TRANSIENT RESPONSE METHOD IN HETEROGENEOUS CATALYSIS

The steady-state flow method has been widely used in the kinetic study of heterogeneous catalysis. Under the conditions of steady state, all elementary steps in series are progressing at the same rate and hence the measured rates hardly tell the precise kinetic structure, or mechanism, of catalytic reactions which usually consist of several elementary steps including adsorption of reactants, surface reaction, and desorption of products. In the kinetic analyses of any given reactions, it is a common practice for the investigator to postulate a number of suspected rate models and then to assess these models to verify a optimal one which best fits observed rate data. Usually, however, there are quite a large number of plausible rate models even for a rather simple reaction, and it is not easy to determine the most adequate model among others even with the help of mathematical model indentification techniques with a electronic computer. This method is based on the assumption that there is a best model which reflects the true mechanism of the reaction sequences among the postulated models. But there is no certification which justifies this assumption. Therefore, even when a rate model is found to fit the rate data very well, the value of parameters appearing in the rate model should be further assessed in regards to their physical significance.     

TRANSIENT RESPONSE METHOD IN HETEROGENEOUS CATALYSIS

The steady-state flow method has been widely used in the kinetic study of heterogeneous catalysis. Under the conditions of steady state, all elementary steps in series are progressing at the same rate and hence the measured rates hardly tell the precise kinetic structure, or mechanism, of catalytic reactions which usually consist of several elementary steps including adsorption of reactants, surface reaction, and desorption of products. In the kinetic analyses of any given reactions, it is a common practice for the investigator to postulate a number of suspected rate models and then to assess these models to verify a optimal one which best fits observed rate data. Usually, however, there are quite a large number of plausible rate models even for a rather simple reaction, and it is not easy to determine the most adequate model among others even with the help of mathematical model indentification techniques with a electronic computer. This method is based on the assumption that there is a best model which reflects the true mechanism of the reaction sequences among the postulated models. But there is no certification which justifies this assumption. Therefore, even when a rate model is found to fit the rate data very well, the value of parameters appearing in the rate model should be further assessed in regards to their physical significance.     

The flow of non-Newtonian solutions through packed beds

The rheological behavior of aqueous solutions of Separan AP-30®, polymethylcellulose, and polyvinylpyrrolidone was studied experimentally. These solutions exhibit non-Newtonian flow behavior in simple shear, and are characterized by one of several 2, 3, or 4 parameter rheological equations. The equations used included the power law, the Ellis model, Spriggs equation, the Herschel-Bulkley equation, and Meter's model. The power law model fits the data for each of the solutions over a limited range of shear rates, whereas the other models, which include either a lower shear rate limiting Newtonian viscosity, and/or an upper shear rate limiting Newtonian viscosity, or a yield stress, fit the data well over a wide range of shear rates from 0.00675 to 1076 sec^?1. The pressure drop-flow rate data for the same aqueous solutions flowing through packed beds were correlated well by the Ergun equation using the various rheological models applied in this work to evaluate a modified fluid viscosity. In each case it was found that the rheological model which best fit the viscometric data also gave the best packed bed friction factor correlation, and that no one model, such as the powerlaw, or the Ellis model, is the best one to use in all cases for all solutions. For polyvinylpyrrolidone solutions large deviations between experimental values of friction factor and those from the Ergun equation occurred for modified Reynolds numbers greater than one. A pseudo viscoelastic parameter was used to improve the friction factor correlation empirically at high Reynolds numbers.     

不同曳力模型及颗粒碰撞恢复系数对短接触旋流反应器内气固流场的影响

为考察曳力模型和颗粒碰撞恢复系数对短接触旋流反应器内流动特性的影响,基于双流体模型, 结合颗粒动力学理论,对反应器内气固两相流场进行模拟研究。分别采用Gidaspow、Wen & Yu和Syamlal-O’Brien 3种曳力模型, 考察颗粒速度特性以及固含率径向分布。对比分析不同曳力模型的计算结果表明,Syamlal-O’Brien模型计算结果与实验结果误差较大,Wen & Yu模型在反应器边壁附近区域的计算结果误差较大,Gidaspow模型计算结果与实验结果最为吻合。此外,颗粒碰撞恢复系数较小时,所得计算值小于实验测量值,当恢复系数为0.95时颗粒扩散效果最好,计算结果与实验数据吻合度最高。     

Mathematical Modeling of Drying Processes of Selected Fruits and Vegetables

This study investigates the behavior of fruit and vegetable samples during drying. The experimental data are fitted to several different thin-layer drying models. Regression analysis is used to determine model parameters, while statistical indicators serve to evaluate the goodness of fit. The power function model gives the best fit for all examined samples. Based on this model, different drying and heat storage technologies can be combined to ensure that the required residual moisture content of an agricultural product is reached. It is demonstrated on the case of a specific Togolese processing plant that under favorable conditions, fossil fuel consumption can be decreased by 33 %.     

QUALITATIVE AND QUANTITATIVE IDENTIFIABILITY ANALYSIS OF NONLINEAR CHEMICAL KINETIC MODELS

Identiriability analysis deals with the problem of uniqueness of the parameters when fitting a model to a set of observations. If the model is not qualitatively identifiable, then several or infinitely many parameter sets generate identical predictions of the observed quantities. Three rigorous approaches are evaluated to study qualitative identiriability of nonlinear dynamic models, with emphasis on chemical kinetic modelling. Analysis of a large variety of systems of higher-order reactions shows that under reasonable experimental conditions such models are rarely unidentifiable in the qualitative sense, although there exist well-known examples of unidentifiable models for monomolecular reaction systems. Kinetic models are, however, frequently unidentifiable in a quantitative sense, when a particular sel of error-corrupted data does not allow for obtaining reliable estimates of the parameters. In such cases the goodness-of-fit depends only on some combinations of the parameters. Performing a logarithmic transformation, the well-known principal component analysis is shown to offer an efficient method for detecting and identifying nonlinear dependences among the parameters, thereby suggesting simpler models leading to meaningful estimates     

Effect of kinetic models on hot spot temperature prediction for phthalic anhydride production in a multitubular packed bed reactor

Although there are several kinetic models for the production of phthalic anhydride from the partial oxidation of o‐xylene, only few studies have compared the effect of the kinetic model on the prediction of the hot‐spot temperature. In this work, the predicted temperature profile for the partial oxidation of o‐xylene to phthalic anhydride in a multitubular packed bed reactor was obtained for different kinetic mechanisms using one‐dimensional pseudo‐homogeneous and heterogeneous models. The predicted temperature profile using the one‐dimensional heterogeneous model with the kinetic model of Calderbank et al. but with the adjusted kinetic and transport parameters proposed by Anastasov presented a good correlation with regard to experimental data. Nevertheless, in the hot‐spot zone deviations, up to 30 K were presented. In conclusion, the temperature performance in the production of phthalic anhydride is suitably predicted by the one‐dimensional heterogeneous model and the Calderbank et al.'s kinetic model. Though, prediction using bidimensional models should be done to establish the best correlation with experimental data.     

Viscoelastic behavior of polymer tape in a wound roll

A viscoelastic computational model is developed that uses experimentally determined viscoelastic material properties as input and can be used to predict the behavior of a tape material in a wound roll as stresses relax over time. Experimental creep test results are used to find best‐fit creep‐compliance parameters to describe two high density data storage tape media. The two tapes used in the analysis are a developmental tape with a poly(ethylenenaphthalate) (PEN) substrate and metal particle (MP) front coat similar to linear tape open (LTO4) (referred to in this work as “Tape C”), and LTO3, a commercially available tape with a PEN substrate and MP front coat. Sets of best‐fit creep‐compliance parameters are determined for both tapes. The differences between the predicted behavior using three‐, five‐, and seven‐parameter Kelvin–Voigt models are evaluated, both for a benchmark case and in a viscoelastic wound roll model. The choice of material model is found to significantly influence the predictions of the wound roll model. The differences between different material models for the same material are on the order of the differences found between the two different materials. A material model with a higher number of creep‐compliance parameters, although more computationally expensive, produces better results, particularly over long spans of time. The relative differences between the three‐, five‐, and seven‐parameter models are shown to be qualitatively consistent for several variations in the computational model setup, allowing predictions to be made based on simple benchmarks. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Profiling solid volume fraction in a conical bed of dry micrometric particles: Measurements and numerical implementations

In order to develop predictive process models in conical fluidized beds, there is an ongoing search for experimental methods and simulation tools to measure and model hydrodynamics parameters. Accordingly, experiments carried out in a conical fluidized bed containing micrometric TiO₂ particles with a wide particle size distribution. An optical fiber technique was employed to determine the effect of particles loading on the solid volume fraction. The axial and radial profiles of solid volume fraction have then been determined to evaluate the sensitivity of different models, including Syamlal-O?Brien (1988), Arastoopour et al., (1990) and Gidaspow (1994) drag models. The Eulerian-Eulerian model with frictional stress models and three different boundary conditions (BCs), consisting of no-slip, partial-slip and free-slip have been used in the numerical simulations. The Gidaspow model with the partial-slip BC gives the best agreement with experimental data for different particle loadings.     

A generalized procedure for the prediction of multicomponent adsorption equilibria

Prediction of multicomponent adsorption equilibria has been investigated for several decades. While there are theories available to predict the adsorption behavior of ideal mixtures, there are few purely predictive theories to account for nonidealities in real systems. Most models available for dealing with nonidealities contain interaction parameters that must be obtained through correlation with binary‐mixture data. However, as the number of components in a system grows, the number of parameters needed to be obtained increases exponentially. Here, a generalized procedure is proposed, as an extension of the predictive real adsorbed solution theory, for determining the parameters of any activity model, for any number of components, without correlation. This procedure is then combined with the adsorbed solution theory to predict the adsorption behavior of mixtures. As this method can be applied to any isotherm model and any activity model, it is referred to as the generalized predictive adsorbed solution theory. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2600–2610, 2015     

Simulation of Turbulent Flow in a Packed Bed

Numerous models for simulating the flow and transport in packed beds have been proposed in the literature with few reported applications. In this paper, several turbulence models for porous media are applied to the gas flow through a randomly packed bed and are examined by means of a parametric study against some published experimental data. These models predict widely different turbulent eddy viscosity. The analysis also indicates that deficiencies exist in the formulation of some model equations and selection of a suitable turbulence model is important. With this realization, residence time distribution and velocity distribution are then simulated by considering a radial profile of porosity and turbulence induced dispersion, and the results are in good agreement with the available experimental data.     

Fluidization of micronic particles in a conical fluidized bed: Experimental and numerical study of static bed height effect

The numerical simulations and experimental data of bed hydrodynamics in a conical fluidized bed unit are compared. Experimental studies have been carried out in a bed containing TiO₂ particles belonging to A/C boundary of Geldart's classification with a wide particle‐size distribution. Thus, pressure measurements and an optical fiber technique allowed determining the effect of static bed height on the fluidization characteristics of micronic particles. Numerical simulations have then been performed to evaluate the sensitivity of gas‐solids drag models. The Eulerian multiphase model has been used with different drag models and three boundary conditions (BC) consisting of no‐slip, partial‐slip, and free‐slip. The numerical predictions using the Gidaspow drag model and partial‐slip BC agreed reasonably well with the experimental bed pressure drop measurements. The simulation results obtained for bed expansion ratio show that the Gidaspow model with the free‐slip BC best fit with the experimental data. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

两相热虹吸循环蒸发侧传热模型比较

两相热虹吸换热器在工业领域应用广泛,其制冷剂内侧的传热过程是热虹吸管设计的基础。然而由于沸腾传热和两相流动的复杂性,基于实验的经验传热模型各自差异很大且适用范围有限,给热虹吸管建模时传热模型选取带来了一定的困难。建立了稳态两相热虹吸循环分布式参数模型,利用5篇文献中4种工质共424个热虹吸管传热实验数据点,对热虹吸管中常用的7种传热模型进行比较评价,为模型选取提供参考。结果发现:Kandlikar流动沸腾模型和Rahmatollah拟合的热虹吸管传热模型模拟精度最好,推荐使用;Cooper池沸腾也有较好的精度,说明核态沸腾在热虹吸管传热中占主导地位; Gungor and Winterton、Liu and Winterton等常用的流动沸腾模型模拟精度差别不大,误差尚可接受;Imura池沸腾模型不适用于热虹吸管传热模拟。     

A COMPARATIVE STUDY OF KINETIC MODELS FOR ION-EXCHANGE USING MACROPOROUS RESINS AND CONCENTRATED SOLUTIONS

ABSTRACT

A “shallow bed” technique was employed for the study of the kinetics of K⁺ ? H⁺ exchange in concentrated solutions with a macroporous ion-exchange resin. Six kinetic models were applied to the experimental data. The fitting of the mathematical models and the behaviour of the kinetic curves when some variables change, show that there does not exist any model based on the Donnan exclusion principle suitable for explaining the experimental data. The best model in these extreme conditions is a modification of the Progressive Conversion mechanism. It can be easily applied to the design of industrial operations.     

Applications of the phenomenological theory to several published experimental cases of sedimentation processes

In one space dimension, the phenomenological theory of sedimentation predicts the sedimentation–consolidation behavior of a flocculated suspension in dependence of two constitutive functions describing its material behavior, the solids flux density (or hindered settling function) and the solid effective stress. These functions are assumed to depend only on the local volumetric solids concentration. In this contribution, we review several experimental and theoretical studies of sedimentation in settling columns. We first resume the theories that have been employed to interpret the experimental measurements and then apply the phenomenological model to the available data. The two constitutive functions involved are determined from the published concentration, permeability and effective stress data. The mathematical model is then solved numerically using these functions, and the resulting predictions of settling behavior are compared with the respective authors’ experimental findings and interpretations. In one case, the information obtained from a batch settling experiment is used to simulate continuous sedimentation.     

Optimal design and operation of an industrial three phase reactor for the oxidation of phenol

Among several treatment methods catalytic wet air oxidation (CWAO) treatment is considered as a useful and powerful method for removing phenol from waste waters. In this work, mathematical model of a trickle bed reactor (TBR) undergoing CWAO of phenol is developed and the best kinetic parameters of the relevant reaction are estimated based on experimental data (from the literature) using parameter estimation technique. The validated model is then utilized for further simulation and optimization of the process. Finally, the TBR is scaled up to predict the behavior of CWAO of phenol in industrial reactors. The optimal operating conditions based on maximum conversion and minimum cost in addition to the optimal distribution of the catalyst bed is considered in scaling up and the optimal ratio of the reactor length to reactor diameter is calculated with taking into account the hydrodynamic factors (radial and axial concentration and temperature distribution).     

Studies of the fischer-tropsch synthesis on a cobalt catalyst II. Kinetics of carbon monoxide conversion to methane and to higher hydrocarbons

Six Langmuir-Hinshelwood-Hougen-Watson models have been derived for the kinetics of conversion of carbon monoxide to hydrocarbons in the Fischer-Tropsch synthesis. The models were fitted to experimental data obtained in an internal recycle reactor over a wide range of operating conditions. Two models, one based on the hydrogenation of surface carbon and the other on a hydrogen-assisted dissociation of carbon monoxide as rate limiting steps were both able to provide a satisfactory fit to the experimental rate data. A general model was also developed for the rate of methanation in the presence of higher hydrocarbons. The same two rate limiting assumptions as those used in formulating the rate of total CO conversion are used in these models. The two models were fitted to experimental data for methane formation. It was the model assuming CH formation as rate limiting that showed the best fit for both CO conversion for CH₄ formation.     

Comparison and evaluation of interphase momentum exchange models for simulation of the solids volume fraction in tapered fluidised beds

An Eulerian computational fluid dynamics (CFD) model with granular flow extension was used to simulate a gas–solid fluidised bed in a tapered reactor. Various drag coefficient models were evaluated, which are used to calculate the drag force, describing the momentum transfer between the gas and solid phases. Comparison and evaluation between time-averaged solids volume fractions obtained from experiments and from simulations with several drag coefficient models were made. The predicted results obtained by the different drag models were verified using experimental data of Depypere et al. (2009). Initial results using a 2-phase Eulerian model showed poor agreement with experimental results. However, extending the Eulerian model to include 3 solid phases—with different mean particle diameter per phase in order to account for the particle size distribution of the fluidised solid material—yielded good agreement with experimental results. Furthermore, quantitative analyses showed that the modified Gidaspow drag model gave the best agreement between CFD simulations and experimental data.     

The Tank Drainage Problem Revisited: Do These Equations Actually Work?

The tank drainage problem with pipeline attached is studied in this work. Laminar and turbulent formulations of this unsteady‐state flow problem are derived and evaluated by experimental data. Additional literature models are also evaluated for comparison. Several experimental configurations were used including a small tank with a vertical tube, the same with various‐ sized orifices, a large tank with a horizontal pipe, and a large tank including a piping system with elbows, vertical drop and horizontal extension. Not all the models performed well under all conditions. Limitations of the models are discussed. The model derived by Loiacono and the model we derived (an exact equivalent) showed the best for both laminar and turbulent flow, predicting drainage times to better than ± 8%, on average.