Ideal reactors piston flow

There are two important types of ideal, continuous-flow reactors the piston flow reactor or PFR, and the continuous-flow stirred tank reactor or CSTR. They behave very diflerently with respect to conversion and selectivity. The piston flow reactor behaves exactly like a batch reactor. It is usually visualized as a long tube as illustrated in Figure 1.3. Suppose a small clump of material enters the reactor at time t = 0 and flows from the inlet to the outlet. We suppose that there is no mixing between this particular clump and other clumps that entered at different times. The clump stays together and ages and reacts as it flows down the tube. After it has been in the piston flow reactor for t seconds, the clump will have the same composition as if it had been in a batch reactor for t seconds. The composition of a batch reactor varies with time. The composition of a small clump flowing through a piston flow reactor varies with time in the same way. It also varies with position down the tube. The relationship between time and position is... 

We now formalize the definition of piston flow. Denote position in the reactor using a cylindrical coordinate system (r, 6, z) so that the concentration at a point is denoted as a(r, 9, z) For the reactor to be a piston flow reactor (also called plug flow reactor, slug flow reactor, or ideal tubular reactor), three conditions must be satisfied ... 

As a general rule, scaled-down reactors will more closely approach isothermal operation but will less closely approach ideal piston flow when the large reactor is turbulent. Large scaledowns will lead to laminar flow. If the large system is laminar, the scaled-down version will be laminar as well and will more closely approach piston flow due to greater radial diffusion. 

Consider the reaction B — 2A in the gas phase. Use a numerical solution to determine the length of an isothermal, piston flow reactor that achieves 50% conversion of B. The pressure drop in the reactor is negligible. The reactor cross section is constant. There are no inerts. The feed is pure B and the gases are ideal. Assume bin = F and =0, Ui = 1, and k = n some system of units. 

We have considered two types of ideal flow reactor the piston flow reactor and the perfectly mixed CSTR. These two ideal types can be connected together in a variety of series and parallel arrangements to give composite reactors that are... 

This chapter treats the effects of temperature on the three types of ideal reactors batch, piston flow, and continuous-flow stirred tank. Three major questions in reactor design are addressed. What is the optimal temperature for a reaction How can this temperature be achieved or at least approximated in practice How can results from the laboratory or pilot plant be scaled up ... 

Reactor design usually begins in the laboratory with a kinetic study. Data are taken in small-scale, specially designed equipment that hopefully (but not inevitably) approximates an ideal, isothermal reactor batch, perfectly mixed stirred tank, or piston flow. The laboratory data are fit to a kinetic model using the methods of Chapter 7. The kinetic model is then combined with a transport model to give the overall design. 

Figure 2.4. Schematic drawings of a cylindrical flow reactor and a batch reactor. In the ideal case the flow reactor operates as a plug-flow reactor in which the gas moves as a piston down through the tube, whereas the ideal batch reactor is a well-mixed Tank Reactor...

In this section, several cases where there is a spread in drop size distribution will be calculated first for an ideal piston flow reactor in which all liquid parts have the same residence time distribution, and, finally, also the case of a CSTR in which there is a spread in drop size will be calculated, but only for the case of zero-order drop conversion. 

Piston flow signifies that some of the liquid passes through the reactor in plug flow. This liquid, unlike that involved in short-circuiting, has a certain residence time in the reactor. In certain operations, it is essential that the flow approach as close as possible some ideal situation, usually plug flow (e.g., in continuous, large-scale chromatographic separations). 

Exercise 9,5,4, Laboratory experiments on the dehydration of ethyl alcohol indicate that the reaction, C2H5OH —> C2H4 + H O, is second order with respect to the alcohol concentration. The rate constant is 0.52 1 gm-mole" sec at 150 C. It is proposed to construct a small scale tubular reactor which will operate at 2 atm and 150"C to give 35% conversion of the alcohol when the feed rate is 9.9kg/hr. If the reactor has a diameter of 10cm, what length will be required Ideal gas behavior and piston flow through the reactor may be assumed and... 

To describe patterns of combustion processes, ideal models are often introduced such as piston flow or a perfectly stirred reactor as well as an ideal stirred boiler. For describing the flameless oxidation the model of the loop reactor is appropriate. Figure 23.6 shows different combinations of loop reactors. Here the piston flow (k, = 0) and the well-stirred reactor (k, = °°) can be considered as limiting cases of loop reactors. 

The ideal tubular reactor is one in which elements of the homogeneous fluid reactant stream move through a tube as plugs moving parallel to the tube axis. This flow pattern is referred to as plug flow or piston flow. The velocity profile at a given cross section is flat and it is assumed that there is no axial diffusion or backmixing of fluid elements. 

The tubular reactor is so named because the physical configuration of the reactor is normally such that the reaction takes place within a tube or length of pipe. The idealized model of this type of reactor is based on the assumption that an entering fluid element moves through the reactor as a differentially thin plug of material that fills the reactor cross section completely. Thus, the terms piston flow or plug flow reactor (PFR) are often employed to describe the idealized model. The contents of a specific differential plug are presumed to be uniform in temperature and composition. This model may be used to treat both the case where the tube is packed with a solid catalyst (see Section 12.1) and the case where the fluid phase alone is present. 

By analyzing the above terms, we observe that Per oo is negligible and the other terms are of the same order of magnitude 0 (1). The axial dispersion cannot be neglected, since Pe is finite. When the dispersion and diffusion coefficients are small and of the same order of magnitude, they are similar to a piston flow because the velocity profile is uniform in radial cross section. In this case, one obtains the equation of an ideal reactor. 

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