Kinetics mass transfer limitation

Catalyst supports such as silica and alumina have low thermal conductivities so that temperature gradients within catalyst particles are likely in all but the finely ground powders used for infrinsic kinetic studies. There may also be a film resisfance fo heaf fransfer af fhe exfemal surface of the catalyst. Thus the internal temperatures in a catalyst pellet may be substantially different than the bulk gas temperature. The definition of the effectiveness factor, Equation 10.23, is unchanged, but an exothermic reaction can have reaction rates inside the pellet that are higher than would be predicted using the bulk gas temperature. In the absence of a diffusion limitation, rj > 1 would be expected for an exothermic reaction. (The case > 1 is also possible for some isothermal reactions with weird kinetics.) Mass transfer limitations may have a larger... 

Reaction rates typically are strongly affected by temperature (76,77), usually according to the Arrhenius exponential relationship. However, side reactions, catalytic or equiHbrium effects, mass-transfer limitations in heterogeneous (multiphase) reactions, and formation of intermediates may produce unusual behavior (76,77). Proposed or existing reactions should be examined carefully for possible intermediate or side reactions, and the kinetics of these side reactions also should be observed and understood. 

Checking the absence of external mass transfer limitations is a rather easy procedure. One has simply to vary the total volumetric flowrate while keeping constant the partial pressures of the reactants. In the absence of external mass transfer limitations the rate of consumption of reactants does not change with varying flowrate. As kinetic rate constants increase exponentially with increasing temperature while the dependence of mass transfer coefficient on temperature is weak ( T in the worst case), absence... 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

However, the pattern is complicated by several factors. The sugar molecules to be hydrogenated mutarotate in aqueous solutions thus coexisting as acyclic aldehydes and ketoses and as cyclic pyranoses and furanoses and reaction kinetics are complicated and involve side reactions, such as isomerization, hydrolysis, and oxidative dehydrogenation reactions. Moreover, catalysts deactivate and external and internal mass transfer limitations interfere with the kinetics, particularly under industrial circumstances. 

Owing to its nature as a test reaction, rather the reactor and its operational modes were tested, mainly to determine mass transfer limits (see Section 3.3.11.3). It was also used for kinetic studies on the performance of various catalysts. 

The first two data sets were in good accordance, whereas a fit to the intrinsic kinetics without correction was only valid for short residence times and large flow rates. This is the consequence of achieving a low degree of liquid/liquid dispersion at low flow rates, i.e. the reaction becomes mass-transfer limited in this regime. 

However, under working conditions, with a current density j, the cell voltage E(j) decreases greatly as the result of three limiting factors the charge transfer overpotentials r]a,act and Pc,act at the two electrodes due to slow kinetics of the electrochemical processes (p, is defined as the difference between the working electrode potential ( j), and the equilibrium potential eq,i). the ohmic drop Rf. j, with the ohmic resistance of the electrolyte and interface, and the mass transfer limitations for reactants and products. The cell voltage can thus be expressed as... 

Prior to conducting the DOE (design of experiments) described in Table 3, it was established that no reaction took place in the absence of a catalyst and that the reactions were conducted in the region where chemical kinetics controlled the reaction rate. The results indicated that operating the reactor at 1000 rpm was sufficient to minimize the external mass-transfer limitations. Pore diffusion limitations were expected to be minimal as the median catalyst particle size is <25 pm. Further, experiments conducted under identical conditions to ensure repeatability and reproducibility in the two reactors yielded results that were within 5%. 

It has been shown that the development of wormholes in carbonate rocks is a consequence of diffusion-limited (mass-transfer-limited) kinetics of attack (6). Such kinetics prevail in most of these rocks, i.e. limestones and dolomites, providing that, for the latter, the temperature is larger than about 200°F (90°C) (7-8). 

The reaction will then appear to follow first-order kinetics, regardless of the functional form of the intrinsic rate expression and of the effectiveness factor. This first-order dependence is characteristic of reactions that are mass transfer limited. The term diffusion controlled is often applied to reactions that occur under these conditions. 

Equations 12.4.22 and 12.4.24 indicate that the observed reaction order will differ from the intrinsic reaction order in the presence of intraparticle and/or external mass transfer limitations. To avoid drawing erroneous conclusions about intrinsic reaction kinetics, we must be careful to either eliminate these limitations by proper choice of experimental conditions or to properly take them into account in our data analysis. 

The difference in mole fractions is most significant in the case of S02 where this difference is 15% of the bulk phase level. This result indicates that external mass transfer limitations are indeed significant, and that this difference should be taken into account in the analysis of kinetic data from this system. Note that there is a difference in nitrogen concentration between the bulk fluid and the external surface because there is a change in the number of moles on reaction, and there is a net molar flux toward... 

The units on the rate constants reported by DeMaria et al. indicate that they are based on pseudo homogeneous rate expressions (i.e., the product of a catalyst bulk density and a reaction rate per unit mass of catalyst). It may be assumed that these relations pertain to the intrinsic reaction kinetics in the absence of any heat or mass transfer limitations. 

Intraparticle Mass Transfer. One way biofilm growth alters bioreactor performance is by changing the effectiveness factor, defined as the actual substrate conversion divided by the maximum possible conversion in the volume occupied by the particle without mass transfer limitation. An optimal biofilm thickness exists for a given particle, above or below which the particle effectiveness factor and reactor productivity decrease. As the particle size increases, the maximum effectiveness factor possible decreases (Andrews and Przezdziecki, 1986). If sufficient kinetic and physical data are available, the optimal biofilm thickness for optimal effectiveness can be determined through various models for a given particle size (Andrews, 1988 Ruggeri et al., 1994), and biofilm erosion can be controlled to maintain this thickness. The determination of the effectiveness factor for various sized particles with changing biofilm thickness is well-described in the literature (Fan, 1989 Andrews, 1988)... 

The performance of adsorption processes results in general from the combined effects of thermodynamic and rate factors. It is convenient to consider first thermodynamic factors. These determine the process performance in a limit where the system behaves ideally i.e. without mass transfer and kinetic limitations and with the fluid phase in perfect piston flow. Rate factors determine the efficiency of the real process in relation to the ideal process performance. Rate factors include heat-and mass-transfer limitations, reaction kinetic limitations, and hydro-dynamic dispersion resulting from the velocity distribution across the bed and from mixing and diffusion in the interparticle void space. 

It can be observed that the initial rate of polymerization decreases and the autoacceleration peak is suppressed as the TED concentration is increased. The TED molecules generate dithiocarbamyl (DTC) radicals upon initiation. As a result, termination may occur by carbon-carbon combination which leads to a dead polymer and by carbon-DTC radical reaction which produces a reinitiatable ( living ) polymer. The cross-termination of carbon-DTC radicals occurs early in the reaction (with the carbon-carbon radical termination), and this feature is observed by the suppression of the initial rate of polymerization. As the conversion increases, the viscosity of the system poses mass transfer limitations to the bimolecular termination of carbon radicals. As has been observed in Figure 3, this effect results in a decrease in the ktCC. However, as the DTC radicals are small and mobile, the crosstermination does not become diffusion limited, i.e., the kinetic constant for termination of carbon-DTC radicals, ktCS, does not decrease. Therefore, the crosstermination becomes the dominant reaction pathway. This leads to a suppression of the autoacceleration peak as the carbon-DTC radical termination limits the carbon radical concentration to a low value, thus limiting the rate of polymerization. This observation is in accordance with results of previous studies (10) with XDT and TED, where it was found that when there was an excess of DTC radicals, the carbon radical concentration was lower and the cross-termination reaction was the dominant termination pathway. 

Because of the operating principles of the equipment, especially in the isoperibolic mode, complex calculation and calibration procedures are required for the determination of quantitative kinetic parameters and the energy release during decomposition. Also, for a reaction with a heterogeneous mixture such as a two-phase system, there may be mass transfer limitations which could lead to an incorrect T0 determination. 

Three concentrations of each redox couple that ranged over two orders of magnitude were examined as well as a solution containing only electrolyte. The details of these comprehensive experiments will be published elsewhere (22.) however, several pertinent features are described here. The kinetic currents were measured at constant potential. In order to eliminate mass transfer limitations to the current, a jet electrode configuration was utilized (42). The capacitance of the space charge layer (Csc) was measured at the same potentials simultaneously with the kinetic currents. 

Wick, L. Y., Colangelo-Failla, T. and Harms, H. (2001). Kinetics of mass transfer-limited microbial growth on solid PAHs, Environ. Sci. Technol, 35, 354-361. 

Aiken, III, J.D. and Finke, R.G., Nanocluster formation synthetic, kinetic, and mechanistic studies. The detection of, and then methods to avoid, hydrogen mass-transfer limitations in the synthesis of polyoxoanion- and tetrabutylammonium-stabilized, near-monodisperse 40 6 A Rh(0) nanoclusters, J. Am. Chem. Soc., 120, 9545, 1998. 

Modem catalysts have to be very active and very (100%) selective, that is, they have to catalyze the desired reaction in the temperature window, where the equilibrium conversion is the highest possible and the reaction rate is high enough to permit suitable process economics. To engineer the reaction, one has to obtain first the intrinsic reaction rate, free of heat- and mass-transfer limitations. In many cases this is very difficult, because in the core of the catalytic process there are several physical and chemical steps that must occur and which may preclude the reaction running in the kinetic regime. These steps are as follows ... 

---