Methanation rate expression

In microkinetics, overall rate expressions are deduced from the rates of elementary rate constants within a molecular mechanistic scheme of the reaction. We will use the methanation reaction as an example to illustrate the... 

A global rate expression for CO methanation over a nickel catalyst is given by Lee (1973) and Vatcha (1976). They report that a Langmuir-Hinshelwood rate law of the form... 

The rate expression is given in terms of partial pressures and this is now rewritten in terms of the number of moles x of methane converted to CS Consider 1 mole of gas entering the reactor, then at any cross-section (distance z along the tube from the inlet) the number of moles of reactant and product may be written in terms of x as follows ... 

All hydrocarbons in the feed higher than methane are assumed to be instantly cracked into CH4, CO2, 112, and CO. Consequently the reaction system inside a reformer tube is described by the rate expressions of the kinetics of steam reforming in the methane reactions I, II, and III. 

Rate expressions for gas-phase reactions are sometimes based on partial pressures. A literature source5 gives k = 1.1 x 10 3 mol/(cm3 atm2 h) for the reaction of gaseous sulfur with methane at 873 K. 

The corresponding rate expressions for the methanation reaction are the following ... 

The rate expressions for the Fischer-Tropsch reaction (analogous to the expressions for methanation) are as follows ... 

The normal butenes were pyrolyzed in the presence of steam in a nonisothermal flow reactor at 730°-980°C and contact times between 0.04 and 0.15 sec to obtain conversion covering the range between 3% and 99%. Isomerization reactions accompanied the decomposition of these olefins however, the decomposition was the dominant reaction under these conditions. Pyrolysis of 1-butene is faster than that of either cis- or trans-2-butene. Methane, propylene, and butadiene are initial as well as major products from the pyrolysis of the n-butenes. Hydrogen is an initial product only from the 2-butenes. Ethylene appears to be an initial product only from 1-butene it becomes the most prominent product at high conversions. Over the range of conditions of potential practical interest, the experimental rate expressions for the disappearance of the respective butene isomers, have been derived. 

Further oxidation of C2f/6 to form CO2 and H2O is also considered in their analysis. Their kinetic rate expressions are complicated and involve reactions between adsorbed methane or ethane and the lattice oxygen, filling of oxygen vacancy by oxygen, coupling of the methyl radicals to form ethane, and reactions between the methyl or ethyl radicals and oxygen to form carbon dioxide. The equations can be found in their paper. 

Jiang et al. [225] fitted a five-step global mechanism to a detailed methane oxidation mechanism. They identified the dominant reactions in the detailed mechanism and determined the rate expressions for the steps of the global mechanisms on the basis of the rate of the corresponding reaction rates of the detailed model. The reduced model was also tested in reactive shock calculations. 

Dependence on the product methane. If the methane were adsorbed on the surface, the partial pressure of methane would appear in the denominator of the rate expression and the rate would vary inversely with methane concentration ... 

Under steady state reaction conditions, the effects of CO2 on the methane coupling reaction over Li/MgO catalyst were quantitatively determined. Poisoning effects of CO2 on carbon oxide formation rate, C2 formation rate, and methane conversion were observed for all methane to oxygen ratios and all temperatures. However, C2 selectivity is relatively unaffected by CO2 partial pressure. The mechanism described here accounts for important elementary steps, especially the effects of carbon dioxide. Under the low conversion conditions used in this study, further oxidation of C2 products to CO and CO2 is assumed negligible. These reactions will become more important at high conversions. Rate expressions derived from the mechanism match well the experimental conversions and selectivities. 

Figure 3. Effect of temperature on the rate of methane evolution expressed per gram of organic carbon. For the Condor shale, Curve 1 represents the normal shale Curve 2 represents the carbonaceous shale.

Figure 6. Comparison of the observed and calculated rate of methane evolution expressed per gram of...

Plot the experimental F/F,-vs-x data given in Table 4-6 as F/F, vs —In (1 — Xj). This method of plotting should result in a straight line if the assumed rate expression is correct. Figure 4-3 shows that this is not true if the rate is first order with respect to methane. At a constant reactants ratio of a = 2.0 the points fall on a straight line, but the data for other ratios deviate widely from the line. 

The problem of the kinetics of coke formation is a very Important especially with the Increasing demand for the use of low steam to methane ratios [ 10]. Kinetic rate expressions for the coke formation need to be developed. These rate equations should give the rate of coke formation 1n terms of the partial pressure of the various components and not only 1n terms of the carbon deposition and time it should also take Into consideration pore blockage as well as active site coverage by coke. 

MPa, the range of the steam to methane molar ratio 3-5, and the range of hydrogen to methane molar ratio from 1-3.25. They reached the following rate expression ... 

For complex reactions such as the oxidation of methane no mathematically simple rate laws can be formulated. The rates of any of the species involved are complicated functions of the concentrations of all the other participating reactants and intermediates, temperature, pressure, sometimes also wall conditions of the vessel, and other parameters. Isolated elementary reactions, in contrast, obey comparatively simple rate laws. Table 2-2 summarizes rate expressions for several basic types of homogeneous elementary reactions. Let us single out for the purpose of illustration the bimolecular reaction A+B— C+D. On the left-hand side of the rate expression one has equality between the rates of consumption of each reactant and the rates of formation of each product, in accordance with the requirements of stoichiometry. On the right-hand side, the product of reactant concentrations expresses the notion that the rate of the reaction at any instant is proportional to the number of encounters between reactant molecules of type A and B occurring within unit time and volume. The rate coefficient kbltn is still a function of temperature, but it is independent of the concentrations. The same is assumed to hold for the rate coefficients of the other types of elementary reactions in Table 2-2. At a constant temperature the rate coefficients are constants and the equations can be integrated to yield the concentrations of reactants and products as a function of time. 

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. 

Develop a rate expression for the synthesis of methane. The reaction is proposed to proceed as follows over a ruthenium catalyst [8]. The overall reaction is... 

At the present time, the fuels which can be described by this modeling approach include hydrogen, carbon monoxide, methane, methanol, ethane, ethylene, acetylene, propane, and propylene. The reaction mechanism used to describe the oxidation of these fuels has been developed and validated in a series of papers (3-7). The elementary reactions and their rate expressions are summarized in Reference (7) and are not reproduced here due to space limitations. Reverse reaction rates are computed from the forward rates and the appropriate thermodynamic data (8). This mechanism has been shown to describe the oxidation of methane (3,A), methanol (5), ethylene (6), and propane and propylene (7) over wide ranges of experimental conditions. It has also been used to describe the shock tube oxidation of ethane (4,9), and acetylene (10). 

Nonetheless, rate expressions more complex than a simple power law are sometimes useful. For example, a power law expression does not provide any insight into the reasons for changing reactant order (i.e., a changing value of a ) with temperature or organic reactant concentration. However, such effects are frequently observed in oxidation reactions and are often consistent with more fundamentally based rate expressions. Consider, for example, what one would suppose to be the simple oxidation of methane. Golodets (p. 445) states that methane oxidation over metal oxide catalysts may be interpreted by the following mechanism ... 

This is a so-called Eley-Rideal mechanism, meaning that methane from the gas phase reacts directly with an adsorbed oxygen species (Step 3). The rate expression from the above mechanism is ... 

Equilibrium was assumed to be maintained between ethane, C2HX and gaseous hydrogen, and the mono-carbon species were swiftly somehow converted into methane the second process was rate-determining. This led to a rate expression of the form... 

The oxygen concentration, like that of methane, is replaced by its initial value (Oj)o since, as is known, the maximum is reached at very small conversions. It is well worth noting that this rate expression has a remarkably simple form in spite of the complexity of the phenomenon. Indeed, it is once more of the servicreable type of the law of mass action, a rather unexpected result which emphasizes the great generality of our Rule IV of Chapter 1. 

Derive a rate expression for the maximum rate of oxidation of methane, following the reaction pattern discussed above but with one exception Assume that the rate-determining radical is HO and that its linear termination is the only pertinent termination step. 

This work focuses on the kinetic study of the methane catalytic combustion in a honeycomb monolith wash-coated with Pd/y-AhOa (homemade). The experimental conditions were chosen to adequately represent the operation of a domestic-scale catalytic heater, i.e. relatively high volumetric flowrates and high methane molar fractions (Lopez et al., 2000). From experimental data (obtained at conditions of negligible mass transfer resistances) and using a mathematical model for the laboratory reactor, the intrinsic kinetic parameters are calculated for a power law type rate expression. 

For the on-cell reforming of methane, the reaction rate expression for CH4 can be written as [35]... 

A low effectiveness factor — see Figure 3.23 — implies that the effectiveness factor and thus the effective rate for the steam reforming of methane is inversely proportional to the Thiele modulus [199] and hence the equivalent particle diameter assuming that the particle is isotherm. For a first-order equilibrium rate expression, a general effectiveness factor can be evaluated as shown in [199] [389]. For a large equilibrium constant, this equation can be simplified to ... 

Early work on the kinetics of the steam reforming of methane [59] was based on the assumption that the methane adsorption was ratedetermining, in agreement with the general assumption of a first-order dependence on methane concentration. Later work by Khomenko et al. [271] avoided the discussion of a rate-determining step instead, the researchers inserted the quasi steady-state approximation in terms of the Temkin identity [75], and the following rate expression was obtained for the temperature range of 470-700°C ... 

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