Multistage CSTR

Multistage CSTR Since tubular reactor performance can be simulated by a series of CSTRs, multistage CSTR tracer models are useful in analyzing data from empty tubular and packed-bed reactors. The solution for a tracer through n CSTRs in series is found by induction from the solution of one stage, two stages, and so on. 

For complex reac tions and with multistage CSTRs, more than three steady states can exist (as in Fig. 23-17c). Most of the work on multi-phcities and instabilities has been done only on paper. No plant studies and a very few laboratoiy studies are mentioned in the comprehensive reviews of Razon and Schmitz Chem. Eng. Sci., 42, 1,005-1,047 [1987]) and Morbidelli et al. (in Carberry and Varma, Chemical Reaction and Reactor Engineering, Dekker, 1987, pp. 973-1,054). 

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... 

Distribution models are curvefits of empirical RTDs. The Gaussian distribution is a one-parameter function based on the statistical rule with that name. The Erlang and gamma models are based on the concept of the multistage CSTR. RTD curves often can be well fitted by ratios of polynomials of the time. 

Multistage CSTR This model has a particular importance because its RTD curve is beU-shaped hke those of many experimental RTDs of packed beds and some empty tubes. The RTD is found by induction by solving the equations of one stage, two stages, and so on, with the result. 

A stirred-tank flow reactor may be single-stage or multistage. As an ideal backmix flow reactor, it is referred to as a CSTR or multistage CSTR this is treated in Chapter 14. Nonideal flow effects are discussed in Chapter 20. 

The use of a single-stage CSTR for HF alkylation of hydrocarbons in a special forced-circulation shell-and-tube arrangement (for heat transfer) is illustrated by Perry et al. (1984, p. 21-6). The emulsion copolymerization of styrene and butadiene to form the synthetic rubber SBR is carried out in a multistage CSTR. 

Figure 14.11 Basis for graphical solution for multistage CSTR (for A +. .. - products)...

The following example illustrates a simple case of optimal operation of a multistage CSTR to minimize the total volume. We continue to assume a constant-density system with isothermal operation. 

For CSTRs in parallel with the feed split as for optimal performance, the fact that two (or more) reactors behave the same as one CSTR of the same total volume means that the RTD is also the same in each case. Here, we consider the RTD for CSTRs in series, as in a multistage CSTR (Section 14.4). In the following example, the RTD is obtained for two tanks in series. The general case of N tanks in series is considered in Chapter... 

Many chemical and biological processes are multistage. Multistage processes include absorption towers, distillation columns, and batteries of continuous stirred tank reactors (CSTRs). These processes may be either cocurrent or countercurrent. The steady state of a multistage process is usually described by a set of linear equations that can be treated via matrices. On the other hand, the unsteady-state dynamic behavior of a multistage process is usually described by a set of ordinary differential equations that gives rise to a matrix differential equation. 

Tubular Reactor with Dispersion As discussed earlier, a multistage CSTR model can be used to simulate the RTD in pilot and commercial reactors. The dispersion model, similar to Fick s molecular diffusion law with an empirical dispersion coefficient De replacing the diffusion coefficient, may also be used. 

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