Bubble diameter agitated vessels

The hold-up and bubble diameter in mechanically agitated vessels are given by the following empirical expressions ... 

In these equations, a is the specific interfacial area for a significant degree of surface aeration (m2/m3), I is the agitator power per unit volume of vessel (W/m3), pL is the liquid density, o is the surface tension (N/m), us is the superficial gas velocity (m/s), u0 is the terminal bubble-rise velocity (m/s), N is the impeller speed (Hz), d, is the impeller diameter (m), dt is the tank diameter (m), pi is the liquid viscosity (Ns/m2) and d0 is the Sauter mean bubble diameter defined in Chapter 1, Section 1.2.4. 

The physical technique just described directly measures the local surface area. The determination of the overall interfacial area in a gas-liquid or a liquid-liquid mechanically agitated vessel requires the application of this technique at various positions in the vessel because of variations in the local gas (or the dispersed-phase) holdup and/or the local Sauter mean diameter of bubbles or the dispersed phase. The accuracy of the average interfacial area for the entire volume of the vessel thus depends upon the homogeneity of the dispersion and the number of carefully chosen measurement locations within the vessel. 

Bubbles. Mass transfer between gas bubbles and a liquid phase is oF importance in a variety of operations—gas-liquid reactions in agitated vessels, aerobic reimamaiions, aed absorption or distillation in tray columns. As in liquid-liquid transfer, dispersion of a phase into small units greatly increases tha avtalable area for transfer. If the fractional holdup (volume gas/total volume) of the gas in a gas-liquid mixture is Hs, the imerfacial area par unit volume for bubbles of diameter dB is given by... 

The simulations have been performed for the vessel and impeller geometries used by Bombac et al. [38,39] in their systematic investigations of the distribution of specific gas hold-up at different speeds of agitation. These measurements were performed by using conductivity sensors. For the prediction of the interfacial forces it is necessary to estimate a representative bubble diameter. If the fluid... 

In Example 7.4-1, k, was small. For mass transfer of O2 in a solution to a microorganism with = 1 m, the term 2D g/D would be 100 times larger. Note that at large diameters the second term in Eq. (7.4-1) becomes small and the mass-transfer coefficient Icj, becomes essentially independent of size D. In agitated vessels with gas introduced below the agitator in aqueous solutions, or when liquids are aerated with sintered plates, the gas bubbles are often in the size range covered by Eq. (7.4-1) (B2, C3, Tl). 

The evidence is that the mass-transfer resistance lies entirely within the liquid phase [23, 24, 101], and for gas bubbles of diameter likely to be encountered in agitated vessels... 

This form is partieularly appropriate when the gas is of low solubility in the liquid and "liquid film resistanee" eontrols the rate of transfer. More eomplex forms whieh use an overall mass transfer eoeffieient whieh ineludes the effeets of gas film resistanee must be used otherwise. Also, if ehemieal reaetions are involved, they are not rate limiting. The approaeh given here, however, illustrates the required ealeulation steps. The nature of the mixing or agitation primarily affeets the interfaeial area per unit volume, a. The liquid phase mass transfer eoeffieient, kL, is primarily a funetion of the physieal properties of the fluid. The interfaeial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dj, whieh is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraetion of the total fluid volume (gas plus liquid) whieh is oeeupied by gas bubbles. 

In a bubble-column reactor for a gas-liquid reaction, Figure 24.1(e), gas enters the bottom of the vessel, is dispersed as bubbles, and flows upward, countercurrent to the flow of liquid. We assume the gas bubbles are in PF and the liquid is in BMF, although nonideal flow models (Chapter 19) may be used as required. The fluids are not mechanically agitated. The design of the reactor for a specified performance requires, among other things, determination of the height and diameter. 

Repeat Example 24-2 for the xylene (B) oxidation reaction carried out in an agitated tank reactor (instead of a bubble-column reactor). Use the data given in Example 24-2 as required, but assume the diameter D is unknown. Additional data are the power input without any gas flow is 8.5 kW the impeller rotates at 2.5 Hz the height and diameter of the tank are the same (h = D) the impeller diameter is DI3, and the impeller contains 6 blades assume ubr = 1.25usg. In addition to the vessel dimensions for the conversion specified (/B = 0.16), determine the power input to the agitator (P,). 

For bubble columns with height/diameter > 5, a simple open pipe at the bottom of the column is often adequate. For height/diameter < 5, a ring or finger-style perforated pipe sparger is desirable to obtain uniform radial distribution of the gas and to prevent excessive channeling of the gas up the center of the vessel. For heat transfer in bubble agitated columns, see Hart (1976) and Tamari and Nishikawa (1976). 

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