Two-Phase Stirred Tank Reactors

Stirred tanks are often used for gas-liquid reactions. The usual geometry is for the liquid to enter at the top of the reactor and to leave at the bottom. The gas enters through a sparge ring underneath the impeller and leaves through the vapor space at the top of the reactor. A simple but effective way of modeling this and many similar situations is to assume perfect mixing within each phase. 

FIGURE 11.1 A two-phase, continuous-flow stirred tank reactor. 

The interfacial area AtV usually excludes the contact area between the vapor space and the liquid at the top of the reactor. The justification for this is that most gas-liquid reactors have gas bubbles as a dispersed phase. This gives a much larger interfacial area than the nominal contact area at the top of the reactor. There are exceptions—e.g., polyester reactors where by-product water is removed only through the nominal interface at the top of the reactor— but these are old and inefficient designs. This nominal area scales as while the contact area with a dispersed phase can scale as S. 

Mass Transfer Rates. Mass transfer occurs across the interface. The rate of mass transfer is proportional to the interfacial area and the concentration driving force. Suppose component A is being transferred from the gas to the liquid. The concentration of A in the gas phase is Ug and the concentration of A in the liquid phase is u . Both concentrations have units of moles per cubic meter however they are not directly comparable because they are in different phases. This fact makes mass transfer more difficult than heat transfer since the temperature is the temperature regardless of what phase it is measured in, and the driving force for heat transfer across an interface is just the temperature difference Tg—Ti. For mass transfer, the driving force is not Ug—ai. Instead, one of the concentrations must be converted to its equivalent value in the other phase. 

The conversion is carried out using the equilibrium relationship between the gas- and liquid-phase concentrations. Usual practice is to assume Henry s law. Thus, the gas-phase concentration that is equivalent to u is Kh ai, where Kh is 

Henry s law constant is dimensionless when Ug and ai have units of moles per cubic meter, but published values for Kh sometimes have units of atmospheres or torr per mole fraction. Thus the gas phase concentration is often expressed in terms of its partial pressure and the liquid phase concentration is expressed as a mole fraction. The asterisks in Equation 11.1 remind us that Henry s law is an equilibrium relationship. Equation 11.1 is not satisfied merely because gas and liquid phases are brought in brief contact. Instead, the difference between Ug and its liquid phase equivalent, KhOi, provides the driving force for mass transfer that could ultimately lead to equilibrium and the satisfaction of Equation 11.1  

Equation 11.2 replaces the liquid phase concentration with an equivalent gas phase concentration. It is obviously possible to do it the other way, replacing the gas phase concentration with an equivalent liquid concentration. Then 

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Example 11.7 Carbon dioxide is sometimes removed from natural gas by reactive absorption in a tray column. The absorbent, typically an amine, is fed to the top of the column and gas is fed at the bottom. Liquid and gas flow patterns are similar to those in a distillation column with gas rising, liquid falling, and gas-liquid contacting occurring on the trays. Develop a model for a multitray CO2 scrubber assuming that individual trays behave as two-phase, stirred tank reactors. 

By using CFD, the fluid flows can be taken into closer examination. Rigorous submodels can be implemented into commercial CFD codes to calculate local two-phase properties. These models are Population balance equations for bubble/droplet size distribution, mass transfer calculation, chemical kinetics and thermodynamics. Simulation of a two-phase stirred tank reactor proved to be a reasonable task. The results revealed details of the reactor operation that cannot be observed directly. It is clear that this methodology is applicable also for other multiphase process equipment than reactors. 

Membrane Reactors. Consider the two-phase stirred tank shown in Figure 11.1 but suppose there is a membrane separating the phases. The equilibrium relationship of Equation (11.4) no longer holds. Instead, the mass transfer rate across the interface is given by... 

The typical bioreactor is a two-phase stirred tank. It is a three-phase stirred tank if the cells are counted as a separate phase, but they are usually lumped with the aqueous phase that contains the microbes, dissolved nutrients, and soluble products. The gas phase supplies oxygen and removes by-product CO2. The most common operating mode is batch with respect to biomass, batch or fed-batch with respect to nutrients, and fed-batch with respect to oxygen. Reactor aeration is discussed in Chapter 11. This present section concentrates on reaction models for the liquid phase. 

The decomposition reaction A -> B + C occurs in the liquid phase. It has been suggested that your company produce C from a stream containing equimolar concentrations of A and B by using two continuous stirred tank reactors in series. Both reactors have the same volume. The reaction is first-order with respect to A and zero-order with respect to B and C. Each reactor... 

A cascade consisting of two identical stirred-tank reactors is to be used to manufacture the intermediate product B, which is formed and consumed in the following sequence of hquid-phase reactions ... 

Pangarkar VG, Yawalkar AA, Sharma MM, Beenackers AACM. (2002) Particle—hquid mass transfer coefficient in two-/three-phase stirred tank reactors. Ind. Eng. Chem. Res., 41 4141 167. 

Danckwerts 1970). Therefore, the first step in the sequence is gas-liquid mass transfer. Knowledge of volumetric gas-liquid mass transfer coefficient, k a, and the gas-liquid mass transfer rate is an important aspect of design/scale-up of two- and three-phase stirred tank reactors. A detailed discussion on various methods of correlating the various mass transfer coefficients is available in Chapter 6. Therefore, the discussion presented in this chapter will be focused on scale-independent universal correlations that are desirable in any scale-up procedure. 

Residence time experiments have been used to explore the hydrodynamics of many chemical processes. Examples include fixed and fluidized bed reactors, chromatography columns, two-phase stirred tanks, distillation and absorption columns, and trickle bed reactors. 

The first fiow characteristics of single phase stirred tank reactors were performed using the HFA technique. For example, Gtinkel and Weber [77] used a hot-wire technique to measure instantaneous fluid velocities in the bulk flow and between the impeller blades in baffled stirred vessels. The HFA technique was later used to measure the first instantaneous fluid velocities in dispersed two-phase (gas-liquid) dispersions. Attempts were also performed to measure the local gas void fraction. Many examples of such investigations of two-phase bubble column flows can be found in the literature [67, 72, 76, 135, 199]. 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

TABLE 11.2 Two-Phase Reactions in a Stirred Tank Reactor... 

The stirred batch reactors are easy to operate and their configurations avoid temperature and concentration gradient (Table 5). These reactors are useful for hydrolysis reactions proceeding very slowly. After the end of the batch reaction, separation of the powdered enzyme support and the product from the reaction mixture can be accomplished by a simple centrifugation and/or filtration. Roffler et al. [114] investigated two-phase biocatalysis and described stirred-tank reactor coupled to a settler for extraction of product with direct solvent addition. This basic experimental setup can lead to a rather stable emulsion that needs a long settling time. 

The classical CRE model for a perfectly macromixed reactor is the continuous stirred tank reactor (CSTR). Thus, to fix our ideas, let us consider a stirred tank with two inlet streams and one outlet stream. The CFD model for this system would compute the flow field inside of the stirred tank given the inlet flow velocities and concentrations, the geometry of the reactor (including baffles and impellers), and the angular velocity of the stirrer. For liquid-phase flow with uniform density, the CFD model for the flow field can be developed independently from the mixing model. For simplicity, we will consider this case. Nevertheless, the SGS models are easily extendable to flows with variable density. 

The dispersion agents are produced in two stirred tank reactors with a capacity of two (Dl) and four (D2) batches along with two (Dl) and four (D2) storage tanks with a capacity of one batch each. The organic phase is produced in one out of two stirred tank reactors with a capacity of one organic phase batch each no intermediate storage is provided for the organic phase. 

Attempts have been made to expand the technique to include the analysis of soil biotransformations f23.29V While the hydrodynamic nature and physical structure of soil systems vary widely and are difficult to establish with certainty, two limiting conditions may be specified. The first is where the soil particles are suspended and all phases are well-mixed. This case is not typically found in nature, but is found in various types of engineered soil-slurry reactors. The reactors currently used in our systems experiments include continuous stirred tank reactors (CSTRs) operated to minimize soil washout. 

Reductive alkylation is an efficient method to synthesize secondary amines from primary amines. The aim of this study is to optimize sulfur-promoted platinum catalysts for the reductive alkylation of p-aminodiphenylamine (ADPA) with methyl isobutyl ketone (MIBK) to improve the productivity of N-(l,3-dimethylbutyl)-N-phenyl-p-phenylenediamine (6-PPD). In this study, we focus on Pt loading, the amount of sulfur, and the pH as the variables. The reaction was conducted in the liquid phase under kinetically limited conditions in a continuously stirred tank reactor at a constant hydrogen pressure. Use of the two-factorial design minimized the number of experiments needed to arrive at the optimal solution. The activity and selectivity of the reaction was followed using the hydrogen-uptake and chromatographic analysis of products. The most optimal catalyst was identified to be l%Pt-0.1%S/C prepared at a pH of 6. 

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