Mathematical model, bubble columns

Saxena, S. C., Rosen, M., Smith, D. N., and Ruether, J. A., Mathematical Modeling of Fischer-Tropsch Slurry Bubble Column Reactors, Chem. Eng. Comm., 40 97 (1986)... 

In 1976 he was appointed to Associate Professor for Technical Chemistry at the University Hannover. His research group experimentally investigated the interrelation of adsorption, transfer processes and chemical reaction in bubble columns by means of various model reactions a) the formation of tertiary-butanol from isobutene in the presence of sulphuric acid as a catalyst b) the absorption and interphase mass transfer of CO2 in the presence and absence of the enzyme carboanhydrase c) chlorination of toluene d) Fischer-Tropsch synthesis. Based on these data, the processes were mathematically modelled Fluid dynamic properties in Fischer-Tropsch Slurry Reactors were evaluated and mass transfer limitation of the process was proved. In addition, the solubiHties of oxygen and CO2 in various aqueous solutions and those of chlorine in benzene and toluene were determined. Within the framework of development of a process for reconditioning of nuclear fuel wastes the kinetics of the denitration of efQuents with formic acid was investigated. 

Known scale-up correlations thus may allow scale-up even when laboratory or pilot plant experience is minimal. The fundamental approach to process scaling involves mathematical modeling of the manufacturing process and experimental validation of the model at different scale-up ratios. In a paper on fluid dynamics in bubble column reactors, Lubbert and coworkers (54) noted ... 

Fig. 7.4 Schemes for mathematical models of a gas-liquid bubble column (a) and a gas-liquid stirred reactor (b). B = bubble phase, H = reactor head, L = liquid phase, Fg = gas flow rate ...

The mathematical model of a semitechnical rectification column with stationary 0])eration was elaborated and experimentally tested by GroBhennig [267]. The tests were made in an NVV 310 bubble-cap column with 35 plates using the system chloroform-carbon tetrachloride. A comparison showed that even the simplified version of the model gave satisfactory agreement. 

Liquid-phase oxidation of gaseous substrates with O2, such as the oxidation of ethylene to acetaldehyde (Wacker process) is another example of this class of reactions. A mathematical model for a bubble column reactor for this reaction, assuming plug flow of gas and mixed flow of liquid, was developed (Rode et al., 1994). It was shown that a critical oxygen concentration in the inlet is necessary to sustain the catalytic cycle, and a model for predicting this was proposed (Bhattacharya and Chaudhari, 1990). 

A recent paper describes a mathematical model for the chlorination of polyethylene in a bubble column reactor, the model was used to optimize product quality in the continuous chlorination of polyethylene. Another theoretical treatment deals with the change in polymer reactivity during the course of a macromolecular reactions in solution or in the melt. The reactivity of a transforming unit in the polymer depends on its microenvironment, including nearest neighbours on the same chain and on other chains, as well as small molecules in the reacting system. The equations derived describe the kinetic curve, the distribution of units, and the compositional heterogeneity of the products. 

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. 

This basic model seems contrived, in that no direct experimental justification is given for it by Pelton and Goddard [47], Indeed these workers argue [47] that groups in this treatment are a mathematical convenience to facilitate the derivation and not a physically observable cluster of bubbles. However, in a later paper, which uses a similar model, Pelton [48] claims to observe formation of secondary bubbles in the foam column. It is claimed that they expand in size by coalescence until the buoyancy force exceeds the yield stress in the foam whereupon they rise rapidly to the top of the foam column and rupture. 

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