Underflow particle size

In other cases, the underflow rate is not available but a sample of the underflow can be taken. Providing the sample is representative of the underflow, the underflow particle size distribution (PSD) can be ascertained. This PSD may also be independently computed from measured PSDs of the feed and the overflow streams and compared with the measured underflow PSD. The two underflow PSDs thus determined should agree. If not, there is something wrong with one or more of the measurements. This technique has been used in practice as a means of checking the accuracy of the feed and overflow measurements. See also the discussion around Eqs. (3.2.3) and (3.2.4). 

The products are an oversize (underflow, heavies, sands) and an undersize (overflow, lights, slimes). An intermediate size can also be produced by varying the effective separating force. Separation size maybe defined either as a specific size in the overflow screen analysis, eg, 5% retained on 65 mesh screen or 45% passing 200 mesh screen, or as a d Q, defined as a cut-off or separation size at which 50% of the particles report to the oversize or undersize. The efficiency of a classifier is represented by a performance or partition curve (2,6), similar to that used for screens, which relates the particle size to the percentage of each size in the feed that reports to the underflow. 

By convention, classification has been defined as the particle size of which 1 % to 3 % reports to the cyclone overflow with coarser particles reporting to the cyclone underflow. Recent investigations reported by Arterbum (1999) have defined classification as the particle size of which 50% reports to the overflow and 50% to... 

Figure 52 also shows that the actual recovery curve does not decrease below a certain level. This indicates that a certain amount of material is always recovered to the underflow and bypasses classification. If a comparison is made between the minimum recovery level of solids to the liquid that is recovered, they are found to be equal. Therefore it is assumed that a percent of all size fractions reports directly to the underflow as bypassed solids in equal proportion to the liquid split. Then each size fraction of the actual recovery curve is adjusted by an amount equal to the liquid recovery to produce the "corrected recovery" curve shown in Figure 52. As the Djoc point changes from one application to another, the recovery curves shift, along the horizontal axis. In order to determine a single graph which represents the corrected recovery curve, the particle size of each size fraction is divided by the Dj value and a "reduced recovery" curve can be plotted, as shown in Figure 53. Studies reported by Arterburn have shown that this curve remains constant over a wide range of cyclone diameters and operating conditions when applied to a slurry...

In processes where classification or separation of particles is required, the efficiency of separation will be a function of one or more distributed properties of the particles. The function which describes the efficiency with which particles are separated by size (d) is usually termed the grade efficiency, G(d). For particles in a narrow size interval between d and d + Ad, G(d) is defined as the mass ratio of such particles in the underflow to that in the feed. The overall separation efficiency E corresponds to the particle size d for which G(d) equals E. 

For each test a 15-mL quantity of slurry was mixed with a 500-mL quantity of O.IM NaOH solution to maintain pH at 13. After digesting overnight, the slurry was wet screened on a B.S. 350-mesh screen to remove +43- xm oversize particles. The underflow then was passed through a micropore filter of nominal pore size of 1.2 xm. The coal thus was fractionated into three particle size ranges. 

A DMS cyclone cut point ( 50 is greater than the density of the medium and is closely related to the density of the cyclone underflow. The size distribution of the magnetite particles is very important for dense-medium cyclones, and magnetite that is 90% below 325 mesh (45 /xm) was... 

To separate solids having about the same density but with a range of partide size, separate based on cut diameter and use air or liquid classifiers such as cyclones, hydrocyclones or spiral classifiers Particle size 25-2000 [xm feed solids concentration 5 to 40%. Cut diameter is the particle diameter that has equal chance to report to either the overflow or the underflow streams. 

If the fuU size distribution of a material is known then the grade efficiency based on particle number, length, area, mass or volume will be the same as any ctor required to convert between these quantities will cancel. Very often in practice, however, the fiill size distribution is not accurately known, there may well be a large amount of the distribution in the finest channel of the equipment used for particle size analysis. It is therefore advisable to work in terms of a mass distribution, and to provide a grade efficiency based on this. The total mass firaction of feed solids reporting to the underflow is termed the gross efficiency [Bradley, 1965], or total solids recovery. 

The liquid-solid hydrocyclone, shown schematically in Fig. 3.4-3, functions like a gas-solid cyclone. The hydrocyclone is also known as a hydroclone. The primary independent parameters that influence the ability of a hydrocyclone to make a separation are size and geometry of the hydrocyclone, particle size and geometry, solids loading, inlet velocity, split between overflow and underflow, density differential, and liquid viscosity. A reasonable estimate of Ae particle cut diameter (50% in underflow and overflow) d o) is given by the following dimensionless relationship, developed initially by Bradley ... 

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.)... 

If, in order to practically assess the performance of solid-fluid separators, a reduced grade efficiency curve is used, the particle size which gives 50% efficiency in such a curve is called the reduced cut size and is represented by x o-The maximum attainable efficiency related to particle size would be that minimum particle size with 100% probability of being reported to the underflow. Graphically, by extrapolating the end part of the curve to the horizontal axis, such size will be obtained. It has been proved that in practice, the maximum of the efficiency is around 98%, and the minimum size corresponding to this efficiency is represented by Xgg and known as the approximate limit of separation. 

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... 

Clearly, most real cases will be somewhere in between, when the particle concentration varies with position throughout the cyclone body anywhere between that of the clean liquid and the underflow concentration. Accordingly, the suspension density and apparent viscosity will vary, and different feed solids particle size distributions will result in different spatial distributions of these two variables. 

Both the pressure drop and the separation efficiency (as all the other performance criteria we may be interested in) depend strongly on the cumulative effect of the density and viscosity distributions within the cyclone flow and the precise knowledge of these distributions (for any distribution of particle size in the feed) is essential for any model to work. To predict these spatial distributions, together with the complex effects of underflow orifice crowding, internal flow eddies and turbulence, short circuit flow, turbulent pick-up of solids from the boundary layer, non-Newtonian behaviour of... 

This theory was first suggested by Fahlstrom who proposed that the cut size is primarily a function of the capacity of the underflow orifice and of the particle size analysis of the feed. He argued that the crowding effect, or hindered discharge through the apex, can swamp the primary interaction to the extent that the cut size can be estimated from the mass recovery to the underflow. 

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