Volume semibatch reactors

Equation 9.1.46 is the dimensionless energy balance equation for gas-phase, constant-volume semibatch reactors. The correction factor of the heat capacity is... 

The rate terms for the different reactions comprising E, r,y are given by Equations E5.3.2-E5.3.8. Using these equations. Equation El 1.2.1 can be resolved into the following set of variable volume semibatch reactor equations ... 

As expected, heat exchanged per unit of volume in the Shimtec reactor is better than the one in batch reactors (15-200 times higher) and operation periods are much smaller than in a semibatch reactor. These characteristics allow the implementation of exo- or endothermic reactions at extreme operating temperatures or concentrations while reducing needs in purifying and separating processes and thus in raw materials. Indeed, since supply or removal of heat is enhanced, semibatch mode or dilutions become useless and therefore, there is an increase in selectivity and yield. 

In order to illustrate how the mode of operation can positively modify selectivity for a large reactor of poor heat-transfer characteristics, simulations of the reactions specified in Example 5.3.1.4 carried out in a semibatch reactor were performed. The reaction data and process conditions are essentially the same as those for the batch reactor, except that the initial concentration of A was decreased to cao = 0.46 mol litre, and the remaining amount of A is dosed (1) either for the whole reaction time of 1.5 h with a rate of 0.1 mol m s", or (2) starting after 0.5 h with a rate of 0.15 mol m " s". It is assumed that the volume of the reaction mixture and its physical properties do not change during dosing. The results of these simulations are shown in Fig. 5.3-15. The results of calculation for reactors of both types are summarized in Table 5.3-3. 

Where the composition within the reactor is uniform (independent of position), the accounting may be made over the whole reactor. Where the composition is not uniform, it must be made over a differential element of volume and then integrated across the whole reactor for the appropriate flow and concentration conditions. For the various reactor types this equation simplifies one way or another, and the resultant expression when integrated gives the basic performance equation for that type of unit. Thus, in the batch reactor the first two terms are zero in the steady-state flow reactor the fourth term disappears for the semibatch reactor all four terms may have to be considered. 

Semibatch reactors are commonly used for small-volume chemical production. This reactor type is frequently used for biological reactions and for polymerization. In the batch reactor. 

The same example was solved using MINOPT (Rojnuckarin and Floudas, 1994) by treating the PFR model as a differential model. The required input files are shown in the MINOPT manual. Kokossis and Floudas (1990) applied the presented approach for large-scale systems in which the reactor network superstructure consisted of four CSTRs and four PFR units interconnected in all possible ways. Each PFR unit was approximated by a cascade of equal volume CSTRs (up to 200-300 CSTRs in testing the approximation). Complex reactions taking place in continuous and semibatch reactors were studied. It is important to emphasize that despite the complexity of the postulated superstructure, relatively simple structure solutions were obtained with the proposed algorithmic strategy. 

In Chapter 3, the analytical method of solving kinetic schemes in a batch system was considered. Generally, industrial realistic schemes are complex and obtaining analytical solutions can be very difficult. Because this is often the case for such systems as isothermal, constant volume batch reactors and semibatch systems, the designer must review an alternative to the analytical technique, namely a numerical method, to obtain a solution. For systems such as the batch, semibatch, and plug flow reactors, sets of simultaneous, first order ordinary differential equations are often necessary to obtain the required solutions. Transient situations often arise in the case of continuous flow stirred tank reactors, and the use of numerical techniques is the most convenient and appropriate method. 

Figure 5-20. Semibatch reactor concentrations, volume versus time.

A liquid-phase chemical reaction with stoichiometry A B takes place in a semibatch reactor. The rate of consumption of A per unit volume of the reactor contents is given by the first-order rate expression (see Problem 11.14)... 

Writii the Semibatch Reactor Eqaations in Terms of Concentrations. Recalling that the number of moles of A is just the product of concentration of A, C, and the volume V, we can rewrite Equation (4-51) as... 

Rework Example 4-10. Plot the molar flow rates of A, B, and C as a function of reactor length (i.e., volume) for different values of between kf = 0.0 (a conventional PFR) and kj = 7.0min , What parameters would you expect to affect your results the most Vary the parameters k,k, Kc,Ffji to study how the reaction might be optimized. Ask such questions as What is the effect of the ratio of It to or of k, t to What generalizations can you make How would your an.swer change if the reactor temperature were raised significantly What if somEone claimed that membrane reactora were not as safe as. semibatch reactors What would you tell them ... 

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. 

Figure 4-17 shows a special type of semibatch reactor system in which there is a continuous feed, no withdrawal of product, and a mass m i of component A initially in the reactor. The application of Eq. (4-12) will be considered for a reactor of this type when the rate equation is nOt first order and when the volume of the reaction mixture varies. Since there is no exit stream, Eq. (4-12) takes the form... 

Figure 9.1 Semibatch reactors (a) liquid phase (variable volume) and (b) gas phase (constant volume).

Consider first a semibatch reactor with liquid-phase reactions. To derive a relation for the change in the volume of the reactor, we write an overall mass balance over the reactor ... 

For constant volume, gas-phase semibatch reactors, Vuit) = V (0) = and the design equation (Eq. 9.1.2) reduces to... 

The small reactor volumes and the flexible arrangement of microstructured devices can be applied to design multipurpose plants, and traditional batch and semibatch reactors can be replaced. A considerable process intensification and enhanced product selectivity and yield have been shown [20]. Furthermore, continuous reactor operation may help in providing consistent product quality. 

The differences between a single CSTR and a batch reactor are similar to those between semibatch and batch reactors, except that they are usually more pronounced. The addition of more reactors to a series system tends to reduce some of the observed performance differences. A typical example of different behavior is the heat release profile. An advantage often cited for continuous reactor systems is a constant heat load with fully used reactor volume. Batch reactors are not usually operated full, and the heat load is nonuniform. In addition, portions of the batch reaction cycle are devoted to charging and emptying the reactor and sometimes for heating the reagents to polymerization temperature. Thus, the production rate per unit volume can be higher in a continuous system. 

Some reactor models require a more general structure than the ODE, dxjdt = fix, t). The nonconstant density, nonconstant volume semibatch and CSTR reactors in Chapter 4 are more conveniently expressed as differential-algebraic equations (DAEs). To address these models, consider the more general form of implicit ODEs... 

Consider the process illustrated in Figure 4.17, where the second-order irreversible reaction A + B C is carried out in a semibatch reactor. Since there is a large excess of A present within the reactor, we may take the kinetics of the reaction to be pseudo-first-order in B, and since this is not a constant-volume operation let us write a molal balance on B. 

Consider the reaction Ag -I- B C taking place in a semibatch reactor with a concentration Cg and an active volume V. Assume the reaction is first order to A and to B and that the gas-phase resistance is negligible. The unsteady-state material balance for A is... 

In Equations 6.70-6.74, is the propagation rate coefficient for the addition of monomer j to a growing polymer radical ending in monomer i, (pi is the mole fraction of radicals ending in monomer i, [P ] is the total concentration of radicals in the reactor, P is the time-varying feed rate of monomer i to the semibatch reactor, V is the reactor volume, MW is the molecular weight of monomer i, is the rate of polymerization of monomer i, and and are the densities of monomer i and the polymer, respectively. 

Unlike batch/semibatch reactors, the mean residence time of a CSTR at steady state is defined by the ratio of volume inside the reactor to volumetric feed rate, which at equal density of feed and reactor contents is equal to the reactor space time. The advantage of the CSTR over the batch or semibatch reactor is that it is ideally suitable for long runs of continuous production of a polymer product. Once the reactor process is brought to steady state, uniform quality and consistent product is made. However, the CSTR requires several reactor turnovers (at least 3-4) before the process is at steady state and uniform product is made [10]. 

In the analysis of batch reactors, the two flow terms in equation (8.0.1) are omitted. For continuous flow reactors operating at steady state, the accumulation term is omitted. However, for the analysis of continuous flow reactors under transient conditions and for semibatch reactors, it may be necessary to retain all four terms. For ideal well-stirred reactors, the composition and temperature are uniform throughout the reactor and all volume elements are identical. Hence, the material balance may be written over the entire reactor in the analysis of an individual stirred tank. For tubular flow reactors the composition is not independent of position and the balance must be written on a differential element of reactor volume and then integrated over the entire reactor using appropriate flow conditions and concentration and temperature profiles. When non-steady-state conditions are involved, it will be necessary to integrate over time as well as over volume to determine the performance characteristics of the reactor. 

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