Conventional Filtration Filtration is a unit operation of separating solids from fluids. Screening is defined as a unit operation that separates materials into different sizes. Filtration also sepa- rates materials into different “sizes,” so it is a form of screening, but filtration strictly pertains to the separation of solids or particles and fluids such as in water. The microstrainer discussed in Chapter 5 is a filter. In addition to the microstrainer, other examples of this unit operation of filtration used in practice include the filtration of water to produce drinking water in municipal and industrial water treatment plants, filtration of secondary treated water to meet more stringent discharge requirements in wastewater treatment plants, and dewatering of sludges to reduce their volume. To differentiate it from Chapter 8, this chapter discusses only conventional filtration. Chapter 8 uses membranes as the medium for filtration; thus, it is titled advanced filtration. Mathematical treatments involving the application of linear momentum to fil- tration are discussed. Generally, these treatments center on two types of filters called granular and cake-forming filters. These filters are explained in this chapter. 7.1 TYPES OF FILTERS Figures 7.1 to 7.8 show examples of the various types of filters used in practice. Filters may be classified as gravity, pressure, or vacuum filters. Gravity filters are filters that rely on the pull of gravity to create a pressure differential to force the water through the filter. On the other hand, pressure and vacuum filters are filters that rely on applying some mechanical means to create the pressure differential necessary to force the water through the filter. The filtration medium may be made of perforated plates, septum of woven materials, or of granular materials such as sand. Thus, according to the medium used, filters may also be classified as perforated plate, woven septum , or granular filters . The filtration medium of the microstrainer mentioned above is of perforated plate. The filter media used in plate-and-frame presses and vacuum filters are of woven materials. These units are discussed later. Figures 7.1 and 7.2 show examples of gravity filters. The media for these filters are granular. In both figures, the influents are introduced at the top, thereby utilizing gravity to pull the water through the filter. Figure 7.1a is composed of two granular filter media anthrafilt and silica sand; thus, it is called a dual-media gravity filter . Figure 7.1a is a triple-media gravity filter, because it is composed of three media: anthrafilt, silica sand, and garnet sand. Generally, two types of granular gravity filters are used: slow-sand and rapid- sand filters. In the main, these filters are differentiated by their rates of filtration. 7 TX249_frame_C07.fm Page 327 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero 328 Slow-sand filters normally operate at a rate of 1.0 to 10 m 3 /d . m 2 , while rapid-sand filters normally operate at a rate of 100 to 200 m 3 /d . m 2 . A section of a typical gravity filter is shown in Figure 7.2. The operation of a gravity filter is as follows. Referring to Figure 7.2, drain valves C and E are closed and influent value A and effluent valve B are opened. This allows the influent water to pass through valve A, into the filter and out of the filter through valve B, after passing though the filter bed. For effective operation of the filter, the voids between filter grains should serve as tiny sedimentation basins. Thus, the water is not just allowed to swiftly pass through the filter. For this to happen, the effluent valve is slightly closed so that the level of water in the filter rises to the point indicated, enabling the formation of tiny sedimentation basins in the pores of the filter. As this level is reached, influent and effluent flows are balanced. It is also this level that causes a pressure differential pushing the water through the bed. The filter operates at this pressure differential until it is clogged and ready to be backwashed (in the case of the rapid-sand filter). Backwashing will be discussed later in this chapter. In the case of the slow-sand filter, FIGURE 7.1 (a) Dual-media filter; (b) triple-media filter. FIGURE 7.2 A typical gravity filter. Influent Effluent Effluent Influent Intermix zone Intermix zone Coarse media Coarse media Finer media Finer media Finest media Finest media Underdrain chamber Underdrain chamber Anthrafilt Silica sand Anthrafilt Silica sand (a) (b) Garnet sand Water level during filtering Water level during backwashing Wash-water trough Bed expansion limit Sand Influent Drain Effluent A C B Drain Underdrain system Wash water 500 mm 650 mm 600 mm freeboard 500 mm 10 m Wash-water tank h Lb l 2 E Cornroller TX249_frame_C07.fm Page 328 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero 329 it is not backwashed once it is clogged. Instead, the layer of dirt that collects on top of the filter (called smutzdecke ) is scraped for cleaning. As shown, the construction of the bed is such that the layers are supported by an underdrain mechanism. This support may simply be a perforated plate or septum. The perforations allow the filtered water to pass through. The support may also be made of blocks equipped with holes. The condition of the bed is such that the coarser heavy grains are at the bottom. Thus, the size of these holes and the size of the perforations of the septum must not allow the largest grains of the bed to pass through. Figure 7.3 shows a cutaway view of a pressure filter. The construction of this filter is very similar to that of the gravity filter. Take note of the underdrain construc- tion in that the filtered water is passed through perforated pipes into the filtered water outlet. As opposed to that of the gravity filter above, the filtered water does not fall through a bottom and into the underdrain, because it had already been collected by the perforated pipes. The coarse sand and graded gravel rest on the concrete subfill. Using a pump or any means of increasing pressure, the raw water is introduced to the unit through the raw water inlet. It passes through the bed and out into the outlet. The unit is operated under pressure, so the filter media must be enclosed in a shell. As the filter becomes clogged, it is cleaned by backwashing. Thickened and digested sludges may be further reduced in volume by dewater- ing. Various dewatering operations are used including vacuum filtration, centrifuga- tion, pressure filtration, belt filters, and bed drying. In all these units, cakes are formed. We therefore call these types of filtration cake-forming filtration or simply cake filtration . Figure 7.4a shows a sectional drawing of a plate-and-frame press. In pressure filtration , which operates in a cycle, the sludge is pumped through the unit, forcing its way into filter plates . These plates are wrapped in filter cloths . With the filter cloths wrapped over them, the plates are held in place by filter frames in alternate plates-then-frames arrangement. This arrangement creates a cavity in the frame between two adjacent plates. FIGURE 7.3 Cutaway view of a pressure sand filter. (Courtesy of Permutit Co.) Raw water inlet Filtered water outlet Weir Drain Sump Manhole Inlet baffle Fine sand Coarse sand Graded gravel Concrete subfill Header lateral strainer system with expansible strainer heads Adjustable jack legs TX249_frame_C07.fm Page 329 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero 330 Physical–Chemical Treatment of Water and Wastewater FIGURE 7.4 (a) Sectional drawing of a plate-and-frame press (from T. Shriver and Co.); (b) an installation of a plate-and-frame press (courtesy of Xingyuan Filtration Products, China). TX249_frame_C07.fm Page 330 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero 331 Two channels are provided at the bottom and top of the assembly. The bottom channel serves as a conduit for the introduction of the sludge into the press, while the top channel serves as the conduit for collecting the filtrate. The bottom channel has connections to the cavity formed between adjacent plates in the frame. The top channel also has connections to small drainage paths provided in each of the plates. These paths are where the filtrate passing through cloth are collected. As the sludge is forced through the unit at the bottom part of the assembly (at a pressure of 270 to 1,000 kPa), the filtrate passes through the filter cloth into the drainage paths, leaving the solids on the cloth to accumulate in the cavities of the frames. As determined by the cycle, the press is opened to remove the accumulated and dewatered sludge. Figure 7.4b shows an installation of a plate-and-frame press unit. Figures 7.5 to Figure 7.7 pertain to the use of rotary vacuum filters in vacuum filtration. In vacuum filtration , a drum wrapped in filter cloth rotates slowly while the lower portion is submerged in a sludge tank (Figure 7.7a). A vacuum applied in the underside of the drum sucks the sludge onto the filter cloth, separating the filtrate and, thus, dewatering the sludge. A rotary vacuum filter is actually a drum over which the filtration medium is wrapped. This medium is made of a woven material such as canvas. This medium is also called a filter cloth . The drum is made of an outer shell and an inner shell. These two shells form an annulus. The annulus is then divided into segments, which are normally 30 cm in width and length extending across the entire length of the drum. Figure 7.7a shows that there are twelve segments in this vacuum filter. The outer shell has perforations or slots in it, as shown in the cutaway view of Figure 7.6. Thus, each segment has a direct connection to the filter cloth. The purpose of the segments is to provide the means for sucking the sludge through the cloth while it is still submerged in the tank. Each of the segments are connected to the rotary valve through individual pipings. As shown in Figure 7.7a, segments 1 to 5 are immersed in the sludge, while FIGURE 7.5 A rotary vacuum filter in operation. (Courtesy of Oliver United Filters.) Water Wash liquor Filtrate Air Blowback Drum Scraper or “doctor knife” Cake being removed Drive TX249_frame_C07.fm Page 331 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero segments 6 to 12 are not. Pipes V 1 and V 2 of the rotary valve are connected to an external vacuum pump, as indicated in Figure 7.7b. The design of the rotary valve is such that when segments are submerged in the sludge such as segments 1 to 5, they are connected to pipe V 1 through their individual connecting pipes. When segments are not submerged such as segments 6 to 12, the design is also such that these segments are connected to pipe V 2 . This arrangement allows for suction of sludge into the filter cloth over the segment when it is submerged ( V 1 ) and drying of the sludge when the segment is not submerged ( V 2 ). We can finalize the description of the operation of the vacuum filter this way. As the segments that had been sucking sludge while they were still submerged in FIGURE 7.6 Cutaway view of a rotary vacuum filter. (Courtesy of Swenson Evaporator Co.) FIGURE 7.7 (a) Cross section of a rotary vacuum filter; (b) flow sheet for continuous vacuum filtration. Stationary valve plate Rotating wear plate Port Segments Drum Wash spray nozzles Filter medium Agitator arm Scraper Repulper Tank To separator and vacuum pump Discharge head Valve TX249_frame_C07.fm Page 332 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero 333 the tank emerge from the surface, their connections are immediately switched from V 1 to V 2 . The connection V 2 completes the removal of removable water from the sludges, whereupon the suction switches to sucking air into the segments promoting the drying of the sludges. The “dry” sludge then goes to the scraper (also called doctor blade ) and the sludge removed for further processing or disposal. Figure 7.7b shows the fate of the filtrate as it is sucked from the filter cloth. Two tanks called vacuum receivers are provided for the two types of filtrates: the filtrate removed while the segments are still submerged in the tank and the residual filtrate removed when the segments are already out of the tank. Vacuum receivers are provided to trap the filtrate so that the filtrate will not flood the vacuum pump. Also note the barometric seal. As shown, this is in parallel connection with the suction vacuum of the filter. The vacuum pressure is normally set up to a value of 66 cm Hg below atmospheric. Any vacuum set for the filter will correspondingly exert an equal vacuum to the barometric seal, on account of the parallel connection. Hence, the length of this seal should be set equivalent to the maximum vacuum expected to be utilized in the operation of the filter. If, for example, the filter is to be operated at 51 cm, where 13.6 is the mass density of mercury in gm/cc, and 1 is the density of water also in gm/cc. Thus, from this result, the length of the barometric seal should be 6.94 m if the operational vacuum is 51 cm Hg. The design in Figure 7.7b shows the length as 9.1 m. Figure 7.8a shows another type of filter that operates similar to a rotary vacuum filter in that it uses a vacuum pressure to suck sludge into the filter medium. This type of filter is called a leaf filter. A leaf filter is a filter that operates by immersing a component called a leaf into a bath of sludge or slurry and using a vacuum to suck the sludge onto the leaf. An example of a leaf filter is shown in Figure 7.8b. As indicated, it consists of two perforated plates parallel to each other, with a separator screen providing the spacing between them. A filter is wrapped over the plate assem- bly, just like in the plate-and-frame press. Each of the leaves are then attached into a hub through a clamping ring. The hub has a drainage space that connects into the central pipe through a small opening. As indicated in the cutaway view on the right of Figure 7.8a, several of these leaves are attached to the central pipe. Each of the leaves then has a connection to the central pipe through the small opening from the drainage space. The central pipe collects all the filtrates coming from each of the leaves. In operation, a vacuum pressure is applied to each of the leaves. The feed sludge is then introduced at the feed inlet as indicated in the drawing. The sludge creates a slurry pool inside the unit immersing the leaves. Through the action of the vacuum, the sludge is sucked into the filter cloth. As the name implies, this is a rotary leaf filter. The leaves are actually in the form of a disk. The disks are rotated, immersing part of it in the slurry, just as part of the drum is immersed in the case of the rotary vacuum filter. As the immersed part of the disks emerge from the slurry pool into the air, the filtrate are continuously sucked by the vacuum resulting in a dry cake. 51 13.6()1()∆h H 2 O ; ∆h H 2 O 6.94 m== TX249_frame_C07.fm Page 333 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero 334 Physical–Chemical Treatment of Water and Wastewater FIGURE 7.8 A rotary leaf filter showing cutaway view at right end (courtesy of Swenson Evaporator Co.); (b) section of a leaf. Feed inlet (a) Screw conveyor Discharge connection Hollow shaft Filtrate outlet Central pipe Leaf Leaf Separator screen Separator screen Perforated plates Perforated plates Filter cloth Filter cloth Clamping rings Clamping rings Filter leaf hub Filter leaf hub Central pipe (b) Drainage space Drainage space TX249_frame_C07.fm Page 334 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero 335 A mechanism is provided for the cake to drop into a screw conveyor below for continuous removal. This mechanism does not require opening of the case for removal of the cake. It may be noticed that some of the filters discussed are operated continuously and some are not. For example, the rapid sand filter, the slow sand filter, the pressure filter, and the rotary vacuum filter are all operated continuously. The plate-and-frame press is operated as a batch. Thus, filters may also be classified as continuous and discon- tinuous . Only the plate-and-frame press is discussed in this chapter as a representation of the discontinuous type, but others are used, such as the shell-and-leaf filters and the cartridge filters. The first operates in a mode that a leaf assembly is inserted into a shell while operating and retracted out from the shell when it is time to remove the cake. The second looks like a “cartridge” in outward appearance with the filter medium inside it. The medium could be thin circular plates or disks stacked on top of each other. The clearance between disks serves to filter out the solids. 7.2 MEDIUM SPECIFICATION FOR GRANULAR FILTERS The most important component of a granular filter is the medium. This medium must be of the appropriate size. Small grain sizes tend to have higher head losses, while large grain sizes, although producing comparatively smaller head losses, are not as effective in filtering. The actual grain sizes are determined from what expe- rience has found to be most effective. The actual medium is never uniform, so the grain sizes are specified in terms of effective size and uniformity coefficient. Effective size is defined as the size of sieve opening that passes the 10% finer of the medium sample. The effective size is said to be the 10th percentile size P 10 . The uniformity coefficient is defined as the ratio of the size of the sieve opening that passes the 60% finer of the medium sample ( P 60 ) to the size of the sieve opening that passes the 10% finer of the medium sample. In other words, the uniformity coefficient is the ratio of the P 60 to the P 10 . For slow-sand filters, the effective size ranges from 0.25 mm to 0.35 mm with uniformity coefficient ranging from 2 to 3. For rapid-sand filters, the effective size ranges from 0.45 mm and higher with uniformity coefficient ranging from 1.5 and lower. Plot of a sieve analysis of a sample of run-of-bank sand is shown in Figure 7.9 by the segmented line labeled “stock sand ….” This sample may or may not meet the required effective size and uniformity coefficient specifications. In order to transform this sand into a usable sand, it must be given some treatment. The figure shows the cumulative percentages (represented by the “normal probability scale” on the ordinate) as a function of the increasing size of the sand (represented by the “size of separation” on the abscissa). Let p 1 be the percentage of the sample stock sand that is smaller than or equal to the desired P 10 of the final filter sand, and p 2 be the percentage of the sample stock sand that is smaller than or equal to the desired P 60 of the final filter sand. Since the percentage difference of the P 60 and P 10 represents half of the final filter sand, p 2 − p 1 must represent half of the stock sand that is transformed into the final TX249_frame_C07.fm Page 335 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero filter sand. Letting p 3 be the percentage of the stock sand that is transformed into the final filter sand, p 3 = 2( p 2 − p 1 ) (7.1) Of this p 3 , by definition, 10% must be the P 10 of the final sand. Therefore, if p 4 is the percentage of the stock sand that is too fine to be usable, p 4 = p 1 − 0.1 p 3 = p 1 − 0.1(2)( p 2 − p 1 ) (7.2) The plot in the figure shows an increasing percentage as the size of separation increases, so the sum of p 4 and p 3 must represent the percentage of the sample stock sand above which the sand is too coarse to be usable. Letting p 5 be this percentage, p 5 = p 4 + p 3 (7.3) Now, to convert a run-of-bank stock sand into a usable sand, an experimental curve such as Figure 7.9 is entered to determine the size of separation corresponding to p 4 and p 5 . Having determined these sizes, the stock sand is washed in a sand washer that rejects the unwanted sand. The washer is essentially an upflow settling FIGURE 7.9 Sieve analysis of run-of-bank sand. 99 98 95 90 80 70 60 50 40 30 20 10 5 2 1 0.5 0.2 0.1 Normal probability scale 10 -2 2 3 4 5 6 7 8 9 10 -1 2 3 4 5 6 7 8 9 1 Size of separation (cm) Filter sand (wanted) E = 5 × 10 -2 cm, U = 1.5 Stock sand (available) E = 3 × 10 -2 cm, U = 2.8 Analysis of stock sand Site of separation cm × 10 -2 Cumulative weight % 1.05 1.49 2.10 2.97 4.2 5.9 8.4 11.9 16.8 23.8 33.6 0.2 0.9 4.0 9.9 21.8 39.4 59.8 74.4 93.3 96.8 100.0 TX249_frame_C07.fm Page 336 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero [...]... 0.38 0.32 0. 27 0.23 0.18 0.01 0.05 0.15 0.18 0.18 0.20 0.15 0. 07 0.01 fp xi x f pi -i = -0 .333 di 1.24(0 .77 )d pi 86 .75 123.18 159.16 186.53 225.43 2 67. 34 316.56 371 .32 473 . 97 763.28 77 41.44 38,899.02 64,221.10 93,955.69 1 47, 033.13 154 ,74 0.68 99,432.26 23,168.33 ∑ = 629, 977 .93 2 2 x 2l ( 1 – n ) V s 2 ( 0 .76 ) ( 1 – 0.42 ) ( 0.00135 ) - h L = - - ∑ f pi -i = ... dual-media filter composed of anthracite as the upper 30-cm part and sand as the next lower 30-cm part of the filter The results are shown in the following table, where co is the concentration of solids at the influent and c is the concentration of solids in the water in the pores of the filter If the respective average sizes of the anthracite and sand layers are 1.6 mm and 0.5 mm, what is the length of. .. (a) Direction of flow of slurry (b) (c) FIGURE 7. 11 (a) Büchner funnel filtration assembly; (b) leaf filter assembly; and (c) mechanics of cake filtration © 2003 by A P Sincero and G A Sincero Physical Chemical Treatment of Water and Wastewater Filtrate TX249_frame_C 07. fm Page 356 Friday, June 14, 2002 4:32 PM 356 Vacuum gage Büchner funnel Filter paper Vacuum gage TX249_frame_C 07. fm Page 3 57 Friday, June... because it is arbitrary and therefore independent of t Substituting Eqs (7. 31) and (7. 32) in Equation (7. 29), ∂q ∂c - S o dl + V s S o -dl = 0 ∂t ∂l (7. 33) (Since the solids are conservative substances, the total derivative is equal to zero.) Dividing out Sodl and rearranging, ∂q ∂c - = – V s ∂t ∂l (7. 34) The numerical counterpart of Equation (7. 34), using n as the index for time and m as the index... 4.0 ln 2 ln -hd 1 0.06 b = = = 2.21 Ans q2 7. 2 ln -ln -1 .08 q 1 Uniform sand, diameter = 0 .7 mm: hd 1 0.06 a = - = - = 0.0216 Ans h q 11 4.0 ( q1 ) d2 2  ln -   ln   h d 1  q 1 ( 1.60 )  ln -   ln -   0.06  1.60 h d2 4.0 ln -ln -hd 1 0.06 b = = = 2.18 Ans q2 11 ln -ln -1 .60 q 1 Similar... than p5 have been removed Example 7. 1 If the effective size and uniformity coefficient of a proposed filter −2 is to be 5(10 ) cm and 1.5, respectively, perform a sieve analysis to transform the run -of- bank sand of Figure 7. 9 into a usable sand −2 Solution: From Figure 7. 9, for a size of separation of 5(10 ) cm, the percent −2 −2 p1 is 30 Also, the P60 size is 5(10 )(1.5) = 7. 5(10 ) cm From the figure, the... −0. 075 −0. 07 −0.06 — 600 qi 3 (mg/cm ) 900 hdi 3 (m ) qi 3 (mg/cm ) — — 12.96 0.15 3.84 0.01 0 .72 0.00 0.64 0.00 0. 576 0.015 — — ∑hi = 0. 175 1200 hdi 3 (m ) qi 3 (mg/cm ) — — 19.44 0.35 5 .76 0.0 27 1.08 0.00 0.96 0.00 0.864 0.0 37 — — ∑hi = 0.414 hdi 3 (m ) — — 25.92 0.64 7. 68 0.05 1.44 0.001 1.28 0.001 1.15 0. 07 — — ∑hi = 0 .76 2 The terminal head loss of 3 m is composed of the clean water head loss of. .. direction to that of the velocity vector v ) Therefore, ˆ ∫ °A cv ⋅ n η dA ∂m ˙ ∂c ∂c -dl = Q -dl = V s S o -dl = - l ∂l ∂l (7. 31) Vs is the superficial velocity of flow in the bed Also, over the same differential length dl and cross-sectional area So of bed, ∂ ∫ V q dV ∂q ∂q ∂ ( qdV ) - = = - dV = - S o dl ∂t ∂t ∂t ∂t (7. 32) d V in the second term has been taken out of the parentheses,... 10 ) - 4 µc kg ⋅ m 8.9 ( 10 ) ( 23.5 ) 2 For −∆P = 111. 67 kN/m : V (L) t (sec) t/V 0.5 1.0 1.5 2.0 2.5 3.0 6.8 19.0 34.6 53.4 76 .0 102.0 13.6 19.0 23. 07 26 .7 30.4 34 ( 13.6 + 19.0 + 23. 07 )/3 – ( 26 .7 + 30.4 + 34 )/3 m = -( 0.5 + 1.0 + 1.5 )/3 – ( 2.0 + 2.5 + 3.0 )/3 s 6 s = 7. 87 = 7. 87 ( 10 ) -6 2 L m N – ∆P = 111, 670 -2 m 2 6 2 2m... water head loss of 0 .79 3 m and the head loss due to deposited solids of hs h d = 3 – 0 .79 3 = 2.21 m 900 0.414 1200 0 .76 2 x 2.21 x 2.21 1500 2.26 2100 4.64 160 2448 200 240 y 14 87 x – 1200 2.21 – 0 .76 2 = -1 200 – 900 0 .76 2 – 0.414 x = 2448 min x – 1500 2.21 – 2.26 - = -1 500 – 2100 2.26 – 4.64 x = 14 87 y – 2448 - = 14 87 – 2448 y = 1968 . TX249_frame_C 07. fm Page 329 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero 330 Physical Chemical Treatment of Water and Wastewater FIGURE 7. 4 (a) Sectional drawing of a. m== TX249_frame_C 07. fm Page 333 Friday, June 14, 2002 4:32 PM © 2003 by A. P. Sincero and G. A. Sincero 334 Physical Chemical Treatment of Water and Wastewater FIGURE 7. 8 A rotary leaf. mm and higher with uniformity coefficient ranging from 1.5 and lower. Plot of a sieve analysis of a sample of run -of- bank sand is shown in Figure 7. 9 by the segmented line labeled “stock sand