Conversion profiles, fractional

Figure 6-6. Temperature versus fractional conversion profiles for various rates of heat input in a batch reactor.

Reconsider Example 4-8. Plot the conversion profile for the case when tl le entering pressure is increased by a factor of 5 and the particle diameter decreased by a factor of 5. (Recall that alpha is a function of the panicle diameter and Fj).) What did you leam from your plot What. should jl your next settings of a and to leam more Assume turbulent flow. Consider adding an inert to the reaction in Example 4-9, keeping the total i molar flow rate at a constant. Plot the exit conversion and the equilibrium conversion as a function of the mole fraction of an inert. What are the advantages and disadvantages of adding an inert ... 

To quantify the effect of the incomplete mixing on reaction rates in the front of the reactor channel, this same simulation was repeated assuming second order kinetics (first order in each of the two components) and Cjj = C2j = 100 mol m. A rate constant of 1.0 X 10 m moh s was used to give an intermediate level of conversion (near 25%). This case can be compared with a simulation in which the inlet boimdary conditions were changed to assume complete mixing (50 mol m of each component across the entire inlet cross section). The axial fractional conversion profiles for these two cases (unmixed and premixed feeds) are shown in Fig. 13.4, where the unmixed feed curve is the average of the calculated values for the two components. The computed conversions for the two components were... 

For this case it will be necessary to calculate the steady-state temperature and fractional conversion profiles along the length of the tubular reactor. For a plug flow reactor the appropriate differential material balance for the reaction at hand is... 

Figure 6.2. Fractional-conversion profiles in adiabatic catalyst beds vs contact time. Curve a represents the behavior of the first catalyst bed of an ammonia converter. Curve b refers to the third catalyst bed, which operates in a range of comparatively low reaction rates, of the same converter.

Hydrolysis of disaccharides — cellobiose, maltose and lactose — was investigated over A, X, and Y type zeolites. The conversion profiles of the hydrolysis of cellobiose over NaX are shown in Fig. 4.19. The reaction was carried out at 373 K and initial reactant concentration of 1.0 wt%, and a catalyst loading of 0.1 gcm . Total conversion is based on the amount of cellobiose consumed by the reaction. A very large fraction of the reaction occurs within the first 0.5 h and the entire reaction terminates after 1 h. The pH profile of the reaction broth is also shown in Fig. 4.19. Upon addition... 

The fractional conversions in terms of both the mass balance and heat balance equations were calculated at effluent temperatures of 300, 325, 350, 375, 400, 425, 450, and 475 K, respectively. A Microsoft Excel Spreadsheet (Example6-ll.xls) was used to calculate the fractional conversions at varying temperature. Table 6-7 gives the results of the spreadsheet calculation and Eigure 6-24 shows profiles of the conversions at varying effluent temperature. The figure shows that die steady state values are (X, T) = (0.02,300), (0.5,362), and (0.95,410). The middle point is unstable and die last point is die most desirable because of die high conversion. 

Using the same values of the kinetic parameters as in Type 1, and given C o = 0-1 mo 1/1, it is possible to solve Equation 6-155 with Equations 6-127 and 6-128 simultaneously to determine the fractional conversion X. A computer program was developed to determine the fractional conversion for different values of (-iz) and a temperature range of 260-500 K. Eigure 6-30 shows the reaction profile from the computer results. 

The Microsoft Excel Spreadsheet (OPTIMUM63.xls) was used to evaluate T p for varying values of X. Table 6-12 gives the results of the spreadsheet calculation, and Figure 6-34 illustrates the profile of Tgp( against X, showing that the optimum temperature progression decreases as the fractional conversion increases. 

Conversely, the optimization is now constrained to be at a fixed (optimized) temperature, but the chlorine addition profile optimized. Both the feed addition profile and the total chlorine feed are optimized. The optimum temperature reaches its upper bound of 150°C. Chlorine addition is 75.0 kmol and the batch cycle is 1.35 h. The resulting fractional yield of MBA from BA now reaches 97.4%. 

The estimated time required to achieve a fractional conversion of 0.99 is 1.80 h, and the temperature at this time is 333.5 K, if the reactor operates adiabatically. The fA(t) profile is given by the values listed in the second and last columns the T(t) profile is given by the third and last columns. 

For exothermic, reversible reactions, the existence of a locus of maximum rates, as shown in Section 5.3.4, and illustrated in Figures 5.2(a) and 18.3, introduces the opportunity to optimize (minimize) the reactor volume or mean residence time for a specified throughput and fractional conversion of reactant. This is done by choice of an appropriate T (for a CSTR) or T profile (for a PFR) so that the rate is a maximum at each point. The mode of operation (e.g., adiabatic operation for a PFR) may not allow a faithful interpretation of this requirement. For illustration, we consider the optimization of both a CSTR and a PFR for the model reaction... 

In this section, we apply the axial dispersion flow model (or DPF model) of Section 19.4.2 to design or assess the performance of a reactor with nonideal flow. We consider, for example, the effect of axial dispersion on the concentration profile of a species, or its fractional conversion at the reactor outlet. For simplicity, we assume steady-state, isothermal operation for a simple system of constant density reacting according to A - products. 

For a simple system, the continuity equation 21.6-1 may be put in forms analogous to 21.5-2 and 21.54 for the axial profile of fractional conversion, fA, and amount of catalyst, W, respectively ... 

The products were solvent fractionated into hexane soluble (HS), hexane insoluble-benzene soluble (HI-BS), and benzene insoluble (Bl) fractions. The yields of these solvent-fractionated products after hydrotreatment of SRC are plotted against the reaction time in Fig. 13. The overall activities of the catalysts were very similar to those of the commercial catalyst in spite of their lower surface areas. Both exploratory catalysts (Cat-A and Cat-B) showed similar reaction profiles, which were markedly different from those of the commercial catalyst. The BI fraction decreased over the exploratory catalysts equally as well as the over the commercial catalyst. However, the HS fraction hardly increased as long as the BI fraction was present. As the result, the HI-BS fraction increased to a maximum just before the BI fraction disappeared and then rapidly decreased to complete conversion after about 9 hr. The rate of HS formation increased correspondingly during this time. Thus, the exploratory catalysts were found to exhibit a preferential selectivity for conversion of heavier components of SRC, compared to the commercial catalyst. These results emphasize that the chemical and physical natures of the support are important in catalyst design (49). 

Fig. 4.27 represents the velocity profiles v(r) and degrees of conversion P(r) at the exit of a reactor for different values of Da/Da and constant [A] = 0.7 mol%. At Da = 0.5 (a rather low degree of conversion at the axis of the reactor), a low-viscosity stream flows out (breaks through) into the central zone (Fig. 4.27 b, curves 1 and 2). This means that the end-product leaving the reactor is a mixture consisting of two species (fractions) with very different molecular weights, leading to the appearance of a pronounced bimodal MWD-H, which is not due to the chemical process but is a direct consequence of the hydrodynamic situation in the reactor. 

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