Uniformly mixed batch reactor

As there is no entering or leaving flow in the batch reactor, the material balance equation for a reactant A in a liquid of constant density is given as 

Integration of Equation 7.2 for the irreversible first-order and second-order reactions leads to the previously given Equations 3.15 and 3.22, respectively. 

Similarly, for enzyme-catalyzed reactions of the Michaelis-Menten type, we can derive Equation 7.3 from Equation 3.31. 

Effects of Mixing on Reactor Performance 7.2.2.1 Uniformly Mixed Batch Reactor 

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Equations 7.10-7.12 are identical in forms with those for the uniformly mixed batch reactor, that is. Equations 3.15, 3.22, and 7.3, respectively. It is seen that the time from the start of a reaction in a batch reactor (t) corresponds to the residence time in a PFR (r). 

Reactors with idealized flow patterns are ideal reactors, and are simplifled borderline cases. Three cases are of particular importance (Figure 4.10.1), the ideal, that is, uniformly mixed batch reactor, the ideal plug flow reactor (PFR), where no axial mixing and complete (radial) mixing across is assumed, and the continuous stirred tank reactor (CSTR). Ideal reactors are popular in chemical engineering as they are easy to treat vith regard to their performance equations. 

Ideal reactors have idealized flow patterns. Four cases are important, the uniformly mixed batch reactor, the plug flow reactor (PFR), the continuous stirred tank reactor (CSTR), and a cascade of CSTRs. Real reactors are arbitrarily complicated, but can be regarded as composed of elements of ideal reactors. Modeling is possible, if we know how to account for non-ideal flow. 

If the compositions vary with position in the reactor, which is the case with a tubular reactor, a differential element of volume SV, must be used, and the equation integrated at a later stage. Otherwise, if the compositions are uniform, e.g. a well-mixed batch reactor or a continuous stirred-tank reactor, then the size of the volume element is immaterial it may conveniently be unit volume (1 m3) or it may be the whole reactor. Similarly, if the compositions are changing with time as in a batch reactor, the material balance must be made over a differential element of time. Otherwise for a tubular or a continuous stirred-tank reactor operating in a steady state, where compositions do not vary with time, the time interval used is immaterial and may conveniently be unit time (1 s). Bearing in mind these considerations the general material balance may be written ... 

Piston flow is a convenient approximation of a real tubular reactor. The design equations for piston flow are relatively simple and are identical in mathematical form to the design equations for well-mixed batch reactors. The key to their mathematical simplicity is the assumed absence of any radial or tangential variations within the reactor. The dependent variables a, b,. .. T, P change in the axial, down-tube direction but are completely uniform across the tube. This allows the reactor design problem to be formulated as a set of ODEs in a single independent variable z. As shown in previous chapters, such problems are readily solvable given the initial values... 

In a batch reactor, the reaclants are loaded at once the concentration then varies with time, but at any one time it is uniform throughout. Agitation seiwes to mix separate feeds initially and to enhance heat transfer. In a semibatch operation, some of the reactants are charged at once and the others are then charged gradually. 

In a batch vessel, the question of good mixing will arise at the start of the batch and whenever an ingredient is added to the batch. The component balance, Equation (1.21), assumes that uniform mixing is achieved before any appreciable reaction occurs. This will be true if Equation (1.55) is satisfied. Consider the same vessel being used as a flow reactor. Now, the mixing time must be short compared with the mean residence time, else newly charged... 

It is assumed that all the tank-type reactors, covered in this and the immediately following sections, are at all times perfectly mixed, such that concentration and temperature conditions are uniform throughout the tanks contents. Fig. 3.10 shows a batch reactor with a cooling jacket. Since there are no flows into the reactor or from the reactor, the total mass balance tells us that the total mass remains constant. 

Figure 5.4a compares the profiles for a mixed-flow and plug-flow reactor between the same inlet and outlet concentrations, from which it can be concluded that the mixed-flow reactor requires a larger volume. The rate of reaction in a mixed-flow reactor is uniformly low as the reactant is instantly diluted by the product that has already been formed. In a plug-flow or ideal-batch reactor,... 

Coker, E.N., Dixon, A.G., Thompson, R.W., and Sacco, A. (1995) Zeolite synthesis in unstirred batch reactors II. Effect of non-uniform pre-mixing on the crystallization of zeolites A and X. Micropor. Mater., 3, 537-646. 

In the batch reactor, or BR, of Fig. 5.1 the reactants are initially charged into a container, are well mixed, and are left to react for a certain period. The resultant mixture is then discharged. This is an unsteady-state operation where composition changes with time however, at any instant the composition throughout the reactor is uniform. 

Batch-stirred tank reactor (BSTR) In this type of reactor, the reactants are fed into the container, they are well mixed by means of mechanical agitation, and left to react for a certain period of time. This is an unsteady-state operation, where composition changes with time. However, the composition at any instant is uniform throughout the reactor. 

The simplest reactor configuration for any enzyme reaction is the batch mode. A batch enzyme reactor is normally equipped with an agitator to mix the reactant, and the pH of the reactant is maintained by employing either a buffer solution or a pH controller. An ideal batch reactor is assumed to be well mixed so that the contents are uniform in composition at all times. 

While vinyl acetate is normally polymerized in batch or continuous stirred tank reactors, continuous reactors offer the possibility of better heat transfer and more uniform quality. Tubular reactors have been used to produce polystyrene by a mass process (1, 2), and to produce emulsion polymers from styrene and styrene-butadiene (3 -6). The use of mixed emulsifiers to produce mono-disperse latexes has been applied to polyvinyl toluene (5). Dunn and Taylor have proposed that nucleation in seeded vinyl acetate emulsion is prevented by entrapment of oligomeric radicals by the seed particles (6j. Because of the solubility of vinyl acetate in water, Smith -Ewart kinetics (case 2) does not seem to apply, but the kinetic models developed by Ugelstad (7J and Friis (8 ) seem to be more appropriate. 

When considering the use of microreaction technology, from the perspective of high-throughput organic synthesis, the main benefit that this technique offers is increased reaction control, which in itself affords many practical advantages to the user. As a result of the small reactor dimensions, rapid mixing of reactants, and an even temperature distribution are observed, which not only increase the uniformity of reaction conditions, but also afford increased reaction safety, selectivity, reproducibility, and efficiency when compared to conventional batch reactors where hot spot formation can lead to the formation of by-products and the risk of thermal runaway. 

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