Isothermal CSTR

To understand this, consider the following case which is limited to a homogeneous reaction executed in an isothermal CSTR as shown in Figure 9.1.1. Isothermal here means feed and discharge are at the reaction temperature, and all heat is removed by heat transfer through the walls. 

Tha heat removed includes the heal carried by the sensible heat of the reacting fluid also. If the feed was at a lover temperature than the reactor then q,d = (F/ V ) p c (T - To). For the example it was assumed that T - To 0 for simplicity sake as the isothermal CSTR. 

Example 14.1 shows how an isothermal CSTR with first-order reaction responds to an abrupt change in inlet concentration. The outlet concentration moves from an initial steady state to a final steady state in a gradual fashion. If the inlet concentration is returned to its original value, the outlet concentration returns to its original value. If the time period for an input disturbance is small, the outlet response is small. The magnitude of the outlet disturbance will never be larger than the magnitude of the inlet disturbance. The system is stable. Indeed, it is open-loop stable, which means that steady-state operation can be achieved without resort to a feedback control system. This is the usual but not inevitable case for isothermal reactors. 

Suppose the following reactions are occurring in an isothermal CSTR ... 

Single Isothermal CSTR with complex reaction... 

A reaction with rate equation, r = k C2/ (1 + k2C), is to be conducted in an isothermal CSTR, Examine the possibility of the occurrence of more than one steady state conversion. 

M perfectly mixed, isothermal CSTR has an outlet weir. The flow rate over the weir proportional to the height of hquid over the weir, h, to the 1.5 power. The weir height is. The cross-sectional area of the tank is A. Assume constant density. 

Benzene is nitrated in an isothermal CSTR in three sequential irreversible reactions ... 

The equations describing the series of three isothermal CSTRs were developed in Sec. 3.2. 

Example 9Ji, Consider the isothermal CSTR of Example 6.6. The equation describing the system in terms of perturbation variables is... 

Two isothermal CSTRs are conneaed by a long pipe that acts like a pure deadtime of D minutes at the steadystate flow rates. Assume constant throughputs and holdups and a first-order irreversible reaction... 

Our old friend the three-isothermal CSTR process has the following openloop transfer function relating controlled and manipulated variables ... 

If a proportional controller is used in the three-isothermal CSTR process, a controller gain of 22.6 gives a phase margin of 45°. A gain of 20 gives a maximum closedloop log modulus of +2 dB with a closedloop resonant frequency of 1.1 radian per minute. 

D.D. Bruns and J.E. Bailey. Nonlinear feedback control for operating a non-isothermal CSTR near an unstable steady state. Chem. Eng. Sci., 32 257-264, 1977. 

We took the 4- sign on the square root term for second-order kinetics because the other root would give a negative concentration, which is physically unreasonable. This is true for any reaction with nth-order kinetics in an isothermal reactor There is only one real root of the isothermal CSTR mass-balance polynomial in the physically reasonable range of compositions. We will later find solutions of similar equations where multiple roots are found in physically possible compositions. These are true multiple steady states that have important consequences, especially for stirred reactors. However, for the nth-order reaction in an isothermal CSTR there is only one physically significant root (0 < Ca < Cao) to the CSTR equation for a given T. ... 

AUTOCATALYSIS IN WELL-STIRRED OPEN SYSTEMS THE ISOTHERMAL CSTR... 

REACTION IN A NON-ISOTHERMAL CSTR STATIONARY STATES AND SINGULARITY THEORY... 

For instance, if we consider the simple case of the adiabatic non-isothermal CSTR, the stationary-state condition is given by eqn (7.27). Writing x for the extent of reaction, we have... 

Now that the recipes for locating the various changes in the qualitative form of the stationary-state locus have been presented, we can go on to examine the origin of the behaviour in the cubic autocatalytic system with the additional uncatalysed step, and for the non-adiabatic non-isothermal CSTR which has been asserted in previous sections. 

OSCILLATORY BEHAVIOUR IN THE ISOTHERMAL CSTR AUTOCATALYTIC SYSTEMS... 

Three model kinetic schemes have been studied relatively intensively with periodic forcing the first-order non-isothermal CSTR of chapter 7 the Brusselator model, which is closely related to the cubic autocatalysis of chapters 2 and 3 and the surface reaction model discussed in 12.6. We will use the last of these to introduce some of the general features. 

The specific models we will analyse in this section are an isothermal autocatalytic scheme due to Hudson and Rossler (1984), a non-isothermal CSTR in which two exothermic reactions are taking place, and, briefly, an extension of the model of chapter 2, in which autocatalysis and temperature effects contribute together. In the first of these, chaotic behaviour has been designed in much the same way that oscillations were obtained from multiplicity with the heterogeneous catalysis model of 12.5.2. In the second, the analysis is firmly based on the critical Floquet multiplier as described above, and complex periodic and aperiodic responses are observed about a unique (and unstable) stationary state. The third scheme has coexisting multiple stationary states and higher-order periodicities. 

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