Hougen-Watson model

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. 

It has been suggested that the rate limiting step in the mechanism is the chemisorption of propionaldehyde and that the hydrogen undergoes dissociative adsorption on nickel. Determine if the rate expression predicted by a Hougen-Watson model based on these assumptions is consistent with the experimentally observed rate expression. 

Ender these conditions the Hougen-Watson model is consistent with the experimentally observed rate expression. 

We should also point out that the adsorption equilibrium constants appearing in the Hougen-Watson models cannot be determined from adsorption equilibrium constants obtained from nonreacting systems if one expects the mathematical expression to yield accurate predictions of the reaction rate. One explanation of this fact is that probably only a small fraction of the catalyst sites are effective in promoting the reaction. 

Is the experimental data consistent with this rate expression If so, what is the value of the rate constant What type of Hougen-Watson model gives rise to this form for the rate expression ... 

Buzzi-Ferraris, G., and Donati, G. 1974. A powerful method for Hougen-Watson model parameter estimation with integral conversion data. Chem. Eng. Sci. 29 1504-9. 

Shabaker (SI), for the hydrogenation of propylene over a platinum alumina catalyst, selected a Hougen-Watson model of the form... 

From a consideration of either Eqs. (113) or (114) (K3), it is evident that a saddle point is predicted from the fitted rate equation. This could eliminate from consideration any kinetic models not capable of exhibiting such a saddle point, such as the generalized power function model of Eq. (1) and the several Hougen-Watson models so denoted in Table XVI. 

The Hougen-Watson model, which accounts for the fact that a kinetically stable intermediate occupies surface sites, consists of two possible elementary steps that can be rate limiting. Furthermore, the adsorption terms in the denominator of the rate law must account for fractional surface coverage by the intermediate. If ... 

The final form of the Hougen-Watson model for the six-step mechanism described by (14-71) is... 

Since there are three equilibrium constants (i.e., Ka, Kb, and / eq.Rxi) and one kinetic rate constant that one seeks to determine via linear least-squares analysis, it is necessary to have an independent measurement of either Ka or via adsorption studies on the same high-surface-area catalyst in a pulverized state. For example, if this catalyst is exposed to pure gas A and Ka is determined via linear least-squares analysis of its adsorption isotherm, then some of the other temperature-dependent parameters in the Hougen-Watson model are calcnlated as follows from ao, ai and a2. 

Modification of the Hougen-Watson Model to Correct for Dissociative Adsorption of a Reactant... 

In addition to calculating kinetic and equilibrium constants in the Hougen-Watson model via numerical values for ao, a, and U2, the success of this procedure suggests that the mechanism proposed and the choice of a rate-limiting step are reasonable, based on actual experimental data. For completeness, simultaneous solution of the three equations in steps 4 to 6 yields the following results for the kinetic and adsorption/desorption equilibrium constants in terms of the parameters in the polynomial model ... 

The kinetic rate constant for adsorption of A is calculated from the intercept (i.e., 2/oo), and the adsorption/desorption equilibrium constant for reactant B is obtained from the ratio of slope to intercept (i.e 2ai/ao). If this procedure is successful, then one can be confident that the proposed five-step mechanism given by (14-124) and the choice of single-site adsorption of reactant A as the slow step are reasonable assumptions because the resulting Hougen-Watson model agrees with experimental data. 

The Hougen-Watson model that is consistent with the six-step mechanism given by (14-138) is constructed by focusing on dual-site adsorption of A2. Hence,... 

INTERPRETATION OF HETEROGENEOUS KINETIC RATE DATA VIA HOUGEN-WATSON MODELS... 

The Hougen-Watson model for this mechanism, in which single-site chemical reaction is rate limiting, is proportional to the first power of v ... 

If the single-site mechanism is best, then the following rearrangement of the Hougen-Watson model at the reactor inlet allows one to calculate kforward.surf.Rx and Fa via linear least-squares analysis using a first-order polynomial ... 

These two steps are combined to generate the slow step upon which the Hougen-Watson model is developed ... 

Now, the Hougen-Watson model adopts the following form ... 

Hougen-Watson model for this four-step mechanism is based on the third step, which is irreversible. Hence,... 

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... 

PSEUDO-FIRST-ORDER KINETIC RATE EXPRESSIONS THAT CAN REPLACE HOUGEN-WATSON MODELS AND GENERATE LINEARIZED ORDINARY DIFFERENTIAL EQUATIONS FOR THE MASS BALANCE... 

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