Reactors concentration profiles

In the preceding section, the choice of reactor type was made on the basis of which gave the most appropriate concentration profile as the reaction progressed in order to minimize volume for single reactions or maximize selectivity for multiple reactions for a given conversion. However, after making the decision to choose one type of reactor or another, there are still important concentration effects to be considered. 

Fig. 9. Bubble-wake interactions in a gas—Hquid-soHd reactor (a) soHds concentration profile within bubble-wake domain, where A—A and B—B represent planes through the bubble, vortex, and wake (b) projected impact of interactions on reaction rate as function of particle si2e and Hquid velocity, where (—)...

A useful classification of lands of reaclors is in terms of their concentration distributions. The concentration profiles of certain limiting cases are illustrated in Fig. 7-3 namely, of batch reactors, continuously stirred tanks, and tubular flow reactors. Basic types of flow reactors are illustrated in Fig. 7-4. Many others, employing granular catalysts and for multiphase reactions, are illustratea throughout Sec. 23. The present material deals with the sizes, performances and heat effects of these ideal types. They afford standards of comparison. 

The following details establish reactor performance, considers the overall fractional yield, and predicts the concentration profiles with time of complex reactions in batch systems using the Runge-Kutta numerical method of analysis. 

FIGURE 5.4 Concentration profiles for an endothermic reaction in an adiabatic reactor. 

FIGURE 9.3 Temperature and concentration profiles at the point of maximum temperature for the packed-bed reactor of Example 9.1. 

FIGURE 9.5 Reactant concentration profiles for a thermal runaway in the packed-bed reactor of Examples 9.1 and 9.2 Ti = 704K. 

A substantial investment in algebra is needed to evaluate the six constants, but the result is remarkable. The exit concentration from an open system is identical to that from a closed system. Equation (9.20), and is thus independent of Dt and Dou The physical basis for this result depends on the concentration profile, a(z), for z<0. When Z) = 0, the concentration is constant at a value if until z = 0+, when it suddenly plunges to u(0+). When D >0, the concentration begins at when z = —oo and gradually declines until it reaches exactly the same concentration, u(0+), at exactly the same location, z = 0+. For z>0, the open and closed systems have the same concentration profile and the same reactor performance. 

The axial dispersion model is readily extended to nonisothermal reactors. The turbulent mixing that leads to flat concentration profiles will also give flat temperature profiles. An expression for the axial dispersion of heat can be written in direct analogy to Equation (9.14) ... 

A one-dimensional isothermal plug-flow model is used because the inner diameter of the reactor is 4 mm. Although the apparent gas flow rate is small, axial dispersion can be neglected because the catalj st is closely compacted and the concentration profile is placid. With the assumption of Langmuir adsorption, the reactor model can be formulated as. 

The reactivities of spray-dried sorbents were examined in a fast fluidized bed. The reactor was operated at a carbonation temperature of 50 °C, and a gas velocity of 2 m/s with an initial sorbent inventory of 7 kg to compare CO2 concentration profiles in effluent gas for spray-dried Sorb NH series and NX30 sorbent. Figure 5 shows the comparison of CO2 concentration profiles in effluent gas of Sorb NHR, NHR5, and NX30 in a fast fluidized-bed reactor. The CO2 removals of Sorb NHR and NHR5 were initially maintained at a level of 100 % for a short period of time and quickly dropped to a 10 to 20 % removal level. 

Fig. 1 Concentration profiles of CO, Oj and Hj inside a countercurrent moving bed reactor.

For fast reactions Da becomes large. Based on that assumption and standard correlations for mass transfer inside the micro channels, both the model for the micro-channel reactor and the model for the fixed bed can be reformulated in terms of pseudo-homogeneous reaction kinetics. Finally, the concentration profile along the axial direction can be obtained as the solution of an ordinary differential equation. 

The reversible formation of a complex by Ni ions and the bi dentate ligand pyridine-2-azo-p-dimethylaniline is a simple and thus reliable reaction, not accompanied by side reactions [17]. Kinetic rate law and rate constants for the reaction are known. The time demand of the reaction fits the short time scales typical for micro reactors. The strong absorption and the strong changes by reaction facilitate analysis of dynamic and spatial concentration profiles. 

GL 21] ]no reactor] ]P 22] Depending on the reaction velocity, different concentration profiles were simulated [73]. At 10 mm s reaction occurs over the full length and is not completed. At 1 mm s the reaction, reaction starts much earlier. 

According to the boundary conditions, the concentration profile for A must change with a discontinuity at the reactor entrance, as shown in Fig. 4.16. 

Figure 4.16. Concentration profiles in the tubular reactor for extreme and intermediate values of the dispersion number. 

Axial concentration profile in a tubular reactor. Dimensionless form,n-th- kinetics To be compared to TUBE... 

Figure 5.90. Dynamic concentration profiles at each axial position in the reactor.

Figure 5.93. The reactor responded to the changes according to these concentration profiles.

Auto-refrigerated reactor 357 Automatic control 94 Axial concentration profiles 563 Axial dispersion 560, 578... 

The breakthrough time observed in the NOx concentration profile (obtained by addition of the NO and N02 concentrations) indicates that during the initial part of the pulse, the NO fed to the reactor is completely stored on the catalyst surface. 

At steady state, the right side vanishes, and one obtains an equation that describes in pseudo homogeneous fashion the concentration profile in the reactor. 

For isothermal systems this equation, together with an appropriate expression for rv, is sufficient to predict the concentration profiles through the reactor. For nonisothermal systems, this equation is coupled to an energy balance equation (e.g., the steady-state form of equation 12.7.16) by the dependence of the reaction rate on temperature. 

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