Fractional holdup

Consequently, for the same fractional holdup there are more bubbles per unit volume as the bubble size decreases, causing bj (which is a yardstick for the distance between adjacent bubbles) to decrease, resulting in more and more interaction between adjacent bubbles. This is one type of interaction that is taken into account in this analysis. 

In extraction column design, the model equations are normally expressed in terms of superficial phase velocities, L and G, based on unit cross-sectional area. The volume of any stage in the column is then A H, where A is the cross-sectional area of the column. Thus the volume occupied by the total dispersed phase is h A H, where h is the fractional holdup of dispersed phase, i.e., the droplet volume in the stage, divided by the total volume of the stage and the volume occupied by the continuous phase, in the stage, is (1-h) A H. 

Figure 3.55. Correlation of dispersed phase fractional holdup values with aqueous (L ) and solvent (O ) flow rates.

As explained in Sec. 3. 3. 1.11, the fractional holdup of the dispersed phase in agitated extraction columns will vary with changing phase flow rate. This dynamic variation in the holdup along the column will cause a dynamic velocity profile in both phases. 

INLET AQUEOUS FLOW RATE INLET ORGANIC FLOW RATE HEIGHTS OF END SECTIONS HEIGHT OF COMPARTMENT CONSTANT IN HOLDUP RELATION CONSTANT IN HOLDUP RELATION INITIAL FRACTIONAL HOLDUP... 

The fractional holdup of the dispersed phase in agitated extraction columns varies as a function of flowrate. Under some circumstances it may be important to model the corresponding hydrodynamic effect. The system is represented below as a column containing seven agitated compartments or stages. 

For a given range of feed flow rate, L, it is assumed that the fractional holdup, h, and the solvent phase flow rate, G, can be correlated in the form... 

The three types of fractional holdup are related as follows (Behkish, 2004) ... 

Another parameter, similar to fractional holdup but different in value, is the volume fraction of solid and liquid in the slurry (Koide, 1996 Kantarci et al., 2005). 

Smith (1981) uses the parameter VB, referred to in his book as gas holdup, which is defined as the volume of bubbles per unit volume of liquid, which is different from the fractional holdup value ... 

It is obvious that we need a trial-and-error procedure. A good approximation for sluny reactors is a fractional liquid holdup of 85%. This value can be used to initiate the iteration procedure. At first we assume a value of the liquid fractional holdup hL, and tlius the values of liquid volume VL, mass volume AfL, and solids volume Vs are known. Then, we can evaluate the parameters s0 and s. Note that at this point, the procedure is complicated due to one more trial-and-error procedure associated with the evaluation of gas fractional holdup hG (eq. (3.260)). After the evaluation of hG, the gas volume VG is known. Then we can re-evaluate the liquid volume (VL = VR — VG — Vs) and compare it with the assumed value. The iteration continues until these two values are the same. 

Figure 14.18. Holdup at flooding, power input, and slip velocity in an RDC (Kosters, in Lo, Baird, and Hanson, 1983). (a) Fractional holdup at flooding, hf, as a function of flow ratio of the phases, (b) Power input to one rotor as a function of rotation speed N and radius R. (c) Slip velocity versus power input group for density difference of 0.15 g/mL, at the indicated surface tensions (dyn/cm).

VL = total volume - film volume = e/a - zL where c is the fractional holdup of liquid and a is the interfacial area per unit volume of liquid. Accordingly the remaining boundary condition at zL is... 

To estimate the total interfacial area in a given volume, the ad value is multiplied by the fractional holdup of dispersed phase in the total volume. 

With a gas superficial velocity of 1.5 m/s, for equal mass flow of gas and liquid, with gas density 0.001 of liquid density, and with 500- im-diameter droplets falling at a terminal settling of 2.5 m/s, Eq. (14-179) gives a fractional holdup of liquid of... 

For bubble systems (gases dispersed in liquids) fractional holdup can approach 0.5 as shown by Fig. 14-104. However, before reaching this holdup, the bubble systems shift to an unstable mix of bubbles and vapor jets. Hence an exact... 

Flows in kmol/h Temperatures in deg. C Pressures in kPa Compositions in mole fraction Holdups in m3... 

Most of these types of equipment have at least several hundred installations. The sizing of full scale equipment still requires pilot planting of particular systems. The scaleup procedures require geometrical and hydrodynamic similarities between the pilot and full scale plants. Hydrodynamic similarity implies equalities of droplet diameters, fractional holdups, and linear superficial velocities. Also preserved are the specific radial discharge rates, defined by QIDH = (volumetric flow rate)/(vessel dia) (compartment height). 

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