Langmuir—Hinshelwood—Hougen—Watson kinetic equation

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. 

The pre-exponentials and the apparent activation energies corresponding to the rate coefficients ki, k2 and ks had to be estimated from the experimental data sets from fovir batch reactor and ten CSTR experiments. The initial concentration of reactant A and the temperature were varied. The kinetic rate equations of the catalytic reactions can be described by using the following so-called Langmuir-Hinshelwood Hougen-Watson equations. 

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. 

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). 

Firstly, is a kinetic expression, a rate law, such as, e.g., the Langmuir-Hinshelwood-Hougen-Watson rate expressions in heterogeneous catalysis, and as such has no universal applicability. It is derived on the basis of mass action kinetics and does reduce to the fundamental thermodynamic Nemst equation for i = 0, thus q = 0. ° Nevertheless, experimental deviations can be expected as with any other, even most successful, rate expression. 

Two-dimensional diffusion occurs axially and radially in cylindrically shaped porous catalysts when the length-to-diameter ratio is 2. Reactant A is consumed on the interior catalytic surface by a Langmuir-Hinshelwood mechanism that is described by a Hougen-Watson kinetic model, similar to the one illustrated by equation (15-26). This rate law is linearized via equation (15-30) and the corresponding simulationpresented in Figure 15-1. Describe the nature of the differential equation (i.e., the mass transfer model) that must be solved to calculate the reactant molar density profile inside the catalyst. 

Steps 3-5 are strictly chemical and consecutive to each other Hougen-Watson-Langmuir-Hinshelwood rate equations describing the rate of the purely chemical phenomenon consisting of steps 3-5 have been derived in Chapter 3 on the kinetics of catalysed reactions. In the transport-limited situation the supply of reactant and/or the removal of reaction product will not be sufficiently fast to keep pace with the potential intrinsic rate, and the concentrations of A and B inside the pores will be different from the corresponding concentrations in the bulk of the fluid phase. 

A higher form of interpretation of the effect of solvents on the rate of heterogeneously catalyzed reactions was represented by the Langmuir-Hinshelwood kinetics (7), in the form published by Hougen and Watson (2), where the effect of the solvent on the reaction course was characterized by the adsorption term in the kinetic equation. In catalytic hydrogenations in the liquid state kinetic equations of the Hougen-Watson type very frequently degrade to equations of pseudo-zero order with respect to the concentration of the substrate (the catalyst surface is saturated with the substrate), so that such an interpretation is not possible. At the same time, of course, also in these cases the solvent may considerably affect the reaction. As is shown below, this influence is very adequately described by relations of the LFER type. 

Rate expressions of the form of Equation 5.153 are known as Hougen Watson or Langmuir-Hinshelwood kinetics [17, This form of kinetic expression is often used to describe the species production rates for heterogeneously catalyzed reactions. We complete the section on the kinetics of elementary surface reactions by returning to the methane synthesis reaction listed in Section 5.2. The development proceeds exactly as outlined in Section 5.2. But now it is necessary to add a site-balance expression (Equation 5,129) in Step 3. 

The use of Langmuir isotherms to interpret kinetic data was proposed by Hinshelwood [2] and discussed at length by Hougen and Watson [3]. Surface reaction rates are assumed to depend on the fraction of sites covered by different species. If the surface is at adsorption-desorption equilibrium, the equations for etc. are used in the rate expressions, and the surface... 

---