Improving the Estimation Accuracy of Copper Oxide Leaching in an Ammonia–Ammonium System Using RSM and GA-BPNN

In this study, a response surface methodology (RSM) model was used to analyze and optimize the factors affecting copper leaching efficiency in a copper oxide ammonia-ammonium (AA) system based on the parameters of AA concentration (ammonium hydroxide and ammonium bicarbonate matched with 1: 1), leaching time, grinding fineness, liquid-solid ratio, and temperature. The RSM analysis showed that five individual variables had a significant influence and that the interaction between AA concentration and leaching time had the most significant influence on leaching efficiency. In order to improve the estimation accuracy of the copper leaching efficiency, a model consisting of a genetic algorithm and a back propagation neural network (GA-BPNN) was used to optimize the operation index. A back propagation feed forward neural network with 3 layers (5–10–1) was applied to predict copper leaching efficiency. The genetic algorithm was applied to analyze the optimal leaching conditions. The results revealed that the GA-BPNN model outperformed the RSM model for predicting and optimizing copper oxide AA leaching. The optimization results of the GA-BPNN resulted in an R² of 0.99827 and the highest predicted copper leaching efficiency of 79.49% was obtained under the conditions of an AA concentration of 4.78 mol/L, a leaching time of 157 min, a grinding fineness of 86.86% (–74 μm content account), a liquid-solid ratio of 2.87: 1, and a temperature of 313.17 K. A prediction and optimization method combining RSM and GA-BPNN, as used in this paper, can be further employed as a reliable and accurate method for ore leaching.     

Mathematical modeling of an exothermic leaching reaction system: pressure oxidation of wide size arsenopyrite participates

In the design of processes involving exothermic reactions, as is the case of several sulfide leaching systems, it is desirable to utilize the energy liberated by the reaction to drive the reactor toward autogenous operation. For optimal reactor design, models which couple leaching kinetics and heat effects are needed. In this paper, the principles of modeling exothermic leaching reactions are outlined. The system investigated is the high-temperature (160 °C to 200 °C) pressure (O2) oxidation of arsenopyrite (FeAsS). The reaction system is characterized by three consecutive reactions: (1) heterogeneous dissolution of arsenopyrite particles, (2) homogeneous oxidation of iron(II) to iron(III), and (3) precipitation of scorodite (FeAsO4-2H2O). The overall kinetics is controlled by the arsenopyrite surface reaction. There was good agreement between laboratory-scale batch tests and model predictions. The model was expanded to simulate the performance of large-scale batch and single-stage continuous stirred tank reactor (CSTR) for the same rate-limiting regime. Emphasis is given to the identification of steady-state temperatures for autogenous processing. The effects of operating variables, such as feed temperature, slurry density, and retention time, on reactor operation and yield of leaching products are discussed.     

响应曲面法优化产氨细菌浸矿试验研究

为了研究产氨细菌浸矿条件,采用响应曲面法对产氨细菌浸出碱性铜矿石的工艺条件进行优化,并揭示各因素对铜浸出效果的影响水平及其交互作用规律。研究结果表明,采用响应曲面法的中心组合设计(CCD)模型对试验结果进行回归分析,响应值精确度为98.85%。各因素对铜浸出效果影响的大小为:细菌初始接种量>助浸剂浓度>矿浆浓度。产氨细菌浸出碱性铜矿石最佳工艺条件为:细菌初始接种量30%,矿浆浓度14%,助浸剂浓度0.04 mol/L。在此条件下,浸出144 h后,铜浸出率可达47.32%,比优化前提高了4.67%。     

Treatment of a Nigerian covellite ore. Part I: Dissolution kinetics study by ammonia solution

In the present work, the leaching kinetics of covellite ore in ammonia solution was studied and the following variables, the solution concentration, reaction temperature and particle size were considered. A kinetics model representing the effects of these variables on the leaching rate was developed and it was ascertained that the leaching rate increases with increasing solution concentration, reaction temperature and decreasing particle size. At optimal conditions, 75.1% of covellite ore was reacted within 120 min and the leaching reaction was diffusion controlled by surface chemical mechanism. The calculated activation energy of 56.98 kJ/mol supported the proposed dissolution process.     

Modelling a Skin-Pass Rolling Process by Means of Data Mining Techniques and Finite Element Method

 An experience is presented using the finite element method (FEM) and data mining (DM) techniques to develop models that can be used to optimize the skin-pass rolling process based on its operating conditions. A FE model based on a real skin-pass process is built and validated. Based on this model, a group of FE models is simulated with different adjustment parameters and with different materials for the sheet; both variables are chosen from pre-set ranges. From all FE model simulations, a database is generated; this database is made up of the above mentioned adjustment parameters, sheet properties and the variables of the process arising from the simulation of the model. Various types of data mining algorithms are used to develop predictive models for each of the variables of the process. The best predictive models can be used to predict experimentally hard-to-measure variables (internal stresses, internal strains, etc) which are useful in the optimal design of the process or to be applied in real time control systems of a skin-pass process in-plant.     

Reliability as Tool for Hydraulic Network Planning

This paper presents a methodology to evaluate the reliability of water distribution systems that can be used in the design phase and for identifying repair works to be carried out on existing systems. The methodology is based on the statistical analysis of dimensionless performance indices (hydraulic performance indices) derived from a large number of simulations of various water system demand scenarios and∕or operating conditions. The hydraulic reliability index is assumed as the probability that, under a given operating condition, the hydraulic performance index will be above a certain threshold. Finally, the system's overall reliability (mechanical + hydraulic) is estimated using the overall reliability index, which is defined by the weighted mean of the hydraulic performance indices obtained for the various operating conditions. A case study using this methodology shows the concrete possibilities of applying this approach to a wide spectrum of cases, and the small influence on overall system reliability normally exerted by such events as the failure of links, pipes, and valves.     

湿法炼锌废渣综合浸出过程动力学研究

炼锌废渣———铜镉渣的浸出受酸度、液固比、反应温度、浸出时间等诸多因素的影响。从动力学的角度分析整个浸出流程,研究综合浸出时的最优化条件,并建立了符合固膜扩散控制的数学模型:1-23η-(1-η)23=ket,并通过Arrhenius经验公式,求得反应活化能。     

A mathematical model for heap leaching of one or more solid reactants from porous ore pellets

A mathematical model is derived in dimensionless form for heap leaching of one or more solid reactants from nonreactive, porous, spherical ore particles. The model is for the interpretation of column and heap leaching data and for use in the design and scaleup of heap leaching pro-cesses. Data from experimental column leaching tests are presented which validate the model. The scope of the present study is limited to the case where the rate-controlling reagent is a component of the lixiviant solution only and not of the gas phase. The effects of particle-scale kinetic factors, heap scale and operating variables, competition between multiple solid reactants, and particle size distribution are examined using the concept of the heap effectiveness factor. It is shown that heaps operate either «homogeneously,» with distribution of reagent throughout the heap at all times, or in a «zone-wise» manner, depending mostly on a single parameter. The observed value of this parameter deviates from the predicted value in inverse proportion to the degree of contact effectiveness between the lixiviant solution and the ore particles. A rough correlation between the contact effectiveness and Reynolds number is generated from the simulation of column test results.     

Optimization of Hollow-Fiber Design and Low-Pressure Membrane System Operation

An approach is presented for the numerical optimization of low-pressure membrane filtration processes. A multidimensional optimization of an ultrafiltration system is formulated for cost minimization and numerically solved for key optimal design and operating variables. Hollow-fiber ultrafiltration operation under steady-state conditions is assumed and optimized with respect to fiber radius, fiber length, crossflow velocity, transmembrane pressure, and system recovery. Optimizations are performed over variable raw water conditions using a sequential quadratic programming (SQP) algorithm. For typical small to moderately sized low-pressure membrane facilities (≈1 mgd), optimal fiber design and membrane system operation is predicted to be largely influenced by the characteristic dominance of capital costs over operating costs. Thus, total treatment costs tend to be optimal at values of decision variables where permeate fluxes are maximized, within the constraints prescribed by the system, and assuming a fixed membrane cost per unit area. For raw waters demonstrating apparent to significant membrane fouling, optimal membrane treatment is predicted to be achieved by using relatively narrow hollow fibers and relatively high crossflow velocities. For relatively clean raw waters demonstrating very high sustainable permeate fluxes, operating at low crossflow velocities—or perhaps even under the dead-end mode of operation—appears to provide the most cost-effective operation.     

Particle Classification Optimization of a Circulating Air Classifier

ABSTRACT

Undoubtedly, wet processing of ores requires huge quantity of water. This provides enough incentive for dry beneficiation of ores which has great promise predominantly from an environmental standpoint and water scarcity in the mining and processing industries. Therefore, the present investigation made an attempt to effectively address the issues related to dry classification of minerals. In this study, a three-factor-three-level Box–Behnken factorial design combined with response surface methodology (RSM) was employed for modeling and optimization of operational parameters of a circulating air classifier. The three main operating parameters studied were air flow rate, feed rate, and guide vane angle. The primary and interaction effects of operating variables were evaluated using RSM while generating the second-order response functions for both the responses, cut size and size selectivity increment. The values of cut size and size selectivity increment obtained using predictive models were in excellent agreement with the observed values. The optimization of these predictive response models resulted in the optimal values of air flow rate, feed rate, and guide vane angle for achieving better classification efficiency. This study establishes that the Box–Behnken factorial design combined with RSM effectively model the performance of circulating air classifier.     

硫化锌精矿空气氧化硫酸浸出的动力学研究

硫化锌精矿的浸出受精矿粒度、酸度、反应温度、催化剂加入量、浸出时间等诸多因素的影响。从动力学的角度分析整个浸出流程,研究综合浸出的最优化条件,使锌的浸出率可达98%以上,并建立了符合混合控制的数学模型:1-(1-α)1/3=8.07×10-7D-1[H+]-0.47[Fe2+]0.14exp(-11072/RT)t+B,通过Arrhenius经验公式,求得反应活化能为11.0727 kJ/mol。     

Optimization Study of Calcium Leaching From Steelmaking Slag

 Abstract： In order to study calcium leaching behavior for the steelmaking slag, factors that influence the leaching yield have been optimized. The results show that granularity of the slag, liquid to solid ratio (in short for L/S), temperature and reaction time have a significant effect on the leaching yield. The optimal conditions for leaching are determined as follows: 1) the granularity at 75 μm, L/S at 100, temperature at 60 ℃; 2) the granularity at 75 μm, L/S at 50, temperature at 40 ℃. Finally, the optimal leaching yield under these conditions is about 15%.     

Application of response surface methodology and central composite rotatable design for modeling and optimization of sulfuric leaching of rutile containing slag and ilmenite

In this study, application of the Response Surface Methodology and the Central Composite Design (CCD) technique for modeling and optimization of the influence of several operating variables on titanium recovery in a leaching process were investigated. The four main leaching parameters, namely temperature, acid concentration, leaching time and solid to liquid ratio, were changed during-the leaching experiments based on the CCD. A total of 30 leaching experiments were designed and carried out in the CCD method according to software-based designed matrix. According to the results, i.e., titanium recoveries with these four parameters as well as empirical model equations were developed. The model equations were then individually optimized by using quadratic programming to maximize titanium recoveries for both ilmenite and slag within the experimental range. The predicted values for titanium recoveries for both ilmenite and slag were found to be in a reasonable agreement with the experimental values, with R ² as correlation factor being 0.963 and 0.916 for ilmenite and slag, respectively.     

Dissolution behaviour of a beryl ore for optimal industrial beryllium compound production

This study involves the leaching of the beryl ore with sulphuric acid (H₂SO₄) solution for predicting optimal beryllium extraction conditions with the aim of assessing the importance of leachant concentration, reaction temperature and particle size on the extent of dissolution. A kinetic model to represent the effects of these variables on the leaching rate was developed. It was observed that the dissolution of beryl ore increases with increasing H₂SO₄ concentration, temperature, decreasing particle size and solid to liquid ratio. At optimal leaching conditions, 89.3% of the ore was reacted by 1.25?mol/L at 75°C temperature and 120 minutes with moderate stirring, where 1612.0?mg/L Be²⁺, 786.7?mg/L Al³⁺, 98.1?mg/L Fe³⁺ and 63.4?mg/L Ag⁺ were found as major species in the leach liquor. The unleached products constituting about 10.7% were examined by X-ray diffraction (XRD) and found to contain primarily, siliceous compounds such as Xonotlite, Antigorite, Chrysolite and Kaolinite.     

高磷鲕状赤铁矿酸浸脱磷动力学

在HSC6.0计算软件热力学分析的基础上,采用正交实验确定了高磷鲕状赤铁矿酸浸脱磷保铁的最佳工艺,并以最佳工艺为基础进行了酸浸过程中脱磷和铁损反应的动力学研究。热力学分析表明H_2SO_4为最佳酸浸用酸。正交实验得出最佳酸浸条件为:H+浓度为0.5mol/L的H_2SO_4溶液、酸浸时间40min、温度298K、液固比200mL∶14g、搅拌速度100r/min。在该条件下,脱磷率可达98.89%,铁损率仅为0.51%。通过SEM-EDS对酸浸前后高磷鮞状赤铁块矿试样分析表征得出:经H_2SO_4浸出后,磷灰石基本完全溶解,含铁矿相未发生明显反应。动力学分析显示:优化条件下,酸浸脱磷反应在298~328K内符合收缩未反应核模型,浸出过程主要受内扩散控制,表观活化能为11.24kJ/mol;铁损反应在298~328K内遵循收缩未反应核模型,浸出过程主要受化学反应控制,表观活化能为42.24kJ/mol。     

A GENETIC ALGORITHMS BASED MULTI-OBJECTIVE OPTIMIZATION APPROACH APPLIED TO A HYDROMETALLURGICAL CIRCUIT FOR OCEAN NODULES

Several hydrometallurgical processes have been studied for the extraction of metals from lean ores utilizing various flow sheet options. Of particular significance is the grade of the ore being treated, the energy consumed and associated costs, options for byproduct recovery, and the relative price of the products. A process scheme needs to be optimized for simultaneously maximizing metal throughput and minimizing the direct operating costs incurred within constraints set for the operating variables. This leads to a multi-objective optimization problem. The range of input grades for raw material, which a flowsheet can handle, needs to be worked out based on an optimization exercise. A lean manganese-bearing resource such as polymetallic sea nodules has been chosen in this article for the development of an optimization approach based on which the input raw nodules grades are to be treated by a particular flowsheet. Only the chemical consumption costs have been adopted in this article as a measure of direct operating costs. A linear simulation model for the flowsheet has been developed, keeping a set of design parameters constant. The solutions generated by using a sequential modular approach become inputs to an optimization procedure based on a multi-objective genetic algorithm belonging to the differential evolution family. The variables considered in the optimization task are the grade of nodules and reactivity of different species inside the reactor. A nickel equivalent (t/h function) has been suggested as a measure of productivity, as it indirectly enhances the input manganese ore grade through a price ratio effect. This productivity function was maximized with the simultaneous minimization of direct chemical costs. Pareto optimal solutions were generated with grades of nodules and reactivity in the leach reactor as decision variables. The effect of the price ratio on the Pareto optimal solutions was also investigated. The various cases investigated clarifies the methodology for choosing an appropriate ore grade range for a given process flowsheet. Appropriate decisions regarding the nature of raw material to be used for a given flowsheet are then found on the basis of the Pareto optimal solutions.     

Optimal Channel Cross Section with Composite Roughness

For channels with composite roughness, an equivalent uniform roughness coefficient and flow geometric elements are used in an optimal design method using the Manning equation. The optimal design problems are formulated in a nonlinear optimization framework with the objective function being a cost function per unit length of the canal. Constraints are the Manning equation, positive values for design variables, and specified values of side slopes or top width. The constrained problem is transformed into an unconstrained problem using the Lagrangian multipliers. To obtain an optimal solution for the resulting unconstrained problem, the first-order necessary conditions for optima are applied. The resulting simultaneous nonlinear equations are solved using the computational methodology developed. This technique is applied to illustrative numerical examples. The evaluations establish the potential applicability of the developed computational methodology for optimal design of open channel cross sections with composite roughness.     

响应曲面法优化钒钛磁铁矿提钒试验

 钒钛磁铁矿中的铁、钒以及钛等元素的高效回收,对钒钛磁铁矿资源的综合利用有非常重要的意义。研究表明,多种因素对钒钛磁铁矿的钠化-还原-熔分耦合过程的熔分程度及元素的收得率有重要影响。针对钒钛磁铁矿采用钠化-还原-熔分耦合工艺实现铁、钒及钛元素的综合回收,根据Box-Behnke原理设计方案,选取配煤量、配碱量及还原温度3个试验因素,通过响应曲面法研究各因素对钒钠化浸出指数的影响规律,并对试验因素进行优化。通过分析试验结果,建立相应的多项式模型,得到最优的工艺条件为,配煤量25.00%,配碱量58.29%,还原熔分温度1 251.84 ℃,钠化浸出指数响应值90.19%。在最佳条件下做验证试验,发现钠化浸出指数为 87.15%,误差仅为3.37%,证明响应曲面法预测模型具有可靠性和准确性。     

Application of response surface methodology for modelling of TiC coating on AISI D2 steel using a mechanical milling technique

The aim of this work is to identify relationships between the input variables and the process responses and to develop predictive models that could be used in the design of coating AISI D2 steel substrate with TiC powder by a ball milling process. A ‘one-factor design’ combining a response surface methodology with a modified cubic model was employed to modelling and optimisation of key operating factors involved in the ball milling procedure. The mentioned experiment was performed by changing these three variables, milling duration in the range of 10–50?h, fine and coarse powder particle size and as-received and hardened substrate. Coating thickness, microhardness and scratch hardness number were defined as process responses. Predicted values of responses obtained by using this model were in good agreement with experimental values. Optimum condition (24?h milling, hardened substrate and fine powder particle) supported the respective experimental test.     

Evaluation of velocity-dependent in situ leaching processes: Single-porosity model

A methodology to characterize processes of in situ leaching is developed to study various parameters that may affect the recovery of a valuable mineral and to assure a successful application of the in situ leaching technology. A leaching kinetics model is first derived based on the concept of representative elementary volume (REV) in porous ore deposits. Every parameter in the model is clearly defined and may be easy to obtain in practice. Then the governing equations are obtained for transport of both the reagent and the dissolved mineral in porous ore deposits. These equations are solved by a fully three-dimensional computer simulator. Effects on the mineral recovery of parameters such as lumped rate constant, ore porosity, injection flux, and macrodispersivities are investigated through the three-dimensional case with one injection well. It is found that all of these four parameters, interconnected through the ore porosity, significantly affect the effectiveness of the in situ leaching. Furthermore, the flow velocity of leach solution within an ore deposit may be the key parameter to the design of a real leaching mine because all of the other three parameters are site specific.