Of perfectly mixed vessel

Challenge 2.1. Relationship between the mixing capacity and the number of tanks in series of perfectly mixed vessels model (a string of perfectly mixed tanks of equal size model)... 

Since it is not easy to express the RTD function by using an accurate formula, the mixing phenomena have been frequently discussed based on mixing models that can sufficiently express RTD. One such model is the series of perfectly mixed vessels model (a string of perfectly mixed tanks of equal size model hereafter SPMV model). This model consists of a series of equivolume perfect mixing tanks as shown in Figure 2.4(a). 

The "tanks-in-series" model is based on a series of perfectly mixed vessels, some features of which have been discussed in example 12.6.3.A. For the tanks-in-series model, Example 12.6.3.A gives... 

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. 

Their conclusions are that the gas residence-time distribution in their mixing vessel is intermediate between that to be expected from one perfectly-mixed vessel and that from two perfectly-mixed vessels of equal size in cascade. The cascade behavior of two equal-sized mixers is approached with a relatively large impeller located half-way between the bottom and top surfaces. The response curve becomes similar to that of one perfectly-mixed vessel when small impellers are used or if the impeller is located below the half-way point. 

Unlike the situation in a plug flow reactor, the various fluid elements mix with one another in a CSTR. In the limit of perfect mixing, a tracer molecule that enters at the reactor inlet has equal probability of being anywhere in the vessel after an infinitesimally small time increment. Thus all fluid elements in the reactor have equal probability of leaving in the next time increment. Consequently there will be a broad distribution of residence times for various tracer molecules. The character of the distribution is discussed in Section 11.1. Because some of the... 

The butylene feed stream is spht and fed into each of a series of perfectly mixed tanks (usually in one large vessel). This stepwise addition of butylene and the large excess of isobutane that is used both help to prevent undesirable reaction of butylene molecules with each other to form high-boiling, low octane polymers. Low temperature (40°F) also favors the desired iCJC reaction. 

Multistage Experiments Air Induced. Measurement of the system response to a step change in the feed-oil concentration showed that the flotation cells behaved as perfectly mixed vessels. Thus, the removal rate for each oil drop size can be calculated from a simple material balance ... 

A perfectly mixed vessel therefore can be considered as a batch vessel during the time required for the bubbles to sweep the vessel contents exactly once (i.c., up to /, = l/ 2 ). The definition of the singlebubble collection efficiency ( ) requires that the observed removal efficiency ( ) should equal after one bubble sweep. This assumes that all the oil drops that collide with a bubble stick to it. The solution of the First-order rate equation for a batch vessel for /j l/ 2 and ( = R yields ... 

The classical batch reactor is a perfectly mixed vessel in which reactants are converted to products during the course of a batch cycle. All variables change dynamically with time. The reactants are charged into the vessel. Heat and/or catalyst is added to initiate reaction. Reactant concentrations decrease and product concentrations increase with time. Temperature or pressure is controlled according to some desired time trajectory. Batch time is also a design and operating variable, which has a strong impact on productivity. 

MSMPR crystallizer A vessel operating in a continuous manner in which crystallization occurs and whose contents are perfectly mixed. As a result of perfect mixing, all variables descriptive of the mother liquor and crystals are constant throughout the vessel and are identical to corresponding variables in the product stream leaving the vessel. 

The most commonly used model of a mixed vessel is the fractional tubularity (delay-lag) model in which some part of the reactor is taken as exhibiting plug-flow conditions and contributing a delay and the rest of the reactor is taken as perfectly mixed (uniform concentrations) contributing a first-order lag (/( ,). The delay and lag in series are taken as describing the reactor residence time distribution (RTD). The delay-lag representation was validated using both CFD analysis and experimental residence time distributions (Walsh, 1993). 

Figure 4. Transient responses to slug (left) and step (right) inputs of reactant for first order reaction and selected kr values. The flow has the same residence time distribution as two perfectly mixed vessels in sequence. For slug input, c0 = m /V.

When dispersion is complete and uniform, the contents of the vessel are perfectly mixed with respect to both phases. In that case, the concentration of the solute in each of the two phases in the vessel is uniform and equal to the concentrations in the two-phase emulsion leaving the mixing tank. This is called the ideal CFSTR (continuous-flow-stirred-tank-reactor) model, sometimes called the perfectly mixed model. Next we develop an equation to estimate the Murphree-stage efficiency for liquid-liquid extraction in a perfectly mixed vessel. 

The transient mass balance for a perfectly mixed vessel for which M units of tracer are injected into the inlet stream is ... 

It is appropriate, however, to make some comment here on a few common departures from MSMPR operation. Three basic types of continuously operated mixed-suspension crystallizer are shown in Figure 9.7. In the simple MSMPR unit Figure 9.7a), where the outflow is of identical composition to that in the perfectly mixed vessel, the crystal and liquor residence times are equal ... 

Multiple flushing (displacement) treatments may be done to further reduce the partial pressure of water, because the work chamber is seldom a perfectly mixed vessel (Chapters 2.15 and 4.9). 

A deaning chamber is substantiaiiy iess weii mixed than perfect - at least because the racked parts block fluid flow and cause the flow patterns to be non-uniform. And the chamber shape, while often radially symmetrical, is not longitudinally symmetrical. So, the less than perfectly mixed vessel will retain a fluid component longer than would be expected from the assumption of perfect mixing. Deviation from the well-mixed residence time will be different for every vessel shape and loading of parts, and will be specifically unpredictable (Chapter 2.13.1). 

In a continuously well-mixed dryer, where the residence time distribution is that of a perfectly mixed vessel, Eq. (3) becomes... 

The assumption of perfect mixing applied in the batch and continuous MSMPR crystallizer models does not always apply, however, especially as vessel size increases. Methods for accounting for imperfect mixing and scale-up are considered in the next chapter. 

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