Residence times in CSTRs

Figure 3-5 Residence times in CSTR (shaded rectangle) and PFTR (area under curve) from the 1/r plot.

Calculate the ratio of residence times in CSTR and PFTR for the wth-order irreversible reaction... 

Figure 4.9 Bistability in the chlorite-iodide reaction as measured by (a) 460-nm absorbance (proportional to [I2]) and (b) an iodide-selective electrode. Dashed arrows indicate spontaneous transitions between states. Reciprocal residence time in CSTR = 5.4 X 10-- s-, [ClOjjo = 2.4 X 10-" M, pH = 3.35. (Adapted from Citri and Epstein, 1987.)...

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,... 

FIG. 23-7 Imp ulse and step inputs and responses. Typical, PFR and CSTR. (a) Experiment with impulse input of tracer, (h) Typical behavior area between ordinates at tg and ty equals the fraction of the tracer with residence time in that range, (c) Plug flow behavior all molecules have the same residence time, (d) Completely mixed vessel residence times range between zero and infinity, e) Experiment with step input of tracer initial concentration zero. (/) Typical behavior fraction with ages between and ty equals the difference between the ordinates, h — a. (g) Plug flow behavior zero response until t =t has elapsed, then constant concentration Cy. (h) Completely mixed behavior response begins at once, and ultimately reaches feed concentration. 

A factor in addition to the RTD and temperature distribution that affects the molecular weight distribution (MWD) is the nature of the chemical reaciion. If the period during which the molecule is growing is short compared with the residence time in the reactor, the MWD in a batch reactor is broader than in a CSTR. This situation holds for many free radical and ionic polymerization processes where the reaction intermediates are very short hved. In cases where the growth period is the same as the residence time in the reactor, the MWD is narrower in batch than in CSTR. Polymerizations that have no termination step—for instance, polycondensations—are of this type. This topic is treated by Denbigh (J. Applied Chem., 1, 227 [1951]). 

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. 

The Residence Time Distribution. All fluid elements have the same residence time in a batch reactor, but there will be a wide spread in residence times in a CSTR. 

Consider the entry of a small amount of fluid as tracer into the PFR at time t = 0. No tracer leaves the PFR until t = VPF/q0 = fPF, the mean residence time in the PFR, and hence no tracer leaves the two-vessel system, at the exit from the CSTR, during the period 0 sk fpF. As a result,... 

Figure 5. 2. Impulse and step inputs and responses. Typical7 PFR and CSTR. CaD Experiment with impulse input of tracer. CbD Typical behavior area between ordinates at ta and tb equals the fraction of the tracer with residence time in that range. Cc3...

From these graphs of 1 /r versus Cao Ca w can construct the residence times in PFTR and CSTR, as shown in Figure 3-5. 

With two equal-volume reactors, the overall conversion in these two reactors is independent of which reactor is first but in general it is a common strategy to use a CSTR first where the conversion is low and then switch to a PFTR as the conversion becomes high to rninirnize total reactor volume. The total residence time from CSTR+PFTR in series is indicated by the 1/ r plots in Figure 3-1 1. 

Figure 5-10 Residence times in a PFTR md CSTR for adiabatic reactors. The CSTR cm reqmre a much smdler i T than the PFTR and can exhibit multiple steady states for some T (arrows). 

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... 

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. 

The reactor is believed equivalent to a PFR in series with a CSTR. A second order reaction with kC0 =2.5 is to be processed there. Find (a) the residence time in each element (b) conversion in segregated flow (c) ideal conversion with the PFR first in series (d) ideal conversion with the CSTR first in series. 

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