Temperature reactor modeling

The increase in efficiency between the first- and second-generation reactors was attributed to less water in the feed and lower operating temperatures. Reactor models indicated that the major source of heat loss was by thermal conduction. The selective methanation reactor lowered the carbon monoxide levels to below 100 ppm, but at the cost of some efficiency. The lower efficiency was attributed to slightly higher operating temperatures and to hydrogen consumption by the methanation process. Typical methane levels in the product stream were 5-6.2%. ... 

The selectivity is 100% in this simple example, but do not believe it. Many things happen at 625°C, and the actual effluent contains substantial amounts of carbon dioxide, benzene, toluene, methane, and ethylene in addition to styrene, ethylbenzene, and hydrogen. It contains small but troublesome amounts of diethyl benzene, divinyl benzene, and phenyl acetylene. The actual selectivity is about 90%. A good kinetic model would account for aU the important by-products and would even reflect the age of the catalyst. A good reactor model would, at a minimum, include the temperature change due to reaction. 

Steady performance data from the second reactor are shown in Figure 11.10, where the pressure drop did not rise exponentially and the conversion and selectivity remained at 75 and 83%, respectively. The reactor was further analyzed after operation, shown in Figure 11.11, to confirm the lack of carbon deposition. Reactor models were pivotal to developing a robust design for this high-temperature and... 

In Fig. 1, a comparison can be observed for the prediction by the honeycomb reactor model developed with the parameters directly obtained from the kinetic study over the packed-bed flow reactor [6] and from the extruded honeycomb reactor for the 10 and 100 CPSI honeycomb reactors. The model with both parameters well describes the performance of both reactors although the parameters estimated from the honeycomb reactor more closely predict the experiment data than the parameters estimated from the kinetic study over the packed-bed reactor. The model with the parameters from the packed-bed reactor predicts slightly higher conversion of NO and lower emission of NHj as the reaction temperature decreases. The discrepancy also varies with respect to the reactor space velocity. 

Having set up a model to describe the dynamics of the system, a very important first step is to compare the numerical solution of the model with any experimental results or observations. In the first stages, this comparison might be simply a check on the qualitative behaviour of a reactor model as compared to experiment. Such questions might be answered as Does the model confirm the experimentally found observations that product selectivity increases with temperature and that increasing flow rate decreases the reaction conversion ... 

Mathematical models of tubular chemical reactor behaviour can be used to predict the dynamic variations in concentration, temperature and flow rate at various locations within the reactor. A complete tubular reactor model would however be extremely complex, involving variations in both radial and axial... 

Example 14.1 Consider again the chlorination reaction in Example 7.3. This was examined as a continuous process. Now assume it is carried out in batch or semibatch mode. The same reactor model will be used as in Example 7.3. The liquid feed of butanoic acid is 13.3 kmol. The butanoic acid and chlorine addition rates and the temperature profile need to be optimized simultaneously through the batch, and the batch time optimized. The reaction takes place isobarically at 10 bar. The upper and lower temperature bounds are 50°C and 150°C respectively. Assume the reactor vessel to be perfectly mixed and assume that the batch operation can be modeled as a series of mixed-flow reactors. The objective is to maximize the fractional yield of a-monochlorobutanoic acid with respect to butanoic acid. Specialized software is required to perform the calculations, in this case using simulated annealing3. 

Another approach to scale-up is the use of simplified models with key parameters or lumped coefficients found by experiments in large beds. For example, May (1959) used a large scale cold reactor model during the scale-up of the fluid hydroforming process. When using the large cold models, one must be sure that the cold model properly simulates the hydrodynamics of the real process which operates at elevated pressure and temperature. 

Level (3) global e.g., reactor model some key parameters reactor volume, mixing/flow, residence time distribution, temperature profile, reactor type... 

In Table 17.2, fA (for the reaction A products) is compared for each of the three flow reactor models PFR, LFR, and CSTR. The reaction is assumed to take place at constant density and temperature. Four values of reaction order are given in the first column n = 0,1/2,1, and 2 ( normal kinetics). For each value of n, there are six values of the dimensionless reaction number MAn = 0, 0.5, 1, 2, 4, and °°, where MAn = equation 4.3-4. The fractional conversion fA is a function only of MAn, and values are given for three models in the last three columns. The values for a PFR are also valid for a BR for the conditions stated, with reaction time t = t and no down-time (a = 0), as described in Section 17.1.2. 

The comparison in Table 6 illustrates the method but it is only an approximate comparison. In order to account for differences in apparent activation energy between the catalysts, a full reactor model integrating the reaction rate over the full temperature range of the bed is necessary for calculation of the exact catalyst volume. 

In Figure 2.4, data for the equilibrium constants of esterification/hydrolysis and transesterification/glycolysis from different publications [21-24] are compared. In addition, the equilibrium constant data for the reaction TPA + 2EG BHET + 2W, as calculated by a Gibbs reactor model included in the commercial process simulator Chemcad, are also shown. The equilibrium constants for the respective reactions show the same tendency, although the correspondence is not as good as required for a reliable rigorous modelling of the esterification process. The thermodynamic data, as well as the dependency of the equilibrium constants on temperature, indicate that the esterification reactions of the model compounds are moderately endothermic. The transesterification process is a moderately exothermic reaction. 

Figure 2.11 Equilibrium constant for the formation of DEG from EG as a function of temperature, calculated by using the Gibbs Reactor model of the commercial process simulator Chemcad (Chemstations)...

Let us consider the batch reactor modeled in Sec. 3.9 (Fig. 3.9). Steam is initially fed into the jacket to heat up the system to temperatures at which the consecutive reactions begin. Then cooling water must be used in the jacket to remove the exothermic heats of the reactions. 

Another important effect that can be analyzed is the relation between the equilibrium reactor temperature and the equilibrium jacket temperature. It is known that temperature difference between cooling jacket and the reactor must be increased as the volume of the reactor increases. Figure 8 shows this effect clearly. When the reactor has a small volume the difference Tg — Tj is very small, consequently the heat transfer process is slower and the operation control is easier. Table 2 quantitatively summarizes the effects previously commented for a typical reactor modelled by Eq.(23) with the parameters defined in table 1. As the reactor volume varies from 0.0126 to 42.41 m , lower jacket temperatures are required and the operation control is more difficult. 

Nitrogen and hydrogen-rich feeds are mixed, compressed and further combined with a high-pressure recycle stream. The mixture is then reacted at high pressure and temperature. Here the reactor model is assumed to be... 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

A significant step in the numerical solution of packed bed reactor models was taken with the introduction of the method of orthogonal collocation to this class of problems (Finlayson, 1971). Although Finlayson showed the method to be much faster and more accurate than that based on finite differences and to be easily applicable to two-dimensional models with both radial temperature and concentration gradients, the finite difference technique remained the generally accepted procedure for packed bed reactor model solution until about 1977, when the analysis by Jutan et al. (1977) of a complex butane hydrogenolysis reactor demonstrated the real potential of the collocation procedure. 

Table VII shows that, for the methanation reactor model, the dynamic response of the gas temperatures and CO and C02 concentrations should be much faster (by two orders of magnitude) than the response of the catalyst and thermal well temperatures. This prediction is verified in the dynamic responses shown in Figs. 18 and 19 and the previous analysis of the thermal and concentration wave velocities.

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