Plug flow conditions

Reaction temperature in short residence time reactor 90°C, cooling water — 80-85°C in lower part and 40-50°C in upper part Aging reactor post-falling film reactor required residence time 0.5 h at 90-95°C, plug flow conditions... 

The influence of dispersion on the yield of an intermediate produced in a series reaction has also been studied. When 3 JuL is less than 0.05, Tichacek s results (22) indicate that the fractional decrease in the maximum amount of intermediate formed relative to plug flow conditions is approximated by l/uL itself. Results obtained at higher dispersion numbers are given in the original article. 

Since all of the tube diameters of interest are less than 1 ft, it is evident that in all three cases the flow will be highly turbulent and assumption of plug flow conditions will be quite appropriate. 

An approximate design procedure for packed tubular reactors entails the assumption of plug flow conditions through the reactor. Discuss critically those effects which would ... 

Part (b) The effluent from a system like that of part (a) is at 200 F with A = 0.1955 lbmol/cuft. It proceeds to storage through a pipeline of 50 cuft volume under plug flow conditions. The specific rate as a function of temperature in °F is k = 4+0.2(T-200). Find the temperature and concentration at the exit of the pipeline. 

The primary difference between the PRF and the SBR during react is that the equivalent to true plug flow conditions can be established in an SBA but cannot be achieved in a single activated sludge tank because of the dispersion resulting from the aeration system. However, a cascade of CMFRs consisting three or four tanks in series can be considered as a suitable approximation (Wilderer et al., 2001). 

Concerning the hydrodynamics and the dimensioning of the test reactor, some rules of thumb are a valuable aid for the experimentalist. It is important that the reactor is operated under plug-flow conditions in order to avoid axial dispersion and diffusion limitation phenomena. Again, it has to be made clear that in many cases testing of monolithic bodies such as metal gauzes, foam ceramics, or monoliths used for environmental catalysis, often needs to be performed in the laminar flow regime. 

Both the mass-transfer approach as well as the diffusion approach are required to describe the influence of mass transport on the overall polycondensation rate in industrial reactors. For the modelling of continuous stirred tank reactors, the mass-transfer concept can be applied successfully. For the modelling of finishers used for polycondensation at medium to high melt viscosities, the diffusion approach is necessary to describe the mass transport of EG and water in the polymer film on the surface area of the stirrer. Those tube-type reactors, which operate close to plug-flow conditions, allow the mass-transfer model to be applied successfully to describe the mass transport of volatile compounds from the polymer bulk at the bottom of the reactor to the high-vacuum gas phase. 

Example 2.2. Fluid is flowing through a constant-diameter cylindrical pipe sketched in Fig. 2.2. The flow is turbulent and therefore we can assume plug-flow conditions, i.e., each slice of liquid flows down the pipe as a unit. There are no radial gradients in velocity or any other properties. However, axial gradients can exist. 

Example 2.5. Instead of fluid flowing down a pipe as in Example 2.2, suppose the pipe is a tubular reactor in which the same reaction A A B of Example 2.3 takes place. As a slice of material moves down the length of the reactor the concentration of reactant decreases as A is consumed. Density p, velocity v, and concentration can aU vary with time and axial position z. We stiU assume plug-flow conditions so that there are no radial gradients in velocity, density, or concentration. 

The part of this process that is described by a force balance is the liquid flowing through the pipe. It will have a mass equal to the volume of the pipe (j4j,L) times the density of the liquid p. This mass of liquid will have a velocity v (ft/s) equal to the volumetric flow divided by the cross-sectional area of the pipe. Remember we have assumed plug-flow conditions and incompressible liquid, and therefore all the liquid is moving at the same velocity, more or less like a solid rod. If the flow is turbulent, this is not a bad assumption. 

A 6-inch ID pipe, 300 feet long, connects two process units. The liquid flows through the pipe in essentially plug-flow conditions, so the pipe acts as a pure deadtime. This deadlime varies with the flow rate through the pipe. From time equals zero, the flow rate is 1000 gpm for 2 minutes. Then it drops to 500 gpm and holds constant for 3 minutes. Then it jumps to 2000 gpm for 2 minutes and finally returns to 1000 gpm. Liquid density is 50 lh, ft. ... 

For the common case of continuous operation for both phases, where gas flows under plug-flow condition and liquid under complete mixed-flow condition, and for a reaction of the form (nonreacting liquid phase)... 

Note that the gas-phase concentration CGz varies with the distance from the entrance z due to the plug-flow condition. If the gas phase is in complete mixed flow, then CG z - CG>0. Finally, the component mass balance around the catalyst is... 

Note that the gas-phase is flowing under plug-flow condition, and thus its concentration will change with position CG z. Thus, the procedure of the formulation of the overall rate is made for a certain axial position (z) in the reactor where at steady state, the gas-phase concentration is constant. 

In general, the material balances and the corresponding solutions for trickle and bubble bed reactors are the same, under the assumption that the plug-flow condition holds for both phases. Of course, the appropriate correlations should be used for the estimation of mass transfer coefficients. However, in packed bubble bed reactors, the liquid-phase is frequently found in a complete mixed state, and thus some adjustments have to be made to the aforementioned models. Two special cases will be presented here. 

It is interesting to check the Peclet number of the fixed bed. The Reynolds number is 0.154, and for this low value, the most appropriate correlation is that of Chung (eq. (3.314)). The resulting particle Peclet number is 0.39 and thus, the bed Peclet number is 151.98, which is fairly high, and we can assume that the plug-flow condition is assured. 

From Table 1-15 of Appendix I, we find that the diffusion coefficient of toluene in air is 8.7 X 10-6 m2/s. Then, using the properties of ah at 25 °C (Table 1-6, Appendix I), we find that Sc = 1.74 and Rep = 6.92, and using the Edwards-Richardson correlation (eq. (3.317)) the particle Peclet number is found to be 1.98 and thus, the bed Peclet number is 609.2, which is fairly high, and plug-flow condition can be assumed. 

Note that the gas phase flows under plug-flow condition, and thus the concentrations of both reactants change with position (CG z). For a constant gas-phase concentration of A, the reaction rate is constant and the reaction term can be drawn out of the integration and the above equation becomes (Smith, 1981)... 

Estimate the height of the bed to achieve the same performance of the reactor by using the appropriate simplified model, assuming that the liquid phase remains saturated with 02 throughout the reactor length, plug-flow conditions exist, and the external wetting of the catalyst particle is complete. 

The conditions (a), (b), (c), and (d) are met since we have the experimental value of the gas-liquid mass transfer coefficient, the wetting efficiency is given to be 100%, plug-flow condition is assumed in the original study, and the expansion factor is zero as the oxygen concentration has been taken as constant. 

If all the dimensionless parameters in a reaction model are kept constant with scale change, a similarity in the reactor performance is expected, provided that the basic assumptions of the model remain unchanged in both scales, e.g. in our example the plug flow condition of gas in the bubble phase. 

While the batch process is the dominant one in current use, researchers and companies have attempted to create continuous bioreactor systems. Lopez et al. immobilized Candida rugosa in polymethacrylamide hydrazide beads and polyurethane foam 3 with the intent to achieve the continuous production of lipase enzymes. Despite flow problems with the polyurethane foam, it showed high lipolytic activity. Biomass buildup was problematic. Feijoo et al. immobilized Phanerochaete chry-sosporium on polyurethane foam in packed bed bioreactors under near-plug flow conditions. Continuous lignin peroxidase production was accomplished, the rate of which was studied as a function of recycle ratio. 

There are many chemically reacting flow situations in which a reactive stream flows interior to a channel or duct. Two such examples are illustrated in Figs. 1.4 and 1.6, which consider flow in a catalytic-combustion monolith [28,156,168,259,322] and in the channels of a solid-oxide fuel cell. Other examples include the catalytic converters in automobiles. Certainly there are many industrial chemical processes that involve reactive flow tubular reactors. Innovative new short-contact-time processes use flow in catalytic monoliths to convert raw hydrocarbons to higher-value chemical feedstocks [37,99,100,173,184,436, 447]. Certain types of chemical-vapor-deposition reactors use a channel to direct flow over a wafer where a thin film is grown or deposited [219]. Flow reactors used in the laboratory to study gas-phase chemical kinetics usually strive to achieve plug-flow conditions and to minimize wall-chemistry effects. Nevertheless, boundary-layer simulations can be used to verify the flow condition or to account for non-ideal behavior [147]. 

The objective of this exercise is to evaluate the potential of oxidation of unbumed hydrocarbons in the exhaust channel of lean-bum natural gas engines. Use GRI-Mech 3.0 (GRIM30. mec [366]) as starting mechanism and assume plug-flow conditions in the exhaust channel. 

Rules-of-thumb to ensure plug-flow conditions in packed beds... 

For the plug flow condition of Figure 6.1(b), the balance is made in terms of the differential changes across a differential length dL of the vessel, which is... 

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