The CSTR

Continuous-Flow Stirred-Tank Reactor. In a continuous-flow stirred-tank reactor (CSTR), reactants and products are continuously added and withdrawn. In practice, mechanical or hydrauHc agitation is required to achieve uniform composition and temperature, a choice strongly influenced by process considerations, ie, multiple specialty product requirements and mechanical seal pressure limitations. The CSTR is the idealized opposite of the weU-stirred batch and tubular plug-flow reactors. Analysis of selected combinations of these reactor types can be useful in quantitatively evaluating more complex gas-, Hquid-, and soHd-flow behaviors. 

If severe heat-transfer requirements are imposed, heating or cooling zones can be incorporated within or external to the CSTR. For example, impellers or centrally mounted draft tubes circulate Hquid upward, then downward through vertical heat-exchanger tubes. In a similar fashion, reactor contents can be recycled through external heat exchangers. 

The RTD is a distinctive characteristic of mixing behavior. In Fig. 7-2>e, the CSTR has an RTD that varies as the negative exponential of the time and the PFR is represented by a vertical line at = 1. Multistage units and many packed beds have beU-shaped RTDs, like that of... 

In a sequence of PFR and CSTR, better performance is obtained with the PFR last. Performance of reversible reactions is improved with the CSTR at a higher temperature. 

The value of n is the only parameter in this equation. Several procedures can be used to find its value when the RTD is known experiment or calculation from the variance, as in /i = 1/C (t ) = 1/ t C t), or from a suitable loglog plot or the peak of the curve as explained for the CSTR battery model. The Peclet number for dispersion is also related to n, and may be obtainable from correlations of operating variables. 

Example (d) The rate equation and the CSTR material balance of this process are ... 

As another example of the first interac tion, a potential parameter in the analysis of the CSTR is estimating the actual reactor volume. CSTR shown in Fig. 30-7. The steady-state material balance for this CSTR having a sin e reaction can be represented as ... 

As can be seen for infinite recycle ratio where C = Cl, all reactions will occur at a constant C. The resulting expression is simply the basic material balance statement for a CSTR, divided here by the catalyst quantity of W. On the other side, for no recycle at all, the integrated expression reverts to the usual and well known expression of tubular reactors. The two small graphs at the bottom show that the results should be illustrated for the CSTR case differently than for tubular reactor results. In CSTRs, rates are measured directly and this must be plotted against the driving force of... 

Notice on tliis graph that the 25°C experiments were informative, and results were in the measurable range. At 135°C some intermediate, semi-quantitative results could be seen. At 285°C no detectable adsorption could be seen. Taking the high adsorption result at 25°C as 22.4 mL/kg, this converts to 0.001 mole/kg. Compare this with the 0.22 mole/kg needed for measurable result in the CSTR case in the previous section. 

With a high heat removal rate, corresponding to an almost vertical line, as was the case in the experiments in the CSTR, the full heat generation curve could be measured. An intersection could be achieved between the heat generation curve and the very steep heat removal line at the point where the non-existent middle point was, but this was just one of the many stable solutions possible and not an unstable point. ... 

Aris (1969) pointed out that the mathematical definition of the CSTR stability problem and the catalyst particle problem cooled by the feed flow were essentially identical. 

For a perfeetiy mixed CSTR, it is assumed that the vessel eontents are perfeetiy homogeneous and have the same eomposition as the exit stream. Considering a step input into the CSTR, a maeroseopie material balanee gives... 

Thischapterhasbeendevotedtocontinuousreactorsandtheiranalyses.Wehaveexamined the powerful idealizations of the CSTR and PER. Pseudo-steady states and steady states... 

The flow of slurry within all the agitated erystallizer vessels illustrated is elearly eomplex and mixed to a greater or lesser extent at the mieroseopie level. In order to ease theoretieal analysis a new type of vessel therefore had to be invented This idealized vessel has beeome known as the eontinuous MSMPR erystallizer, after Randolph and Lawson (1988). The MSMPR is the erystal-lization analogue of the CSTR (eontinuous stirred tank reaetor) employed in idealizations of ehemieal reaetion engineering. 

Reliable kinetie data are of paramount importanee for sueeessful modelling and seale-up of preeipitation proeesses. Many data found in the literature have been determined assuming MSMPR eonditions, analogous to the CSTR model in reaetion engineering. Here, a method developed by Zauner and Jones (2000a) is outlined. 

The ICR flow rate was five to eight times faster than the CSTR. The overall conversion of sugars in the ICR at a 12 hour retention time was 60%, At this retention time, the ICR was eight times faster than CSTR, but in the CSTR an overall conversion rate of 89% was obtained. At the washout rate for the chemostat, the ICR resulted in a 38% conversion of total sugars. Also, the organic acid production rate in the ICR was about four times that of the CSTR. At a higher retention time of 28 hours, the conversion of glucose in the ICR and CSTR are about the same, but the conversion of xylose reached 75% in the ICR and 86% in the CSTR. 

Equations 11 and 12 are only valid if the volumetric growth rate of particles is the same in both reactors a condition which would not hold true if the conversion were high or if the temperatures differ. Graphs of these size distributions are shown in Figure 3. They are all broader than the distributions one would expect in latex produced by batch reaction. The particle size distributions shown in Figure 3 are based on the assumption that steady-state particle generation can be achieved in the CSTR systems. Consequences of transients or limit-cycle behavior will be discussed later in this paper. 

One of the most promising ways of dealing with conversion oscillations is the use of a small-particle latex seed in a feed stream so that particle nucleation does not occur in the CSTRs. Berens (3) used a seed produced in another reactor to achieve stable operation of a continuous PVC reactor. Gonzalez used a continuous tubular pre-reactor to generate the seed for a CSTR producing PMMA latex. 

Since a CSTR operates at or close to uniform conditions of temperature and composition, its kinetic and product parameters can usually be predicted more accurately and controlled with greater ease. The CSTR can often be operated at a selected conversion level to optimize space-time yield, or where a particular product parameter is especially favored. 

A schematic drawing is shown in Fig. 14. Two "prepoly CSTR s in parallel, each with a 1400-kg. holduo, fed a total of 44 kg./hr. of syrup at 80 C and 33-35% conversion to a second-stage LFR. The CSTR s were cooled via jackets and internal cooling coils, and slowly agitated with gate-type agitators. 

The reactors had relatively limited heat transfer capability and polyrates therefore had to be kept low. This was accomplished by operating at low temperatures. (The rate in the CSTR s was about. 5%/hr.). Since chain transfer agents were not employed, product Staudinger molecular weight was about 100,000, very high by current commercial standards. 

The use of the CSTR and LFR by this process follows the guidelines discussed in Section 2.3.2. The former is used for the first polymerization stage where viscosity is relatively low. The latter where viscosities are high enough to suppress backmixing and where very high exit conversions are desired. 

This process uses three CSTR s followed by an LFR for finishing. The CSTR designs change to accommodate the changing mixing and heat transfer requirements as conversion rises. 

In summary, we have considered three characteristic times associated with a CSTR /mix, ri/2, and t. Treating the CSTR as a perfect mixer is reasonable provided that /mix is substantially shorter than the other characteristic times. 

Also assume that the pilot- and full-scale vessels will operate at the same temperature. This means that A(o-out,bout, . )and/i/2 will be the same for the two vessels and that Equation (1.49) will have the same solution for provided that 7 is held constant during scaleup. Scaling with a constant value for the mean residence time is standard practice for reactors. If the scaleup succeeds in maintaining the CSTR-like environment, the large and small reactors will behave identically with respect to the reaction. Constant residence time means that the system inventory, pV, should also scale as S. The inventory scaleup factor is defined as... 

Figures 1.6 and 1.7 display the conversion behavior for flrst-and second-order reactions in a CSTR and contrast the behavior to that of a piston flow reactor. It is apparent that piston flow is substantially better than the CSTR for obtaining high conversions. The comparison is even more dramatic when made in terms of the volume needed to achieve a given conversion see Figure 1.8. The generalization that...

Compare these results with those of Equation (2.22) for the same reactions in a batch reactor. The CSTR solutions do not require special forms when some of the rate constants are equal. A plot of outlet concentrations versus t is qualitatively similar to the behavior shown in Figure 2.2, and i can be chosen to maximize bout or Cout- However, the best values for t are different in a CSTR than in a PFR. For the normal case of bi = 0, the t that maximizes bout is a root-mean, t ix = rather than the log-mean of... 

Equation (2.23). When operating at tmax, the CSTR gives a lower yield of B and a lower selectivity than a PFR operating at its t ix-... 

Example 4.8 Find the yield for a first-order reaction in a composite reactor that consists of a CSTR followed by a piston flow reactor. Assume that the mean residence time is ij in the CSTR and ti in the piston flow reactor. 

Example 4.12 used N stirred tanks in series to achieve a 1000-fold reduction in the concentration of a reactant that decomposes by first-order kinetics. Show how much worse the CSTRs would be if the 1000-fold reduction had to be achieved by dimerization i.e., by a second order of the single reactant type. The reaction is irreversible and density is constant. 

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