More Related Content Similar to 150507 2015년 춘계 한국자원리싸이클링학회 발표자료 (박승수) Similar to 150507 2015년 춘계 한국자원리싸이클링학회 발표자료 (박승수) (20) 3. 3
(PCB)
, FR-4 ,
/
JKSimMet, Metsim, Modsim
PCB
Trial/Error
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)
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
9.
1. Feed
2.
3. Screen size 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
Breakage matrix: 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 Knelson concentrator ( 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
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
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. /
Particle size, 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, Density of 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.
