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LHHW rate equations

Table 2.1 Individual terms of LHHW rate equations for fhe surface reaction-controlling cases of various catalytic reactions. Table 2.1 Individual terms of LHHW rate equations for fhe surface reaction-controlling cases of various catalytic reactions.
The differential method of data analysis is convenient since it requires only one experiment for rate equations containing only one reactant and is readily applied to determine reaction parameters of power law or LHHW rate equations. The rate equations may be linearized to allow the use of linear regression... [Pg.31]

Langmuir-Hinshelwood-Hougen-Watson (LHHW) Rate Equations (1947) Hougen and Watson analyzed several types of catalytic reactions with different ratedetermining steps (adsorption, surface reaction), different types of adsorption (one or more species, dissociative or molecular adsorption), and different types of reactions (mono- or bimolecular, reversible or irreversible). They derived a general rate equation based on three terms ... [Pg.233]

The first step of the reaction on a solid catalyst is the sorption of at least one reactant. If two reactants are adsorbed, the rate follows the so-called Langmuir-Hinshelwood mechanism, which is based on the assumption that both reactants are adsorbed on the surface (equilibrium). If only one reactant is adsorbed on the surface of the catalyst and reacts with the second species coming from gas phase, the rate follows the Eley-Rideal-mechanism. Other more complex situations may be described by Langmuir-Hinshelwood-Hougen-Watson (LHHW) rate equations. [Pg.267]

Figure 4. LHHW rate equation for reversible reactions. Figure 4. LHHW rate equation for reversible reactions.
Figure 5. LHHW rate equation for irreversible reactions (C-C scission reactions such as parafiBn hydrocracking, opening of naphthene rings, and ring dealkylation). Figure 5. LHHW rate equation for irreversible reactions (C-C scission reactions such as parafiBn hydrocracking, opening of naphthene rings, and ring dealkylation).
Most standard chemical engineering tests on kinetics [see those of Car-berry (50), Smith (57), Froment and Bischoff (19), and Hill (52)], omitting such considerations, proceed directly to comprehensive treatment of the subject of parameter estimation in heterogeneous catalysis in terms of rate equations based on LHHW models for simple overall reactions, as discussed earlier. The data used consist of overall reaction velocities obtained under varying conditions of temperature, pressure, and concentrations of reacting species. There seems to be no presentation of a systematic method for initial consideration of the possible mechanisms to be modeled. Details of the methodology for discrimination and parameter estimation among models chosen have been discussed by Bart (55) from a mathematical standpoint. [Pg.319]

In general, the use of Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type of rate equation for representing the hydrogenation kinetics of industrial feedstocks is complicated, and there are too many coefficients that are difficult to determine. Therefore, simple power law models have been used by most researchers to fit kinetic data and to obtain kinetic parameters. [Pg.441]

In this project, we make use of platinum-type catalyst on silica gel. Although this is less selective than more modem palladium-based catalysts, kinetic data are available in the literature as an LHHW model [2], better suited for flexible reactor design. The reaction rate equations are ... [Pg.138]

The kinetic rate equations developed by Xu and Froment (1989a) based on the (LHHW) approach are more general relative to the previous rate expressions available in the literature and discussed in the previous section. This rate equation explains a number of contradictions in the work of earlier investigators. [Pg.43]

In the interest of generality, we consider hypothetical reactions and derive rate equations for a few typical LHHW models (Hougen and Watson, 1947 Yang and Hougen, 1950 Satterfield, 1980, Butt, 1980 Doraiswamy and Sharma, 1984 Boudart and Djega-Mariadassou, 1984). As the Langmuir isotherm is the basis of all LHHW models, we begin by a simple derivation of this isotherm. [Pg.172]

Focusing on the case where surface reaction is controlling, the basic procedure in developing a LHHW model is to write the rate equation in terms of the surface coverage of reactant A rather than its concentration [/ ]. Sometimes, as in reactions requiring a second (vacant) site for adsorbing a product (e.g.,... [Pg.174]

In some bimolecular reactions like disproportionation of propylene to butylene and ethylene and hydrogenation of ethylene to ethane, a modified form of LHHW models has to be used. Here, the reaction is assumed to occur by a molecule of one of the reactants (say A) striking an obsorbed molecule of B (or another A). Thus the rate equation would be (or aPb if reacts... [Pg.175]

In the developments already presented, the rate equations used were simple power law expressions. But, as discussed previously, catalytic rate equations are much more complex and often require the use of LHHW models. Many attempts have been made to incorporate these models in the analysis (e.g., Chu and Hougen, 1962 Krasuk and Smith, 1965 Roberts and Satterfield, 1965, 1966 Hutchings and Carberry, 1966 Schneider and Mitschka, I966a,b Kao and Satterfield, 1968 Rajadhyaksha et al., 1976 see in particular Aris, 1975 Luss, 1977). Clearly, graphical representation becomes cumbersome when a large number of adsorbed species is involved. However, the problem is quite tractable where only one species is adsorbed. [Pg.196]

Estimation of the kinetic parameters in Langmiiir - Hinshelwood - Hougen -Watson (LHHW) type rate equations, using experimental data sets obtained from a batch and a CSTR reactor. [Pg.632]

Power function models, on the other hand, directly utilize the concept of reaction order. Unlike homogeneous reactions, the reaction orders encountered in solid-catalyzed reactions can be negative or positive, integer, fractional, or zero moreover, product concentrations may also appear in the rate equation. Due to the simplicity of their form, power function models are considerably easier to handle and integrate than the full LHHW expressions and are preferred especially if the reaction is affected by diffusional limitations. These models cannot, however, be used to discriminate between other than grossly different mechanisms, and they are reliable only within the limits of the reaction conditions used to obtain the kinetic data. [Pg.27]

This example demonstrates that the dependence of the initial rate -Ra)o on total pressure Pt gives a clear indication of the rate-controlling step and hence of the form of the LHHW equation. The linear P dependence observed for adsorption-controlling cases and the independence from P of desorption-controlling cases are similar in all reaction types. The Pt dependence of -Ra)o for surface reaction-controlling cases of dual-site or bimolecular reactions is generally expressed by rate equations with a squared term in the denominator ... [Pg.29]

The major problem in describing the FT reaction kinetics is the complexity of its reaction mechanism and the large number of species involved. As discussed above, the mechanistic proposals for the FTS used a variety of surface species and different elementary reaction steps, resulting in empirical power law expressions for the kinetics. However, the rate equations of Langmuir—Hinshelwood—Hougen—Watson (LHHW) have been applied based on a reaction mechanism for the hydrocarbon-forming reactions. In most cases, the rate-determining step was assumed to be the formation of the monomer. [Pg.351]

Focusing now on the case where surface reaction is controlling, the basic procedure in developing an LHHW model is to write the rate equation in terms of the surface coverage of reactant A rather than its concentration [A], Sometimes, as in reactions requiring a second (vacant) site for adsorbing a product (e.g., A —> P + / ), the rate will also directly depend on the fraction of surface covered by vacant sites 6 and when there is dissociation of a reactant, a pair of adjacent vacant sites should be available, so that the rate of adsorption would now be proportional to 6F rather than 9. One of the characteristics of the surface reactions is that in most of the situations the adsorption is much faster than the rest of the steps. In such a situation, we can easily assume that the adsorption step is at pseudoequilibrium, indicating that the rate of adsorption is equal to the rate of desorption ... [Pg.161]

Recall that there are a number of reactions where homogeneous catalysis involves two phases, liquid and gas, for example, hydrogenation, oxidation, carbonylation, and hydroformylation. The role of diffusion becomes important in such cases. In Chapter 6, we considered the role of diffusion in solid catalyzed fluid-phase reactions and gas-liquid reactions. The treatment of gas-liquid reactions makes use of an enhancement factor to express the enhancement in the rate of absorption due to reaction. A catalyst may or may not be present. If there is no catalyst, we have a simple noncatalytic gas-liquid heterogeneous reaction in which the reaction rate is expressed by simple power law kinetics. On the other hand, when a dissolved catalyst is present, as in the case of homogeneous catalysis, the rate equations acquire a hyperbolic form (similar to LHHW models discussed in Chapters 5 and 6). Therefore, the mathematical analysis of such reactions becomes more complex. [Pg.469]

Hyperbolic equations were used in Chapter 6 to represent reactions catalyzed by solid surfaces. They are referred to as LHHW models and they can be empirically extended to homogeneous catalysis in liquid phase reactions. The actual rate equation to be used for a given reaction will depend on the regime of that reaction. Methods of discerning the controlling regimes for catalytic gas-liquid reactions described in the gas-liquid chapter were based on simple power law kinetics. Extension of these methods to gas-Uquid reactions catalyzed by homogeneous catalysts involves no new principles, but the mathematics becomes more... [Pg.469]

Such rate expressions are often termed Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations and are widely used in chemical engineering [see Froment and BischofT (79)]. The usual procedure is to postulate plausible mechanisms without considering cycles, as in Example 1. In such cases it may be desirable to develop the complete list of possible direct mechanisms even if further considerations can rule out some as being unlikely. The following example illustrates a typical case. [Pg.297]

For mechanism 1-b the LHHW method leads to the following equation for the overall deactivation rate ... [Pg.401]

An excellent illustration of the LHHW theory is catalytic cracking of n-alkanes over ZSM-5 [8]. For this reaction, the observed activation energy decreases from 140 to -50 ( ) kj/mol when the carbon number increases from 3 to 20. The decrease appeared to linearly depend on the carbon number as shown in Fig. 3.11. This dependence can be interpreted from a kinetic analysis that showed that the hydrocarbons (A) are adsorbed weakly under the experimental conditions. The initial rate expression for a rate-determining surface reaction applies (3.30), which in the limiting case of weak adsorption of A reduces to Eqn. (3.52). The activation energy is then represented by equation (3.53). [Pg.101]

In that work, the kinetic equation obtained for the whole range of compositions is based on a LHHW mechanism in which IB and MeOH, both adsorbed on the resin, react to form MTBE. The rate-controlling step is surface reaction. As a simplification in the activities calculation, the authors consider that the reaction mixture is composed by three compounds methanol, MTBE and a C4 pseudo-compound that includes all hydrocarbons. In the absence of product, the proposed kinetic equation is... [Pg.542]

In some situations, the kinetic descriptions of Eqs. (3.80), (3.81) can be even more simplified. Considering that the reaction rate can be determined from experimental data and that for an irreversible reaction the value of/" (Cr) is known and that for a reversible reaction the value of/ (Cr) —/ (Cp)/A eq, is known, the kinetic resistance can be determined. Using this resistance in a description of steady-state kinetic data can be advantageous because in contrast with the original LHHW equation, this equation is linear regarding the estimated coefficients ki. [Pg.55]

Providing the full equation is correct, LHHW equations can be extrapolated to calculate reaction rates at other conditions not included in the kinetic study. They give a general idea about the reaction mechanism postulated for deriving the model equation(s) nevertheless, good fit of data to the model is only a necessary but not sufficient condition for deciding on a particular reaction mechanism. LHHW equations usually compUcate the mathematics of reactor design and reactor control, particularly if diffusion effects are present... [Pg.27]

The definite advantages to the use of both formulations under appropriate conditions are evident however, care must be taken not to apply either of the models arbitrarily. Estimation of reaction orders is desirable in a number of applications, and LHHW equations can be reduced to power law form by making the most abimdant surface intermediate (MASI) approximation, if the fractional surface coverage of one adsorbed intermediate is much greater than all others under reaction conditions [21]. Alternatively, catalytic rate data analysis can be started by expressing the rate in terms of a power function model and then... [Pg.27]

Regime between 1 and 2 (reaction in bulk) In this regime, the rate is controlled by both film diffusion and reaction kinetics. Assuming that the reaction is represented by a typical LHHW eqnation, the following equations must be solved simultaneously for the enhancement factor ... [Pg.470]

The quasi-equilibrium assumption is frequently used in the heterogeneous catalysis, since the surface reaction steps are often rate-Hmiting, while the adsorption steps are rapid. This is not necessarily true for large molecules. Here we consider the application of the quasi-equilibrium hypothesis on two kinds of reaction mechanisms, an Eley-Rideal mechanism and a Langmuir-Hinshelwood mechanism. The rate expressions obtained with this approach are referred to as Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations in the literature, in honor of the pioneering researchers. [Pg.23]


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Langmuir-Hinshelwood-Hougen-Watson LHHW) rate equations

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