Semibatch reactor constant volume

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

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

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... 

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. 

An initial charge of A (methylnaphthalene) is taken in the reactor at a concentration of [A]i, B (hydrogen peroxide solution) at a concentration of [fiJo is added, and the products are withdrawn, both continuously, at the same rate. This mode of operation is continued for a certain length of time corresponding to a fraction /sB of the total time, after which the flow of B is stopped, and the reaction is continued in the batch mode for the remaining fraction of time (1 -/sb)- This may be regarded as constant volume, semibatch operation. 

Modeling of a semibatch reactor (Figure 16.1) enables to determine the reaction rate pseudoconstants. For lack of physical data, a number of assumptions have to be made. The volume of the liquid phase is the function of composition, temperature, pressure, and mass of EO reacted with raw material. At a constant temperature (185 5°C), the volume of the liquid phase increases due to an increased solubility of EO. However, the rate of change is relatively low compared to the reaction rate. The universal functional activity coefficient (UNIFAC) method [43] was used to calculate the activity coefficients. The method was adopted for the heterogeneous liquid-liquid-vapor system as the limited solubility of liquid components was observed. The... 

We can envision a mechanism of one or more steps for each of these unit operations and we can write a rate equation for each step. We can then relate each of these individual rate equations to an overall rate constant. For a mechanism with two or more steps in series, one step will be slower than the other steps we say this slow step is the rate controlling step. For example, a gas—liquid reaction in a laboratory-sized reactor is either heat transfer controlled or reaction rate controlled. If we cannot supply heat fast enough to maintain the reaction or if we cannot remove heat fast enough to control the reaction, we say the reaction is heat transfer controlled. If, on the other hand, we can supply or remove heat faster than required by the reaction, then we say the reaction is reaction rate controlled. In general, laboratory-sized batch and semibatch reactors have large heat transfer surface area to reaction volume ratios therefore, transferring heat to... 

The reaction should be carried out adiabatically in a semibatch reactor, feeding hexanol into the liquid maleic acid. The reactor volume is 500 dm, and no solvent is used. Maleic acid melts at 53°C. A maximum temperature of 100°C may not be exceeded due to the formation of by-products. The reaction is of second order, and the rate constant is expressed as... 

Phase 1 flows at the constant flow rate Q] through the reactor phase 2 is contained within the reactor. Total volume in the reactor of the flow-through phase is V] and of the contained phase is V2 This can represent a number of reactors such as catalyst slurry (phase 1 is liquid and phase 2 is solid)j semibatch bubble columns (phase 1 is gas, phase 2 is liquid), packed-bed or... 

The complex liquid phase reactions discussed in Example 8-6 now t e place in a semibatch reactor where A is fed to B with F n =. 1 moiymtn. The volumetric flow rate is 10 dmVmin and the initial reactor volume is 1, (XX) dm. The rate constants are... 

The CSTR operator, Rc, has an identical term to describe accumulation under transient operation. The algebraic sum of the two other terms indicates the difference of in-flow and out-flow of that species. This operator also describes semibatch or semicontinuous operation in cases where the volume can be assumed to be essentially constant. In the more general case of variable volume, V must be included within the differential accumulation term. At steady state, it is a difference equation of the same form as the differential equation for a batch reactor. 

Solution The process described is neither flow nor batch, but semibatch in nature. However, with assumptions which are reasonably valid, the problem can be reduced to that for a constant-density batch reactor. If the density of the solution remains constant and the hydrogen chloride vaporizes and leaves the solution, the volume of the liquid-phase reaction will be constant. Then the relationship between the composition of the substances in the liquid phase is governed by rate expressions of the type used in this chapter. Assume that the reactions are second order. Then the rate of disappearance of benzene, determined entirely by the first reaction, is... 

X 10 N/m. Choose room-temperature operation, T = 30°C = 303.16 K. Initial gas volume = nRgT/P = (267.75 x 8314 x 303.16)/ .8 x 10 = 3749 m. Since this volume is very high compared to the reactor volume of 10 m, choose semibatch mode of operation with continuous supply of feed gas and removal of residual gas to maintain the reactor pressure. In view of this, a slurry of Ca(OH)2 in water is prepared and CO2 is bubbled through it for 4 h. The mother liquid phase will be initially saturated with Ca(OH)2. As the reaction proceeds, CaCOj precipitates out. The mother liquor can be separated from the solid CaC03 precipitate by filtration. For ease of operation and control, assume constant gas flow rate. 

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. 

An alternate approaeh to improved selectivity for this system is to add A slowly over the course of the reaction and to carry out a semibatch reaction. The reactor might be two-thirds to three-quarters full at the start, and the fluid volume increases as A is added and no product withdrawn. Figure 3.4 shows the calculated concentration curves for the same kinetics and as for Figure 3.3, with the feed of A at a slow, constant rate for 14 hours. 

T o avoid or minimize the formation of mixed products, the preferred method is to operate at constant pH by using a simultaneous addition of reactants (semibatch process). However, even using this mode, mixtures are produced, albeit to a lesser degree, because the change in liquid volume in the reactor alters both the concentration of the reactants and the hydrodynamics. A further improvement, therefore, is to perform the process continuously rather than batch-wise. Even then it is important to minimize concentration gradients in the reactor through good process control. 

Formalism for Combined Reaction and Semibatch Flow The following summarizes the ACOMP approach presented in [38]. Expressions were derived for the concentration of monomer and polymer in the reactor, while reactions are occurring, when N solutes in solution are allowed to flow into the reactor, each at their own rate, which need not be constant, such that solute s has caused a change in reactor volume at time t of AVft), where Qft) is the instantaneous flow rate of liquid from a reservoir containing component s into the reactor. In the following, q is a constant withdrawal rate from the reactor q (ernes ) that feeds the ACOMP extraction/dilution/conditioning front end. 

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