Plug flow reactor cascade

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. 

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-... 

Size Comparisons Between Cascades of Ideal Continuous Stirred Tank Reactors and Plug Flow Reactors. In this section the size requirements for CSTR cascades containing different numbers of identical reactors are compared with that for a plug flow reactor used to effect the same change in composition. 

The ratio of equations 8.3.58 and 8.3.57 gives the relative total space time requirement for a cascade of stirred tank reactors vis a vis a plug flow reactor. 

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

The system mostly applied in practice for supply of ozone is the bubble column and the stirred tank reactor. With these reactor systems it is always possible to set up the complete reactor modification as a plug flow reactor, a continuous flow single stirred tank reactor or a cascade of stirred tank reactors. 

Several continuous stirred tank reactors are often operated in series or cascade as shown in Fig. 13. In this way, the disadvantages of the relatively low reactant concentration on the one hand, and by-passing on the other, may be partially off-set. As the number of tanks in series increases, the performance of the complete system approaches that of a plug-flow reactor and, in the limit of an infinite number of tanks, becomes equal to it. 

The bioreactor has been introduced in general terms in the previous section. In this section the basic bioreactor concepts, i.e., the batch, the fed-batch, the continuous-flow stirred-tank reactor (CSTR), the cascade of CSTRs and the plug-flow reactor, will be described. 

The representation of different types of reactor units in the approach proposed by Kokossis and Floudas (1990) is based on the ideal CSTR model, which is an algebraic model, and on the approximation of plug flow reactor, PFR units by a series of equal volume CSTRs. The main advantage of such a representation is that the resulting mathematical model consists of only algebraic constraints. At the same time, however, we need to introduce binary variables to denote the existence or not of the CSTR units either as single units or as a cascade approximating PFR units. As a result, the mathematical model will consist of both continuous and binary variables. 

FIGURE 7.15 Cumulative weight distribution versus dimensionless size for a cascade of reactors with nucleation only in the first tank or for a dispersed plug flow reactor with nucleation only at the entrance to the reactor. Data from Abegg and Balaktishnan [331. 

I. G. Farbenindustrie in Germany implemented such a concept to produce polystyrene commercially in the 1930s. Two CSTRs in parallel followed by a plug flow reactor were used in their process. During World War II, Union Carbide applied for a patent (US Patent 2496653, 1950) for a continuous polystyrene process. Their process consisted of three cascade CSTR reactors followed by a plug flow reactor. The temperature in the three CSTR reactors is 100, 115-120 and 140 °C, respectively. The conversion at the outflow of the third CSTR reactor is around 85 %. The temperature in the plug flow reactor is between 210 and 215 °C. The final conversion at the plug flow reactor was claimed to be 97 %. 

Other chemical companies have also designed their own continuous process to produce high-impact polystyrene (HIPS), such as the Dow process, which consists of three elongated reactors in series (US Patent 2727 884, 1955) the BASF process, which consists of a prepolymerization CSTR followed by cascade of three CSTRs (US Patent 3 658 946, 1972) the Shell process, which consists of three CSTRs followed by a plug flow reactor (US Patent 4011 284, 1977) and the Monsanto process, which consists of a CSTR followed by a horizontal plug flow reactor (US Patent 3 903 202, 1975). 

In order to increase the driving force for crystallization or increase the yield per pass through the system, a continuous crystallization system can be intentionally operated as a cascade, as shown in Fig. 7-9. A significant number of these crystallizers in series become, in effect, a plug flow reactor. 

This can be illustrated by an extension of the scenario presented above Initially, there is no rule for mapping a plug flow reactor to a cascade of two reactors. Instead, the first time the situation occurs, the mapping is performed manually The user creates the reactor cascade in the simulation model and adds a link to the integration document. From this link, the link template in Fig. 3.27 b) is abstracted. The link template is consistency-checked against the available link types. It is detected that the link template fits the ReactorCascadeLink type from Fig. 3.26 and, therefore, it is permanently added to the rule base and applied in further runs of the integrator. 

Figure E8.5.1 shows the reaction curve for a cascade of equal-size tanks, and compare them to those of a plug-flow reactor and a single CSTR.

An optimized cascade of three CSTRs 144.17 L A plug-flow reactor (from Example 7.1) 100.08 L... 

A very common variation of the CSTR is a cascade of n CSTRs. With an increasing number of reaction vessels, the cascade approximates to the plug-flow reactor. The product concentration increases stepwise from vessel to vessel. For example, a two-stage cascade can be used to overcome effects of product inhibition, e.g. in the synthesis of L-tert-leucine 1421 or GDP-Manl144, 145l The basis for calculating reactor operation conditions is the formulation of mass balances for all reaction components for the distinct reactor type. The mass balances for the above reactors can be formulated as follows ... 

A plug flow reactor may be realized using immobilized enzymes within a column reactor or using soluble enzymes within a cascade of membrane reactors. A batch or a repetitive batch process with soluble enzymes (see below) has the same productivity as the plug flow reactor. 

In order to improve the flow characteristics through the tubular reactor, 10 lengths (each 50 cm) of static mixer elements were inserted at 100 cm internals along the tube. Residence-time distribution studies using a pulse of potasiun chloride as tracer shewed that this tubular reactor had the flow characteristics equivalent to a cascade of 35 stirred tanks in series. Thus for practical purposes, this tube can be considered to have flow characteristics equivalent to those of a plug flow reactor. 

The space time required to accomplish the specified conversion in a plug flow reactor (18.6 h) is sufficiently long that it makes the use of a tubular reactor impractical for the operating conditions specified. For these conditions a cascade of stirred-tank reactors would be more appropriate for use. 

S.3.2.3 Size Comparisons Between Cascades of Ideal Continuous Stirred-Tank Reactors and Plug Flow Reactors... 

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