Underflow mass flow solids

Density Gauges These are used to measure the density or suspended solids content of the feed and underflow streams. Gamma radiation devices are the most commonly used for automatic control, but ultrasonic devices are effective in the lower range of slurry density. Marcy pulp density scales are an effective manually operated device. A solids mass flow indication is usually obtained by combining a density gauge output with the output from a flowmeter. 

The solids concentration can be expressed in terms of either the solids volume fraction (mass ratio of solids to fluid (R). If volume fraction of solids in the feed stream (flow rate gf) and (pu is the volume fraction of solids in the underflow (flow rate gu), then the solids ratio in the feed, Rf = [(mass of solids)/(mass of fluid)]feed, and in the underflow, Ru = [(mass of solids)/(mass of liquid)]u, are given by... 

Flocculant addition rate can be regulated in proportion to the thickener volumetric feed rate or solids mass flow in a feed-forward mode, or in a feed-back mode on either rake torque, underflow density, settling solids (sludge) bed level, or solids settling rate. Of these, feedforward on mass flow or feed-back on bed level are probably the most common. In some feed-forward schemes, the ratio multiplier is trimmed by one of the other parameters. 

Underflow is usually withdrawn continuously on the bases of bed level, rake torque, or underflow solids concentration in a feed-back mode. Most installations incorporate at least two of these parameters in their underflow withdrawal control philosophy. For example, the continuous withdrawal may be based on underflow solids density with an override to increase the withdrawal rate if either the rake torque or the bed level reaches a preset value. In some cases, underflow withdrawal has been regulated in a feed-forward mode on the basis of thickener feed sohds mass flow rate. Any automated underflow pumping scheme should incorporate a lower limit on volumetric flow rate as a safeguard against line pluggage. 

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. 

Estimator of sample size, constant in Equation 3.12 (L/T), mass flow rate of solids in underflow (M/T), volumetric flow rate of underflow (L /T)... 

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). 

An unknown value x is assigned to the mass flow rate of the solubles in the outflow of washed solids from the final stage (the system underflow)— see Figure 15.14. This unknown x will carry through the system and appear as a factor in the solubles balance around all stages in the system. The difference... 

The mass flow rates of solids in a minimum number of streams needed for fiiU mass balances are given notation. Usually the system feed and the individual underflow streams are best for this, as shown in Figure 16.21. Equations relating the overall and individual total efficiencies are then written with the notation selected (using the definition of total efficiency as mass flow rate of solids in the underflow to that in the feed) ... 

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. 

If there is no net flow of gas out the cyclone underflow, the captured solids fraction is a pure solids stream, and it may be possible to determine the mass flow of this fraction by collecting the underflow solids for a known time, and weighing. This method can often be applied in both an industrial and a laboratory installation. 

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. 

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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