ENVS 355 Data, data, data Models, models, models Policy, policy, policy.
Models
9
208 Unit Operation Model Guide USIM PAC 3.2 3.2 – Level 1 models Model 204 – Spiral Concentrator (1) Spiral 31 parameters Two output streams # Parameters Default value 1 Number of units in parallel 1 2 Nominal solid flowrate per unit (t/h) 2 3 Nominal volumetric flowrate per unit (m3/h) 3 4 Specific gravity of water + slimes (kg/dm 3 ) 1 5 Minimum specific gravity for corrected cut-point (kg/dm 3 ) 3.5 6 Percent solids in the heavy stream (%) 70 7 Maximum particle size tolerated by the unit (mm) 2.5 8 Lower size of the optimum separation range (mm) 0.06 9 Upper size of the optimum separation range (mm) 2 10 Minimum recovery of light particles in the heavy stream 0.05 11 Minimum recovery of heavy fine particles 0.1 12 Minimum recovery of heavy coarse particles 0.3 13 Maximum recovery of heavy particles in the optimum range 0.98 14 Corrected cut-point specific gravity for coarse particles 0 15 Particle size at minimum cut-point specific gravity (mm) 0.1 16 Power of cut-point specific gravity according to fine size 1 17 Adjustment of cut-point specific gravity according to fine size 0 18 Power of cut-point specific gravity according to coarse size 1 19 Adjustment of cut-point specific gravity according to coarse size 0 20 Minimum corrected imperfection 0.3 21 Corrected imperfection for the coarse fraction 0 22 Particle size at minimum corrected imperfection (mm) 0.5 23 Power of corrected imperfection according to fine size 1 24 Adjustment of corrected imperfection according to fine size 0 25 Power of corrected imperfection according to coarse size 1 26 Adjustment of corrected imperfection according to coarse size 0 27 Power of corrected imperfection according to solids flowrate 1 28 Adjustment of corrected imperfection according to solids flowrate 0 29 Power of corrected imperfection according to volumetric flowrate 1
Transcript of Models
208 Unit Operation Model Guide
USIM PAC 3.2
3.2 – Level 1 models
Model 204 – Spiral Concentrator (1)
Spiral 31 parameters Two output streams
# Parameters Default value
1 Number of units in parallel 1
2 Nominal solid flowrate per unit (t/h) 2
3 Nominal volumetric flowrate per unit (m3/h) 3
4 Specific gravity of water + slimes (kg/dm3) 1
5 Minimum specific gravity for corrected cut-point (kg/dm3) 3.5
6 Percent solids in the heavy stream (%) 70
7 Maximum particle size tolerated by the unit (mm) 2.5
8 Lower size of the optimum separation range (mm) 0.06
9 Upper size of the optimum separation range (mm) 2
10 Minimum recovery of light particles in the heavy stream 0.05
11 Minimum recovery of heavy fine particles 0.1
12 Minimum recovery of heavy coarse particles 0.3
13 Maximum recovery of heavy particles in the optimum range 0.98
14 Corrected cut-point specific gravity for coarse particles 0
15 Particle size at minimum cut-point specific gravity (mm) 0.1
16 Power of cut-point specific gravity according to fine size 1
17 Adjustment of cut-point specific gravity according to fine size 0
18 Power of cut-point specific gravity according to coarse size 1
19 Adjustment of cut-point specific gravity according to coarse size 0
20 Minimum corrected imperfection 0.3
21 Corrected imperfection for the coarse fraction 0
22 Particle size at minimum corrected imperfection (mm) 0.5
23 Power of corrected imperfection according to fine size 1
24 Adjustment of corrected imperfection according to fine size 0
25 Power of corrected imperfection according to coarse size 1
26 Adjustment of corrected imperfection according to coarse size 0
27 Power of corrected imperfection according to solids flowrate 1
28 Adjustment of corrected imperfection according to solids flowrate 0
29 Power of corrected imperfection according to volumetric flowrate 1
Unit Operation Model Guide 209
USIM PAC 3.2
30 Adjustment of corrected imperfection according to volumetric flowrate
0
31 Spiral material (Steel or Fiberglass) Steel
Model focus example Model focus/Jig/Jig 1
This model is derived from the description of the gravity concentration of ores by means of Fournol's density partition curves (H. Fournol: "Méthodes de calcul des possibilités d'épuration - prévision et garantie des résultats industriels", Rev. Ind. Minérale, June 1974, pp. 5-19). This curve uses a log-normal law to represent the corrected density partition curves in units such as shaking tables, spirals and jigs; that is to say units which do not use a dense medium as the means of concentration.
The curve of gravity partition takes the following form:
F'CCCF 121
where:
F probability of a particle of specific gravity to report to the heavy stream
1C minimum probability to report to the heavy stream (parameter #10)
2C maximum probability to report to the heavy stream
F value of the corrected density partition curve for a particle of specific gravity ,
O u
dueF' 2
2
21
with:
sp
s
II.O log
1log67440
2
where:
p cut-point specific gravity
s pulp specific gravity (parameter #4)
I imperfection
The parameters ( I , p , 1C and 2C ) of the density partition curve are determined for each particle size class by using a model, derived by BRGM, which takes into account the size of the particles, the volumetric and solid flowrates for each unit and type of unit (jig, shaking table, spiral concentrator).
210 Unit Operation Model Guide
USIM PAC 3.2
Computation of the maximum probability for a particle to report to the heavy product stream as a function of its size: dC2
maxmin22
maxsupsupmax
maxmin2max2min22
supinfmax22
infinf
min2max2min22
if
if
if
if
ddCdC
dddddddCCCdC
dddCdC
ddddCCCdC
c
cc
ff
where:
fC min2 minimum recovery of heavy fine particles (parameter #11)
cC min2 minimum recovery of heavy coarse particles (parameter #12)
max2C maximum recovery of heavy particles (parameter #13)
infd lower limit of the optimal particle size range (parameter #8)
supd upper limit of the optimal particle size range (parameter #9)
maxd maximum particle size tolerated by the unit (parameter #7)
Computation of the corrected cut-point specific gravity as a function of particle size: dp
1
1
minmin
11
min
if
1
11
ifln
dd
dd
d
ddddd
c
f
c
cppcpp
fpp
where:
minp minimal corrected cut-point specific gravity (parameter #5)
pc corrected cut-point specific gravity for coarse particles (parameter #14)
1d particle size corresponding to the minimal corrected cut-point specific gravity (parameter #15)
Unit Operation Model Guide 211
USIM PAC 3.2
f adjustment parameter #16
f adjustment parameter #17
c adjustment parameter #18
c adjustment parameter #19
If account is not to be taken of the variation in p as a function of the particle size then the
following values are entered: 0f and 0c .
Computation of the corrected imperfection as a function of particle size: dI
0
0
minmin
00
min
if
1
11
ifln
dd
dd
IIIdI
ddddIdI
Ic
If
Ic
Icc
If
where:
minI minimal corrected imperfection (parameter #20)
cI corrected imperfection for coarse particle (parameter #21)
0d particle size corresponding to the minimal corrected imperfection (parameter #22)
If adjustment parameter #23
If adjustment parameter #24
Ic adjustment parameter #25
Ic adjustment parameter #26
If account is not to be taken of the variation in I as a function of particle size then the following values are entered: 0If and 0Ic
Computation of the corrected imperfection as a function of the volumetric and solids flowrates
vs QQXdII ,1
212 Unit Operation Model Guide
USIM PAC 3.2
with:
***
**
if11,
if1,
vvv
vv
s
ssvs
vvs
ssvs
NQQNQQ
NQQQQX
NQQNQQQQX
vs
s
where: *sQ nominal solids mass flowrate (parameter #2)
*vQ nominal volumetric flowrate (parameter #3)
N number of units in parallel (parameter #1)
s adjustment parameter #27
s adjustment parameter #28
v adjustment parameter #29
v adjustment parameter #30
If account is not to be taken of the variations of I as a function of the flowrates, then the following values are entered: 0s and 0v
General shape of the partition surface in the density - size space
5001000
15002000
2500
30002
34
56
7
0.0
0.2
0.4
0.6
0.8
1.0
Unit Operation Model Guide 213
USIM PAC 3.2
0 500 1000 1500 2000 2500 3000
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Specific gravity = 7.1
Particle sizes (µm)
Structure and use of the model The model allows three levels of use:
1. Defining the gravity partition curve as a function of particle size distribution by defining parameters #1 through #13 in order to define the partition curve. At this level, the corrected specific gravity cut-point and the imperfection are considered constant.
2. Taking into account the variation of the corrected specific gravity cut-point as a function of the particle size by defining parameters #14 through #19, taking into account the variation of the imperfection as a function of the particle size by defining parameters #20 through #26.
3. Taking into account the variation of the imperfection as a function of the flowrates by defining parameters #27 through #30.
The levels 2 and 3 are independent but you always have to define the parameters requested for the 1st level of use.
NotesParameters #8 through #13 are determined using an experimental partition curve.
The imperfection is calculated applying the following formula to the gravity partition curves (Tromp's curve):
sc
ccI50
2575
2where:
s pulp specific gravity (parameter #4)
214 Unit Operation Model Guide
USIM PAC 3.2
Capital cost
The capital cost C (in Canadian Dollar 1982) of a spiral depends on its nominal capacity *sQ (parameter #2) and its material type (parameter #31):
bsaQC *
where:
Material *sQ (st/h) a b
Steel 30005.1 *sQ 1472 1.00
Fiberglass 30001 *sQ 2448 0.870
This capital cost is updated and converted.
Ref: A.L. Mular, �Mining and Mineral Processing Equipment Cost and Preliminary Capital Cost Estimation", Canadian Institute of Mining and Metallurgy, 1982, vol. 25, p. 91.
Unit Operation Model Guide 215
USIM PAC 3.2
Model 209 – Jig (1)
Jig 32 parameters Two output streams
# Parameters Default value
1 Number of units in parallel 1
2 Nominal solid flowrate per unit (t/h) 100
3 Nominal volumetric flowrate per unit (m3/h) 100
4 Specific gravity of water + slimes (kg/dm3) 1
5 Minimum specific gravity for corrected cut-point (kg/dm3) 3.5
6 Percent solids in the heavy stream (%) 50
7 Maximum particle size tolerated by the unit (mm) 20
8 Lower size of the optimum separation range (mm) 1
9 Upper size of the optimum separation range (mm) 12
10 Minimum recovery of light particles in the heavy stream 0.02
11 Minimum recovery of heavy fine particles 0.1
12 Minimum recovery of heavy coarse particles 0.3
13 Maximum recovery of heavy particles in the optimum range 0.98
14 Corrected cut-point specific gravity for coarse particles 0
15 Particle size at minimum cut-point specific gravity (mm) 2
16 Power of cut-point specific gravity according to fine size 1
17 Adjustment of cut-point specific gravity according to fine size 0
18 Power of cut-point specific gravity according to coarse size 1
19 Adjustment of cut-point specific gravity according to coarse size 0
20 Minimum corrected imperfection 0.15
21 Corrected imperfection for the coarse fraction 0.15
22 Particle size at minimum corrected imperfection (mm) 2
23 Power of corrected imperfection according to fine size 1
24 Adjustment of corrected imperfection according to fine size 0
25 Power of corrected imperfection according to coarse size 1
26 Adjustment of corrected imperfection according to coarse size 0
27 Power of corrected imperfection according to solids flowrate 1
28 Adjustment of corrected imperfection according to solids flowrate 0
29 Power of corrected imperfection according to volumetric flowrate 1
30 Adjustment of corrected imperfection according to volumetric flowrate
0
31 Jigging area (m2) 0.14
216 Unit Operation Model Guide
USIM PAC 3.2
32 Jig type (Simplex or Duplex) Simplex
Model focus example Model focus/Jig/Jig 1
This model is identical to the Spiral model.
Capital cost
The capital cost C (in Canadian Dollar 1982) of a jig depends on its area A (parameter #31) and its type (parameter #32):
baAC
where:
Type A (in2) a b
22.21724 A 6498.7 0.05716 Simplex
86422.217 A 742.7 0.4603
16.23396 A 4930 0.1786 Duplex
86416.233 A 1069.8 0.4589
This capital cost is updated and converted.
Ref: A.L. Mular, �Mining and Mineral Processing Equipment Cost and Preliminary Capital Cost Estimation", Canadian Institute of Mining and Metallurgy, 1982, vol. 25, p. 99.
