Gas and Liquid Phases Completely Mixed

This is the simplest situation from the computational point of view, since the concentrations of A and B are uniform and no differential equations are involved. The continuity equation for the gas-phase component A may be written 

Since A is distributed over two phases, a second continuity equation for A, this time for the liquid phase, is required. This can be written, for the bulk of the liquid. 

When the reaction is very slow and takes place entirely in the bulk, the mass transfer and reaction are purely in series. As mentioned in Chapter 6, Na in (14.2.1-1) and (14.2.1-2), then, equals Ai(Ca/ - C. But since Q again differs from zero, the complete system, (14.2.1-1), (14.2.1-2), and (14.2.1-3), has to be solved. An example of application of these design equations is given in a later section on stirred tank gas-liquid reactors. 

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The model worked out in Sec. 14.2.a, with the gas and liquid phase completely mixed, is adopted here. 

For the common case of continuous operation for both phases, where gas flows under plug-flow condition and liquid under complete mixed-flow condition, and for a reaction of the form (nonreacting liquid phase)... 

Continuous flow of both phases in upflow and complete mixing of phases For packed bubble columns (upflow of both gas and liquid phases), under the assumption of complete mixed flow, the backmixing model of Ramachandran and Chaudhari (1980) is applicable. The relevant equations are presented in Section 3.5.1 for the continuous flow of gas and slurry phases in complete mixed-flow conditions (slurry CSTR reactor). 

Figure 1 is a schematic diagram of the experimental setup. The test section is a horizontal rectangular channel 40 mm in height (H), 160 mm in width (W), and 6,000 mm in length (L). The rectangular channel is completely constructed of transparent acrylic resin, as shown in Figure 2. Tap water and air are used as the gas and liquid phases, respectively. Water is circulated by a 2.2 kW pump fed by a water reservoir 4.2 m away. Air bubbles are injected into the horizontal channel from the upper inner surface of the channel. An array of capillary needles produces bubbles 10-100 mm in length. Before the air and water are mixed, their volumetric flow rates are measured. After leaving the horizontal channel, the gas-liquid mixture is dumped into a tank that acts as a bubble remover when the liquid phase is recirculated it is free of bubbles. At the end of the horizontal channel tracer particles are added to the water to act as ultrasound reflectors. The mean particle diameter is 200 pm and the particle density is 1020 kg/m3. These tracer particles are assumed to...

Despite the simplicity of the process described above, its application on an industrial scale requires careful control of each step of the process. This is especially true for the activation step during which the Co(II) to Co(III) oxidation requires accurate monitoring and the completion time must be precisely determined. The kinetic law that governs the oxidation reaction, whether chemical resistance or mass transfer limited, is also of fundamental importance for scale-up as it applies to the design of the vessel for proper mixing of the gas and liquid phases. Suitable analytical methods were required for the characterization of the activation step before scale-up could be undertaken. 

Microreactors are defined by their size rather than construction. Microreactors are miniaturized with channels between the (sub-)millimeter scale and nanometer scale. Microreactors mix the gas and liquid phases pneumatically or mechanically. The size of the complete bioreactor construction is less important. A microreactor example is shown in Figure 10.6. Microreactors are generally compounded into microreactor elements, which are placed into nuxing units. These units are placed into microreactor devices, which have inputs and outputs for all the microreactor units placed within it. Microreactor devices are placed in parallel or in series in order to achieve the necessary conversion. Finally, the output is treated... 

The model worked out in Section 14.2.3, with the gas phase in plug flow and the liquid phase completely mixed will be applied here. 

Assuming (1) complete mixing in the gas and liquid phase, (2) constant gas flow rate, (3) absorption with slow reaction and (4) neglecting convective transport of A (ul (c/ lo " c/ l) 0) the following relation between the conversion of A and B can be derived... 

If the process is continuous and in the complete mixed-flow mode, for both the gas and slurry phases, the equations derived for agitated sluny reactors are valid (see Section 3.5.1) (Ramachandran and Chaudhari, 1980) by simply applying the appropriate mass transfer coefficients. Note that in sluiiy-agitated reactors, the material balances are based on the volume of the bubble-free liquid. Furthermore, in reactions of the form aA(g) + B(l) — products, if gas phase concentration of A is constant, the same treatment holds for the plug flow of the gas phase. 

In slurry reactors, the liquid phase is completely backmixed, whereas backmixing in the gas and solid phases may not be complete. The gas-phase mixing depends on the design of the impeller and the nature of the bubbles, as well as the superficial gas velocity. The presence of gas reduces liquid-phase mixing however, an increase in gas flow increases the mixing. The mixing is also dependent upon the coalescence rate of the bubbles. 

Reaction Engineering with Idealized Models Liquid / slurry phase- complete mixing Gas phase- complete mixing or plug flow No heal transfer limitations Reactor volume for different degrees of mixing and for different values of malts transfer coctTicient Heat transfer area for different values of overall heal transfer coeflicients... 

The decomposition of calcium carbonate (Eq. 13.2-3), or any other reaction in which the reaction products and reactants do not mix in the gas or liquid phase, represents a, fundamentally different situation from that just considered, and such a reaction may go to completion. To see why this occurs, consider the reaction of Eq. 13.2-3 in a constant temperature and constant pressure reaction vessel, and let Ncaco2,o md Nqo-,0 represent the number of moles of calcium carbonate and carbon dioxide, respectively, before the decomposition has started. Also, since none of the species in the reaction mixes with the others, we use pure component molar than partial molar Gibbs energies in the analysis. Then,... 

The initial choice of the reactor diameter can be oriented as follows, by way of example. Suppose the concentration of A in the liquid is in equilibrium with that in the gas phase, that is, (C )<,u, = (pa)ouJH- Consider the overall material balance for gas and liquid completely mixed, Eq. 14.2.a-2 ... 

The total volume gas and liquid is 7.38 m —only slightly more than in the stirred case, whereas (Gi)out is even lower. This is easily explained on the basis of the model, which assumes plug flow for the gas in the nonstirred case, against complete mixing in the stirred case. Some design aspects of a continuous stirred tank for the liquid-phase oxidation of toluene into phenol have been discussed by van Dierendonck et al. [ 1974]. ... 

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