Catalyst reaction rate expressions

Effectiveness Factors for Hougen-Watson Rate Expressions. The discussion thus far and the vast majority of the literature dealing with effectiveness factors for porous catalysts are based on the assumption of an integer-power reaction rate expression (i.e., zero-, first-, or second-order kinetics). In Chapter 6, however, we stressed the fact that heterogeneous catalytic reactions are more often characterized by more complex rate expressions of the Hougen-Watson type. Over a narrow range of... 

Most real reactors are not homogeneous but use catalysts (1) to make reaction occur at temperatures lower than would be required for homogeneous reaction and (2) to attain a higher selectivity to a particular product than would be attained homogeneously. One may then ask whether any of the previous material on homogeneous reactions has any relevance to these situations. The answer fortunately is yes, because the same equations are used. However, catalytic reaction rate expressions have a quite different meaning than rate expressions for homogeneous reactions. 

In Eqn. 5.3-1, rj is the effectiveness factor of the catalyst with respect to the dissolved gaseous reactant and the temperature of the outer surface. The rate of reaction within the catalyst pores is comprised in rj. R is the reaction rate expressed in moles of gaseous reactant, A, per unit of bubble-free liquid, per unit of time. Reaction is irreversible. In equation (1) it has not been assumed that the gas is pure gas A, its concentration in the bubbles being Cg. Also, Henry s law for the gas is assumed and written as in Eqn. 5,3-4. Using Henry s law, Eqn. 5.3-4, the intermediate concentrations (Cs, CL) can be eliminated using the above system of equations. This provides an expression of the global rate in terms of an apparent constant, ko, that contains the various kinetic and mass transfer steps. Therefore, the observed rate can be written as ... 

For the same type of catalyst we have observed in a recirculation laboratory reactor multiplicity, periodic and chaotic behavior. Unfortunately, so far we are not able to suggest such a reaction rate expression which would be capable of predicting all three regimes [8]. However, there is a number of complex kinetic expressions which can describe periodic activity. One can expect that such kinetic expressions combined with heat and mass balances of a tubular nonadiabatic reactor may give rise to oscillatory behavior. Detailed calculations of oscillatory behavior of singularly perturbed parabolic systems describing heat and mass transfer and exothermic reaction are apparently beyond, the capability of both standard current computers and mathematical software. 

The second premise behind partial control is the concept of dominance. We introduced this concept earlier when we discussed reaction rate expressions. There we mentioned that temperature often plays a dominant role for the rate of reaction especially when the activation energy is high. We also mentioned that a key component in the rate expressions can dominate the rate particularly when the component has a low concentration (e.g., limiting reactant or the catalyst). 

J. Franckaerts and G. F. Froment [Chem. Eng. Sci., 19 (1964) 807] investigated the reaction listed in Exercise 3 over the same temperature range using a CuO/CoO/Cr203 catalyst. The rate expression obtained in this work was of the form ... 

The kinetics of partial oxidation, ATR, and dry reforming of liquid hydrocarbons have also been reported recently.103,155 Pacheco et al.155 developed and validated a pseudo-homogeneous mathematical model for the ATR of isooctane and the subsequent WGS reaction, based on the reaction kinetics and intraparticle mass transfer resistance. They regressed the kinetic expressions from the literature for partial oxidation and steam reforming reactions to determine the kinetics parameters for the ATR of isooctane on Pt/ceria catalyst. The rate expressions used in the reformer modeling and the parameters of these rate expressions are given in Tables 2.19 and 2.20, respectively. 

The catalyst packed was assumed to be the commercial Cu/ZnO catalyst for lower-temperature WGS reaction. A number of studies on the reaction kinetics of the commercial WGS catalyst, Cu0/Zn0/Al203, have been published.43-48 Based on the experimental data of the commercial catalyst (ICI 52-1), Keiski et al.47 suggested two reaction rates for the low-temperature WGS reaction in the temperature range 160-250 °C. The first was dependent only on CO concentration and gave an activation energy of 46.2kJ/mol. The second reaction rate was dependent on CO and steam concentrations with a lower activation energy of 42.6kJ/mol. Because of the proximity of our operation conditions to theirs and the fact that steam is in excess in most of the membrane reactors, Keiski and coworkers first reaction rate expression was chosen for this work. The reaction rate is given in Equation 9.5,... 

The rate of a chemical reaction is a function of the temperature, the composition of the reacting mixture, and, if present, the catalyst. The relationship between the reaction rate and these parameters is commonly called the rate expression or, sometimes, the rate law. Chemical kinetics is the branch of chemistry that deals with reaction mechanisms and provides a theoretical basis for the rate expression. When such information is available, we use it to obtain the rate expression. In many instances, the reaction rate expression is not available and should be determined experimentally. 

Data Molecular mass of product B is 28 g/mol Bulk density of the catalyst bed is 1.30 kg/L The mass-based reaction rate expression is... 

Finally, another area of overlap is the potential presence of a false activation energy. This occurs when film diffusion is coupled with, say, a hrst-order reaction at the catalyst surface. The mass transfer rate r = k a ic - Cj). In contrast, the inherent reaction rate is r = These two can be combined to give an expression for the snrface concentration c, = kf cl(k + k, which is difficult to measure. This expression can be snbstitnted in the original reaction rate expression to give r = with an effective rate constant of = ll(llk, + k. Thns, if the inherent rate obeys the Arrhenius dependence on temperatnre, k, = A exp(-A yR7), and if kf is constant, the observed Arrhenius activation energy, AEq = RT d In k(/d(l/T), would be deceptively low. 

Size/Weight/Cost Modeling A kinetic model was established for estimating the size, weight and cost of monolith reactors with washcoated Pt/ceria catalysts, using Arrhenius data obtained from micro-reactor tests. A reaction rate expression for Pt/ceria catalysts was derived from kinetic data, which was... 

On the far right of the numerator we have two parameters that may be difficult to obtain independently. They are the adsorption equilibrium constant for B and the surface equilibrium constant for the reaction Asurf Bsurf- Our goal is to clear these by reexpressing them in terms of something that is unchanging. After all both of these may be strong functions of the catalyst structure and composition. The overall reaction A B is, however, one which is fixed at any temperature and pressure by the overall equilibrium constant. This is independent of the catalyst. Therefore we want to use this in the reaction rate expression. Here is how we do it ... 

The reaction takes place at 130°C over an activated carhon catalyst. The rate expression for this irreversihle reaction is... 

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