Temkin—Pyzhev equation

The Temkin-Pyzhev equation deseribes the net rate of synthesis over promoted iron eatalyst as ... 

Based on the experimental data which covered the pressure range from below 1 atm up to 500 atm, it was proposed that near equilibrium, the reaction rate is described by the following equation, which is often referred to in the literature as the Temkin-Pyzhev equation... 

Nothing more will be said about the synthesis data except to point out that one numerical change has to be made in the kinetic equation according to a much later paper by Anderson and Tour ( 32). This has yet to be applied to the FNRL data. The Temkin-Pyzhev equations without this added refinement represent the data for 3 1, 1 1, and 1 3 H N fairly well. ... 

A logarithmic value of the reaction-rate constant taken from Temkin-Pyzhev equation as a function of reciprocal temperature for the catalysts pressed at different pressures is presented in figure 1. This function is nonlinear, the reason for this being an increase of the diffusion effects together with increasing temperature. 

Note Temkin-Pyzhev equation r = kifN2(fH2/fNHs) 2(fNH3/fH2 ) (" = T = ... 

Temkin-Pyzhev equations mentioned above was in agreement with a number of kinetic measurement made on various catalysts such as Mo, W, Tc, Ru, Os and promoted Fe. One characteristic feature of ammonia synthesis rate is the retardation by the product ammonia, and reasonably explained by the Temkin theory. The assumption of rate determining step is also supported by the chemisorption of nitrogen. 

An attempt was made by Ozaki et al to verify the mechanism, on which the Temkin-Pyzhev equation was derived, by comparing the rate of the following two reactions obtained on the same catalyst ... 

At present, Temkin-Pyzhev equation expressed by fugacity is still applied frequently for the design of industrial reactors with iron-based ammonia synthesis catalysts ... 

This equation is the well-known Temkin or Temkin-Pyzhev equation, which can be easily integrated for practical applications. 

Another assumption for the Temkin-Pyzhev equation is that the nitrogen adsorption is not influenced by hydrogen and ammonia, an assumption which seems to be corroborated by the experimental data of Emmett and Brunauer [7]. 

The data obtained on singly promoted catalysts, however, could not to be fitted to the Temkin-Pyzhev equation. Their performance depended in a highly complex manner on the temperature and the partial pressures and the activation energy depended on the temperature and even displayed hysteresis effects. These deviations from Temkin-Pyzhev kinetics could be removed by impregnating the catalyst with a KOH solution although the activity dropped considerably. 

Brunauer et al. [29] extended the range of the Eqs. (12), (13), (14), which are the basis for the Temkin-Pyzhev equation. In order to develop an adsorption isotherm, Brunauer et al. subdivided the surface into elements each following (the original) Langmuir isotherm, so that... 

The Temkin-Pyzhev equation is thus only valid at medium surface coverage as already pointed out by the authors. 

In 1943, Emmett and Kummer [23] presented the results of high pressure experiments on a doubly promoted catalyst (3.02% AI2O3,0.94% K2O) at 33.3, 66.6 and 100 atm, H2/N2 ratios 3/1,1/1 and 1/3 and space velocities from 25 000 to 125000 h" at 370, 400 and 450°C were used. The data were analysed with the Temkin-Pyzhev equation using a = P = 0.5. The rate constant k was constant with variations in space velocity, except at 370 °C where it decreased with an increase in space velocity of 5. Apparent activation energy for decomposition was found to be from 45 000 to 53 000 cal/mol. 

Although the Temkin-Pyzhev equation seemed to fit the data reasonably well with respect to variations in space velocity and temperature, all data sets exhibited a clear decrease in the rate constant with increasing pressure. 

Using a P value of approx. 0.3 as found by Love and Emmett [26] an attempt was made to calculate the data by the Temkin-Pyzhev equation with a = 0.67, but this gave a poorer agreement. With respect to changes in gas composition the agreement with a = 0.67 was fair at 370 and 400 °C, but the rate constant varied by a factor 2 at 450 °C between the 3 1 and 1 3 H2/N2 mixtures. 

In 1947, Temkin and Kiperman [31] gave a general discussion of the Temkin-Pyzhev equation and its usefulness for both the synthesis reaction and the decomposition. They pointed out that it would not be valid at low ammonia partial pressures because the equilibrium... 

In a series of experiments with triply promoted catalyst at 1 atm, 400 °C and SV = 30000 at different H2/N2 ratios Nielsen [35] found that maximum conversion was obtained at a H2/N2 ratio of 1.5 as predicted by the Temkin-Pyzhev equation (Eq. (22)) when the backward reaction can be ignored. At 330 atm, 450 °C, and SV = 15 000 the decomposition rate constant (k in Eq. (31)) was however found to increase with approximately a factor of two when the H2/N2 was increased from 1/1 to 6/1. 

Further discussions by Temkin et al. of the use of the Temkin-Pyzhev equation can be found in [36]. 

Annable was the first to use the Temkin-Pyzhev equation to analyze operating data from industrial ammonia units [38] an adiabatic reactor operating at 245 atm and a multibed quench reactor operating at 300 atm. 

For a given inlet gas composition, pressure, and temperature, numerical integration was carried out throughout the reactor. The rate constant k2 in the Temkin-Pyzhev equation was adjusted so that the calculated temperature profiles matched the measured ones. Radial gradients and axial heat conduction were ignored. The catalyst particles were assumed to have the same temperature... 

The Temkin-Pyzhev equation was also used to analyze the performance of a catalyst charge with a feed gas containing larger amount of poisons than the experiments above. The activity was only one third of the activity of a catalyst operating with a relatively pure gas. A bend in the Arrhenius plot could be observed around 450 °C. The Temkin-Pyzhev equation with the as-found constants was eventually used to find the optimum temperature curve in an ideal as well as a practical reactor. 

They used the original Temkin-Pyzhev equation with a = 0.5 to correlate the data, but agreement between theory and experiment was even less satisfactory than that obtained by Emmett and Kummer [23]. 

Bokhoven et al. in a review article [42] critically discussed the application of the Temkin-Pyzhev equation to fit the data published before 1955. They quote their own unpublished results of synthesis experiments at 1 atm on a doubly promoted catalyst at 350 °C with H2/N2 = 3.0. The best fit is obtained with a = 0.6. 

Bookhoven attributed the different pressure dependencies of k2 in the various studies to differences in the catalysts used. The results on doubly promoted catalyst are best fitted by the Temkin-Pyzhev equation. It was noted that K2O addition to singly promoted catalysts lowers its activity at 1 atm, but increases it at 200 atm. 

Shishkova et al. [46] confirmed the validity of the Temkin-Pyzhev equation at pressures up to 300 atm using a commercial catalyst in a recycle reactor. 

The experimental data were presented in the form of curves showing the space time yield (cm NH3 produced per cm per hour) as a function of space velocity. All data were evaluated with the Temkin-Pyzhev equation modified for high pressure (Eq. (61)) according to Temkin [34]. The ideal solution method was selected for calculating the fugacities. 

The Temkin-Pyzhev equation in form of Eq. (61) was found to describe the variations with space velocity not too close to equilibrium fairly well, but k2 was clearly decreasing with pressure. To fit the data, the partial molar volumes of nitrogen would have to be in the order of 200 or 500 cm /mol instead of the more probable 20-50 cm /mol. The activation energies for decomposition were calculated at the different pressure levels. 

Both Temkin [54] and Kwan [55] showed that assuming a simple Freun-dlich isotherm can also lead to the Temkin-Pyzhev equation. 

The experimental data were first fitted to the Temkin-Pyzhev equation. It was noted that the value of a decreased from 0.8 to 0.4 with increasing efficiency. This can be attributed to low coverage by nitrogen, thus making the assumptions for the Temkin-Pyzhev equations invalid as noted by Brunauer [27] and also Temkin [17], [31]. At a fixed temperature and at relative high efficiencies, k still depended on pressure. Ozaki et al. correlated the data with Eq. (68) and found k independent of pressure but K dependent on pressure. A successful fit, however, was obtained using Eq. (69) with both k and K independent of pressure. 

Ozaki et al. also extended the Temkin-Pyzhev equation by using the isotherm developed by Brunauer et al. [27]. 

Brill and Tauster [57] carried out experiments on doubly promoted catalysts. No experimental details about catalysts or reduction procedures were given. The constant a in the Temkin-Pyzhev equation was increased from 0.11 to 0.7 for doubly promoted catalyst between 182 and 369 °C and from 0.47 to 0.7 for singly promoted catalyst between 242 and 286 °C. There was no change in... 

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