Catalytic reactions rate models, Langmuir-Hinshelwood

Reaction rates for the start-of-cycle reforming system are described by pseudo-monomolecular rates of change of the 13 kinetic lumps. That is, the rates of change of the lumps are represented by first-order mass action kinetics with the same adsorption isotherm applicable to each reaction step. Following the same format as Eq. (4), steady-state material balances for the hydrocarbon lumps are derived for a plug-flow, fixed bed catalytic reformer. A nondissociation, Langmuir-Hinshelwood adsorption model is employed. Steady-state material balances written over a differential fractional catalyst volume dv are the following ... 

Exemplary results of modeling processes inside the catalytic layer are presented in Fig. 9. The solid lines show the dependency of the overall effectiveness factor on the relative distribution of the catalyst between the comers and the side regions. The two cases represent two levels of the first-order rate constants, with the faster reaction in case (b). As expected, the effectiveness factor of the first reaction drops as more catalyst is deposited in the comers. The effectiveness factor for the second reaction increases in case (a) but decreases in case (b). The latter behavior is caused by depletion of B deep inside the catalytic layer. What might be surprising is the rather modest dependency of the effectiveness factor on the washcoat distribution. The explanation is that internal diffusion is not important for slow reactions, while for fast reactions the available external surface area becomes the key quantity, and this depends only slightly on the washcoat distribution for thin layers. The dependence of the effectiveness factor on the distribution becomes more pronounced for consecutive reactions described by Langmuir-Hinshelwood-Hougen-Watson kinetics [26]. 

Ivanov et al. (1980) modelled a class of Langmuir-Hinshelwood reactions, and by analyzing the mathematical model given in two dimensions, they obtained limit cycle oscillations and showed that the influence of adsorbed species on the catalytic reaction rate may lead to periodic oscillations. 

These assumptions are the basis of the simplest rational explanation of surface catalytic kinetics and models for it. The preeminent of these, formulated by Langmuir and Hinshelwood, makes the further assumption that for an overall (gas-phase) reaction, for example, A(g) +...- product(s), the rate-determining step is a surface reaction involving adsorbed species, such as A s. Despite the fact that reality is known to be more complex, the resulting rate expressions find wide use in the chemical industry, because they exhibit many of the commonly observed features of surface-catalyzed reactions. 

Based on the Langmuir-Hinshelwood expression derived for a unimolecular reaction system (6) Rate =k Ks (substrate) /[I + Ks (substrate)], Table 3 shows boththe apparent kinetic rate and the substrate concentration were used to fit against the model. Results show that the initial rate is zero-order in substrate and first order in hydrogen concentration. In the case of the Schiff s base hydrogenation, limited aldehyde adsorption on the surface was assumed in this analysis. Table 3 shows a comparison of the adsorption equilibrium and the rate constant used for evaluating the catalytic surface. 

When a simple, fast and robust model with global kinetics is the aim, the reaction kinetics able to predict correctly the rate of CO, H2 and hydrocarbons oxidation under most conditions met in the DOC consist of semi-empirical, pseudo-steady state kinetic expressions based on Langmuir-Hinshelwood surface reaction mechanism (cf., e.g., Froment and Bischoff, 1990). Such rate laws were proposed for CO and C3H6 oxidation in Pt/y-Al203 catalytic mufflers in the presence of NO already by Voltz et al. (1973) and since then this type of kinetics has been successfully employed in many models of oxidation and three-way catalytic monolith converters... 

The theoretical calculations described have recently been supported by an extraordinary kinetic analysis conducted by Vanrysellberghe and Froment of the HDS of dibenzothiophene (104). That work provides the enthalpies and entropies of adsorption and the equilibrium adsorption constants of H2, H2S, dibenzothiophene, biphenyl, and cyclohexylbenzene under typical HDS conditions for CoMo/A1203 catalysts. This work supports the assumption that there are two different types of catalytic sites, one for direct desulfurization (termed a ) and one for hydrogenation (termed t). Table XIV summarizes the values obtained experimentally for adsorption constants of the various reactants and products, using the Langmuir-Hinshelwood approach. As described in more detail in Section VI, this kinetic model assumes that the reactants compete for adsorption on the active site. This competitive adsorption influences the overall reaction rate in a negative way (inhibition). 

Langmuir-Hinshelwood rate expressions of all the reactions of the network were used in the kinetic modeling of the HDN of quinoline by Satterfield et al. (80, 81, 88). Their assumption that there is a single catalytic site for all reactions is too simple. Nevertheless, they collected an impressive body of kinetic data and pinpointed the reactions that were close to equilibrium and those which were kinetically significant. Gioia and Lee (100) extended these studies to higher pressures (up to 15 MPa H2). Only one model survived their regression analysis of the kinetic data. In this model, it was necessary to assume that 1,2,3,4-THQ reacted directly not only to o-propylaniline but also to propylbenzene (PB) and propylcyclohexene (PCHE). Their analysis does not appear to be very reliable, however. First,... 

The Langmuir-Hinshelwood kinetic model describes a reaction in which the rate-limiting step is reaction between two adsorbed species such as chemisorbed CO and 0 reacting to form C02 over a Pt catalyst. The Mars-van Krevelen model describes a mechanism in which the catalytic metal oxide is reduced by one of the reactants and rapidly reoxidizd by another reactant. The dehydrogenation of ethyl benzene to styrene over Fe203 is another example of this model. Ethyl benzene reduces the Fe+3 to Fe+2 whereas the steam present reoxidizes it, completing the oxidation-reduction (redox) cycle. This mechanism is prevalent for many reducible base metal oxide catalysts. There are also mechanisms where the chemisorbed species reacts... 

For most reaction systems, the intrinsic kinetic rate can be expressed either by a power-law expression or by the Langmuir-Hinshelwood model. The intrinsic kinetics should include both the detailed mechanism of the reaction and the kinetic expression and heat of reaction associated with each step of the mechanism. For catalytic reactions, a knowledge of catalyst deactivation is essential. Film and penetration models for describing the mechanism of gas-liquid and gas-liquid-solid reactions are discussed in Chap. 2. A few models for catalyst deactivation during the hydrodesulfurization process are briefly discussed in Chap. 4. 

This can be justified if we suppose that the reaction occurred between the two reactants adsorbed on the same catalytic centres and that the bromo-compounds were more strongly adsorbed than the chloro-compounds, the fluoro substituted reactant being less strongly adsorbed than the corresponding monosubstituted halobenzenes. According to the Langmuir-Hinshelwood model the initial reaction rate for the reaction between 3-chlorofluorobenzene and bromobenzene can be written as follows (Equation 2) which is in agreement with the kinetic orders found experimentally. 

Capsule membrane PTC systems are more amenable to a mechanistic analysis than typical triphase systems where the mechanism of interaction between the aqueous and organic phases with the catalytic sites is complex and not understood. A mechanism for capsule membrane PTC involving mass transfer and smface reaction for both PTC and IPTC reactions has been developed by Yadav and Mehta(1993), Yadav and Mistry (1995). A Langmuir-Hinshelwood type model with the anchored quaternary-nucleophile complex as the active site was assumed to govern the overall rate of reaction... 

Microkinetic modeling is a framework for assembling the microscopic information provided by atomistic simulations and electronic structure calculations to obtain macroscopic predictions of physical and chemical phenomena in systems involving chemical transformations. In such an approach the particular catalytic reaction mechanism is expressed in terms of its most elementary steps. In contrast to the Langmuir-Hinshelwood-Hougen-Watson (LHHW) formulations, no rate-determining mechanistic step (RDS) is assumed. 

This is a mathematical expression for the steady-state mass balance of component i at the boundary of the control volume (i.e., the catalytic surface) which states that the net rate of mass transfer away from the catalytic surface via diffusion (i.e., in the direction of n) is balanced by the net rate of production of component i due to multiple heterogeneous surface-catalyzed chemical reactions. The kinetic rate laws are typically written in terms of Hougen-Watson models based on Langmuir-Hinshelwood mechanisms. Hence, iR ,Hw is the Hougen-Watson rate law for the jth chemical reaction on the catalytic surface. Examples of Hougen-Watson models are discussed in Chapter 14. Both rate processes in the boundary conditions represent surface-related phenomena with units of moles per area per time. The dimensional scaling factor for diffusion in the boundary conditions is... 

The feed stream is stoichiometric in terms of the two reactants. Diatomic A2 undergoes dissociative adsorption. Components B, C, and D experience single-site adsorption, and triple-site chemical reaction on the catalytic surface is the rate-controlling feature of the overall irreversible process. This Langmuir-Hinshelwood mechanism produces the following Hougen-Watson kinetic model for the rate of reaction with units of moles per area per time ... 

This equation, the Langmuir-Hinshelwood equation, was first proposed by Langmuir and Hinshelwood in the 1920-30s for solid-catalyzed gas-phase reactions under the assumption that adsorption and desorption rates are high compared with rates of other chemical transformations on the catalyst surface. In this model, adsorption-desorption steps are considered to be at equilibrium. Later, Hougen, and Watson proposed a similar equation, the Hougen-Watson equation, for a reversible catalytic reaction, again under the assumption that the adsorption-desorption steps are at equilibrium. 

To model a catalytic reaction, some knowledge of the elementary reaction steps must be assumed. For ammonia synthesis it is usually accepted that the dissociative chemisorption of nitrogen is the rate-limiting step, a process which requires two adjacent open sites on the catalyst surface. " Using Langmuir-Hinshelwood kinetics the rate of ammonia synthesis (denoted by r) can be written as... 

Water present in the catalytic systems shows versatile effects on reaction rates. Heath and Gates found the induction period in the dehydration of t-butyl alcohol and also noted that water addition reduced the induction time. This effect of water was attributed to the swelling of the resin network. The swelling reduces intraparticle resistance to mass transport, and makes an increasing fraction of the catalytic sites accessible to the reactant. Though water accelerated the reaction initially, it also inhibited the reaction. The retardation with water was observed also in estrification of salicic acid with methanol and benzene propylation. The retarding effect of water was explained by a kinetic expression based on the Langmuir-Hinshelwood model, in which the competitive chemisorption of water and a reactant (alcohol or acid) is assumed. 

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