SEDIMENTATION Aim - rapid removal of solid material by gravitational settling Drawbacks – colloidal material is slow settling Mustafa Nasser 2012

ADDITION OF CHEMICALS BEFORE SEDIMENTATION TO AGGREGATE COLLOIDAL PARTICLES TO PRECIPITATE DISSOLVED IMPUTITIES Mustafa Nasser 2012

Water and Wastewater Treatment Settling of discrete particles Settling of flocculating particles Mustafa Nasser 2012

Water and Wastewater Treatment Need to consider Dilute suspensions – potable water Concentrated suspensions - wastewater Mustafa Nasser 2012

DILUTE SUSPENSIONS The concentration of particles is not high enough for the settling of individual particles to influence each other The settling velocity is the same as for a single paritcle Mustafa Nasser 2012

CONCENTRATED SUSPENSIONS Interference in the flow patterns about particles The downwards flux of particles is enough to displace significant amounts of water that moves upwards There is a decrease in the settling velocity compared to a single particle Mustafa Nasser 2012

What is the removal efficiency? How can the amount of solids that will be removed in a settling tank be determined? What is the removal efficiency? What size of tank is required? Mustafa Nasser 2012

Sedimentation Theory Mustafa Nasser 2012

Type – 1: Discrete particle settling Type – 2: Flocculant settling Sedimentation Theory Particle-fluid separation processes are difficult to describe by theoretical analysis, mainly because the particles involved are not regular in shape, density, or size. The various regimes in settling of particles are commonly referred to as: Type – 1: Discrete particle settling Type – 2: Flocculant settling Type – 3: Hindered (zone) settling Type – 4: Compression settling Mustafa Nasser 2012

These particles settle at constant settling velocity. Settling Regimes Type – I – Discrete particle settling Type I settling (discrete of free settling) is the settling of discrete particles in low concentration, with flocculation and other interparticle effects being negligible These particles settle at constant settling velocity. They settle as individual particles and do not flocculate during settling Examples: Settling of sand, grit Applications: Presedimentation for sand removal prior to coagulation Mustafa Nasser 2012

Type – II – Flocculant settling Type Settling Regimes Type – II – Flocculant settling Type Type II settling is the settling of flocculent particles in a dilute suspension. As coalescence occurs, particle masses increase and particles settle more rapidly. Particles flocculate during sedimentation. These types of particles occur in alum or iron coagulation Mustafa Nasser 2012

Type – III – Hindered (zone) settling Settling Regimes Type – III – Hindered (zone) settling Type III settling, settling in which particle concentration causes interparticle effects. Flocculation and rate of settling is a function of particle concentration Particles remain in a fixed position relative to each other, and all settle at a constant velocity Mass of particles settle as a zone Zones of different particle concentrations (different layers) may develop as a result of particles with different settling velocities State of compression is reached at the bottom. Mustafa Nasser 2012

Type – IV – Compression settling Settling Regimes Type – IV – Compression settling Type IV settling, settling of particles that are of such a high concentration that the particles touch each other and settling can occur only by compression of the compacting mass. Compression settling occurs at lower depths of the sedimentation tanks Rate of compression is dependent on time and the force caused by the weight of solids above the compression layer. Both discrete and flocculant particles may settle by zone or compression settling However, flocculent particles are the most common type encountered. Mustafa Nasser 2012

Settling Types Mustafa Nasser 2012

Type – I – Discrete particle settling Sedimentation Theory Type – I – Discrete particle settling Settling of discrete particles in low concentration, with flocculation and other interparticle effects being negligible When particles settle discretely, the particle settling velocity can be calculated and the basins can be designed to remove a specific particle size STOKE’s LAW Particle falling in a fluid accelerates until the frictional resistance, or drag on the particle is equal to the gravitational force of the particle. Isaac NEWTON Settling velocity remains constant Terminal velocity Mustafa Nasser 2012

Type – I – Discrete particle settling Sedimentation Theory Type – I – Discrete particle settling Terminal settling velocity depends on various fluid and particle properties. To calculate the settling velocity Particle shape is assumed to be spherical Particles that are not spherical can be expressed in terms of a sphere of an equal volume. Mustafa Nasser 2012

Acting Forces on Particle B G F All particles immersed in a fluid are subject to a buoyancy force, B A gravitational force G is always acting on the particle due to its mass Whenever relative motion exists between a particle and a surrounding fluid, the fluid will exert a drag upon the particle creating a drag force, F Flow direction In a flowing viscous fluid, the drag force is made up of two components: A pressure drag force, Fp A shear stress drag force, Fs B Flow direction

For creeping flow (flow at very low velocities, v relative to the sphere), the total drag force F on the particle with a diameter D in a fluid of viscosity  is given by Stoke’s law: F = Fs + Fp = 2Dv + Dv = 3Dv

Turbulent Flows Turbulence may arise either from an increased fluid velocity or from artificial roughening of the forward face of the immersed body (or particle)

Reynolds Number, Re To characterize the fluid flows on particle Dimensionless group Definition: : density of the fluid : viscosity of the fluid v : the velocity of the fluid relative to the particle D : the diameter of the particle As Re increases, the pressure drag force becomes proportionately less and, at value greater than about 20, flow separation occurs with the formation of vortices in the wake of the sphere. So, changes of Re in the nature of the flow would effect on the force exerted on the particle.

Drag Force on a Spherical Particle The most satisfactory way of representing the relation between drag force and velocity involves the use of two dimensionless groups: Reynolds number, Re Drag coefficient, CD Stokes Law R’ is the force per unit projected area of particle in a plane perpendicular to the direction of motion

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Value of CD decreases as the value of Re increases Mustafa Nasser 2012

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where φ is the shape factor required to correct for the lack of sphericity. For a perfectly spherical particle φ = 1. Mustafa Nasser 2012

(Data ρw = 998.2 kg m-3, μ = 1.002 x10-3 Pa s). Example: Find the settling velocity of a sphere with a diameter of 0.5 mm and a density of 2650 kg m-3 settling in water at 20 0C. At this temperature the kinematic viscosity is 1.003x10-6 m2/s (Data ρw = 998.2 kg m-3, μ = 1.002 x10-3 Pa s). Note: μ = (kinematic viscosity * density) =1.003 x10-6 *998.8 = 1.002 x10-3 Mustafa Nasser 2012

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Vt = 0.224 m/s not similar with the calculated one using Newton Vp = 0.109 The second iteration is to use Vp = 0.109 and then calculate Re = 0.09 m/s Mustafa Nasser 2012

Vp = 0.09 m/s not similar with the calculated one using Newton Sedimentation Tank Vp = 0.09 m/s not similar with the calculated one using Newton Vp = 0.109 Then third iteration use 0.09 valued to estimate: CD, Re and new Vp Stop solution is reached Mustafa Nasser 2012

It is seldom possible to use the above analysis in the design of settling tanks for both water and wastewater treatment because the size of the particles must be known and the correction factor for sphericity must be determined Mustafa Nasser 2012

Particles whose terminal settling velocity exceeds the liquid Settlement in Tanks Particles whose terminal settling velocity exceeds the liquid up flow velocity will be retained In an horizontal flow rectangular settling tanks, settling particles have both horizontal and rectangular parts. L: Horizontal distance travelled H: Depth of water W: Width of tank t: time of travel Vertical distance travelled Mustafa Nasser 2012

Settling Column Analysis for Type 1 Suspensions The setting velocity of a dilute suspension can be determined indirectly from the analysis of the mass settlement rate in a settling column. Put the suspension in a settling column, ensuring that it is well mixed so that the concentration is uniform throughout. Allow the suspension to settle under quiescent conditions and observe the concentration of settling particles at the bottom of the settling column, as a function of time. Mustafa Nasser 2012

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The design of settling vessels is usually based on the results of settling column tests carried out using the material in question. Mustafa Nasser 2012

Mustafa Nasser 2012 Water Surface Z0 Initial Concentration, C0 Sample Point, Concentration, C(t) Velocity, u(t)  z0 / t Water Surface Initial Concentration, C0 Particle Flux = C(t)u(t) Mustafa Nasser 2012

Bottom of the settling zone Settling Column z0 Water Surface Sampling Point Particle with settling velocity v0 travels distance z0 in time t0 and reaches the bottom of the settling zone. Particle with settling velocity vp travels distance zp in time t0 and does not reach the bottom of the settling zone. Particle with settling velocity vp travels distance zp in time t0 and reaches the bottom of the settling zone. Particle with settling velocity vp travels distance zp in time t0 and passes the bottom of the settling zone. zp All particles dp > d0 are removed in time t0 The fraction of particles of size dp < d0 removed in time t0 is z0 Bottom of settling zone Mustafa Nasser 2012

The fraction removed is also in the ratio of the settling velocities Remembering that The fraction removed is also in the ratio of the settling velocities Mustafa Nasser 2012

x x0 All particles dp > d0 will settle in t0 (i.e. vp > v0) v0 Velocity Mustafa Nasser 2012

All particles dp > d0 will settle in t0 (i.e. vp > v0) The fraction of all particles dp > d0 is Some particles dp < d0 will settle in t0 (i.e. vp < v0) The fraction of particles size dp is The fraction of all particles 0 < dp < d0 is Mustafa Nasser 2012

The total fraction of particles that are removed in t0 is Get all the information from the graph of x as a function of v The integral is evaluated numerically Remember x is the fraction of particles that remains in suspension Mustafa Nasser 2012

The following results were obtained from a 1.8 m settling column. Time :– 0 60 80 100 130 200 240 420 /(min) Concentration:– 300 189 180 168 156 111 78 27 /(mg l1) What is the theoretical removal efficiency in a settling basin with a loading rate of 24.7 m day1?  (This is a volumetric flow of 24.7 m3 day1 per m2 of settling basin area). Mustafa Nasser 2012

At time t = 0 the initial concentration C0 = 300 mg l1. The depth of the settling zone is 1.8 m. Calculate e.g 189/300 = 0.63; 180/300 = 0.60 e.g. 1.8/60 = 0.03; 1.8/80 = 0.0225 Time /(min) 60 80 100 130 200 240 420 xi 0.63 0.60 0.56 0.52 0.37 0.26 0.09 vi, /(m min1)0.03 0.0225 0.018 0.01385 0.009 0.0075 0.004286 Mustafa Nasser 2012

Calculate v0 for a loading rate of 25 m per day This corresponds to a residence time of minutes x0 is found from the graph or by linear interpolation So x(105) = 166/300 = 0.55 Mustafa Nasser 2012

x0 =0.55 x v0 =0.01738 m/min Velocity (m per min) Mustafa Nasser 2012

The mass fraction of solids that remain in suspension is x0 = 0.55 The mass fraction of solids that has settled is (1 - x0) = 0.45 The mass fraction of slow settling particles is Mustafa Nasser 2012

xi vi Δxi Average vi Δxi vi N.B. x0 xi vi Δxi Average vi Δxi vi 0.553 0.01736 0.033 0.01561 0.000515 0.520 0.01385 0.150 0.01142 0.001713 0.370 0.00900 0.110 0.00825 0.0009075 0.260 0.00750 0.170 0.00589 0.001002 0.090 0.00429 0.090 0.00214 0.001926 0.000 0.0000 To four significant figures, the sum of xiv = 0.004331 Mustafa Nasser 2012

The integral is evaluated The total mass fraction removed, X, is X = (1 – x0) + 0.249 =(1 – 0.55) + 0.249 = 0.45 + 0.249 = 0.699 That is the solids removal is 70%. ( two sig. fig.) Mustafa Nasser 2012

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