150507 2015년 춘계 한국자원리싸이클링학회 발표자료 (박승수)
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2
3
(PCB)
, FR-4 ,
/
JKSimMet, Metsim, Modsim
PCB
Trial/Error
4
,
Recycling
Programming tool: MATLAB R2015a
PCB
2 (Copper, FR-4)
(Dliberation ≒ 600 )
Zhang and Forssberg, 1997, Wen et al., 2005
5
2. :
(a) FR-4 PCB , (b)
(a) (b)
Modeling
Shredder, Cut crusher
Dmax = 4 mm
, FR-4
: 30%
500
6
3.
graph
D50 Dmax
Andrews-Mika diagram
Beta distribution
modeling
7
4.
Andrews-Mika diagram
𝑝 𝑔 = (1 − 𝐿0 − 𝐿1)𝑔𝛼−1 1 − 𝑔 𝛽−1
Beta(𝛼, 𝛽)
𝑔: 품위
𝑝(𝑔) : 특정입도에서품위𝑔의질량분율
𝐿0: 품위가 0인입자들의질량분율
𝐿1: 품위가 1인입자들의질량분율
/
graph
Andrews-Mika diagram
: 500
: 10-60%
8
5.
/
1. Feed
2.
3. Screen size screen Product
4. Screen size
5. Screen size 3,4
ProductGrinding
MillScreen undersize
oversize
( - )
( + )
Feed
9
6.
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)
𝑝𝑛∘ = 𝐶𝐷𝑝𝑛−1
∘ = 𝐶𝐷𝐶𝐷𝑝𝑛−2∘ = ⋯ = 𝐶𝐷 𝑛𝑓
𝑝𝑛∗ = 𝐼 − 𝐶 𝐷𝑝𝑛−1
∘
𝑝𝑛 = σ𝑘=1𝑛 𝑝𝑛
∗
Run the circulation until; 𝑝𝑛∘ ≈ 0
oversize
undersize
10
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−
𝑥𝑏
𝑛𝐹 𝑥 =
𝑥
𝜅
𝛼
Start
Stop
𝑝∘ ≈ 0 ?
𝑝∘ ← 𝐶𝐷𝑓𝑝∗ ← 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
Knelson concentrator
5 chamber (fluidizing water)
chamber
chamber
13
𝑁
𝑄
PCB 분쇄물FR-4
9. Knelson concentrator
Knelson concentrator ( )
(𝐹𝑑) (𝐹𝑐)
𝐹𝑑 : , ,
𝐹𝑐 : , , chamber ,
Fd
Particle properties (𝑑, 𝜌𝑠)
Operating condition (𝑄,𝑁)
𝑓(𝑑, 𝜌𝑓 , 𝑄)
𝑁
r
𝑄 Fc𝑓(𝑑, 𝜌𝑠, 𝑟, 𝑁)
14
10. Knelson concentrator
1. Feed Knelson concentrator ( KC)
2. KC chamber /
3. 2.
4. 2. 3. Product1, Product2
15
FeedKnelson
Concentrator
Operating Condition
Product1
Product2
11.
Mathematical expression
𝐹𝑑 =1
2𝜌𝑓𝑣
2𝐴𝑠𝐶𝐷 =𝜋
8𝜌𝑓𝐷
2 𝑄
𝐴
2𝐶𝐷
𝐹𝑐 =𝑚𝑉2
𝑟=
4
6𝜋3𝜌𝑠𝐷
3𝑅𝑁2
𝑋 =𝐹𝑑
𝐹𝑐=
241
𝜋2×
1
𝐴2𝑅×
𝜌𝑓
𝜌𝑠×
𝐶𝐷
𝐷×
𝑄
𝑁
2
𝑋 > 1: overflow (tailings)
𝑋 < 1: underflow (concentrate)
시료의변수
𝜌𝑠: 입자, 유체의밀도
𝐷: 입자의직경
공정변수
𝑄: 유동수의유입량
𝑁: chamber의회전수
기타상수
𝐶𝐷: 입자의저항계수 (Drag coefficient)
𝐴: 유동수(fluidizing water)의유입면적
𝑅: 입자의회전반경
1st
chamberFeed2nd
chamber
3rd
chamber
4th
chamber
5th
chamber Tailingso/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
Algorithm
17
Start
𝑗 ← 1(grade class)
Enter 𝑄,𝑁, 𝜌𝑓 , 𝑓
𝑖 ← 1(particle size)
Initiate 𝑝1, 𝑝2
𝑝1 ← 𝑝1 + 𝑓𝑖,𝑗
𝑋𝑓𝑖,𝑗 < 1 ?
calc. 𝑋𝑓𝑖,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
Stopno
no
no
no
yes yes
yes
yes13.
algorithm
Simulation
stream
(Particle size distribution)
/ (Particle size / grade distribution)
/
(Grade) vs. (Recovery)
(Newton’s efficiency)
18
Grinding MillKnelson
Concentrator
Product1
Feed
Product2
14.
Screen size
Feed
D80: 2,000 → 110
D50: 1,800 → 100
Feed
Screen size 500
19
15. screen size
simulation
/
20
16. / / simulation
(aperture size: 500 )
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
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
Re
co
ve
ry
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)
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
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
Re
co
ve
ry
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
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 =𝐹𝑑𝐹𝑐
=241
𝜋2×
1
𝐴2𝑅×𝜌𝑓
𝜌𝑠×𝐶𝐷𝐷×
𝑄
𝑁
2
: 34.56%
: 89.29 %
: 67.74%
26
Grinding MillKnelson
Concentrator
Product1
Feed
Product2
Feed Ground product Concentrate Tailings
24. /
① ②③
④
① ② ③ ④
,
,
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
28
29
30
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
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
/
Particle size, Particle size distribution of feed
Breakage, Selective and Screening matrix of grinding mill
Particle size distribution of product
ProductGrinding
MillScreen undersize
oversize
( - )
( + )
Feed
33
6.
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
FeedKnelson
Concentrator
Operating Condition
Product1
Product2
11.
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