Second order reactions residence time distributions

Part (c) in Example 15.15 illustrates an interesting point. It may not be possible to achieve maximum mixedness in a particular physical system. Two tanks in series—even though they are perfectly mixed individually—cannot achieve the maximum mixedness limit that is possible with the residence time distribution of two tanks in series. There exists a reactor (albeit semi-hypothetical) that has the same residence time distribution but that gives lower conversion for a second-order reaction than two perfectly mixed CSTRs in series. The next section describes such a reactor. When the physical configuration is known, as in part (c) above, it may provide a closer bound on conversion than provided by the maximum mixed reactor described in the next section. 

A vessel has a residence time distribution represented by the given equations. A second order reaction with C0 = 1 is conducted in this vessel and... 

Figure 17.3. Ratio of volumes of an n-stage CSTR battery and a segregated flow reactor characterized by a residence time distribution with variance a2 = 1/n. Second-order reaction.

Exercise 9.9.4. Show that the distribution function of residence times for laminar flow in a tubular reactor has the form 2z /Zp, where tp is the time of passage of any fluid annulus and the minimum time of passage. Diffusion and entrance effects may be neglected. Hence show that the fractional conversion to be expected in a second order reaction with velocity constant k is 2B[1 + j lnu5/(5 + 1)] where B = akt n and a is the initial concentration of both reactants. (C.U.)... 

Figure 5. Possible extremes of transient response to step change of reactant input concentration for second order reaction and selected values of kccT. The flow has the same residence time distribution as two perfectly mixed vessels in sequence. Solid curves complete segregation. Broken...

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we discuss assume that the residence-time distribution function may be attributed to one or the other of these flow situations. The first class of nonideal flow conditions leads to the segregated flow model of reactor performance. This model may be used with the residence-time distribution function to predict conversion levels accurately for first-order reactions that occur isothermally (see Section 11.2.1). The second... 

The catalytic dehydration of isopropanol was studied under tiansirat conditimis in a catalytic microreactor. The reaction is characterised by educt inhibition and shows a pronounced stop-effect . Therefore, the average productivity under forced poiodic operation can be considerably higher compared to the maximal productivity obtainable at steady state. For high rates of the sorption processes and surface reactions involved, the timal cycle time for the forced concentration variations lies in the order of seconds. As microreactors are characterized by low mass storage capacity and narrow residence time distribution, they are particularly suitable for periodic operation at relatively high fiequencies. Tis could be demonstrated in the present study. 

The liquid-phase, second-order reaction 2A —> R will be run in a continuous, agitated reactor that has the same residence time distribution as an ideal CSTR. At the operating conditions of the reactor, kCpjjX = 2.0, where k is the second-oiderrateconstantatreactortemperature, Cao is the inlet concentration of A, and r is the spacetime. 

Bimolecular reactions, such as those in Reactions 7.12-7.14, have second-order rate constants (k) typically on the order of 1-4 x 10 cm molecule" s H69). The number of collisions (Z collisions s ) that occur between cations and sample molecules in the Cl source can be estimated by multiplying the rate constant times the density of molecules in the source (N molecule cm ). At a pressure of 0.5 Torr and a temperature of 473 K, the density (N) is approximately 10 molecules/cm and therefore, Z = 1-4 x 10 collisions s The residence time (t) of most cations in a typical Cl source is on the order of 10 s. More details on the parameters that effect the residence time of cations are given in Section 7.4.3. The number of collisions a cation undergoes is approximately 100-400 collisions (Z x t). This range of collisions permits equilibria to be sufficiently established in order to assume a Boltzman distribution of internal energy of the cations. The clustering Reactions 7.15 have rate constants typically on the order of 10 cm molecule" s Note that this is a third-order rate constant since it depends on the total pressure of the Cl source. When a cation and a neutral molecule collide to form a complex [M- -C]+, it is initially in an excited state and must be stabilized by collisions with the reagent gas for observation. In the absence of such stabilization, the complex... 

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