Gas and Liquid Phase in Plug Flow

This is a situation more likely to be approximated in a packed tower. The continuity equation for A in a differential tower volume may then be written 

Note that this equation is nothing but (6.3.1-5). The relationship between Pa and Cb is derived from a balance on A over the top or bottom section of the column, depending upon the nature of the problem absorber or reactor design. In the first case, for example, when p om and (Cg)in are given and for countercurrent operation, a balance on the upper part of the column may be written when the liquid feed does not contain any A  

Examples of application of this model will be given later. 

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Example 12-2 An aqueous solution contains 10 ppm by weight of an organic contaminant af molecular weight 120, which must be removed by air oxidation in a lo-cm-diameter bubble column reactor at 25°C. The liquid flows downward in the tube at an average velocity af 1 cm/sec. The air at 1 atm is admitted at 0.1 liter/sec and is injected as bubbles 1 mm diameter, which rise at 2 cm/sec. Assume no coalescence or breakup and that both gas and liquid are in plug flow. The reaction in the Hquid phase has the stoichiometry A + 2O2 products with a rate C. ... 

The mass balances [Eqs. (Al) and (A2)] assume plug-flow behavior for both the gas/vapor and liquid phases. However, real flow behavior is much more complex and constitutes a fundamental issue in multiphase reactor design. It has a strong influence on the reactor performance, for example, due to back-mixing of both phases, which is responsible for significant effects on the reaction rates and product selectivity. Possible development of stagnant zones results in secondary undesired reactions. To ensure an optimum model development for CD processes, experimental studies on the nonideal flow behavior in the catalytic packing MULTIPAK are performed (168). 

Similar to the two previous cases (see Sections 9.5.2 and 9.5.3), the problem is solved numerically, whereas the liquid film region is discretized in a spatially uniform grid. The process is considered as an isothermal operation, assuming plug flow of both phases and constant flow rate values of both gas and liquid phases due to low solute concentrations [70]. In the bulk liquid, reaction equilibrium condition is used as a boundary condition for the film region. In order to describe film diffusion, the simple Fick s law is applied. 

Determinations of Peclet number were carried out by comparison between experimental residence time distribution curves and the plug flow model with axial dispersion. Hold-up and axial dispersion coefficient, for the gas and liquid phases are then obtained as a function of pressure. In the range from 0.1-1.3 MPa, the obtained results show that the hydrodynamic behaviour of the liquid phase is independant of pressure. The influence of pressure on the axial dispersion coefficient in the gas phase is demonstrated for a constant gas flow velocity maintained at 0.037 m s. 

The point and overall efficiencies are the same when the phases in the froth are completely mixed. This is more likely for small columns and for very high gas-to-liquid ratios for larger columns. When the liquid is in plug flow, > E. To deduce point efficiency values from measured overall efficiency values, a model involving mixing tendencies must be available, as discussed later. 

Slurry back-mixing in the enhanced SBCR is significantly reduced by the addition of the down-comer/dip-tube flow path consequently, the gas and liquid phases likely exhibited more plug-flow behavior. Thus, for a given space velocity, the enhanced SBCR should yield a higher conversion than that of a CSTR [4]. Differences in conversion between the enhanced SBCR and CSTR reactor types may also be caused by the dissimilarity of heat and mass transfer phenomena. In addition, the relatively large L/D ratio of the SBCR may also contribute to its plug-flow characteristics. 

The dispersion coefficients Dq and Di are included to account for deviations from plug flow in both gas and liquid phases, as mentioned above. Equations (8-191) and (8-192) include all possibihties (or at least as many as we are willing to consider at this point), so we can now look at individual cases of interest by chipping away the particular parts that do not apply. 

The model worked out in Sec. 14.2.C, with the gas phase in plug flow and the liquid phase completely mixed will be applied here. 

In writing Equation 16.17, plug flow (PF) was assumed for both the gas and liquid phases. Thus this equation should be valid for packed columns. 

In most cases, the models start out from coarse assumptions (e.g. plug flow or straight-line flow) and do not consider the spatial and time-line changes of the gas and liquid phase velocities and the different holdups. 

Phases gas-liquid, liquid-liquid, gas-liquid and solid (bio). Intermediate reaction rates. High capacity, high conversion in both gas and liquid phases. Intensive dispersion of gas in liquid. Large number of plates gives plug flow. Some flexibility in varying liquid holdup and exchange heat via cods on plates, d = 40-100 0.6 < Ha < 3. 

Pseudo first order reactions with respect to the gaseous reactant, i,e, in case of large excess of B, have been studied in detail to describe systems as oxidation of ethanol, hydrogenation of a-methyl styrene, hydrogenation of aniline etc. Limiting cases, such as plug flow of both gas and liquid phases [46] or a constant concentration in the gas phase [48], were analysed as well as the general case of finite values of dispersion coefficients in both phases [52,58],... 

Mathematical models for different kinds of gas-liquid reactors are based on the mass balances of components in the gas and liquid phases. The flow pattern in a tank reactor is usually close to complete backmixing. In the case of packed and plate columns, it is often a good approximation to assume the existence of a plug flow. In bubble columns, the gas phase flows in a plug flow, whereas the axial dispersion model is the most realistic one for the liquid phase. For a bubble column, the ideal flow patterns set the limit for the reactor capacity for typical reaction kinetics. 

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