Overflow mass flow solids

Diagram of mass balance in a separator M mass flow rate of solids in the feed, M mass flow rate of separated solids, M, mass flow rate of nonseparated solids, F(x) cumulative percentage oversize of feed solids, F (x) cumulative percentage oversize of separated solids, F,(a ) cumulative percentage oversize of nonseparated solids, Q. volumetric flow rate of feed suspension, U volumetric flow rate of underflow suspension, O volumetric flow rate of overflow suspension. 

The total efficiency can be determined from three different combinations of the material streams involved (equation 3.5 combined with the mass balance in equation 3.1) the mass flow rates of the solids are usually determined by measuring the total volumetric flow rates and the corresponding solids concentrations the mass flow rate is, of course, the product of the two. The combination giving the smallest standard deviation of Ei (if all the variables are subject to random errors only) is that of the overflow and underflow streams. (The same conclusion applies to the testing of G x).)... 

Mp is the mass flow rate of the feed suspension Mq is the mass flow rate of the overflow suspension Mu is the mass flow rate of the underflow suspension yp is mass fraction of solids in the feed yo is mass fraction of sohds in the overflow yu is mass fraction of sohds in the underflow... 

If the solids to be washed are much coarser than the cut sizes in all stages of the washing train, complete separation in each stage may be assumed and the mass balance calculations become trivial (i.e. each underflow stream carries the same mass flow rate of the solids, equal to the feed rate, and all overflows are free of solids). 

Consider a single-entry separator used either for separating solid particles from a fluid or separating solid particles having sizes above a particular value from those having sizes below the particular value. Let u/Jy. be the total mass flow rate of solids in the feed fluid whose total volumetric flow rate is Qf. In such a separator, there are only two product streams, the overflow (/ = 1) and the underflow (/ = 2). The total mass flow rate of solids in the overflow and the underflow are, respectively, and u/Jj- The overflow is identified with essentially the carrier fluid and the finer particles, whereas the underflow is assumed to have most of the coarser particles and small amounts of carrier fluid. Figure 2.4.1 illustrates this for a hydrocyclone (Talbot, 1980). Sizes of various natural and industrial particles are shown in Figure 2.4.2. 

The mass flow of the feed solids is sometimes known in an industrial installation from measurements taken elsewhere in the plant. In an experimental laboratory rig, a test is often of a limited duration, and the mass of feed solids can be determined accurately by weighing the entire charge. If these options are not workable, the inlet solids flow has to be determined by on-line sampling from the piping upstream of the cyclone or swirl tube, or inferred from measurements or information regarding the solids flow rate in the overflow and underflow streams. 

Let Q, Qo, Qfi = Volumetric flow-rates of feed, overflow and sediment (m /s), W = Mass flowrate of solids (kg/s), F = Mass ratio of liquid to solid in feed (kg/kg) and S = Mass ratio of liquid to solid in sediment (kg/kg). 

A fluidized bed is made up of a mass of particles buoyed up out of permanent contact with each other by a flowing fluid. Turbulent activity in such a bed promotes high rates of heat and mass transfer and uniformity of temperature and composition throughout. The basic system includes a solids feeding device, the fluidizing chamber with a perforated distributing plate for the gas, an overflow duct for removal of the dry product, a cyclone and other equipment for... 

It is assumed that the solute-free solid is insoluble in the solvent and that the flow rate of this solid is constant throughout the cascade. The solid is porous and carries with it an amount of solution that may or may not be constant. Let L refer to the flow of this retained liquid and V to the flow of the overflow solution. The flows V and L may be expressed in mass per unit time or may be based on a definite flow of dry solute-free solid. Also, in accordance with standard nomenclature, the terminal concentrations are as follows ... 

If the solids rate, e, pf, and Pg are all constant, then from Eq. ri4-5dl Uj = U = constant. If U is constant, then an overall mass balance shows that the overflow rate, Oj, must also be constant. Thus, to have constant flow rates we assume ... 

The total efficiency Ej- is the fraction of particles of the feed which are exiting through the underflow or the tails stream. When Et equals 1, the separation between the solid and the overflow fluid is complete. If the carrier fluid stream is the preferred one containing finer particles, then obviously Et = (l- )< where ff is the cut defined by (2.2.10a) in terms of only the solid particle flow rates. The grade ciency Gr of particles of size Vp is the ratio of the mass of particles of size Vp in the underflow to that in the feed. It depends on Tp and the separator characteristics. If the particle classifier or the solid-liquid separator is of any use, then at least all particles of size r, should be in the underflow. To generalize,Gr rp=oo = 1. As Tp 0, tends to a limiting value defined by (Svarovsky, 1977, chap. 3)... 

Using such a formalism (Davis et al, 1989), we can obtain the following mass balance relations for the total volumetric flow rate, total solids flow rate and the flow rate of solids having a particular settling velocity Up t (subscript j = 1, overflow subscriptj = 2, underflow) ... 

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