Least-squares adjustment of mathematical model of heat and mass transfer processes during solidification of binary alloys

Classical boundary and initial-boundary value problems in heat and mass transfer are generally formulated in a mathematically unique way. Boundary and initial conditions together with physical properties of the thermodynamic system are treated as exactly known. The influence of different kinds of mathematical model simplifications on the accuracy of solution and reliability of the model are not usually analyzed. The problems become more complicated when inverse ill-posed initial-boundary problems are considered. The widely used procedure of model validation is based on direct comparison of analytical or numerical solution, unique in a mathematical sense, with measurement results. The main feature of the method presented in this article is that all experimental results are included into the mathematical model. Thus, because of the inevitable errors of measurements, the system of model equations becomes internally contradicted as the number of unknown variables is less than the number of equations. In consequence, basic laws of energy and mass conservation are not satisfied. To adjust the experimental data to the mathematical model, an orthogonal least-squares method is proposed. Special attention has been paid to the coupling of experimental data with the nucleation and grain growth models formulated by Rappaz and co-workers. Theoretical considerations are illustrated with experimental data for an Al-Si alloy.     

Single-Sludge Nitrogen Removal Model: Calibration and Verification

The objective of this work was to calibrate and verify a modified version of a mathematical model of a single-sludge system for nitrification and denitrification. The new model is based on long-term experimental results, and the main modifications are related to the biological oxygen demand removal kinetics and biomass activity expressions. The model consists of 22 equations with 54 parameters, including 19 kinetic and stoichiometric coefficients. Experiments were performed on four bench-scale units and one pilot plant fed with domestic wastewater. Six sets of runs were carried out under different operational conditions. In the calibration procedure, a mathematical algorithm was implemented, in which an optimal set of coefficients was selected. Several coefficients were directly determined experimentally. Model verification was based on the comparison of experimental results with the values predicted by the mathematical model using a fixed set of model coefficients for each set of runs. From the verification results, the model is considered to be a useful one for the design of a new treatment system and operation of an existing one.     

A dynamic mathematical model of the complete grate/kiln iron–ore pellet induration process

Induration (drying and hardening) of iron ore pellets is an energy-intensive feed preparation step for both the blast furnace and direct reduction routes to iron. It is commonly carried out by a ‘grate/kiln’ process. A mathematical model of the process is described, in which mechanistic models of the grate furnace, kiln, and cooler are linked to enable simulation of the entire process. The model includes equations for the gas stream pressure balances and process controller responses, and provides dynamic solutions. The validation of the model for an operating plant is discussed and steady-state solutions are compared with data from the plant.     

Rates of extraction of cobalt from an aqueous solution to D2EHPA in a growing drop cell

A technique has been developed to study the rate of extraction of cobalt from an aqueous phase into a growing drop of heptane containing di(2-ethylhexyl) phosphoric acid (D2EHPA). The hydrodynamics of the growing drop are accounted for. Experiments have been carried out at the single temperature of 25 ± 0.1°C Sphere the pH, aqueous cobalt concentration and the organic D2EHPA concentration have been varied. A mathematical model is given which is based upon the control of rate by mass transfer with chemical reaction. The model fits the experimental data well considering the experimental errors and the complexity of the transfer of solute where fresh surfaces are continually produced by the growing drop.     

A kinetic model of the peirce-smith converter: Part I. Model formulation and validation

A kinetics-based mathematical model of the Peirce-Smith converter has been developed. The model considers mass transfer, heat transfer, and reactions between each of the phases present in the converter. Model validation is carried out using industrial data obtained from both copper and nickel converters. The model is generally able to predict the temperature and compositional variations of the converters to within the errors of the industrial data. However, the interactions between the white metal and slag during the copper blow are not understood sufficiently to model well.     

Kinetic Studies on Evaporation of Liquid Vanadium Oxide, VO x (Where x?=?4 or 5)

As part of the Swedish National Eco-steel project, the present work was carried out with a view to study the evaporation of vanadium as V₂O₅ with a focus on the health hazards. The evaporation rate was followed by monitoring the mass loss from liquid V₂O₅ melts by thermogravimetric analysis (TGA) in the temperature range 1723?K to 1873?K (1450?°C to 1600?°C). The studies were carried out under three different oxygen partial pressures, viz, oxygen, air, or CO₂. The experiments were carried out in the isothermal mode. The Arrhenius activation energies for the evaporation reaction in different atmospheres were calculated from the results. A mathematical model was developed in order to describe the kinetics of the evaporation process. Good agreement could be achieved between the mathematical model and the experimental results. Evaporation coefficients and enthalpies in different atmospheres were also estimated. The present results may also have implications in recovering vanadium values from different vanadium sources.     

Study of inclusion re-entrainment in a filter bed

Filtration is widely used in various processes such as water treatment and aluminum casting for the removal of unwanted impurities called inclusions. The deposited inclusions can re-enter the flow as a result of the unfavorable hydrodynamic conditions within the system or flow instabilities, such as flow stop/start periods during casting cycles in the aluminum industry. In this project, the re-entrainment of inclusions was studied as a function of filter-bed length, particle size, inlet inclusion concentration, and inlet velocity. A physical model using water containing PVC particles as inclusions was built. Experiments were carried out under continuous-flow as well as interrupted-flow conditions in this pilot-scale filter. It was found that the smaller bed particles and longer bed length enhance the deposition and reduce the re-entrainment of inclusions. Increasing the inlet velocity has a negative effect on the deposition and increases the re-entrainment. A one-dimensional mathematical filtration model has also been developed, and its predictions were compared with the experimental data from the pilot filter and the plant. This article presents the experimental study, its results, and the comparison between model predictions and experimental data. Applicability of the model to aluminum filtration is also illustrated.     

六碳糖和五碳糖同步糖化与共发酵的数学模型

Reliable production of biofuels and specifically bioethanol has attracted a significant amount of research recently. Within this context,this study deals with dynamic simulation of bioethanol production processes and in particular aims at developing a mathematical model for describing simultaneous saccharification and co-fermentation (SSCF) of C6 and C5 sugars. The model is constructed by combining existing mathematical models for enzymatic hydrolysis and co-fermentation. An inhibition of ethanol on cellulose conversion is introduced in order to increase the reliability. The mathematical model for the SSCF is verified by comparing the model predictions with experimental data obtained from the ethanol production based on kraft paper mill sludge. When fitting the model to the data, only the yield coefficients for glucose and xylose metabolism were fine-tuned, which were found to be 0.43 g.g-1 (ethanol/glucose) and 0.35 g.g-1 (ethanol/xylose) respectively. These promising validation results encourage further model application to evaluate different process configurations for lignocellulosic bioethanol technology.     

Mathematical simulation and experimental verification of melting resulting from the coupled effect of natural convection and exothermic heat of mixing

When melting processes are associated with an exothermic heat of mixing, unique coupled transport phenomena take place. In this article, a mathematical model has been developed to simulate these unique coupled heat and mass transfer events. The model was based on the control-volume finite difference approach and on an enthalpy method. In order to verify the mathematical model, a low-temperature physical model was established consisting of ice and sulfuric acid solutions. In this physical model, both temperature and velocity measurements were carried out. The model predictions were compared with experimental measurements, and they were found to be in good agreement. The model was also applied to a high-temperature system, namely, the melting of silicon metal in liquid high carbon iron. The predictions distinguished two periods present in the entire melting process. In the first period, the silicon was heated up. The second period, i.e., free melting period, occurred in tandem with the exothermic reaction, and consequently, the melting process was greatly accelerated. As was the case with the low-temperature physical model, as with the high-temperature system, good agreement was obtained between the predicted results and the experimental measurements.     

应用Minesight软件评估某钨矿资源

以福建某矿山为例，运用地质统计学方法，通过分析钨品位的统计分布特征，进行变异函数的计算及结构研究，建立了矿床的数学模型，并且通过交叉验证工作，以模型结果与实际矿床进行了比较，对模型及其估值结果作出综合评价。     

Modelling of electrovortex and heat flows in dc arc furnaces with bottom electrode

Abstract

The article is devoted to the investigation of interaction between electrovortex and heat flows of liquid metal in dc arc furnaces with a bottom electrode. A mathematical model of liquid steel flows in a dc arc furnace with a bottom electrode was developed, and an algorithm of a three-stage solution was produced based on standard software packages. The results of electromagnetic, heat transfer and hydrodynamic analysis in industrial dc arc furnaces are given. It is shown that the Lorentz force makes up ～30% of the volumetric gravity force and makes the main contribution to vortex flow of liquid metal in a dc arc furnace. The convection flows with the maximum heat power of furnace make a significant contribution to the vortex flow of liquid metal, and the maximum value of the vortex flow velocity is ～1·5 times more than the movement without convection. The verification of results has been carried out by comparing them with general electrovortex flows theory, experimental data and results of similar software packages.     

基于深度学习的带钢精轧过程自由宽展预测

为提高带钢精轧过程宽度的控制精度,以实际生产数据为驱动,建立深度学习网络模型,对自由宽展进行预测。采用拉伊达准则对实际生产数据进行清洗,对清洗后的数据进行相关性分析,并提取相关系数大于给定阈值的特征。基于预处理后的特征数据,对深度学习网络进行训练,建立自由宽展预测模型。针对测试实例,分别采用该模型与传统数学模型进行预测,并从均方误差、最大偏差以及误差分布等多个方面进行对比分析。结果表明,所建立的深度学习预测模型,具有更高的预测精度和更好的性能指标。     

Pyrolysis Kinetics of Rice Husk in Different Oxygen Concentrations

The effects of oxygen on the pyrolysis of rice husk were investigated with a thermal gravimetric analysis (TGA) reaction system. Pyrolysis experiments of rice husk were carried out in N2, 10% O2, and air at the heating rates of 2, 5, and 10?K/min. The TGA curves indicated two principal reactions, distinguished by significant and distinct mass changes over the experimental range. Oxygen enhanced the pyrolysis reactions of intermediates, which was produced from the first stage reaction of rice husk. A simple kinetic model was proposed for the pyrolysis of rice husk in different oxygen concentrations. The corresponding activation energies, preexponential factors, and reaction orders were determined. The experimental results were satisfactorily fitted by the proposed kinetic model.     

Gas-solid reaction-rate enhancement by pressure cycling

An experimental study and mathematical modeling of the effects of external pressure cycling on gas-solid reactions have been conducted using the reduction of nickel oxide pellets by hy-drogen. Experiments were carried out in two phases: In the first phase, the intrinsic kinetic parameters were measured, and in the second phase, the gas-solid reaction was carried out under a constant or cycling external pressure. The effects of the frequency and amplitude of pressure cycling were studied at various reaction conditions. Pressure cycling substantially increases the overall rate of the reaction. A mathematical model was developed from the first principles to establish the extent of the overall reaction-rate enhancement and subsequently to analyze the experimental observations. The calculated values from the mathematical model are in good agreement with the experimental results. The effects are most pronounced when the overall rate under a constant pressure is controlled by diffusion. Depending on the reaction condition, a very large degree of rate enhancement could be achieved. Furthermore, low-amplitude pressure waves, like acoustic waves, could significantly increase the rates of gas-solid reactions. M.B. ABOUKHESHEM, formerly Graduate Student, Department of Metallurgical Engineering, University of Utah.     

浓缩过程数学模型及其在浓缩机设备选型中的应用(续)

利用现象学理论和数学理论建立的沉降过程数学模型和偏微分方程数值方法,对磁选工艺和浮选工艺的尾矿之絮凝沉降过程进行数值模拟,并按照实际絮凝沉降工艺过程进行试验。通过分析比较沉降试验数据与模拟数据,证明所采用的数学模型能够正确描述具有絮凝反应的工业实际沉降过程,可作为工业沉降工艺设计及沉降设备选型设计的理论依据。     

A methodology for optimally designing console panels for use by a single operator

A seven-step methodology is presented to determine a dimensionally correct optimal layout of a console panel for a single operator. This methodology integrates the steps in the layout design process and uses a mathematical optimization model from facility design to obtain the optimal panel layout. A major difference in this methodology from previous work is that the mathematical optimization model incorporates factors that are only partially included in previous mathematical models. In addition, it includes the areas of the panel components as a new factor. This methodology is illustrated by the design of a nuclear power plant console panel.     

Three-Dimensional CFD-Population Balance Simulation of a Chemical Vapor Synthesis Reactor for Aluminum Nanopowder: Nucleation, Surface Growth, and Coagulation

A chemical vapor synthesis (CVS) process for synthesizing aluminum nanopowder as a reactant for various hydrogen-storage materials was simulated using a mathematical technique that combines computational fluid dynamics (CFD) with the population balance model. In this process, aluminum powder is produced by reacting aluminum chloride with magnesium in the vapor phase. The CFD model solves the three-dimensional (3-D) turbulent governing equations of fluid flow, heat and mass transfer, and chemical kinetics in a multiphase domain. The population balance model incorporates nucleation, surface growth, and coagulation. The nucleation rate is computed using an expression from the classical nucleation theory. The growth rate is obtained by the combined effect of vapor condensation and coagulation. A comparison of the model predictions with the available experimental data showed good agreement under different operating conditions without the need of adjustable parameters. According to the results, the final particle size is determined by particle coagulation in this particular CVS process. The new model proposed in this article can be applied to other similar systems with confidence even without the need of any experimental data and can be used for scale-up of the process.     

Macroexothermic phenomena in exothermic additions: mathematical and physical modelling

In this paper a mathematical model is presented to predict the macroexothermic phenomena occurring when exothermic additions in lump form are assimilated in ferrous metals. The macroexothermic phenomena take place during the free assimilation period of exothermic additions in ferrous metals. These phenomena are characterized by unique coupled heat, mass and momentum transport phenomena. The presence of a moving boundary complicates further these phenomena. The model uses the Simpler algorithm to solve numerically the pertinent partial differential equations. The extensive verification of the model was carried out in two contexts. The first was, in a low temperature physical model consisting of ice immersion in different sulfuric acid solutions. The melting of ice in these solutions is extremely exothermic. In this physical model, both temperature and velocity measurements were carried out. The model results were compared with experimental measurements and they were found to be in excellent agreement. The second context employed high temperatures, involving the assimilation of silicon in high carbon liquid iron. The model was also applied to predict the position of the moving boundary for these high temperature experiments and a good agreement was obtained. In addition new dimensionless convective heat transfer correlations that quantify these complex phenomena are presented.     

Two-Dimensional Numerical Simulation of Primary Settling Tanks by Hybrid Finite Analytic Method

In order to investigate the turbulent flow and mass transfer in primary settling tanks, numerical simulations are conducted by using a modified k?ε two-layer model based Boussinesq’s approximation to model the Reynolds stress in primary settling tanks, and solving the governing equations using a hybrid finite analytic method (HFAM). The simulation results obtained using the mathematical model are compared with the experimental data and simulation results available in the literature, and the results of comparison indicate that the profiles of the primary velocity field are in line with the experimental results and the flow-through curve obtained using the mathematical model are in good agreement with the curves based on experimental data. It is therefore concluded that the HFAM approach can be used to simulate the turbulent flow and mass transfer in a primary settling tank, and the modified k?ε two-layer model can be used to establish the velocity field distribution at the bottom of a primary settling tank.