Hold-up solids concentration

Slurry Modes of Transportation, 237 Slurry Hold-up and Solid Concentration, 239 Solids and Fluid Mean Resistance Times, 243 Prediction of Hold-up Solids Concentration, 243... 

Figure 31 demonstrates the effect of the drum speed on the mean solids concentration in the drum for the same conditions as in Figure 30. For the cases of Cp = 21.0% and 45.9%, the hold-up solids concentration decreased with the drum speed. However, for the case of Cp = 7.8%, the hold-up mean solids concentration was independent of the drum speed. At a given drum speed, the slurry mean solids concentration in the drum increased with Cp.

The results shown in Figures 25 and 31 indicate that for a given Cp the mean solids concentration in the drum with lifters is lower than that for the drum without lifters. This trend is due to higher axial particle velocities encountered in drums with lifters. For the drum with lifters, the variation of the slurry mean solids concentration with the drum speed was much less pronounced than that observed for the drum without lifters. Also, the effect of Cp on the hold-up solids concentration was more pronounced for the drum with lifters. 

Figure 35b displays the variation of the average hold-up solids volumetric concentration with the drum speed for the same conditions as in Figure 35a. For the case of 10% feed solids concentration, the hold-up solids concentration decreased sharply with the drum speed. The dependence of C on the drum speed decreased for the higher feed solids concentration. In all cases, at a drum speed of about 2.62 s", the hold-up solids concentration approached its respective feed solids concentration. This result indicated that at drum speeds > 2.62 s" both the solids and the water moved in the drum with the same forward velocity. At low drum speeds, the average hold-up solids concentration approached 45%, irrespective of the feed solids concentration.

Figure 36a is similar to Figure 35a, but for a slurry feed rate of 0.04 kg/s. The percent slurry hold-up behavior was similar to that for = 0.02 kg/s. The variation of the hold-up solids concentration ratio, C/Cp, is shown in Figure 36b. It is clear that for drum speeds > 2.62 s, all the curves for the various Cp values approached a limiting value of C/Cp = 1.0. This result is, once again, indicative that both the water and the solids move with the same axial velocity similar to a homogeneous slurry. The maximum deviation of C/Cp from unity occurs at low drum speeds, signifying a large relative velocity for the water and the solids. This case is that of a stratified slurry flow.

Figure 39 shows the mean residence time for the solids, water, X, and the ratio xJXf. As would be deduced from the variation of the hold-up solids concentration shown in Figures 35b and 36b, the mean residence time of the solids in the drum is higher than that of the water at low values of the drum speed. However, for N > 2.62 s , the ratio of xjx approached unity, indicating complete suspension of the solids. Figure 39c depicts that xjx was not sensitive to variation in the slurry feed rate. However, as would be expected, the individual values of the x and x, were affected by the slurry flow rate (Figures 39a and 39b). 

Figure 37. Effect of drum speed on the average hold-up solids concentration.

Figure 35 shows the variation of the percent slurry hold-up and hold-up slurry concentration for the case of 80 pm silica sand at a slurry flow rate of 0.02 kg/s. The working liquid was water at 23°C. Figure 35a shows that the percent slurry hold-up in the drum decreased with the drum speed. For the cases of 10 to 30% feed solids concentration, the asymptotic hold-up value was about 20%, which was slightly higher than the minimum hold-up of 16.2%. However, for the case of a feed solids concentration of 40%, the asymptotic percent slurry hold-up was higher. 

At the end of the incubation period the fermentation culture mixture is adjusted to pH 2 with concentrated hydrochloric acid, the solid material present is removed by filtration, and the filter cake is washed with water. The washings are combined with the main filtrate, adjusted to pH 7.0, and 15.5 liters of the filtered culture liquid is introduced into a columnar exchanger d /a" i.d.) packed with 380 ml of carboxylic acid resin which has been preliminarily washed in succession with two liters of an aqueous solution of 37.5 grams of sodium hydroxide and with two liters of water. The column containing paromomycin is washed with two hold-up volumes of water and is eluted with 0.5 N hydrochloric acid. 

The y-ray absorption method of determining in-line concentration (hold-up) of particles depends on the different degree to which the solid and the liquid attenuate y-rays details of the method are given in the literature 1314). 

For the transport of coarse particles, the relative velocity between the liquid and solids is an important factor determining the hold-up, and hence the in-line concentration of solids. Cloete et a/. 65) who conveyed sand and glass ballotini particles through vertical... 

The effective viscosity depends on the solid hold-up, on particle size and distribution, on the surface properties, on the particle shape and density, on the properties of the liquid (p, p, d), on temperature, and the shear stress in the column. Depending on the solid concentration encountered in BSCR, we can classify the suspensions into "dilute" and "concentrated" groups. 

They are best suited to liquid-liquid separations and clarification duties, but not high solids concentrations due to the limited solids hold-up capacity. They can handle small-density difference separations and best suited to batch processes. They are difficult to clean, and as large-scale laboratory units, best avoided unless another type of centrifuge design will not work. 

Solid bowl centrifuges are similar to tubular centrifuges, but with a larger diameter bowl and running at slower speeds. Feed rates can be as high as 10 m3/hr, provided that the solids concentration in the feed is not too high, as the solids hold-up is again limited. 

Figure 15.17 Comparison of experimental (symbols) and calculated (solid lines) chromatograms of a 3-component mixture. Dimensionless concentrations, relative to the feed concentrations, dimensionless time relative to the hold-up time. Reprinted with permission from A. Wiesel, H. Schmidt-Traub, ]. Lenz, ]. Strube, J. Chromatogr. A, 1006 (2003) 101 (Fig. 10).

Molar concentration units (moles of i in one liter of solution) practically equal molal concentrations for natural waters holding up to about 7000 mg/L of total dis.solved solids (TDS). Below this TDS level, the difference between ppm (parts per million) and mg/L, and between molar (M) and molal (m or mol/kg) concentrations can be ignored. Molal concentrations are independent of temperature, whereas molar concentrations are not. 

The gas hold-up of the HyperCat system was studied using an air-water system. The gas superficial velocities were varied from 0.1-1.0 m/s. The results are shown in Figure 2. The HyperCat gas hold-up is slightly lower than that in a conventional bubble column reactor ( 30% reduction) and comparable to that in a slurry bubble column with 30-35% solids concentration (4). 

Four problems (a) maximization of recovery of the concentrate stream and the number of nonlinking streams in the circuit (N ), (b) maximization of profit and N, (c) maximization of recovery of valuable mineral in the concentrate stream and N, and (d) maximization of solids hold-up and N. Four problems were considered. One aim of the smdy was to simplify floatation circuits. Guria et al. (2005b)... 

Continuous crystallizers frequently employ draft tubes to enforce mixing up and down the vertical axis. Even with draft tubes, however, the solids will not be uniformly distributed in general. Figure 8.3 shows solids distribution in a laboratory model of a draft tube crystallizer (Green and Robertson 1993). Notice that there are variations with vertical position inside the crystallizer. In addition, the average concentration inside the draft tube is different from that outside because the net particle velocity and therefore particle hold-up is different where the particle settling velocity is opposite the net flow, i.e., in up flow than where they settle in the net direction of the flow, i.e., down flow. This is discussed in more detail in Mullin (1994), Jones and Mullin (1973), and the experimental modeling section below. 

The first relationship represents the effect of initial slurry concentration on the average solids hold-up ... 

An experimental run consisted of rotating the drum at a given speed and maintaining predetermined flow rates of solids and water. Steady state conditions were assumed to have been achieved when the discharge slurry had the same flow rate and composition as those of the feed inlet slurry. Steady state was usually reached about 30 minutes after start-up. When steady state conditions were reached, the drum rotation was stopped simultaneously with the slurry feed. The slurry hold-up in the drum and slurry solids concentration were determined from the mass and volume of the drum contents. The drum slurry hold-up and its solids concentration were measured within 5% of the value. The percent slurry hold-up is defined as the percentage of total volume of slurry in the drum to the drum volume. The solids volumetric concentration, C, was determined from the slurry hold-up density, P ,. using... 

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