Operating points chemical reactor

A cascade of three continuous stirred-tank reactors arranged in series, is used to carry out an exothermic, first-order chemical reaction. The reactors are jacketed for cooling water, and the flow of water through the cooling jackets is countercurrent to that of the reaction. A variety of control schemes can be employed and are of great importance, since the reactor scheme shows a multiplicity of possible stable operating points. This example is taken from the paper of Mukesh and Rao (1977). 

When a reactor is operating at steady state, the rate of energy release by chemical reaction must be equal to the sum of the rates of energy loss by convective flow and heat transfer to the surroundings. This statement was expressed in algebraic form in equations 10.3.4 and 10.4.6 for the CSTR and PFR, respectively. It will serve as the physical basis that we will use to examine the stability of various operating points. 

Chemical reactors intended for use in different processes differ in size, geometry and design. Nevertheless, a number of common features allows to classify them in a systematic way [3], [4], [9]. Aspects such as, flow pattern of the reaction mixture, conditions of heat transfer in the reactor, mode of operation, variation in the process variables with time and constructional features, can be considered. This work deals with the classification according to the flow pattern of the reaction mixture, the conditions of heat transfer and the mode of operation. The main purpose is to show the utility of a Continuous Stirred Tank Reactor (CSTR) both from the point of view of control design and the study of nonlinear phenomena. 

At some point in most processes, a detailed model of performance is needed to evaluate the effects of changing feedstocks, added capacity needs, changing costs of materials and operations, etc. For this, we need to solve the complete equations with detailed chemistry and reactor flow patterns. This is a problem of solving the R simultaneous equations for S chemical species, as we have discussed. However, the real process is seldom isothermal, and the flow pattern involves partial mixing. Therefore, in formulating a complete simulation, we need to add many additional complexities to the ideas developed thus far. We will consider each of these complexities in successive chapters temperature variations in Chapters 5 and 6, catalytic processes in Chapter 7, and nonideal flow patterns in Chapter 8. In Chapter 8 we will return to the issue of detailed modeling of chemical reactors, which include all these effects. 

The data given below are results of 25 design points performed at five temperatures and with five different time periods, with the idea of establishing effects of the given factors on conversion in a chemical reactor. To avoid inequality effects, five chemical reactors and five operators were included in the experiment. So, 25 design points were done in five reactors with five operators by design of experiment of a 5x5 Graeco-Latin square in such a way that each operator used each reactor only once at each temperature and for a constant conversion time period. Characters denote reactors and numbers the operators. Do the analysis of variance. 

In contrast to classical chemical reactors, a fuel cell provides the possibility to control the reaction rate directly from outside by setting the cell current, because the local cell current density and the local reaction rate are related by a constant factor. This operation of a fuel cell at constant cell current is more important than the potentiostatic operation from a technical point of view, as fuel cells typically are characterized by current-voltage plots. Because the integral Eq. (15) has to be included in the analysis, the investigation of the galvanostatic operation is more difficult and requires numerical methods. In the following, numerical bifurcation... 

The first issue is fulfilled if the plant does not operate in unstable points or dangerous conditions. In this process the most risky place is the chemical reactor, where hot spots may occur. There are fire and explosion risks too, but these should be normally managed by standard safety measures. 

In HTC, the reaction is conducted at the boiling point of EDC at 1.5 to 5 bar and 90 to 150 °C. In this manner the heat of reaction, which is seven times the heat of EDC vaporization, can be used advantageously for purification. The chemical reactor may be integrated as a reboiler of a distillation column, or designed as independent equipment (Figure 7.3b). A disadvantage of HTC would be lower selectivity, but some patents claim that modified catalysts and/or the use of inhibitors make possible operation up to 150 °C. 

Chemical reactors are inherently nonlinear in character. This is primarily due to the exponential relationship between reaction rate and temperature but can also stem from nonlinear rate expressions such as Eqs. (4.10) and (4.11). One implication of this nonlinearity for control is the change in process gain with operating conditions. A control loop tuned for one set of conditions can easily go unstable at another operating point. Related to this phenomenon is the possibility of open-loop instability and multiple steady states that can exist when there is material and/or thermal recycle in the reactor. It is essential for the control engineer to understand the implications of nonlinearities and what can be done about them from a control standpoint as well as from a process design standpoint. 

Step 3 of our plantwide control design procedure involves two activities. The first is to design the control loops for the removal of heat from exothermic chemical reactors. We dealt with this problem in Chap. 4, where we showed various methods to remove heat from exothermic reactors and how to control the temperature in such reactors. At that point we assumed that the heat was removed directly and permanently from the process (e.g., by cooling water). How-ever. it is wasteful to discard the reactor heat to plant utilities when we need to add heat in other unit operations within the process. Instead, a more efficient alternative is to heat-integrate various parts of the plant by the use of process-to-process heat exchangers. 

For db/dt > 0.6, the bed operates in the slugging regime which is not very interesting from a chemical reactor engineering point of view. 

In many chemical plants the main reaction is a highly exothermic one. Consequently, the hot reactor effluent is often used to preheat the feed to the reactor (Figure 25.2a). Such feed-effluent heat exchange may lead to serious stability problems in the operation of the reactor. In particular, if 7/ is the temperature of the feed to the reactor, the temperature of the reactor effluent Tr follows the sigmoidal curve shown in Figure 25.2b. Furthermore, a heat balance around the heat exchanger shows that 7 depends linearly on T, (Figure 25.2b). Therefore, the steady-state operation will correspond to one of the three possible points Pi, Pi, or Pi, where the two lines intersect. 

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