Plug flow assumption

A particularly important consideration in designing contactors for gas-liquid reactions is the validity of the ideal flow assumption [plug flow (PF) or mixed flow (MF)] normally used in the design. Numerous studies have been reported on the role of nonideality (i.e., backmixing) in gas-liquid contactors, and based on these, some qualitative guidelines... 

Effect of Axial Dispersion on Column Performance. Another assumption underlying standard design methods is that the gas and the Hquid phases move in plug-flow fashion through the column. In reaHty, considerable departure from this ideal flow assumption exists (4) and different fluid... 

Ejfects of Gas and Liquid Mixing As noted previously, it is necessary in most instances to convert point efficiency E g to Murphree plate efficiency E, ,. This is true because of incomplete mixing only in small laboratoiy or pilot-plant columns, under special conditions, is the assumption E g = E, , likely to be valid. For a crossflow plate with no hquid mixing there is plug flow of hquid. For this condition of liquid flow, Lewis [Ind. Eng. Chem., 28, 399 (1936)] analyzed effects of gas mixing on efficiency. He considered three cases ... 

In the holding section of a continuous sterilizer, correct exposure time and temperature must be maintained. Because of the distribution of residence times, the actual reduction of microbial contaminants in the holding section is significantly lower than that predicted from plug flow assumption. The difference between actual and predicted reduction in viable microorganisms can be several orders of magnitude therefore, a design based on ideal flow conditions may fail. 

Previously, the RTD funetions for flow systems were deseribed. In praetiee, the RTD is determined experimentally by injeeting a traeer at the inlet of the system and monitoring the response at the outlet information about the system is derived from these results. In a tubular reaetor, the RTD measurements are used to determine how elosely the plug flow assumption is obeyed. 

A one-dimensional isothermal plug-flow model is used because the inner diameter of the reactor is 4 mm. Although the apparent gas flow rate is small, axial dispersion can be neglected because the catalj st is closely compacted and the concentration profile is placid. With the assumption of Langmuir adsorption, the reactor model can be formulated as. 

In a properly operated bubble-column reactor, the liquid phase can be considered to be perfectly mixed, i.e. concentrations in the liquid are the same everywhere and correspond to those in the effluent. The gas is supposed to flow like a piston, i.e. the reactor is a plug-flow reactor with respect to the gas. These two assumptions are not entirely true, but within a certain flow regime they are not far from the reality. 

Equations (8) are based on the assumption of plug flow in each phase but one may take account of any axial mixing in each liquid phase by replacing the molecular thermal conductivities fc, and ku with the effective thermal conductivities /c, eff and kn eff in the definition of the Peclet numbers. The evaluation of these conductivity terms is discussed in Section II,B,1. The wall heat-transfer terms may be defined as... 

The Plug Flow Reactor (PFR)—Basic Assumptions and Design Equations... 

In order to characterize the flow regime and thereby justify the plug flow assumption, it is... 

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. 

The loss coefficient is seen to be a function only of the geometry of the system (note that the assumption of plug flow implies that the flow is highly turbulent). For most systems (i.e., flow in valves, fittings, etc.), the loss coefficient cannot be determined accurately from simple theoretical concepts (as in this case) but must be determined empirically. For example, the friction loss in a sudden contraction cannot be calculated by this simple method due to the occurrence of the vena contracta just downstream of the contraction (see Table 7-5 in Chapter 7 and the discussion in Section IV of Chapter 10). For a sharp 90° contraction, the contraction loss coefficient is given by... 

If it is suspected (or known) that the plug flow assumption does not hold, a separate tracer study is needed to characterize the flow distribution within the pipes. These data are then used to adjust both the concentration and the sampling time, as required. If the nature of flow and mixing in the vessel is independent of the flow characteristics in the pipes, then the o1 curve for the vessel may be calculated from... 

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

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. 

In analysing the behaviour of a tubular reactor, the simplest assumption to make is that plug flow occurs. In plug flow, there is negligible diffusion relative to bulk flow and, over any cross-section normal to the fluid motion, the mass flow rate and fluid properties are uniform. This situation is quite closely approached in many industrial reactors and it means that... 

Since Re > 2300, flow will be in the turbulent regime and the plug flow assumption will be a good approximation to conditions in the reactor. With a longer, narrower pipe of the same volume, the Reynolds number would have been higher and plug flow would have been approached even more closely. 

With the same aspect ratio as before, this corresponds to a Reynolds number of about lO" and flow will again be turbulent. The reactor dispersion number is 0.002, which again implies that the performance of the actual reactor will be very close to that calculated on the basis of the plug-flow assumption. 

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