Power law rate expression

This rate, measured the previous way, must be correlated with the temperature and concentration as in the following simple power law rate expression ... 

A simple power law rate expression (usually first order) will be sufficient if Arrhenius constants can be fitted. 

For a single cylindrical pore of length L and a reactant A diffusing into the pore, where a first-order reaction takes place at the pore surface, the power law rate expression... 

UV/H202 oxidation of aromatic hydrocarbon and phenolic compound and an empirical power-law rate expression were used for the destruction of such compounds (Sundstrom et al., 1989). 

In contrast to so-called microkinetic analyses, an important aspect of chemical reaction engineering involves the use of semiempirical rate expressions (e.g., power law rate expressions) to conduct detailed analyses of reactor performance, incorporating such effects as heat and mass transport, catalyst deactivation, and reactor stability. Accordingly, microkinetic analyses should not be considered to be more fundamental than analyses based on semiempirical rate expressions. Instead, microkinetic analyses are simply conducted for different purposes than analyses based on semiempirical rate expressions. In this review, we focus on reaction kinetics analyses based on molecular-level descriptions of catalytic processes. 

Kinetics. The coefficients of the kinetic power-law rate expression for CO hydrogenation... 

Examples of power law rate expressions are shown in Table 1.4.2. 

Gardner et al. reported that H2S catalytic partial oxidation technology with an AC catalyst is a promising method for the removal of H2S from fuel cell hydrocarbon feedstocks.206 Three different fuel cell feedstocks were considered for analysis sour natural gas, sour effluent from a liquid middle distillate fuel processor, and a Texaco 02-blown coal-derived synthesis gas. Their experimental results indicate that H2S concentration can be removed down to the part per million level in these plants. Additionally, a power-law rate expression was developed and reaction kinetics compared with prior literature. The activation energy for this reaction was determined to be 34.4 kJ/g mol with the reaction being first order in H2S and 0.3 order in 02. 

If surface reaction is assumed to be rate limiting and irreversible (and no adsorbed inerts are involved), the overall rate expression for consumption of A becomes -rA = A aCa/(1 + KaCa + KbCb), where k is the surface reaction rate constant and Ka and A b are adsorption equilibrium constants. If the surface is only sparsely covered, i.e., KaCa + KbCb 1, this can be approximated as simply va kKACA = k CA-This illustrates how a simple power law rate expression can apply, under some circumstances, for what is actually a relatively complex mechanism. 

Unsupported two-component oxide systems were used by Stroud in 1975 [169]. In their composition, the first component was preferably molybdenum oxide and the second cupric oxide (i.e., Mo03- CuO). The reaction conditions were 20 bar and 485°C, and the yield was 490 g/kg-cat/hr of oxygenated products, including methanol, formaldehyde, ethanol, and acetaldehyde. The work by Stroud used oxygen as the oxidant. Liu et al. [170] used nitrous oxide as the oxidant at 1 bar over the 1.7% Mo/Si02 catalyst. A combined selectivity of 84.6% towards methanol and formaldehyde was obtained with a conversion of 8.1%. They also used a different catalytic system of 1.7% Mo03 supported on Cab-O-SilM-5 silica. Their kinetic study obtained a power law rate expression of the Arrhenius plot for CH4 concentration was... 

Kinetic modeling of diesel autothermal reforming is extremely complicated. Diesel fuel consists of a complex variable mixture of hundreds of hydrocarbon compounds containing paraffins, isoparaffins, naphthenes, aromatics, and olefins. To simplify the model, a steady-state power law rate expression for the diesel reforming over each type of catalyst used in this study was developed. A linearized least-squares method of data analysis was used to determine the power law parameters from a series of diesel ATR experiments. The power law rate model for diesel autothermal reaction may be written as ... 

From the kinetic data a power law rate expression was derived ... 

Quantitative rate data on the catalytic reduction of nitrates in drinkable water are relatively scarce. One of the first works concerning kinetics is that of Tacke and Vorlop who employed a Pd-Cu bimetallic catalyst containing 5wt.% of Pt and 1.25 wt.% of Cu in a slurry reactor. Measurements of the initial rates resulted in a power-law rate expression. They reported a power of 0.7 with respect to the nitrate concentration, and an independency on the hydrogen partial pressure providing this pressure exceeded 1 bar. Pintar efa/. reported a complete kinetic model of the Langmuir-Hinshelwood type written in the form... 

The power law expression was widely adopted in the literature for CO oxidation [25-27]. This form is simplified from a Langmuir-Hinshelwood (L-H) expression and not suitable for small CO concentrations [30]. Therefore a full L-H expression for CO oxidation is necessary to account for a wide range of CO concentrations (Equation 27.4). The H2 oxidation was previously modeled using empirical power law rate expressions by others [29]. However, in PrOx in the presence of CO, the rate-limiting CO desorption strongly inhibits H2 and O2 adsorption and the subsequent H2 oxidation. Hence the incorporation of Pco in the H2 oxidation rate expression is necessary (Equation 27.5). The kinetics of the r-WGS reaction were well studied previously [31], in which an empirical reversible rate expression [32] is attractive due to its relative simplicity and its appropriateness in PrOx kinetic studies, as demonstrated previously [29]. 

Few kinetic models have been reported for the reaction of coke combustion on reforming catalyst. The reason of this is the complexity of the phenomena involved in this process. A single power law rate expression, first order on both... 

The kinetic analysis of thermolysis revealed that the process is comprised of two successive steps—an initial fast step followed by a slower second step for COD reduction. The two steps can be represented by a simple global power-law rate expression giving first order with respect to COD, for both the steps (Figure 6.19). 

The same authors performed a kinetic study of the WGS reaction over a Lao.7Ceo.2Fe03 perovskite-hke catalyst in the temperature range of 550-600 °C [70]. It was found a power-law rate expression (Eq. (20.4)), which involved six variables and correlates with the experimental data with good accuracy ... 

In order to study the NO reduction rate as a function of the reactant concentrations NO and NH3 a series of experiments were carried out in which the NO conversion level was measured with different levels of inlet reactant concentations. The experimental data are then correlated by minimizing the sum of squares of the difference between experimental and calculated rate constants by means of a Nelder Mead optimalization procedure, using the power law rate expression... 

The rate constant and the exponents (orders of reaction) can be determined in the usual way using, for instance, initial rate data or the excessive concentration method (Levenspiel 1972). From the power law thus determined, one may postulate a L-H rate expression that in turn can be verified kinetically up to a certain point. As discussed in Chapter 2, it may suffice just to use the power law rate expression in some cases. 

The intrinsic kinetic data obtained from an integral reactor operated at 4 atm and 488°K are given below for the catalytic reaction, A 2B + D. The bulk volume of catalyst is 20 cm and the feed rate is 30 1/hr. Obtain a power-law rate expression that best fits the data. 

Here v is the number of moles of gaseous species produced per unit mole of gaseous reactant, and is the mole fraction of reactants in the bulk. In Eq. (4.2.29) a power-law rate expression was used for the chemical reaction step. The boundary conditions are the same as those given by Eqs. (4.2.21) and (4.2.22). The solution of Eq. (4.2.29) then gives the overall rate of reaction per unit area of external surface. 

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