Micro- and Nanoparticle Technology ied and luidized Beds Dr. K. Wegner - Lecture 10.04.018 10. pril 018
low through a packed bed of particles pplications, e.g. - low of liquid or gas through a filter cake - low of reactants through a bed of catalyst particles - ied bed separators for adsorption of substances - ied bed dryer cross d V D pipe H article volume fractionϕ Micro- and Nanoparticle Technology - S018
Bed structures for monodisperse spheres article volume fraction : Volume of particles ϕ 1 ε Total volume Simple cubic packing ϕ 0 56 porosity, void fraction or voidage ace-centered cubic packing. ϕ 0. 741 Random packing ϕ 0. 6 Micro- and Nanoparticle Technology - S018 3
or fied beds (no particle movement): Def. V! u u0 cross sec tion v rel u : velocity of the approaching flow u 0 : superficial velocity ( Leerrohrgeschwindigkeit ) v rel : relative velocity ttention! The real velocity inside pores is: v local or simplicity, the dimensionless numbers (e.g. Reynolds-#) are formed with the velocity of the approaching flow u. u 0 ε Micro- and Nanoparticle Technology - S018 4
ressure drop across a packed bed cross d V u 0 cross D pipe v H rel Starting point: Laminar flow through a capillary Hagen-oiseuille: p 3 η u Re Now, the capillary is not straight and does not have a circular cross-section. Therefore: p C 1 0 H D u0 H η ε D e h with equivalent length H e C < 1 H Micro- and Nanoparticle Technology - S018 5
D H is the hydraulic diameter of the pore. In general, the hydraulic diameter is defined as: D h 4 flow area 4 fluid volume in tube wetted perimeter wetted surface area Hydraulic diameter for a packed bed: D h 4 V 0 4 ε V 0 with 0 : surface area of pores surface area of particles Using the volume-specific surface area: 4 ε V Dh 1 ε V ( ) V 0 V V Micro- and Nanoparticle Technology - S018 6
Micro- and Nanoparticle Technology - S018 7 ( ) 3 0 1 0 1 1 4 ε ε η ε η V h e bed u H C C D H u C p Thus, ( ) 3 0 3 1 ε ε η V bed u H C p C 3 typically has values of 3.5 5.5 for porosities of 0.3 0.45. or a randomly packed bed of monosized spheres with V 6/d and C 3 5: Carman-Kozeny equation describing laminar flow (Re < 1) through randomly packed particles ( ) 3 0 1 180 ε η ε bed d u H p ( ) bed d u H p ρ ε ε 0 3 1 Re 180 or 1 < Re
Empirical correlation assuming combined laminar and turbulent flow: Ergun equation p H bed ψ with ( 1 ε ) ε 3 u d 0 ρ ( 1 ε ) ψ 150 + 1.75 Re 1 < Re < 4000 for fluids with ρ const. and η const. and in case the bed contains a large number of particles (homogeneity). Note: p p bed p,empty Micro- and Nanoparticle Technology - S018 8
Derive an average specific force for the packed bed by comparing the flow forces (drag force) acting on the bed with its apparent weight (forces are average values over all particles): n in general: n G D B cross p H bed cross p bed ( 1 ε)( ρ ρ ) g H ( 1 ε)( ρ ρ ) g with Ergun-eq.: G D B ψ ε 3 u0 g d ( ρ ρ ) ρ with r p u0 g d p inertial forces gravitational forces n 4 3 ε 3 ψ r 3 4 ( ρ ρ ) ρ Compare single sphere: n α ( Re ) 3 4 p r ( ρ ρ ) ρ or flow opposing the gravitational force: n 1 Micro- and Nanoparticle Technology - S018 9
pplications of acked Beds in Industry Separation processes in manufacturing of chemicals: bsorption, etraction, distillation Distillation columns in an oil refinery acking in distillation column (B/R Instr. Corp.) Eamples of packing material Increase of interface area between liquids and gasses to improve mass transfer and separation efficiency. Micro- and Nanoparticle Technology - S018 10
pplications of acked Beds in Industry Separation processes in off-gas treatment: Scrubbing Clean gas out Scrubbers are used to wash out undesired pollutants from gas streams, esp. acidic gases. Off-gas in In wet scrubbing, pollutants are absorbed in a solution where a packed bed is often used to increase the liquid surface area. Cleaning liquid to recirculation acked Tower Wet Scrubber icture: U.S. Environmental rotection gency In dry scrubbing, pollutants are absorbed on particles (e.g. in a packed bed). Micro- and Nanoparticle Technology - S018 11
pplications of acked Beds in Industry Chemical reactions over a fied bed of catalyst particles Eample: ischer-tropsch Synthesis e.g. nco + (n+1) H C n H n+ + nh O Type B reactor with iron catalyst (00 m 3 ) 00 50 C, 5 bar. Removal of reaction heat by pressurized (boiling) water. ) diabatic and B) multi-tube fied bed reactor with heat removal. Ertl, Knözinger, Weitkamp, Handbook of heterogeneous catalysis Vol 3, Wiley-VCH, 1997 Typical particle diameters: mm (high pressure drop) 10 mm (low specific surface area) Challenge: Heat management, esp. for eothermic reactions Micro- and Nanoparticle Technology - S018 1
luidized Bed Reactors luidizing a bed of catalyst particles can yield to the following advantages over fied bed reactors: Smaller particles can be used, increasing the solid-fluid echange area. Uniform temperature distribution due to intensive solids miing (no hot spots). High heat transfer coefficients between bed and immersed heating or cooling surfaces. Easy handling and transport of particles due to fluid-like behavior. Uniform (solid) product in batch-wise process because of intensive solids miing Micro- and Nanoparticle Technology - S018 13
Eamples of luidized Bed Reactors Gas, out Gas bubbles Cyclone separator Distributor plate Solids recirculation luidization gas, in luidized Bed Circulating luidized Bed Ertl, Knözinger, Weitkamp, Handbook of heterogeneous catalysis Vol 3, Wiley-VCH, 1997 Micro- and Nanoparticle Technology - S018 14
Eamples of luidized Bed Reactors Eample: ischer-tropsch Synthesis with the Synthol reactor, a type of circulating fluidized bed reactor (a) Hopper with e-catalyst particles (b) Standpipe with catalyst (c) Riser (d) Heat echanger tube bundles (e) Reactor Mean porosity in riser: 85% 3 1 m/s gas velocity; 350 C Ertl, Knözinger, Weitkamp, Handbook of heterogeneous catalysis Vol 3, Wiley-VCH, 1997 Micro- and Nanoparticle Technology - S018 15
Synthol Reactor at Sasol Sasol: South frican Synthetic Oil Ltd. (originally) Suid-frikaanse Steenkool en Olie Images: www.sasol.com (right) and UMichigan (top); Micro- and Nanoparticle Technology - S018 16
pplications of luidized Beds Chemical rocesses Reaction (on catalyst particles), combustion (e.g. coal), absorption hysical rocesses Drying, coating, granulation, absorption, miing, heating/cooling Eample: luidized bed coating ( Wurster coater ) article recirculation Coating solution spray Spray nozzle Distributor plate luidization air Micro- and Nanoparticle Technology - S018 17
Disadvantages of luidized Bed Reactors luidized bed reactors generally have the following drawbacks: Epensive solid separation and gas purification because of solids entrained in fluidizing gas. Erosion of internals and attrition of solids resulting from high particle velocities. Backmiing of (product) gas because of high solids miing rate resulting in lower conversion. ossibility of de-fluidization due to agglomeration of solids Undesired reaction gas bypass or broadening of the residence time distribution in case of inhomogeneous bed fluidization. Scale-up can be difficult. Micro- and Nanoparticle Technology - S018 18
States of mobility in fluid-solids systems Vorte formation Gas-solids systems ied bed Bubbles Choking slugging Strands Dispersion increasing fluid velocity Homogeneous flow approaching particles Liquid-solids systems ied bed Dispersion (dense) Dispersion (dilute) Micro- and Nanoparticle Technology - S018 19
owder luidization according to Geldart Geldart (1973) classified powders according to their fluidization properties in air at ambient T and p: Group : Initially non-bubbling fluidization, followed by bubbling fluidization and bed epansion with increasing fluid velocity. Stable bubble size is reached; good miing and homogeneity. Small particle size and/or low density Group B: Only bubbling fluidization; coalescence of bubbles. Some bed epansion; good miing (< Group ) and homogeneity. Most powders Geldart, D. (1973), owder Technol. 7, 85-9. Micro- and Nanoparticle Technology - S018 0
Geldart owder Classification Group C: Very fine cohesive powders, which are incapable of fluidization. Strong interparticle forces. ormation of channels and discrete plugs but no bubbles. luidization problems might be overcome by mechanical action (vibration / stirring) Source:. Rhodes, Introduction to owder Technology ; nd ed. 008, J. Wiley Micro- and Nanoparticle Technology - S018 1
Geldart owder Classification Group D: Large particles. ormation of slowly rising large bubbles that can lead to spouting. Little miing and bed homogeneity. (ρ ρ ) in kg/m 3 spouting bed (right) is a fluid bed in which the air forms a single opening through which some particles flow and fall to the outside. Image: Rhodes (008). Sauter diameter Source: H. Schubert Handbuch der mechanischen Verfahrenstechnik, 003; Wiley-VCH Micro- and Nanoparticle Technology - S018
U mf : minimum fluidization velocity Source:. Rhodes, Introduction to owder Technology ; nd ed. 008, J. Wiley Micro- and Nanoparticle Technology - S018 3
luid flow through particle beds - luidization Eamples: Solid-fluid separation Reactions of solids / utilizing solids Miing of solids and fluids Transport of solids with/through fluids Distinguish according to dynamic state: Stationary packing (fied bed) Moving bed luidized bed Solids transport Micro- and Nanoparticle Technology - S018 4
verage load factor for fied bed, fluidized bed and particle transport ϕ0, L const article transport ϕ ϕl ϕ > 0 ϕ L > ϕ > 0 ied bed luidized bed p H ρ ρ ϕ g ( ) 10 1 luidized bed Epanding fluidized bed minimum fluidization velocity u mf n 10 0 ( 1 ϕ ) ε0 0 10 1 ( 1 ϕ ) ε 0 ε > L L 10 10 1 10 0 10 1 10 v Re rel d ν Micro- and Nanoparticle Technology - S018
orces in different fluidization states Compressive forces (buoyancy) Viscous forces Gravity Inertial forces riction forces betw. particles riction forces particles - wall Impact betw. particles Impact particles - wall Clustering of particles due to shape dheasive / repulsive forces Bulk solids luidized bed Solids transport Higher particle mobility leads to a larger number of forces. Spatiotemporal distribution of particles. Velocity, momentum, mass, concentration, temperature,... Even today, the mathematical description of such systems is hardly possible. Micro- and Nanoparticle Technology - S018 6 () () ()
Similarity of fluid-solids flows general similarity description of fluid-solids flows is not possible. Simplified case: No forces due to friction, impact or adhesion low direction opposing gravity Monodisperse spheres No demiing/segregation urther: 1) Geometric similarity of ) Re 3) r 4) u ( ρ ρ ) u d ν ρ g d const const const systems ied beds, stationary fluidized beds: Circulating fluidized beds, solids transport: u 0! u u vrel u0 c u 0 : superficial velocity; c: particle velocity Micro- and Nanoparticle Technology - S018 7 v rel
ressure drop in upright particle transport cceleration of particle flu along dh. Differential momentum balance, no wall friction: p-dp u 0 c+dc 1) ressure drop keeping particles in flotation (stationary fluidized bed with height H, cross ): dh cross ( p ) H ϕ ( ρ ρ ) g z float cross p c n cross cross H ϕ ( pz ) float ( ρ ρ ) g 1 u 0 Micro- and Nanoparticle Technology - S018 8
) ressure drop due to acceleration of particles (transport) cross ( dp) m dc acc Integrate: cross ( dp) acc m cross H 0 H dc ( p p ) m ( c c ) m c p 0 acc cross 0 z z H z H z 0 Contribution of n acc G D B the particle acceleration cross cross H ϕ ( pz ) acc ( ρ ρ ) g n acc to the load factor n ( dc ) dt g : p p p Total pressure drop: z ( z ) ( z ) acc float Load factor: + p 1 H ϕ z n + acc ( ρ ρ ) g Micro- and Nanoparticle Technology - S018 9 n
Description of mobility states of a flow through particle beds ssume monodisperse spheres and homogeneous approaching flow Load factors: Bulk solids (packed bed): luidized bed: n n ( ϕ, ) 3 r ξ Re ( 4 ρ ρ ) ξ ( ϕ, ) Re 3 r 4 ρ ( ρ ρ ) ρ 1 1 loatation and particle transport: n ξ ( ϕ, ) Re 3 r 4 ( ρ ρ ) ρ 1 loatation and transport of single particles: n ( ) α Re 3 r 4 ( ρ ρ ) ρ 1 Micro- and Nanoparticle Technology - S018 30
Homogeneous fluidized beds - drag coefficients The Ergun equation can not be etended to fluidized beds. Based on eperiments, Lewis, Gilliland and Bauer developed a correlation describing drag in homogeneous fluidized beds: ξ ( ϕ, Re ) α ( Re ) α( Re ) 4. 65 ( 1 ) 4. ϕ 65 ε The correlation can be applied for the range φ 0.6 (beginning fluidization) to φ 0 (floating single particles). Comparison with a single particle settling at steady state (terminal velocity) gives for a stationary fluidized bed: u u 0 sphere, terminal n ε with Re < 1: n 4.65 (typical) Re > 500: n.4 Micro- and Nanoparticle Technology - S018 31
Develop r-ω diagrams for a fluidized bed by substituting α(re ) with ξ(φ,re ). Remember: Definition of r and Ω number for single sphere at steady state Repν f Substitute v rel d n α ( ρ ρ ) 3 g d p p f 3 α p p ν ρ 4 Substitute 3 p f ρf ( Re ) 1 f Ω p 3 v rel g v d f 4 f p Re ( Re ) Re r ( ρ ρ ) α( Re ) p Re ρ f v ν g d p 3 p ν rel f f p ρ p 4 3 ρ f Re p p rchimedes-# depends only on fluid and particle properties! Omega-# or Lijatschenko-# Micro- and Nanoparticle Technology - S018 3
10 6 10 5 10 4 10 3 10 10 1 Ω v rel 3 ρ ν g (ρ - ρ ) 4 3 Re ξ (ϕ, Re ) particle örderung transport n>1 n >1 10 1 10 10 3 n 1 10 4 homogene Wirbelschicht n 1 r-ω diagram for a fluidized bed of monodisperse spheres Ω 10 0 10-1 10-10 -3 10-4 10-5 10-6 10-7 10-8 10 - Re 10 0 Schweben Einzelpartikel ϕ0, n1 Increasing Erhöhung Relativgeschwindigkeit relative velocity Lockerung Schüttung ϕ0.6, n1 Schüttgut bulk solids n <1 n < 1 (fied bed) r g d 3 (ρ - ρ ) ν ρ 3 4 ξ (ϕ, Re ) Re 10-10 -1 10 0 10 1 10 10 3 10 4 10 5 10 6 10 7 10 8 10 9 r Remember: ied beds, stationary fluidized beds: u vrel u 0 u 0 : superficial velocity; c: particle velocity Micro- and Nanoparticle Technology - S018 33
Ω 10 6 10 5 10 4 10 3 10 10 1 10 0 10-1 10-10 -3 10-4 10-5 10-6 Ω v rel 3 ρ ν g (ρ - ρ ) r 10 3 Re 10 1 Re 10 0 n100 ϕ 0 n10 ϕ 0 n1 ϕ 0 ϕ0.1 ϕ0. Re 10-1 ϕ0.3 r 10-3 n1000 ϕ 0 ϕ0.4 r 10 r 10 1 r 10 0 r 10 - r 10-4 ϕ0.5 Re 10 r 10-1 r 10 3 n1 ϕ0.6 Re 10-1 Re 10 3 n0.1 ϕ0.6 r 10-5 n100 r 10 Re 10 0 Transport (ϕ 0, n>1) luidized Bed (ϕ L ϕ 0, n1) ied Bed (ϕ 0 0.6, n<1) Re 10 1 n10 Re 10 4 r 10 0 Re r 10-1 r 10 1 ϕ 0 n1 0.1 0. 0.3 0.4 0.5 n1 ϕ0.6 n1 Re 10 3 r 10 - ϕ0.6 n0.1 d v rel ν r 10-3 Re 10 r 10-4 r 10-5 r * 3 4 r ρ (ρ - ρ ) r v rel g d r g d 3 (ρ - ρ ) ν ρ General r-ω diagram for a fluidized bed taking also inhomogeneous fluidization into account Dark grey region: homogeneous fluidized bed (e.g. for liquid-solids systems) Light grey region: inhomogeneous fluidized beds (often observed for gas-solids systems) Remember: ied beds, stationary fluidized beds: u vrel u 0 Circulating fluidized beds, particle transp. v u0 c 10-1 10 0 10 1 10 10 3 r 10 4 10 5 10 6 10 7 10 8 Micro- and Nanoparticle Technology - S018 34 u rel u 0 : superficial velocity; c: particle velocity
Type of reactor Typical reactors article movement by: Gas/solids flow article size article residence time Gas residence time Heat and mass transfer Temperature control Space-time yield Bulk solids luidized bed Solids transport overflow throughflow luidized bed Circulating luidized bed Muffle kiln Multi-decker passage kiln Rotary kiln Belt-dryer Mechanics Small to very large Counter-flow Co-flow Cross-flow Toploader kiln Grate stoker furnace / kiln urnaces for pellets heating Gravity Mechanics Medium to very large luidized bed luidized bed roaster Multi-decker fluidized bed Gravity luid flow Co-flow Circulating fluidized bed Venturi fluidized bed Counter-flow (in steps) Cross-flow (in steps) Medium Very small - small Hours - days hours minutes lash dryer Cyclonepreheater Smelting cyclone Burner Gravity luid flow Co-flow Einstrom Rückf. Counterflow steps Very small Seconds or less Seconds Seconds Seconds or less Very low Low - medium High Very high Very high Medium - good Bad - medium Good Very good Medium - good Very low - medium medium Medium - high high Very high luid-solids reactors Solids Gas Micro- and Nanoparticle Technology - S018 35