Plug-flow reactors with 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). 

A feed containing Ca0 = 1.5 and Cb0 - 1.75 lbmol/cuft is charged at the rate of 100 cuft/hr to a CSTR followed by a plug flow reactor with half the residence time of the CSTR. The concentration leaving the system is to be Ca2 = 0.4. Find the composition C.1 leaving the CSTR and the sizes of the two reactors. Also, find the concentrations with the same sizes when the PFR is first. 

It is worthwhile to compare the conversion obtained in an isothermal plug flow reactor with that obtained in a CSTR for given reaction kinetics. A fair comparison is given in Fig. 7.3 for irreversible first-order kinetics by showing the conversion obtained in both reactors as a function of To- The conversion of A obtained in a plug flow reactor is higher than that obtained in a CSTR. This holds for every positive partial reaction order with respect to A. For multiple reactions selectivities and yield enter into the picture. 

Aris (1991a), in addition to the case of M CSTRs in series, has also analyzed two other homotopies the plug flow reactor with recycle ratio R, and a PFR with axial diffusivity and Peclet number P, but only for first-order intrinsic kinetics. The values M = 1(< ), R = >(0), and P = 0( o) yield the CSTR (PFR). The M CSTRs in series were discussed earlier in Section IV,C,1. The solutions are expressed in terms of the Lerch function for the PFR with recycle, and in terms of the Niemand function for the PFR with dispersion. The latter case is the only one that has been attacked for the case of nonlinear intrinsic kinetics, as discussed below in Section IV,C,7,b. Guida et al. (1994a) have recently discussed a different homotopy, which is in some sense a basically different one no work has been done on multicomponent mixture systems in such a homotopy. 

The second reactor is to be a plug flow reactor with an effective volume of 1600L. Oxygen is injected at several points along the length of the reactor to maintain a constant concentration of this species over the entire length of the PFR. This concentration is such that the aforementioned rate expression and rate constant remain valid. What fraction of the C that enters the CSTR is converted to P in the indicated combination of reactors ... 

Conversion reactions cannot be used with Plug Flow Reactors or CSTRs. In general, they should only be used in Conversion Reactors. 

Figure 19.10 A matrix of membrane reactor configurations (al) semibatch tank reactor with ESU (SBR or BR-ESU) (a2 and a3) batch reactor with flat and tubular ISU (BR-ISU) (hi and b2) continuously stirred reactor with flat and tubular ISU (CSTR-ISU) (c) plug-flow reactor with ESU (PFR-ESU) and (d) PER with ISU (PFR-ISU).

A first order reaction is carried out in a CSTR. The reaction product hydrolyses slowly under reaction conditions. At a degree of conversion of 0.5 the selectivity is 0.86. One wishes to raise this to at least 0.93. With eq. (3.65) we find = 6. The degree of conversion has to be reduced to 0.31. An alternative is a plug flow reactor with = 0.5 and = 0.94 see eq. (3.63). 

We wish to compare the performance of two reactor types plug flow versus CSTR with a substrate concentration of Csf = 60g-m 3 and a biomass yield of Y = 0.1. In a plug flow bioreactor with volume of 1 m3 and volumetric flow rate of 2.5 m -li what would be the recycle ratio for maximum qx compared with corresponding results and rate models proposed for the chemostat ... 

The performance data for plug versus mix reactor were obtained. The data were collected as the inverse of qx vs inverse of substrate concentration. Table E.1.1 shows the data based on obtained kinetic data. From the data plotted in Figure E.1.1, we can minimise the volume of the chemostat. A CSTR works better than a plug flow reactor for the production of biomass. Maximum qx is obtained with a substrate concentration in the leaving stream of 12g m 3. 

A tubular bioreactor design with operational may lead to a CSTR, having sufficient recycle ratio for plug flow that behave like chemostat. The recirculation plug flow reactor is better than a chemostat, with maximum productivity at C, 3 g-m 3. Combination of plug flow with CSTR which behave like chemostat was obtained from the illustration minimised curve with maximum rate at CSf = 3 g-m-3. 

Runaway criteria developed for plug-flow tubular reactors, which are mathematically isomorphic with batch reactors with a constant coolant temperature, are also included in the tables. They can be considered conservative criteria for batch reactors, which can be operated safer due to manipulation of the coolant temperature. Balakotaiah et al. (1995) showed that in practice safe and runaway regions overlap for the three types of reactors for homogeneous reactions (1) batch reactor (BR), and, equivalently, plug-flow reactor (PFR), (2) CSTR, and (3) continuously operated bubble column reactor (BCR). 

Unlike the situation in a plug flow reactor, the various fluid elements mix with one another in a CSTR. In the limit of perfect mixing, a tracer molecule that enters at the reactor inlet has equal probability of being anywhere in the vessel after an infinitesimally small time increment. Thus all fluid elements in the reactor have equal probability of leaving in the next time increment. Consequently there will be a broad distribution of residence times for various tracer molecules. The character of the distribution is discussed in Section 11.1. Because some of the... 

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. 

Comparison of performance of a series of N equal-size CSTR reactors with a plug flow reactor for the first-order reaction... 

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

The previous chapters have discussed the behaviour of non-linear chemical systems in the two most familiar experimental contexts the well-stirred closed vessel and the well-stirred continuous-flow reactor. Now we turn to a number of other situations. First we introduce the plug-flow reactor, which has strong analogies with the classic closed vessel and which will also lead on to our investigation of chemical wave propagation in chapter 11. Then we relax the stirring condition. This allows diffusive processes to become important and to interact with the chemistry. In this chapter, we examine one form of the reaction-diffusion cell, whose behaviour can be readily understood by comparison with the responses observed in the CSTR. 

Figure 17.12. Ratio of volumes of an n-stage CSTR battery and a plug flow reactor as a function of residual concentration ratio C/C0 with a rate equation r = kC2.

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