Liquid dispersion coefficient

Cova (3 ) measured the solid concentration profiles of a Raney nickel catalyst with an average diameter of 15.7 ym in a h.6 cm id reactor, using water and acetone as the liquids. He developed a sedimentation diffusion model, assuming solid and liquid dispersion coefficients were equal, and slurry settling velocities were independent of solid concentration. The model was then applied to data for Raney nickel in 6.35 and kk.J cm id bubble columns, in both cocurrent and countercurrent flow. 

Oxygen transfer limited cell growth in tower loop reactors. In addition to the assumptions in 1.3.2 it can be assumed that the medium is completely free of a gas phase in the loop, furthermore,the longitudinal liquid dispersion coefficient in the loop can be neglected. These two assumptions hold true for tower reactors with an outer loop which has a considerably smaller cross-sectional area than the tower cross-sectional area (13, 14). ... 

Table 6.9 Correlations for liquid dispersion coefficients in three-phase slurry and three-phase fluidized beds.

Bai et al (2012) have carried out DBM simulations to computationally measure the key quantities of the bubbly flow in a square bubble column in terms of the turbulent liquid dispersion coefficient. This was done by releasing two sets of neutrally buoyant tracer particles in the fiquid phase and recording their dispersion with time one at the top of the column (tracer 0) and one set at the bottom. It was found that with increasing superficial gas velocity, the dynamics of the liquid in the column is enhanced, and hence the turbulent dispersion coefficient increases. The obtained dispersion coefficients are shown in Fig. 8 and are well within the spread of literature correlations. Note that this spread can be attributed to differences in geometry of the studied bubble columns. The power of the DBM is that it accounts for the details of the geometry and thereby provides a predictive capability that is hard to match when using empirical correlations. 

TABLE 22-5 Comparison of Axial-Dispersion Coefficients for Several Liquid-Solid Contactors... 

J. Chem. Educ., 50, 864 (1973)], theory shows that the degree of separation that is obtained increases as the liquid column is made taller. But unfortunately it decreases as the column is made wider. In simple terms, the latter effect can be attributed to the increase in the dispersion coefficient as the column is widened. 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

Liquid Dispersion Spray columns are used with slurries or when the reaction product is a solid. The absorption of SO9 by a hme slurry is an example. In the treatment of phosphate rock with sulfuric acid, offgases contain HF and SiF4. In a spray column with water, solid particles of fluorosilic acid are formed but do not harm the spray operation. The coefficient /cl in spray columns is about the same as in packed columns, but the spray interfacial area is much lower. Considerable backmixing of the gas also takes place, which helps to make the spray volumetri-caUy inefficient. Deentrainment at the outlet usually is needed. 

Where FCl is the solute gas-liquid partition coefficient, r is the tendency of the solvent to interact through k- and n-electron pairs (Lewis basicity), s the contribution from dipole-dipole and dipole-induced dipole interactions (in molecular solvents), a is the hydrogen bond basicity of the solvent, b is its hydrogen bond acidity and I is how well the solvent will separate members of a homologous series, with contributions from solvent cavity formation and dispersion interactions. 

Gal-Or and Hoelscher (G5) have recently developed a fast and simple transient-response method for the measurement of concentration and volumetric mass-transfer coefficients in gas-liquid dispersions. The method involves the use of a transient response to a step change in the composition of the feed gas. The resulting change in the composition of the liquid phase of the dispersion is measured by means of a Clark electrode, which permits the rapid and accurate analysis of oxygen or carbon dioxide concentrations in a gas, in blood, or in any liquid mixture. 

In addition, it was concluded that the liquid-phase diffusion coefficient is the major factor influencing the value of the mass-transfer coefficient per unit area. Inasmuch as agitators operate poorly in gas-liquid dispersions, it is impractical to induce turbulence by mechanical means that exceeds gravitational forces. They conclude, therefore, that heat- and mass-transfer coefficients per unit area in gas dispersions are almost completely unaffected by the mechanical power dissipated in the system. Consequently, the total mass-transfer rate in agitated gas-liquid contacting is changed almost entirely in accordance with the interfacial area—a function of the power input. 

Bubble size in the circulating beds increases with Ug, but decreases with Ul or solid circulation rate (Gs) bubble rising velocity increases with Ug or Ul but decreases with Gs the ffequeney of bubbles increases with Ug, Ul or Gs. The axial or radial dispersion coefficient of liquid phase (Dz or Dr) has been determined by using steady or unsteady state dispersion model. The values of Dz and D, increase with increasing Ug or Gs, but decrease (slightly) with increasing Ul- The values of Dz and Dr can be predicted by Eqs.(9) and (10) with a correlation coefficient of 0.93 and 0.95, respectively[10]. 

Specific interface in gas/liquid systems Mass-transfer coefficient Time-dependent dispersion coefficient Knudscn number Reaction rate constant... 

The liquid flow rate directly influences the dispersion coefficient. Investigate its influence on peak width. 

Kang, Fan and Kim(96) measured coefficients for heat transfer from a cone-shaped heater to beds of glass particles fluidised by water. They also found that the heat transfer coefficient passed through a maximum as the liquid velocity was increased. The heat transfer rate was strongly influenced by the axial dispersion coefficient for the particles, indicating the importance of convective heat transfer by the particles. The region adjacent to the surface of the heater was found to contribute the greater part of the resistance to heat transfer. 

The overall heat transfer coefficient between the gas-liquid dispersion on the tray and the cooling medium in the tubes is dependent upon the gas velocity, as pointed out by Poll and Smith148 , but is usually in the range 500-2000 W/m2 K. 

Equation (9.27) defines the so-called axial dispersion coefficient Dax as a model parameter of mixing. Nd is the dispersion flow rate, c the concentration of the tracer mentioned earlier, and S the cross-sectional area of the column. The complete mole flow rate of the tracer consists of an axial convection flow and the axial dispersion flow. The balance of the tracer amount at a cross section of the extractor leads to second-order partial differential equations for both phase flows at steady state. For example, for continuous liquids ... 

---