Size distribution overflow

Required Overflow Size Distribution Multiplier Required Overflow Size Distribution Multiplier ... 

The feed enters near the center of the tank, and the liquid flows upward and overflows the top of the tank. The solids loading of the feed is 0.5 lbm of solids per gallon of slurry, and the feed rate is 50,000 gpm. What is the total solids concentration and the particle size distribution in the overflow Density of solids is 100 lbm/ft3. Assume that (1) the particles are spherical (2) the particles in the tank are unhindered and (3) the feed and overflow have the same properties as water. 

A scoop that is positioned in the hydrocyclone vortex to obtain the desired particle size distribution in the overflow stream. 

The sharpness of cut can be expressed in terms of the differences in size distribution F(d) of the solids in the underflow Fu(d), in comparison with that of the overflow F0(d). These are well resolved when the cut is sharp. The values of dso and da converge as the... 

Figure 55 Typical size distributions by volume, for the feed flow and the overflow, if the hydrocyclone is operated for fines removal. The ordinate value is defined by volume percentage divided by interval width.

Table 3. Relationship ofP50c to Overflow Size Distribution.

It (1 ) deals with the derivation of relations giving the particle size distribution in the bed, overflow, and carryover streams and their respective weights. This theory will be extended to include the effects of particle growth or shrinkage (Z>1 or Z<1). For typical combustion of char containing sulfur followed by sulfur dioxide absorption by limestone, relations will be derived to determine the extent of sulfur retention. The reaction, carryover, and overflow rates will be evaluated with particular attention to their dependence on Z. 

P3(Cs) Is the size distribution of the particles in the bed and overflow stream for a feed of fixed particle size The... 

Adopting the approach developed above for the char particles combustion, the size distribution function of limestone particles as a result of sulfation reaction in the overflow stream which is the same as in the bed is given by. 

The mathematical model for char combustion described in the previous two sections is applicable to a bed of constant volume, i.e., to a fluidized bed of fixed height, Hq, and having a constant cross-sectional area, Aq. The constant bed height is maintained by an overflow pipe. For this type of combustor operating for a given feed rate of char and limestone particles of known size distributions, the model presented here can predict the following ... 

Figure 21. Overflow rate in sedimentation tank effects on particle size distribution function...

The operation of the fines-destruction process is similar to that of clear-liquor advance as shown in Figure 64.4, the difference is that when the clear liquor is used, the small particles return back to the product flow, thus increasing the proportion of small crystals. For the fines-destruction operation, very small fines can be withdrawn, and the suspension density of the overflow is very small. The number of crystals in the crystallizer decreases as a result of eliminating the small-sized particles. This operation is very useful in increasing the size of crystals in a system that has a high rate of nucleation. This method does, however, lead to a wide particle size distribution. 

Recirculating crystals return to the agitator through the annulus between the draft tube and the baffle. The latter as shown here is an extension of the shell of the upper chamber. The volume between the baffle and the outer wall allows the slurry to separate. The crystals fall toward the bottom, and the clarified mother liquor overflows from the top of this section. This mother liquor can go on to further processing or return to the bottom of the crystallizer. The rate of withdrawal of mother liquor determines the clarifying efficiency behind the baffle. It can be varied to control the amount or size of fine crystals that leave the crystallizer. These crystals can redissolve in a fines killer if the circulating mother liquor is heated or if an unsaturated feed stream is introduced. The latter is the normal practice in the recovery of Glauber s salt from caustic evaporators. This action keeps the fines out of the final crystal product and makes the particle size distribution narrower. 

The conversions mentioned above are to be avoided whenever possible, because of inherent errors in such procedures, by using a method that would give the desired type of distribution directly. Different methods give different types of distributions and the selection of a method should be done on the basis of both the particle size and the type of distribution required. In common processing applications, for example, solid-fluid separations, it is the size distribution by mass that is usually of interest, because the separation efficiency is based on gravimetric means. There are, however, cases such as liquid clarification where turbidity of the overflow is of importance, and size distribution by surface or even by number would be more relevant. Figure 2.23 shows the four types of distribution in a diagram. 

Data on a screening operation is presented in Table 9.1. Particle size distributions of feed, overflow, and underflow are given as cumulative frequency. The screen used for separation has an aperture size of 460 pm, and 1000 kg/h of feed are processed obtaining 650 kg/h of overflow. Calculate the efficiency of the operation. 

Having the particle size distributions of the three streams, as well as two of their flow rates. Equation 9.8 can be used to evaluate efficiency. Fractions Xp, Xq, and Xpj can be determined from a plot of equivalent sieve diameter versus cumulative frequencies of the feed, overflow, and underflow, at the cut diameter Plotting data from Table 9.1, the graph in Figure 9.3 is obtained. 

Collect the underflow and overflow samples, weigh them, and analyze them for their particle size distributions using the set of sieves required and following the procedure given in Section 2.7. (Laboratory exercise particle size analysis by different methods.)... 

Table 10.2 presents the particle size distributions for the overflow and underflow through the hydrocyclone. Therefore, Equation 10.28 would be the appropriate to derive the grade efficiency. Since the separation was carried out in a hydrocyclone, and this type of device normally presents a dead flux effect previously described. Equation 10.29 should be used to derive the reduced grade efficiency. Carrying out the proper computations using the tabulated data and the equations mentioned. Table 10.3 is obtained. 

Determine the particle size distribution of overflow and underflow streams with an instrumental particle sizer. 

Imperfection in the performance of any real separation equipment can be characterized by the separation efficiency. In this chapter basic definitions are given together with the relationships between the efficiency and particle size distributions of various combinations of the feed, underflow or overflow product streams. Practical considerations for grade efficiency testing and total efficiency prediction are given, together with worked examples. 

Me is the mass flow rate of the coarse material in the underflow (in kg s Mf is the mass flow rate of the fine material in the overflow (in kg s ) AF x) Ax is the size distribution frequency of the feed AFc x) Ax is the size distribution frequency of the coarse material AFi x)IAx is the size distribution frequency of the fine material X is the particle size... 

For the size distribution of the fine product in the overflow, equation 3.38 is used directly graphically, Figure 3.14 can also be used for this except that in this case the areas above the curve are integrated. Alternatively, if the coarse product distribution has been worked out first, the mass balance in equation... 

The experimental grade efficiency given in Figure 7.3 was evaluated from size distributions of the feed and the overflow suspensions (measured by the Ladal X-ray Centrifugal Sedimentometer ), and from the total efficiency obtained by simple gravimetric concentration measmements (see chapter 3, Efficiency of Separation for the method). Figure 7.3 also gives the predicted curve from equation 7.9 (K = 1.2 x 10 m s , X2 = 30.87 s) which in this case becomes... 

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