a flotation cell to be reduced to one single equation, overcoming the need of numerical methods for simulation purposes. Moreover, it is shown that reliable prediction of grade and recovery can be obtained without detailed information on the pulp hydrodynamics or on any froth sub-process either than drainage, bubble bursting and bubble coalescence.     

A nonstationary parameter model for the sandstone creep tests

The rock masses of hydro-fluctuation belt experience seepage pressure following impoundment in the Three Gorges Reservoir; its creep behaviors are significant for reservoir bank slopes. To study the creep behaviors under seepage pressure (0, 1.45, and 1.75 MPa), we performed creep tests using representative landslide sandstone in the Three Gorges Reservoir and investigated the sandstone creep behaviors under the coupling effects of seepage pressure and stress. Previous researches on rocks have usually regarded the creep constitutive parameter as a constant; however, in this study, a nonlinear, nonstationary, plastic-viscous (NNPV) creep model which can describe the curve of sandstone creep tests is proposed. The rock-creep parameters under three levels of seepage pressure were identified, and theoretical curves using the NNPV model agreed well with the experimental data, indicating that the new model cannot only describe the primary creep and secondary creep stages under varying seepage pressures but also, in particular, perfectly describes the tertiary creep stage. Finally, the sensitivity of the NNPV model parameters is analyzed, and the result shows that the nonstationary coefficient α and the nonlinear coefficient m are main parameters affecting the tertiary creep stage.     

Response of sand ripples to change in oscillatory flow

Ripples take time to evolve to a new equilibrium state in response to a change in wave-generated oscillatory flow. The paper presents results from flow tunnel experiments designed to examine oscillatory flow transient ripple processes under controlled, full-scale laboratory conditions. The experiments include study of the growth of ripples from flat bed and the evolution of existing ripples to new equilibrium ripples in response to a step change in the flow. In general, ripples evolve through a combination of two main processes: (i) from a flat bed or from a bed consisting of ripples that are smaller than the equilibrium ripples through a combination of 'slide' and 'merge'; (ii) from a bed consisting of ripples that are larger than the equilibrium ripples through a combination of 'split' and 'merge'. The experimental results show that equilibrium ripple geometry is independent of initial bed morphology while the time to reach equilibrium is largely independent of the initial bed and the equilibrium ripple size. The time to reach equilibrium depends strongly on the mobility number, and a new empirical equation relating mobility number and the number of flow cycles to equilibrium is proposed. This equation is combined with a simple exponential function for ripple height growth or decay to produce a new empirical model for ripple height evolution, which gives a reasonably good overall agreement with the measurements. The model is based on experiments involving one sediment size only and further work is needed to develop the model for other sand sizes.     

A transversely isotropic thermo-poroelastic model for claystone: parameter identification and application to a 3D underground structure

A transversely isotropic thermo-poroelastic constitutive law is developed and implemented in the finite element code Code_Aster (EDF, France). It is then validated using an analytic solution for an inclined borehole in a transversely isotropic medium. A strategy for identifying the parameters of the transversely isotropic thermo-poroelastic model based on an inverse method is proposed on the basis of different laboratory tests. To demonstrate the efficiency and applicability of the model, it is then applied in a three-dimensional numerical model of an underground structure in a parameter sensitivity study. The results of the modelling highlight the importance of accounting for anisotropic phenomena when determining the dimensions of underground facilities. The whole approach is presented in the paper, from model development to application to 3D numerical modelling to an engineering case study.     

A low-dimensional subsurface model for saturated and unsaturated flow processes: ability to address heterogeneity

A low-dimensional model that describes both saturated and unsaturated flow processes in a single equation is presented. Subsurface flow processes in the groundwater, the vadose zone, and the capillary fringe are accounted for through the computation of aggregated hydrodynamic parameters that result from the integration of the governing flow equations from the bedrock to the land surface. The three-dimensional subsurface flow dynamics are thus described by a two-dimensional equation, allowing for a drastic reduction of model unknowns and simplification of the model parameterizations. This approach is compared with a full resolution of the Richards equation in different synthetic test cases. Because the model reduction stems from the vertical integration of the flow equations, the test cases all use different configurations of heterogeneity for vertical cross-sections of a soil-aquifer system. The low-dimensional flow model shows strong consistency with results from a complete resolution of the Richards equation for both the water table and fluxes. The proposed approach is therefore well suited to the accurate reproduction of complex subsurface flow processes.     

Dynamic model of flotation cell banks — circuit analysis

While all mineral industry flotation circuits are stable, they are sensitive to low-frequency perturbations in the feedrate. In both countercurrent and cocurrent circuits, the lead cell is more sensitive to feed variations. The frequency response predicts the amount of extra cell capacity needed to handle the maximum feed due to a sinusoidal forcing function. Feedback loops are more significant than sump delays. The countercurrent $\text{4 × 4}$ circuit floating quartz, with a 200-sec retention time, requires 75 minutes for the concentration of quartz in the input to the first cell to reach 95% of its steady-state value. Countercurrent circuits were found superior to cocurrent circuits in all respects.