Average cake concentration

Range of wash volume, gal/ft2 Solute removed, lbm/ft2 Cumulative solute removed, lbm/ft2 Average wash concentration, lbm/gal Mass of solute remaining, lbm/ft2 Present solute on moisture-free basis Average cake concentration, lbm/gal... 

Stages (iii) - (v) can be sinq>lified considerably by assuming an average cake concentration provided by Equation (2.40). Both procedures can be entered readily into a standard computer spreadsheet program. 

Run No. Cake Moisture, percent Average Chloride Concentration in Scrubber Liquor, percent Scrubber Feed Scrubber Discharge Comments... 

Calculate the average wash concentration CWjav. The instantaneous wash concentration C, , shown as the third column in Table 14.4, is plotted against volume of wash (the second column in Table 14.4) in Fig. 14.8. Now, by a material balance for the solute in the cake,... 

It is necessary to calculate the volumetric slurry concentration (()j and the average cake porosity Sja,. Using Equation (22.8) with and 5 replacing and leads to... 

Average concentration of liquid in the cake. Cay. average solute concentration of total liquid remaining in the cake. 

Starting with the fraction of perlite/in the first colnmn, colnmns 2 and 3 contain the experimental valnes of and for a pressure filtration of 200 kPa. In column 4, values of the suspension concentration are shown as they reflect the addition of perlite. The time required to produce a cake with L = 0.014 m is tabulated in column 5. The short time of <1 sec for/= 0.667 results from the high slurry concentration of cp p = 0.156 compared with an average cake solidosity of = 0-18. A more detailed analysis of the cake would provide the variation of Sj with the distance x in the cake. An experiment with/= 0.333 indicated that Sj at the cake snrface had an approximate value of = 0.1 and at the medium, it reached a value in the range of 0.3 to 0.4. With/= 0.333, the concentration of (Pjp = 0.085 indicates the suspension is close to = 0.10 and when/= 0.667, the value of = 0.156 is probably larger than indicates that the snspension is actually a cake. Calculations in the table for/= 0.333 and 0.667 cannot be taken serionsly as the equations are only valid for true slurries. However, they indicate that concentrations in excess of/= 0.333 are impractical. 

Thus a logarithmic plot of pressure drop over the filter cake against time yields a strai t line if average values of pecibc resistance and cake concentration exist. 

In equations (4.70) and (4.72) the average solids concentration in the cake expressed in terms of a volume fraction has been used to represent the cake structure. Several alternative expressions for cake structure are found in the literature, the two most coimnon involve the cake porosity (s ) and the voids ratio (e)... 

Sodium carbonate monohydrate crystals from the crystallizers are concentrated in hydroclones and dewatered on centrifuges to between 2 and 6% free moisture. This centrifuge cake is sent to dryers where the product is calcined 150°C to anhydrous soda ash, screened, and readied for shipment. Soda ash from this process typically has a bulk density between 0.99—1.04 g/mL with an average particle size of about 250 p.m. 

Individial filter cake compositions vary widely. As conversion increases, sulfur and ash increase while oxygen and hydrogen and possibly nitrogen concentrations in the filter cakes decrease. The average filter cake yield is 30 weight percent of the as-fed coal. The sulfur in the filter cake averaged 49 percent of the sulfur in the coal feed and is made up of the sulfur remaining after partial pyrite decomposition and sulfate sulfur. 

Data collected for each run Included cation concentration using ICP and H concentration by titration. Filtering characteristics were determined using solid and liquid yield rates, as well as back pressures during the filtration cycle. The filter cake was characterized by moisture content and particle size. Selected samples of the cake were analyzed using SEM to determine average particle size and shape. 

In RO, a colloidal deposit on the membrane introduces an additional resistance, Rf, and could also cause cake-enhanced concentration osmotic pressure (CEOP) [24]. The CEOP phenomenon is discussed in Section 6.3.4. Large-scale RO plants tend to be operated at a fixed production rate, requiring a fixed average flux. 

Fig. 1. Glucose concentration over time for semibatch saccharification experiments at 15% (w/w) initial insoluble solids concentration and 20 FPU/g of cellulose enzyme loading. Filtration was applied at two different times to remove glucose (vertical dashed lines). VF Only vacuum filtration was applied alone VF+UF ultrafiltration was also applied following vacuum filtration VF, Washed Vacuum filtration was applied and the filter cake was washed with water. Error bars represent averages 1 SD for two repeated experiments.

Related Calculations. The average concentration of solute in the cake consists of mass of solute remaining divided by void volume. These values appear as the final column in Table 14.5. 

Measured pressure build up versus accumulated amount of fly ash is shown in Fig. 5 a). Calculated fly ash accumulation is based on averaged dust load measured gravimetiically during die respective filtration cycle. Observed pressure loss is close to ideal behavior for surface filtration (i.e. inconqiressible cake formation and constant dust concentration). Calculated specific cake resistance is shown in Fig. 5 b). 

V - average gas velocity thorough filter cake [m/s] c - dust concentration in flue gas [kg/m ]... 

An aqueous suspension of calcium silicate (p = 1950 kg/m ) at 20°C was filtered at a constant pressure of 68.9 kPa in a small press with an area of 428.7 cm. The slurry concentration was 0.495% by weight and the average moisture content of the cake was 70.63% by weight. Calculate the specific and medium resistances on the basis of the following data (Hosseini 1977) ... 

Average wash liquid concentration, average concentration of total wash liquid coming out of the cake. 

Onstream hours Fly ash loading Adipic acid concentration, ppm (controlled) Scrubber gas velocity, ft/sec Liquid-to-gas ratio, gal/Mcf Slurry solids concentration, wt % (controlled) Scrubber inlet pH (controlled) Oxidation tank level, ft Oxidation tank residence time, min Effluent hold tank residence time, min Average percent SO2 removal Average inlet SO2 concentration, ppm SO2 make-per-pass, m-moles/liter Percent oxidation of sulfite to sulfate Air stoichiometry, atoms oxygen/mole SO2 absorbed Oxidation tank pH Percent limestone utilization Scrubber inlet liquor gypsum saturation, % Filter cake solids content, wt % 1,688 High 1,300 1,700 5.4- 9.4 85 150 15 5.0- 5.1 18 2.8 8.3 93.4 2,660 4.0- 8.9 99.8 1.4- 2.4 4.9 92.6 93 86... 

An expression for the average concentration in a filter cake can be deduced by a similar approach to that used in the derivation of Equation (2.38). This leads to ... 

In most practical industrial filtrations involving conq)ressible cakes, filtration equations (2.41)-(2.43) are applied using an average value for cake resistance and conc tratiou which is usually measured. For a more detailed understanding of the cake structure solids concentration profiles have to be measured or assumed, thereby Equations (2.45)-(2.50) can be used to determine the overall filtration resistance, throughput rate, cake depth, etc. If it is possible to measure these fimctions and profiles... 

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