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![ Particle
(Flowrate) FlowRate 1 x 1
( )
(Components) Componentsi 1 x 2
i ( ), text
ex> {‘Copper’, ‘FR-4’}
(Density) Densityi 1 x 2
i
ex> [2 9]
(Particle size range) PSRi 1 x 13
i (Nominal size)
ex> [45 62.5, 90, 125, … 2,800]
31](https://image.slidesharecdn.com/3fa5ca14-9811-409b-bed1-25df47fc1626-151021050604-lva1-app6892/85/150507-2015-31-320.jpg)
![ Particle ( )
(Particle size distribution) PSDi 1 x 13
i
ex> [0.1, 0.15, … 0.1]
(Grade distribution) GDi,j 13 x 12
i j
ex> [0 0.1 0.12, … 0.1]
(Drag coefficient) C_D 1 x 1
ex> 0.47
32](https://image.slidesharecdn.com/3fa5ca14-9811-409b-bed1-25df47fc1626-151021050604-lva1-app6892/85/150507-2015-32-320.jpg)
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150507 2015년 춘계 한국자원리싸이클링학회 발표자료 (박승수)
- 2.
- 3. 3 (PCB) ,FR-4 , / JKSimMet, Metsim, Modsim PCB Trial/Error
- 4. 4 , Recycling Programming tool: MATLAB R2015a
- 5. PCB 2(Copper, FR-4) (Dliberation ≒ 600 ) Zhang and Forssberg, 1997, Wen et al., 2005 5 2. : (a) FR-4 PCB , (b) (a) (b)
- 6. Modeling Shredder,Cut crusher Dmax = 4 mm , FR-4 : 30% 500 6 3. graph D50 Dmax
- 7. Andrews-Mika diagram Beta distribution modeling 7 4. Andrews-Mika diagram 𝑝 𝑔 = (1 − 𝐿0 − 𝐿1) 𝑔 𝛼−1 1 − 𝑔 𝛽−1 Beta(𝛼, 𝛽) 𝑔: 품위 𝑝(𝑔) : 특정 입도에서 품위𝑔 의 질량분율 𝐿0: 품위가 0인 입자들의 질량분율 𝐿1: 품위가 1인 입자들의 질량분율
- 8. / graph Andrews-Mikadiagram : 500 : 10-60% 8 5. /
- 9. 1. Feed 2. 3. Screensize screen Product 4. Screen size 5. Screen size 3,4 Product Grinding Mill Screen undersize oversize ( - ) ( + ) Feed 9 6.
- 10. 𝑓: Feed (𝑛× 1) 𝑝: Product (𝑛 × 1) 𝐵: Breakage matrix (𝑛 × 𝑛) 𝑆: Selective matrix (𝑛 × 𝑛) 𝐶: Screening matrix (𝑛 × 𝑛) 𝐼: Identity matrix (𝑛 × 𝑛) Grinding and screening matrix (1st stage) 𝑝 = 𝐵𝑆 + 𝐼 − 𝑆 𝑓 = 𝐷𝑓 𝑝1 ∘ = 𝐶𝑝 = 𝐶𝐷𝑓 = 𝐶 𝐵𝑆 + 𝐼 − 𝑆 𝑓 𝑝1 ∗ = 𝐼 − 𝐶 𝑝 = 𝐼 − 𝐶 𝐷𝑓 = 𝐼 − 𝐶 𝐵𝑆 + 𝐼 − 𝑆 𝑓 Circulation (nth stage) 𝑝 𝑛 ∘ = 𝐶𝐷𝑝 𝑛−1 ∘ = 𝐶𝐷𝐶𝐷𝑝 𝑛−2 ∘ = ⋯ = 𝐶𝐷 𝑛 𝑓 𝑝 𝑛 ∗ = 𝐼 − 𝐶 𝐷𝑝 𝑛−1 ∘ 𝑝 𝑛 = σ 𝑘=1 𝑛 𝑝 𝑛 ∗ Run the circulation until; 𝑝 𝑛 ∘ ≈ 0 oversize undersize 10
- 11. Matrix Breakagematrix: RR dist’n model (b=0.1, n=1) Selective matrix: GGS dist’n model (a=0.5, k=1) Screening matrix: Ideal partition curve * Both breakage and selective functions are size independent 11 7. Breakage, Selective, Screening function graphical expression 𝐹 𝑥 = 1 − 𝑒 − 𝑥 𝑏 𝑛 𝐹 𝑥 = 𝑥 𝜅 𝛼
- 12. Start Stop 𝑝∘ ≈ 0 ? 𝑝∘ ←𝐶𝐷𝑓 𝑝∗ ← 𝐼 − 𝐶 𝐷𝑓 𝑝 ← 𝑝 + 𝑝∗ Enter 𝑓, 𝐵, 𝑆, 𝐶 Print 𝑝𝐷 ← 𝐵𝑆 + 𝐼 − 𝑆 Initialize 𝑝 𝑓 ← 𝑝∘ yes no Algorithm 12 8. Algorithm
- 13. Knelson concentrator 5 chamber (fluidizing water) chamber chamber 13 𝑁 𝑄 PCB 분쇄물 FR-4 9. Knelson concentrator
- 14. Knelson concentrator( ) (𝐹𝑑) (𝐹𝑐) 𝐹𝑑 : , , 𝐹𝑐 : , , chamber , Fd Particle properties (𝑑, 𝜌𝑠) Operating condition (𝑄, 𝑁) 𝑓(𝑑, 𝜌 𝑓, 𝑄) 𝑁 r 𝑄 Fc 𝑓(𝑑, 𝜌𝑠, 𝑟, 𝑁) 14 10. Knelson concentrator
- 15. 1. Feed Knelsonconcentrator ( KC) 2. KC chamber / 3. 2. 4. 2. 3. Product1, Product2 15 Feed Knelson Concentrator Operating Condition Product1 Product2 11.
- 16. Mathematical expression 𝐹𝑑 = 1 2 𝜌 𝑓 𝑣2 𝐴 𝑠 𝐶 𝐷 = 𝜋 8 𝜌 𝑓 𝐷2 𝑄 𝐴 2 𝐶 𝐷 𝐹𝑐 = 𝑚𝑉2 𝑟 = 4 6 𝜋3 𝜌𝑠 𝐷3 𝑅𝑁2 𝑋 = 𝐹 𝑑 𝐹𝑐 = 241 𝜋2 × 1 𝐴2 𝑅 × 𝜌 𝑓 𝜌 𝑠 × 𝐶 𝐷 𝐷 × 𝑄 𝑁 2 𝑋 > 1: overflow (tailings) 𝑋 < 1: underflow (concentrate) 시료의 변수 𝜌𝑠: 입자, 유체의 밀도 𝐷: 입자의 직경 공정 변수 𝑄: 유동수의 유입량 𝑁: chamber의 회전 수 기타 상수 𝐶 𝐷: 입자의 저항계수 (Drag coefficient) 𝐴: 유동수(fluidizing water)의 유입 면적 𝑅: 입자의 회전반경 1st chamberFeed 2nd chamber 3rd chamber 4th chamber 5th chamber Tailings o/f o/f o/f o/f u/f o/f u/f u/f u/f u/f Concentrate 16 12. Knelson concentrator u/f, o/f
- 17. Algorithm 17 Start 𝑗 ←1 (grade class) Enter 𝑄, 𝑁, 𝜌 𝑓, 𝑓 𝑖 ← 1 (particle size) Initiate 𝑝1, 𝑝2 𝑝1 ← 𝑝1 + 𝑓𝑖,𝑗 𝑋𝑓 𝑖,𝑗 < 1 ? calc. 𝑋𝑓 𝑖,𝑗 in nth chmb. 𝑛 ← 1 (chamber no.) End of 𝑗? End of 𝑖? 𝑛 ← 𝑛 + 1 𝑗 ← 𝑗 + 1 𝑝2 ← 𝑝2 + 𝑓𝑖,𝑗 𝑛 = 5 ? 𝑖 ← 𝑖 + 1 Print 𝑝1, 𝑝2 Stop no no no no yes yes yes yes 13. algorithm
- 18. Simulation stream (Particle size distribution) / (Particle size / grade distribution) / (Grade) vs. (Recovery) (Newton’s efficiency) 18 Grinding Mill Knelson Concentrator Product1 Feed Product2 14.
- 19. Screen size Feed D80: 2,000 → 110 D50: 1,800 → 100 Feed Screen size 500 19 15. screen size simulation
- 20. / 20 16. // simulation (aperture size: 500 )
- 21. Fluidizing water/ Q = 6, 12 L/min , / u/f o/f Fluidizing water o/f Yield, Recovery 21 17. Fluidizing water u/f, o/f / (N=1,000 rpm) Q = 6 L/min, overflow Q = 12 L/min, overflow Q = 6 L/min, underflow Q = 12 L/min, underflow
- 22. Fluidizing water 22 18.Fluidizing water Recovery vs. Grade graph (N = 1,000 rpm) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Recovery Grade of concentrate Q = 3 L/min Q = 6 L/min Q = 9 L/min Q = 12 L/min 27% 63% 11% 5% 0% 10% 20% 30% 40% 50% 60% 70% Newton's efficiency 3 L/min 6 L/min 9 L/min 12 L/min 19. Fluidizing water Newton’s efficiency (N = 1,000 rpm)
- 23. Chamber / N=500, 1,000 rpm / Chamber , u/f 23 20. Chamber u/f, o/f (Q=6 L/min) N = 500 rpm, overflow N = 1,000 rpm, overflow N = 500 rpm, underflow N = 1,000 rpm, underflow
- 24. Chamber / 24 21.Chamber Recovery vs. Grade graph (Q = 6 L/min) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Recovery Grade of concentrate N = 1,250 rpm N = 1,000 rpm 5% 30% 63% 59% 0% 10% 20% 30% 40% 50% 60% 70% Newton's efficiency 500 rpm 750 rpm 1,000 rpm 1,250 rpm 22. Chamber Newton’s efficiency (Q = 6 L/min) N = 750 rpm N = 500 rpm ←N
- 25. Q: 3,6, 9, 12 L/min N: 500, 750, 1,000 1,250 rpm Max. Newton effi.: 63% #1. Q: 3 L/min, N: 500 rpm #2. Q: 6 L/min, N: 1,000 rpm 25 63% 5% 0% 0% 43% 30% 5% 1% 27% 63% 11% 5% 0% 59% 44% 11% 0% 10% 20% 30% 40% 50% 60% 70% 3 L/min 6 L/min 9 L/min 12 L/min 500 rpm 750 rpm 1,000 rpm 1,250 rpm 23. Fluidizing water Chamber Newton’s efficiency 𝑋 = 𝐹𝑑 𝐹𝑐 = 241 𝜋2 × 1 𝐴2 𝑅 × 𝜌 𝑓 𝜌𝑠 × 𝐶 𝐷 𝐷 × 𝑄 𝑁 2
- 26. : 34.56% : 89.29 % : 67.74% 26 Grinding Mill Knelson Concentrator Product1 Feed Product2 Feed Ground product Concentrate Tailings 24. / ① ② ③ ④ ① ② ③ ④
- 27. , , Knelson concentrator (Newton efficiency) #1. Q: 3 L/min, N: 500 rpm #2. Q: 6 L/min, N: 1,000 rpm : 34.56% : 89.29 % : 67.74% 27
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- 31. Particle (Flowrate)FlowRate 1 x 1 ( ) (Components) Componentsi 1 x 2 i ( ), text ex> {‘Copper’, ‘FR-4’} (Density) Densityi 1 x 2 i ex> [2 9] (Particle size range) PSRi 1 x 13 i (Nominal size) ex> [45 62.5, 90, 125, … 2,800] 31
- 32. Particle () (Particle size distribution) PSDi 1 x 13 i ex> [0.1, 0.15, … 0.1] (Grade distribution) GDi,j 13 x 12 i j ex> [0 0.1 0.12, … 0.1] (Drag coefficient) C_D 1 x 1 ex> 0.47 32
- 33. / Particlesize, Particle size distribution of feed Breakage, Selective and Screening matrix of grinding mill Particle size distribution of product Product Grinding Mill Screen undersize oversize ( - ) ( + ) Feed 33 6.
- 34. Flowrate, Densityof solid, Particle size, Particle size distribution, Drag coefficient of feed Rotating number, Flowrate of fluidizing water, Density of the fluid Flowrate, Particle size distribution of concentrate and tailings 34 Feed Knelson Concentrator Operating Condition Product1 Product2 11.