USE OF THE INTERCHANGE MODEL TO PREDICT ENTRAINMENT IN VERTICAL ANNULAR FLOW

Entrapment, E, in vertical gas-liquid annular flows may be pictured as a balance between the rate of atomization, RA, of the liquid layer and the rate of deposition of drops, R D. Laboratory measurements of RA, RD and E are reviewed. Theoretical analyses are discussed which picture RA as related to the growth of wavelets through a Kelvin-Helmholtz instability and RB as being directly proportional to the root-mean-square of the turbulent velocity fluctuations of the drops. An equation for E can be developed, which assumes that the deposition constant is independent of drop concentration and that the rate of atomization varies linearly with the flow rale of the liquid in the film. Limitations of this approach, suggested by measurements of RA and RD at large liquid flows, are discussed.     

MODEL REDUCTION IN A CLASS OF MULTI-PHASE SYSTEMS

It is shown how very general multi-phase models with a single, well-mixed reactive phase can be reduced to the simple model of a stirred tank.     

MODEL REDUCTION IN A CLASS OF MULTI-PHASE SYSTEMS

It is shown how very general multi-phase models with a single, well-mixed reactive phase can be reduced to the simple model of a stirred tank.     

湖南界牌土的化学组成和颗粒组成与干燥强度间定量关系的数学模型

本工作,选用湖南界牌土作原料,对所选原料进行颗粒分级和量化处理,依据最优化的基本理论,经二次回归正交试验设计,测量其干燥强度,最后应用回归技术建立了原料的干燥强度与其化学组成和颗粒组成之间的定量关系的数学模型,并用数学方法和工艺原理对其影响因素进行了分析讨论,结果表明界牌土的化学组成和颗粒组成对其干燥强度有着重大的影响。     

RH真空处理过程中钢中氧含量预测模型

针对３００ｔ钢包ＲＨ真空处理低碳铝镇静钢的多次试验数据，建立了ＲＨ处理过程中钢中氧含量的定量预测模型，得到了钢中氧含量的预测公式模型综合考虑了纯脱气时间、真空室吹氩流量、钢水环流量、钢包渣中ＦｅＯ＋ＭｎＯ含量、钢包内衬材质等因素的影响，并对改进ＲＨ操作进行了讨论     

A THEORETICAL MODEL FOR PARTICLE SEGREGATION IN A FLUIDIZED BED DUE TO SIZE DIFFERENCE

An a priori model has been developed for the prediction of particle segregation in a fluidized bed of particles of same density. The model predicts the phase equilibrium of any two-component system by taking into account the Uml of both components and the minimum concentration of fines for minimum bed viscosity. An extension of the model to a multi-component system leads to an algorithm which allows the prediction of the quantity and the concentration profiles of particles in both phases of a segregated fluidized bed. The algorithm requires only the initial concentration profile or the mixture and the physical properties of each component and the fluidizing gas. A good agreement between the predicted and the previously measured concentration profiles of both a two-size and a wide size mixture shows the adequacy of the model.     

SCATTERING EFFECTS IN A FURNACE SLAB

The major mode of heat transfer in industrial combustion furnaces is that of radiation. The effects of radiative scattering are therefore of great importance in furnace design. This study investigates the behavior of both anisotropic and isotropic scattering using a computer-simulated model of a typical combustion furnace

The furnace model employed is based on the zoning method of Hottel and the Monte-Carlo statistical approach. To study scattering effects, subroutines to simulate isotropic and anisotropic scattering have been added on to the model developed in earlier work with non-scattering mediums. Anisotropic scattering distributions studied include both forward and backward skewed profiles

To simplify the three-dimensional model, a three by four meter slab of a semi-infinite furnace is studied. Each stab is rectangular in shape, containing twelve cubical zones and incorporating a single burner. Model results are presented in the form of temperature contours and total surface heat fluxes for different scattering albedoes and profiles.     

绝热轴向固定床中气流均布的数学模型

以前文为基础,在 0.4m、0.535×0.535 m 以及1.32×1.32 m 的装置中,对侧向进、出口绝热轴向固定床反应器的气流均布问题作了进一步的研究。采用瓷球促使反应器内气流均匀分布,根据理论分析和实验结果提出了数学模型,得到气流不均匀度的表达式:s=[k_1-k_2(H/D)~(k3)][1-exp(-1/k_4Eu)]     

A TWO ZONE UNEQUAL VOLUME MODEL TO DESCRIBE MIXING IN CHEMICAL AND BIOCHEMICAL PROCESSES

The effect of imperfect mixing in a single batch reactor was studied using a two-tank system model with internal recycle and unequal volumes. The double-valued relationship between the reactant in each tank of the model for the A → B biochemical/chemical reversible and irreversible reactions was used to analyze mixing patterns in poorly mixed stirred-tank reactors.     

STEADY STATE AND DYNAMIC MODELLING OF A PACKED BED REACTOR FOR THE PARTIAL OXIDATION OF METHANOL TO FORMALDEHYDE I. MODEL DEVELOPMENT

Several levels of mathematical models involving one and two dimensions as well as single and multiple phases are used to predict the steady state and dynamic behavior of a packed bed reactor for the partial oxidation of methanol to formaldehyde. Parametric sensitivity is examined for several heat and mass transfer parameters, kinetic parameters, and operating conditions. Yield is compared for various models, and significant differences are observed between the one-dimensional and two-dimensional models. The dynamic behavior after step changes in the operating conditions is found to be qualitatively similar for different models.     

SELECTIVITY STUDIES IN THE PHOTOCHLORINATION OF METHANE I: REACTOR MODEL AND KINETIC STUDIES IN A NON-ISOTHERMAL, POLYCHROMATIC ENVIRONMENT

The photochlorination of methane employing nitrogen as an inert diluent is studied in a continuous flow, tubular, non-isothermal, bench-scale, polychromatically irradiated photoreactor with particular emphasis on selectivities.

Using a mechanistic sequence of 22 steps, predictions from the mathematical model are compared with experimental results obtained for three different nominal temperatures (297.9 K, 312.8 K and 322.2 K) and three different radiation sources (40, 360 and 1200 W ) that also differ in their output emission characteristics.

An extremely high sensitivity to some of the values of the employed specific rate constants is found, particularly when an accurate prediction of selectivities is being sought. However, within the reported or attributable errors in the published values of the kinetic constants( ± 5%), the experiments show very good agreement with the computed predictions obtained from the mathematical model of the photoreactor.

Using these experimental results that show excellent reproducibility a complete and reliable set of process independent reaction kinetic constants, and a verified reactor model are obtained which can be used for photoreactor design purposes, including selectivity optimization.     

INTERPRETATION OF MICROMIXING EFFECTS ON FAST CONSECUTIVE-COMPETING REACTIONS IN SEMI-BATCH STIRRED TANKS BY A SIMPLE INTERACTION MODEL

A model is proposed for interpreting micromixing experiments in a semi-batch reactor. In these experiments, a fast consecutive-competing reaction system is used A + B → R, R + B → S, B being added either dropwise or as a pulse into an excess of A. A segregation index X_s = 2n_s/n_B0 is measured after completion of the reaction for various locations of the injection point. The macroscopic flow pattern is assumed to be known, essentially characterized by the recirculation time t_c. Micromixing then takes place within the cloud via a mechanism of interaction with the mean environment (IEM model, micromixing time t_m). Experimental results published by Barthole et al. (precipitation of barium sulphate) and Bourne et al. (diazo coupling) are successfully interpreted by this model. The influence of stirring speed, injection volume, concentration of species and mode of injection (pulse or dropwise) are especially well accounted for. This model provides a simple method for predicting the influence of mixing on selectivity in semi-batch reactors.     

SOLIDS DISTRIBUTION IN STIRRED SLURRY REACTORS: INFLUENCE OF SOME MIXER CONFIGURATIONS AND LIMITS TO THE APPLICABILITY OF A SIMPLE MODEL FOR PREDICTIONS

The features of solids concentration distribution were investigated in baffled and unbaffled tanks of high aspect ratio, stirred with multiple radial, mixed-flow or axial impellers. In the baffled tanks the average profiles can be predicted with the sedimentation-dispersion model regardless of impeller type - in spite of slight systematic departures from the average trend at the impeller plane and/or midway between the impellers. This is hardly possible for the unbaffled tanks due to lack of physical foundation of this simple model. When the unbaffled tank is stirred with hydrofoil impellers, an inverted profile is even obtained. The mentioned departures and this last anomalous behaviour are qualitatively discussed with reference to particle-turbulence interaction.     

MODEL PREDICTIVE CONTROL AND DYNAMIC OPERABILITY STUDIES IN A STIRRED TANK: RAPID TEMPERATURE CYCLING FOR CRYSTALLIZATION

A stirred-tank reactor was built with the objective of rapid and accurate temperature control in the reaction vessel. A first-principles heat transfer model was developed for the jacketed batch system, with the jacket inlet temperature used to control the vessel temperature. A model predictive controller was implemented to follow a rapidly changing temperature profile that cycled between steep heating and cooling motifs, and it was tested experimentally at progressively shorter temperature cycles. For a water-solvent-water-jacket system, a cycle consisting of increasing and decreasing the temperature by 15°C over a period of 20 min was achieved in practice. The performance of the MPC controller was explained by calculating the dynamic operability characteristics of the process.     

SOLIDS DISTRIBUTION IN STIRRED SLURRY REACTORS: INFLUENCE OF SOME MIXER CONFIGURATIONS AND LIMITS TO THE APPLICABILITY OF A SIMPLE MODEL FOR PREDICTIONS

The features of solids concentration distribution were investigated in baffled and unbaffled tanks of high aspect ratio, stirred with multiple radial, mixed-flow or axial impellers. In the baffled tanks the average profiles can be predicted with the sedimentation-dispersion model regardless of impeller type - in spite of slight systematic departures from the average trend at the impeller plane and/or midway between the impellers. This is hardly possible for the unbaffled tanks due to lack of physical foundation of this simple model. When the unbaffled tank is stirred with hydrofoil impellers, an inverted profile is even obtained. The mentioned departures and this last anomalous behaviour are qualitatively discussed with reference to particle-turbulence interaction.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3. The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3. The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3 The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3 The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.