Of residence times in a CSTR

For the consecutive reactions 2A B and 2B C, concentrations were measured as functions of residence time in a CSTR. In all experiments, C o = 1 lb moPfF. Volumetric flow rate was constant. The data are tabulated in the first three columns. Check the proposed rate equations,... 

The dimensionless diffusion coefficient D can be regarded in some sense as the reaction-diffusion equivalent of the flow rate, or the inverse of the residence time, in a CSTR. In fact, we can interpret D as the quotient of the chemical and diffusional timescales... 

In order to show that there is not a unique residence time in a CSTR, consider the following experiment. A CSTR is at steady state and a tracer species (does not react) is flowing into and out of the reactor at a concentration C°. At r = 0, the feed is changed to pure solvent at the same volumetric flow. The material balance for this situation is ... 

The performance of a single CSTR can he quite different from that of a batch reactor for a number of reasons. First, the distribution of reactor residence times in a CSTR is quite broad. This leads to broad size and age distributions of the latex particles. By contrast, the polymer particles in a batch reactor are usually all formed near the h< inning of the reaction and the particle size and age distrihutions of the product latex are narrow. 

Dependence of isobutane oxidation on temperature and the residence time in a CSTR was discussed by Caprio et al. (1981). Different oscillations were detected. Jensen and Ray (1980-1, 2) studied horatian oscillations, see Section E.ll... 

As indicated above, a change in a variable—say, the residence time in a CSTR—can cause period doubling and further complications of the wave pattern. Chaos can be viewed as the ultimate result of such variations piling complications upon one another while ever shortening the span within which a new pattern persists. 

Figure ILL The relation between the degree of conversion of massive and porous solid particles, when surface reaction is rate determining, and the dimensionless residence time in a CSTR, according to eqs, (ILl) and (112), The dimensionless residence time is the ratio of the mean residence time X and the time required for complete dissolution t.

The particles in the latex stream leaving a continuous stirred-tank reactor (CSTR) would have a broad distribution of residence times in the reactor. This age distribution, given by Equation 5, comes about because of the rapid mixing of the feed stream with the contents of the stirred reactor. 

Material balances relating concentration and temperature of adiabatic reaction in a CSTR are obtained for several different rate equations or conditions. The curves are drawn with feed concentration Caf = 1 and residence time t = 1 in the equation,... 

A way of transforming a two-variable system to one of higher order is to make one of the parameters in the system a function of time. Thus with a CSTR we might vary the pumping rate (and hence alter the residence time) in a time-dependent and perhaps oscillatory manner. The interaction of the original chemical non-linearity and the imposed forcing shows similar patterns to that displayed by the map. Finally, chemical systems with three or more independent concentrations may drive themselves, of their own free will so to speak, to the heights of complexity. 

Figure 2. Isothermal polymerization of methyl methacrylate in a CSTR (1 5). a. Predicted steady-state monomer conversion vs. reactor residence time for the solution polymerization of MMA in ethyl acetate at 86 °C. h. Steady-state and dynamic experiments for the isothermal solution polymerization of MMA in ethyl acetate (solvent fraction O.k) ( ) steady states,...

Macro- and miniemulsion polymerization in a PFR/CSTR train was modeled by Samer and Schork [64]. Since particle nucleation and growth are coupled for macroemulsion polymerization in a CSTR, the number of particles formed in a CSTR only is a fraction of the number of particles generated in a batch reactor. For this reason, their results showed that a PFR upstream of a CSTR has a dramatic effect on the number of particles and the rate of polymerization in the CSTR. In fact, the CSTR was found to produce only 20% of the number of particles generated in a PFR/CSTR train with the same total residence time as the CSTR alone. By contrast, since miniemulsions are dominated by droplet nucleation, the use of a PFR prereactor had a negligible effect on the rate of polymerization in the CSTR. The number of particles generated in the CSTR was 100% of the number of particles generated in a PFR/CSTR train with the same total residence time as the CSTR alone. 

Observation (i) above can be understood in terms of droplet nucleation and the lack of competition between nucleation and growth. A mechanistic understanding of observation (ii) above was provided by Samer and Schork [64]. Nomura and Harada [136] quantified the differences in particle nucleation behavior for macroemulsion polymerization between a CSTR and a batch reactor. They started with the rate of particle formation in a CSTR and included an expression for the rate of particle nucleation based on Smith Ewart theory. In macroemulsion, a surfactant balance is used to constrain the micelle concentration, given the surfactant concentration and surface area of existing particles. Therefore, they found a relation between the number of polymer particles and the residence time (reactor volume divided by volumetric flowrate). They compared this relation to a similar equation for particle formation in a batch reactor, and concluded that a CSTR will produce no more than 57% of the number of particles produced in a batch reactor. This is due mainly to the fact that particle formation and growth occur simultaneously in a CSTR, as suggested earlier. 

The ratio (1 /v) is the volume of mixture in the reactor divided by the volume of mixture fed to the reactor per unit time and is called the space time, t. The inverse of the space time is called the space velocity. In each case, the conditions for the volume of the feed must be specified temperature, pressure (in the case of a gas), and state of aggregation (liquid or gas). Space velocity and space time should be used in preference to contact time or holding time since there is no unique residence time in the CSTR (see below). Why develop this terminology Consider a batch reactor. The material balance on a batch reactor can be written [from Equation (3.2.1)] ... 

Thus, the mean residence time for a CSTR is the space time. The fact that (t) = t holds for reactors of any geometry and is discussed in more detail in Chapter 8. 

Earlier it was shown that generally the mean residence time in a reactor is equal to V/u, or t. This relationship can be shown in a simpler fashion for the CSTR. Applying the definition of a mean residence time to the RTD for a CSTR, we obtain... 

First consider the CSTR followed by the PFR (Figure 13-19). The residence time in the CSTR will be denoted by tj and the residence time in the PFR by If a pulse of tracer is injected into the entrance of the CSTR, the CSTR output concentration as a function of time will be... 

CSTRs produce the narrowest possible MWDs for fast-chain-growth, short-chain lifetime polymerizations like free-radical and coordination metal catalysis. The mean residence time in the CSTR will be minutes to hours, and the chain lifetimes are fractions of a second. Any chain that initiates in the CSTR will finish its growth there. All the polymer molecules are under identical, well-mixed conditions and will have as narrow an MWD (typically PD 2) as is possible for the given kinetic scheme. 

The main disadvantage of continuous operation is that the reaction rate is nearly always lower than the average rate for a batch reaction. In most cases, the batch reaction rate decreases as the conversion increases, and in the CSTR the reaction rate is the same as the final reaction rate in the batch reactor. For high conversions, the final rate may be several-fold lower than the average rate, and the average residence time in the CSTR must then be several-fold greater than the reaction time in a batch reactor. 

The average residence time in the CSTR is the volume V divided by the volumetric flow rate F, or l = V/F. The ratio of CSTR residence time to batch residence time is readily derived for simple kinetic models. For a first-order reaction in a CSTR, the steady-state material balance is... 

Output and Visualization Upon specification of a feed point Cj and CSTR residence time t, a CSTR effluent concentration C (or many concentrations in the case of multiple steady states) can be obtained. Unlike the PFR, which operates over a range of achievable concentrations, the CSTR operates at distinct concentrations for a fixed Cf and T. Specification of a different Cj or r results in a different value for C as a result. 

Results in a distinct set of points that satisfy the CSTR equation for a residence time. Many residence times give a CSTR locus. 

S.4.3.2 CSTR Locus from the Feed To plot the CSTR locus from the feed point, the system of CSTR equations must be solved (simultaneously) over a range of residence times. In comparison to the Van de Vusse system, the kinetics for this system is more difficult to solve analytically. Numerical solution of the CSTR locus is therefore required. 

For the first criterion, one compares the reactor volumes based on the average residence time for a given extent of reaction or final conversion. The average residence time depends on the reaction kinetics and therefore the reaction rate, which in turn depends on whether the reaction takes place at constant volume or variable volume. In a system at constant volume, one obtains directly a ratio between the volumes, because the average residence time is equal to space time which is defined as the ratio between reactor volume and inlet volumetric flow in the reactor. For the same conversion, the ratio between volumes is proportional. Since the average residence time in a PFR reactor is similar to the reaction time in a batch reactor, we may assume that they have similar behaviors and then we compare only the ideal tubular reactors (PFR — plug flow reactor) to the ideal tank reactors (CSTR—continuous stirred-tank reactor). 

So far we have studied separately the continuous-flow stirred tank reactor (CSTR) and the plug flow reactor (PFR) each with their distinct characteristics. When comparing them, we have seen that for the same final conversion, the volume of the CSTR is always larger than that of the PFR, especially for high conversions. Additionally, the average residence time in the CSTR is also higher than that in the PFR. It is important to note, however, that the yield and selectivity are always higher in a PFR as compared to a CSTR. 

Trains of up to 12 large CSTRs are used in the production of waterborne polymer commodities such as SBR [65]. Large CSTRs are not well adapted to the production of specialties because of the difficulties associated with grade transitions. Flexibility significantly increases by decreasing the average residence time in the CSTR. Thus, the production of a family of specialty emulsion polymers in a single CSTR has been reported [66]. 

As a consequence of this condition, in a CSTR all cells with t < F(cells with t < t ) are not yet ripe enough for production. Only those cells with a lifetime t >t t > t ) contribute to production. With the aid of the mathematical function that describes the residence time distribution in the liquid phase of a CSTR (Equ. 3.11), one can write... 

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