Concentrations solids

An appreciation of the different forms of solid concentration that may be quoted, and means to convert from one form to another, are essential in reconciling ej erimental data with the mathematical description of filtration. It is probable that expenmental data wUl be obtained in the form of mass fiaction or s, for the filter cake or shirry concentrations repectively, as this readily follows firom drying and wd ung the sanples. Concentration by volume fi action comes fi-om the definition of draisity and some cancelling  

Concentration in terms of mass of solids per unit volume (Cm) follows by a similar route  

It is oft assumed that w can be obtained from Cm / (the shiny mass per nwh volume liquid concentration) as follows  

For a more rigorous treatment of the dry mass of cake per unit filter area it is usual to start with the cake moisture ratio, defined as  

Mass of wet cake Mass of cake solids + Mass of cake Uquid 

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To keep the frequency of backwash and the washwater demand down, and to prevent undesirable cake formation on the filter surface, deep bed filtration is appHed to very dilute suspensions of solids concentrations less than 0.1% by volume. 

Separation Efficiency. Similarly to other unit operations in chemical engineering, filtration is never complete. Some soflds may leave in the hquid stream, and some Hquid will be entrained with the separated soHds. As emphasis on the separation efficiency of soHds or Hquid varies with application, the two are usually measured separately. Separation of solids is measured by total or fractional recovery, ie, how much of the incoming solids is coUected by the filter. Separation of Hquid usually is measured in how much of it has been left in the filtration cake for a surface filter, ie, moisture content, or in the concentrated slurry for a filter-thickener, ie, solids concentration. 

The constant s depends on impeller configuration and C is solids concentration. Several other researchers have since developed similar correlations which include effects of a few additional parameters such as D/T, C/D, and H/T. The corresponding exponents of these parameters vary in range —1 to —1.7 for D/T, 0.15 to 0.2 for CjD, and -- 0.33 for DJT. 

A cocurrent evaporator train with its controls is illustrated in Fig. 8-54. The control system applies equally well to countercurrent or mixed-feed evaporators, the princip difference being the tuning of the dynamic compensator/(t), which must be done in the field to minimize the short-term effects of changes in feed flow on product quality. Solid concentration in the product is usually measured as density feedback trim is applied by the AC adjusting slope m of the density function, which is the only term related to x. This recahbrates the system whenever x must move to a new set point. 

Blowdown discards a portion of the concentrated circulating water due to the evaporation process in order to lower the system solids concentration. The amount of blowdown can be calculated according to the number of cycles of concentration required to limit scale formation. Cycles of concentration are the ratio of dissolved sohds in the recirculating water to dissolved solids in the makeup water. Since chlorides remain soluble on concentration, cycles of concentration are best expressed as the ratio of the chloride content of the circulating and makeup waters. Thus, the blowdown quantities required are determined from... 

J. Y. Oldshiie, Chemical Engineering Progress, Mixing of Slurries Near the Ultimate Settled Solids Concentration, 77(5) 95-98 (1981). 

Figure 18-82 illustrates the relationship between solids concentration, iuterparticle cohesiveuess, and the type of sedimentation that may exist. Totally discrete particles include many mineral particles (usually greater in diameter than 20 Im), salt crystals, and similar substances that have httle tendency to cohere. Floccnleut particles generally will include those smaller than 20 [Lm (unless present in a dispersed state owing to surface charges), metal hydroxides, many chemical precipitates, and most organic substances other than true colloids. 

There is a gradual transition from particulate setthug into the zone-settling regime, where the particles are constrained to settle as a mass. The principal characteristic of this zone is that the setthug rate of the mass, as observed in batch tests, will be a function of its solids concentration (for any particular condition of flocculation, particle density, etc.). 

The solids concentration ultimately will reach a level at which particle descent is restrained not only by hydrodynamic forces but also partially by mechanical support from the particles below therefore. 

FIG. 18 82 Combined effect of particle coherence and solids concentration on the settling characteristics of a suspension. 

These data may be evaluated by selecting different nominal overflow rates (equivalent to settling rates) for each of the detention-time values, and then plotting the suspended-solids concentrations for each nominal overflow rate (as a parameter) against the detention time. For a specified suspended-sohds concentration in the effluent, a cui ve of overflow rate versus detention time can be prepared from this plot and used for optimizing the design of the equipment. 

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 suspended-solids concentration can be plotted on log-log paper as a function of the sampling (detention) time. A straight line usually wih resiilt, and the required static detention time t to achieve a certain suspended-sohds concentration C in the overflow of an ideal basin can be taken directly from the graph. If the plot is a straight hne, the data are described by the equation... 

The former requires measurement of the initial settling rate of a pulp at different solids concentrations varying from feed to final underflow value. The area reqmrement for each solids concentration tested is calciilated by equating the net overflow rate to the corresponding interfacial settling rate, as represented by the following equation for the unit area ... 

The method is apphcable for unflocculated pulps or those in which the ionic characteristics of the solution produce a flocculent structure. If polymeric flocculants are used, the floccule size will be highly dependent on the feed concentration, and an approach based on the Kynch theoiy is preferred. In this method, the test is carried out at the expec ted feed solids concentration and is continued until underflow concentration is achieved in the cyhnder. To determine the unit area, Talmage and Fitch (op. cit.) proposed an equation derived from a relationship equivalent to that shown in Eq. (18-45) ... 

FIG. 18-84 Characteristic relationship between thickener unit area and underflow solids concentration (fixed flocciilant dosage and pulp depth). 

FIG. 18-85 Depth correction factorto he applied to unit areas determined with Wilhelm-Naide and direct methods. Velocity ratio calculated using tangents to settling cun e at a particular settled solids concentration and at start of test. 

Continuous clarifiers generally are employed with dilute suspensions, principally industrial process streams and domestic municipal wastes, and their primary purpose is to produce a relatively clear overflow. They are basically identical to thickeners in design and layout except that they employ a mechanism of hghter construction and a drive head with a lower torque capability. These differences are permitted in clarification applications because the thickened pulp produced is smaller in volume and appreciably lower in suspended solids concentration, owing in part to the large percentage of relatively fine (smaller than 10 Im) solids. The installed cost of a clarifier, therefore, is approximately 5 to 10 percent less than that of a thickener of equal tank size, as given in Fig. 18-94. 

The principal advantage of the tilted-plate clarifier is the increased capacity per unit of plane area. Major disadvantages are an underflow solids concentration that generally is lower than in other gravity clarifiers and difficulty of cleaning when scahng or deposition occurs. The lower underflow composition is due primarily to the reduced com-... 

The factors which may make CCD a preferred choice over other separation systems include the following rapidly settling solids, assisted by flocculation relatively high ratio of solids concentration between underflow and feed moderately high wash ratios allowable (2 to 4 times the volume of hquor in the thickened underflows) large quantity of sohds to be processed and the presence of fine-size sohds that are difficult to concentrate by other means. A technical feasibihty and economic study is desirable in order to make the optimum choice. 

The shiny should always be defined as completely as possible by noting suspended solids concentration, particle size distribution, viscosity, density of solids and liquid, temperature, chemical composition, and so on. 

Pretreatment Chemicals Even though the suspended solids concentration of the slurry to be tested may be correct, it is frequently necessary to modify the sluriy in order to provide an acceptable filtration rate, washing rate, or final cake moisture content. The most common treatment, and one which may provide improvement in all three of these categories, is the addition of flocculating agents, either inorganic chemicals or natural or synthetic polymers. The main task at this point is to determine which is the most effective chemical and the quantity of chemical which should be used. 

Agitation by a wide spatula may be substituted for hand agitation, but only after it has been determined by feel that the spatula will provide the needed agitation. If this cannot be done, then confirmation of proper agitation must be based on back-calculated feed solids concentrations and/or particle size analyses of the filter cakes. 

Cake Filters Filters that accumulate appreciable visible quantities of solids on the surface of a filter medium are called cake filters. The slurry feed may have a solids concentration from about 1 percent to greater than 40 percent. The filter medium on which the cake forms is relatively open to minimize flow resistance, since once the cake forms, it becomes the effective filter medium. The initial filtrate therefore may contain unacceptable sohds concentration until the cake is formed. This situation may be made tolerable by recycling the filtrate until acceptable clarity is obtained or by using a downstream polishing filter (clarifying type). 

The solids recovery in the cake can be inferred from measurements using Eq. (18-90). It is shown as a function of G-seconds for different feed solids concentration in Fig. 18-141 see also theoiy discussed below. 

Imperforate Bowl Tests The amount of supernant hquid from spin tubes is usually too small to warrant accurate gravimetric analysis. A fixed amount of shiny is introduced at a controlled rate into a rotating imperforate bowl to simulate a continuous sedimentation centrifuge. The liquid is collected as it overflows the ring weir. The test is stopped when the solids in the bowl build up to a thickness which affects centrate quality. The solid concentration of the centrate is determined similarly to that of the spin tube. 

Interestingly, the solid concentration in the shiny layer ( ), does not remain constant with time as in gravitational sedimentation. Instead, (t), decreases with time uniformly in the entire shiny layer in accordance to ... 

In Eqs. (18-103) and (18-104), under hindered setthng and 1 g, the solids flux is assumed to be a hnear function of p, decreasing at a rate of Vg. Also, the sohds flux is taken to be zero at the maximiim solids concentration (b max- As G/g 1, this solids flux behavior based on 1 g is assumed to be ratioed By G/g. 

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