Of CSTRs

Plug flow reactors with recycle exhibit some of the characteristics of CSTRs, including the possibility of multiple steady states. This topic is explored by Penmutter Stah dity of (%emical Reactors, Prentice-Hall, 1972). 

An economical optimum number of CSTRs and their auxiliaries in series is 4 to 5. 

CSTRs and other devices that require flow control are more expensive and difficult to operate. Particularly in steady operation, however, the great merit of CSTRs is their isothermicity and the fact that their mathematical representation is algebraic, involving no differential equations, thus maldng data analysis simpler. 

Real reactors deviate more or less from these ideal behaviors. Deviations may be detected with re.sidence time distributions (RTD) obtained with the aid of tracer tests. In other cases a mechanism may be postulated and its parameters checked against test data. The commonest models are combinations of CSTRs and PFRs in series and/or parallel. Thus, a stirred tank may be assumed completely mixed in the vicinity of the impeller and in plug flow near the outlet. 

Figure 23-7 illustrates the responses of CSTRs and PFRs to impmse or step inputs of tracers. 

FIG. 23-17 Multiple steady states of CSTRs, stable and unstable, adiabatic except the last item, (a) First-order reaction, A and C stable, B unstable, A is no good for a reactor, the dashed line is of a reversible reaction, (h) One, two, or three steady states depending on the combination Cj, Ty). (c) The reactions A B C, with five steady states, points 1, 3, and 5 stable, (d) Isothermal operation with the rate equation = 0 /(1 -I- C y = (C o Cy/t. 

Various experimental methods to evaluate the kinetics of flow processes existed even in the last centuty. They developed gradually with the expansion of the petrochemical industry. In the 1940s, conversion versus residence time measurement in tubular reactors was the basic tool for rate evaluations. In the 1950s, differential reactor experiments became popular. Only in the 1960s did the use of Continuous-flow Stirred Tank Reactors (CSTRs) start to spread for kinetic studies. A large variety of CSTRs was used to study heterogeneous (contact) catalytic reactions. These included spinning basket CSTRs as well as many kinds of fixed bed reactors with external or internal recycle pumps (Jankowski 1978, Berty 1984.)... 

The spread of CSTR use for kinetic studies only started in the 1960s. References can be found even earlier than that of Bodenstein (1908) although most of these references discuss only the use for homogeneous kinetic studies. In view of this background, the story of the development at Union Carbide Corporation may be interesting. 

Tubular reactors have empty spaces only between the catalyst particles. This eliminates one big disadvantage of CSTRs. On the other hand, the mathematical description and analysis of the data become more complicated. For chemical reaction studies it is still useful to detect major changes or differences in reaction mechanism. 

Adesina, A. A., Design of CSTRs In Tandem Revisited, Chemical Engineering Education, pp. 164-168, Summer 1992. 

Figure 8-38. Residence time distributions of some commerciai and fixed bed reactors. The variance, equivaient number of CSTR stages, and Peciet number are given for each reactor. (Source Wales, S. M., Chemicai Process Equipment—Seiection and Design, Butterworths, 1990.)...

Their studies also showed the importanee of the reaeting system kineties for better design operation of CSTR reaetors. 

This is a recursion formula for the exact case. We would like to be able to apply this to any number n of CSTRs in series and find an analytical and then quantitative result for comparison to the exact PFR result. To do this weneedrecursive programming. There are threeprogrammingstylesin Mathematica Rule-Based,Functional,and Procedural.Wewill attackthisprobleminrecursionwith Rule-Based,Functional,and Procedural programming. WecanbeginbylookingattherM/e-tosed recursioncodesforCaandCbinanynCSTRs. 

Monod kinetics are considered in a CSTR with an organism growing with an initial substrate concentration of 50g-l 1 and kinetic parameters of Ks = 2g-l 1 and /Amax = 0.5lr. (a) What would be the maximum dilution rate for 100% yield of biomass with maximum rate (b) If the same dilution is used, what would be number of CSTRs in series ... 

Excessive backmixing can be very difficult to prevent at low reactant viscosities, so an LFR may not be practicable where dissolved polymer solids are low, either due to low conversions or high solvent levels. Under these conditions, LFR behavior can be approached by incorporating a sufficient number of CSTR s in series. 

As can be seen, the principal differences of this process from the earlier German process includes a) reflux cooling of the first reaction zone, b) the possible division of the first reaction zone into a series of CSTR s and c) the incorporation of a devolatilization step. 

Numerical calculations are the easiest way to determine the performance of CSTRs in series. Simply analyze them one at a time, beginning at the inlet. However, there is a neat analytical solution for the special case of first-order reactions. The outlet concentration from the nth reactor in the series of CSTRs is... 

Thus, the limit gives the same result as a piston flow reactor with mean residence time t. Putting tanks in series is one way to combine the advantages of CSTRs with the better yield of a PFR. In practice, good improvements in yield are possible for fairly small N. 

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

Cross-flow reactors are fed continuously with streams of components of the reaction mixture whereby some components are introduced at the inlet, while others are introduced at other locations. The reaction mixture flows out continuously from the end of the reaction zone. A cascade of CSTRs with additional feeds to individual reactors represents a cross-flow reactor system. Cross-flow reactors are also operated at steady-state conditions ... 

Parallel reactions, oai = om2, a i = am = 0, Ei > E2. The. selectivity to the desired product increases with temperature. The highest allowable temperature and the highest reactant concentrations should be applied. A batch reactor, a tubular reactor, or a cascade of CSTRs is the best choice. 

Consecutive reactions, isothermal reactor cmi < cw2, otai = asi = 0. The course of reaction is shown in Fig. 5.4-71. Regardless the mode of operation, the final product after infinite time is always the undesired product S. Maximum yields of the desired product exist for non-complete conversion. A batch reactor or a plug-flow reactor performs better than a CSTR Ysbr.wux = 0.63, Ycstriiuix = 0.445 for kt/ki = 4). If continuous operation and intense mixing are needed (e.g. because a large inteifacial surface area or a high rate of heat transfer are required) a cascade of CSTRs is recommended. 

Algebraic equations Steady state of CSTR with first-order kinetics. Algebraic solution and optimisation (least squares. Draper and Smith, 1981). Steady state of CSTR with complex kinetics. Numerical solution and optimisation (least squares or likelihood function). 

Schematic representation of CSTR indicating process variables.

In order to reduce the disparities in volume or space time requirements between an individual CSTR and a plug flow reactor, batteries or cascades of stirred tank reactors ard employed. These reactor networks consist of a number of stirred tank reactors confiected in series with the effluent from one reactor serving as the input to the next. Although the concentration is uniform within any one reactor, there is a progressive decrease in reactant concentration as ohe moves from the initial tank to the final tank in the cascade. In effect one has stepwise variations in composition as he moves from onfe CSTR to another. Figure 8.9 illustrates the stepwise variations typical of reactor cascades for different numbers of CSTR s in series. In the general nonisothermal case one will also en-... 

ILLUSTRATION 8.7 DETERMINATION OF CSTR SIZE REQUIREMENTS FOR CASCADES OF VARIOUS SIZES— GRAPHICAL SOLUTION... 

ILLUSTRATION 8.8 DETERMINATION OF REACTOR SIZE REQUIREMENTS FOR A CASCADE OF CSTR s—ALGEBRAIC APPROACH... 

These relations support our earlier assertion that for the same overall conversion the total volume of a cascade of CSTR s should approach the plug flow volume as the number of reactors in the cascade is increased. 

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