Isothermal reactor with complex reaction

CSTRCOM - Isothermal Reactor with Complex Reaction... 

Isothermal Reactor with Complex Reaction 265 Continuous Stirred-Tanks, Tracer Experiment 273 Deactivating Catalyst in a CSTR 268 Distribution of an Insecticide in an Aquatic Ecosystem 581... 

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. 

In the following sections, we will discuss the synthesis of isothermal and nonisothermal reactor networks with complex reaction mechanisms. 

The basic idea in the synthesis approach of isothermal reactor networks with complex reaction mechanisms proposed by Kokossis and Floudas (1990) consists of... 

Trickle-bed reactors, wherein gas and liquid reactants are contacted in a co-current down flow mode in the presence of heterogeneous catalysts, are used in a large number of industrial chemical processes. Being a multiphase catalytic reactor with complex hydrodynamics and mass transfer characteristics, the development of a generalized model for predicting the performance of such reactors is still a difficult task. However, due to its direct relevance to industrial-scale processes, several important aspects with respect to the influence of external and intraparticle mass transfer effects, partial wetting of catalyst particles and heat effects have been studied previously (Satterfield and Way (1972) Hanika et. al., (1975,1977,1981) Herskowitz and Mosseri (1983)). The previous work has mainly addressed the question of catalyst effectiveness under isothermal conditions and for simple kinetics. It is well known that most of the industrially important reactions represent complex reaction kinetics and very often multistep reactions. Very few attempts have been made on experimental verification of trickle-bed reactor models for multistep catalytic reactions in the previous work. 

Sampling of a two-fluid phase system containing powdered catalyst can be problematic and should be considered in the reactor design. In the case of complex reacting systems with multiple reaction paths, it is important that isothermal data are obtained. Also, different activation energies for the various reaction paths will make it difficult to evaluate the rate constants from non-isothermal data. 

Most publications dealing with chromatographic reactors focus on theoretical issues of this very complex system. Models of different complexity were derived and used to predict the behavior of chromatographic reactors. Such models typically take into consideration different types of mass transfer, adsorption isotherms, flow profiles, and reactions. A general scheme of these models, not including the reaction, is presented in Fig. 4. There are also several review papers... 

The chemical engineer almost never encounters a single reaction in an ideal single-phase isothermal reactor. Real reactors are extremely complex with multiple reactions, multiple phases, and intricate flow patterns within the reactor and in inlet and outlet streams. An engineer needs enough information from this course to understand the basic concepts of reactions, flow, and heat management and how these interact so that she or he can begin to assemble simple analytical or intuitive models of the process. 

We have used CO oxidation on Pt to illustrate the evolution of models applied to interpret critical effects in catalytic oxidation reactions. All the above models use concepts concerning the complex detailed mechanism. But, as has been shown previously, critical. effects in oxidation reactions were studied as early as the 1930s. For their interpretation primary attention is paid to the interaction of kinetic dependences with the heat-and-mass transfer law [146], It is likely that in these cases there is still more variety in dynamic behaviour than when we deal with purely kinetic factors. A theory for the non-isothermal continuous stirred tank reactor for first-order reactions was suggested in refs. 152-155. The dynamics of CO oxidation in non-isothermal, in particular adiabatic, reactors has been studied [77-80, 155]. A sufficiently complex dynamic behaviour is also observed in isothermal reactors for CO oxidation by taking into account the diffusion both in pores [71, 147-149] and on the surfaces of catalyst [201, 202]. The simplest model accounting for the combination of kinetic and transport processes is an isothermal continuously stirred tank reactor (CSTR). It was Matsuura and Kato [157] who first showed that if the kinetic curve has a maximum peak (this curve is also obtained for CO oxidation [158]), then the isothermal CSTR can have several steady states (see also ref. 203). Recently several authors [3, 76, 118, 156, 159, 160] have applied CSTR models corresponding to the detailed mechanism of catalytic reactions. 

In a recent survey [19] it was noted that a realistic model for catalytic oxidation reactions must include equations describing the evolution of at least two concentrations of surface substances and account for the slow variation in the properties of the catalyst surface (e.g. oxidation-reduction). For the synchronization of the dynamic behaviour for various surface domains, it is necessary to take into consideration changes in the concentrations of gas-phase substances and the temperature of the catalyst surface. It is evident that, in the hierarchy of modelling levels, such models must be constructed and tested immediately after kinetic models. On the one hand, the appearance of such models is associated with the experimental data on self-oscillations in reactors with noticeable concentration variations of the initial substances and products (e.g. ref. 74) on the other hand, there was a gap between the comprehensively examined non-isothermal models with simple kinetics and those for the complex heterogeneous catalytic reactions... 

However, since the QSSA has been used to elucidate most reaction mechanisms and to determine most rate coefficients of elementary processes, a fundamental answer to the question of the validity of the approximation seems desirable. The true mathematical significance of QSSA was elucidated for the first time by Bowen et al. [163] (see also refs. 164 and 165 for history and other references) by means of the theory of singular perturbations, but only in the case of very simple reaction mechanisms. The singular perturbation theory has been applied by Come to reaction mechanisms of any complexity with isothermal CFSTR [118] and batch or plug flow reactors [148, 149]. The main conclusions arrived at for a free radical straight chain reaction (with only quadratic terminations) carried out in an isothermal reactor can be summarized as follows. 

Multiple steady states are not associated exclusively with temperature-dependent reactor operations. For some types of more complex reaction kinetics, steady-state multiplicity can exist under isothermal conditions. For example, Matsura and Rato [T. Matsura and M. Rato, Chem. Eng. Sci., 22, 171 (1967)]... 

Hydrogenation of citral was selected as an example, because it nicely illustrates a case with complex stoichiometry and kinetics, which is typical for fine chemicals. The stoichiometric scheme is displayed in Fig. 4. The reaction system is relevant for the manufacturing of fragrancies, since some of the intermediates, name citronellal and citronellol have a pleasant smell. Thus the optimization of the product yield is of crucial importance. Isothermal and isobaric experiments were carried under hydrogen pressure in the monolith reactor system at various pressures and temperatures (293-373K, 2-... 

In isothermal reactors the reaction rate constant is in principle the same throughout the reaction medium, so that relative simple calculation methods such as presented in Chapters 3 and 7 may be applied. When a reactor is well mixed, it is usually also isothermal, and this situation is the simplest to model. This is treated in section 8.3. For calculating conversions in reactors with temperature profiles, complex non-linear differential equations have to be solved, usually requiring complicated numerical calculation methods. These problems will be indicated briefly in section 8.4. 

In this chapter, the dynamics of ideally stirred tank reactors will be analyzed. First, the assumptions, required to limit model complexity, will be discussed. Next, various types of reaction will be considered such as simple first-order reactions, equilibrium reactions, parallel reactions, etc. Subsequently, the analysis will be expanded to include non-isothermal reactors. Numerical examples of chemical reactors are given and the non-linear model descriptions are compared with the linearized model descriptions. 

The various differential equations of Table 6.1 are nonlinear and eoupled, and, in principle, they must be solved numerically, which takes exeessive computational time. For isothermal reactors for time-invariant rate constants, it is possible to derive a complete analytical solution, which is given in Appendix 6.1. However, actual reactor performance is always nonisothermal in addition, rate constants (particularly kp and k ) are dependent on reaction parameters in a very complex way. Tables 6.2 and 6.3 show the physical properties and rate constants for polystyrene and polymethyl methacrylate systems. Several researchers have attempted to solve for the reactor performance for these systems, and all of them have reported that the differential equations of Table 6.1 (along with the energy balance relation) take excessive computational time. The following discussion minimizes this problem by using the isothermal solution presented in Appendix 6.1. 

Performing a reaction under isothermal conditions is somewhat more complex. It requires two temperature probes, one for the measurement of the reaction mass temperature and a second for the jacket temperature. Depending on the internal reactor temperature, the jacket temperature is adjustable. The simplest method is to use a single heat carrier circuit to act either on the flow rate of cooling water or on the steam valve. With a secondary heat carrier circulation loop, the temperature controller acts directly on the heating and cooling valves by using a conventional... 

The mathematical complexity involved with temperature variations has limited most of the studies cited in this paper to the isothermal case. Since few commercial polymerization reactor systems can or should operate isothermally, there is a clear need to develop techniques to permit fuller application of reaction engineering to nonisothermal systems. In polymerizations as in simpler reactions, changes in temperature or temperature profile can have larger effects on rate and distribution than even reactor type. 

Emulsion polymerization is usually carried out isothermally in batch or continuous stirred-tank reactors. Temperature control is much easier than for bulk or solution polymerization because the small ( 0.5 fim) polymer particles, which are the locus of the reaction, are suspended in a continuous aqueous medium. This complex, multiphase reactor also shows multiple steady states under isothermal conditions. In industrial practice, such a reactor often shows sustained oscillations. Solid-catalyzed olefin polymerization in a slurry batch reactor is a classic example of a slurry reactor where the solid particles change size and characteristics with time during the reaction process. 

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