Complete back-mixing

Equation (100) applies also to a continuous-flow reactor in which the contents experience no back-mixing (equiveilent to plug flow) time has been eliminated from the expressions. When complete back-mixing is achieved in a continuous-flow reactor, concentration gradients are absent and we have... 

If the same reactions occur in a continuous-flow reactor with complete back-mixing then, at steady-state conditions... 

It is composed of an inlet chamber, four completely back-mixed flotation chambers, and an outlet chamber. Gas is drawn down by the vortex set up by rotors in each one of the chambers and dispersed in the fluid. 

If the kinetic parameters k /k2 = 7300/1.63 = 4480 and the mol ratio cAqA/cBqB = 1.05 are known, it is possible to calculate the selectivities SR which would result from the ideal plug-flow tubular reactor and in the completely back-mixed vessel. The corresponding values are 0.001 and 0.008 respectively. This is in good agreement with the results obtained for high values of x cB/cA. 

Reactor Staging. For practical purposes the H-Oil reactor can be considered as a completely back-mixed system. In such a reactor, the... 

It is as well immaterial, whether it is assumed that both phases are completely back-mixed or not. 

We will concern ourselves with this problem using the series network of reactions. We will explore the differences between the complete back-mixed CSTR and the axially distributed but radially well-mixed PFR. 

What is the maximum yield if the fluid bed is completely back-mixed ... 

It is known that under finite axial dispersion or complete back mixing and at steady-state isothermal conditions, autocatalytic reactions may exhibit oscillations, isolas, and other multiplicity features [21-24]. Cordonier et al. analyzed the forced oscillations of such systems [25]. 

The Peclet number is an important dimensionless parameter in convective transfer, and is the product of the Reynolds number and Schmidt number. The Peclet number, Pe = 0 corresponds to complete back mixing, while Pe = oo corresponds to plug flow. Large values of the Peclet number result when mixing is therefore not extensive. 

Liquid completely back-mixed, everywhere of uniform concentration x . this case, Eq. (6.54) reverts to Eq. (6.47), and... 

In tray towers, entrainment of liquid in the gas is a form of back mixing, and there are back mbcing and axial mixing on the trays, which we have already considered. In sparged vessels, the liquid is essentially completely back-mixed to a uniform solute concentration. Both phases are largely completely mixed in mechanically agitated vessels. 

The residence time is the volume divided by the volumetric throughput flow. For a completely back mixed volume, the residence time becomes a process time constant. For a plug flow volume, the residence time becomes a dead time. Real systems for pH control can be approximated as a combination of plug flow and back mixed volumes. Thus, the residence time is split between a process time constant and process dead time. 

FIGURE 8.30 Cumulative residence time distribution function versus reduced time in an extender for fluids with various values of the power-law index and compared to values for plug flow and complete back-mixing continnons stirred tank reactor (Bigg and Middlemann, 1974). 

The number density n is given as a fimction of the particle variables such as diameter, volume, or other properties, denotes the particle velocities in 3D external space in a completely back-mixed system this term vanishes. Vi is related to internal convective particle variables in crystallization processes it defines the growth rate. The B- and D-terms denote sources (birth) and sinks (death) for nucleation, a omeration, and breakage. The gradient of the flux j denotes exchange across the boundaries of the balancing volume. In Section 5.3, we will discuss particular solutions of this equation. 

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