Size distribution underflow

In hydroseparator tests, it is necessaiy to measure solids concentrations and size distributions of both the supernatant sample withdrawn and the frac tion remaining in the cylinder. The volume of the latter sample should be such as to produce a solids concentration that would be typical of a readily pumped underflow shiny. 

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... 

The experimental results reported in this paper demonstrate the ability of a flat-bottom hydrocyclone to separate the coarse fraction of ammonium sulfate crystals from a slurry which contains crystals of a wide size range. It appears that the grade efficiency curve, which predicts the probability of a particle reporting to the underflow of the cyclone as a function of size, can be adjusted by a change in the underflow diameter of the hydrocyclone. These two observations lead to the suggestion to use hydrocyclone separation to reduce the crystal size distribution which is produced in crystallisers, whilst using a variable underflow diameter as an additional input for process control. 

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... 

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. 

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... 

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. 

Simple, fundamental theories which take no or little account of the effect of the flow ratio (or the size of the underflow orifice), of the feed concentration and of the feed size distribution. The influence of some cyclone dimensions on the cyclone performance is included. 

When operating a hydrocyclone with a free underflow orifice discharging into atmospheric pressure, the discharging slurry can be observed to have different shapes depending on the feed size distribution, separation efficiency... 

Now that Ey is known, it is possible to calculate other values of the predicted performance of the system, such as the concentrations or particle size distributions in the system overflow and underflow (consult examples in chapter 3)—the methods are the same as for single separators because the system is now treated as a single stage. If particle sizes and/or concentrations are needed in any of the streams within the network then a full mass balance calculation is needed and this is dealt with in the following section. 

As the flow passes through a separator, the feed size distribution is processed by the grade efficiency curve/function of the separator. In keeping with established practice, each size class is split into the underflow and overflow as specified by the grade efficiency taken at its mid-point as shown in Figure 16.23. Note that in order to illustrate the point more clearly. Figure 16.23 has a small number of size classes. 

The underflow of the suspension is passed freely to the centrifuge. Depending on the crystal size distribution, there is a choice of at least four different types of centrifuges (Figure 11.23). The sieve decanter and the peeler-type centrifuge are selected for the separation of finer products. The pusher-type centrifuge or the sieve/worm centrifuges are used for coarser products. While the pusher-type... 

The grade efficiency curve can be determined by measuring the total efficiency and the particle size distribution of any two of the three streams (feed, underflow, and overflow). One of the following equations can be used for calculating the grade efficiency ... 

Once the grade efficiency curve is known for a given set of operating conditions, the total efficiency Et (recovery of solids into the underflow) expected with a particular of a cumulative particle size distribution F(x) feed can be predicted using the following relationship ... 

Consider the separation of dust particles from air by means of two cyclones connected in the following fashion. Feed air containing dust enters cyclone 1 the feed particle size distribution is Ff (Pp) = l-e"" p. The underflow from cyclone 1 is introduced with a small amount of air as feed to a small cyclone 2. The underflow from cyclone 2 is collected as dust from the system. The overflow air from cyclone 2 is mixed with the overflow air from cyclone 1 to obtain the cleaned air. The grade efficiency of the ith cyclone is given by... 

Although the grade efficiency function enables one to determine easily the particle size distribution in the overflow and the underflow if the feed particle size distribution is known, a quantity, S, called sigma, is frequently used in practice to compare different centrifuges (Ambler, 1952). It is defined by the relation... 

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). 

Inject a feed of a wide size distribution into a laboratory cyclone or, in the case of an commercial installation, utilizing the solids already reporting to and from the cyclone, collect samples and perform size analyses on any two of the feed, the overflow and the captmed (underflow) fractions. Then use Eq. (3.2.6) to calculate rj(x). To obtain reasonably accmate results, the overflow fraction should be one of the fractions analysed. 

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. 

Other factors to be considered include inlet and outlet designs. Installing inlet baffles with sized opening will enhance flow distribution across entire width and depth of the basin. Underflow baffles following the floatable removal system can also increase the removal efficiency of floatable particles. However, baffles must be deep enough to prevent pulling of the floatable particles under the baffle. It is recommended that flow velocity under the baffle should be limited to 1 ft/min (21). 

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