Title of Publication Edited by TMS (The Minerals, Metals & Materials Society), 2006
APPLIED METALLURGICAL PROCESS TESTING AND PLANT OPTIMIZATION WITH DESIGN OF EXPERIMENTATION SOFTWARE Corby G. Anderson, Ph.D. Director The Center for Advanced Mineral and Metallurgical Processing Montana Tech, 1300 West Park Street, Room 214 ELC Building Butte, Montana 59701 Telephone: 406-496-4794; Facsimile: 406-496-4512 E-mail:
[email protected] WEB: www.mtech.edu/CAMP
Key Words:
Applied testing, design of experimentation, flotation, flowsheet development, hydrometallurgy, NSC pressure leaching, plant optimization, statistical software Abstract
Laboratory testing, interpretation and application of metallurgical technologies can be tedious, time consuming and costly. This paper outlines the use of proven statistical design of experimentation software for rapid optimization of laboratory testing and operating plants with limited representative sample utilization. This results in less costly required testing, a more thorough understanding of results and the ability to simultaneously optimize several variables and outcomes at once. At the Center for Advanced Mineral and Metallurgical Processing, this testing methodology has been used successfully in many metallurgical development and plant optimization projects thereby confirming its real world utility and application. Accordingly, several applied examples in flotation and hydrometallurgy will be outlined in this paper. This will include flotation testing of a copper gold ore, flotation testing of a copper, cobalt and gold ore, optimization of an industrial hydrometallurgical jarosite circuit and optimization of industrial nitrogen species catalyzed pressure leaching of a copper enargite concentrate. Introduction While flotation technology is now 100 years old, the testing, interpretation and application of lab results can be tedious, costly and time consuming requiring extensive sample collection and preparation. In addition, recent applications like hydrometallurgical pressure leaching and associated unit operations, such as precipitation, still remain more of an art than a quantifiable science. This paper will elucidate the application of STAT-EASE Design-Expert software to minimize required laboratory testing while rapidly optimizing multiple results and outcomes in a statistically valid manner. The STAT-EASE program is based on proven design of experiment fundamentals. In this paper, the real world application of this
methodology for lab testing, plant optimization and process development will be elucidated. The Application to Flotation Testing of a Copper and Gold Ore Based on previous work along with current legal issues concerning limiting cyanide use in Montana, flotation with gravity concentration was the process chosen to develop the Elkhorn copper gold ore deposit. A review of previous scoping level test work revealed significant results on optimal collector and frother usage, grind time, and float time were missing on the Elkhorn Mt. Hagen ore deposits (Anderson and Fayram 2005). Because of client budget constraints and a limited quantity of representative core samples material available, STAT-EASE statistical software was used to minimize the number of flotation experiments required to identify a statistical representative experimental set. This commercially licensed program based on fundamentals of design of experiments provides highly efficient: 1. Two-level factorial screening studies so that the vital factors which affect process can be identified. 2. Response surface methods to find ideal process settings and achieve optimal performance. 3. Mixture design techniques to discover optimal formulations. Among other features, the program offers rotatable 3D plots for visualization of response surfaces. Again, the key feature is the ability to set up statistically valid design of experiment matrices which allow a minimum amount of experimentation to take place. This saves both time and money allowing robust flotation testing and optimization to occur with a minimal amount of ore sample used. A complete discourse on the computer software and statistical design of experimentation fundamentals for chemical processing is beyond the scope of this paper but pertinent references are provided for the reader’s convenience (Anderson and Whitcomb 2000, Box and Draper 1987, Box 2000, Cochran 1957, Cornell 1990, Hinkelmann and Kempthorne 1994, Kempthorne 1975, Lorenzen and Anderson 1993, Meyer and Napier-Munn 1999, Montgomery 2001, Napier-Munn and Meyer 1999, Neter 1990, Pazman 1986, STAT EASE 2002 ,Wu and Hamada 2000). Elkhorn Ore Composite Development The Mt. Hagen ore composite was collected from different drill holes going across the deposit from north to south and top to bottom. No special considerations were given to the sample other than ensuring that the sample was taken from an ore run and the appropriate interval assigned. Approximately twelve inches of sample were taken from the appropriate interval and recorded. No special considerations were made for oxide, sulfide, or waste. Upon arrival at the CAMP laboratory, all samples were crushed to minus 3/8 inch and thoroughly mixed. A sample for assaying was split from the material using a Jones
Splitter. This composite was assayed for gold, silver, and copper. The gold assays were completed using metallic screen fraction analysis at 100 mesh to identify any coarse gold. Multi-element ICP analysis and X-ray diffraction analysis were also completed. Table I identifies the composite ore average analysis. Table I: Elkhorn Goldfields – Mt. Hagen Ore Weighted Average Composite C O M P O S ITE
23-S ep
W E IG H TE D AV E R AG E AU , O Z /TN C O M P O S ITE AS S AY HOLE
0.204
W E IG H T
AU G R AD E
CU, % 0.40 C U G R AD E
AU W E IG H T C U W E IG H T
C E G 04-12
21.2
0.180
0.55
3.825
11.58
C E G 04-18
9.6
0.151
0.02
1.452
0.23
C E G 04-11
25.3
0.260
0.39
6.589
9.82
C E G 04-10
10.5
0.133
0.40
1.394
4.15
C E G 04-24
50.3
0.210
0.41
10.544
20.85
TO TAL
116.9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
23.80
46.63
0.204
0.40
Elkhorn Ore Flotation Testing Flotation testing was guided and completed using STAT-EASE diagnostic software. The software requires the development of a statistically valid design of the experiment matrix using several variables and outcomes. In the case of the Mt. Hagen deposit testing, the variables used were grind time, pH, flotation time, and the addition or not of sodium sulfide. In addition, the testing was used to simultaneously identify four outcomes: gold and copper with grade and recovery. The grind time variable was developed to review the effects of grinding and liberation at a base size of 150 mesh. A shorter grind time would add capacity and lower costs. A longer grind time will better liberate the ore and typically improve recovery. Based on previous testing, a twenty-five minute grind time gave an 80% passing 150 mesh ore size. The grinding pulp density was 50% solids by weight in a laboratory ball mill. Sodium sulfide was used as a sulfidizing agent variable to promote flotation of oxidized copper and gold bearing minerals. Testing was completed to identify a response based on use or no use. Variable pH’s of 8.5 or 10.5 were chosen to both promote and depress pyrite and pyrrhotite. At pH 8.5, pyrite and pyrrhotite tend to be promoted. At pH 10.5, both pyrite and pyrrhotite are effectively depressed. This difference in pH was used to assist in identifying the source of the gold and how to best optimize the gold recovery.
Flotation testing was completed with a Denver Laboratory flotation machine. The density of the flotation pulp was a constant 40% solids by weight. Each ore charge for the testing was 1,000 grams. Variable float times were used to optimize the float machine size requirements. The collector chosen for this project was Cytec Aerofloat 3477. It was used at a constant dosage. This collector is a common dithiophosphate based collector. It was chosen because of its selectivity towards gold and copper and its positive results in previous testing of other Elkhorn ore deposits. The frother chosen for the testing was pine oil used at a constant dosage. Pine oil was chosen in other Elkhorn ore deposit flotation testing because it minimized negative effects of specific minerals with the deposit. With the development of the pertinent variables and measurable outcomes, several choices of matrix sizes and sample numbers can be developed. Accordingly, a higher number of tests can improve the statistical reliability of the data being developed. In the case of Mt. Hagen ore testing, four variables with four measurable outcomes were identified. The total number of samples and the size of the matrix required two to the power of four or sixteen total possible tests. The user of STAT-EASE can select a total, half, or quarter of this testing matrix to identify a statistically valid outcome. For this real world project, there were significant restraints on both budget and sample quantity. A one half STAT-EASE matrix was chosen containing eight tests that would statistically validate the testing of the sixteen total possible combinations. STAT-EASE software also has the ability to add midpoints into the data testing. Although this adds to the size of the sample matrix, midpoint testing adds extra results which can improve the outcome. In the Mt. Hagen ore testing two replicate mid-point tests were conducted based on the STAT-EASE testing matrix. Thus, a total of 10 tests were utilized as follows: Table II: STAT-EASE One Quarter Design of Experiment Matrix TEST
GRIND TIME, MIN
SULFIDE DOSAGE, GRAMS
pH
FLOAT TIME
1
30
1.0
8.5
15
2
20
0.0
8.5
15
3
25
0.5
9.5
17.5
4
30
1.0
10.5
20
5
30
0.0
10.5
15
6
25
0.5
9.5
17.5
7
20
1.0
10.5
15
8
20
0.0
10.5
20
9
20
1.0
8.5
20
10
30
0.0
8.5
20
This represents the eight tests determined by the software along with two midpoint replicate tests (i.e., test numbers 3 and 6 above). Upon completing the initial ten diagnostic flotation tests based on the above STAT-EASE matrix, the test results are illustrated in Table III and Table IV.
Table III: Elkhorn Goldfields – Mt. Hagen STAT-EASE Matrix Assay Results ASSAYS
Sample #
CONCENTRATE Au (oz/t) 0.608 0.474 0.606 0.592 0.524 0.452 0.618 0.918 0.508 0.416
1 2 3 4 5 6 7 8 9 10
Ag (oz/t) 0.18 0.38 0.58 0.48 0.54 0.32 1.40 1.34 0.36 0.50
TAILS Cu (%) 0.87 0.66 0.61 0.73 0.71 0.46 0.69 1.25 0.60 0.46
Au (oz/t) 0.056 0.182 0.052 0.068 0.068 0.064 0.062 0.124 0.088 0.102
Ag (oz/t) 0.14 0.14 0.14 0.24 0.24 0.14 0.18 0.08 0.10 0.12
Cu (%) 0.026 0.035 0.024 0.026 0.027 0.019 0.020 0.051 0.059 0.026
Table IV: Elkhorn Goldfields – Mt. Hagen STAT-EASE Matrix Recovery Results
Sample # 1 2 3 4 5 6 7 8 9 10
Au (%) 80.8% 45.1% 78.7% 74.2% 75.3% 81.4% 77.2% 47.5% 69.9% 68.5%
RECOVERIES TO CONCENTRATE Ag (%) 33.32% 46.12% 56.82% 39.83% 47.13% 58.54% 72.52% 67.21% 59.20% 68.96%
Cu (%) 92.9% 85.6% 89.0% 90.3% 91.2% 93.7% 92.1% 75.0% 80.4% 90.4%
The above recovery data was entered into the STAT-EASE statistical software and modeled to optimize the flotation requirements for the MT. Hagen deposit. STATEASE gives several options to transform the data into a statistical probability plot that allows for the best statistical presentation of each outcome. Figure 1 is an example of the half normal plot for gold recovery of the Mt. Hagen deposit.
DESIGN-EXPERT Plot Gold Recov ery A: Grind Time B: Sulf ide Dose C: pH D: Float Time
Half Normal plot 99
97
Half Normal %probability
95
B 90 85
A
80 70 60 40 20 0
0.00
4.06
8.12
12.19
16.25
|Effect| Figure 1: Example STAT-EASE Half Normal Plot Upon finding a graphical transformation to fit the variables with the outcomes, STATEASE allows you to add and remove effects generated from the variables to statistically optimize the data. Based on the reviewing the statistical outcome of gold recovery, the probability that the gold recovery would be maximized using this data was 92.7%. A review was completed on all the outcomes (gold and copper recovery and gold and copper grade) and all outcome were found to have probabilities over 90%. Based on this data no further testing was completed on the Mt. Hagen deposit. In reviewing the STAT-EASE variable data, plots such as Figure 2 and 3 can be created.
D E S I G N -E XP E R T P lo t G o ld R e c o v e ry
In te r a c tio n G r a p h D: Flo a t T im e
8 7 .5 4 6 4
X = A : G rin d Tim e Y = D : F lo a t Tim e D e s ig n P o in t s
2
7 4 .5 2 3 2
Gold Recovery
D - 15.000 D + 20.000 A c t u a l F a c t o rs B : S u lf id e D o s e = 0 . 0 0 C : pH = 10.50
6 1 .5
4 8 .4 7 6 8
2
3 5 .4 5 3 6
2 0 .0 0
2 2 .5 0
2 5 .0 0
2 7 .5 0
3 0 .0 0
A : G ri n d T i m e
Figure 2: Variable Interaction Graph for Gold Recovery Without Sulfide Use
Interaction Graph
DESIGN-EXPERT Plot Gold Recov ery
D: Float Time
93.0464
X = A: Grind Time Y = D: Float Time Design Points
81.0348
2
Gold Recovery
D- 15.000 D+ 20.000 Actual Factors B: Sulf ide Dose = 1.0069.0232 C: pH = 10.50
2
57.0116
45
20.00
22.50
25.00
27.50
30.00
A: Grind Time
Figure 3: Variable Interaction Graph for Gold Recovery with Sulfide Use
The above noted interaction graphs plot grind time against recovery with float time, pH, and sulfide dose as variables. As noted on the first graph, the sulfide dose is zero grams and on the second graph the sulfide dose is one gram. Based on a review of the graph, the expected gold recovery is shown in Table V. TABLE V: Statistical Model Predicted Gold Recoveries Variable
Grind Time, Mins
Sulfide Dose, Grams
Recovery, %
Grind Time
20.00
0.00
48.5
Grind Time
20.00
1.00
78.0
Grind Time
30.00
0.00
74.5
Grind Time
30.00
1.00
78.0
By reviewing the above data, sulfide dose is extremely important for low grind times in that recovery is improved approximately 30%. Sulfide dose is not very important for higher grind times and recovery is only improved approximately 3.5%. In the case of a small ball mill with low grind times, sulfide dose optimizes recovery. Sulfide dose would not be important in the case where excess grinding capacity exists. All of the variables can be manipulated together using various graphing techniques to optimize the specific flotation requirements for the specific orebody. In the case of the Mt. Hagen deposit, Table VI identifies the rougher flotation variables that would be expected to maximize the recoveries in Mt. Hagen ore. Table VI: Mt. Hagen Optimal Rougher Flotation Parameters Factor
Parameter
Grind Time
30 MinS
Float Time
15 TO 17.5 MinS
pH
10.5
Sulfide Addition
Yes
In summary, in real world situations where limited representative testing material is available or cost and time are significant issues, proper design of experimentation using STAT-EASE has the ability to identify statistically valid subsets and allow for rapid optimization and design. The Application to Flotation Testing of a Copper, Cobalt and Gold Ore The Idaho Cobalt Project deposits owned by Formation Capital Corporation are situated within the Idaho Cobalt Belt, a mineral district characterized by stratiform occurrences of cobalt, copper, and gold. The Sunshine, East Sunshine, and Ram deposits occur associated with biotite-rich interbeds of volcanic origin within a series of coarsening-upward sequences of argillite, siltite, and quartzite of the middle unit of the Yellowjacket Formation. The main cobalt ore mineral is cobaltite
(CoFe)AsS while the main copper mineral is chalcopyrite (CuFeS2). The cobaltite grains are generally small, ranging from less than 10 microns to 1 millimeter. The mineralization in the nearby Sunshine and Ram deposits is low in sulfides. Oxidation is prevalent near surface especially where pyrite is present. Gold and silver is present in most of the ores in the area. The Proven and Probable reserves, containing an average of 30% dilution mainly due to narrow high-grade horizons amount to 1,093,818 tons at a grade of 0.65% cobalt, 0.49% copper and 0.6 grams per tonne of gold. Recently, CAMP has completed flotation test work on core from the 1999-2000 Ram drilling program and large diameter PQ core using the STAT EASE design of experimentation methodology (Anderson, 2002). The PQ core drilling yielded samples of the quality listed in Table VII. TABLE VII: The Analysis of Ram Ore Core Samples Sample 4-3021 5-3021 6-3021 3-3022 4-3022 5-3022 7-3022 2-3023 3-3023 4-3023 5-3023 6-3023 7-3023
Co, % 0.482 0.364 0.932 0.162 2.130 0.109 0.123 0.025 0.851 0.284 0.834 0.494 1.010
Cu, % 0.074 0.360 0.286 0.028 0.050 0.366 0.123 0.929 0.037 0.074 0.389 1.630 0.285
Au, t.o../ton 0.018 0.018 0.044 0.014 0.032 0.016 0.046 0.014 0.038 0.016 0.018 0.012 0.048
A bulk composite sample was made up for metallurgical testing from a combination of these samples. As well, samples of 4-3021, 4-3022, 2-3023, 3-3023, 6-3023 and 7-3023 were split out and saved for comparative flotation testing of individual horizons. The metallurgical testing ore composite assays are illustrated in Table VIII. Table VIII: Composite Ram Ore Head Grade Co, % 0.574
Cu, % 0.294
Au, t.o./ton 0.020
Flotation Testing and Optimization In order to provide pay metal maximum recovery, simplify the milling circuit design and operation and minimal environmental tailings impact, it was decided to produce a bulk copper, cobalt and gold bearing concentrate. A statistically valid test matrix was setup using STAT-EASE modeling software and lab bulk flotation testing was carried out on composite ore sample. Variables tested included grind time, rougher collector type and dosage, scavenger collector type and dosage and the use or not of copper sulfate as an activator. Not including replicates, full factorial flotation testing would
require sixty four tests to validly determine the affects of these variables. A statistically valid one quarter (i.e., sixteen tests) STAT-EASE test matrix was set up along with midpoints and replicates. This amounted to only twenty tests as opposed to sixty four. Then, sequential rougher and scavenger flotation testing was carried out on the composite ore sample. The details are shown in Tables IX and X. Table IX: Flotation Recovery Testing Criteria 1,000 grams of ore at 50% ball mill solids with a 43% volume charge. Frother is always AF 65 at 0.1 grams. Copper sulfate activator conditioning is always 10 minutes. Solids Density is 400 g/L. Float cell volume is 2.5 liters. Rougher collector conditioning is always 5 minutes. Rougher flotation is always 5 minutes. Scavenger collector conditioning is always I minute. Scavenger flotation is always 5 minutes. PAX is Potassium Amyl Xanthate. SIX is Sodium Isopropyl Xanthate. Table X: Design of Experimentation One Quarter Matrix for Six Variables Grind
Activator
Rougher
Rougher
Scavenger
Scavenger
Test
Time
Dosage
Collector
Dosage
Collector
Dosage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
75 min 75 min 75 min 45 min 45 min 45 min 45 min 75 min 75 min 75 min 45 min 75 min 45 min 75 min 45 min 45 min 75 min 75 min 60 min 60 min
0.0 g 0.0 g 1.0 g 0.0 g 1.0 g 1.0 g 1.0 g 1.0 g 0.0 g 0.0 g 0.0 g 1.0 g 1.0 g 1.0 g 0,0 g 0.0 g 1.0 g 1.0 g 0.5 g 0.5 g
PAX SIX PAX SIX PAX SIX SIX SIX PAX SIX SIX SIX PAX PAX PAX PAX SIX SIX SIX SIX
1.0 g 1.0 g 1.0 g 1.0 g 1.0 g 1.0 g 0.25 g 0.25 g 0.25 g 0.25 g 0.25 g 1.0 g 0.25 g 0.25 g 1.0 g 0.25g 1.0 g 1.0 g 0.625g 0.625g
SIX PAX PAX PAX PAX SIX PAX PAX PAX SIX SIX SIX SIX SIX SIX PAX SIX SIX PAX PAX
The rougher testing grade and recovery results are shown in Table XI.
0.25 g 1.0 g 0.25g 0.25g 1.0 g 0.25g 1.0 g 0.25g 1.0 g 0.25g 1.0 g 1.0 g 0.25g 1.0 g 1.0 g 0.25g 1.0 g 1.0 g 0.625g 0.625g
Table XI: Flotation Optimization Testing Results
Test 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Co Rec., % 92.82 90.88 93.81 87.26 90.00 85.54 80.44 92.28 91.99 89.63 64.04 91.23 88.49 92.68 90.82 91.99 94.73 93.47 91.33 92.64
Cu Rec., % 90.86 91.25 91.15 90.79 90.08 88.90 87.69 85.86 92.47 89.28 89.70 89.38 89.67 89.66 92.66 92.74 91.71 88.14 91.81 91.32
Average
89.30
90.26
Co %, Cu %, Rougher Rougher Au Rec., % Conc. Grade Conc. Grade 73.13 4.47 3.06 73.38 7.78 3.49 47.98 6.00 3.84 72.92 5.68 2.19 86.33 6.17 4.25 53.36 10.05 6.92 72.16 10.24 5.66 72.30 8.04 4.65 74.47 5.76 2.51 73.75 4.70 2.52 72.48 4.33 7.52 86.99 5.92 3.02 73.21 9.45 6.24 73.18 5.35 3.08 68.05 3.71 2.00 75.38 7.01 4.46 66.37 3.88 3.07 73.86 6.11 4.76 67.89 3.97 1.87 76.09 4.03 3.16 71.66
6.13
3.91
Au o/T, Rougher Conc. Grade 0.104 0.072 0.180 0.066 0.066 0.112 0.278 0.092 0.582 0.120 0.192 0.108 0.246 0.24 0.10 0.16 0.11 0.17 0.13 0.11 0.16
All of these test results were modeled using the STAT EASE software. Due to space constraints not all of the results will be presented. However, illustrative of the robustness of this testing methodology, even minor ore constituents such as gold were effectively and accurately modeled with limited statistically based lab testing. The computer model results for gold follow.
Table XII: STAT-EASE Design of Experiment Gold Recovery Data
Figure 4: Gold Analysis of Variance Data
Factor Intercept A-Grind, min B-Rougher Collector C-Rougher Dosage D-Scavenger Collector E-Scavenger Dosage F-Activator Dosage AB AD AF BF ABF
Coefficient Estimate 71.82 0.081 0.35 -1.55 -0.048 4.06 -1.13 4.36 4.91 -0.66 0.16 4.66
DF 1 1 1 1 1 1 1 1 1 1 1 1
Standard Error 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65
t for Ho Coeff=0 0.12 0.54 -2.37 -0.074 6.22 -1.73 6.67 7.52 -1.01 0.25 7.13
Prob>(t) 0.9077 0.6200 0.0767 0.9448 0.0034 0.1593 0.0026 0.0017 0.3716 0.8151 0.0020
Figure 5: Statistical Model Final Fit as a Function of Variables and Variable Interactions Gold Recovery, % +71.82 +0.081 +0.35 -1.55 -0.048 +4.06 -1.13 +4.36 +4.91 -0.66 +0.16 +4.66
= *A *B *C *D *E *F *A*B *A*D *A*F *B*F *A*B*F
Figure 6: Final Statistical Model Equation in Terms of Coded Factors
VIF 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Gold Recovery, % +84.10 -0.26 +2.82 -2.07 -39.40 +5.42 +19.98 +0.041 +0.66 -0.35 -36.97 +0.62
= * Grind, min * Rougher Collector * Rougher Dosage, lb/ton * Scavenger Collector * Scavenger Dosage, lb/ton * Activator Dosage, lb/ton * Grind, min * Rougher Collector * Grind, min * Scavenger Collector * Grind, min * Activator Dosage, lb/ton * Rougher Collector * Activator Dosage, lb/ton * Grind, min * Rougher Collector * Activator Dosage, lb/ton
Figure 7: Final Statistical Model Equation in Terms of Actual Factors Table XIII: Actual Gold Recovery Values Versus the Predicted Statistical Model Values
The individual fitted results of all the computer modeling for cobalt, copper and gold recovery and grade were then simultaneously optimized. To do this, the individual derived flotation model equation results were inputted to a spreadsheet in terms of maximizing recovery of metal content and value. The total recovery value was calculated in the model by using prices of $0.90/USD /lb of Cu, $10.00/USD/lb of Co and $275.00/USD/t.o. of Au for the metals values recovered. The optimized and fitted model output was as follows.
Table XIV: Stat-Ease Statistical Model Flotation Equation Spreadsheet Optimization Model Predicted Co Recovery = Predicted Cu Recovery = Predicted Au Recovery =
94.68 % 90.97 % 68.86 %
Co Value Cu Value Au value
$ 108.70 $ 4.81 $ 3.79
Spreadsheet Optimized Conditions Total Value $ 117.30 Grind Time 75 min Rougher Collector PAX Rougher Dosage 1.0 g Scavenger Collector SIX Scavenger Dosage 1.0 g CuSO4 Activator Dosage 1.0 g Analogous, cleaner flotation optimization work followed by confirmatory locked cycle testing was also undertaken to successfully develop the final flowsheet. Due to space limitations in this paper, this will not be illustrated and the reader is directed to a related publication for these details (Anderson 2002). Application to Optimization of a Hydrometallurgical Jarosite Circuit Stillwater Mining operates two PGM ore milling facilities in Montana. One is at the East Boulder mine while the other is at the mine at Nye. The operation of each is similar and the older Nye facility will be focused on as an operating example (Turk 2000). The Stillwater Nye concentrator has been expanded from 450 to 2700 tonnes per day of ore capacity since it’s startup in 1987. The feed material comes from a jaw crusher system designed to crush the mined ore to minus 150 mm. Further communication is performed via a closed circuit SAG mill, pebble mill and ball milling circuit. This produces a cyclone sized ore product of p80 145 microns that reports to rougher flotation and flash flotation based on size. The Nye concentrator uses four major flotation reagents. These are potassium amyl xanthate promoter, Cytec 3477 promoter, CMC for talc suppression and sulfuric acid for pH adjustment. In essence, the operating philosophy is focused on maximum recovery of all sulfides that bear the PGM’s. The rougher concentrate is subjected to two stages of cleaning followed by final column cell flotation. This produces a bulk copper and nickel sulfide concentrate containing the PGM’s. The tails from the rougher circuit are reground and subjected to middling and scavenger flotation. The final mill tails report to the mine paste backfill plant or the tailings pond. Concentrate is transferred in bins from the East Boulder and Nye mills to the smelter as a filter cake. The concentrate is approximately 10% moisture and contains 0.2% of platinum and palladium per tonne in an approximate ratio of 3 to 1 Pd to Pt. The bins of filter cake are sampled, dried, and pneumatically conveyed to the concentrate bin for smelting in the electric furnace. Recycled PGM bearing automotive catalysts are also fed through this pneumatic system to the electric furnace. The electric furnace feed consists of dry concentrate, limestone, and dust and is fed through an airslide. Converter slag and crushed reverts are fed through two bins located above the furnace. The electric furnace is rectangular with 3 in-line prebaked electrodes. The furnace lining consists of magnesia-chrome refractory bricks, with copper coolers installed in the slag zone.
The furnace produces two products, slag and matte. Furnace slag contains oxide materials (mostly SiO2 and FeO) and is removed several times a day into a pit for aircooling. The slag exits the furnace at 1500-1550°C (2700-2800°F) and when cool is transferred back to the ore milling facilities for recovery of any metals left in the slag. Furnace matte contains about 0.8% per ton of platinum and palladium as well as copper, nickel, sulfur and iron. It is tapped from the furnace approximately every 8 hours into ladles and granulated in preparation for converting. Granulated furnace matte is converted in Top Blown Rotary Converters (TBRC’s) using oxygen. Converter slag is poured into ladles, granulated, dried and returned to the electric furnace. Converter matte is poured into ladles, granulated, dried and transported to the Base Metals Refinery (BMR). The converter matte now contains approximately 2.0 % per tonne of platinum and palladium. All off-gases first pass through baghouses for particulate capture before being cleaned of sulfur dioxide (S02) in scrubbers. Over 99.7% of the sulfur dioxide is captured from the off-gases. A sodium regeneration circuit provides caustic for the scrubbing system. Gypsum generated in the regeneration process is pressure filtered into low moisture cake and is trucked away for resale to the cement or agricultural industries. The Stillwater Base Metals Refinery (i.e. BMR) process consists of matte grinding, atmospheric leaching, pressure leaching, PGM concentrate separation and iron precipitation (Newman and Makwana 1997). First, the converter matte from the smelter is ground batch-wise in a tower mill to yield a 70% solids slurry in water, with 80% of the solids passing 74 pm. The ground matte is leached with the recycled acidic pressure leach solution and oxygen in a series of five cascading agitated tanks. Some of the nickel and iron are extracted from the matte, while some of the copper present in the pressure leach solution is precipitated according to the following typical reactions: NiO + H2SO4 + 0.5 02 ÆNiS04 + H 2 O
(1)
Ni3S2 + H2SO4 + 0.5 02 Æ NiS04 + 2 NiS + H 2 O
(2)
Ni3S2 + 2 CuSO4 Æ Cu2S + 2 NiS04 + NiS
(3)
FeO + H2SO4 + 0.5 02 Æ FeSO4 + H2O
(4)
The dissolved iron remains essentially in the ferrous state under the prevailing low pH (2.0 to 2.2) condition of the atmospheric leach process. Any PGM present in the feed solution are also co-precipitated with the copper. The unleached residue from the atmospheric leach process is separated by thickening and then leached further under elevated temperature and oxygen pressure. The atmospheric leach residue consists essentially of millerite (NiS), digenite (Cu1.8S), djurleite (Cu1.96S) and iron in the form of magnetite and hydrated ferric oxide. The principal reactions in the pressure leach process are of the type shown below. NiS + 2 02 Æ NiS04
(5)
Cu2S + H2SO4 + 2.5 02 Æ 2 CuSO4 + H2O
(6)
Fe2O3 + 3 H2SO4 Æ Fe2(SO4)3 + 3 H2O
(7)
Magnetite, if present, does not dissolve at the relatively low acid concentrations (20 to 25 g/L) and temperature (130 to 135°C) prevailing in the pressure leach process.
The atmospheric leach thickener overflow solution is polish filtered and then treated to precipitate most of the iron as ammonium jarosite, which is filtered and returned to the smelter. The iron precipitation process is necessary to meet the requirements of the nickel-copper sulfate solution customer. The iron precipitation process also acts as a backstop to precipitate or catch any soluble and insoluble PGM that may be present in the atmospheric leach solution. The iron is precipitated as ammonium jarosite according to the following reactions. 2 FeSO4 + 0.5 O2 + H2SO4 Æ Fe2(SO4)3 + 3 H2O
(8)
3 Fe2(SO4)3 +2 NH3 + 12 H2O Æ 2 NH4Fe3(OH)6(SO4)2 + 5 H2SO4
(9)
The matte grinding, pressure leaching, PGM concentrate separation and iron precipitation circuits are designed to operate batch-wise, while the atmospheric leach circuit is designed to operate on a continuous basis during each shift. The plant produces a final readily refined bullion concentrate of about 60% PGM content. As well, by-product nickel sulfate and copper metal are now produced from this zero discharge hydrometallurgical facility. In 1999, CAMP was contracted to optimize the performance of the Stillwater Base Metals Refinery jarosite precipitation circuit. The goal was to find the multivariate operating parameters to substantially reduce residual iron in solution to consistently below 10 ppm. To achieve this bulk representative samples of BMR plant process solutions were provided to CAMP for laboratory testing. Then the pertinent controllable plant variables of pH, temperature and reaction time were tested using STAT EASE Design of Experimentation methodology. The full factorial design matrix for this is illustrated in Table XV. Table XV: STAT EASE Full Design Matrix for Jarosite Precipitation Optimization Std 4 7 6 2 1 3 8 5
Run 1 2 3 4 5 6 7 8
pH 3.50 2.90 3.50 3.50 2.90 2.90 3.50 2.90
Temp, F 210.0 210.0 170.0 170.0 170.0 210.0 210.0 170.0
Time, Hrs. 4.00 8.00 8.00 4.00 4.00 4.00 8.00 8.00
The results of testing were modeled with an adjusted R-squared fit value of 0.9929 or, in real terms, near perfection. The resultant values and those predicated by the fitted model are shown in Table XVI. Figure 8 illustrates the final statistical model equation in terms of actual plant factors. Figures 9 is a graphical illustration with time held constant at four hours of results iron concentration as a function of temperature and pH. In essence, the testing and STAT EASE modeling indicated that plant iron values consistently below 10 ppm would be achieved by increasing the pH to 3.5 and lowering the operating temperature to 170 F while keeping the plant residence time the same as always. These recommendations were made, implemented in the plant and proved successful.
Table XVI: STAT EASE Model Fit of Jarosite Precipitation Optimization Diagnostic Case Statistics Standard Order 1 2 3 4 5 6 7 8
Actual Value 3.65 250.00 3.73 62.50 2.55 250.00 9.43 43.48
Predicted Value 0.42 253.23 6.96 59.27 5.78 246.77 6.21 46.71
Residual 3.23 -3.23 -3.23 3.23 -3.23 3.23 3.23 -3.23
Leverage 0.875 0.875 0.875 0.875 0.875 0.875 0.875 0.875
1.0/Solution Fe, gpl = -5456.14 +1861.19 * pH +24.54 * T, F +22.11 * Time, Hrs -8.35 * pH* T, F -4.92 * pH*Time, Hrs -0.038 * T, F*Time, Hrs Figure 8: Final Jarosite Statistical Model Equation in Terms of Actual Factors
Figure 9: Graphical Illustration of Residual Fe Concentration at Constant Time as a Function of Temperature and pH
The Application to Hydrometallurgical Treatment of an Enargite Concentrate The use of nitric acid in sulfide oxidation is not new. However, only the nitrogen species catalyzed (i.e. NSC) sulfuric acid oxidative pressure leach has ever been built and operated successfully on a long term industrial scale (Anderson 2004). Moreover, it has been thoroughly studied and it has found successful application in oxidation of other feedstocks as well. It offers several definitive advantages. First of all it is the only proven industrial process over the long term for pressure leaching of copper sulfides and direct recovery of precious metals without the use of cyanide. Second, the rate of reaction is much faster and subsequent required reactor volume is thus smaller. Third, the process does not require excessively high temperatures or pressures. Fourth, the oxidation reduction solution potential (i.e., ORP) can be adjusted and controlled to be extremely high so it oxidizes almost any sulfide at low oxygen overpressures. Fifth, the materials of construction are readily available stainless steels so there is no need for titanium cladding or brick with lead liners. Thus, the capital and maintenance costs are less. Also, because of the simpler internal design, direct heat exchange can be utilized in-situ for optimal temperature control. Further, in a manner analogous to existing Ni/Co laterite HPAL systems, the energy from the in-situ heat exchanger can be readily utilized for optimizing the plant heat balance or co-generating electrical power resulting in significant process operating cost savings. Sixth, there is no need for a dip tube or special design radial agitators with cowlings and the like. Oxygen transfer is innate with the enhanced nitrogen species chemistry. So, without titanium, or a titanium dip tube in particular, there is much less oxygen fire danger. Seventh, the design of the feed pump system is far less of a challenge as is the flash system and the choke system. Eighth, like a smelter, precious metals recovery can be high and direct. Ninth, there is no sophisticated chloride chemistry or resultant corrosion issues to deal with. Tenth, by-product elemental sulfur formation, handling and treatment for contained gold recovery is proven and readily accomplished and value added by-products such as sodium sulfate, sodium hydroxide, sulfuric acid, ammonium sulfate fertilizer and gypsum can be produced from the waste streams. Finally, there is minor amount of nitrogen species utilized which reports almost entirely to the gas phase upon autoclave flashing. This is readily destroyed and scrubbed using commercially available equipment. So, there are no major economic or environmental issues with the use of the small amount of nitrogen species utilized. NSC Pressure Leaching Fundamentals The commonly reported leach reaction of a sulfide mineral with nitric acid in conjunction with sulfide acid is shown below. 3MeS (s)+ 2HNO3 (aq) + 3H2SO4 (aq) Æ 3MeSO4 + 3S° (s) + 2NO (g) + 4H2O
(10)
However, it is postulated that the actual reaction species is NO+ and not NO3- . The addition of or presence of NO2- instead of NO3- accelerates the formation of NO+. As shown in Table 17, the NO+/NO couple is capable of an extremely high redox potential. So, NO+ is readily formed from nitrous rather than nitric acid. For example, a convenient source of nitrous acid can be sodium nitrite. When it is added to an acidic solution, nitrous acid is readily formed.
NaNO2 (aq) + H+ Æ HNO2 (aq) + Na+
(11)
Nitrous acid further reacts to form NO+. HNO2 (aq) + H+ Æ NO+ (aq) + H2O
(12)
The NO+ then reacts with the mineral and oxidizes the sulfide to sulfur 2MeS (s) + 4NO+ (aq) Æ 2Me+2 (aq) + 2S° + 4NO (g)
(13)
Of course, at higher temperatures and/or nitrogen species concentrations the sulfide can be fully oxidized to sulfate. Table XVII: Relative Potentials of Hydrometallurgical Oxidizers E°h Oxidant Redox Equation (pH = 0, H2 ref.) Fe+3 Fe+3 + e- Æ Fe+2 0.770 V HNO3 NO3- + 4H+ +3e- Æ NO + 2H2O 0.957 V + HNO2 NO2 + 2H + e Æ NO + H2O 1.202 V O2 (g) O2 + 4H+ + 4e- Æ 2H2O 1.230 V Cl2 (g) Cl2 (g) + 2e- Æ 2Cl1.358 V NO+ NO+ + e- Æ NO 1.450 V As can be seen, nitric oxide gas, NO, is produced from the oxidation of sulfides. As this gas has a limited solubility in aqueous solutions, it tends to transfer out of solution. In the pressure leach system, a closed vessel with an oxygen overpressure is used. The nitric oxide gas emanating from the leach slurry accumulates in the headspace of the reactor where it reacts with the supplied oxygen to form nitrogen dioxide gas. The NO is then regenerated to NO+. Overall this can be viewed as: NO (g) + O2 (g) ÅÆ 2NO2 (g)
(14)
2NO2 (g) ÅÆ 2NO2 (aq)
(15)
2NO2 (aq) + 2NO (aq) + 4H+ ÅÆ 4NO+ (aq) + 2H2O
(16)
Since the nitrogen species is continuously regenerated, its role in the overall reaction as the actual oxidizer is not obvious. The net overall reaction has the sulfide mineral reacting with the acid solution and oxygen to solubilize the metal value into the sulfate solution and form some elemental sulfur. Of course, at higher temperatures and/or nitrous acid concentrations the sulfide would be fully oxidized to sulfate. 2MeS (g) + 4H+ + O2 (g) Æ 2Me+2 (aq) + 2S° + 2H2O
(17)
Overall, the nitrogen intermediates serve as an expedient means to transport oxygen to the surface of the solid particle and allow the resulting reaction to take place at a heightened redox potential. This inherent asset of the unique system precludes the use of high temperatures and high pressures, which lead to higher costs in other pressure leach processes. For example, commonly available stainless steel can be used for the reactor vessel. And, complete oxidation of sulfide to sulfate can be achieved without
the excessive conditions found in other pressure leach systems. Thus, the rapid kinetics of the system leads to smaller reactor volumes and higher unit throughputs. Finally, 99.9% of the nitrogen species utilized in the leach system report to the gas phase when the pressure vessel is flashed and they are readily destroyed and contained by commercially available scrubber systems. So, environmental impacts are minimized and the NSC leach plant solutions contain little or no nitrogen species. Recently, this proven industrial pressure leaching technology has been applied to the treatment of copper enargite concentrates. The initial testing was guided and optimized by Stat Ease Design of Experimentation software. The copper concentrate analysis used in testing was as follows. Table XVIII: Analysis of Copper Enargite Concentrate Cu, % 19.7
Fe, % 24.3
As, % 5.43
TS, % 34.3
For this Stat-Ease Design Expert software was used. The ¼ testing matrix shown in Table XIX. was set up and the tests were run according to this table and the conditions shown in Table XIX. Table XIX: STAT-EASE Design Expert ¼ Test Matrix Std 1 7 5 10 3 4 6 2 8 9
Run 1 2 3 4 5 6 7 8 9 10
Grind Time 0 min 0 min 0 min 5 min 0 min 10 min 10 min 10 min 10 min 5 min
Initial Acid Max. Temp. Leach Time 50 g/L 150 C 120 min 100 g/L 130 C 60 min 50 g/L 150 C 60 min 75 g/L 140 C 90 min 100 g/L 130 C 120 min 100 g/L 150 C 60 min 50 g/L 130 C 120 min 50 g/L 130 C 60 min 100 g/L 150 C 120 min 75 g/L 140 C 90 min
Table XX: Nitrogen Species Catalyzed Partial Oxidation Leach Test Conditions Grind Time = Table 18 Initial Free Sulfuric Acid = Table 18 Reactor Working Pressure = 620 kPag Slurry Solids Content = Table 18 Maximum Temperature = Table 18 Total Time = Table 18 Nitrogen Species Concentration = 2.0 g/L
Table XXI illustrates the test results while Figures 10 and 11 indicated the copper optimization equations derived from the successful STAT EASE computer modeling effort. Table XXI: Copper Enargite Concentrate NSC Testing Results Std Run As Rec. Cu Rec Fe, Rec 1 1 38.21 % 38.96 % 80.57 % 7 2 18.34 % 26.56 % 84.15 % 5 3 27.75 % 30.03 % 80.34 % 10 4 48.44 % 53.81 % 78.55 % 3 5 11.38 % 19.18 % 58.29 % 4 6 29.73 % 74.39 % 1.07 % 6 7 65.63 % 68.80 % 69.92 % 2 8 58.99 % 86.92 % 32.17 % 8 9 53.30 % 55.97 % 65.92 % 9 10 48.44 % 53.81 % 78.55 % Cu Recovery +50.10 +21.42 -6.08 -4.76 -0.26 -4.37 +2.00 -2.08
= *A *B *C *D *E *B*C *B*E
Figure 10: Final Equation in Terms of Coded Factors Cu Recovery +62.98042 +4.28375 -0.12732 -0.28707 -0.026375 +0.061833 +2.13467E-003 -2.76833E-003
= * Grind Time * Solids * Initial Acidity * Temperature * Leach Time * Solids * Initial Acidity * Solids * Leach Time
Figure 11: Final Equation in Terms of Actual Factors Table XXII shows the perfect model fit with an R-squared of 1.0. Grind time, initial acidity and percent solids are clearly the key factors for optimizing copper recovery.
Table XXII: Cu Recovery ANOVA for Selected Factorial Model Analysis of variance table [Partial sum of squares] Sum of Source Squares Model 4366.95 A 3670.10 B 295.37 C 181.36 D 0.56 E 153.04 BC 32.04 BE 34.49 Curvature 22.01 Pure Error 0.000 Cor Total 4388.95 Std. Dev. Mean C.V. PRESS Factor Intercept A-Grind Time B-Solids C-Initial Acidity D-Temperature E-Leach Time BC BE Center Point
Standard Order 1 2 3 4 5 6 7 8 9 10
DF 7 1 1 1 1 1 1 1 1 1 9
0.000 50.84 0.000 N/A Coefficient Estimate 50.10 21.42 -6.08 -4.76 -0.26 -4.37 2.00 -2.08 3.71
DF 1 1 1 1 1 1 1 1 1
Mean Square 623.85 6.366E+007 3670.10 6.366E+007 295.37 6.366E+007 181.36 6.366E+007 0.56 6.366E+007 153.04 6.366E+007 32.04 6.366E+007 34.49 6.366E+007 22.01 6.366E+007 0.000
F Value < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
R-Squared Adj R-Squared Pred R-Squared Adeq Precision
1.0000 1.0000 N/A N/A
Standard Error 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
95% CI Low 50.10 21.42 -6.08 -4.76 -0.26 -4.37 2.00 -2.08 3.71
Table XXIII: Diagnostics Case Statistics Actual Predicted Value Value Residual 38.96 38.96 0.000 86.92 86.92 0.000 19.18 19.18 0.000 74.39 74.39 0.000 30.03 30.03 0.000 68.80 68.80 0.000 26.56 26.56 0.000 55.97 55.97 0.000 53.81 53.81 0.000 53.81 53.81 0.000
Run Order 1 8 5 6 3 7 2 9 10 4
95% CI High 50.10 21.42 -6.08 -4.76 -0.26 -4.37 2.00 -2.08 3.71
DESIGN-EXPERT Plot Cu Recovery Design Points
Cu Recovery
100.0
X = B: Solids Y = C: Initial Acidity Actual Factors A: Grind Time = 10.0 D: Temperature = 130.0 E: Leach Time = 60.0
72.8
C: Initial Acidity
81.3
76.0
62.5
81.0
43.8
25.0 50.0
62.5
75.0
87.5
100.0
B: Solids
Figure 12: NSC Pressure Oxidation Enargite Copper Recovery as a Function of % Solids and Initial Acidity With Constant Temperature, Grind Time and Leach Time Table XXIV: Final STAT EASE Optimized NSC Pressure Oxidation of Copper Enargite Concentrate Result Optimized Nitrogen Species Catalyzed Partial Oxidation Leach Conditions. Grind Time = 25 minutes Initial Free Sulfuric Acid = 25 g/L Reactor Working Pressure = 620 kPag Slurry Solids Content = 50 g/L Maximum Temperature = 130 C Total Tine = 60 minutes Nitrogen Species Concentration = 2.0 g/L Particle Size = 80% passing 10 micron Copper Recovery = 96.7 % Iron Recovery = 78.46 % Arsenic Recovery = 87.3 % Acid Generation = 0.1273/g Concentrate % Sulfur Oxidized to Solution = 73.1 % Figure 12 offers a visual model example of copper recovery as a function of % solids and initial acidity while Table XXIV presents the final successfully optimized NSC pressure leach test conditions and results as applied to enargite concentrates.
Summary This paper has illustrated the successful use of statistically valid design of experiments using STAT-EASE design of experimentation software. This methodology provides a low cost and rapid process for real world process laboratory testing, plant optimization and flow sheet development, particularly when minimal financial resources, time and representative samples are a constraint. References 1. Anderson, C. G., The Mineral Processing and Industrial Nitrogen Species Catalyzed Pressure Leaching of Formation Capital's Cobaltite and Chalcopyrite Concentrates, ALTA Ni/Co and Cu International Conference, May 2002, Perth W.A. Australia 2. Anderson, C. G., Applications of NSC Pressure Leaching, Pressure Hydrometallurgy 2004, CIM meeting, Banff, Alberta, Canada, October 2004. 3. Anderson, C.G. and Fayram, T.S, The Use of Design of Experimentation Software in Applied Flotation Testing, Centenary of Flotation Symposium, AuSIMMSME, Brisbane, Australia, June 2005. 4. Anderson, M. J. and Whitcomb, P. J., DOE Simplified: Practical Tools for Effective Experimentation, ISBN: J-56327-225-3, Published May 2000, Productivity, Inc. 5. Box, G.E.P., and Draper, N.R. Empirical Model Building and Response Surfaces ISBN: 0-471-81033-9, Published January 1987, Wiley-Interscience. 6. Box, G.E.P., Box on Quality and Discovery: with Design, Control, and Robustness, Published 2000, Wiley, New York. 7.
Cochran, W.G., Experimental Designs, Published 1957, Wiley, New York.
8. Cornell, J., Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data, 2nd Ed., ISBN: 0-471-52221-X, Published April 1990, John Wiley and Sons. 9. Hinkelmann, K. and Kempthorne, O. (Editor), Design and Analysis of Experiments: Introduction to Experimental Design, ISBN: 0471551783, Published March 1994, John Wiley & Sons. 10. Kempthorne, O., The Design and Analysis of Experiments, Published 1975, Robert E. Krieger Publishing Co., Huntington, New York. 11. Lorenzen, T. J. and Anderson, V. L., Design of Experiments: A No-Name Approach, ISBN: 0-8247-9077-4, Published 1993, M. Dekker, New York. 12. Meyer D. and Napier-Munn T.J. ,Optimal Experiments for Time Dependent Mineral Processes, Australian and New Zealand Journal of Statistics, 1999.
13. Montgomery, D. C, Design and Analysis of Experiments, 5th Ed., ISBN: 0471-31649-0, Published 2001, John Wiley and Sons. 14. Napier-Munn T.J. and Meyer D.H., A Modified Paired T-test for the Analysis of Plant Trials with Auto Correlated in Time, Minerals Engineering, Vol. 12, No. 9, 1093-1109, 1999. 15. Neter, J., Applied Linear Statistical Models: Regression, Analysis of Variance, and Experimental Designs, Published 1990, Irwin, Homewood, Illinois. 16. Newman, L. and Makwana, M., “Commissioning of the Stillwater Mining Company Base Metals Refinery”, Hydrometallurgy and Refining of Nickel and Cobalt, Proceedings of the 27th Annual Hydrometallurgical Meeting, The Metallurgical Society of CIM, Sudbury, Ontario, August 1997. 17. Pazman, A. Foundations of Optimum Experimental Design, Published 1986, D. Reidel, Boston. 18. STAT-EASE Design-Expert Reference Manual, STAT-EASE Corporation, Minneapolis, Minnesota, 2002. 19. Turk, D.J., Stillwater Mining Company Nye Concentrator Operation, SME Annual Meeting, Preprint 00-10, Salt Lake City, Utah, February, 2000. 20. Wu, C.J.F. and Hamada, M. Experiments: Planning, Analysis, and Parameter Design Optimization, ISBN: 0-471-25511-4, Published 2000, Wiley, New York.
