Batch reactors space time

At constant pressure and granted ideal plug flow, the behavior of a tubular reactor at steady state is mathematically analogous to that of a batch reactor A volume element of the reaction mixture has no means of knowing whether it is suspended tea bag-style in a batch reactor or rides elevator-style through a tubular reactor being exposed to the same conditions it behaves in the same way in both cases. As in a batch reactor, what is measured directly are concentrations—here in the effluent—and a finite-difference approximation is needed to obtain the rate from experiments with different reactor space times and otherwise identical conditions. For a reaction without fluid-density variation ... 

A guideline for choosing a suitable method is to avoid approximations as much as possible. Thus, plots of concentration, or a function of concentrations, versus time or reactor space time are preferred for evaluation of experiments with batch, tubular, and differential recycle reactors, in which concentrations are directly measured and rates can only be obtained by a finite-difference approximation (see eqns 3.1, 3.2, 3.5, 3.6, and 3.8). On the other hand, plots of the rate, or a function of the rate, versus concentration or a function of concentrations serve equally well for evaluation of results from CSTRs or differential reactors without recycle (gradientless reactors), where concentrations and rate are related to one another by algebraic equations that involve no approximations (see eqns 3.3, 3.4, or 3.7). 

If fluid density does not vary with conversion, use same plots as for constant-volume batch, with reactor space time t substituted for time t. 

The condition expressed by the Bodenstein approximation rx = 0 is often misleadingly called a steady state. It is not. It is not a time-independent state, only a state in which a specific variation with time (or reactor space time) is small compared with the others. In fact, some older textbooks applied what they called the steady-state approximation to batch reactions in order to derive the time dependence of the concentrations, unwittingly leading the incorrect presumption of a steady state ad absurdum. And a continuous stirred-tank or tubular reactor may, and usually does, come to a true steady state, even if the Bodenstein approximation is and remains inapplicable. [The approximation compares process rates r, it is irrelevant for its validity whether or not the reactor comes to a steady state, that is, whether the rates of change, dC /dr, become zero.]... 

All steps from the second on amount to insertion of an ethoxy block between a previously inserted block and the —OH group, and so have very similar rate coefficients. Usually, the original alcohol reacts at a slighdy lower rate. If the reaction is carried out at constant partial pressure of ethene oxide, each insertion including the first is pseudo-first order in the alcohol or ethoxy alcohol reactant. With increasing reaction time in batch, successive adducts reach maximum concentrations and then decay to form higher adducts, as shown for a calculated case in Figure 5.11. The variation in yield structure with reactor space time in a continuous stirred-tank reactor is similar, but with less pronounced concentration maxima. 

Equations 5.63 to 5.65 give the selectivity as a function of time or reactor space time. More helpful in practice, however, is the dependence on fractional conversion, fA. For a batch reactor ... 

Whether deactivation is parallel or sequential, its rate equation must be integrated simultaneously with that for the desired reaction. For deactivation, the integration is over time, for the desired reaction in a flow reactor it is over reactor space time. Only in a batch reactor is the independent variable the same. Even so, numerical computation is usually necessary. 

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]. 

Observe that points A and B are situated closely to one another in c -Cb space however, their corresponding equilibrium solutions are significantly different. Thus, we must be cautious when choosing starting points for fed-batch reactors if CSTR solutions are required, and, if possible, an analysis similar to that of Figure 7.33 should be performed, to understand how concentrations evolve in the fed-batch reactor over time. 

Meyer et al. examined the formation of rose oxide by the oxidation ofdtronellol with singlet oxygen in a temperature-resistant glass (Borofloat) microreactor [9]. A 10 mL P-citronellol-ethanol solution with Ru(T>py)3Cl2 is circulated through the microchannel reactor (hold-up volume 0.27 mL). Products are identified by H PLC analysis. After an irradiation time of 40 min, space-time yields of 0.8 mmol L min are obtained. In a comparable batch process, space-time yields are 10 times lower. 

This book will emphasize the use of space time, since it is analogous to real time in a batch reactor. Space velocity can be a bit counterintuitive. Conversion increases as space time increases, but conversion decreases as space velocity increases. 

Biocatalysts in nature tend to be optimized to perform best in aqueous environments, at neutral pH, temperatures below 40 °C, and at low osmotic pressure. These conditions are sometimes in conflict with the need of the chemist or process engineer to optimize a reaction with respect to space-time yield or high product concentration in order to facilitate downstream processing. Furthermore, enzymes and whole cells are often inhibited by products or substrates. This might be overcome by the use of continuously operated stirred tank reactors, fed-batch reactors, or reactors with in situ product removal [14, 15]. The addition of organic solvents to increase the solubility of substrates and/or products is a common practice [16]. 

Chapter 1 treated the simplest type of piston flow reactor, one with constant density and constant reactor cross section. The reactor design equations for this type of piston flow reactor are directly analogous to the design equations for a constant-density batch reactor. What happens in time in the batch reactor happens in space in the piston flow reactor, and the transformation t = z/u converts one design equation to the other. For component A,... 

GL 13] [R 1] [P 12] By using a nickel plate, space-time yields up to 401 mol 1 h were achieved in the falling film micro reactor [6]. Control experiments in a batch reactor at a 30 min reaction time resulted in a space-time yield of only 1.3 mol 1 h , hence orders of magnitude smaller. By using an iron plate, space-time yields up to 346 mol h were achieved in the falling film micro reactor. 

Figure 5.66. Space-time yields, SPTYB, profiles in the batch reactor as a result of varying TIMEON (A - 1000, B - 8, C - 9, D -15).

Analogous to time as a measure of batch process performance, space-time (r) can be defined for a continuous reactor ... 

For constant fluid density the design equations for plug flow and batch reactors are mathematically identical in form with the space time and the holding time playing comparable roles (see Chapter 8). Consequently it is necessary to consider only the batch reactor case. The pertinent rate equations were solved previously in Section 5.3.1.1 to give the following results. 

Bioremediation of Soil Particles 591 Spouted Bed Reactor Mixing Model 390 Steady-State, Two-Pass Heat Exchanger 515 Multicomponent, Semi-Batch Steam Distillation 508 Space-Time-Yield and Safety in a Semi-Continuous Reactor 365... 

The research group of Van Leeuwen reported the use of carbosilane de-ndrimers appended with peripherial diphenylphosphino end groups (i.e. 25, Scheme 26) [37]. After in situ complexation with allylpalladium chloride, the resultant metallodendrimer 25 was used as catalyst in the allylic alkylation of sodium diethyl malonate with allyl trifluoroacetate in a continuous flow reactor. Unlike in the batch reaction, in which a very high activity of the dendrimer catalyst and quantitative conversion of the substrate was observed, a rapid decrease in space time yield of the product was noted inside the membrane reactor. The authors concluded that this can most probably be ascribed to catalyst decomposition. The product flow (i.e. outside the membrane reactor)... 

Just as the reaction time t is the natural performance measure for a batch reactor, so are the space-time and space-velocity the proper performance measures of flow reactors. These terms are defined as follows ... 

This example shows that t and r are not, in general, identical. Now which is the natural performance measure for reactors For batch systems Chapter 3 shows that it is the time of reaction however, holding time does not appear anywhere in the performance equations for flow systems developed in this chapter, Eqs. 13 to 19, while it is seen that space-time or does naturally appear. Hence, r or V/F o is the proper performance measure for flow systems. 

In an isothermal batch reactor 70% of a liquid reactant is converted in 13 min. What space-time and space-velocity are needed to effect this conversion in a plug flow reactor and in a mixed flow reactor ... 

In this reactor the product could be synthesized with a space-time yield of 64 g d with an excellent enantiomeric and diastereomeric excess ee and de >99%). The biocatalyst consumption could be decreased 30-fold to 15 gproduct gwcw by using the membrane reactor as compared with a batch reactor. The corresponding (2S,5S)-hexanediol can also be obtained via biocatalysis [20]. 

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