Concentration profile in a PFR

Figure 5.11 presents typical concentration profiles in a PFR with cooling. As known for consecutive reactions A — P —-—> R, the maximum achievable yield in the intermediate P depends on the ratio ki/k2. There is an optimal per-pass conversion and residence time. Good selectivity may be obtained either at lower conversion with less selective catalyst, but spending more for recycles, or with more selective catalyst at higher conversion. Thus, operating the reaction system at variable per-pass conversion may be used to manipulate the selectivity pattern. 

There is a one-to-one relation between the concentration profile in a PFR to that in a standard batch for the same initial condition and residence time. Residence time in the PFR is equivalent to batch reaction time in a standard batch. The reaction time of the batch may therefore be calculated from the residence time of the PFR. The PFR residence time is given as... 

Figure 3.22 Concentration profile in a cascade with five stages in comparison with a PFR and a single CSTR.

FIG. 7-3 Concentration profiles in fiatch and continuous flow a) fiatch time profile, (h) semifiatcli time profile, (c) five-stage distance profile, (d) tubular flow distance profile, (e) residence time distributions in single, five-stage, and PFR the shaded area represents the fraction of the feed that has a residence time between the indicated abscissas. 

Compare a z) for first- and second-order reactions in a PFR. Plot the profiles on the same graph and arrange the rate constants so that the initial and final concentrations are the same for the two reactions. 

Some aspects of reactor behavior are developed in Chapter 5, particularly concentration-time profiles in a BR in connection with the determination of values of and k2 from experimental data. It is shown (see Figure 5.4) that the concentration of the intermediate, cB, goes through a maximum, whereas cA and cc continuously decrease and increase, respectively. We extend the treatment here to other considerations and other types of ideal reactors. For simplicity, we assume constant density and isothermal operation. The former means that the results for a BR and a PFR are equivalent. For flow reactors, we further assume steady-state operation. 

Based on the reaction network in Example 18-8, calculate and plot the temperature (7)-volume (V) profile and the concentration (c,)-volume profiles for a set of independent species in a PFR operated adiabatically. Consult the paper by Spencer and Pereira (1987) for appropriate choice of feed conditions and for kinetics data For thermochemical data, consult the compilation of Stull et al. (1969), or an equivalent one. 

The results obtained with the same parameters employed in Figure 4.24 but considering a PFR rather than a CSTR are shown in Figure 4.25. In this case, regarding the concentration profile of Si, after one sharp peak the system acts as a rectifier. The concentration profiles of S2 and B are characterized by bell-shaped signals that appear every 20 min, and they appear with a phase shift of 20 min. The signal represented by the concentration profile of A is a repetitive signal with a time period of 40 min. 

Figure 4.26 presents the results obtained for a CSTR with Q = 6 mL/h, [A]o = 0.3 mM, and a cycle time of 5 min. In this case the time period of the output signals represented by Si, S2, and B is reduced to 10 min. Results for the case when a PFR is employed with the same parameter values are presented in Figure 4.27. Here the oscillations disappear and all the concentration profiles reach a constant value after the transient time.

In a PFR with immobilized enzymes, the increase in residence time t is achieved much more simply than the replenishment of spent enzyme. Especially in cases where a smooth enzyme concentration profile in both axial and radial dimensions of the PFR is aimed for, replacement of immobilized enzyme is difficult. Soluble enzymes, however, are best investigated in a CSTR according to the second method. 

For a series reaction network the most important variable is either time in batch systems or residence time in continuous flow systems. For the reaction system A - B - C the concentration profiles with respect to time in a batch reactor (or residence time in a PFR) are given in Figure 6. 

The residence-time distribution of the PFR was shown to be arbitrarily sharp because all molecules spend identical times in the PFR. We introduced the delta function to describe this arbitrarily narrow RTD. We added a dispersion term to the PFR equations to model the spread of the RTD observed in actual tubular reactors. We computed the full, transient behavior of the dispersed plug-flow model, and displayed the evolution of the concentration profile after a step change to the feed concentration. 

In this type of reactor, as the name implies, the flow is laminar. In other words, the radial concentration profile is parabolic and not uniform as in a PFR. This is because there is hardly any mixing and the reactant concentration profile closely matches the velocity profile (lowest near the wall to highest at the center). Thus each element of fluid flowing through the reactor is completely independent of the other elements, so that the fluid as a whole tends to behave as a macrofluid. In essence, therefore. Equation 13.10 would be valid for this case also. Integrated... 

Figure 5.15 (a) Concentration profiles of components A and B in a PFR from the feed. After r 80 s, little change in the species concentrations is observed, (b) PFR trajectory, corresponding to a PFR from the feed point, plotted in c -Cg space. 

For reactions with positive order, the performance of such a cascade reactor has a specific function between an ideal plug flow reactor and a single CSTR. This can easily be understood comparing the reactant concentration as function of the reactor volume. In a PFR the concentration and, therefore, the transformation rate diminishes with increasing volume from the reactor entrance to the outlet. The low specific performance of a CSTR can be explained by the overall low concentration corresponding to the outlet concentration. In the cascade, the concentration diminishes stepwise from one vessel to the next. This is shown schematically for a series with N=5 vessel in Figure 3.22. With increasing number of equal sized vessels the concentration profile approaches that of a PFR. 

For given reaction conditions and residence time in a PFR, the axial concentration profile and the outlet conversion depends strongly on the ratio between mixing time and characteristic reaction time. This ratio can be interpreted as a second Damkohler number for mixing Dall. ... 

Plug Flow Reactor (PFR) A plug flow reactor is a tubular reactor where the feed is continuously introduced at one end and the products continuously removed from the other end. The concentration/temperature profile in the reactor varies with position. 

A plug-flow reactor (PFR) may be used for both liquid-phase and gas-phase reactions, and for both laboratory-scale investigations of kinetics and large-scale production. The reactor itself may consist of an empty tube or vessel, or it may contain packing or a fixed bed of particles (e.g., catalyst particles). The former is illustrated in Figure 2.4, in which concentration profiles are also shown with respect to position in the vessel. 

In the examples in Sections 7.1 and 7.2.1, explicit analytical expressions for rate laws are obtained from proposed mechanisms (except branched-chain mechanisms), with the aid of the SSH applied to reactive intermediates. In a particular case, a rate law obtained in this way can be used, if the Arrhenius parameters are known, to simulate or model the reaction in a specified reactor context. For example, it can be used to determine the concentration-(residence) time profiles for the various species in a BR or PFR, and hence the product distribution. It may be necessary to use a computer-implemented numerical procedure for integration of the resulting differential equations. The software package E-Z Solve can be used for this purpose. 

The system considered in Figure 4.15 differs from the one in Figure 4.14 in the number of compartments considered in the reactor (n). It can be seen that when three compartments are considered, different information processing takes place, and regarding the concentration profiles of Si and B the system acts as a rechher. Very similar behavior is obtained when n is considered to be 5, and the reactor is actually a PFR. These results are presented in Figure 4.16. In this case the system acts as a rectiher regarding the concentrahon prohles of Si, S2, and B. 

The results represented in Figure 4.17 are obtained when the system is operated as a CSTR with Q = 6 mL/h. It can be seen that after the transient hme, oscillatory output signals with a period time of 40 min are obtained and they are represented by the concentration profiles of Si, S2, A, and B. Thus, this system converts the sharp input signals to oscillatory signals with the same period of time of the input signal (40 min) but with different amplitudes. Very similar behavior is observed when a PFR is considered (n = 5), and these results are presented in Figure 4.18. 

The effect of the maximum reaction rates, Vm,i, on the concentrations of Si and B when the CSTR is considered is presented in Figure 4.32. The concentration prohle of B changes from constant concentration when Vm, = 0.1 mM/min, to an oscillatory signal when Vm,i = 0.2 mM/min and to sharp on/off behavior when Vm,i = 0.4 mM/min. Similar characteristics of the signal can be seen in the concentration profiles of Si. When the PFR is considered, increase in Vm,i leads to effects resembling those shown in Figure 4.33. Here a time lag is observed in the concentration profiles of B and the period times for the on/off periods obtained when Vm,i = 0.4 mM/min are larger. 

The calculations discussed above (Figures 4.72 to 4.77) were performed for a PFR. Figures 4.78 to 4.80 refer to a packed bed reactor with n = 3. In this case the effect of the concentration range of the external inhibitor on the signal obtained was investigated. The data in Figures 4.78 to 4.80 differ from one another with respect to the cycle time, r, of the concentration profile of... 

The mean residence time for the optimized PFR reactors in Example 6.4 is about 0.8 h and boni is about 3.4 kg mol m . Find the optimal temperature profile T(z) that maximizes the concentration of component B in the competitive reaction sequence of Equation 6.1 for a PFR subject to the constraint that t = 0.8 h. Assume ajn = 4.5 kg mol m . ... 

Figure 8.12 shows the transient profiles. We see the reactor initially has zero A concentration. The feed enters the reactor and the A concentration at the inlet rises rapidly. Component A is transported by convection and diffusion down the reactor, and the reaction consumes the A as it goes. After about t = 2.5, the concentration profile has reached its steady value. Given the low value of dispersion in this prob lem, the steady-state profile is close to the steady-state PFR profile for this problem. o... 

In a tubular reactor, the concentration and temperature may vary both in time and space. One speaks about a distributed system. The ideal plug flow reactor (PFR) model is the most used. Because of the flat velocity profile, the concentrations and temperature varies only along the length. Consider for simplification a homogeneous reaction. The unsteady state material balance of the reactive species leads to the following equation ... 

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