Velocity Pulse Model for Turbulent Diffusion from Flowing Water into a Sediment Bed

The “velocity pulse model” simulates the transfer of turbulence from flowing water into a sediment bed, and its effect on the diffusional mass transfer of a solute (e.g., oxygen, sulfate, or nitrate) in the sediment bed. In the “pulse model,” turbulence above the sediment surface is described by sinusoidal variations of vertical velocity in time. It is shown that vertical velocity components dampen quickly inside the sediment when the frequency of velocity fluctuations is high and viscous dissipation is strong. Viscous dissipation (ν) inside the sediment is related to the apparent viscosity depending on the structure of the sediment pore space, i.e., the porosity and grain diameter, as well as inertial effects when the flow is turbulent. A value ν/ν0 between 1 and 20 (ν0 is kinematic viscosity of water) has been considered. Turbulence penetration into the sediment is parametrized by the Reynolds number Re = UL/ν and the relative penetration velocity W/U, where U=amplitude of the velocity pulse; and W=penetration velocity; L = WT=wave length of the velocity pulse; and T is its period. Amplitudes of vertical velocity components inside the sediment and their autocorrelation functions are computed, and the results are used to estimate eddy viscosity inside the sediment pore system as a function of depth. Diffusivity in the sediment pore system is inferred by using turbulent or molecular Schmidt numbers. Turbulence penetration from flowing water can enhance the vertical diffusion coefficient in a sediment bed by an order of magnitude or more. Penetration depth of turbulence is higher for low frequency velocity pulses. Vertical diffusivity inside the pore system is shown to decrease more or less exponentially with depth below the sediment/water interface. Vertical diffusivities in a sediment bed estimated by the “velocity pulse model” can be used in pore water quality models to describe vertical transport from or into flowing surface water. The analysis has been conducted for a conservative material, but source and sink terms can be added to the vertical transport equation.     

Estimation of Mass Transport Parameters of Organic Compounds through High Density Polyethylene Geomembranes Using a Modifield Double-Compartment Apparatus

A modified double-compartment apparatus (MDCA) is used to estimate mass transport parameters of organic compounds through high density polyethylene (HDPE) geomembranes and to investigate the effects of aging and external tension of HDPE geomembranes on the mass transport of organic compounds. A developed one-dimensional partition–diffusion mass transport model successfully explains the mass transport of the organic compounds through the HDPE geomembranes in a dilute aqueous solution–geomembrane system. Similar to batch immersion tests, the HDPE–water partition coefficient (KHDPE–W) values of organic compounds are found to have close relationships with the octanol–water partition coefficient and the aqueous solubility; furthermore, the diffusion coefficient (D) values decrease with the increase of their molecular diameter. For HDPE geomembranes served in the landfill liner for 5 years and stretched by 8% of their initial length, KHDPE–W values for organic compounds increase by 5–58%, D values for organic compounds increase by 10–86%, and breakthrough times are faster, indicating more amounts of organic compounds may break through the HDPE geomembrane in fields than expected. The mass transport parameters from MDCA tests could be used with those from batch immersion tests interchangeably after mass loss and immobilization of organic compounds in MDCA tests are considered.     

Application of simplified rapid equilibrium models in simulating experimental breakthrough curves from fixed bed biosorption reactors

A modelling approach for a fixed bed biosorption column is presented. The Advection–Dispersion–Reaction (ADR) equation has been applied as the basic modelling equation for the special case of Local Equilibrium (LE). The model implements the minimum parameters for describing a fixed bed biosorption column, employing the geometrical dimensions of the bed, the packing arrangement, the operating conditions of the system, and the sorptive characteristics of the biosorbent material. An apparent axial dispersion coefficient has been used as a key parameter of the model. The authors compare model predictions to selected examples of experimental biosorption breakthrough curves reported from pilot scale work. Although the main assumption of the model is that biosorption equilibrium is rapid, the use of an apparent overall dispersion coefficient makes the model applicable for the cases where mass transfer resistances are present in the liquid and solid phases.     

Surface diffusion from a needle source including the effect of volume diffusion into the bulk

The problem of determining the quantity of diffusant to be found on and beneath the surface of a solid at any radial distance from a cylindrical source of constant strength on the surface has been solved using a Laplace transform technique. The movement of diffusant from the surface into the bulk through volume diffusion was taken into account. The integrals in the solution were evaluated numerically for a wide range of experimentally realizable conditions and the results given in a table. Experimental data can be analyzed with the help of this table to yield the product of the surface diffusion coefficient and the thickness of the surface layer. It is shown that, in general, these two quantities cannot be determined separately from data obtained in a conventional experiment because the amount of diffusant in the surface layer is usually only a small fraction of the total measured at any point.     

The extraction mechanism of thulium in di(2-ethyl hexyl) phosphoric acid-nitric acid system

Distribution ratios (D) and interfacial mass transfer coefficients in the case of extraction of thulium(III) with di(2-ethyl hexyl) phosphoric acid (HDEHP) in cyclohexane have been measured at different concentrations of nitric acid and HDEHP as well as at various stirring speeds of the two phases in a constant interface cell. From a study of the effect of stirring on the mass transfer coefficients it is observed that the overall extraction process is controlled by interfacial chemical reaction as well as by diffusion of interfacial chemical species across the interface. The latter is dependent on the rate of stirring. At stirring rates up to ～75 min^?1 the diffusional process is the rate determining step. On the other hand, when the stirring rate is ～400 min^?1, the diffusional step becomes very fast. At such high stirring speeds, the system belongs to a true kinetic regime, which was evaluated through computer simulation.     

Enhanced Dissolution of Trichloroethene: Effect of Carbohydrate Addition and Fermentation Processes

Remediation of source areas is challenging because lingering contaminants are often present as nonaqueous phase liquid (NAPL) and sorbed mass, and therefore difficult to remove via biodegradation or other commonly used remedial methods. Experimental results indicate that enhanced dissolution of a model NAPL, trichloroethene (TCE), can occur through the addition and/or subsequent fermentation of a dilute molasses solution. Enhanced mass transfer occurs by two mechanisms, depending upon whether the molasses solution is fresh or has fermented. The addition of fresh molasses worked to increase TCE solubility (>200%), thereby increasing mass transfer from the NAPL phase. Mixing TCE NAPL with a fermented molasses solution, however, increased TCE mass flux via the formation of a NAPL/aqueous phase emulsion. In addition, fermented liquid may have also decreased the soil partitioning coefficient (Kd) of TCE, indicating that enhanced transfer of sorbed mass to the aqueous phase could also occur in the presence of fermented molasses. These results provide guidance on how remedial systems may be optimized to increase NAPL and sorbed-mass dissolution and are therefore important, particularly when bioremediation is used to polish residual source zones.     

Kinetics of mass transfer during nitrogen injection in industrial Fe—Cr—Ni—Mo-melts

Experiments on the injection of nitrogen into Fe—Cr—Ni—Mo alloys in 30 t VOD-Iadles have been carried out. The nitrogen contents obtained by nitrogen injection were between 0.05 and 0.17% for an initial nitrogen content of about 0.02%. Calculations of mass transfer associated with a rising nitrogen bubble indicate very high mass transfer rates for different nitrogen activities. The high efficiency of nitrogen gas measured in industrial practice agrees with these calculations. The specific interface area increases proportionally with the gas flow rate. According to reports in literature, nitrogen mass transfer can be described either as a 1st or 2nd order reaction. Both possibilities have been examined and the experimental results evaluated accordingly. In order to make possible a comparison with literature rate constants were first determined using comparable methods, i.e. on the assumption that the concentration difference is the driving force for mass transfer. The rate constants depend on the composition of the alloy. Assuming spherical cap bubbles with an equivalent diameter of 2.5 cm, the mass transfer coefficient was estimated to be about 5 to 8.10^?3cm s^?1, using a 1st order reaction model; the apparent activation energy then has a value of about 100 kJ/Mol. If a 2nd order reaction model is assumed, the apparent activation energy has a value of about 125 kJ/Mol. Using the activity difference as the driving force for mass transfer, it was found that the kinetics of mass transfer in multi component alloys could be treated in a homogeneous manner. The mass transfer coefficient calculated in this way for a 1st order reaction lies between about 26 to 37.10^?3cms^?1 and the actual activation energy has a value of about 25 kJ/Mol. The evaluation of the experimental results using a second order reaction model gives an equally good correlation between the rate constants and the gas flow rate as that obtained using a 1st order reaction model. In this case the actual activation energies determined are slightly higher - 40 kJ/Mol. However, the activation energies in both cases (i.e. with or without regard to the nitrogen activity) do not lie in the range of activation energies associated with a process controlled by interface reactions. Due to the low concentrations, it is not possible to make a definite statement about the order of the reaction. However, the activation energies determined fit better to a 1st order reaction model. Relations have been derived which, assuming a 1 st order reaction, and taking into account the composition of the alloy, enable prior calculation of suitable parameters for nitrogen injections in industrial melts. This allows a more precise process control.     

RH真空室加渣对熔池内渣钢间传质影响的水力学模拟

在RH真空精炼中,覆盖渣处于大包熔池内的弱搅拌区,渣钢反应很弱,对依靠渣钢反应去除硫等有害元素或吸附钢水中夹杂物有很大的影响,降低了精炼效率。为了提高除硫等精炼效率,利用水模拟钢水,机油模拟渣,苯甲酸模拟渣-钢间传输物质来研究RH装置真空室内加渣时的加渣量、吹气量和浸渍管插入深度对渣钢传质的影响。试验结果表明,采用真空室内加渣方法渣钢之间的容量传质系数提高了60～130倍,大大提高了渣钢传质速度,为实际生产中通过真空室内加渣加强渣钢传质以提高除硫等精炼操作提供了理论依据。     

Measuring Aqueous-Air and Sorbed-Aqueous Mass Transfer Coefficients for Application in Soil Vapor Extraction

Soil vapor extraction (SVE) is a common remediation practice typically implemented without a rigorous design process because of insufficient or unspecific design data. Field observations have shown that the mass of contaminant removed by SVE often tails off over time. Significant time has been spent modeling SVE to gain a better understanding of the governing processes and the cause of tailing. Studies have shown that improper mass transfer coefficients affect modeling accuracy. As a result, considerable effort has been spent studying the mass transfer coefficients directly related to the non-aqueous-phase liquid (NAPL), with less emphasis on aqueous air and sorbed-aqueous mass transfer coefficients, despite affecting the observed tailing behavior. Accordingly, a laboratory and modeling study was undertaken with toluene to determine the appropriate aqueous air and sorbed-aqueous mass transfer coefficients. SVE column data generated in laboratory experiments were used to back-calculate the mass transfer coefficients by using FRACMAT, a numerical model. The developed experimental protocol allowed the placement of toluene contamination in the unsaturated soil environment without the development of a NAPL phase. The data generated by the SVE column with soils with organic matter and without organic matter, showed that the aqueous-air mass transfer coefficient was exponential, with the aqueous concentration the independent variable. For the zero to moderate organic matter content soils tested, the aqueous-air mass transfer coefficient varied from 1??s-1 to 0.001??s-1. Some sorbed contamination was also observed, requiring a sorbed-aqueous mass transfer coefficient. Numerical modeling with FRACMAT showed that the best sorbed-aqueous mass transfer coefficient was a constant value of 0.01??s-1. The aqueous-air mass transfer coefficient was observed to be the controlling rate limitation in SVE when no NAPL was present in the soil with the zero to moderate organic matter content soil. Studies with silty loam soil showed that additional mass transfer resistances occurred, which could be attributed to the increase in organic matter content and decrease in particle size.     

Parametric Study of One-Dimensional Solute Transport in Deformable Porous Media

Formulation for the effect of dissipation of excess pore water pressure on one-dimensional advective-diffusive transport of solutes in clays is presented. The formulation is based on the effect of the rate of consolidation or swelling and excess pore pressure or suction dissipation on transient, nonlinear advective component of transport through clay. One partial differential equation is presented for advective diffusive transport that is dependent upon soil/solute properties and transient hydraulic head gradient, which is calculated from the Terzaghi consolidation equation. Finite difference method is used to solve the system of partial differential equations for consolidation and solute transport. Four hypothetical cases are evaluated to demonstrate the effect of consolidation under loading and swelling under hydraulic gradient on advective-diffusive transport and breakthrough in single and double drainage clay layer. The results show that consolidation in doubly drained clay impacts concentration profiles, but does not significantly impact breakthrough of the diffusive flux. Consolidation under single drainage conditions, significantly impacts the diffusional flux. When drainage path is the same as the diffusional flux, consolidation accelerates transport and breakthrough time can be less than 5% of the diffusional breakthrough time under no consolidation. Swelling under hydraulic gradient application can either accelerate or retard the advective diffusive flux, depending upon the ratio of the effective diffusion coefficient relative to the coefficient of consolidation. Higher the effective diffusion coefficient and lower the coefficient of consolidation result in an increase in the effect of pressure dissipation on transport.     

Axial Dispersion and Mass Transfer Controlled Simulation Study of Chromium (VI) Adsorption onto Tree Leaves and Activated Carbon

In this paper, the feasibility and efficacy of chromium (Cr(VI)) removal using three different kinds of tree leaves viz. Emblica officinalis, Azadirachta indica, Eucalyptus agglomerata, and the activated carbon is examined through batch and continuous flow experiments. Pretreatments were given to the selected tree leaf powders to remove the natural pigments and lignin present. Batch and continuous flow experiments have been conducted to study the kinetics of adsorption, effects of pH, adsorbent dose, contact time, bed depth, flow rate, and initial Cr(VI) concentration on Cr(VI) adsorption onto the selected adsorbents. The adsorption capacity is observed higher for Emblica officinalis followed by Eucalyptus agglomerata and Azadirachta indica. The adsorption equilibrium is reached in less than 30 min and the maximum Cr(VI) uptake occurred at pH 3.0 under the test conditions. The results are also compared with the commercially available activated carbon. A mathematical model incorporating diffusion, advection, and mass transfer mechanisms available in the literature has been simplified and is then tested to simulate the laboratory and literature data. A simple method for the determination of saturation Cr(VI) concentration along the length of column has been presented. The study reveals that the model incorporating the molecular diffusion and the mass transfer mechanisms simulates better the Cr(VI) adsorption onto tree leaf powders than the literature model and the advection term plays only a negligible role due to low flow rates applied during the experiments. The model parameters, i.e., axial dispersion coefficient, “DL” and the external mass transfer coefficient, “kf” are found in the order of 10?5–10?6?m2/s and 10?9–10?11?m/s, respectively.     

废钢熔化的热模试验

 为了解废钢的熔化速度和熔化机理,在250 kg感应炉中进行了热模拟试验。测量熔化速度采用直径为[?20～?50 mm]的Q235圆钢,熔池温度为1 300、1 400和1 600 ℃。根据试棒直径不同确定在熔池中浸泡时间。根据钢棒浸泡前后的质量和尺寸差别,计算出熔池为1 300、1 400和1 600 ℃时,其质量熔化速度分别为1.8～4.0、3.5～6.5和12.6 g/s;径向熔化速度为0.012～0.026、0.035～0.045和0.060 mm/s。熔池液体与试棒之间的对流换热系数在1 400 ℃时为32 931 W/（m2·℃）,1 600 ℃时为32 884 W/（m2·℃）。在温度为1 300 ℃时,碳在液体与试棒之间的对流传质系数为6.3×10－5 m/s,温度为1 400 ℃时为6.4×10－5 m/s。热模拟试验所测得的钢棒熔化速度、液-固相之间的对流换热系数、碳的对流传质系数都与国外冶金工作者的试验结果相近,可以作为炼钢生产中计算废钢熔化的基础数据。     

A contribution to the theoretical description of metal-slag reaction kinetics

In this paper the main aspects of a theoretical model of mass transfer through liquid-liquid interfaces under non-turbulent flow conditions are described. The model is based on the general boundary layer theory of momentum and mass transfer. Expressions for calculation of the mass transfer coefficients on the metal and slag side of the phase boudary are presented. It is shown that the model comprises as limiting cases the mass transfer through free surfaces and at solid walls.     

An experimental study on heat transfer process of multiple mist impinging jets

Mist jet impingement cooling is an enhanced heat transfer method widely used after the continuous galvanizing process.The key of a successful design and operation of the mist jet impingement cooling system lies in mastering heat transfer coefficients.The heat transfer coefficients of high temperature steel plates cooled with multiple mist impinging jets were experimentally investigated,and the effects of gas and water flow rates on heat transfer coefficients were studied.The test results illustrate that the gas flow rate has little effect on the mist heat transfer rate.It is also found that the water flow rate has a great impact on the heat transfer coefficient.When the water flow rate ranges from 0.96m3/h to 1.59 m3/h,an increase in the rate will produce a higher heat transfer coefficient with a maximum of 5650 W/(m2·K).Compared with the conventional gas jet cooling,the heat transfer coefficient of the mist jet cooling will be much higher,which can effectively strengthen the after-pot cooling.     

SVE Design: Mass Transfer Limitation due to Molecular Diffusion

Vaporization and soil adsorption are the two mass transfer mechanisms that control contaminant recovery rates for soil vapor extraction (SVE) systems. At most soil remediation sites, contaminants are distributed among three phases, namely, soil particles, pore water, and soil vapor. Contaminant mass transfer from adsorption sites into a convective vapor stream involves desorption, diffusion through pore water, and vaporization into soil vapor. An SVE design model is proposed to describe this three-phase mass transfer process and assist the design and evaluation of SVE systems. The model contains analytical solutions developed to estimate contaminant concentrations in the vapor phase and predict contaminant removal rates. Monitoring data from two full-scale SVE systems were used for model development and calibration. The results suggest that contaminant diffusion through the pore water is the rate-limiting step and leads to remediation inefficiency of an SVE system. Mass transfer retardation from molecular diffusion in water is likely the major contributing component to the venting efficiency coefficient of Staudinger et al.     

Using Continuum Approach to Quantify the Remediation of Nonaqueous Phase Liquid Contaminated Fractured Permeable Formations

This study addresses the feasibility of using a continuum modeling approach to simulate pump-and-treat remediation of nonaqueous phase liquid (NAPL) contaminated fractured permeable formations. A simplified discrete fracture model, which incorporates permeable blocks with embedded parallel equidistant constant aperture fractures, was used to simulate the NAPL dissolution in an idealized fractured permeable formation. The applicability of this model is defined by the ranges of a dimensionless mobility number and interphase mass transfer coefficient. A continuum based model able to simulate phenomena predicted by the discrete fracture model has also been used. Three dimensionless parameters referring to organic solute advection and dispersion, and the continuum interphase mass transfer coefficient govern the performance of the continuum model. The nonlinear relationships between the discrete fracture and continuum model have been identified and formulated. However, the simplified conceptual models of this study may be inapplicable to many types of fractured formations. Ranges of possible use of the continuum modeling were determined in terms of dimensionless parameters. The discrete fracture and continuum approaches of this study can be useful for the preliminary evaluation of ideas concerning optimization of the remediation of NAPL contaminated fractured permeable formations.     

Physical modeling of gas/liquid mass transfer in a gas stirred ladle

The absorption of gas through the plume eye and of an injected gas in a steelmaking ladle process was investigated, using a physical model of CO₂ absorption into a NaOH solution. The results show that the inert gas escaping through the plume eye is ineffective in protecting the bath from the atmosphere, and placing an oil layer (simulated slag) decreases the absorption rate significantly. Increasing the flow rate of the inert gas not only exposes more of the liquid surface to the CO₂ atmosphere, but also increases the mass transfer coefficient at the surface. The overall mass transfer between an injected CO₂ gas and NaOH solution includes the mass transfer through the surface of the bath as well as the mass transfer in the bubble dispersion zone. The difference between the mass transfer in the bubble dispersion zone and the overall mass transfer was found to be significant for relatively low gas flow rates. The mass transfer coefficient of CO₂ in the bubble dispersion zone was estimated using available information regarding the bubble size and velocity. Mass transfer coefficient estimated for the constant bubble frequency regime shows a dependence on gas flow rate. However, if a constant characteristic size of bubbles is assumed as an alternative approach, the mass transfer coefficient is independent of the gas flow rate.     

Electrode mass transfer under conditions of natural and forced convection

In order to investigate the mass transfer to a cathode under conditions of natural and forced convection, silver was plated under conditions where the deposition rate was controlled by mass transfer. Rather than analyzing chemically for the deposited silver, it was determined locally by electrochemical stripping. This enabled the mass transfer coefficients to be determined accurately over the whole surface of the electrode under conditions of natural convection, electrolyte jetting, and gas sparging. In general, the mass transfer coefficient was enhanced significantly only in the very close vicinity of the agitation source. An improved sparger design with closely spaced multiple bubble sources was found to enhance overall mass transfer. formerly Graduate Student, Department of Mate-rials Science and Metallurgy, University of Cambridge     

Development of a mathematical model for multihearth roasters

A simultaneous heat and mass transfer model has been developed for the multiheart roasters, considering dead roasting of chalcopyrite as a typical roasting reaction. Various mass and energy balances have been worked out during the development of this model yielding coupled nonlinear partial differential equations with highly complex boundary conditions. These equations have been solved numerically using a line-by-line finite difference approach to obtain profiles of gas temperature, solid temperature, oxygen concentration, and solid fraction reacted in the roaster. The trend of the computed results appears to be realistic and can be easily explained from simple physical considerations. The effects of gas preheating and the heat transfer coefficient between the solid and the gas upon the roasting process are examined. The results show that gas preheating is beneficial for the roasting process, and the process parameters, such as particle size, gas flow rate,etc., must be adjusted so as to give the desirable value of the heat transfer coefficient needed for proper roasting.     

Kinetics of mass transfer of manganese and silicon between liquid iron and slags

The kinetics of mass transfer of Mn and Si between liquid iron and slags were investigated in laboratory experiments at 1600°C in MgO crucibles with 1500 g iron and 250 g slag. Three different slags consisting of CaO-MgO-MnO-SiO₂, MgO-MnO-SiO₂ and MgO-MnO-Al₂O₃-SiO₂ were used. The concentration-vs.-time curves, experimentally measured under defined flow conditions generated by gas stirring, were evaluated by application of a multi-component transport model in order to obtain the mass transfer coefficients. The numerical values of the thus determined measured mass transfer coefficients were compared with values calculated by a theory of mass transfer at liquid-liquid interfaces. The measured and theoretical values were in good agreement with each other in the case of reduction of MnO from the slag by Si in the metal, provided that the measurements had been carried out below a critical stirring intensity, above which metal droplets were emulsified in the slag. Experiments, where sulphur was dissolved in the metal melt and where the sulphur contents were systematically varied, showed no changes of the mass transfer coefficient in comparison to sulphur-free melts. The experimental mass transfer coefficients for the reduction of silica from the slag by manganese in the metal were smaller than those calculated by the mentioned mass transfer theory. This could be explained by inhibition of surface renewal under the influence of solid reaction products precipitated at the interface.