PFR reactions

The overall Pr - Pfr reaction is associated with a change in the dichroic orientation of the long-wavelength transition moment [33,58-63]. It has been interpreted to reflect the overall orientational effect composed of the... 

We have already generated the AR in for this system in Chapter 3, where the procedure shown involved repeated use of batch (PFR) reactions followed by partial mixing with fresh feed for a subsequent batch. This process is somewhat lengthy and impractical in practice. 

The cooling duties required for the PSR are comparable to those for the PSA unit in the PSA PFR option and are much lower than those required for both PFR units (both isolated and in series with a PFR). The cooling strategy is important to guarantee reactor stability and prevent runaways. For a PFR, reaction rates can only be controlled over the catalyst temperature. In contrast, in the PSR a kind of self control is exerted by the fact that reactants need to desorb prior to being able to react. This renders the PSR far less sensible to temperature rises than the PFR. As a result the non-isothermally operated PSR can attain superior selectivity over the PFR for a wider operating regime. 

A further step in the study of cyclohexadienones as PFR reaction intermediates has consisted in the secondary photolysis of these relatively long-lived species by using the two-laser-two-color technique, which gives rise to formation of a dienic ketene, absorbing at k =330nm (Fig. 31.1) [31]. 

In another land of ideal flow reactor, all portions of the feed stream have the same residence time that is, there is no mixing in the axial direction but complete mixing radially. It is called a.plugflow reactor (PFR), or a tubular flow reactor (TFR), because this flow pattern is characteristic of tubes and pipes. As the reaction proceeds, the concentration falls off with distance. 

Selectivity A significant respect in which CSTRs may differ from batch (or PFR) reaclors is in the product distribution of complex reactions. However, each particular set of reactions must be treated individually to find the superiority. For the consecutive reactions A B C, Fig. 7-5b shows that a higher peak value of B is reached in batch reactors than in CSTRs as the number of stages increases the batch performance is approached. 

In a sequence of PFR and CSTR, better performance is obtained with the PFR last. Performance of reversible reactions is improved with the CSTR at a higher temperature. 

For the consecutive reactions A B C, a higher yield of intermediate B is obtained in batch reac tors or PFRs than in CSTRs. 

Simple combinations of reactor elements can be solved direc tly. Figure 23-8, for instance, shows two CSTRs in series and with recycle through a PFR. The material balances with an /i-order reaction / = /cC are... 

Although they are both flow reactors, there are large differences in the behavior of PFRs and CSTRs. The reaction rate decreases as the reactants are consumed. In piston flow, the reactant concentration gradually declines with increasing axial position. The local rate is higher at the reactor inlet than at the outlet, and the average rate for the entire reactor will correspond to some average composition that is between and In contrast, the entire... 

FIGURE 1.8 Comparison of reactor volume required for a given conversion for a first-order reaction in a PFR and a CSTR. 

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. 

Compare these results with those of Equation (2.22) for the same reactions in a batch reactor. The CSTR solutions do not require special forms when some of the rate constants are equal. A plot of outlet concentrations versus t is qualitatively similar to the behavior shown in Figure 2.2, and i can be chosen to maximize bout or Cout- However, the best values for t are different in a CSTR than in a PFR. For the normal case of bi = 0, the t that maximizes bout is a root-mean, t ix = rather than the log-mean of... 

Solution With Z>, = 0, a reaction wiU never start in a PFR, but a steady-state reaction is possible in a CSTR if the reactor is initially spiked with component B. An anal5dical solution can be found for this problem and is requested in Problem 4.12, but a numerical solution is easier. The design equations in a form suitable for the method of false transients are... 

There is an interior optimum. For this particular numerical example, it occurs when 40% of the reactor volume is in the initial CSTR and 60% is in the downstream PFR. The model reaction is chemically unrealistic but illustrates behavior that can arise with real reactions. An excellent process for the bulk polymerization of styrene consists of a CSTR followed by a tubular post-reactor. The model reaction also demonstrates a phenomenon known as washout which is important in continuous cell culture. If kt is too small, a steady-state reaction cannot be sustained even with initial spiking of component B. A continuous fermentation process will have a maximum flow rate beyond which the initial inoculum of cells will be washed out of the system. At lower flow rates, the cells reproduce fast enough to achieve and hold a steady state. 

Example 4.13 Determine the outlet concentration from a loop reactor as a function of Qi and q for the case where the reactor element is a PFR and the reaction is first order. Assume constant density and isothermal operation. 

Suppose you have two identical PFRs and you want to use them to make as much product as possible. The reaction is pseudo-first-order and the product recovery system requires a minimum conversion of 93.75%. Assume constant density. Do you install the reactors in series or parallel Would it affect your decision if the minimum conversion could be lowered ... 

The results of Example 5.2 apply to a reactor with a fixed reaction time, i or thatch- Equation (5.5) shows that the optimal temperature in a CSTR decreases as the mean residence time increases. This is also true for a PFR or a batch reactor. There is no interior optimum with respect to reaction time for a single, reversible reaction. When Ef < Ef, the best yield is obtained in a large reactor operating at low temperature. Obviously, the kinetic model ceases to apply when the reactants freeze. More realistically, capital and operating costs impose constraints on the design. 

Example 5.4 Determine the optimum reaction time for the consecutive reactions of Example 5.3 for the case where the operating temperature is specified. Consider both a CSTR and a PFR. 

Use Scalable Heat Transfer. The feed flow rate scales as S and a cold feed stream removes heat from the reaction in direct proportion to the flow rate. If the energy needed to heat the feed from to Tout can absorb the reaction exotherm, the heat balance for the reactor can be scaled indefinitely. Cooling costs may be an issue, but there are large-volume industrial processes that have Tin —40°C and Tout 200°C. Obviously, cold feed to a PFR will not work since the reaction will not start at low temperatures. Injection of cold reactants at intermediate points along the reactor is a possibility. In the limiting case of many injections, this will degrade reactor performance toward that of a CSTR. See Section 3.3 on transpired-wall reactors. 

Example 6.4 Find the best combination of reaction temperature and volume for the example reaction using isothermal and adiabatic PFRs. 

Compare the (unconstrained) optimal temperature profiles of 10-zone PFRs for the following cases where (a) the reactions are consecutive as per Equation (6.1) and endothermic (b) the reactions are consecutive and exothermic (c) the reactions are competitive as per Equation (6.6) and endothermic and (d) the reactions are competitive and exothermic. 

Determine the best two-zone PFR strategy for the competitive, endothermic reactions of Equation (6.6). 

If the enzyme charged to a batch reactor is pristine, some time will be required before equihbrium is reached. This time is usually short compared with the batch reaction time and can be ignored. Furthermore, 5o Eq is usually true so that the depletion of substrate to establish the equilibrium is negligible. This means that Michaelis-Menten kinetics can be applied throughout the reaction cycle, and that the kinetic behavior of a batch reactor will be similar to that of a packed-bed PFR, as illustrated in Example 12.4. Simply replace t with thatch to obtain the approximate result for a batch reactor. 

Unsteady behavior in an isothermal perfect mixer is governed by a maximum of -I- 1 ordinary differential equations. Except for highly complicated reactions such as polymerizations (where N is theoretically infinite), solutions are usually straightforward. Numerical methods for unsteady CSTRs are similar to those used for steady-state PFRs, and analytical solutions are usually possible when the reaction is first order. 

The difference between complete segregation and maximum mixedness is largest when the reactor is a stirred tank and is zero when the reactor is a PFR. Even for the stirred tank case, it has been difficult to find experimental evidence of segregation for single-phase reactions. Real CSTRs approximate perfect mixing when observed on the time and distance scales appropriate to industrial reactions, provided that the feed is premixed. Even with unmixed... 

Based on the kinetic mechanism and using the parameter values, one can analyze the continuous stirred tank reactor (CSTR) as well as the dispersed plug flow reactor (PFR) in which the reaction between ethylene and cyclopentadiene takes place. The steady state mass balance equations maybe expressed by using the usual notation as follows ... 

The kinetic parameters associated with the synthesis of norbomene are determined by using the experimental data obtained at elevated temperatures and pressures. The reaction orders with respect to cyclopentadiene and ethylene are estimated to be 0.96 and 0.94, respectively. According to the simulation results, the conversion increases with both temperature and pressure but the selectivity to norbomene decreases due to the formation of DMON. Therefore, the optimal reaction conditions must be selected by considering these features. When a CSTR is used, the appropriate reaction conditions are found to be around 320°C and 1200 psig with 4 1 mole ratio of ethylene to DCPD in the feed stream. Also, it is desirable to have a Pe larger than 50 for a dispersed PFR and keep the residence time low for a PFR with recycle stream. 

Runaway criteria developed for plug-flow tubular reactors, which are mathematically isomorphic with batch reactors with a constant coolant temperature, are also included in the tables. They can be considered conservative criteria for batch reactors, which can be operated safer due to manipulation of the coolant temperature. Balakotaiah et al. (1995) showed that in practice safe and runaway regions overlap for the three types of reactors for homogeneous reactions (1) batch reactor (BR), and, equivalently, plug-flow reactor (PFR), (2) CSTR, and (3) continuously operated bubble column reactor (BCR). 

Figure 5.4-69. Parallel reactions of different reaction order I SBR or PFR, 2 CSTR.

---