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CHAPTER SEDIMENTATION AND FLOTATION Ross Gregory WRc Swindon Frankland Road, Blagrove Swindon, Wiltshire England Thomas F Zabel WRc Medmenham Medmenham, Oxfordshire England James K Edzwald Professor, Department of Civil and Environmental Engineering University of Massachusetts Amherst, Massachusetts U.S.A Sedimentation and flotation are solid-liquid separation processes used in water treatment mostly to lower the solids concentration, or load, on granular filters As a result, filters can be operated more easily and cost effectively to produce acceptablequality filtered water Many sedimentation and flotation processes and variants of them exist, and each has advantages and disadvantages The most appropriate process for a particular application will depend on the water to be treated as well as local circumstances and requirements HISTORY OF SEDIMENTATION Early History Sedimentation for the improvement of water quality has been practiced, if unwittingly, since the day humans collected and stored water in jars and other containers 7.1 7.2 CHAPTER SEVEN Water stored undisturbed and then poured or ladled out with little agitation will improve in quality, and this technique is used to this day As societies developed, reservoirs and storage tanks were constructed Although constructed for strategic purposes, reservoirs and storage tanks did improve water quality Various examples are known that predate the Christian era Ancient surface water impounding tanks of Aden were possibly constructed as early as 600 B.C and rainwater cisterns of ancient Carthage about 150 B.C (Ellms, 1928).The castellae and piscinae of the Roman aqueduct system performed the function of settling tanks, even though they were not originally intended for that purpose Modern Sedimentation The art of sedimentation progressed little until the industrial age and its increased need for water Storage reservoirs developed into settling reservoirs Perhaps the largest reservoirs constructed for this purpose were in the United States at Cincinnati, Ohio, where two excavated reservoirs held approximately 1480 ML (392 million gallons) and were designed to be operated by a fill-and-draw method, though they never were used in this way (Ellms, 1928) The development of settling basins led to the construction of rectangular masonry settling tanks that assured more even flow distribution and easier sludge removal With the introduction of coagulation and its production of voluminous sludge, mechanical sludge removal was introduced Attempts to make rectangular tanks more cost-effective led to the construction of multilayer tanks Very large diameter [60-m (200-ft)] circular tanks also were constructed at an early stage in the development of modern water treatment Other industries, such as wastewater treatment, mineral processing, sugar refining, and water softening, required forms of sedimentation with specific characteristics, and various designs of settling tanks particular to certain industries were developed Subsequently, wider application of successful industrial designs were sought From this, circular radial-flow tanks emerged, as well as a variety of proprietary designs of solids-contact units with mechanical equipment for premixing and recirculation The inclined plate settler also has industrial origins (Barham, Matherne, and Keller, 1956) (Figure 7.1), although the theory of inclined settling dates back to experiments using blood in the 1920s and 1930s (Nakamura and Kuroda, 1937; Kinosita, 1949) Closely spaced inclined plate systems for water treatment have their origins in Sweden in the 1950s, resulting from a search for high-rate treatment processes compact enough to be economically housed against winter weather Inclined FIGURE 7.1 Early patent for inclined settling (Source: Barham et al., 1956.) SEDIMENTATION AND FLOTATION 7.3 FIGURE 7.2 The pyramidal Candy floc-blanket tank (Source: by PWT.) tube systems were spawned in the United States in the 1960s The most recent developments have involved combining inclined settling with ballasting of floc to reduce plant footprint further (de Dianous, Pujol, and Druoton, 1990) Floc-Blanket Sedimentation and Other Innovations The floc-blanket process for water treatment emerged from India about 1932 as the pyramidal Candy sedimentation tank (Figure 7.2) A tank of similar shape was used by Imhoff in 1906 for wastewater treatment (Kalbskopf, 1970) The Spaulding Precipitator soon followed in 1935 (Figure 7.3) (Hartung, 1951) Other designs that were mainly solids contact clarifiers rather than true floc-blanket tanks were also introduced The Candy tank can be expensive to construct because of its large sloping sides, so less costly structures for accommodating floc blankets were conceived The aim was to decrease the hopper component of tanks as much as possible, yet to provide good flow distribution to produce a stable floc blanket Development from 1945 progressed from tanks with multiple hoppers or troughs to the present flat-bottom tanks Efficient flow distribution in flat-bottom tanks is achieved with either candelabra or lateral inlet distribution systems (Figures 7.4 and 7.5) An innovation in the 1970s was the inclusion of widely spaced inclined plates in the floc-blanket region (Figure 7.5) Other developments that also have led to increased surface loadings include the use of polyelectrolytes, ballasting of floc with disposable or recycled solids, and improvements in blanket-level control The principal centers for these developments have been in the United Kingdom, France, and Hungary SEDIMENTATION THEORY The particle-fluid separation processes of interest to water engineers and scientists are difficult to describe by a theoretical analysis, mainly because the particles 7.4 CHAPTER SEVEN FIGURE 7.3 The Spaulding Precipitator solids contact clarifier (Source: Hartung, 1951.) involved are not regular in shape, density, or size Consideration of the theory of ideal systems is, however, a useful guide to interpreting observed behavior in more complex cases The various regimes in settling of particles are commonly referred to as Types to The general term settling is used to describe all types of particles falling through FIGURE 7.4 The flat-bottom clarifier with candelabra flow distribution (Source: by PWT.) SEDIMENTATION AND FLOTATION 7.5 FIGURE 7.5 The Superpulsator flat-bottom clarifier with lateral-flow distribution (Source: Courtesy of Infilco Degremont, Inc., Richmond, VA.) a liquid under the force of gravity and settling phenomena in which the particles or aggregates are suspended by hydrodynamic forces only When particles or aggregates rest on one another, the term subsidence applies The following definitions of the settling regimes are commonly used in the United States and are compatible with a comprehensive analysis of hindered settling and flux theory: Type Settling of discrete particles in low concentration, with flocculation and other interparticle effects being negligible Type Settling of particles in low concentration but with coalescence or flocculation As coalescence occurs, particle masses increase and particles settle more rapidly Type Hindered, or zone, settling in which particle concentration causes interparticle effects, which might include flocculation, to the extent that the rate of settling is a function of solids concentration Zones of different concentrations may develop from segregation of particles with different settling velocities Two regimes exist—a and b—with the concentration being less and greater than that at maximum flux, respectively In the latter case, the concentration has reached the point that most particles make regular physical contact with adjacent particles and effectively form a loose structure As the height of this zone develops, this structure tends to form layers of different concentration, with the lower layers establishing permanent physical contact, until a state of compression is reached in the bottom layer Type Compression settling or subsidence develops under the layers of zone settling The rate of compression is dependent on time and the force caused by the weight of solids above 7.6 CHAPTER SEVEN Settling of Discrete Particles (Type 1) Terminal Settling Velocity When the concentration of particles is small, each particle settles discretely, as if it were alone, unhindered by the presence of other particles Starting from rest, the velocity of a single particle settling under gravity in a liquid will increase, where the density of the particle is greater than the density of the liquid Acceleration continues until the resistance to flow through the liquid, or drag, equals the effective weight of the particle Thereafter, the settling velocity remains essentially constant This velocity is called the terminal settling velocity, vt The terminal settling velocity depends on various factors relating to the particle and the liquid For most theoretical and practical computations of settling velocities, the shape of particles is assumed to be spherical The size of particles that are not spherical can be expressed in terms of a sphere of equivalent volume The general equation for the terminal settling velocity of a single particle is derived by equating the forces upon the particle These forces are the drag fd, buoyancy fb, and an external source such as gravity fg Hence, fd = fg − fb (7.1) The drag force on a particle traveling in a resistant fluid is (Prandtl and Tietjens, 1957): CDv2ρA fd = ᎏ (7.2) where CD = drag coefficient v = settling velocity ρ = mass density of liquid A = projected area of particle in direction of flow Any consistent, dimensionally homogeneous units may be used in Eq 7.2 and all subsequent rational equations At constant (i.e., terminal settling velocity) vt fg − fb = Vg(ρp − ρ) (7.3) where V is the effective volume of the particle, g is the gravitational constant of acceleration, and ρp is the density of the particle When Eqs 7.2 and 7.3 are substituted in Eq 7.1 CDv2t ρA ᎏ = Vg(ρp − ρ) (7.4a) 2g(ρp − ρ)V vt = ᎏᎏ CDρA ΅ (7.4b) ΅ (7.5) rearranging: ΄ 1/2 When the particle is solid and spherical, 4g(ρp − ρ)d vt = ᎏᎏ 3CDρ ΄ where d is the diameter of the sphere 1/2 SEDIMENTATION AND FLOTATION 7.7 FIGURE 7.6 Variation of drag coefficient, CD, with Reynolds number, Re, for single-particle sedimentation The value of vt is the difference in velocity between the particle and the liquid and is essentially independent of horizontal or vertical movement of the liquid, although in real situations there are secondary forces caused by velocity gradients, and so on Therefore, the relationship also applies to a dense stationary particle with liquid flowing upward past it or a buoyant particle with liquid flowing downward Calculation of vt for a given system is difficult because the drag coefficient, CD, depends on the nature of the flow around the particle This relationship can be described using the Reynolds number, Re (based on particle diameter), as illustrated schematically in Figure 7.6, where ρvd Re = ᎏ µ (7.6) and µ is the absolute (dynamic) liquid viscosity, and v is the velocity of the particle relative to the liquid The value of CD decreases as the value of Re increases, but at a rate depending on the value of Re, such that for spheres only: Region (a): 10−4 < Re < 0.2 In this region of small Re value, the laminar flow region, the equation of the relationship approximates to CD = 24/Re (7.7) This, substituted in Eq 7.1, gives Stokes’ equation for laminar flow conditions: g(ρp − ρ)d2 vt = ᎏᎏ 18µ (7.8) Region (b): 0.2 < Re < 500 to 1000 This transition zone is the most difficult to represent, and various proposals have been made Perhaps the most recognized 7.8 CHAPTER SEVEN representation of this zone for spheres is that promoted by Fair, Geyer, and Okun (1971): 24 CD = ᎏ + ᎏ + 0.34 Re Re1/2 (7.9) For many particles found in natural waters, the density and diameter yield Re values within this region Region (c): 500 to 1000 < Re < × 105 In this region of turbulent flow, the value of CD is almost constant at 0.44 Substitution in Eq 7.5 results in Newton’s equation: (ρp − ρ)gd vt = 1.74 ᎏᎏ ρ ΄ ΅ 1/2 (7.10) Region (d): Re > × 105 The drag force decreases considerably with the development of turbulent flow at the surface of the particle called boundary-layer turbulence, such that the value of CD becomes equal to 0.10 This region is unlikely to be encountered in sedimentation in water treatment Effect of Particle Shape Equation 7.4b shows how particle shape affects velocity The effect of a nonspherical shape is to increase the value of CD at a given value of Re As a result, the settling velocity of a nonspherical particle is less than that of a sphere having the same volume and density Sometimes, a simple shape factor, Θ, is determined, for example, in Eq 7.7: 24Θ CD = ᎏ Re (7.11) Typical values found for Θ for rigid particles are (Degremont, 1991): Sand Coal Gypsum Graphite flakes 2.0 2.25 4.0 22 Details on the settling behavior of spheres and nonspherical particles can be found in standard texts (e.g., Coulson and Richardson, 1978) Flocculation A shape factor value is difficult to determine for floc particles because their size and shape are interlinked with the mechanics of their formation and disruption in any set of flow conditions When particles flocculate, a loose and irregular structure is formed, which is likely to have a relatively large value shape factor Additionally, while the effective particle size increases in flocculation, the effective particle density decreases in accordance with a fractal dimension (Lagvankar and Gemmel, 1968; Tambo and Watanabe, 1979) (see Chapter 6) Flocculation is a process of aggregation and attrition Aggregation can occur by Brownian diffusion, differential settling, and velocity gradients caused by fluid shear, namely flocculation Attrition is caused mainly by excessive velocity gradients (see Chapter 6) The theory of flocculation detailed in Chapter recognizes the role of velocity gradient (G) and time (t) as well as particle volumetric concentration Φ For dilute SEDIMENTATION AND FLOTATION 7.9 suspensions, optimum flocculation conditions are generally considered only in terms of G and t: Gt = constant (7.12) Camp (1955) identified optimum Gt values between 104 and 105 for flocculation prior to horizontal flow settlers In the case of floc-blanket clarifiers (there being no prior flocculators), the value of G is usually less than in flocculators, and the value of Gt is about 20,000 (Gregory, 1979) This tends to be less than that usually considered necessary for flocculation prior to inclined settling or dissolved air flotation In concentrated suspensions, such as with hindered settling, the greater particle concentration (e.g., volumetric concentration, Φ) contributes to flocculation by enhancing the probability of particle collisions, and increasing the velocity gradient that can be expressed in terms of the head loss across the suspension Consequently, optimum flocculation conditions for concentrated suspensions may be better represented by Fair, Geyer, and Okun (1971); Ives (1968); and Vostrcil (1971): GtΦ = constant (7.13) The value of the constant at maximum flux is likely to be about 4000, when Θ is measured as the fractional volume occupied by floc, with little benefit to be gained from a larger value (Gregory, 1979; Vostrcil, 1971) Measurement of the volumetric concentration of floc particle suspensions is a problem because of variations in particle size, shape, and other factors A simple settlement test is the easiest method of producing a measurement (for concentrations encountered in floc blanket settling) in a standard way (e.g., half-hour settlement in a graduated cylinder) (Gregory, 1979) A graduated cylinder (e.g., 100 mL or L) is filled to the top mark with the suspension to be measured: the half-hour settledsolids volume is the volume occupied by the settled suspension measured after 30 min, and it is expressed as a fraction of the total volume of the whole sample The process of flocculation continues during conditions intended to allow settlement Assuming collision between flocculant particles takes place only between particles settling at different velocities at Stokes’ velocities, then the collision frequencies Νij between particles of size di and dj of concentrations ni and nj is given by Amirtharajah and O’Melia (1990): πg(s − 1) (Nij)d = ᎏᎏ (di − dj)3(di − dj)ninj 72ν (7.14) where s is the specific gravity of particles and ν is the kinematic viscosity Settlement in Tanks In an ideal upflow settling tank, the particles retained are those whose terminal settling velocity exceeds the liquid upflow velocity: Q vt ≥ ᎏ A (7.15) where Q is the inlet flow rate to the tank, and A is the cross-sectional area of the tank In a horizontal-flow rectangular tank, the settling of a particle has both vertical and horizontal components, as shown in Figure 7.7: tQ L=ᎏ HW (7.16) 7.10 CHAPTER SEVEN FIGURE 7.7 Horizontal and vertical components of settling velocity (Source: Fair, Geyer, and Okun, 1971.) where L = horizontal distance traveled t = time of travel H = depth of water W = width of tank and for the vertical distance traveled, h: h = vt (7.17a) Hence, the settling time for a particle that has entered the tank at a given level, h, is h t=ᎏ v (7.17b) Substitution of this in Eq 7.16 gives the length of tank required for settlement to occur under ideal flow conditions: hQ L=ᎏ vHW (7.18a) hQ v=ᎏ HLW (7.18b) or If all particles with a settling velocity of v are allowed to settle, then h equals H, and, consequently, this special case then defines the surface-loading or overflow rate of the ideal tank, v*: Q v* = ᎏ L*W (7.19a) Q v* = ᎏ A* (7.19b) 7.73 SEDIMENTATION AND FLOTATION TABLE 7.4 Comparison of Qualities Achieved with Flotation,* Sedimentation,† and Filtration (Colored Low-Alkalinity Water) Following Iron Coagulation (Rees, Rodman & Zabel 1979a, Zabel & Melbourne 1980) Type of Water Source Flotation-treated‡ Flotation-filtered Sedimentationtreated Sedimentationfiltered Turbidity (NTU) Dose Color (mgFe/L) (PtCo) 3.2 0.72 0.19 0.50 — 8.5 — 6.0§ 45 0 0.29 — pH 6.2 4.8 9.0 5.05 10.5 Iron Manganese (mg/L) (mg/L) Aluminum (mg/L) 0.70 0.58 0.01 0.36 0.11 0.16