Water Treatment Part 3 Sedimentation - Memphis

CIVL 1112Water Treatment - SedimentationTreatment ProcessesSedimentationSedimentation is the downwards movement of an objectrelative to its surrounding medium, due to the force of ir flotation (DAF) is a method whereby bubbles areproduced by the reduction of pressure in a water streamsaturated with air.SedimentationThe purpose of sedimentation is to remove preexisting solids,as well as the precipitates formed in coagulation andflocculation.SedimentationThe purpose of sedimentation is to remove preexisting solids,as well as the precipitates formed in coagulation andflocculation.SedimentationModel of a circular settlement tank with sludge scrapers wasused to estimate the distribution of particulate concentrationover time1/7

CIVL 1112Water Treatment - onSedimentationClick HERE for animations about sedimentation Sedimentation is the accumulation through gravity ofparticulate matter at the bottom of a waterandWildlife.htm This natural process is frequently used to separatecontaminants from air, water, and wastewater. There are four types of settling: discrete flocculant hindered compressionSedimentation Discrete - Individual particles settle independently, neitheragglomerating nor interfering with the settling of the otherparticles present. This occurs in water with a lowconcentration of particles. Flocculant - Particle concentrations are high enough thatagglomeration occurs. This reduces the number ofparticles and increases average particle mass. Theheavier particles sink faster.Sedimentation Hindered - Particle concentration is sufficient thatparticles interfere with the settling of other particles. Compression - In the lower reaches of clarifiers whereparticle concentrations are highest, particles can settleonly by compressing the mass of particles below.2/7

CIVL 1112Water Treatment - SedimentationSedimentation3/7SedimentationIf the Vp Vh then settling can occurwVpQVhVhPath of smallestconsistently settledparticlezQQQVpsludge layersludge layerLLSedimentationSedimentationIf the Vp Vh then “short-circuiting can occurThe horizontal velocity, Vh, of a particle can be approximatedby considering the flowrate, Q, and the cross-sectional flowarea of the tank.VhQVpQ Vh AQVh sludge layerLSedimentationQwzLwzt QVh LQwzQASedimentationThe residence time of water in the sedimentation tank can beapproximated as:Vh Vh tEstimate of the residence time of water in a smallsedimentation tank where Q 1 liter/min, L 6 in.,w 6 in., and z 10 in. (dimensions of a tank in the lab).t t Lwz 6in.(6in.)10in. Q1,000 mlmin360in.3 min 16.39ml 5.9 min1000ml in.3

CIVL 1112Water Treatment - SedimentationSedimentation Discrete settling, can be analyzed by calculating the settlingvelocity of the individual particles contained within the water.4/7SedimentationThe forces acting on a settling particle are:FbFd The forces acting on a particle are: gravity in the downward direction, drag acting in the upward direction as the particle settles upward buoyancy due the water displaces by the particleFg is the force due to gravityFd is the drag forceFb is the buoyant forceFgFg Fd FbSedimentationThe gravitational force can be expressed as:Fg mp gSedimentationThe drag on the particle can be calculated by the dragequation from fluid mechanicsFd Using the density and volume of the particle yields:Fg pVp gwhere: p is the density of the particle, lb-mass/ft.3,Vp is the volume of the particle, ft.3, andwhere1Cd A w v 22Cd is the drag coefficient, dimensionless,A is the particle cross-sectional area, ft.2, w is the density of water, lb-mass/ft.3,v is the velocity, ft./sec.g is the gravitational constant, ft./s2SedimentationThe buoyant force acting on the particle is:Fb mw gSedimentationBy balancing the forces acting on a settling particle and usingthe relationships for Fg the force due to gravity, Fd the dragforce, and Fb the buoyant force, the following relationshipcan be developed:Substituting the particle volume and density of water, yields:Fb wVp gwhere: w is the density of water, lb-mass/ft3,12 pVp g Cd A w v 2 wVp g

CIVL 1112Water Treatment - SedimentationSedimentationSolving for the settling velocity, v, results in:v 2( p w )Vp gCd A wSedimentationAt low Reynolds numbers (for NRe, 1) Cd, can beapproximated by:24Cd NReFor Reynolds Numbers is transition flow, 1 NRe 10,000,the drag coefficient for spheres is:If the particle is assumed to round and the formulas for areaand volume of a sphere are used:v 4( p w )d p gwhere dp is thediameter of theparticle3Cd wSedimentationThe Reynolds Number is:NRe vd where u is the absolute viscosity of the water, lb-forcesec./ft.2 (at 500F, μ 2.73(10-5) lb.-sec./ft.2).For NRe, 1 the particle settling velocity can be estimated asa function of the properties of the particle and water, and theparticle diameter, orvp ( p w )d 2 g18 SedimentationThe overflow rate is calculated in the following way:OFR where:5/7QAOFR is the overflow rate, gal./ft.2-day,Q is the flowrate, gal./day, andA is the clarifier area, ft.2.Cd 243 0.34NReNReFor turbulent flow, NRe 10,000, the relationship for the dragcoefficient for spheres is:Cd 0.4SedimentationThis relationship is known as Stokes' law, and the velocity isknown as the Stokes velocity.vp ( p w )d 2 g18 The vertical velocity of water in a settling basin is oftendescribed as the overflow rate (OFR).It is usually expressed as gal./ft.2-day (m3/m2-day).Sedimentation Example 1 Estimate the settling velocity of sand ( p 2,650kg/m3) with a mean particle diameter of 0.21 mm. Assume the sand is approximately spherical. Using a safety factor of 1.4 to account for inlet andoutlet losses, estimate the area required for a chamberto remove the sand if the flowrate is 0.10 m3/sec(1,000 liters 1 m3).

CIVL 1112Water Treatment - SedimentationSedimentation Example 1The density of water at 200C is 998 kg/m3 and the viscosity ofwater at 200C is 1.01(10-3) N-s/m2 (Newton kg-m/s2). TheStokes settling velocity is:( p w )d g2v p v s OFR 18 2 kgkg m 4 2650 3 998 3 2.1 10 m 9.81 2 mm s kg 18 1.01 10 3ms 6/7Sedimentation Example 1Knowing the overflow rate, the area required is:30.10 mQs (1.4) 3.6m 2A (SF ) mOFR0.039swhere SF is the safety factor, 1.4 0.039 m/s 3.9 cm/sSedimentation Example 2Sedimentation Example 2Group ProblemGroup Problem Estimate the settling velocity of the floc particles we haveseen in lab - especially the jar test results. What are “good” estimates of the particle density anddiameter? Use Stokes' law to estimate the settling velocity. Let’s assume the following values: What are “good” estimates of the particle density anddiameter? Particle density 1,100 kg/m3 Particle diameter 10-4 m How does your estimate compare to what you have seen inthe lab?Sedimentation Example 2Sedimentation Example 2Group ProblemGroup Problemv p v s OFR ( p w )d 2 gOFR 5.5 x 10-4 m/s 0.055 cm/s18 2 kgkg m 4 1,100 3 998 3 1 10 m 9.81 2 mm s kg 18 1.01 10 3 ms 2 30.48 cm 1 gal 0.055cm cm 86, 400 s OFR cm 2 day 3785.41 cm 3 s1 ft OFR 1,166.3 gpd2ft 2For ferric chloride typical OFRs are in the 700 - 1,000 gpd/ft.2 5.5 x 10-4 m/s 0.055 cm/s

CIVL 1112Water Treatment - SedimentationSedimentation Example 3Group Problem If the settling velocity of the floc particles is 0.055 cm/s,determine the area of the sedimentation tank. Assume a factor of safety of 1.37/7Sedimentation Example 3Knowing the overflow rate and the minimum flowrate,the area required is:A 31cm750 mlQmlmin(SF ) (1.3)OFR0.055 cm 60 ssmin 295.5 cm 22 Assume the system flowrate can varying from 750 ml/minto 1,250 ml/min 1in. A 295.5 cm 2 2.54 cm 45.8 in.2In lab, each tank is 6 in. by 6 in. or 36 in.2. How does your estimate compare to what you have seen inthe lab?Sedimentation Example 3Knowing the overflow rate and the maximum flowrate,the area required is:3A 1cm1,250 mlQm l 492.4 cm 2min(SF ) (1.3)cmOFR60 s0.055smin2 1in. A 492.4 cm 2 2.54 cm 76.3 in.2In lab, each tank is 6 in. by 6 in. or 36 in.2.Therefore, for this estimate of particle velocity we need 2.1 tanksor 3 sedimentation tanksTreatment ProcessesAny Questions?Therefore, for this estimate of particle velocity we need 1.27 tanksor 2 sedimentation tanksSedimentation Example 3Group Questions What if the settling velocity of the floc particles is greaterthan the computed 0.055 cm/s? What if the settling velocity of the floc particles is less thanthe computed 0.055 cm/s? How do these estimates compare to what you have seen inthe lab?

CIVL 1112 Water Treatment - Sedimentation 6/7. Sedimentation Example 3 If the settling velocity of the floc particles is 0.055 cm/s, determine the area of the sedimentation tank. Assume a factor of safety of 1