Reaction resistances

The model postulates two significant resistances in series diffusion through the growing shell ( R.jyp) and polymerization at the catalyst surface (R(jat catalytic reaction resistance,... 

The series nature of the model permits calculation of the overall reaction resistance (Rq ) simply by summing the individual resistances ... 

Equation (1) consists of various resistance terms. l/Kj a is the gas absorption resistance, while 1/ K,a corresponds to the maleic anhydride diffusion resistance and l/i k represents the chemical reaction resistance. The reaction rate data obtained under the reaction conditions of 250°C and 70 atm were plotted according to equation (1). Although catalytic reaction data with respect to time on stream were not shown here, a linear correlation between reaction rate data and catalyst loading was observed as shown in Fig. 2. The gas absorption resistance (1/ a) was -1.26 h, while the combined reaction-diffusion resistance (lJK,a + 1 T]k) was determined to be 5.57 h. The small negative value of gas absorption resistance indicates that the gas-liquid diffusion resistance was very small and had several orders of magnitude less than the chanical reaction resistance, as similarly observed for the isobutene hydration over Amberlyst-15 in a slurry reactor [6]. This indicates that absorption of malei c anhydride in solvent was a rapid process compared to the reaction rate on the catalyst surface. 

The proportionality factor p (units Q. cm ) formally has the same function as the electric resistance (per unit cross-sectional area) in Ohm s law, hence is sometimes called the reaction resistance. However, this resistance is not ohmic. 

Equation (6.42) is a generalization of Eqs. (6.25) and (6.30) it shows that the formal resistance is the sum of reaction resistance (the first term in parentheses) and diffusion resistance (the second and third terms). Equation (6.40) yields directly the important relation... 

The kinetics of H2 oxidation has been investigated on a Ni/YSZ cermet nsing impedance spectroscopy at zero dc polarization. The hydrogen reaction appears to be very complex. The electrode response appears as two semicircles. The one in the high-freqnency range is assumed to arise partly from the transfer of ions across the TPB and partly from the resistance inside the electrode particles. The semicircle observed at low freqnencies is attributed to a chemical reaction resistance. The following reaction mechanism is suggested ... 

The rectification ratio is obtained by multiplying JFR by the reaction resistance Rr ... 

Assume that the particle is spherical and isothermal, that both gas-film mass transfer resistance and reaction resistance are significant, and that the Ranz-Marshall correlation for k g is applicable. Do not make an assumption about particle size, but assume the reaction is first-order. 

If the pressure of hydrogen in the reactor is 1 bar, calculate 3%, the rate of reaction per unit volume of reactor, and comment on the relative values of the transfer/reaction resistances involved in the process. 

Figure 5.10 is EIS of marmatite electrode in O.lmol/L KNO3 solution with different pH modifiers at open circuit potential. This EIS is very complicated. Simple equivalent circuit can be treated as the series of electrochemical reaction resistance R with the capacitance impedance Q == (nFr )/(icR ) resulting fi-om adsorbing action, and then parallel with the capacitance Ca of double electric... 

In Fig. 7.27, there appears a single capacitive reactance loop in different pH media. The eapacitive reactance loop radius is bigger in the lime medium than that without lime. The reaction resistance increases from 14000 in the absence of lime to 15000 in the presence of lime. EIS exhibits passivation characteristic. The results indicate the formation of surface oxidation products which prevent the transferring of electron, giving rise to the increase of surface resistance and descending of corrosive current. It may be mainly because of the following reactions on the surface of galena in the lime medium besides Eq. (7-12) ... 

Figure 7. (A, top) Simple battery circuit diagram, where Cdl represents the capacitance of the electrical double layer at the electrode—solution interface (cf. discussion of supercapacitors below), W depicts the Warburg impedance for diffusion processes, Rj is the internal resistance, and Zanode and Zcathode are the impedances of the electrode reactions. These are sometimes represented as a series resistance capacitance network with values derived from the Argand diagram. This reaction capacitance can be 10 times the size of the double-layer capacitance. The reaction resistance component of Z is related to the exchange current for the kinetics of the reaction. (B, bottom) Corresponding Argand diagram of the behavior of impedance with frequency, f, for an idealized battery system, where the characteristic behaviors of ohmic, activation, and diffusion or concentration polarizations are depicted.

A , as defined by Equation (7.6), has no practical meaning. In order to drive water electrolysis at a practical rate, a A V > A must be applied. This implies that part of the electrical energy is spent to overcome reaction resistances ... 

The applied potential difference, according to Equation (7.14), includes a thermodynamic contribution and a kinetic contribution (dissipation). The latter is determined by the factors that govern the reaction resistances. To a first approximation, dissipation can be ascribed to three main factors (Figure 7.1) ... 

Here, k can be visualized as the number of successful jumps per unit time across the surface energy barrier eb into the reaction volume (Fig. 5-9). A particularly useful form for k is found if one regards 1/Ar to be a generalized resistivity obtained by adding together the diffusional and the reactional resistivities... 

Let us finally comment on the morphological stability of the boundaries during metal oxidation (A + -02 = AO) or compound formation (A+B = AB) as discussed in the previous chapters. Here it is characteristic that the reaction product separates the reactants. 1 vo interfaces are formed and move. The reaction resistance increases with increasing product layer thickness (reaction rate 1/A J). The boundaries of these reaction products are inherently stable since the reactive flux and the boundary velocity point in the same direction. The flux which causes the boundary motion pushes the boundary (see case c) in Fig. 11-5). If instabilities are occasionally found, they are not primarily related to diffusional transport. The very fact that the rate of the diffusion controlled reaction is inversely proportional to the product layer thickness immediately stabilizes the moving planar interface in a one-... 

Even better yields of C result if components X and Y are incorporated in the same catalyst particle, rather than if they exist as separate particles. In effect, the intermediate product B no longer has to be desorbed from particles of the X type catalyst, transported through the gas phase and thence readsorbed on Y type particles prior to reaction. Resistance to intraparticle mass transfer is therefore reduced or eliminated by bringing X type catalyst sites into close proximity to Y type catalyst sites. Curve 4 in Fig. 3.10 illustrates this point and shows that for such a composite catalyst, containing both X and Y in the same particle, the yield of C for reaction 3 is higher than it would have been had discrete particles of X and Y been used (curve 3). 

The following can be concluded from Eq. (8.21) (1) A large particle has very large diffusion resistance and (2) An increase in Ts yields reduced reaction resistance. The inference made by Tamir in Ref. [5] on the influence of T is incorrect. 

EDLC with very low internal resistance (no electrochemical reaction resistance), very high capacitance and extremely long cycle life (ca. 106 cycles) can be com-... 

Figure 2. Electrical analog of transport and reaction resistances in the Kunni-Levenspiel model using the data of Massimillia and Johnstone (9)...

Let us consider a shallow fluidized bed combustor with multiple coal feeders which are used to reduce the lateral concentration gradient of coal (11). For simplicity, let us assume that the bed can be divided into N similar cylinders of radius R, each with a single feed point in the center. The assumption allows us to use the symmetrical properties of a cylindrical coordinate system and thus greatly reduce the difficulty of computation. The model proposed is based on the two phase theory of fluidization. Both diffusion and reaction resistances in combustion are considered, and the particle size distribution of coal is taken into account also. The assumptions of the model are (a) The bed consists of two phases, namely, the bubble and emulsion phases. The voidage of emulsion phase remains constant and is equal to that at incipient fluidization, and the flow of gas through the bed in excess of minimum fluidization passes through the bed in the form of bubbles (12). (b) The emulsion phase is well mixed in the axial... 

In this model, the steps can be classified into two categories, mass transport and surface reaction steps. The slowest of these steps determines if the process is mass transport or surface reaction limited. At lower temperatures the deposition rate is generally surface reaction limited. As the temperature increases, the surface reaction rate rises exponentially, resulting in a mass transport limited because transport becomes the slowest step in the series of deposition steps. Reaction resistances are often used to predict rate-limiting steps in CVD process. 

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