Kinetic mass transfer model

It is clear that in addition to thermodynamic models, kinetic mass transfer models can bring about some additional information that is required for a better definition of the system. In this context, natural analogues provide some of the required scale and time-frames necessary for the testing of kinetic mass transfer models and the Cigar Lake ore deposit is probably the better constrained for such an exercise. 

The kinetic mass transfer model developed to take into consideration the geochemical evolution of the Cigar Lake ore deposit was mainly done by simulating the evolution of the Al-Si system in the Cigar Lake ore deposit system. To this aim the system formed by kaoli-nite, gibbsite and illite as main aluminosilicate solid phases was considered and kinetics for the dissolution-precipitation processes were taken from the open scientific literature (Nagy et al. 

Bruno, J., Casas, I., Cera, E. Duro, L. 1997. Development and application of a model for the long-term alteration of U02 spent nuclear fuel. Test of equilibrium and kinetic mass transfer models in the Cigar Lake ore deposit. Journal of Contaminant Hydrology, 26, 19-26. 

Bencala K. E. (1983) Simulation of solute transport in a mountain pool-and-riffle stream with a kinetic mass transfer model for sorption. Water Resour. Res. 19, 732—738. 

Many wastewater flows in industry can not be treated by standard aerobic or anaerobic treatment methods due to the presence of relatively low concentration of toxic pollutants. Ozone can be used as a pretreatment step for the selective oxidation of these toxic pollutants. Due to the high costs of ozone it is important to minimise the loss of ozone due to reaction of ozone with non-toxic easily biodegradable compounds, ozone decay and discharge of ozone with the effluent from the ozone reactor. By means of a mathematical model, set up for a plug flow reactor and a continuos flow stirred tank reactor, it is possible to calculate more quantitatively the efficiency of the ozone use, independent of reaction kinetics, mass transfer rates of ozone and reactor type. The model predicts that the oxidation process is most efficiently realised by application of a plug flow reactor instead of a continuous flow stirred tank reactor. 

Alkylation Reactor Model Kinetics, Mass Transfer and Dynamics... 

Apart from the analysis of kinetics, mass transfer, and equilibrium of the processes at a fundamental level, the analysis of material, and in fixed beds energy balances in the reactors, as well as a number of analytical solutions of the reactors models are presented. Furthermore, the hydraulic behavior of the reactors is presented in detail. Hydraulic analysis is basically... 

Figure 5.6 Diagram of the kinetic processes involved in the mass transfer model of VOCs from material surfaces adopted from (Sparks et al., 1996).

In extraction columns, it is possible to find droplet swarms where the local velocities near the droplet surface are higher, this being due to the lower free area available for the countercurrent flowing continuous phase. Wake and Marangoni influences make the prediction of a physical mass transfer coefficients difficult. With reactive extraction the influence of interfacial kinetics on overall mass transfer is generally not negligible. In any case, a combination of reactive kinetics with any eddy mass transfer model is recommended, whereas the latter could rely on correlations derived for specific column geometries. 

Dynamic adsorption is a mass-transfer problem that can be treated with complex mass-transfer models, where many parameters that have to be calculated by independent batch kinetic studies or estimated by appropriate correlations are required [97,98],... 

The algorithm of the kinetics and mass transfer model is a system of algebraic equations that are developed in the following way. The key variable is AN, the change in the amount of a particular reactant or product component involved in a reaction step during an interval At. The material balance of a step is,... 

The author would like to acknowledge the help of Frank Zybert who did the detailed programing of the kinetics and mass transfer model. 

In 1978, Karlberg and Thelander [5] described the flow injection extraction (FIE) technique, and in 1979 Murray [6] improved the microextraction, reducing the amount of solvent to 200 pL. The main disadvantage of these methods was the necessity to use complicated equipment. Jeannot and Cantwell [7] and, independently, Hee and Lee [8] introduced a simpler kind of microextraction in which a solvent drop is applied, single drop microextraction (SOME). They designed a microreactor with 8 pL of -octane in a Teflon tube (Fig. 14.3) [7]. The authors performed measurements of diffusion coefficients and the kinetics of the system, which suggested a mass transfer model. 

This part demonstrates how deterministic models of impedance response can be developed from physical and kinetic descriptions. When possible, correspondence is drawn between hypothesized models and electrical circuit analogues. The treatment includes electrode kinetics, mass transfer, solid-state systems, time-constant dispersion, models accounting for two- and three-dimensional interfaces, generalized transfer functions, and a more specific example of a transfer-function tech-nique.in which the rotation speed of a disk electrode is modulated. 

To simulate the effects of reaction kinetics, mass transfer, and flow pattern on homogeneously catalyzed gas-liquid reactions, a bubble column model is described [29, 30], Numerical solutions for the description of mass transfer accompanied by single or parallel reversible chemical reactions are known [31]. Engineering aspects of dispersion, mass transfer, and chemical reaction in multiphase contactors [32], and detailed analyses of the reaction kinetics of some new homogeneously catalyzed reactions have been recently presented, for instance, for polybutadiene functionalization by hydroformylation in the liquid phase [33], car-bonylation of 1,4-butanediol diacetate [34] and hydrogenation of cw-1,4-polybutadiene and acrylonitrile-butadiene copolymers, respectively [10], which can be used to develop design equations for different reactors. 

A complete parametric study of the unsteady state mass transfer model clearly shows that tp, the pulse period, 4, the polarization, A, the aspect ratio, and DF, the duty factor have a profound effect on the evolution and the final shape of the deposit. Large polarization s and aspect ratios lead to deposition that is mass transfer controlled. This results in keyhole formation, as the concentration gradient inside a high aspect ratio trench is very large. On the other hand, when the deposition is kinetically controlled (i.e. for small values of polarization and aspect ratio) the gradient down the length of the trench is much smaller and deposition proceeds at nearly the bulk concentration. This leads to conformal deposition, as there is negligible variation in the deposition rate at the mouth and at the bottom of the trench. 

The three-phase nonequilibriimi model developed in our laboratory which includes kinetics, mass transfer and heat transfer models [6] is used to predict the yield and selectivity of EGME from the reaction of ethanol and EO. The model predicts fliat die conversion of EO would reach 94 % and 99 % selectivity to EGME at an operating pressure of 235 kPa and a reflux ratio of 2. The model predictions are in excellent agreement with experimental data (Table 2). This result shows that our three-phase non-equilibrium model could be used for the prediction of yield and selectivity in a CD process. 

Through this step and based on experimental evidence we try to develop the appropriate model to describe the test chamber kinetics. As was anticipated in the introduction of this Chapter, from a conceptual point of view, two broad categories of models can be developed empirical-statistical and physical-based mass transfer models. It should be emphasized that, in several cases, even the fundamentally based mass transfer models are indistinguishable from the empirical ones. This happens because the mass transfer models are generally very complex in both the physical concept involved and the mathematical treatment required. This often leads the modelers to introduce approximations, making the mass transfer models not completely distinguishable from some empirical models in terms of both functional formulations and descriptive capabilities. Considering the current status of models which have been developed to describe VOC emissions (and/or sink processes), we could define the mass transfer models as hybrid-empirical models. 

Two-dimensional diffusion occurs axially and radially in cylindrically shaped porous catalysts when the length-to-diameter ratio is 2. Reactant A is consumed on the interior catalytic surface by a Langmuir-Hinshelwood mechanism that is described by a Hougen-Watson kinetic model, similar to the one illustrated by equation (15-26). This rate law is linearized via equation (15-30) and the corresponding simulationpresented in Figure 15-1. Describe the nature of the differential equation (i.e., the mass transfer model) that must be solved to calculate the reactant molar density profile inside the catalyst. 

The simplified homogeneous mass transfer model for diffusion and Langmuir- Hin-shelwood chemical kinetics within the internal pores of an isolated catalytic pellet is written in dimensionless form for reactant A or A2 (i.e., ua = —1) ... 

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