7 ÅA 44514 / 010 / 016 Fluid and Particulate systems 44514 /016 LIQUID/SOLID SEPARATIONS Filtration, Sedimentation, Centrifuges Ron Zevenhoven ÅA Thermal and Flow Engineering ron.zevenhoven@abo.fi 7.1 Filtration (liquids) RoNz /4
Principle of filtration Feed Cake Medium Filtrate RoNz 3 Filtration theory 1 of 4 Flow through a packing (Re < 0.) : Darcy s Law velocity, u layer thickness, L pressure drop, p dynamic viscosity, cake solids mass/m, w Ruth equation u 1 (1 ) u p K L Specific cake resistance,, with cake porosity : 1 K (1 ) solid solid using dw = (1-) solid dx p ( w R) RoNz 4
Filtration theory of 4 Solids fraction S s (kg/kg) Solids fraction S c (kg/kg) Volume V (m 3 ) Cake Mass balance Medium w V f (, S V f ( s Unit w: kg/m, S c w (1 S S ), S s c, S c ) 1- S Ss s c ) Ss 1 S where 1- S Sc c s Note : U and V per m² surface, A! Throughput Q (m³/s) = u A RoNz 5 Filtration theory 3 of 4 Constant pressure drop filtration u t / V R /(-p) dv dt f V ( p) R V ( p) t tan = ƒ/ (-p) V RoNz 6
Filtration theory 4 of 4 Constant velocity (or: flow) filtration dv u constant p dt -p R u f u t u R tan = ƒ u t RoNz 7 Horizontal belt filter RoNz 8
Principle of operation of a rotary drum filter ~ Constant pressure filtration N rotation /min (rpm), drum radius R (m), length L (m), submerged angle (0... ) : volume element A = R L is submerged for a time t = / ( N) (min) RoNz 9 Cake discharge methods for rotary drum filters RoNz 10
Cake resistance,, and compressible cakes 1 Equate Kozeny-Carman equation for flow through granular layer and Darcy s Law: u 3 ( p) 5(1 ) Sv L p K L and definition of cake resistance, 5(1 ) 3 solid S πd π d 6 v 6 with specific surface Sv, for spheres Sv d RoNz 11 Cake resistance,, and compressible cakes Specific cake resistance for compressible cake, for pressure p: or p 1p 0 1 Compressing from height L 0, voidage 0 L 1, 1, with mass balance over filter cake solids w ( kg / m L0 (1 0) L1 (1 1) p u L (1 ) solid ) RoNz 1
Filter press: principle and process cycle steps RoNz 13 Belt press filter RoNz 14
Larox pressure filter (nowadays part of Outotec) RoNz 15 7. Sedimentation RoNz 16
Sedimentation Particles are separated by gravity The stationary fall velocity or terminal settling velocity w T of a particle occur when equilibrium is reached between the gravity, pulling the particle downwards, and the drag force plus the net lift, pulling the particle upwards. RoNz 17 Stationary fall velocity w T For a particle, with the density ρ p, volume V p, and projection area A prj, falling alone in a, with the density ρ and viscosity η, pertains Vp g ( p ) wt C A The drag coefficient C D is a function of Re. If the particle is a sphere and the velocity is low (Re<0.), the Stokes Law giving C D = 4/Re be used for expressing the drag force, and the fall velocity can be calculated by w T d p g ( p 18 D ) p prj g 10.1 RoNz 18/4
Restrained sedimentation When the amount of particles is so high that they affect each others fall velocities, the fall velocity can be calculated in the laminar area as if the sedimentation was not restrained, if the density ρ and viscosity η are changed to the suspension density ρ S and suspension viscosity η S. The viscosity η S of the suspension V S can be estimated by for example: VS (if the particles are spherical, with V/V s = 1/(1-ε) ) More common: S ( 1 1. 5 ) 1 V = volume total V s = volume dispersed matter V 3 VS 10. RoNz 19 Batch settling test for fine suspensions These interfaces move towards each other RoNz 0
Settling curve Kynch representation u i = sedimentation velocity of particles at concentration C i : u i = (H 1 -H i )/t i (tangent to the curve) and C i = C 0 H 0 /H i RoNz 1 From batch settling test to mass flux curve u = dh/dt h vs. t c vs. u vs. c Time, t (s) Settling speed, u (m/s) Solid conc., c (kg/m 3 ) Mass flux (kg/m²s) = u c RoNz
Concentration profile in a clarifier (steady-state) Clear zone Feed zone Thickening zone Feed Effluent Dry solids concentration Sludge discharge RoNz 3 Continuous thickener/clarifier /1 Coe - Clevenger 1. Batch flux : = uc = batch. + Downward velocity, v, due to discharge Mass balance u u c u = u c u u = u c/c u In the settling zone: c s =c u constant, u s = u u cont. = (u u + v) c u cont. = (u + v)c Eliminate unknown v, and u u << u cont. = u. ( 1/c - 1/c u ) v= Ψ cont / c u u u and u u = u c/c u << u, u u u -u Cross-sectional area, A (m²), needed for total discharge mass flow M (kg/s) equals A = M / cont. RoNz 4
Continuous thickener/clarifier / Mass balance: V feed c feed = A ( batch + vc) = V discharge c discharge (V = volume flow, m³/s, c = concentration, kg/m³) Mass flux: V feed c feed / A = batch + vc = v c discharge = The resultant mass flux vs. concentration curve has a maximum and a minimum for! Yoshioka: Operate the settling zone of the clarifier at the concentration where min occurs, (minimising that much water is taken out too) i.e. find the maximum throughput where there is still a minimum in the total mass flux curve. RoNz 5 Solid flux curve for continuous thickener vs. c min Batch curve Total flux curve Convection due to discharge Tangent according to Yoshioka c optimmum Solid conc., c (kg/m 3 ) RoNz 6
Yoshioka construction vs. c min Batch curve min / u Tangent according to Yoshioka c optimum Solid conc., c (kg/m 3 ) RoNz 7 Continuously operating circular thickener RoNz 8/4
Layout of a clarifier RoNz 9 7.3 Centrifuges RoNz 30
Centrifuges Purpose : mainly solid / liquid and liquid/liquid separations: suspensions & emulsions (viscosity of liquid >> viscosity of gas!) Types : 1. Centrifugal,. Sedimentational, 3. Liquid/liquid + s and - s +: small size, - : costs when compared to filters Horizontally mounted basket centrifuge with automatic solids discharge (A: feed, D: scraper, K : outlet ) RoNz 31 A bowl / disc centrifuge lefthand side of drawing: design for liquid separations, denser liquid is taken off via F and I, lighter liquid via G right hand side of drawing: design for liquid/solid separations, liquid is taken off via K, solids are retained in space between walls and end of discs RoNz 3
Particle in a centrifuge r 1 r ( Drag force and centrifugal force in equilibrium: dr 3d p m r dt with reduced mass m mass - volume surroundin g density) integratio n over time t gives : r r 1 m exp 3d p t RoNz 33 The concept of Amblers value For e.g. a settling tank with efficiency,, particle settling velocity,v, and area, A, the throughput, Q, can be given as Q = va/. Similarly, for a centrifuge the throughout can be given as Q = v/. Amblers (unit: m²) allows for comparison of centrifuges with other separation devices. RoNz 34
A solid bowl centrifuge L r r 1 Feed Time to travel from r r to r r For 50% cut - off, dr Force balance : dt Q 18 From this Amblers Σ value follows via d r 50 18 r ln r1 r Q wt 18 r ln d r Time available : throughput Q V/t with bowl volume V particles are removed outside radius r Vd In a gravity field these particles have settling velocity 50 : t 50 r 1 r d g 50 wt 18 V r g ln r1 r RoNz 35 7.4 Hydrocyclones RoNz 36
Hydrocyclones Very often the particles are dispersed in water hence hydrocyclones (also for oil droplets in water). Tangential feed inlet; coarse particles out via bottom outlet; water (liquid) and fine particles out via top outlet. Bottom outlet diameter small compared to gas cyclones. Typical operational conditions (R = volume flow ratio): Standard hydrocyclone and its efficiency d pc = 50% cut size See for more detail section 8. (Gas cyclones) and C06 (source picture) RoNz 37 7.5 Exercises 13 RoNz 38
Exercises 13 13.1 A slurry is being filtered on a rotary vacuum drum filter. What is the effect on the throughput, Q (m³/s) of the filter when : a. The vacuum is changed from 0.3 bar to 0.6 bar under-pressure b. The submerged area of the filter is doubled c. The time needed for a full rotation of the drum is doubled d. The concentration of solids in the incoming slurry is doubled. The cake that is formed may be considered incompressible, the resistance of the filter medium may be neglected. S s = 0.005 kg/kg, S c = 0.60 kg/kg. Filtation time = submerged time Δt = Δφ /( π N) Assume constant pressure filtration RoNz 39 Exercises 13 13. A continuous, circular-shape clarifier must be designed for a suspension of silicate particles (particle density ρ s = 700 kg/m³). Sedimentation tests were carried out in a 350 mm cylinder, during which the height of the interfaces could be registered. Depending on the initial volume fraction, φ s (v/v), of the solids in the initial slurry, the following results were obtained, giving the height of clear liquid, in mm, as given in the table on the next page. The throughput of the clarifier should be 100 tonnes/day solids. Calculate the cross-sectional area, A(m²), of the clarifier, using a. The Coe-Clevenger approach, b. The Yoshioka construction. RoNz 40
Exercises 13 time (min) φ s = 0.0 φ s = 0.04 φ s = 0.06 φ s = 0.1 φ s = 0.18 5 186 90 50 0 1 7 45 130 70 8 17 10 36 180 98 40 Data question 13. 15 330 44 150 60 3 0 331 306 00 80 4 5 33 310 50 100 54 30 33 31 7 10 64 35 33 313 8 140 74 40 314 88 160 84 50 314 94 00 104 60 314 94 30 15 70 94 4 146 80 50 167 90 50 179 100 50 180 110 180 10 180 RoNz 41 Further reading Scarlett, B., Vervoorn, P.M.M. Particle technology I, course notes Delft Univ. of Technol., Delft (1988) Iinoya, K., Gotoh, K., Higashitani, K. (1991) Powder technology handbook, Marcel Dekker, New York Ives, K.J. (Ed.) The scientific basis of filtration Nato Advanced Study Institute Series, Series E: Applied Sciences No., Noordhoff, Leyden (1975) Baumann, E.R. Considerations on the design of a clarifier (in Dutch) PT/Procestechniek 41, 7, (1986) 9-3 Coulson, J.M., Richardson, J.F., Backhurst, J.R., Harker, J.H. Chemical Engineering, Vol. : Unit Operations Pergamon Press, Oxford (1983) Fitch, B. Sedimentation of flocculent suspensions: state of the art AIChE J. 5(6) (1979) 913-930 C06: Crowe, C.T., ed., Multiphase Flow Handbook. CRC Press, Taylor & Francis Group (006) Chapter 7 RoNz 4