Plug flow constant area

FIG. 23-7 Imp ulse and step inputs and responses. Typical, PFR and CSTR. (a) Experiment with impulse input of tracer, (h) Typical behavior area between ordinates at tg and ty equals the fraction of the tracer with residence time in that range, (c) Plug flow behavior all molecules have the same residence time, (d) Completely mixed vessel residence times range between zero and infinity, e) Experiment with step input of tracer initial concentration zero. (/) Typical behavior fraction with ages between and ty equals the difference between the ordinates, h — a. (g) Plug flow behavior zero response until t =t has elapsed, then constant concentration Cy. (h) Completely mixed behavior response begins at once, and ultimately reaches feed concentration. 

This analysis refers to a small area for vertical flow, and Emv is therefore the point or local Murphree efficiency. The relation between this point efficiency and the tray efficiency depends on the nature of the liquid mixing on the tray. If there is complete mixing of the liquid, x = xn for the liquid, and ye and y will also be constant over a horizontal plane. The tray efficiency EMv = Emv. With no mixing of the liquid, the liquid may be considered to be in plug flow. If ye = mx + b and Emv is taken as constant over tray, it may be shown" 91 that ... 

The above equations assume that the liquid-phase reactant C, the product of the reaction, and the solvent are nonvolatile. The effective interfacial area for mass transfer (nL) and the fractional gas holdup (ii0o) arc independent of the position of the column. The Peclet number takes into account any variations of concentration and velocity in the radial direction. We assume that Peclet numbers for both species A and C in the liquid phase are equal. For constant, 4 , Eq. (4-73) assumes that the gas-phase concentration of species A remains essentially constant throughout the reactor. This assumption is reasonable in many instances. If the gas-phase concentration does vary, a mass balance for species A in the gas phase is needed. If the gas phase is assumed to move in plug flow, a relevant equation would be... 

The full potential of the hydrostatic extrusion technique became apparent in 1974, when the production of ultra high mudulus polyethy lenes with stiffnesses up to 60 GPa were reported The main process parameter in hydrostatic extrusion is the nominal extrusion ratio Rj, the ratio of the billet cross-sectional area to that of the die exit (assuming deformation occurs at constant volume, which is a very good approximation). Because polymers can exhibit die swell in extrusion, it is convenient also to define an actual extrusion ratio R, based on the ratio of the initial and final billet cross-sections. R is, of course, direcUy comparable to the draw ratio in tensile drawing (assuming plug-flow) and in practice R R for all but the lowest reduction ratios. 

Since the cross-sectional area for flow is constant, one may employ the plug flow model described in Chapter 10 with a constant inlet velocity. For this case. 

Consequently, we see that Equation (1-11) applies equally well to our model of tubular reactors of variable and constant cross-sectional area, although it is doubtful that one would find a reactor of the shape shown in Figure 1-11 unless it were designed by Pablo Picasso. The conclusion drawn from the application of the design equation to Picasso s reactor is an imponant one the degree of completion of a reaction achieved in an ideal plug-flow reactor tPFR) does not depend on its shape, only on its total volume. 

B [%] represents the concentration decrease expected along a theoretical streamline plug flow without mixing and a single degradation process with a constant isotope fractionation factor. Co is the concentration of contaminants in the source area and Q is the concentration of contaminants along the flow path. R is the isotope ratio calculated ... 

To carry out an exothermic reaction in a tubular reactor under nearly isothermal conditions, a small diameter is needed to give a high ratio of surface area to volume. The reactor could be made from sections of jacketed pipe or from a long coil immersed in a cooling bath. The following analysis is for a constant jacket temperature, and the liquid is assumed to be in plug flow, with no radial gradients of temperature or concentration and no axial conduction or diffusion. 

An issue that is not adequately addressed by most models (EQ and NEQ) is that of vapor and liquid flow patterns on distillation trays or maldistribution in packed columns. Since reaction rates and chemical equilibrium constants are dependent on the local concentrations and temperature, they may vary along the flow path of liquid on a tray, or from side to side of a packed column. For such systems the residence time distribution could be very important, as well as a proper description of mass transfer. On distillation trays, vapor will rise more or less in plug flow through a layer of froth. The liquid will flow along the tray more or less in plug flow, with some axial dispersion caused by the vapor jets and bubbles. In packed sections, maldistribution of internal vapor and liquid flows over the cross-sectional area of the column can lead to loss of interfacial area. 

Consider the reaction used as the basis for Illustrations 10.1 to 10.3 (A B). Determine the volume required to produce 2 million pounds of B annually in a plug flow reactor operating under the conditions described below. The reactor is to be operated 7000 h annually with 97% conversion of the A fed to the reactor. The feed enters at 163°C. The internal pipe diameter is 4 in. and the piping is arranged so that the effective reactor volume can be immersed in a heat sink maintained at a constant temperatnre of 160°C. The overall heat transfer coefficient based on the inside area of the pipe may be taken as 200 kcal/(h-m -K). Volumetric expansion effects are negligible. 

Fast chemical reaction conditions also change the conditions of the reaction torch front lower boundary formation (Figure 4.5, points 5, 6). With an increase of the chemical reaction constant value k, the ratio of the linear rates of the reactant supply to the reactor, necessary for the torch mode lower boundary formation, decreases. The kinetic parameters of the chemical reaction, in this case, the rate constants, do not change the area where the corresponding macrostructures are formed. The ratio of rates V1/V2, necessary for torch mode and quasi-plug flow mode formation, shifts to the area of their smaller values. 

Simple equations can be derived to estimate the mendirane area for a given gas separation separation problem. Here it is assumed that the penneability coefficients remain constant and the separation occurs under isothermal condition. The calculations are dependent on the flow pattern in the module. The most simple equations are obtained by assuming complete mixing both in feed and penneate. This concept may be found in systems which operate at low recovery. Most gas separation systems resembles cross-flow conditions, i.e. plug flow at the feed side and complete mixing at the permeate side. These two concepts will be discussed here. In case of counter-current and co-current flow conditions the equations are somewhat different and the (terivations applicable for these systems can be found in literature. For vapour penneation the same approach can be used, however the... 

A better approximation to the plug flow is reached at Re >2300, that is, by turbulent flow. Due to turbulence, the flow rate differences between the middle areas of the reactor and zones at the wall are compensated constantly. This flow cannot be always realized in practice because of the great reactor length and a high residence time required by such systems. 

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