CSTRs with multiple reactions

As discussed in Chapter 4, to describe the operation of a CSTR with multiple reactions, we have to write Eq. 8.1.1 for each independent chemical reaction. The solution of the design equations (the relationships between Z Js and t) provide the reaction operating curves and describe the reactor operation. To solve the design equations, we have to express the rates of the chemical reactions that take place in the reactor in terms of Z s and t. Below, we derive the auxiliary relations used in the design equations. 

Below, we describe the design formulation of isothermal CSTRs with multiple reactions for various types of chemical reactions (reversible, series, parallel, etc.). In most cases, we solve the equations numerically using mathematical software. In some simple cases, we obtain anal5dical solutions. 

The design formulation of nonisothermal CSTRs with multiple reactions follows the same procedure outlined in the previous section—we write the design equation, Eq. 8.1.1, for each independent reaction. However, since the reactor temperature, out> is not known, we should solve the design equations simultaneously with the energy balance equation (Eq. 8.1.14). 

Design and operation of isothermal CSTRs with multiple reactions. 

Figure 6.9 Operating conditions for a CSTR with multiple reactions. Diiferent steady-state possibilities are illustrated by lines A, B, and C.

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. 

Equation 4.3.22 is the reaction-based design equation for CSTRs, written for the mth-independent reaction. To describe the operation of the reactor with multiple reactions, we have to write Eq. 4.3.22 for each independent reaction. 

In the remainder of the chapter, we discuss how to apply the design equations and the energy balance equations to determine various quantities related to the operations of CSTRs. In Section 8.2 we examine isothermal operations with single reactions to illustrate how the rate expressions are incorporated into the design equation and how rate expressions are determined. In Section 8.3, we expand the analysis to isothermal operations with multiple reactions. In Section... 

Exercise 6.3 CSTR energy balance with multiple reactions Ailyl chioxlde Is to be produced in a 0.83 CSTR 120]... 

Aris et al. have primarily analyzed whether the steady-state multiplicity features in a CSTR arising from a cubic rate law also can arise for a series of successive bimolecular reactions [26]. Aris et al. have showed that the steady-state equations for a CSTR with bimolecular reactions scheme reduces to that with a cubic reaction scheme when two parameters e(=k,Cg/k j) and K(=kjC /k j) arising in system equations for the bimolecular reactions tend to zero. Aris et al. have shown that the general multiplicity feature of the CSTR for bimolecular reactions is similar to that of the molecular reactions only at smaller value of e and K. The behavior is considerably different at larger values of e and K. Chidambaram has evaluated the effect of these two parameters (e and K) on the periodic operation of an isothermal plug flow reactor [18]. 

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 experiments and the simulation of CSTR models have revealed a complex dynamic behavior that can be predicted by the classical Andronov-Poincare-Hopf theory, including limit cycles, multiple limit cycles, quasi-periodic oscillations, transitions to chaotic dynamic and chaotic behavior. Examples of self-oscillation for reacting systems can be found in [4], [17], [18], [22], [23], [29], [30], [32], [33], [36]. The paper of Mankin and Hudson [17] where a CSTR with a simple reaction A B takes place, shows that it is possible to drive the reactor to chaos by perturbing the cooling temperature. In the paper by Perez, Font and Montava [22], it has been shown that a CSTR can be driven to chaos by perturbing the coolant flow rate. It has been also deduced, by means of numerical simulation, that periodic, quasi-periodic and chaotic behaviors can appear. 

Continuous reactions in a non-isothermal CSTR-I. Multiplicity of steady states (with P. Cicarelli). Chem. Eng. Sci. 49,621-631 (1994). 

Multiple CSTRs with Reversible Exothermic Reactions... 

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,... 

Thermal stability of chemical reactors is a classic yet active area within chemical engineering science. Considerable research has focused on determining safe operating criteria for batch, CSTR, and tubular reactors. Current work has been directed towards understanding thermal stability in the presence of multiple phases (fluid/solid and gas/liquid) and multiple reactions with realistic, complex reaction rates expressions. The advent of computational methods has allowed for this field to continue to thrive. A sound understanding of these principles may help improve industrial reactor performance by reducing waste and costly separation operations and help maintain a clean environment. 

Example H-5 Piwluetion of Ac etic Anhydride Example 8-9 CSTR with CooUna Coil Example H-IO Parallel Reaction in a PER with Heat Effects Example H-H Multiple Reactions in a CSTR... 

The occurrence of multiple steady states can be illustrated at best by a CSTR in which a high exothermic reaction takes place. A simple method is to examine separately the behaviour of the two terms of the energy balance heat generated by reaction, and heat transferred from the reactor. The heat generated is proportional with the reaction rate and the thermal effect ... 

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