Mixing semibatch reactors

In this chapter we have found that a reactor type that is familiar to us and that has intuitively obvious usefulness, namely, the well-mixed semibatch reactor, is also very complex to treat—at least analytically—due to its transient behavior. It is also evident that we would never use this kind of reactor to evaluate even the most basic chemical kinetics. Thus we need a simpler type of reactor that is mathematically more tractable and experimentally more feasible to operate. We will see instances of these in the next chapter. Along the way we have now added the final element that we needed in our Mathematica toolbox, the writing of Modules. We will build on this to produce even more useful Packages in what follows. 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

Semibatch reactors are often used to mn highly exothermic reactions isothermally, to run gas-liquid(-solid) processes isobarically, and to prevent dangerous accumulation of some reactants in the reaction mixture. Contrary to batch of)eration, temperature and pressure in semibatch reactors can be varied independently. The liquid reaction mixture can be considered as ideally mixed, while it is assumed that the introduced gas flows up like a piston (certainly this is not entirely true). Kinetic modelling of semibatch experiments is as difficult as that of batch, non-isotherma experiments. 

Example 14.1 Consider again the chlorination reaction in Example 7.3. This was examined as a continuous process. Now assume it is carried out in batch or semibatch mode. The same reactor model will be used as in Example 7.3. The liquid feed of butanoic acid is 13.3 kmol. The butanoic acid and chlorine addition rates and the temperature profile need to be optimized simultaneously through the batch, and the batch time optimized. The reaction takes place isobarically at 10 bar. The upper and lower temperature bounds are 50°C and 150°C respectively. Assume the reactor vessel to be perfectly mixed and assume that the batch operation can be modeled as a series of mixed-flow reactors. The objective is to maximize the fractional yield of a-monochlorobutanoic acid with respect to butanoic acid. Specialized software is required to perform the calculations, in this case using simulated annealing3. 

In a semibatch reactor, a cold feed may be heated by mixing with the reactor contents. This technique is discussed in Illustration 10.7 later in this section. 

Physically, the semibatch reactor looks similar to a batch reactor or a CSTR. Reaction occurs in a stirred tank, with the following assumptions (1) the contents of the tank are well mixed, and (2) there are no inlet or outlet effects caused by the continuous stream. 

Up to now we have focused on the steady-state operation of nonisothermal reactors. In this section the unsteady-state energy balance will be developed and then applied to CSTRs, plug-flow reactors, and well-mixed batch and semibatch reactors. 

The stirred-iank reactor may be operated as a steady-state flow type (Fig. 3-lu), a batch type (Fig. 3- b), or as a non-steady-state, or semibatch, reactor (Fig. 3-lc). The key feature of this reactor is that the mixing is complete, so that the properties of the reaction mixture are uniform in all parts of the vessel and are the same as those in the exit (or. product) stream. This means that the volume element chosen for the balances can be taken as the volume V of the entire reactor. Also, the composition and temperature at which reaction takes place are the same as the composition and temperature of any exit stream. 

Many specialty chemicals are produced in semibatch reactors where a reactant is added gradually into a batch reactor. This problem concerns the governing equations of such operations without considering chemical reactions. A well-mixed batch reactor initially contains 200 L of pure water. At time t = 0, we start feeding a brine stream with a salt concentration of 180 g/L into the tank at a constant rate of 50 L/min. Calculate ... 

PE = polyethylene PP = polypropylene PS = polystyrene ASR = automobile shredder residue VGO = vacuum gas oil LCO = light cycle oil. SA = Si02/ AI2O3 MOR = mordenite. TD/CD = thermal degradation followed by catalytic degradation COMB = mixed polymer and catalyst in a batch reactor COMS = mixed polymer and catalyst in a semibatch reactor FB = fixed bed flow reactor BIRR = Berty internal recycle reactor. 

There are two basic types of ideal reactors, stirred tanks, for reactions in liquids, and tubular or packed-bed reactors, for gas or liquid reactions. Stirred-tank reactors include batch reactors, semibatch reactors, and continuous stirred-tank reactors, or CSTRs. The criterion for ideality in tank reactors is that the liquid be perfectly mixed, which means no gradients in temperature or concentration in the vessel. 

To get a high selectivity, a semibatch reactor could be used, with A fed continuously to an initial charge of B, as described in Chapter 3. Because of imperfect mixing, there will be regions near the feed pipe where is greater than the bulk concentration and Cg is somewhat depleted. These differences lower the ratio C jC and decrease the local selectivity. The extent of the decrease depends on the relative rates of mixing and reaction. 

A well-mixed batch reactor whose contents are regarded as pseudo-homogeneous in temperature and composition throughout the entire volume occupied by the suspended cells. Aerobic bioreactions are often carried out in a semibatch mode of operation in which oxygen or air is bubbled continuously through the... 

Biological reactors, like their enzymatic counterparts, can also be classified into batch, plug-flow and mixed-flow reactors. However, it is the semibatch reactor that is perhaps the most useful for microbial systems. 

Figure 26.1 Examples of basic photochemical reactors (some adapted from Cassano et al., 1995). (a) tubular photoreactor inside a cylindrical reflector of elliptical cross section (b) annular photoreactor (c) film-type photoreactor (d) single-lamp multitube continuous photoreactor (e) perfectly-mixed semibatch cylindrical photoreactor irradiated from the bottom by a tubular source and a parabolic reflector...

Rg. 9.8. Mixed-metallocene polymerization of ethylene in a semibatch reactor branching (constrained geometry) catalyst CGC-Ti linear catalyst Et[lnd]2ZrCl2. Reactor and kinetic data initial concentration CGC-Ti 8 x 10 kmol m initial concentration Et[lnd]2ZrCl2 3.2 X 10 kmol m monomer molar feed... 

Mesomixing is mixing on a scale smaller than the bulk circulation (or the tank diameter) but larger than the micromixing scales, where molecular and viscous diffusion become important. Mesomixing is most frequently evident at the feed pipe scale of semibatch reactors. 

From this example of a fast, competitive consecutive reaction scheme we can see that nonideal mixing can cause a decrease in selectivity in both continuous and semibatch reactors. Residence time distribution issues can cause a reduction in yield and selectivity for both slow and fast reactions (see Chapter 1), but for fast reactions, the decrease in selectivity and yield due to inefficient local mixing can be greater than that caused by RTD issues alone. In semibatch reactors, poor bulk mixing can also cause these reductions (see Example 13-3). 

Figure 13-11 Mixing configuration for semibatch reactors for mixing-sensitive reactions when in-line reaction systems are not viable. Note the feed directly into the region of highest turbulence and the second impeller used to maintain turbulence and flow in the top third of the tank.

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