such as t4, is called the critical time and the corresponding concentration of solids is called the critical concentration.

As evidenced from this batch analysis, various degrees of sludge thickening can occur. Table 5.3 shows some data that indicate the various thickening, expressed as percent solids, that can result in various units.

After the organic pollutant in raw sewage has been converted to microorganisms, the resulting solids need to be separated. This is done using the secondary clarifier. In the process of clarification, however, on account of the large concentration involved, the solids are also thickened. Because of this, the process of separating the solids in a secondary clarifier actually involves two functions: the clarification function and the thickening function. Each of these two functions will have its own clarification or thickening area requirement. The bigger of the two controls the design of the basin.

Two methods are used to thicken sludges: gravity thickening and flotation thickening. In gravitational thickening, solids are thickened as a result of solids piling

on top of each other and the action of gravity that compresses the accumulated solids. In flotation thickening, the solids stick to the rising bubbles that float toward the surface. Upon exposure to the surface, the bubbles break, leaving the solids that had stuck to the bubbles in concentrated form. This section discusses gravitational thickening as well as the clarification that occurs in the secondary clarifier.

Figure 5.12 may be considered a schematic section of either a secondary clarifier or of a gravitational thickener. This is an implementation of the batch settling test of Figure 5.11 on a continuous mode. Continuous mode means that the thickened solids are continuously removed from the bottom of the tank. As shown, there are also four zones: zone A, zone B, zone C, and zone D. Zone A is the clarification zone. In zone B, the concentration of the solids is constant as indicated by X, the biosolids coming out of the bioreactor X. (Xi corresponds to the co of the batch settling.) In zone C, the concentration varies from low to high in going from the upper to the lower part of the zone. This is where thickening occurs. In zone D, the concentration is constant; the concentration in this zone is the underflow concentration [Xu] and is the concentration that is withdrawn from the bottom of the tank. This zone corresponds to the compression zone in the batch experiment.

Thickening occurs in secondary clarifiers, so the sizing of the clarifier also involves the determination of the thickener area. In designing the clarifier portion of the clarifier, the subsidence velocity of zone B must be determined. This is modeled by allowing a sample to settle in a cylinder and following the movement of the interface between zones A and B over time. This subsidence velocity is equated to the overflow velocity to size the clarifier area Ac. For a pure gravity thickener, although some clarification also occurs, the thickening function is the major design parameter and the clarification function need not be investigated. The method used to size the thickener area is called the solid flux method.

Solids flux method. The design of the thickener area considers zone C. (Note: you do not consider zone D.) As indicated, the concentration of the solids in this zone is variable. Thus, the behavior of the solids is modeled by making several dilutions of the sludge to conform to the several concentrations possible in the zone. The ultimate aim of the experiment is to be able to determine the solids loading into the thickener. The experiment is similar to that of the clarifier design, except that several concentrations are modeled in this instance. Also, it is the relation between subsidence velocity and concentration that is sought. The reason is that if velocity is multiplied by the concentration, the result is the solids loading called the solids flux, the parameter that is used to size the thickener portion.

Performing a material balance at any elevation section of the thickener area (corresponding to zone C), two solid fluxes must be accounted for: the flux due to the gravitational settling of the solids and the flux due to the conveyance effect of the withdrawal of the sludge in the underflow of the tank. Calling the total flux as Gt, the gravity flux as Vc[Xc] and the conveyance flux as Vu[Xc], the material balance equation is

where Vc is the subsidence velocity at the section of the thickening zone, [Xc] is the corresponding solids concentration at the section, and Vu is the underflow velocity computed at the section as Qu/A(, where Qu is the underflow rate of flow and a, is the thickener area at the elevation section considered. Some value of this flux Gt is the one that will be used to design the thickener area and, therefore, must be determined.

Because the solids concentration in the thickening zone is variable, Gt in the zone is also variable. Of these several values of Gt, only one value would make the solids loading at the corresponding elevation section equal to the rate of withdrawal of sludge in the underflow. This particular G, is called the limiting flux Gt(, because it is the one flux that corresponds to the underflow withdrawal rate. Because Ga corresponds to the rate of sludge withdrawal, the thickener area determined from it will be the thickener area for design, if found greater than the area determined considering the clarification function of the unit.

Equation (5.39) may be multiplied throughout by A, producing

Dividing all throughout by At and rearranging,

The value of Vu depends on the value of Qu. If the sludge concentration is to be withdrawn at the concentration [Xu], then Qu must be such that Equation (5.41)

is satisfied. As shown, this equation contains Vu[Xu]. A specific value of this term determines the area A, of the thickener. As will be shown below, this value is Gt(, the limiting flux.

The expression Vc[Xc] + Vu[Xc] can be likened to the flow of traffic in a toll booth terminal. The cars at far distances from the terminal can travel as fast as they can, but upon reaching the terminal, they all slow down to a crawl. The number of cars that leave the terminal at any given time is a function of how fast the terminal fee is paid and processed by the teller. In other words, the terminal controls the rate of flow of traffic. A particular value of Vu[Xu] = Gt = Ga corresponds to the speed at which the fee is paid and processed by the teller, and its location in the thickener corresponds to the terminal. This location is the critical or terminal section.

A number of combinations of the values of the elements of Vc[Xc] + Vu[Xc] can occur before the solids reach the critical section of the thickener. This combination corresponds to the different speeds of the cars; however, upon reaching the section, Vc[Xc] + Vu[Xc] slows down to a crawl, that is, slows down to a one particular value of Vu[Xu]. This "crawl" value of Vc[Xc] + Vu[Xc] would have to be the smallest of all the possible values it can have before reaching the section; this value would also necessarily correspond to the rate of withdrawal at the bottom of the tank. This is the limiting flux Ga, mentioned previously. Thus,

Gt ( = min {(Vu [ Xu ])i} = [ Xu ] min (Vu X = min {(Vc [ Xc ] + Vu[ Xc ]) i} (5.42)

where min means "minimum of" and i is an index for the several values of the parameter. This minimum value of Vu may obtained from the graph of [Xc] and Vu. Note that Ga has a corresponding Qu. If Qu is changed, the value of [Xu] is also changed and, accordingly, a new value of Gti must be determined.

Knowing Gt(, the thickener area A, can now be calculated as a, = q+qr® (5.43)

Qo + Qr = Qi is the influent to the thickener (or secondary clarifier); QR is the recirculation flow; and Qo is the inflow to the overall treatment plant. At is then compared with the clarifier area Ac; the larger of the two is the one chosen for the design. For gravity thickeners, At is automatically used, without comparing it to Ac, because Ac is not actually calculated in designs of thickeners.

Example 5.12 The activated sludge bioreactor facility of a certain plant is to be expanded. The results of a settling cylinder test of the existing bioreactor suspension are shown below. Qo + QR is 10,000 m /d and the influent MLSS is 3,500 mg/L. Determine the size of the clarifier that will thicken the sludge to 10,000 mg/L of underflow concentration.

MLSS = [Xc](mg/L) 1,410 2,210 3,000 3,500 4,500 5,210 6,510 8,210 Vc (m/h) 2.93 1.81 1.20 0.79 0.46 0.26 0.12 0.084

Solution: First, determine area based on thickening:

Gt( = [ Xu ]min ( Vu \ = min( Vc[ Xc ] + Vu [ Xc ]) V» = iX i'^X I [Xu] = 10,000 mg/L

[Xc] (mg/L) 1,410 2,210 3,000 3,500 4,500 5,210 6,510 8,210

The plot is shown next.

The plot is shown next.

Therefore from the plot, min(Vu) = 0.21, and

Gt( = [ Xu ]min ( Vu )i = 10,000 (0.21 ) = 2100 ( mg/L )•( m/h )

Determine area based on clarification: For an MLSS of 3,500 mg/L, settling velocity = 0.79 m/h

Assuming the solids in the effluent are negligible, solids in the underflow = 10,000(3.5) = 35,000 kg/d = 1458.33 kg/h

Therefore, the thickening function controls and the area of the thickener is 694.4 m2 Ans

Flotation may be used in lieu of the normal clarification by solids-downward-flow sedimentation basins as well as thickening the sludge in lieu of the normal sludge gravity thickening. The mathematical treatments for both flotation clarification and flotation thickening are the same. As mentioned in the beginning of this chapter, water containing solids is clarified and sludges are thickened because of the solids adhering to the rising bubbles of air. The breaking of the bubbles as they emerge at the surface leaves the sludge in a thickened condition.

Figure 5.13 shows the flowsheet of a flotation plant. The recycled effluent is pressurized with air inside the air saturation tank. The pressurized effluent is then released into the flotation tank where minute bubbles are formed. The solids in the sludge feed then stick to the rising bubbles, thereby concentrating the sludge upon the bubbles reaching the surface and breaking. The concentrated sludge is then skimmed off as a thickened sludge. The effluent from the flotation plant are normally recycled

270 84 2 2

Effluent

Pressurizing pump

FIGURE 5.13 Schematic of a flotation plant.

Effluent

Pressurizing pump

FIGURE 5.13 Schematic of a flotation plant.

Effluent \

/ Recycle suction

Sludge collector

Float trough

¿^Settled sludge discharge

Float trough

Effluent \

/ Recycle suction

Float sludge discharge

Pressurized 3-«- air-wastewater inlet

Sludge collector

¿^Settled sludge discharge

FIGURE 5.14 Elevational section of a flotation unit. (Courtesy of Enirex, Inc.)

Float sludge discharge

Pressurized 3-«- air-wastewater inlet

FIGURE 5.14 Elevational section of a flotation unit. (Courtesy of Enirex, Inc.)

back to the influent of the whole treatment plant for further treatment along the with the influent raw wastewater. Figure 5.14 shows an elevational section of a flotation unit. The dissolved air concentration of the wastewater in the air saturation tank Caw,t is

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