First-order Reaction Model

Preliminary work showed that first order reaction models are adequate for the description of these phenomena even though the actual reaction mechanisms are extremely complex and hence difficult to determine. This simplification is a desired feature of the models since such simple models are to be used in numerical simulators of in situ combustion processes. The bitumen is divided into five major pseudo-components coke (COK), asphaltene (ASP), heavy oil (HO), light oil (LO) and gas (GAS). These pseudo-components were lumped together as needed to produce two, three and four component models. Two, three and four-component models were considered to describe these complicated reactions (Hanson and Ka-logerakis, 1984). 

From Table 5.6, it is clear that the best fit is given by a first-order reaction model rA = kACA with kA = 0.01306 h 1. 

First-order adsorption kinetics model A simple first-order reaction model is based on a reversible reaction with equilibrium state being established between two phases (A— fluid, B—solid) ... 

Figure 6.4 shows how the extent of reaction depends on the mean residence time (l//cf) for the simple first-order reaction model, with... 

This argument shows that for the first-order reaction model the stationary state always has some sort of stability to perturbations. In fact, this is only a first step and will not reveal Hopf bifurcations or oscillatory solutions, should they occur-. A full stability analysis of typical flow-reaction schemes will appear in the next chapter. 

PCBs available for various uses. For this reason, 2-chlorobiphenyl and a mixture of Aroclor were studied. Samples (100 mL) of the mixtures were prepared with 265 (ig/mL of PCB and 25 pg/mL of Ti02. The pH of the samples was adjusted to 3, 7, and 10. The samples were irradiated under a UVA-340 light source for 120 min. The concentrations of the PCBs were determined using GC. The degradation rate of 2-chlorobiphenyl increased with decreasing pH values. After 1 hour of irradiation, more that 90% of the PCBs had been degraded at pH 3 and pH 7. The degradation rate constant, k, can be determined from the first-order reaction model ... 

Table 10.10 summarizes the kinetic data on SCWO of organic compounds, organic mixtures, ammonia, and carbon monoxide. M and n are the constants in Equation (10.25). These kinetic data can fit the pseudo first-order reaction models proposed by Wightman (1981). The activation energy from... 

Table 21.1 Apparent reaction rate constants for the pyrolysis of PE with a first-order reaction model...

The homogeneous tar conversion is described by an empirical model. The results show that the simple one-tump, single first-order reaction model describes the depletion of the gravimetric tar satisfactory well. The comparison with literature studies shows a good agreement of the determined kinetic parameters. 

In Figure 4, the calculated mass losses for cellulose at different constant heating rates and initial sample masses are compared to experimental TGA results. The TGA curves at heating rates of 0.14 K/min and O.S K/min had been used to evaluate the kinetic parameters for the one step first order reaction model which was incorporated into the model to calculate the sample temperature distribution. Since the temperature gradients in those samples are nearly zero, the results of the heat transport reaction model represent simultaneously the best fit for the assumed reaction model. At a heating rate of 108 K/min, the initial sample mass influences the temperature at which a given mass loss is attained. Cellulose samples with mo = I - 3 mg are affected only to a minor... 

Similarly, the rate of second-order reaction in a grid also decreases as a- 1, and even faster. As a result, the choosing of Cc is more critical. Fig. 9 shows the effect of Cc on surface temperature and burning rate of HMX. Compared with the bum rates using the first-order reaction model, as shown in Fig. 8, the bum rates for second-order reaction are higher at low Cc values, (e.g., 5.5 cm/s for... 

For these reasons, cunxng gas flow rate could have no effect on the conversion provided the same inl pressure is maintained There will stiil be a huge excess the H2 and the system will behave as a quasi first-order reaction modeled as a plug flow reactor. The H > concencarion at all points will be csscnnally the equilibrium satuiaaon liquid... 

We extend the example of Sudicky and Frind (1984) and Cormenza (2000) to illustrate which processes can influence the migration of the daughter product along the fracture. For the first two cases we assume that chemical reactions occur under equilibrium. Only for the last case we use the nonequilibrium first-order reaction model as mentioned above. 

Kinetics of the absorption of CO2 into MDEA-DEA-H2O system was investigated over a temperature range varying from 293K to 313K and total amine concentration from 0.5M to 2M using a laboratory stirred cell reactor. It was observed that the addition of small amounts of DEA to MDEA resulted in a significant enhancement of CO2 absorption rates. A first-order reaction model for MDEA and a zwitterions mechanism for DEA were used to interpret the kinetic data and derive the kinetic parameters associated to the reaction. Beside DEA, H2O and OH, also MDEA acts as a base for the removal of a proton from the zwitterion intermediate. 

Figure 3.24 provides an example of such a plot for the thermal degradation of PEN at 420 °C. A first-order reaction model [Eq. (3.13)] has been found to lit the experimental data better than reaction order models of other n values. Although the g(a)-t plot is characterized by a reasonable correlation coefficient (r = 0.97), it demonstrates obvious systematic deviations from the straight line. The reason is that actual degradation processes tend to be more complex than the simplistic models widely used for their description. The rate constant k(T), obtained from the slope of the g(a) versus t, is 0.00133 s The value of k J can then be used to simulate the experimental a-t data by solving Eq. (3.11) with respect to a. For a first-order reaction model [Eq. (3.13)], the solution is given by... 

Ammonia synthesis reaction is a complex multi-component and reversible reaction, and the kinetic equation can be expressed by power function. For simplification, the multi-component diffusion model is usually simply treated in engineering as a single-component diffusion model of key component, and the utilization ratio of internal surface is obtained by an approximate method from a simplified first-order reaction model. 

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