Bubble column turbulent dispersion

The parameter p (= 7(5 ) in gas-liquid sy.stems plays the same role as V/Aex in catalytic reactions. This parameter amounts to 10-40 for a gas and liquid in film contact, and increases to lO -lO" for gas bubbles dispersed in a liquid. If the Hatta number (see section 5.4.3) is low (below I) this indicates a slow reaction, and high values of p (e.g. bubble columns) should be chosen. For instantaneous reactions Ha > 100, enhancement factor E = 10-50) a low p should be selected with a high degree of gas-phase turbulence. The sulphonation of aromatics with gaseous SO3 is an instantaneous reaction and is controlled by gas-phase mass transfer. In commercial thin-film sulphonators, the liquid reactant flows down as a thin film (low p) in contact with a highly turbulent gas stream (high ka). A thin-film reactor was chosen instead of a liquid droplet system due to the desire to remove heat generated in the liquid phase as a result of the exothermic reaction. Similar considerations are valid for liquid-liquid systems. Sometimes, practical considerations prevail over the decisions dictated from a transport-reaction analysis. Corrosive liquids should always be in the dispersed phase to reduce contact with the reactor walls. Hazardous liquids are usually dispensed to reduce their hold-up, i.e. their inventory inside the reactor. 

Axial mixing in the liquid, induced by the upflow of the gas bubbles, can be substantial in commercial-scale bubble columns, especially in the chum turbulent regime. Due to typically small particle size, the axial dispersion of the solid catalyst in slurry bubble columns is expected to follow closely that of the liquid exceptions are high-density particles. The liquid axial mixing can be represented by an axial dispersion coefficient, which typically has the form... 

Horizontal contactors are essentially bubble columns with an aspect ratio less than one, and the gas is sparged at the bottom as turbulent jets. In order to get fairly uniform gas-liquid dispersion, multiple injection points are employed for the gas. The gas-liquid contact can be further improved using impellers (Fig. 33). The impellers are of a modified propeller type and are mounted on a horizontal shaft. 

Commercial reactors are non isothermal and often adiabatic. In a noniso-thermal gas-liquid reactor, along with the mass dispersions in each phase, the corresponding heat dispersions are also required. Normally, the gas and liquid at any given axial position are assumed to be at the same temperature. Thus, in contrast to the case of mass, only a single heat-balance equation (and corresponding heat-dispersion coefficient) is needed. Under turbulent flow conditions (such as in the bubble-column reactor) the Peclet number for the heat dispersion is often assumed to be approximately equal to the Peclet number for the mass dispersion in a slow-moving liquid phase. 

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

In the bubble column the velocity profile of recirculating liquid is shown in Fig. 27, where the momentum of the mixed gas and liquid phases diffuses radially, controlled by the turbulent kinematic viscosity Pf When I/l = 0 (essentially no liquid feed), there is still an intense recirculation flow inside the column. If a tracer solution is introduced at a given cross section of the column, the solution diffuses radially with the radial diffusion coefficient Er and axially with the axial diffusion coefficient E. At the same time the tracer solution is transported axially Iby the recirculating liquid flow. Thus, the tracer material disperses axially by virtue of both the axial diffusivity and the combined effect of radial diffusion and the radial velocity profile. 

The latter mechanism assumed is the well-known Taylor dispersion (T9, TIO, Til), which has been studied extensively (All, G6, L9, T14, S2). High-speed motion pictures taken by Towell et al. (T23) in a 40-cm bubble column (R3) have shown the presence of turbulent eddies, on a scale roughly equal to the column diameter, with systematic large-scale circulation patterns superimposed. Their pictures showed that liquid near the wall flowed downward, while liquid near the center of the column flowed upward, consistent with the flow theory developed earlier and with the Taylor dispersion mechanism. 

In regard to axial dispersion in unbaffled bubble-flow equipment like liquid-liquid spray columns, gas bubble columns, or fluidized catalyst beds, a close similarity has been supposed as a result of bubble flow and of turbulence induced by bubbles (B3, M33). Baird and Rice (B3) have assumed that the Kolmogoroflf concept for eddy viscosity in isotropic turbulence is applicable to evaluate E in the unbaffled bubble column under turbulent conditions, concluding that Ezt >s 0.35 in cm-sec units,... 

The turbulent kinematic viscosity vt of the fluidized catalyst bed has been determined, as Eq. (3-3 la), from the use of axial dispersion coefficient This is a natural consequence of the analogy between the bubble column and the fluidized catalyst bed of good fluidity (such as in fluidized catalytic cracking). The mean gas holdup (Fig. 36) and the mean bubble velocity along the bed axis (Fig. 37) are reasonably well predicted by applying Eq. (3-3 la) for the fluidized cracking catalyst bed. 

The recent progress in experimental techniques and applications of DNS and LES for turbulent multiphase flows may lead to new insights necessary to develop better computational models to simulate dispersed multiphase flows with wide particle size distribution in turbulent regimes. Until then, the simulations of such complex turbulent multiphase flow processes have to be accompanied by careful validation (to assess errors due to modeling) and error estimation (due to numerical issues) exercise. Applications of these models to simulate multiphase stirred reactors, bubble column reactors and fluidized bed reactors, are discussed in Part IV of this book. 

Instead of arbitrarily considering two bubble classes, it may be useful to incorporate a coalescence break-up model based on the population balance framework in the CFD model (see for example, Carrica et al., 1999). Such a model will simulate the evolution of bubble size distribution within the column and will be a logical extension of previously discussed models to simulate flow in bubble columns with wide bubble size distribution. Incorporation of coalescence break-up models, however, increases computational requirements by an order of magnitude. For example, a two-fluid model with a single bubble size generally requires solution of ten equations (six momentum, pressure, dispersed phase continuity and two turbulence characteristics). A ten-bubble class model requires solution of 46 (33 momentum, pressure. 

Conversely, if chemical reaction in the liquid phase limits the overall reaction rate, a large value of p suggests minimizing the gas-liquid interface and maximizing both liquid volume and turbulent mixing. The best contactor would disperse discrete bubbles in a continuous liquid phase. Both the bubble column... 

In a recent study Jakobsen et al [66] examined the capabilities and limitations of a dynamic 2D axi-symmetric two-fluid model for simulating cylindrical bubble column reactor flows. In their in-house code all the relevant force terms consisting of the steady drag, bulk lift, added mass, turbulence dispersion and wall lift were considered. Sensitivity studies disregarding one of the secondary forces like lift, added mass and turbulent dispersion at the time in otherwise... 

Hagesaether L, Jakobsen HA, Svendsen HF (2002) A Model for Turbulent Binary Breakup of Dispersed Fluid Particles. Chem Eng Sci 57(16) 3251-3267 Hagesaether L, Jakobsen HA, Svendsen HF (2002) Modeling of the Dispersed-Phase Size Distribution in Bubble Columns. Ind Eng Chem Res 41(10) 2560-2570... 

Luo H (1993) Coalescence, break-up and liquid circulation in bubble column reactors. Dr ing Thesis, the Norwegian Institute of Technology, Trondheim Luo H, Svendsen HF (1996) Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions. AIChE J 42(5) 1225-1233... 

Liquid mixing in bubble columns is a result of global convective re-circulation of the liquid phase and turbulent diffusion due to eddies generated by the rising bubbles. By structuring the gas and the liquid flow, HyperCat reduces the axial dispersion for both phases leading to a large reduction in axial dispersion coefficients (Dax)- The real benefit of this reduced dispersion is that it is not a function of the colunm diameter (Dc) as is the case with conventional bubble colunm reactors. 

Baird and Rice first applied the isotropic turbulence theory to correlate the axial dispersion coefficient in Newtonian fluids [39]. Their successful approach has been widely quoted to predict design parameters in bubble columns (Kawase and Moo-Young [40]). It was extended to non-Newtonian fluids by Kawase and Moo-Young [32]. The resulting equation may be written as... 

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