Surface reaction Hougen-Watson models

In addition to the assumptions implicit in the use of the Langmuir isotherm the following assumption is applicable to all Hougen-Watson models the reaction involves at least one species chemisorbed on the catalyst surface. If reaction takes place between two adsorbed species, they must be adsorbed on neighboring sites in order for reaction to occur. The probability of reaction between adsorbed A and adsorbed B is assumed to be proportional to the product of the fractions of the sites occupied by each species (0A9B). Similar considerations apply to termolecular reactions occurring on the surface. 

Hougen-Watson Models for the Case of Equilibrium Adsorption. This section treats Hougen-Watson mathematical models for cases where the rate limiting step is the chemical reaction rate on the surface. In all cases it is assumed that equilibrium is established with respect to adsorption of all species. 

Hougen- Watson Models for Cases where Adsorption and Desorption Processes are the Rate Limiting Steps. When surface reaction processes are very rapid, the overall conversion rate may be limited by the rate at which adsorption of reactants or desorption of products takes place. Usually only one of the many species in a reaction mixture will not be in adsorptive equilibrium. This generalization will be taken as a basis for developing the expressions for overall conversion rates that apply when adsorption or desorption processes are rate limiting. In this treatment we will assume that chemical reaction equilibrium exists between various adsorbed species on the catalyst surface, even though reaction equilibrium will not prevail in the fluid phase. 

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... 

Figure 15-1 Total pressure dependence of the best pseudo-first-order kinetic rate constant when a first-order rate law approximates a Hougen-Watson model for dissociative adsorption of diatomic A2 on active catalytic sites. Irreversible triple-site chemical reaction between atomic A and reactant B (i.e., 2Acr - - Bcr -> products) on the catalytic surface is the rate-limiting step. The adsorption/desorption equilibrium constant for each adsorbed species is 0.25 atm. ...

Studies of the influence of total pressure on the initial reaction rate for pure reactants present in stoichiometric proportions provide a means of discriminating between various classes of Hougen-Watson models. Isolation of a class of probable models by means of plots of initial reaction rate versus total pressure, feed composition, and temperature constitutes the first step in developing a Hougen-Watson rate model. Hougen (14) considered the influence of total pressure for unimolecular and bimolec-ular surface reactions the analysis that follows is adopted from his monograph. 

Example 10.5 Derive a model of the Hougen and Watson type for the overall reaction 2A -> P, assuming that the surface reaction is the ratedetermining step. 

Examples of Hougen-Watson kinetic models, which are also called Langmuir-Hinshelwood models, can be derived for a great variety of assumed surface mechanisms. See Butt and Perry s Handbook (see Suggestions for Further reading in Chapter 5) for collections of the many possible models. The models usually have numerators that are the same as would be expected for a homogeneous reaction. The denominators reveal the heterogeneous nature of the reactions. They come in almost endless varieties, but all reflect competition for the catalytic sites by the adsorbable species. 

Derive a Hougen and Watson kinetic model, assuming that the surface reaction is rate-controlling. 

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]. 

The models described above are termed Langmuir-Hinshelwood-Hougen-Watson (LHHW) models, named after the scientists that contributed a lot to the development of these engineering models. The characteristics of these models are that adsorption follows the Langmuir isotherm, and that reaction takes place between adsorbed species. Sometimes, one distinguishes Eley Rideal models, whereby a molecule reacts directly from the gas phase with a surface complex ... 

Skrzypek el al. mode (19H5) Skrzypek el al. (1985) developed this model based on the Langmuir-Hinshelwood-Hougen-Watson kinetic model to explain the non-monotonic behaviour observed by Calder-bank (1974). They suggested that the reaction rate behaviour can be related to the Langmuir-Hinshelwood kinetic model for bimolecular reactions, where the surface reaction between o-Xylene and oxygen chemisorbed on the active centers is the rate determining step. The rate of appearance of various components can be written as ... 

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 ... 

Since 1 a is only a function of spatial coordinate r, the partial derivative in (19-38) is replaced by a total derivative, and the dimensionless concentration gradient evaluated at the external surface (i.e., ] = 1) is a constant that can be removed from the surface integral in the numerator of the effectiveness factor. In terms of the Hougen-Watson kinetic model and the dimensional scaling factor for chemical reaction that agree with the Langmuir-Hinshelwood mechanism described at the beginning of this chapter ... 

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. 

As pointed out by Levenspid (2000), the usual procedure to study the kinetics of surface-catalyzed reactions is to propose a mechanism based on the Langmuir-Hinshelwood-Hougen-Watson (LHHW) model, derive the corresponding equation, and then fit it to the data at hand. If the fit is good, researchers often claim that thqr have found the actual mechanism. This procedure is questionable, as shown by Topic 4.5.4. It would be better to state that our experimental results are formally described (within the range of the investigated reaction conditions) by the selected kinetic equation (probably out of several possible others). 

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