多孔介质反应体系中的耦合扩散效应

采用不可逆过程热力学方法研究固有强吸热化学反应的多孔介质物质体系,建立了描述该体系内各不可逆过程交互耦合的数学模型,应用有限容积隐式方法数值求解,并以煅烧石灰石为例,计算分析了热扩散现象和达福尔效应对多孔介质体系内传热、传质和化学反应的影响规律。结果表明,在Peclet准数较小的情况下,不能忽略Soret效应和Dufour效应的影响,Soret效应和Dufour效应会加快反应器内产物气体和热量传出的速度,使得颗粒物料层内产物气体浓度和主气流温度都相应降低,固体转化率减小。     

Numerical study of heat and mass transfer in the microwave-assisted and conventional packed bed reactors with an irreversible first-order endothermic chemical reaction

This paper presents a numerical study on heat and mass transfer in the microwave-assisted and conventional packed bed reactors with an irreversible first-order endothermic chemical reaction. The numerical simulations have been carried out using one-dimensional heterogeneous reactor models for the both reactors. The obtained results have been compared applying the criterion of the same electrical powers utilized in the reactors. The effects of the inlet gas temperature and microwave power, gas velocity, bed porosity and the heat of reaction on performance of the packed bed reactors have been presented.     

Axial dispersion coefficients in packed beds at low reynolds numbers

Peclet numbers describing axial dispersion in gas flow through packed beds of spheres were obtained using a two measurement point, pulse technique in a test section four inches inside diameter and 5.14 feet high. Three packing sizes were investigated, corresponding to tube to particle diameter ratios of 6.4, 17, and 66 In the experiments the contribution of the velocity profile to axial spreading was reduced by using thermal conductivity detectors which responded to dispersion only in the central part of the bed cross-section. In this region of a packed bed the velocity profile is relatively flat. The results point to a particle diameter effect which is more pronounced than has been previously reported. This is in accord with the diffusive mechanism of axial dispersion in a packed bed provided dispersion caused by the velocity profile does not affect the measured pulse response. In the absence of velocity profile effects, the spreading of residence times in void cells is caused primarily by the shedding of the decelerated boundary layers on the downstream side of the particles. At low velocities however, molecular diffusion predominates. Implicit in this discussion is the hypothesis that the uniformity of shape and size of packing particles has an important bearing on the manner in which the Peclet number approaches its limiting value as the gas velocity is increased.     

A numerical study of the Dufour and Soret effects on unsteady natural convection flow past an isothermal vertical cylinder

The Dufour and Soret effects on the unsteady laminar free convective flow with mass transfer flow past a semi-infinite isothermal vertical cylinder were studied numerically. The governing partial differential equations were converted into a non-dimensional form and solved numerically by applying a Crank-Nicolson type of implicit finite-difference method with a tri-diagonal matrix manipulation and an iterative procedure. For the hydrogen-air mixture, which is a non-chemical reacting fluid, the profiles of the unsteady dimensionless velocity, temperature and concentration are shown graphically for the different values of thermal and mass Grashof numbers, thermal diffusion parameters (Soret numbers) and diffusion-thermo parameters (Dufour numbers). Finally, the simulated values of the average skin-friction coefficient, the average Nusselt number and the average Sherwood number are presented. The numerical results reveal that for an increasing Soret number or decreasing Dufour number, the time to reach the temporal maximum and the steady-state decreases for the flow variables. As the Soret number increases or the Dufour number decreases, both the skin friction and the Sherwood number increase, whereas the Nusselt number decreases.     

固定床流体流动特征数值模拟

为了研究固定床边壁效应、固定床床层数的变化以及颗粒的填充倾斜角度等参数对床内流体流动状况的影响,基于Ergun方程建立了轴对称多孔介质数学模型。同时对床内流体流动状况进行了研究:在床高确定的情况下,随着床层数的增加,压强降减少;随着颗粒填充倾斜角度的增加,压强降也减少,速度径向分布不均;在固定床边壁附近,气体速度明显增大。计算结果与实验值的比较表明模型能有效地描述固定床压强降和床内流体流动状况。     

Soret Diffusion and Non‐Ideal Dufour Conduction in Macroporous Catalysts with Exothermic Chemical Reaction at Large Intrapellet Damköhler Numbers

The adiabatic temperature rise in catalytic pellets is predicted from a modified version of the Prater equation. Onsager reciprocal relations for coupled heat and mass transfer are violated in an analysis of thermal diffusion in macroporous catalysts with exothermic chemical reaction when Dufour conduction (i.e., the diffusion‐thermo effect) is neglected. In this contribution, Dufour conduction is analyzed for both ideal and non‐ideal pseudo‐binary gas mixtures that simulate the production of methanol from carbon monoxide and hydrogen. In the diffusion‐controlled regime at large intrapellet Damköhler numbers where intermolecular collisions provide the dominant resistance to mass transfer within the catalytic pores, temperatures in the catalytic core could be much greater than predictions based on the original Prater equation when the Prater number exceeds 0.30. The molecular flux of thermal energy includes Fourier's law, the interdiffusional flux, and Dufour conduction. Diffusional mass flux includes Fick's law and the Soret effect. All physicochemical properties of the reactive gas mixture exhibit temperature dependence. There is essentially no difference between maximum intrapellet temperature predictions that include or neglect ideal Dufour conduction when external catalytic surface temperatures range from 300‐400 K and thermal diffusion enhances the flux of “smaller” reactants toward the centre of the catalyst. For “large‐molecule reactants” that participate in exothermic reactions, thermal diffusion opposes Fick's law and Dufour conduction opposes Fourier's law. Under these conditions, it is demonstrated that core temperatures are overestimated by neglecting both off‐diagonal coupling mechanisms (i.e., Soret diffusion and Dufour conduction). Prater numbers greater than unity and unrealistically high gas pressures are required to distinguish between maximum intrapellet temperatures for ideal and real gas simulations, where the latter consider two‐body interactions for Lennard‐Jones molecules in the virial equation of state.     

Low peclet number particle-to-fluid heat and mass transfer in packed beds

For low Peclet numbers most of the experimentally obtained particle-to-fluid heat and mass transfer coefficients in packed beds were found to be some orders of magnitude below the values predicted for a single sphere in cross flow.From theoretical considerations one should expect the transfer coefficients in packed beds to exceed the single sphere predictions as they actually do for higher Peclet numbers.The obvious discrepancy between theory and experiment can be cxplained by a simple model accounting for a nonuniform distribution of the void fraction. The model consists of a packed bed of uniformly sized particles with an average void fraction ψ, where a small part ? of the total cross-sectional area f is assumed to have a larger void fraction ψ₂. Since the same pressure drop applies to both parts of the bed, the superficial velocity will be much larger in the section with the larger void fraction, especially in the range of low Reynolds numbers.Even though in both parts of the packed bed the individual transfer coefficients are taken from a correlation which is based on the single sphere predictions (as it is valid in the range of high Peclet numbers), the apparent overall transfer coefficients for the nonuniform system become much lower, and show the same characteristic variation with Peclet number and the ratio of particle diameter to bed height as the majority of the experimental data.     

THERMAL-DIFFUSION AND DIFFUSION-THERMO EFFECTS ON NATURAL CONVECTION ALONG AN INCLINED STRETCHING SURFACE IN A POROUS MEDIUM WITH CHEMICAL REACTION

The steady natural convection along an inclined stretching surface in the presence of chemical reaction under thermal-diffusion and diffusion-thermo effects is studied. The governing equations for continuity, momentum, energy, and concentration are transformed by similarity transformation and then solved numerically using the Runge-Kutta integration with shooting scheme. Comparisons between the present data with previously published work are performed and found to be in very good agreement with each other. The obtained results show that the flow, thermal, and diffusion fields are influenced appreciably by the effects of endothermic or exothermic chemical reaction, angle of inclination, thermal radiation, magnetic field, and Soret and Dufour numbers. The physical phenomenon can be realized from the graphical profiles and in tabular form to depict special features of the solutions.     

Transient behaviour of encapsulated enzyme reactor systems

Mathematical models are developed for the transient behaviour of encapsulated enzyme reactor systems such as the continuous stirred tank reactor (CSTR) and the packed bed tubular reactor. The rate processes taking place in the encapsulated enzyme bed are approximated by using a combined rate control model of enzyme reaction and membrane diffusion. The change in transient substrate concentration is obtained by using the developed rate expression in the material balance over the substrate as a function of time for the CSTR and as a function of time and position for the packed bed tubular reactor. The effects of various parameters such as the enzymic reaction rate constant, Michaelis constant, diffusional resistance of membranes, and Peclet number on the substrate concentration distribution, which varies with respect to operating time, are investigated. This study affords insight into the transient operating characteristics of the encapsulated enzyme reactor system. The results should be useful in understanding the start-up performance of the reactor systems and to control such reactor systems at desired operating conditions.     

固定床吸附过程传热传质耦合影响数值模拟

引言 多孔介质中物质传递与热量传递相互影响,这种现象最早由Soret和Dufour提出[1].由温度梯度作用产生的传质效应称为Soret效应(热附加扩散效应),它代表由温度场的不均匀性而导致的传质现象;由浓度梯度作用产生的传热效应称为Dufour效应(扩散附加热效应),它代表由浓度场的不均匀性而导致的传热现象.     

Radioisotope tracer study in trickle bed reactors

The residence time distribution (RTD) of liquid phase in trickle bed reactors has been measured for air‐water system using radioisotope tracer technique. Experiments were carried out in a glass column of internal diameter of 0.152 m packed with glass beads and actual catalyst particles of two different shapes. From the measured RTD curves, mean residence time of liquid was calculated and used to estimate liquid holdup. The axial dispersion model was used to simulate the experimental data and estimate mixing index, ie. Peclet number. The effect of liquid and gas flow rates on total liquid holdup and Peclet number has been investigated. Results of the study indicated that shape of the packing has significant effect on holdup and axial dispersion. Bodenstein number has been correlated to Reynolds number, Galileo number, shape and size of the packing.     

EFFECT OF NATURAL CONVECTION ON MASS TRANSFER BETWEEN SOLID PARTICLES AND FLOWING FLUIDS IN PACKED BEDS

Mass transfer between solid particles in a packed bed and a flowing fluid in laminar flow region, where both forced and natural convection are important, was analyzed theoretically. The diffusion equation based on the free surface model proposed by Happel was solved and an approximate solution relating the average Sherwood number to the Peclet number, the Rayleigh number and the void fraction of a packed bed was obtained. The published experimental mass transfer data in packed beds were found to agree well with the theoretical predictions.     

A cell model for the prediction of mixing and mass transfer in packed columns in the presence of a recirculating gas fraction

A cell model for the prediction of mixing and mass transfer in packed columns has been developed. The spatial variation in pore velocities is described in terms of two distinct gas flow channels (only one of which is affected by the irrigating liquid) which discharge into mixing cells. The experimentally observed induced reverse gas flow is accounted for by a recycle stream from any one cell being distributed over a number of lower stages. A closed form expression for the Peclet number in terms of the model parameters is obtained.Steady state absorption of gases is incorporated within the framework of the model by allowing absorption to take place in only one of the two flow channels. No absorption is permitted in the gas mixing regions.The model flow distribution parameters were determined by regression of the absorption model on experimentally determined absorption profiles. Peclet numbers calculated using these parameters are consistent with previously reported experimental data [41].     

填充床中气体流动与气固反应的相互作用

对界面化学反应和粒内扩散联合控制的气固反应,考虑到反应造成的混合气体质量和密度的变化,研究了填充床中等温条件下的快速气固反应和气体运动的相互作用,建立了相应的数学模型.数值分析表明,按耦合分析和非耦合分析得到的混合气体速度完全不同;忽略反应造成的混合气体密度变化,相当于增加一个额外的源项或汇项,因此当反应气体与惰性气体摩尔质量相差较大时,不能忽略反应造成的混合气体密度变化;按耦合分析和非耦合分析得到的浓度场也有很大差别,反应气体浓度波(物质波)阵面的差别也很大;化学反应明显地阻滞反应气体浓度波的推进;当平均压力降和其他条件相同时,反应器越长波阵面推进的量纲1距离越短;反应活跃区的发展对速度场的影响极大.     

A correlation to the solution of the two-phase dispersion model

A correlation to the solution of the two-phase dispersion model has been developed for gas-solid fluidized bed reactors operating in the bubbling regime. An analytical solution was obtained for fractional gas conversion by using an exponential function to characterize the dense phase gas concentration profile. The coefficient of the exponential function was found to depend on gas axial dispersion and, in order to determine this parameter, a Peclet number correlation was developed. Model predicted gas conversions were in excellent agreement with experimental conversions for a variety of fluidized bed reaction data over a conversion range from 2.5 to 99%.     

固定床内石灰石煅烧与传递过程的数值模拟

将固态颗粒填料床视为由规则颗粒堆积而成的松散多孔介质,在推导出传热控制机制下微元体综合速率的基础上,采用局部热不平衡假设建立了一维固定床中石灰石热分解反应与传热、传质耦合的数学模型,运用有效容积法对其离散求解,并采用文献中实验数据对模型进行验证. 计算了不同条件下颗粒物料层内气体和固体骨架的温度场、产物气体浓度场以及固体转化率分布,以得到多孔介质体系内固有化学反应时的传热传质规律. 研究结果对具有强吸热反应的固定床反应器的设计和运行具有一定的参考作用.     

Effect of Non‐Newtonian Characteristics on Convective Liquid‐Solid Heat Transfer in Packed and Fluidised Beds of Spherical Particles

In this work, the field (continuity, momentum and thermal energy) equations togetherwith a cell model have been solved numerically to elucidate the influence of non‐Newtonian (Power law rheology) liquid characteristics on liquid‐solid heat transfer in packed and fluidised beds of spherical particles. The results presented herein relate to wide ranges of conditions of bed voidage, power‐law index and Peclet number but are limited to low Reynolds number (≤1) flow conditions. Within the range of conditions, the effect of power‐law index is found to be small and this is also consistent with the available experimental results on liquid‐solid mass transfer in these systems.     

Dispersion in pulsed systems—III: Comparison between theory and experiments for packed beds

The theoretical development put forth in Part II of this paper is applied to several two-dimensional, spatially periodic porous media in order to determine components of the dispersion tensor for Peclet numbers ranging from 1 to 10⁴. The calculated longitudinal dispersion coefficients show reasonable agreement with experimental data for a packed bed of spheres in a cubic array. This provides support for the theory developed in Part II; however, for randomly packed beds the experimental values of the longitudinal dispersion coefficient are smaller than those predicted using the spatially periodic model. In addition, the functional dependence on the Peclet number for the experimental data differs considerably from that predicted by the theory. The dependence of the dispersion coefficient on distance is discussed from the point of view of the results presented in Part I, and some recent experimental observations and calculated results for the effect of particle size distribution are given. In addition, our calculated values for the lateral dispersion coefficient are compared with experimental values and are found to be too small by about three orders of magnitude at a Peclet number of 10³.     

SORET AND DUFOUR EFFECTS IN A FREE CONVECTIVE DOUBLY STRATIFIED FLOW OVER A VERTICAL PLATE WITH CHEMICAL REACTION

An investigation was performed to study the influence of thermo-diffusion and diffusion-thermo effects in the transient, free convective flow of a viscous, incompressible, and doubly stratified fluid past an isothermal vertical plate in the presence of first-order chemical reaction. The governing boundary layer equations were solved numerically using an implicit finite difference scheme of the Crank-Nicolson type. The effects of the Soret number, Dufour number, thermal stratification parameter, mass stratification parameter, and chemical reaction parameter are analyzed and presented graphically. Also, the influence of the parameters on local as well the average skin-friction coefficient and the rate of heat and mass transfer are analyzed and discussed. The results are compared with particular solutions available in the literature. The present results are found to be in good agreement with the existing solution.     

旋转填料床吸收NO_x缓冲氧化-强化吸收模型

从平推流缓冲-氧化NO和旋转填料床强化吸收NOx的特性出发,建立了涉及平推流反应器中NO气相氧化和旋转填料床强化吸收NOx的物料衡算、气液传质、界面相平衡和液相反应等方程的数学模型,并应用表面更新理论求解了传质系数。结果表明:在NOx较高浓度条件下,短时间达到较高氧化度,在NOx较低浓度条件下,氧化度很快达到50%,但需要较长停留时间才能达到90%氧化度。超重力因子小于90时,NOx吸收率随超重力因子增加而增加,当超重力因子高于90时,吸收率随超重力因子增加而变化不大。模型的数据关联结果良好。