Regions backmix flow

Velocity as a function of radial position Mean velocity in a packed bed based on empty tube Unit step function Volumetric flow rate Volume of vessel Volume of backmix flow region... 

Using the completely stagnant interpretation of deadwater regions, Fig. 23 illustrates some simple combined models and their tracer-response curves. In these models Vh, Vp, and Va stand for the volume of backmix, plug flow, and deadwater regions. If V is the volume of vessel we then have... 

Fix the dispersion coefficients of the dispersed plug flow model, Di = Di or D2, at inflnity or zero to obtain backmix or plug flow in the individual regions. 

Figure 14-18(a) describes a real PFR or PER with channeling that is modeled as two PFRs/PBRs in parallel. The two parameters are the fraction of flow 10 the reactors [i.e., (3 and (1 - p)] and the fractional volume [i.e.. a and (1 - Qf] of each reactor. Figure 14-18(b) describes a real PFR/PBR that has a backmix region and is modeled as a PFR/PBR in parallel with a CSTR. Figures H-19(a) and (b) show a real CSTR modeled as two CSTRs with interchange. In one case, the fluid exits from the top CSTR (a) and in the other case the fluid exits from the bottom CSTR. The parameter p represents the interchange volumetric flow rate and a the fractional volume of the top reactor, where the fluid exits the reaction system. We note that the reactor in model 14-19(b) was found to describe extremely well a real reactor used in the production of terephthalic acid. A number of other combinations of ideal reactions can be found in Levenspiel. ... 

Partially because of the backmixing behavior and partially because of the elEciency of contact between fluid- and catalyst-phases, fluidized beds are less efficient than fixed beds, at least in terms of the amount of catalyst required to attain a given conversion. Although plug flow seems reasonable for the motion of the bubbles, particularly in the Geldhart A-A regions, bubble-emulsion interchange. 

A major concern in backmixing is the fluid in the center region of the screw channel where the axial shear strain is zero or close to zero. In a simple conveying screw the fluid in the inner recirculation region will stay within this region until it reaches the end of the screw. When this happens, the material flowing into the die will be poorly mixed. 

Todd [37] proposed an equation to describe devolatilization in co-rotating twin screw extruders based on the penetration theory discussed in Section 5.4 and Section 7.6. The equation contains the Peclet number (see Eq. 7.371), which represents the effect of longitudinal backmixing. The Peclet number must be measured or estimated to predict the devolatilizing performance of an extruder. Todd selected a Peclet number of 40 to correlate predictions to experimental results. A similar approach was followed by Werner [38], A visualization study was made by Han and Han [39], particularly to study foam devolatilization, They found substantial entrainment of the bubbles in a circulatory flow region in a partially filled screw devolatilizer. Collins, Denson, and Astarita [40] published an experimental and theoretical study of devolatilization in a co-rotating twin screw extruder. The experimentally determined mass transfer coefficients were about one-third those predicted by the mathematical model. They concluded, therefore, that the effective surface area for mass transfer is substantially less than the sum of the areas of the screws and barrel. 

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