Bubble column, mass transfer models

The fundamental principles of the gas-to-liquid mass transfer were concisely presented. The basic mass transfer mechanisms described in the three major mass transfer models the film theory, the penetration theory, and the surface renewal theory are of help in explaining the mass transport process between the gas phase and the liquid phase. Using these theories, the controlling factors of the mass transfer process can be identified and manipulated to improve the performance of the unit operations utilizing the gas-to-liquid mass transfer process. The relevant unit operations, namely gas absorption column, three-phase fluidized bed reactor, airlift reactor, liquid-gas bubble reactor, and trickled bed reactor were reviewed in this entry. 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

Airlift loop reactor (ALR), basically a specially structured bubble column, has been widely used in chemical industry, biotechnology and environmental protection, due to its high efficiency in mixing, mass transfer, heat transfer etc [1]. In these processes, multiple reactions are commonly involved, in addition to their complicated aspects of mixing, mass transfer, and heat transfer. The interaction of all these obviously affects selectivity of the desired products [2]. It is, therefore, essential to develop efficient computational flow models to reveal more about such a complicated process and to facilitate design and scale up tasks of the reactor. However, in the past decades, most involved studies were usually carried out in air-water system and the assumed reactor constructions were oversimplified which kept itself far away from the real industrial conditions [3] [4]. 

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. 

In this case, the material balance in the liquid phase (3.238) is not applicable as both reactants are gases. Furthermore, as in sluny bubble columns, if the liquid is batch, the overall rate based on the bulk gas-phase concentration is used and the overall mass-transfer coefficient K° is found in the solution of the model (Chapter 5). 

Stirred tank reactors (STR) are the most frequently used reactors in lab-scale ozonation, partially due to the ease in modeling completely mixed phases, but they are very seldom used in full-scale applications. There are various modifications with regard to the types of gas diffusers or the construction of the stirrers possible. Normally lab-scale reactors are equipped with coarse diffusers, such as a ring pipe with holes of 0,1-1.0 m3 diameter. The k/ a-values are in the range of 0.02 to 2.0 s (see Table 2-4 ), which are considerably higher than those of bubble columns. From the viewpoint of mass transfer, the main advantage of STRs is that the stirrer speed can be varied, and thus also the ozone mass transfer coefficient, independently of the gas flow rate. 

Huang W H, Chang C Y, Chiu C Y, Lee S J, Yu Y H, Liou H T, Ku Y, Chen J N (1998) A refined model for ozone mass transfer in a bubble column, Journal Environmental Science Health A 33 441-460. 

A detailed model for a gas-liquid column with external recirculation loop has been published by Orejas [11]. The model takes into account the axial dispersion and mass transfer from bubbles. An important conclusion is that the mass-transfer rate is fast compared with the chemical reaction. As a result, a pseudohomoge-neous model for liquid-phase reaction may be applied for design purposes. 

The rapid development of biotechnology during the 1980s provided new opportunities for the application of reaction engineering principles. In biochemical systems, reactions are catalyzed by enzymes. These biocatalysts may be dispersed in an aqueous phase or in a reverse micelle, supported on a polymeric carrier, or contained within whole cells. The reactors used are most often stirred tanks, bubble columns, or hollow fibers. If the kinetics for the enzymatic process is known, then the effects of reaction conditions and mass transfer phenomena can be analyzed quite successfully using classical reactor models. Where living cells are present, the growth of the cell mass as well as the kinetics of the desired reaction must be modeled [16, 17]. 

It is worth emphasizing that Eqs. (13-61) to (13-68) hold regardless of the models used to calculate the interphase transport rates and EJ. With a mechanistic model of sufficient complexity it is possible, at least in principle, to account for mass transfer from bubbles in the froth on a tray as well as to entrained droplets in a spray, as well as transport between the phases flowing over and through the elements of packing in a packed column. However, a completely comprehensive model for estimating mass-transfer rates in all the possible flow regimes does not exist at present, and simpler approaches are used. 

Just as with the gas holdup, gas-liquid interfacial area should also be divided into two parts. The literature, however, gives a unified correlation. The same is true for volumetric gas-liquid mass transfer coefficients and mixing parameters for both gas and liquid phases. The fundamental r.echanism for inter-phase mass transfer and mixing for large bubbles is expected to be different from the one for small bubbles. Future work should develop a two phase model for the bubble column analogous to the two phase model for fluidized beds. 

The determination of volumetric mass transfer coefficients, kLa, usually requires additional knowledge on the residence time distribution of the phases. Only in large diameter columns the assumption is justified that both phases are completely mixed. In tall and smaller diameter bubble columns the determination of kLa should be based on concentration profiles measured along the length of the column and evaluated with the axial dispersed plug flow model ( 5,. ... 

A theoretical T.pproach to analyze the problem of heat transfer is to develop some form of surface renewal model. The rate of surface renewal is found from the knowledge of energy input per unit mass. Recently Deckwer ( ) has analyzed the problem of heat transfer in bubble columns on the basis of surface renewal model. The present study uses the earlier approach. 

For systematic study of several gas-liquid chemical reactions using a laboratory model bubble-cap column, Sharmaet al. (S23) have shown that the presence of electrolytes, size of caps, type of slots, ionic strength, liquid viscosity, and presence of solids do not affect the mass-transfer rates. These rates chiefly depend on the gas and liquid flow rates (S23, M2). The influence of the superficial gas flow rate on ki, and Icq is indicated in Fig. 20. Interfacial area a" per unit area of plate (or per unit floor area) for plate diameters varying between 0.15 and 1.20 m have been grouped in Fig. 21, which with the following correlations (S23) can be used to scale up bubble-cap plates up to 2 or 3 m in diameter ... 

A systematic study of mass transfer in bubble columns by Mashelkar and Sharma (M8, M9, S23) is summarized in Fig. 23. Increasing the superficial gas velocity increases the gas holdup a, the volumetric mass-transfer coefficients, and the interfacial area per unit volume of dispersion, but not the true mass-transfer coefficients. Correlations proposed for ki, seem too specific to be extended to practical systems (H13, FI, A3). Sharma and Mashelkar (S21) found good agreement between their experimental values of and the values from Geddes stagnant sphere model equation (G3) ... 

To simulate the effects of reaction kinetics, mass transfer, and flow pattern on homogeneously catalyzed gas-liquid reactions, a bubble column model is described [29, 30], Numerical solutions for the description of mass transfer accompanied by single or parallel reversible chemical reactions are known [31]. Engineering aspects of dispersion, mass transfer, and chemical reaction in multiphase contactors [32], and detailed analyses of the reaction kinetics of some new homogeneously catalyzed reactions have been recently presented, for instance, for polybutadiene functionalization by hydroformylation in the liquid phase [33], car-bonylation of 1,4-butanediol diacetate [34] and hydrogenation of cw-1,4-polybutadiene and acrylonitrile-butadiene copolymers, respectively [10], which can be used to develop design equations for different reactors. 

If the values of local mean bubble diameter and local gas flux are available, a fluid dynamic model can estimate the required influence of mass transfer and reactions on the fluid dynamics of bubble columns. Fortunately, for most reactions, conversion and selectivity do not depend on details of the inherently unsteady fluid dynamics of bubble column reactors. Despite the complex, unsteady fluid dynamics, conversion and selectivity attain sufficiently constant steady state values in most industrial operations of bubble column reactors. Accurate knowledge of fluid dynamics, which controls the local as well as global mixing, is however, essential to predict reactor performance with a sufficient degree of accuracy. Based on this, Bauer and Eigenberger (1999) proposed a multiscale approach, which is shown schematically in Fig. 9.13. 

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