Ideal reactor first-order kinetics

Both batch and continuous stirred tank reactors are suitable for reactions that exhibit pseudo-zero-order kinetics with respect to the substrate concentration. In other words, under operating conditions the rate is more or less independent of the concentration of the substrate. However, for reactions where pseudo-first-order kinetics with respect to the concentrations of the substrates prevail, a batch tank reactor is preferred. Batch tank reactors are also ideally suited when there is a likelihood of the reactant slowly deactivating the catalyst or if there is a possibility of side product formation through a parallel reaction pathway. 

In contrast, suppose complete micromixing is assumed. Then, for the same RTD, an ideal stirred-tank reactor results. The conversion for a first-order reaction in this case is given by Eq. (4-7), which is identical to the above expression for segregated flow. This verifies the conclusion of Eq. (6-36) that the extent of micromixing does not affect conversion for first-order kinetics (as long as the correct RTD is used). The same develop-... 

The influence of heat transfer on yield and selectivity in scaling up batch and semibatch reactors will be illustrated using a series reaction, taking place in an ideal jacketed stirred-tank reactor. This reaction is composed of two irreversible elementary steps, both exothermic and both with first order kinetics ... 

Step 24. Calculate the outlet conversion of reactant A in an ideal plug-flow tubular reactor with pseudo-volumetric first-order kinetics and no residence-time distribution effects ... 

Notice that the final conversion for first-order kinetics in an ideal packed catalytic tubular reactor depends on interpellet porosity of the packed bed in the following manner ... 

When a reactor is charged with liquid A and B is a gas that is added continuously, it becomes a semibatch reactor. The rates of reaction depend on the concentration of B in the liquid phase, which is a function of gas solubility, pressure, and agitation conditions. However, we are often concerned with the relative reaction rates and the selectivity, which do not depend on Cb if the reaction orders are the same for both reactions. The reactions are treated as pseudo-first-order, and equations are developed for an ideal batch reactor with irreversible first-order kinetics... 

The chief weakness of RTD analysis is that from the diagnostic perspective, an RTD study can identify whether the mixing is ideal or nonideal, bnt it is not able to uniquely determine the namre of the nonideality. Many different nonideal flow models can lead to exactly the same tracer response or RTD. The sequence in which a reacting fluid interacts with the nonideal zones in a reactor affects the conversion and yield for all reactions with other than first-order kinetics. This is one limitation of RTD analysis. Another limitation is that RTD analysis is based on the injection of a single tracer feed, whereas real reactors often employ the injection of multiple feed streams. In real reactors the mixing of separate feed streams can have a profound influence on the reaction. A third limitation is that RTD analysis is incapable of providing insight into the nature... 

Thus, for known kinetics and a specified residence time distribution, we can predict the fractional conversion of reactant which the system of Fig. 9 would achieve. Recall, however, that this performance is also expected from any other system with the same E(t) no matter what detailed mixing process gave rise to that RTD. Equation (34) therefore applies to all reactor systems when first-order reactions take place therein. In the following example, we apply this equation to the design of the ideal CSTR and PFR reactors discussed in Chap. 2. The predicted conversion is, of course, identical to that which would be derived from conventional mass balance equations. 

Process Transfer Function Models In continuous time, the dynamic behaviour of an ideal continuous flow stirred-tank reactor can be modelled (after linearization of any nonlinear kinetic expressions about a steady-state) by a first order ordinary differential equation of the form... 

For first-order irreversible chemical kinetics in a packed catalytic tubular reactor (i.e., n = 1), ideal design strategies are justified if the relative difference... 

If one operates a packed catalytic tubular reactor below the critical value of the mass transfer Peclet number where ideal performance is not achieved, then the following empirical linear correlation allows one to predict the dimensionless molar density of reactant A in the exit stream, 4first-order irreversible chemical kinetics ... 

Ideal Isothermal Packed Catalytic Tubular Reactors with First-Order Irreversible Chemical Kinetics When the External Resistance to Mass Transfer Cannot Be Neglected... 

Figure 30-1 Effect of the mass transfer Peclet number and Pesimpie on dimensionless reactant molar density in the exit stream of a non-ideal packed catalytic tubular reactor with first-order irreversible chemical kinetics and significant external mass transfer resistance. The product of the interpellet Damkohler number, the effectiveness factor, and the catalyst filling factor is 1.

ANALYSIS OF FIRST-ORDER IRREVERSIBLE CHEMICAL KINETICS IN IDEAL PACKED CATALYTIC TUBULAR REACTORS WHEN THE EXTERNAL RESISTANCES TO HEAT AND MASS TRANSFER CANNOT BE NEGLECTED... 

Chin et al. (2007b) used pseudo-first order reaction kinetics combined with the ideal continuous stirred tank reactor (CSTR) model to evaluate the effect of initial concentration of pollutant on the performance of a submerged membrane photocatalytic reactor for the degradation of bisphenol A in water (Equation [21.2]) ... 

At the high recycling ratios the loop reactor operates as an ideal stirred-tank reactor. Therefore, the reaction rate can immediately be determined from the difference in concentration between the feed and the outlet, the throughput and the quantity of catalyst.The rate equation, describing the consumption of xylene and the formation of the reaction products, are considered to be pseudo first order. The parameter of the rate equations, which are the frequency factors and the activation energies, are determined by least square methods. In the above function (Fig. 6b) r is the measured rate, r is calculated with estimated parameters, w represent appropriate weight factors and N is the number of measured values. Because the rate equations could be differentiated v/ith respect to the unknown kinetic parameters, the objective function was minimized by a step-wise regression. 

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