Piston flow

Piston flow is utilized in several cases where heavily contaminated air needs to be removed, for instance in a spray painting booth (Fig. 8.23). 

When there is a very high demand on the cleanness of the air, like in the pharmaceutical industry, piston flow from the ceiling is utilized (Fig. 8.24). 

In practice, piston flow is not very easy to establish. A common way, utilized in cleaiiroonis and paint booths, is to have a filter mat placed all across 

When designing air supply through a filter ceiling, one should ensure that the dynamic pressure in the supply air does not affect the static pressure distribution above the filter ceiling too much. 

In rough environments a filter mat may nor be desirable, due to wear or dust in the supply air. In those cases, perforated sheets are used as a means of creating a piston flow. 

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The gaseous tracer method yields the equivalent piston flow linear velocity of the gas flow in the pipe without any constraints regarding flow regime under the conditions prevailing for flare gas flow. 

Fig. 3. Comtrack 921 pipe prover. Liquid flow through the Comtrak s closed loop is created by the movement of a sealed piston. Flow meters being tested are installed in the loop upstream from the piston. As the piston advances, the caUbration fluid travels through the meters and returns to the back side of...

The tubular (plug flow) reactor in which piston flow of the reacting mixture is assumed, and there is neither mixing nor diffusion in the flow direction. 

Piston flow signifies that some of the liquid passes through the reaetor in plug flow. This liquid, unlike that involved in short-eireuiting, has a eertain residenee time in the reaetor. In eertain operations, it is essential that the flow approaeh as elose as possible some ideal situation, usually plug flow (e.g., in eontinuous, large-seale ehromato-graphie separations). 

Two types of boundary conditions are considered, the closed vessel and the open vessel. The closed vessel (Figure 8-36) is one in which the inlet and outlet streams are completely mixed and dispersion occurs between the terminals. Piston flow prevails in both inlet and outlet piping. For this type of system, the analytic expression for the E-curve is not available. However, van der Laan [22] determined its mean and variance as... 

As Npg—> °° (large u or small [), the system behaves as a piston flow reaetor so that... 

Fig ure 9-3. Models for segregated reaetors Piston flow elements in parallel. 

Figure 9-4. Single-piston flow element with side exits.

High, solvent vapors Light Piston flow, vettical from above Paint booth... 

When designing ventilation systems with piston flow, one should also be aware of the effeas of thermal instabilities. Figure 8.27 shows a room with air... 

A piston Mach number may be related to a flame Mach number if, under the condition of low overpressure, the mass enclosed by the piston flow field is equated to the mass enclosed by a flame flow field ... 

In addition to a near-shock and an acoustic region, Deshaies and Clavin (1979) distinguished a third—a near-piston region—where nonlinear effects play a role as well. As already pointed out by Taylor (1946), the near-piston flow regime may be well approximated by the assumption of incompressibility. For each of these regions, Deshaies and Clavin (1979) developed solutions in the form of asymptotic expansions in powers of small piston Mach number. These solutions are supposed to hold for piston Mach numbers lower than 0.35. 

The piston flow reactor has an advantage over a stirred tank reactor when the kinetics is of positive order, but the reverse is true when the... 

In Fig. 28, the abscissa kt is the product of the reaction rate constant and the reactor residence time, which is proportional to the reciprocal of the space velocity. The parameter k co is the product of the CO inhibition parameter and inlet concentration. Since k is approximately 5 at 600°F these three curves represent c = 1, 2, and 4%. The conversion for a first-order kinetics is independent of the inlet concentration, but the conversion for the kinetics of Eq. (48) is highly dependent on inlet concentration. As the space velocity increases, kt decreases in a reciprocal manner and the conversion for a first-order reaction gradually declines. For the kinetics of Eq. (48), the conversion is 100% at low space velocities, and does not vary as the space velocity is increased until a threshold is reached with precipitous conversion decline. The conversion for the same kinetics in a stirred tank reactor is shown in Fig. 29. For the kinetics of Eq. (48), multiple solutions may be encountered when the inlet concentration is sufficiently high. Given two reactors of the same volume, and given the same kinetics and inlet concentrations, the conversions are compared in Fig. 30. The piston flow reactor has an advantage over the stirred tank... 

Kinetics c/c0 in piston flow reactor Si, Sc o c/c0 in stirred tank reactor St,... 

These two parameters describe the change in fraction unconverted with a percentage change in kt or in c0. The first sensitivity is also the slope of the curves in Fig. 28. The values of these sensitivities are given in Table IX. In a piston flow reactor where the conversion level is c/c0 = 0.1, the value of Stt is —0.23 for the first-order kinetics, —0.90 for the zero-order kinetics, and —4.95 for the negative first-order kinetics. In the stirred tank reactor, the value of the sensitivities Skt is —0.09 for the first-order kinetics, — 0.90 for the zero-order kinetics, and +0.11 for the negative first-order kinetics. A positive sensitivity means that as kt is increased, the fraction unconverted also increases, clearly an unstable situation. 

Tadaki and Maeda (Tl) examined the desorption of carbon dioxide from water in a bubble-column and analyzed the experimental results under the assumption that while the gas phase moves in piston flow, the liquid undergoes axial mixing that can be characterized by the diffusion model. (Shulman and Molstad, in contrast, assumed piston flow for both phases.) Only poor agreement was obtained between the theoretical model and the experimental... 

Gas holdup may be of the same magnitude in the various operations, although for bubble-columns, the presence of electrolytes or surface-active agents appears to be a condition for high gas holdup. The gas residence-time distribution resembles that of a perfect mixer in the stirred-slurry operation, and comes close to piston flow in the others. 

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... 

Example 1.3 Find the outlet concentration of component A from a piston flow reactor assuming that A is consumed by a first-order reaction. 

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 ... 

Here in Chapter 1 we make the additional assumptions that the fluid has constant density, that the cross-sectional area of the tube is constant, and that the walls of the tube are impenetrable (i.e., no transpiration through the walls), but these assumptions are not required in the general definition of piston flow. In the general case, it is possible for u, temperature, and pressure to vary as a function of z. The axis of the tube need not be straight. Helically coiled tubes sometimes approximate piston flow more closely than straight tubes. Reactors with square or triangular cross sections are occasionally used. However, in most of this book, we will assume that PFRs are circular tubes of length L and constant radius R. 

While true, this result is not helpful. The derivation of Equation (1.6) used the entire reactor as the control volume and produced a result containing the average reaction rate, In piston flow, a varies with z so that the local reaction rate also varies with z, and there is no simple way of calculating a-Equation (1.6) is an overall balance applicable to the entire system. It is also called an integral balance. It just states that if more of a component leaves the reactor than entered it, then the difference had to have been formed inside the reactor. 

A differential balance written for a vanishingly small control volume, within which t A is approximately constant, is needed to analyze a piston flow reactor. See Figure 1.4. The differential volume element has volume AV, cross-sectional area A and length Az. The general component balance now gives... 

FIGURE 1.4 Differential element in a piston flow reactor. 

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