Dynamics of the Reactor

A much more interesting case of chaotic dynamics of the reactor can be obtained from the study of the self-oscillating behavior. Consider the simplified mathematical model (8) and suppose that the reactor is in steady state with a reactant concentration of Prom Eq.(8) the equilibrium point [x, y ] can be deduced as follows ... 

The non-linear dynamics of the reactor with two PI controllers that manipulates the outlet stream flow rate and the coolant flow rate are also presented. The more interesting result, from the non-linear d mamic point of view, is the possibility to obtain chaotic behavior without any external periodic forcing. The results for the CSTR show that the non-linearities and the control valve saturation, which manipulates the coolant flow rate, are the cause of this abnormal behavior. By simulation, a homoclinic of Shilnikov t3rpe has been found at the equilibrium point. In this case, chaotic behavior appears at and around the parameter values from which the previously cited orbit is generated. 

The thermal characteristics of a reaction, including its heat production rate, the necessary cooling power, and the reactant accumulation, are fundamental for safe reactor operation and process design. A successful scale-up is achieved, only when the different characteristic time constants of the process, such as reaction kinetics, thermal dynamics of the reactor, and its mixing characteristics are in good agreement [9]. If we focus on the reaction kinetics and thermal dynamics, that is, we consider that the reaction rate is slow compared to the mixing rate, in principle, there are two ways to predict the behavior of the industrial reactors ... 

From (5.15) it can be argued that the heat released by the reaction affects the dynamics of the reactor temperature via the term... 

Flow modeling is an excellent tool for enhancing the performance of any process vessel. Applying such a technique to reactors can be especially fruitful, because of reactors central role in chemical processes. In most reactor-design situations, the reactions and the catalysis system are set beforehand. For any given combination of them, reactor performance becomes a complex function of the underlying transport processes. These in turn are governed by the fluid dynamics of the reactor. 

Equation (4.36) is a non-stiff model that approximates the dynamics of the reactor-condenser system in Figure 4.1 in the original (fast) time scale t. 

Using the symbolic calculation engine available in Matlab ,2 we obtained the following description of the intermediate dynamics of the reactor-condenser process ... 

In the second experiment the reactor feeds were inverted, that is the first feed and the second feed contained 800 and 100 mM of acrylonitrile, respectively. The dynamics of the reactor remained identical (constant flow rate) and the times needed to achieve the first and second steady states in the reactor (fi, t in the scheme) were similar. Interestingly, the inactivation constant evaluated in... 

In order to be uniformly filled in a commercial reactor without causing flow distribution problems, an industrial catalyst must be formed in a certain shape and size. The specifications for catalyst size, shape, and mechanical strength are decided in accordance with the energy balance, pressure drop, and flow dynamics of the reactor design. 

The model used in this section neglects the time delays due to recycles and the capacity of the mixing vessels. Consequently, the model is obtained by the combination of the differential equations describing the dynamics of the reactor and the closed-loop separation. F and c are molar flow rate and reactant concentration, respectively. Dimensionless values are denoted by /=c/c and z=F/Fo with reference to process inlet. Subscripts follow the numbering explained in Fig. 13.18. When two reactants are involved, a second subscript is used. Because high purity product C4 = Z4 = 0. 

Measurements Excite the dynamics of the reactor, e.g. by increasing or decreasing the input flow rate during a short time period, and observe the relaxation back to the equilibrium. During this relaxation phase, measure... 

In spite of the widespread use of fixed-bed reactors, much remains to be done to define the dynamics of the reactor [30], Most of these reactors are operated in the concurrent mode at which the gas and the liquid both flow from the top to the bottom. A number of flow regimes have been distinguished for packed columns in downflow operation [31, 32], Based on the Reynolds number for liquid and gas flows, the flow regimes include (i) trickle flow, (ii) pulsed flow, (iii) dispersed bubble flow, (iv) wavy flow, and (v) spray flow (Figure 12.7) [17]. In general, countercurrent flows lead to much larger pressure drops across the bed, and this would be the case for FTS. Thus, the countercurrent flow mode is not used in today s plants. 

Figure XIX-6 (a) and (b) presents the scheme of heat removal to the PHRS tank and the dynamics of the reactor parameters (the quantity of water in the tank, and maximum temperature of the fuel element cladding) during 120 hours of the accident, corresponding to the water tank volume of 250 m. ...

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