Residence-time distributions single-CSTR

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

We focus attention in this chapter on simple, isothermal reacting systems, and on the four types BR, CSTR, PFR, and LFR for single-vessel comparisons, and on CSTR and PFR models for multiple-vessel configurations in flow systems. We use residence-time-distribution (RTD) analysis in some of the multiple-vessel situations, to illustrate some aspects of both performance and mixing. 

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. 

After studying this chapter the reader will be able to describe the cumulative F(t), external age E(t), and internal age I(t) residence-time distribution functions and to recognize these functions for PFR, CSTR, and laminar flow reactions. The reader will also be able to apply these functions to calculate the conversion and concentrations exiting a reactor using the segregation model and the maximum mixedness model for both single and multiple reactions. 

During this residence time distribution testing, the Photo-CREC-Water I was operated in the single pass mode with no water recycling and samples taken every 10 seconds. The Peclet number assessed with this method was 30 and the number of ideal CSTR tanks was estimated as 15. Since the number of baskets in Photo-CREC-Water I is 16, this demonstrates that each basket can be viewed as a close equivalent to an ideal single mixing stage. 

The distribution of residence times (Equations (8.1) and (8.2)) which was discussed earlier represents another difference between batch or PFTs and CSTRs. Figure 8.1 shows residence time distributions for a single CSTR and differrait numbers of equal-size CSTRs connected in series. All curves are for the same total residence time r = 1.0, where r = n in which n is the number of CSTRs and the mean residence time of each one. If all particles are nucleated in the first CSTR of a CSTR series the curves shown in Figure 8.1 would also represent the age distribution of the particles in the process effluent stream. The particle... 

This is considerably broader (D > 1) than the Poisson distribution (D = 1) resulting from batch polymerization. The broader distribution is, of course, due to the broad residence time distribution of the CSTR. A train of CSTRs in series will give the system more of a PFR character, and the resulting polydispersity will be between that of the PFR and that of the single CSTR. 

These are identical for the limiting values for the batch reactor, except that they require only the assumption of perfect mixing. Thus, while polydispersi-ties of 2.0 and 1.5 for termination by disproportionation and combination respectively represent unattainable minima for batch polymerization, these same values represent feasible operation in a well-mixed CSTR. Thus, the CSTR will give a narrower dead polymer number chain length distribution since it is possible to maintain a constant reaction environment at steady state. The effect of residence time distribution on the polydispersity is negligible since the lifetime of a single radical is far less than the average residence time. Likewise, for a copolymerization in a CSTR at steady state, the constancy of... 

In continuous operation mode, both feed and effluent streams flow continuously. The main characteristic of a continuous stirred tank reactor (CSTR) is the broad residence time distribution (RTD), which is characterized by a decreasing exponential function. The same behavior describes the age of the particles in the reactor and hence the particle size distribution (PSD) at the exit. Therefore, it is not possible to obtain narrow monodisperse latexes using a single CSTR. In addition, CSTRs are hable to suffer intermittent nucleations [89, 90) that lead to multimodal PSDs. This may be alleviated by using a tubular reactor before the CSTR, in which polymer particles are formed in a smooth way [91]. On the other hand, the copolymer composition is quite constant, even though it is different from that of the feed. 

The autoclave reactor is a single or a multiple stage continuous stirred tank reactor (CSTR), as shown in Figures 4.2 and 4.3, with its characteristic residence time distribution. The different reaction zones can be isolated by means of proper baffles at the agitator itself. The number of zones in a multistage autoclave varies between... 

A continuous tubular-loop process has been patented (10) and used for relatively small-scale production. The loop process consists of a tube-pump system in which the rate of latex circulation around the tube loop is considerably greater than the throughput rate. Thus, the distribution of residence times should be nearly the same as that of a single CSTR. 

Because chain lifetimes are much shorter than chain residence times, the instantaneous MWD w(r) of group I polymerization is determined only by the birth condition but not influenced by the residence time. In a steady-state homogeneous CSTR, there is only one single condition for chains to be generated, that is, imder constant r and fi. The MWD of the total polymer WeA(r) represents a single instantaneous distribution and is therefore narrower than those of batch reactor and PFTR, which are cumulative of many instantaneous distributions at various r and p values. 

The main distinction of polymerization in continuous stirred tank reactors (CSTRs) from batch/plug-fiow polymerization is the distribution of reactor residence times. In a single CSTR, the distribution of molecules in residence time (i.e., the probability to be in the reactor during time period t is given by [37, 38]... 

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