Reactor dynamic behavior

IV. Continuous Stiired-Tank Reactors Dynamic Behavior 339... 

Numerical simulations allowed the reproduction of the reactor s dynamic behavior, mainly the thermal balance. Despite the differences between the models, both models reproduced almost in the same way in terms of the reactor and coolant fluid temperature dynamic profiles. Regarding the use of a specific model, the authors advise to take into account some points if the internal heat and mass-transfer coefficients of the catalyst particles are significant. Dynamic Model I is more suitable to represent the reactor dynamic behavior in case of difficulties in the measurement of such parameters. Dynamic Model II must be chosen. For design and simulation studies, where computational time and numeric difficulties for model solution are not limiting factors. Dynamic Model I is the most reliable however, if the same factors are limiting. Dynamic Model II should be the best alternative. 

The model that best describes the mechanism is usually very complicated. For dynamic studies that require much more computation (and on a more limited domain) a simplified model may give enough information as long as the formalities of the Arrhenius expression and power law kinetics are incorporated. To study the dynamic behavior of the ethylene oxide reactor. 

The analysis of the transient behavior of the packed bed reactor is fairly recent in the literature 142-145)- There is no published reactor dynamic model for the monolith or the screen bed, which compares well with experimental data. 

The four main parameters that are important to transpose a reaction from batch reactor to continuous HEX reactor are thermal behavior, hydrodynamics, reactor dynamics, and residence time. 

There are three general stimulus techniques commonly used in theoretical and experimental analyses of reactor networks in order to characterize their dynamic behavior. 

State estimators are used to provide on-line predictions of those variables that describe the system dynamic behavior but cannot be directly measured. For example, suppose we have a chemical reactor and can measure the temperature in the reactor but not the compositions of reactants or products. A state estimator could be used to predict these compositions. 

F. Teymour and W.H. Ray. The dynamic behavior of continuous solution polymerization reactors-IV. Dynamic stabihty and bifurcation analysis of an experimental reactor. Chem. Eng. Sci., 44(9) 1967-1982, 1989. 

Fig. 1. Configuration or alkylation reactors. The refrigeration system basically consists in compressor and depropanizer. The main contribution is the design of an approach to the robust control temperature via heat reaction compensation. Thus, dynamical behavior of the refrigeration system is not considered.

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. 

One approach to developing mathematical models is to begin with one that contains a relatively detailed description of the physical system and then to derive simpler models by identifying those elements that can be approximated while still retaining the essential behavior of the system (see, for example, Aris, 1978). This is the approach that we will follow here. Our particular interest will be in deriving mathematical models of packed bed reactors that are appropriate for use in designing control systems. Thus, we will be interested in models capable of simulating dynamic behavior. 

Figure 21 shows the simulated dynamic behavior of the gas temperatures at various axial locations in the bed using both the linear and nonlinear models for a step change in the inlet CO concentration from a mole fraction of 0.06 to 0.07 and in the inlet gas temperature from 573 to 593 K. Figure 22 shows the corresponding dynamic behavior of the CO and C02 concentrations at the reactor exit and at a point early in the reactor bed. The axial concentration profiles at the initial conditions and at the final steady state using both the linear and nonlinear simulations are shown in Fig. 23. The temporal behavior of the profiles shows that the discrepancies between the linear and nonlinear results increase as the final steady state is approached. Even so, there are only slight differences (less than 2% in concentrations and less than 0.5% in temperatures) in the profiles throughout the dynamic responses and at the final steady state even for this relatively major step-input change.

Finally, in the last section of this chapter, we will introduce the simplest approach for modeling the dynamic behavior of organic compounds in laboratory and field systems the one-box model or well-mixed reactor. In this model we assume that all system properties and species concentrations are the same throughout a given volume of interest. This first encounter with dynamic modeling will serve several pur-... 

Each reactor type has its characteristic hydrodynamic behavior. Knowledge of the hydro-dynamic behavior as well as its mass transfer characteristics is important for evaluating experimental results. Table 2-4 summarizes characteristic features of five important reactor types. 

An example of didactic distortion is the drawing of the phase-planes in Fig. 6, taken from A. Uppal, W. H. Ray, and A. B. Poore. On the dynamic behavior of continuous stirred tank reactors. Chem. Eng. Set 29, 967 (1974). 

Uppal, A., Ray, W. H. and Poore, A. B., 1976, The classification of the dynamic behavior of continous stirred tank reactors—influence of reactor residence time. Chem. Engng ScL 31, 205-214. 

One may be curious to know at which stable steady state a given CSTR is operating. This cannot be decided from the outside. The behavior of the reactor is determined by its previous history. This is a nonphysical and nonchemical initial condition for the reactor. The answer depends upon the dynamic behavior and the initial conditions of the system, and this will be discussed later. 

Bifurcation and Dynamic Behavior of Fluidized Bed Catalytic Reactors... 

Many chemical and biological processes are multistage. Multistage processes include absorption towers, distillation columns, and batteries of continuous stirred tank reactors (CSTRs). These processes may be either cocurrent or countercurrent. The steady state of a multistage process is usually described by a set of linear equations that can be treated via matrices. On the other hand, the unsteady-state dynamic behavior of a multistage process is usually described by a set of ordinary differential equations that gives rise to a matrix differential equation. 

In this section we develop a dynamic model from the same basis and assumptions as the steady-state model developed earlier. The model will include the necessarily unsteady-state dynamic terms, giving a set of initial value differential equations that describe the dynamic behavior of the system. Both the heat and coke capacitances are taken into consideration, while the vapor phase capacitances in both the dense and bubble phase are assumed negligible and therefore the corresponding mass-balance equations are assumed to be at pseudosteady state. This last assumption will be relaxed in the next subsection where the chemisorption capacities of gas oil and gasoline on the surface of the catalyst will be accounted for, albeit in a simple manner. In addition, the heat and mass capacities of the bubble phases are assumed to be negligible and thus the bubble phases of both the reactor and regenerator are assumed to be in a pseudosteady state. Based on these assumptions, the dynamics of the system are controlled by the thermal and coke dynamics in the dense phases of the reactor and of the regenerator. 

The polymerization of ethylene is a highly exothermic reaction and when highly exothermic reactions occur in fluidized-bed reactors, unusual steady state and dynamic behavior may occur. 

The dynamic behavior of fixed-bed reactors has not been extensively investigated in the literature. Apparently the only reaction which has received close attention is the oxidation over platinum catalysts. The investigations reveal interesting and complex dynamic behavior and show the occurrence of oscillatory and chaotic behavior [88-90], It is easy to speculate that further studies of the dynamic behavior of catalytic/biocatalytic reactions will reveal similar complex dynamics like those discovered for the CO oxidation over a Pt catalyst, since most of these phenomena are due to nonmonotonicity of the rate process which is widespread in catalytic systems. 

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