Plug-flow reactors with heat exchange

Thus, the zone model of a reactor implies a combination of sequentially connected adiabatic (autothermal) quasi-isothermal turbulent plug flow reactors and heat exchange elements with external heat removal. 

For average MW and MWD of the polymer obtained in the sequentially connected quasi-isothermal adiabatic turbulent plug flow reactors and heat exchangers with external heat removal, the following relations are true [2] ... 

Just as we approached reactor control in Chap. 4, we will start by exploring the open-loop effects of thermal feedback. Consider Fig. 5.19, which shows an adiabatic plug-flow reactor with an FEHE system. We have also included two manipulated variables that wall later turn out to be useful to control the reactor. One of these manipulated variables is the heat load to the furnace and the other is the bypass around the preheater. It is clear that the reactor feed temperature is affected by the bypass valve position and the furnace heat load but also by the reactor exit temperature through the heat exchanger. This creates the possibility for multiple steady states. We can visualize the different... 

Figure 5.19 Adiabatic plug-flow reactor with feed-effluent heat exchanger and trim heater.

For the phenomena presented in Table 2.1, efficiency can be related to characteristic times by writing a balance of the extensity concerned. For a chemical plug-flow reactor (with an apparent first-order reaction or with heat/mass transfer at constant exchange coefficient), the quantity of this extensity is linearly related to its variation with respect to the reference time, yielding ordinary differential equations such as... 

With Heat Transfer. The tubular reactor is constructed in a similar way as a tube-in-shell heat exchanger or a fired furnace. Process fluid flows inside the tubes and is cooled or heated by the heat transfer medium within the shell. Radial temperature gradients are inherent in tubular reactors with heat transfer, so the plug flow assumption... 

Because of the need to provide a desired inlet temperature in plug flow reactor (PFR) systems, the cold feedstream often needs to be heated. Also the hot effluent stream from the reactor usually needs to be cooled before sending it to the separation section. A heat exchanger network is typically used to preheat the cold feed with the hot reactor effluent. 

The flow of heat across the heat-transfer surface is linear with both temperatures, leaving the primary loop with a constant gain. Using the coolant exit temperature as the secondary controlled variable as shown in Fig. 8-55 places the jacket ( mamics in the secondary loop, thereby reducing the period of the primary loop. This is dynamically advanti reous for a stirred-tank reactor because of the slow response of its large heat capacity. However, a plug flow reactor cooled by an external heat exchanger lacks this heat capacity and requires the faster response of the coolant inlet temperature loop. 

Most of the simulators allow heat input or removal from a plug-flow reactor. Heat transfer can be with a constant wall temperature (as encountered in a fired tube, steam-jacketed pipe, or immersed coil) or with counter-current flow of a utility stream (as in a heat exchanger tube or jacketed pipe with cooling water). 

Reactors are mostly not isothermal, as heat is consumed or released, and perfect mixing or a perfect heat exchange with the surrounding is impossible. However, some reactors are almost isothermal, such as, for example, a well-mixed continuous stirred tank reactor (CSTR). In a batchwise operated stirred tank or in a plug-flow reactor (PFR), isothermal conditions with regard to reaction or residence time (axial position), respectively, are hard to realize. However, the assumption of an isothermal system is helpful for a first examination of reactor types as it simplifies the equations and we can focus on concentration and mixing effects only. Thus, here, we inspect isothermal reactors. Thermal effects are considered in Section 4.10.3. 

In these processes the state variables are not only a function of time but also of the location. Distributed processes possess variables that are continuously distributed with respect to the location. Examples are heat exchangers, plug flow reactors and packed separation columns. These processes can be divided into hypothetical sections in series. 

A typical plug flow reactor could be a tube packed with some solid material (frequently a catalyst). Typically these types of reactors are called packed bed reactors or PBR s. Sometimes the tube will be a tube in a shell and tube heat exchanger. 

Simpler optimization problems exist in which the process models represent flow through a single pipe, flow in parallel pipes, compressors, heat exchangers, and so on. Other flow optimization problems occur in chemical reactors, for which various types of process models have been proposed for the flow behavior, including well-mixed tanks, tanks with dead space and bypassing, plug flow vessels, dispersion models, and so on. This subject is treated in Chapter 14. 

In an adiabatic fixed bed, heat is not exchanged with the environment through the reactor wall. Note that for the derivation of eq. (5.226), it has been assumed that the flow is ideal plug flow and thus the radial dispersion term is eliminated in an adiabatic fixed bed, the assumption of perfect radial mixing is not necessary since no radial gradients exist. 

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