Flow perfect mixing

As predicted from the model, the residence time distribution curve shown in Fig. 3.11 exhibits the feature of perfect mixing with a certain lag time, that is, the feature of plug flow-perfect mixing flow in series. All the experiments yield the results of RTD exhibiting the same feature. 

The flow directions (e.g., co-currcni, counter-current and flow-through) and flow patterns (e.g., plug flow, perfect mixing and fluidized bed) of feed, permeate and retentate streams in a membrane reactor can significantly affect the reaction conversion, yield and selectivity of the reaction involved in different ways. These variables have been widely investigated for both dense and porous membranes used to carry out various isothermal and non-isothermal catalytic reactions, particularly dehydrogenation and hydrogenation reactions. 

Plug flow-perfectly mixed reactor systems (chapter 4.4). 

PLUG FLOW-PERFECTLY MIXED REACTOR SYSTEMS... 

Figure 4.9 Comparison of plug flow, perfect mixing, and laminar flow residence-time distributions.

III plug flow perfectly mixed — plug flow (zero corner Sion)... 

In general, it has been concluded that countercurrent flow is the most efficient flow pattern, requiring the lowest membrane area and producing the highest degree of separation, at the same operating conditions. The order of efficiency for the other three flow patterns is crossflow > cocurrent flow > perfect mixing. 

Part, axial mixing Plug flow Perfect mixing Perfect mixing if particles do Plug flow if... 

FIGURE 6.16 Cumulative residence time distribution function for plug flow, perfect mixing (complete backmixing), Poiseuille flow of Newtonian fluids in circular pipe (CPPF), and parallel plate geometries (PPF). 

Preferential Removal of Crystals. Crystal size distributions produced ia a perfectiy mixed continuous crystallizer are highly constraiaed the form of the CSD ia such systems is determined entirely by the residence time distribution of a perfectly mixed crystallizer. Greater flexibiUty can be obtained through iatroduction of selective removal devices that alter the residence time distribution of materials flowing from the crystallizer. The... 

At the bottom of the column, a liquid sump of constant and perfectly mixed molar liquid holdup Mg is provided. A portion of the hq-uid flowing from this sump passes to a thermosiphon reboiler, with the... 

Equations for the decanter are as follows if it is assumed that (1) there are constant holdups in the decanter of both phases in the same ratio as the ratio of the flow rates leaving the decanter, (2) there is a constant decanter temperature, and (3) the two hquid phases in the decanter are in physical equilibrium and each is perfectly mixed. 

Figure 24-23 is a sketch of continuous culture with recycle. The symbols for flow rates and organism concentrations are F and X, respec tively Assuming perfect mixing and steady state so that the derivatives can be set to zero, mass balances lead to ... 

In using the normalized distribution function, it is possible to directly compare the flow performance inside different reactors. If the normalized function E(6) is used, all perfectly mixed CSTRs have numerically the same RTD. If E(t) is used, its numerical values can change for different CSTRs. 

Equation 9-15 gives the conversion expression for the second order reaction of a macrofluid in a mixed flow. An exponential integral, ei(a), which is a function of a, and its value can be found from tables of integrals. However, the conversion from Equation 9-15 is different from that of a perfectly mixed reactor without reference to RTD. An earlier analysis in Chapter 5 gives... 

The name continuous flow-stirred tank reactor is nicely descriptive of a type of reactor that frequently for both production and fundamental kinetic studies. Unfortunately, this name, abbreviated as CSTR, misses the essence of the idealization completely. The ideality arises from the assumption in the analysis that the reactor is perfectly mixed, and that it is homogeneous. A better name for this model might be continuous perfectly mixed reactor (CPMR). 

The tracer is injected into the duct at a constant rate and mixed with the flowing air. The concentration of the air-tracer mixture is measured further downstream. Assuming perfect mixing and that the air entering the test section has a zero concentration, the air volume flow rate can be calculated based on the mass balance of the tracer... 

The most common type of agitator is turbine. It consists of several short blades mounted on a central shaft. The diameter of a turbine is normally 35 15% of the tank diameter. There are four to six blades for perfect mixing. Turbines with flat blades give radial flow. This is good for gas dispersion in the media, where the gas is introduced just below the impeller, is drawn up to the blades and broken up into uniform fine bubbles. 

The two models commonly used for the analysis of processes in which axial mixing is of importance are (1) the series of perfectly mixed stages and (2) the axial-dispersion model. The latter, which will be used in the following, is based on the assumption that a diffusion process in the flow direction is superimposed upon the net flow. This model has been widely used for the analysis of single-phase flow systems, and its use for a continuous phase in a two-phase system appears justified. For a dispersed phase (for example, a bubble phase) in a two-phase system, as discussed by Miyauchi and Vermeulen, the model is applicable if all of the dispersed phase at a given level in a column is at the same concentration. Such will be the case if the bubbles coalesce and break up rapidly. However, the model is probably a useful approximation even if this condition is not fulfilled. It is assumed in the following that the model is applicable for a continuous as well as for a dispersed phase in gas-liquid-particle operations. 

Fig. 4. Number of perfectly mixed stages-for gas flow in a bubble-column as a function of bed height L and superficial gas velocity u, [Kolbel et al. (K17)].

Liquid residence-time distributions in mechanically stirred gas-liquid-solid operations have apparently not been studied as such. It seems a safe assumption that these systems under normal operating conditions may be considered as perfectly mixed vessels. Van de Vusse (V3) have discussed some aspects of liquid flow in stirred slurry reactors. 

The liquid residence-time distribution is close to plug flow in trickle-flow operation and corresponds to perfect mixing in the stirred-slurry operation, whereas the other types of bubble-flow operation are characterized by residence-time distributions between these extremes. 

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