Modelling of heat and mass transfer during the polymerisation of olefins on heterogeneous Ziegler catalysts

The modelling of heat and mass transfer during the gas and slurry phase polymerisation of olefins is examined. It is demonstrated that it might not be necessary in many cases to calculate concentration gradients in the growing catalyst/polymer complex, and that the currently used representation of heat transfer from small, highly active particles using standard chemical engineering correlations might not be accurate.

Close examination of the morphology of catalyst particles shows that it is unlikely that the particles should be treated as a pseudo-homogeneous medium, and in fact the critical length scale for mass transfer is not the particle radius, but is much smaller. Furthermore, computational fluid dynamic simulations of single and interacting particles shows that convection is not the dominant heat transfer mechanism during the critical stages of the reaction.     

Direct heat and mass transfer in structured packings

Direct heat transfer is an important method in the exchange of heat between two countercurrent process streams within a column. The process can be simulated using either the theoretical stage or the rate based concept. With both concepts, a reliable heat transfer coefficient is needed. Additionally, the rate of the heat transfer coefficient is influenced by the simultaneous mass transfer.

A number of application-dependent methods to estimate the heat transfer coefficient have been developed, mainly for random packings. It is the purpose of this paper to extend this work to structured packings.

A number of experiments with air/water have been performed in a column of 300 mm inner diameter with Mellapak 250.Y, 250.X and 125.X at ambient conditions. A second group of measurements were done using an oil/air system where only sensible heat was transferred.

Based on these experimental results a method was developed to predict the heat transfer coefficient for structured packings. The method is applied to examples of industrial importance, like a gas quench, a gas saturator and a pump-around zone in an atmospheric tower.     

Modeling and simulation of heat and mass transfer during drying of solids with hemispherical shell geometry

A heat and mass transfer model was proposed to describe the moisture and temperature evolution during drying of solid products with hemispherical shell geometry (HSG). The dimensionless form of the model was numerically solved for both several drying conditions and values of a geometrical factor related with the inner radius of the HSG to obtain their moisture and temperature profiles. In addition, average drying kinetics were calculated from the volume integration of local moisture values. A theoretical and numerical approach was used to develop a mass transfer analogy between the proposed HSG and a simpler flat slab-shaped product. These analogies provide simple mathematical expressions for drying process simulation and estimation of diffusion coefficients in solids with the proposed geometry, and may be applicable to other mass and heat transfer operations. Furthermore, the presented procedure may be used to develop similar expressions in other non-traditional or dissection geometries.     

Development of a comprehensive free radical photopolymerization model incorporating heat and mass transfer effects in thick films

A comprehensive kinetic model describing photopolymerization is developed which allows variation of temperature, species concentrations, and light intensity through the thickness of a photopolymerized film. Heat and mass transfer effects are included, as is the generation of heat by both reaction and light absorption. In addition to initiation, propagation, and termination mechanisms, both primary radical termination and inhibition are incorporated into the model. The possible presence and diffusion of an inert solvent are also accounted for. Thus, the model is useful for examining complex polymerization kinetics and behavior in industrially and commercially important thick film photopolymerizations, such as the curing of contact lenses, dental restorative materials, photolithographic resists, and optoelectronic coatings. The comprehensive model is used to predict polymerization rate, temperature, and conversion profiles in a variety of systems. The effects of heat generation and the thermal boundary conditions are explored, with the result that heat generation in thick samples leads to greatly increased conversions approaching 100 percent. Increased temperature in these samples also may lead to the appearance of two rate maxima, with the first due to the temperature increase and the second caused by the autoacceleration process. The magnitude of the temperature increase, along with the resultant effects, is more pronounced in insulated systems.     

Local rates of heat and mass transfer during condensation of non-eutectic vapours of binary immiscible liquids

Heat and mass transfer data are reported for the condensation of vapours of immiscible liquids. Condensation occurred on the outside of 0.0254 m diameter horizontal copper tube. Mixtures of organic vapours in steam have been studied, such mixtures being rich in steam and removed from the eutectic composition.

The condensate flow pattern has been determined experimentally. In systems where the density ratio of the organic to water liquids is less than one, a standing-drop pattern is observed; when the ratio is greater than one, channeling flow is the main feature.

For systems removed from the eutectic composition, diffusional resistance through the vapour phase adjacent to the vapour—liquid interface has a major effect on the transfer rates.     

Insights into fry-drying process of wood through a simplified approach of heat and mass transport phenomena

Fry-drying process of wood involves intense water vaporization. The pressure at a sample core increases over 250 kPa. Under such pressure conditions, vapour transport driven by Darcy's law should be considered as the prevailing phenomenon in a simplified heat and mass transport model. The latter was developed in the absence of mechanical deformation and oil penetration, in a 2D rectangular geometry and solved numerically with commercial finite element software. Free and bound water were distinguished in the energy equation. Despite the directions of vapour flux being orthogonal to the simulation plane, the use of only two adjusted permeabilities (9 × 10⁻¹⁵ and 9 × 10⁻¹⁶ m²) allowed the characterisation of a large amount of wood, regardless of sample size and permeability variability. The model was experimentally validated with local pressure and temperature measurements at the core, temperature alone at three locations and with overall water loss. Beech (Fagus silvatica), oak (Quercus pedonculae) and maritime pine (Pinus pinaster) were considered at both laboratory (0.3 m in length) and industrial (2 m in length) scales in the temperature range from 103 to 180 °C. Evidence of mechanical degrade or cracks was observed at 180 °C due to the sudden decrease in water boiling point and by fluctuations in temperature kinetics.     

Effects of crystal growth rate and heat and mass transfer on solute distribution

The effects of crystal growth rate and heat and mass transfer on solute distribution during solidification of binary melt have been theoretically investigated on the basis of a new theory of solute distribution proposed by the present authors. The solute distribution factor f at the solid-liquid (SL) interface is in inverse proportion to the one-half power of the dimensionless growth rate U. The growth rate U is in proportion to the second power of the normalized concentration difference between the SL interface and bulk melt. A new transport factor K, which describes heat and mass transfer in melt, gives an important contribution to the crystal growth and the solute distribution at the SL interface. The transport factor is used successfully to control the solidification of melt. The flow structure in melt exerts essential influence on the solid purity.     

Re-evaluation of the Nusselt number for determining the interfacial heat and mass transfer coefficients in a flow-through monolithic catalytic converter

The two-equation porous medium model has been widely employed for modeling the flow-through monolithic catalytic converter. In this model, the interfacial heat and mass transfer coefficients have been usually obtained using the asymptotic Nusselt and Sherwood numbers with some suitable assumptions. However, previously it seemed that there existed some misunderstanding in adopting these Nusselt and Sherwood numbers. Up to now, the Nusselt number based on the fluid bulk mean temperature has been used for determining the interfacial heat and mass transfer coefficients. However, the mass and energy balance formulations in the two-equation model indicate that the Nusselt number should be evaluated based on the fluid mean temperature instead of the fluid bulk mean temperature. Therefore, in this study, to correctly model the heat and mass transfer coefficients, the Nusselt number based on the fluid mean temperature was newly obtained for the square and circular cross-sections under two different thermal boundary conditions (i.e., constant heat flux and constant temperature at the wall). In order to do that, the present study employed the numerical as well as analytical method.     

Heat and mass transfer characteristics in a gas-slurry-solid fluidized bed

The gas-slurry-solid fluidized bed is a unique operation where the upward flow of a liquid-solid suspension contacts with the concurrent up-flow of a gas, supporting a bed of coarser particles in a fluidized state. In the present study we measured the gas holdup, the coarse particle holdup, the cylinder-to-slurry heat transfer coefficient, and the cylinder-to-liquid mass transfer coefficient at controlled slurry concentrations. The slurry particles were sieved glass beads of 0.1 mm average diameter and their volumetric fraction was varied at 0, 0.01, 0.05 or 0.1. The slurry and the gas velocities were varied up to about 12 and 15 cm/s, respectively. The coarse particles fluidized were sieved glass beads of average diameters of 3.6 and 5.2 mm. The individual phase-holdup values were measured and served for use in correlating the heat and mass transfer coefficients. The heat and mass transfer coefficients in the slurry flow, gas-slurry transport bed, slurry-solid fluidized bed and gas-slurry-solid fluidized bed operations can be correlated well by dimensionless equations of a unified formula in terms of the Nusselt (Sherwood) number, the Prandtl (Schmidt) number and the specific power group including the energy dissipation rate per unit mass of slurry, with different numerical constants and exponent values, respectively, to the heat and mass transfer coefficients. The presence of an analogy between the heat and mass transfer from the vertically immersed cylinder in these slurry flow, gas-slurry transport bed and gas-slurry-solid fluidized bed systems is suggested.     

An experimentally validated heat and mass transfer model for wax deposition from flowing oil onto a cold surface

A transport model is proposed for wax deposition onto a cold finger from flowing wax-containing oils. The model solves transient energy and mass balances simultaneously for a reversible first-order kinetic rate for precipitation of pseudo-single-component wax, and the effects of yield stress using a critical solid wax concentration to withstand flow-induced stress at the deposit-fluid interface. The model can predict the time evolution of the deposit thickness, and the spatial and temporal evolution of temperature and wax concentration as validated using cold finger experiments. It was found that for high wax content oils, deposit thickness growth is dominated by heat transfer. For low wax content oils that are unable to gel, the thickness growth is slow and accompanied by occasional sloughing. Regardless of the mechanism controlling the growth, mass transfer cannot be neglected as wax diffusion into the deposit continues to take place after the deposit has stopped growing.     

Non-equilibrium thermodynamic analysis of coupled heat and moisture transfer across a membrane

Non-equilibrium thermodynamics theory is used to analyze the transmembrane heat and moisture transfer process, which can be observed in a membrane-type total heat exchanger (THX). A theoretical model is developed to simulate the coupled heat and mass transfer across a membrane, total coupling equations and the expressions for the four characteristic parameters including the heat transfer coefficient, molar-driven heat transfer coefficient, thermal-driven mass transfer coefficient, and mass transfer coefficient are derived and provided, with the Onsager’s reciprocal relation being confirmed to verify the rationality of the model. Calculations are conducted to investigate the effects of the membrane property and air state on the coupling transport process. The results show that the four characteristic parameters directly affect the transmembrane heat and mass fluxes: the heat and mass transfer coefficients are both positive, meaning that the temperature difference has a positive contribution to the heat transfer and the humidity ratio difference has a positive contribution to the mass transfer. The molar-driven heat transfer and thermal-driven mass transfer coefficients are both negative, implying that the humidity ratio difference acts to reduce the heat transfer and the temperature difference works to diminish the mass transfer. The mass transfer affects the heat transfer by 1%–2% while the heat transfer influences the mass transfer by 7%–14%. The entropy generation caused by the temperature difference-induced heat transfer is much larger than that by the humidity difference-induced mass transfer.     

超重力精馏过程传热传质机理研究

以波纹丝网为填料,以立式逆流超重力装置为主要设备,应用热量传递与质量传递理论,建立了超重力精馏装置内气、液温度分布的数学模型;以转子内半径29 mm、外半径63 mm、轴向高度32mm、内置直径1.6 mm、空隙率0.85、比表面积1 750 m2/m3的波纹丝网为填料的超重力装置为精馏设备,以乙醇-水为物系,在常压、室温进料、原料流量20 L/h、原料乙醇质量分数20%、转速800 r/min-1、回流比为1的操作条件下,对模型进行了检验。精馏段气相温度的实测值与模型计算值的偏差为1.41%,提馏段外半径的实测值与模型计算值的偏差为3.87%。     

Four stages of the simultaneous mass and heat transfer during bubble formation and rise in a bubbly absorber

We studied nonisothermal absorption of a solvable gas from growing at an orifice and rising bubble when the concentration level of the absorbate in the absorbent is finite (finite dilution of absorbate approximation). It is shown that simultaneous heat and mass transfer at all stages of bubble growth and rise in a bubbly absorber can be described by a system of generalized equations of nonstationary convective diffusion and energy balance. Solutions of diffusion and energy balance equations are obtained in the exact analytical form. Coupled thermal effects during absorption and absorbate concentration level effect on the rate of mass transfer are investigated. It is found that the rate of mass transfer between a bubble and a fluid increases with the increase of the absorbate concentration level. The suggested approach is valid for high Peclet, Prandtl and Schmidt numbers. It is shown that for the positive dimensionless heat of absorption K thermal effects cause the increase of the mass transfer rate in comparison with the isothermal case. On the contrary, for negative K thermal effects cause the decrease of the mass transfer rate in comparison with the isothermal case. The latter effect becomes more pronounced with the increase of the concentration level of the absorbate in the absorbent. Theoretical results are consistent with the experiments of Kang et al. (Int. J. Refrigeration 25 (2002) 127) for absorption from ammonia gas bubbles rising in water and aqueous ammonia solutions.     

超声波场中蒸汽气泡凝结过程及传热特性

利用高速摄像仪记录有、无超声波时注入过冷水中蒸汽气泡的凝结过程,以分析超声波对蒸汽气泡凝结过程及传热特性的影响。结果表明:在超声波场中,蒸汽气泡表面会形成晶格状毛细波,有效增加气泡表面积,并加强气泡周围流体热边界层扰动,从而导致凝结换热的强化及气泡凝结速度加快。基于15～60 K过冷度下,有、无超声波时较大蒸汽气泡凝结的实验数据,拟合得出有、无超声波时的气泡凝结换热经验关联式,预测误差在±30%以内。     

松木屑颗粒热解过程中的热/质传递规律

为探索在固定床反应器中有机固废颗粒热解过程中的热量、质量传递机理,本研究从颗粒尺度上对有机固废松木屑颗粒热解过程建模分析,模型中考虑了焦油的二次裂解反应及挥发分在颗粒孔隙中的质量、动量传递过程,并采用达西定律模拟了挥发分在颗粒孔隙内的流动现象,对颗粒热解过程的吸热反应以及挥发分逸出时的对流换热对颗粒温度的影响进行考察。基于两步反应动力学模型,探讨了不同颗粒尺寸、热解温度对有机固废松木屑颗粒热解过程的影响。结果表明,热解吸热反应和挥发分的对流换热阻碍了热量向颗粒中心的传递,延长了颗粒达到均温的时间;松木屑颗粒热解时,颗粒内会存在明显的温度梯度,在颗粒表面主要受化学反应动力学限制,在颗粒内部则主要受热量传递过程限制。此外,热解温度越低,粒径越大,颗粒内部的传热阻力越大。松木屑颗粒完全热解所需时间会随着颗粒粒径的增大而增加,但当颗粒粒径在10mm以上时,随着颗粒粒径的增大,颗粒完全热解所需时间的增量要大于10mm以下颗粒。     

Three dimensional iron flow and heat transfer in the hearth of a blast furnace during tapping process

The aim of this research is to numerically simulate iron flow and heat transfer in the hearth of a blast furnace by solving the three-dimensional turbulent Navier-Stokes equation coupled with the transport equation of energy at steady state. Under the effects of conjugate heat transfer and natural convection, a computational fluid dynamic calculation was performed to generate flow field in the hearth and the temperature distribution in the refractories during the tapping process. The accuracy and computation of the model is validated using operation data from BHP Steel's No. 5 blast furnace. The shear stress and heat flux on the wall were then predicted for the different vertical movements, shapes of the coke zone (dead-man), and the lengths of the tap-hole. As shown in the results, it is worth noticing that an increase in the tap-hole length causes the peak values of shear stress to shift in the increasing azimuthal direction at a particular plane, and the location of the peak value of shear stress coincides with the location of higher temperature actually measured on the hearth wall, signifying enhanced heat transfer to the wall at location of peak stress.     

Methanation in a fluidized bed reactor with high initial CO partial pressure: Part I—Experimental investigation of hydrodynamics, mass transfer effects, and carbon deposition

An extensive experimental study on the methanation reaction was carried out in a gas–solid fluidized bed reactor at 320 °C with a stoichiometric ratio of H₂/CO=3. By means of spatially resolved measurements of the axial gas species concentration and temperatures along the fluid bed the effects of different catalyst loadings, gas velocities and dilution rates were observed and analyzed. By applying this technique, it was found that most of the reaction (CO and H₂ conversion) proceeds in the first 20 mm of the bed depending on the experimental conditions. For a few cases, the temperature increases by up to 80 °C from 320 to 400 °C within the first 3 mm of the bed. By increasing the inlet volume flow only by a factor of 1.4, the temperature hotspot diminishes and isothermal behavior develops. For all experiments, a CO conversion of practically 100% was achieved. The experimental data indicate that the dense phase of the fluidized bed is probed and that mass transfer between bubble and dense phase is dominating in the upper part of the bed. It could be shown that both hydrodynamic and chemical boundary conditions influence the methanation reaction inside the fluidized bed reactor.     

Experimental researches on mass and heat transfer in new typical cross-flow rotating packed bed

New typical cross-flow Rotating Packed Bed(RPB)called multi-pulverizing RPB was manufactured.There is enough void in multi-pulverizing RPB,where liquid easily flows and is repeatedly pulverized by light packing,which decreases the material consumed,lightens the weight,and compacts the structure.Mass and heat transfer property in the new type PRB were studied by two experimental models.In the mass transfer model,the axial fan pumping gas press is only 100 Pa,mass transfer coefficient and volumetric mass transfer coefficient are similar to countercurrent RPB,which are an order quantity lager than that in the conventional packed tower.In the heat transfer experiment,the axial fan pumping gas press is only 120 Pa;volumetric heatwhich especially suits the treatment of large gas flow and lower gas pressure drop.