True batch reactors

In true single phase batch reactors the reactants are mixed before the reaction starts. It would seem that transport of matter could never influence the course of chemical reactions then, since a mixture remains mixed. The performance of the reactor could then not be scale dependent. The ideal models presented in section 3.2.1 would then always be applicable, as long as the reactor can be considered isothermal. That is mostly true, but deviations from the ideal situation may occur when the reaction approaches complete conversion. The concentrations of the reactants may become so low, that the average diffusion path becomes large in relation to molecular dimensions, so that diffusion times can no longer be neglected. This is only of practical importance in exceptional cases. Interesting examples are certain polymerizations and polycondensations, see sections 13.3.1 and 13.7. 

In two-phase batch reactors we always have the problem of non-steady state mass transfer. Examples of processes of this type are found in the chemical dissolution of solids in a liquid, see sections 10.3 and 11.2. 

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The same catalyst has been employed in the jasminaldehyde synthesis by condensation of benzaldehydc w ilh heptanal under true batch reactor conditions 25. Ttic target compound was isolated in lower yield (79%) with respect to that obtained by carrying out the reaction with PTBD (99%) but with a considerably higher selectivity (70% vs 49%). In conclusion TBD immobilized on MCM-4I results in a catalyst that is considerably more thermally stable, and shows a better selectivity than PTBD. This is probably an indication for a shape selective reaction in the pore system. The authors also reported the interesting results obtained by testing the MCM-41-TBD in a packed bed micro-reactor (see Table 7). 

In true batch reactors there is usually only one mixed zone, though exceptions occur (see section 5.2.3). 

The results of Example 5.2 apply to a reactor with a fixed reaction time, i or thatch- Equation (5.5) shows that the optimal temperature in a CSTR decreases as the mean residence time increases. This is also true for a PFR or a batch reactor. There is no interior optimum with respect to reaction time for a single, reversible reaction. When Ef < Ef, the best yield is obtained in a large reactor operating at low temperature. Obviously, the kinetic model ceases to apply when the reactants freeze. More realistically, capital and operating costs impose constraints on the design. 

If the enzyme charged to a batch reactor is pristine, some time will be required before equihbrium is reached. This time is usually short compared with the batch reaction time and can be ignored. Furthermore, 5o Eq is usually true so that the depletion of substrate to establish the equilibrium is negligible. This means that Michaelis-Menten kinetics can be applied throughout the reaction cycle, and that the kinetic behavior of a batch reactor will be similar to that of a packed-bed PFR, as illustrated in Example 12.4. Simply replace t with thatch to obtain the approximate result for a batch reactor. 

For transesterification/esterfication, continuous reactors may be more attractive than batch reactors. This is particularly true if a distillation-column reactor can be adopted, as it tends to use a much lower ratio of reactants to drive the reaction to the desired degree of conversion, entailing lower energy lost. Even when metal alcoholates are used these can be recycled, eliminating problems faced in batch plants. Relative process costs may well approach 50% of those in batch plants. Higher purity, less plant down time, better process control, and improved yield are other attractive features of continuous plants (Braithwate, 1995). 

The temperature rise due to this exothermic reaction then approaches the adiabatic temperature rise. The final steady state is always characterized by conditions T = T, and c = 0. A batch reactor, in which a zero order reaction is carried out, always has a unique and stable mode of operation. This is also true for any batch and semibatch reactor with any order or combination of reactions. 

When the specified production capacities are low, processes based on batch reactors will usually have lower capital investment requirements than processes calling for continuous operation, so batch reactors are often preferred for new and untried processes during the initial stages of development. As production requirements increase in response to market demands, it may become more economic to shift to continuous processing but, even in these cases, there are many industrial situations where batch operation is preferable. This is particularly true when the operating expenses associated with the reactor are a minor fraction of total product cost. At low production capacities, construction and instrumentation requirements for batch reactors are usually cheaper than for continuous process equipment. Moreover, it is generally easier to start up, shut down, and control a batch reactor than a comparable capacity continuous flow reactor. 

In heat removal line (2), the heat production line and the heat removal line have only one point of intersection (S3). Here, a critical situation exists. In practice, S3 is not a stable point for operation because a small temperature increase will lead to a runaway reaction. The point S3 is of interest, however, for the calculation of the maximum AT that can be used for safe cooling of a batch reactor. At S3, the reaction temperature T and the AT are at maximum values and the slopes of the two curves are equal. Equation (3-9) and Equation (3-10) are true and valid at point S3. Substituting the value of UAS(T — Tm)max... 

A limitation of the methods described so far is that they have assumed a constant overall yield coefficient and do not allow the endogenous respiration coefficient kd (or alternatively the maintenance coefficient, m) to be evaluated. Equation 5.54 shows that the overall yield, as measured when monitoring a batch reactor, is affected by the growth rate and has the greatest impact when the growth rate is low. Consequently, it is desirable to be able to estimate the values of kd or m, so that the yield coefficient reflects the true growth yield. An equivalent method would be one where the specific rates of formation of biomass and consumption of substrate were determined independently, again without the assumption of a constant overall yield-coefficient. 

As with the batch reactor, the semi-batch reactor operates discontinuously. The difference with true batch operation is that for the semi-batch reactor, at least one of the reactants is added as the reaction proceeds (Figure 7.1). Consequently, the material balance as well as the heat balance will be affected by the progressive addition of one of the reactants. Also, as with the batch reactor, there is no steady state. There are essentially two advantages in using a semi-batch reactor instead of a batch reactor ... 

A plant operability analysis helps to establish the correct cycle time. In certain situations, the batch cycle of the entire plant is not determined by the units around the main reactor. Additional time may be needed downstream for product finishing in equipment that operates in series with the main reactor. The batch cycle time T is a composite of three contributions (1) the sum of the batch residence times t(i) in the M true batch units of the plant that operate in series (2) the sum of the residence times t(j) in the N semicontinuous trains of the plant that operate in series and (3) the sum of the downtimes t(k) in series encountered in the total batch cycle ... 

Batch and Semibatch Polymerization. The reactor is normally operated in a semicontinuous mode by delaying vinyl acetate, solvent, and initiator. The same reactor can be used for stripping the poly(vinyl acetate) solution, provided that careful addition of methanol is used in order to prevent the viscosity in the reactor from becoming excessive (249). The disadvantages of batch polymerization are lack of product consistency and unsatisfactory economics in large scale production (250,251). The true batch reaction, where all the reactants are added to the reactor at time zero, yields a product having a very broad molecular weight distribution of limited commercial value. 

Before true continuous reactor trains became common, many were operated in a semi-continuous mode. Typically, there were three or four reactors in series and the styrene would be polymerized to a certain degree of conversion and transferred to the next vessel. This would allow reactants to be transferred into the vacated vessel and batch polymerization begun. This scheme was successful in normal operation, but a surge vessel was needed in case there was a problem with any of the reactors in sequence. 

For elucidation of mechanisms, rate data at very low conversions may be highly desirable. They can be obtained more easily from a batch reactor than from a CSTR or plug-flow tubular reactor. A standard CSTR would have to be operated at very high flow rates apt to cause fluid-dynamic and control problems. The same is true for a standard tubular reactor unless equipped with a sampling port near its inlet, a mechanical complication apt to perturb the flow pattern. If the problem of confining the reaction to a very small flow reactor can be solved—as is possible, for example, for radiation-induced reactions—a differential reactor operated once-through or with recycle may be the best choice. 

Suppose one has performed experiments with the mixture under consideration in a batch reactor, and one has obtained experimentally the overall kinetics—the R ) function such that dCldt = —R(C). For instance, one could obtain R C) = if the intrinsic kinetics are in fact first order and the initial concentration distribution is (l,x) = exp(—x). If one were to regard R(C) as a true (rather than an apparent) kinetic law, one would eonclude that in a CSTR with dimensionless residence time T the exit overall concentration is delivered by the (positive) solution of TC +C = 1. The correct value is in fact C = , and the difference is not a minor one. (To see that easily, consider the long time asymp-... 

Consider two sets of measurements of a random variable. X—for example, the percentage conversion in the same batch reactor measured using two different experimental techniques. Scatter plots of X versus run number are shown in Figure 2.5-1. The sample mean of each set is 70%, but the measured values scatter over a much narrower range for the first set (from 68% to 73%) than for the second set (from 52% to 95%). In each case you would estimate the true value of X for the given experimental conditions as the sample mean. 70%. but you wouid clearly have more confidence in the estimate for Set (a) than in that for Set (bp... 

An important conclusion from this series of investigations is that the MWD of a branched polymer in a reactor with ideal mixing will be broader than in a batch reactor. The same is true for the degree of branching. 

Section 1.2 developed rate expressions for elementary reactions. These expressions are now combined with the material balances of Section 1.1 to develop reactor design equations, that is, equations to predict final concentrations in a batch reactor or outlet concentrations in a flow reactor. Since reaction rate expressions have units of concentration per time, it may seem that is identical to da/dt. This is true only for... 

The true behaviour of a second-order reaction and a set of experimental points that might be observed as the system is investigated experimentally in a batch reactor. 

The integral in the last expression above is not a simple form and is best evaluated by numerical means. Use of the expansion factor is limited to reactions where there is a linear relationship between conversion and volume. For reactions that have complex sequences of steps, a linear relationship may not be true. Then we must rewrite the rate definition for a batch reactor ... 

When the rate of reaction is given and a feed is to be converted to a value of, say x, Eq. 9.1-2 permits the required reactor volume V to be determined. This is one of the design problems that can be solved by means of Eq. 9.1 -2. Both aspects— kinetic analysis and design calculations—are illustrated further in this chapter. Note that Eq. 9.1-2 does not contain the residence time explicitly, in contrast with the corresponding equation for the batch reactor. E/f o> s expressed here in hr m /kmol 4—often called space time—is a true measure of the residence time only when there is no expansion or contraction due to a change in number of moles or other conditions. Using residence time as a variable offers no advantage since it is not directly measurable—in contrast with V/F q. 

Again, these equations often result in impractical requirements for the operation of the fed-batch reactor in practice that are difficult to accept, yet these conditions must be enforced if the fed-batch to operate on the true AR boundary. 

Moving from a laboratory-sized batch or semi-batch reactor entails changing wall effects. Since we perform most laboratory-sized reactions in glassware, we may not be aware that the chosen steel for our commercial-sized reactor catalyzes the reaction or process. In this case, the commercial-sized reactor will be more efficient than our laboratory-sized reactor. The inverse is true if the material of the commercial-sized reactor inhibits the reaction or process. If we are aware of such a catalytic wall effect, then increasing reactor size decelerates the reaction or process because reactor wall surface area does not increase as rapidly as reaction volume. 

The time t is the contact time or residence time of molecules in the reactor. In the batch reactor, it is assumed that measured time is equal to the average contact time. However, in a continuous system, this time may or may not be equal to the contact time, because the distribution of molecules or properties (in the reactor inside) may not be uniform (or homogeneous), and it depends on the type of flow. Therefore, it is impossible to determine the kinetic properties without knowing the true reaction time. 

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