Holdup distribution

Comparing with the conventional three-phase beds, the axial solid holdup distribution is much more uniform and the radial distribution of gas holdup (sg) is much flatter in circulating beds, due to the relatively high Ul and solid circulation. The values of Eg and bed porosity can be predicted by Eqs. (7) and (8) with a correlation coefficient of 0.94 and 0.95, respectively. 

The simulation starts with a uniform holdup distribution through the column and with the column operating at steady-state. The response to changing inlet organic phase flow rate Gq can be studied by use of the ISIM interactive facility. 

F. Yin, A. Afacan, K. Nandakumar, K.T. Chuang, Liquid holdup distribution in packed columns gamma ray tomography and CFD simulation, Chem. Eng. Process. 41 (5) (2002) 473-483. 

Figure 9.18. Solids holdup distribution in the freeboard region of a fluidized bed.

This example is taken from Mujtaba (1989) and Mujtaba and Macchietto (1992) where the same ternary mixture as in example 1 was considered for the whole multiperiod operation which includes 2 main-cuts and 2 intermediate off-cuts. The column consists of 5 (NT) intermediate plates, a total condenser and a reboiler. The column is charged with the same amount and composition of the fresh feed as was the case in example 1. Column initialisation, holdup distribution and condenser vapour load are also same as those in example 1. 

Fig. 17. Lateral holdup distribution of gas bubbles in fluid bed with l2-cm inner diameter (NT).

Table 10-7 Solution of Examples 10-2 and 10-3 effect of holdup distributions on distillation columns at total reflux (D = 0, B = 0, F = 0)...

Bubble formation and orifice activity are two important factors determining stability. Synchronous bubble formation, where almost all holes are active instantaneously, tends to produce a uniform bubble and gas holdup distribution. The uniform bubble distribution leads to a more stable homogeneous flow regime, less liquid recirculation, and higher gas holdup and gas-liquid mass transfer. Asynchronous orifice operation is often accompanied by alternating or oscillating orifice activity, which leads to flow instability. The instability creates more bubble-bubble interaction and leads to lower gas holdup and gas-liquid mass transfer. Hence, the gas distributor affects the critical superficial gas velocity at which the transition regime is detected. 

Chen JW, Gupta P, Degaleesan S, Al-Dahhan MH, Dudukovic MP, Toseland BA Gas holdup distributions in large-diameter bubble columns measured by computed tomography, Flow Meas Instrum 9 91—101, 1998. http //dx.doi.org/10.1016/S0955-5986(98) 00010-7. 

Figure 432 Time-averaged solids holdup distribution (scale [0-0.6]) (A), solids circulation pattern (B), and lateral profiles of the axial solids flux for different heights (C) in the fluidized bed with a constant inflow, for different gas extraction and addition ratios. Turbulent fluidization regime, superficial gas velocity used from the bottom distributor is 2.0 m/s. Reprinted from Dang et al. (2014) with permission from Elsevier.

Figs. 4.37 and 4.38 show the time-averaged solids holdup distribution with gas extracted or added via the membranes at different positions. Fig. 4.37 clearly shows the effect of gas extraction causing the formation of very densified zones close to membrane walls. Here, the solids holdup can reach values up to the value of a random packed bed with monodisperse particles of the same type. However, analogous to the experimental results presented in Section 2.3.3.2, the term stagnant is not accurate since some movement of the particles is stiU detected, and hence densified zones is a more appropriate term. Even though particles close to membrane walls are... 

For the cases with gas permeation imposed via membranes built in the front and back walls, similar but much less pronounced phenomena can also be observed in Fig. 4.38 for the soHds holdup distribution, i.e., relative densified zones for the cases with gas extraction and relatively lower solids holdup close to the membrane walls for the cases with gas addition, especially for the cases with a high gas permeation ratio of 40%. Note that the very densified zones close to membrane walls, where the values of solids holdup are close to the value of a random packed bed with monodisperse particles of the same type, can be seen in the 140% — 40% (A) case but not in the 120% — 20% (B) case in Fig. 4.38. Close comparison of the sohds holdup distribution for the 140% — 40% (A) and 120% — 20% (B) cases tells that it is possible to avoid very high solids holdups close to membrane walls by increasing the membrane area. 

In contrast to the cases of gas extraction, gas addition shows an opposite effect on the sohds holdup distribution through the bed, resulting in relatively uniformly increased sohds holdup throughout the bed center but decreased solids holdup close to the membrane walls. When increasing the membrane area, and thereby decreasing the permeation velocity, the effect of gas addition was not reduced (i.e., from cases indicated with (A) to cases indicated with (B)). 

Figure 7 Axial particle holdup distribution obtained with different gas outlet configurations. (Nakagawa et al., 1994.)...

Cho YJ, Namkung W, Kim SD, Park S. Effect of secondary air injection on axial solid holdup distribution in a circulating fluidized bed. J Chem Eng Japan 27 158 164, 1996. 

Clearly, there is a need for complete mapping of liquid and gas velocities and turbulence intensities in bubble columns. Until recently only data of Hills (1974) reported liquid time averaged velocities and radial gas holdup profiles taken under identical operating conditions. Yao et al. (1990) present in addition to such data also gas velocity and turbulence intensity profiles. Some data on radial holdup distribution and axial liquid velocity in industrial size columns were presented by Kojima et al. (1980) and Koideetal. (1979). 

The origin of the cylindrical coordinate system is placed at the center of the bath, as shown in Fig. 3.3. The horizontal distance from the side wall is designated by t] =R — r). The distance from the side wall to the nozzle exit, , is varied from 1.75 x 10 to 3.5 x 10 m. The horizontal position at which a peak appears in the gas holdup distribution is designated by a,max and the half-value width by > a,max/2,- These quantities are introduced to represent the horizontal extent of the bubble dispersion region. In the same manner, the peak position and half-value width of the axial mean velocity u are defined. These two representative scales will be discussed in a later section. The attachment length La is defined as the vertical distance from the nozzle exit to the position at which bubbles attach to the side wall. 

At a fixed radiation source head and detector position, the radiation intensily transmitted trough the medium is recorded by the detector. A series of such measurements are obtained along a series of chords in one horizontal plane. This data comprise a projection for the tomographic reconstruction. To obtain the special holdup distribution, the cross-section area is divided into a given number of small cells, assuming that within each cell the value of the local holdup is constant. 

Another type of investigations showing the maldistribution of the liquid phase is the determination of the holdup distribution using die gamma tomography method [141]. The eiqieriments are carried out with metal Pall ring 24.4 mm in a 600 mm diameter column. Ihree types of liquid distributors are used. The first two are presented schematically in Fig. 5. Tire thud (point source inlet) feeds the liquid as a single jet in the centre of the column cross-section. 

Fig. 7. Shaded contour plots of the liquid holdup distribution, at 600 mm packing under the distributor, (a) uniform liquid distributor, 1=17.2 m /(m h) centre inlet liquid distributor, L— 8.6 m /(m h) (c) point source inlet liquid distributor, L= 17.2 m /(m h) ...

Carbonell and Guirardello (1997) performed simulations to establish the hydrodynamics (pressure drop, radial gas and slurry holdup distribution, effective eddy viscosity, and liquid-phase velocity profile). They also superimposed the thermal cracking reactions by accounting the radial variations in these transport properties so as to predict the heavy oil conversion. They found that the liquid recirculatory patterns (backmixing) strongly affect the product yields. However, the validation of the experimental was not carried out using these models. 

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