Reactors, continuous backmix plug-flow

The consequence of recycling is a high backmixing of the liquid phase and a large RTD corresponding to continuous stirred tank reactors. Compared to plug flow reactors (Bo > 100), the specific performance of recycle reactors is significantly... 

The yield that can be attained by a semibatch process is generally higher because the semibatch run starts from scratch, with maximum values of both variables Cg (o) = Cg and k] (o) = k . However, the yield from a continuous run in which t equals the batch time is governed by the product of Cg (t) and kj (t), so > and k (t) = k °. Because neither of these conditions is likely to be fulfilled completely, a continuous polymerization in a backmix reactor will probably always fail to attain the Y attainable by a semibatch reactor at the same t. However, several backmix reactors in series will approach the behavior of a plug flow continuous reactor, which is equivalent to a semibatch reactor. 

Backmix flow reactor or continuously stirred tank reactor. The conversion rate is lower than for plug-flow reactors because the reagent is immediately diluted on being introduced into the reactor. Many flow reactors, e.g. tubular reactors, and especially in the turbulent regime are in this class. 

Finally, some remarks on the operation of mechanically agitated gas-liquid reactors are worth mentioning. The mode of operation (i.e., batch, semibatch, continuous, periodic, etc.) depends on the specific need of the system. For example, the level of liquid-phase backmixing can be controlled to any desired level by operating the gas-liquid reactor in a periodic or semibatch manner. This provides an alternative to the tanks in series or plug flow with recycle system and provides a potential method of increasing the yield of the desired intermediate in complex reaction schemes. In some cases of industrial importance, the mode of operation needs to be such that the concentration of the solute gas (such as Cl2, H2S, etc.) as the reactor outlet is kept at a specific value. As shown by Joshi et al. (1982), this can be achieved by a number of different operational and control strategies. 

Catal5dic gas-phase reactions are generally carried out in continuous fixed-bed reactors, which in the ideal case operate without backmixing. The model reactor is the ideal plug flow reactor, the design equation of which is derived from the mass-balance equation. As we have already learnt, in heterogeneous catalysis the effective reaction rate is usually expressed relative to the catalyst mass / cat, which gives Equation (14-1). The left side of this equation is known as the time factor the quotient is proportional to the residence time on the catalyst. 

The coimterpart of the ideal plug flow reactor is the ideal continuous stirred-tank reactor with complete backmixing of the rection mass. Because of the ideal mixing, the reaction rate is constant, and a simple design equation is obtained for the catalysis reactor (Eq. 14-3). 

To understand the underlying principles of these reactors, which are treated in Parts III and IV, we provide the groundwork in this section by considering the basic reactor types. Thus we first describe the batch reactor (BR) most commonly used in organic synthesis and its continuous counterpart, the plug-flow reactor (PFR). These represent one extreme characterized by total absence of backmix-ing from fluid elements downstream in time or space. On the other extreme, we have the fully (or perfectly) mixed-flow reactor (MFR), also called the... 

In section 3.4 the selectivities of competitive and consecutive reactions were calculated for two reactor types the batch or plug flow reactor (no backmixing), and the perfectly mixed continuous reactor. The following general conclusions can be formulated in terms of backmixing ... 

However, it is very difficult to suspend solid particles effectively and still maintain plug flow. An agitated or pulsed column reactor may be applicable (see section 43,1,5), but then the effects of the residence time distribution have to be taken into account. For large scale operations a series of CSTR s is often more practical, even if the residence time distribution is greater, since it offers better possibilities for effective suspension of coarse particles, and also for heat transfer to the vessel wall. However, one should be aware of the fact that in a continuous reactor with backmixing the conversion of solid particles can never be complete. Because of the residence time distribution, a fraction of the solid particles, those with an individual residence time shorter than the dissolution time, will leave the reactor. For obtaining a complete conversion of the solid, a tubular reactor, that guarantees a certain minimum residence time, will have to be installed after the last CSTR. An alternative is to separate the unconverted solid and return it to the first reactor. 

It was shown that the residence time distribution in the reactor may have a considerable effect, since this influences the concentration profiles of the reactants in time, TTiere are significant differences between batch (or plug flow) reactors and continuous mixed reactors. When the undesired reaction is of a higher order, the CSTR has the highest selectivity. For reactors with other residence time distributions, the qualitative effect of backmixing was discussed in section 7,2.1 A, Quantitative effects can be computed by numerical methods. 

The concept of dispersion is used to describe the degree of backmixing in continuous flow systems. Dispersion models have been developed to correct experimentally recorded deviations from the ideal plug flow model. As described in previous sections, the residence time functions E(t) mdF(t) can be used to establish whether a real reactor can be described by the ideal flow models (CSTR, PFR, or laminar flow) or not. In cases where none of the models fits the residence time distribution (RTD), the tanks-in-series model can be used, as discussed in Section 4.4. However, the use of a tanks-in-series model might be somewhat artificial for cases in which tanks do not exists in reality but only form a mathematical abstraction. The concept of a dispersion model thus becomes actual. 

Equation (2) assumes that the Peclet numbers for all species are equal. The magnitude of the Peclet number characterizes the extent of backmixing within the reactor. At the limiting conditions, an infinite Peclet number means plug flow, while a Peclet number of zero means completely backmixed flow, i.e., the reactor operates just like a continuous stirred tank reactor. 

The residence time distribution of a reactor is a function of the axial mixing within the reactor. The extreme cases are I) the ideal continuous stirred tank reactor (CSTR) with complete mixing and, 2) the ideal plug flow reactor (PFR) without any backmixing of the liquid during its flow through the reactor. The behavior of real reactors lies between these extremes. 

For batch systems a stirred vessel or loop reactor with an in-line mixer is used. Where plug flow is required, for long residence times a cascade of stirred vessels or loop reactors is commonly used, and for short residence times the choice will often be a static mixer or ejectors. For continuous flow systems requiring an approach to backmixed flow, stirred vessels or loop reactors are indicated. 

Example 9.11 Which type of isothermal reactor would produce the narrowest possible distribution of chain lengths in a free-radical addition polymerization continuous stirred tank reactor (CSTR, or backmix), batch (assume perfect stirring in each of the previous), plug-flow tubular, or laminar-flow tubular ... 

Solution, l ree possibilities are sketched in Fig. 12.4. With a semibatch reactor, the more reactive monomer is replenished as the reaction proceeds to maintain/i (and therefore FJ constant. A method for calculating the appropriate rate of addition has been described. In a continuous stirred tank (backmix) reactor, both fi and Fx are constant with time. In a continuous plug-flow reactor, the variation in Fx can be kept small by limiting the conversion per pass in the reactor. Note that the last two techniques require facilities for separating unreacted monomer from the polymer, and in most cases, recycling it. 

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