CSTRs multiple reactions

The reaction of Example 7.4 is not elementary and could involve shortlived intermediates, but it was treated as a single reaction. We turn now to the problem of fitting kinetic data to multiple reactions. The multiple reactions hsted in Section 2.1 are consecutive, competitive, independent, and reversible. Of these, the consecutive and competitive t5T>es, and combinations of them, pose special problems with respect to kinetic studies. These will be discussed in the context of integral reactors, although the concepts are directly applicable to the CSTRs of Section 7.1.2 and to the complex reactors of Section 7.1.4. 

The fed-batch scheme of Example 14.3 is one of many possible ways to start a CSTR. It is generally desired to begin continuous operation only when the vessel is full and when the concentration within the vessel has reached its steady-state value. This gives a bumpkss startup. The results of Example 14.3 show that a bumpless startup is possible for an isothermal, first-order reaction. Some reasoning will convince you that it is possible for any single, isothermal reaction. It is not generally possible for multiple reactions. 

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

It is readily apparent that equation 8.3.21 reduces to the basic design equation (equation 8.3.7) when steady-state conditions prevail. Under the presumptions that CA in undergoes a step change at time zero and that the system is isothermal, equation 8.3.21 has been solved for various reaction rate expressions. In the case of first-order reactions, solutions are available for both multiple identical CSTR s in series and individual CSTR s (12). In the case of a first-order irreversible reaction in a single CSTR, equation 8.3.21 becomes... 

Multiple Reactions—Choosing a reactor type to obtain the best selectivity can often be made by inspection of generalized cases in reaction engineering books. A quantitative treatment of selectivity as a function of kinetics and reactor type (batch and CSTR) for various multiple reaction systems (consecutive and parallel) is presented in [168]. 

In this chapter we consider the performance of isothermal batch and continuous reactors with multiple reactions. Recall that for a single reaction the single differential equation describing the mass balance for batch or PETR was always separable and the algebraic equation for the CSTR was a simple polynomial. In contrast to single-reaction systems, the mathematics of solving for performance rapidly becomes so complex that analytical solutions are not possible. We will first consider simple multiple-reaction systems where analytical solutions are possible. Then we will discuss more complex systems where we can only obtain numerical solutions. 

These are two coupled algebraic equations, which must be solved simultaneously to determine the solutions Cj(x) and T(t). For multiple reactions the + 1 equations are easily written down, as are the differential equations for the transient situation. However, for these situations the solutions are considerably more difficult to find We will in fact consider theaolutions of the transient CSTR equations in Chapter 6 to describe phase-plane trajectories and the stability of solutions in the nonisothermal CSTR. 

For multiple reactions similar arguments hold. For multiple reactions in the CSTR in which A is a reactant v/ = -1) in all reactions, we can write... 

Multiple Isothermal CSTRs in Series with Reaction A -> B... 

The CSTR is particularly useful for reaction schemes that require low concentration, such as selectivity between multiple reactions or substrate inhibition in a chemostat (see Section IV). The reactor also has applications for heterogeneous systems where high mixing gives high contact time between phases. Liquid-liquid CSTRs are used for the saponification of fats and for suspension and emulsion polymerizations. Gas-liquid mixers are used for the oxidation of cyclohexane. Gas homogeneous CSTRs are extremely rare. 

In a recycle reactor, part of the exit stream is recycled back to the inlet of the reactor. For a stirred-tank reactor, recycle has no effect on conversion, since we are essentially just mixing a mixed reactor. For a plug flow reactor, the effect of recycle is to approach the performance of a CSTR. This is advantageous for certain applications such as autocatalytic reactions and multiple reaction situations where we have a PFR but really require a CSTR. 

It is worthwhile to compare the conversion obtained in an isothermal plug flow reactor with that obtained in a CSTR for given reaction kinetics. A fair comparison is given in Fig. 7.3 for irreversible first-order kinetics by showing the conversion obtained in both reactors as a function of To- The conversion of A obtained in a plug flow reactor is higher than that obtained in a CSTR. This holds for every positive partial reaction order with respect to A. For multiple reactions selectivities and yield enter into the picture. 

For the multiple reactions and conditions described in Example 6-6, calculate the conversion of hydrogen and mesitylene along with the exidng concentrations of mesitylene, hydrogen, and xylene in a CSTR,... 

For q multiple reactions and m species, the CSTR energy balance becomes... 

I m not talidng about fun you can have at an amusement park, but CRE fun. Now that we have an understanding on how to solve for the exit concentrations of multiple reactions in a CSTR and how to plot the species concentration down the length of a PER or PER, we can address one of the most important and fun areas of chemical reaction engineering. This area, discussed in Section 6.1, is learning how to maximize the desired product and minimize the undesired product. It is this area that can make or break a chemical process financially. It is also an area that requires creativity in designing the reactor schemes and feed conditions that will maximize profits. Here you can mix and match reactors, feed steams, and side streams as well as vary the ratios of feed concentration in order to maximize or minimize the selectivity of a particular species. Problems of this type are what I call digital-age problems - because... 

After studying this chapter the reader will be able to describe the cumulative F(t), external age E(t), and internal age I(t) residence-time distribution functions and to recognize these functions for PFR, CSTR, and laminar flow reactions. The reader will also be able to apply these functions to calculate the conversion and concentrations exiting a reactor using the segregation model and the maximum mixedness model for both single and multiple reactions. 

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