Model kinetics mass-transfer

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

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 simple pore structure shown in Figure 2.69 allows the use of some simplified models for mass transfer in the porous medium coupled with chemical reaction kinetics. An overview of corresponding modeling approaches is given in [194]. The reaction-diffusion dynamics inside a pore can be approximated by a one-dimensional equation... 

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. 

W. Piatkowski, D. Antos, F. Gritti and G. Guiochon, Study of the competitive isotherm model and mass transfer kinetics for a BET binary system. J. Chromatogr.A 1003 (2003) 73-89. 

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. 

For adsorption rate, LeVan considered four models axial dispersion (this is not really a rate model but rather a flow model), external mass transfer, linear driving force approximation (LDF) and reaction kinetics. The purpose of this development was to restore these very compact equations with the variables of Wheeler equation for comparison. 

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... 

Parameterization of Mass-Transfer and Kinetic Models The mass-transfer and chemical kinetic rates required in the rigorous model are typically obtained from the literature, but must be carefully evaluated and fine-tuning through pilot-plant and commercial data is highly recommended. 

Fundamentals of a method for developing models of mass transfer of low-molecular substances in non-reconstructing microheterogeneous membranes were formulated. The local properties of membranes differ in sorbability with respect to species and in the probability for a species to jump from one sorption site to another. Because of this, the permeability of a membrane depends on the amounts of different-type sites, their mutual arrangement, mutual influence of adjacent molecules, and the probabilities of jumps between different sites. The probabilities of occupation of different sorption sites are described by kinetic equations, which take into account the interactions between species. The atomic-molecular discrete and continuous models of mass transfer for thin and thick films are constructed. 

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. 

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. 

If we instead use the solid film linear driving force model of mass transfer kinetics, we have... 

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. 

To describe the peak shapes of a separation under overload conditions a clear understanding of how the competitive phase equilibria, the finite rate of mass transfer, and dispersion phenomena combine to affect band profiles is required [ 11,66,42,75,76]. The general solution to this problem requires a set of mass conservation equations appropriate initial and boundary conditions that describe the exact process implemented the multicomponent isotherms and a suitable model for mass transfer kinetics. As an example, the most widely used mass conservation equation is the equilibrium-dispersive model... 

In these models equations of the mass action law for most slow mass transfer processes are replaced by equations in partial derivatives, which include velocity. As the mass transfer velocity depends on water composition and at approach to the saturation it decreases, kinetic mass transfer equations have the nature of recurrent (see equations (2.275) and (2.278)), and that is why modeling of mass transfer kinetics is performed using a two-step method of computation described below. 

The balances of mass of the chemical species i and the terms for the adsorption kinetics (mass transfer, pore diffusion) are listed in Table 9.5-1 for the three systems with Cj as the concentration in the fluid phase and Xj as the mass loading of the adsorbent. J3 denotes the mass transfer coefficient of a pellet and sj, is its internal porosity. The tortuosity factor will be explained later. The derivation of equations describing instationary diffusion in spheres has already been presented in Sect. 4.3.3. With respect to diffusion in macropores it is important to consider that diffusion can take place in the fluid as well as in the adsorbate phase. In Table 9.5-1 special initial and boimdaty conditions valid for a completely unloaded bed (adsorption) or totally loaded bed (desorption) are given. In this section only the model valid for a thin layer in a fixed bed with the thickness dz and the volmne / dz will be derived, see Fig. 9.5-2. 

Diffusion is the mass transfer caused by molecular movement, while convection is the mass transfer caused by bulk movement of mass. Large diffusion rates often cause convection. Because mass transfer can become intricate, at least five different analysis techniques have been developed to analyze it. Since they all look at the same phenomena, their ultimate predictions of the mass-transfer rates and the concentration profiles should be similar. However, each of the five has its place they are useful in different situations and for different purposes. We start in Section 15.1 with a nonmathematical molecular picture of mass transfer (the first model) that is useful to understand the basic concepts, and a more detailed model based on the kinetic theory of gases is presented in Section 15.7.1. For robust correlation of mass-transfer rates with different materials, we need a parameter, the diffusivity that is a fundamental measure of the ability of solutes to transfer in different fluids or solids. To define and measure this parameter, we need a model for mass transfer. In Section 15.2. we discuss the second model, the Fickian model, which is the most common diffusion model. This is the diffusivity model usually discussed in chemical engineering courses. Typical values and correlations for the Fickian diffusivity are discussed in Section 15.3. Fickian diffusivity is convenient for binary mass transfer but has limitations for nonideal systems and for multicomponent mass transfer. 

Several differential mass balance models have been proposed to characterize mass transfer kinetics. Among them, the model proposed by Sovova (1994), based on extraction from broken and intact cells (BICs), has been widely used. In this model, the solutes are stored in particle cells and protected by the cell wall. During the pretreatment step, to reduce the particle size and increase the surface area between the solute and fluid, some of the cells are broken and solutes become accessible to the fluid. These easily accessible solutes are denoted as x. The remaining solutes retained in unbroken cells are referred to as intact cells and defined as x. Thus, internal and external resistance control the extraction. Sovova (2005) also proposed a more complete model with additional parameters to consider equilibrium relationships. However, this modified model has not been widely used, due to its complexity, and most published work continues to use the older BIC model with mass transfer coefficients in the fluid (k ) and solid (k) phases, and x as the main parameter. The following assumptions are usually considered ... 

Conventional reactor technologies such as fixed beds and slurry reactors suffer from serious drawbacks. Mass transfer resistance is the crucial factor in the scaleup of processes. Laboratory experiments are often carried out with catalyst particles with diameters clearly less than 1 mm, whereas industrial reactors typically operate with larger catalyst particles ranging from 1 mm to 1 cm. The scale dimensions are illustrated in Figure 9.1. Intrinsic kinetics is thus inevitably coupled to the modeling of mass transfer, as has been illustrated in previous chapters. Internal mass transfer limitations can be suppressed by decreasing the particle size, but the particle sizes in industrial processes cannot be diminished limitlessly, because this would lead to a tremendous increase in the pressiue drop. To overcome this problem, new innovations and structured reactors have been developed, such as catalytic packing element reactors, monoliths, and fiber structures. The aim of these innovations has... 

To model this mass transfer, we have introduced, in addition to the diffusion coefficient D, the surface mass transfer coefficient H representing the above asymptotic sorption-kinetics at contenl/conlainer interface. Both parameters have been determined from sorption tests. Experimental results show that the diffusion coefficient D remains constant, while the surface mass transfer coefficient H increases with amyl acetate concentration and temperature of the solution. 

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