代做EAEE E4200 Fall 2024 Homework 2调试SPSS
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1. Analytical Methods [5 pts]
Indicate the uses for each of the following analytical methods, and whether the measurement gives information about a bulk (whole particle), a near-surface (outer few microns), or a surface (outer few nanometers) property. Note that some methods can yield information about more than one property (e.g., a bulk property and a surface property, such as axial ratio and reflectivity respectively).
|
Method |
Bulk, near-surface, or surface |
|
Particle size by light scattering |
Can be used to determine both the size and shape of colloidal particles Bulk |
|
Atomic Force Microscopy |
High magnification and imaging of the surface of an object Surface |
|
Machine vision systems |
An imaging-based method for automated detection and analysis using computers and software Bulk and surface |
|
Optical microscopy |
Using optical lenses to produce image magnification Bulk and surface |
|
Nuclear Magnetic Resonance |
It is mainly used to study the structure, dynamics and interactions of matter near-surface |
|
Magnetic Resonance Analyzer |
Instruments that use the principle of nuclear magnetic resonance (NMR) to analyse the composition and structure of substances near-surface |
|
X-Ray Fluorescence |
This technique is used for elemental and chemical analyses, especially for the study of metals, glass, ceramics and building materials. Near-surface |
|
X-Ray Diffraction |
The discipline of using X-rays to study the arrangement of atoms in crystals Near-surface |
|
X-Ray Transmission |
A technique for analysing the internal structure and composition of materials by using the principle that X-rays penetrate substances, used in medical imaging and other technologies. Near-surface |
|
X-Ray Photoelectron Spectroscopy |
is a quantitative spectroscopic technique that can be used to line-analyse the elemental composition of an entire surface surface |
|
Contact angles |
A measure of the degree of wetting of a solid by a liquid surface |
|
SEM-EDX, MLA, or QEMSCAN |
Quantitative analysis of the composition and distribution of minerals Surface and near-surface |
|
Near infra-red spectroscopy |
Obtaining information by measuring the absorption and reflection of near-infrared light from a sample, mainly used to analyse the composition, structure and physical properties of materials Near-surface |
|
Mid-range infra-red spectroscopy |
Mid-infrared spectroscopy provides more detailed molecular structure information than near-infrared spectroscopy Near-surface |
|
Raman spectroscopy |
Provides information on the structure and chemical composition of molecules by measuring the scattering properties of a sample in response to incident light. Near-surface |
|
ICP-MS (Inductively Coupled Plasma + Mass Spectroscopy) |
Used to analyse isotopic composition in samples Near-surface |
|
Laser Induce Breakdown Spectroscopy |
It obtains information on chemical composition by exciting the surface of the sample to produce a plasma and then analyzing the spectrum it emits. surface |
|
Human vision |
When no equipment is available, we can determine the size, surface colour and other information about the mineral Bulk and surface |
2. Liberation [20 pts]
What degree of liberation is most preferred? 8 statements are given in the Table below. Using this table, answer the following 3 questions.
a) Select the ones that you believe are the most appropriate. Indicate by YES
b) Rejecting the ones that are not appropriate. Indicate by REJECT
c) RANK the selected ones in the order of importance 1, 2, 3, etc.
Note: The mineral processing plant is the whole plant; it comprises various departments related to the various parts or stages of mineral processing (from crushing all the way to mineral concentrate shipment. The various stages were shown in multiple lectures. For this exam problem Mining, hydrometallurgy, and pyrometallurgy are not included.
|
Degree of Liberation |
Reject or priority # |
|
Sufficient liberation to meet the production (tons) target for the value metal or mineral concentrate of the mineral processing plant |
6 |
|
Sufficient liberation to achieve 90% recovery at an acceptable concentrate grade |
7 |
|
Go all the way - Target Full (100%) liberation to achieve the maximum value element (or mineral) recovery and concentrate grade |
Reject |
|
Sufficient liberation to meet specifications for a saleable concentrate (i.e., mineral product) (e.g., arsenic limit) |
Yes 1 |
|
Sufficient liberation to meet the KPI (key performance index; aka performance goals for operators and management) of the comminution department |
5 |
|
Sufficient liberation to meet the economic model of the mineral processing plant |
3 |
|
Sufficient liberation to meet the KPI of the minerals separation department |
4 |
|
Sufficient liberation to meet the production cost for the mineral processing plant |
2 |
3. Sampling [30 pts]
3.1 A copper ore sample, with a weight of 1.8 kg, contains 3% Cu as CuFeS2 (chalcopyrite) with an assay accuracy of ±0.4% Cu at the 95% confidence level. The mean densities of the chalcopxyrite and gangue minerals are 4.25 and 2.65 g/cm3, respectively. Consider that this ore has a 0of 0.015 m, and that chalcopyrite is essentially liberated from quartz gangue at a particle size of 170 μm. To what particle size must the ore be crushed so that accuracy in the assay of the sample weight will be ±0.1% Cu rather than ±0.4% at 95% confidence? If it is desired to take a sample from the pulp stream after grinding the ore to its liberation size for recovery of chalcopyrite by flotation, what is the minimum sample weight to be taken in order to give an accuracy of ±0.05% at 95% confidence? Assume that classification has given fairly close sizing. Show your calculations.
Hint:
Make use of Gy’s Formula
and the sampling mineralogy constant
Where:
M = Minimum weight of sample [g]
s = Statistical error in sampling
f = Shape factor
g = Particle distribution factor
m = Mineralogical factor
a = Fraction average mineral content of the mineral being sampled
r = Mean density of valuable [g/cm3]
t = Mean density of gangue [g/cm3]
l = Liberation factor
d = Dimension of largest particle in material to be sampled [cm]
3.2. Using the same data in Problem 1, calculate the minimum weight to be taken in order to give an accuracy of ± 0.05% at 95% confidence if the particle size is 300 μm? Show your calculations. How does it compare to the previous result? Discuss your results and conclusions.
So as the accuracy( the number of accuracy of ± N% decrease) and size increase, the sample weight increase.
3.3. List the six factors that affect the amount of sample to be taken and specify their effects on the amount of sample to be taken.
Minimum weight of sample positive correlation with Error(when error increase, the S value decrease) Shape factor, Mineralogical factor, Liberation factor , Mean density of valuable ,Mean density of gangue
4. Particle Size Distributions [25 pts]
Sieve analysis is a common method of determining rough-cut particle size distributions. A ground ore sample is sifted through a stack of screens of decreasing aperture sizes. This is usually done with some vibration to get all the material through to where it belongs. The weight of solids retained on each screen is determined and weight fractions are then computed. The screens are stacked with the smallest aperture screen on the bottom and the largest aperture screen on the top. The size range of material captured on any one screen is designated by two numbers:
i) Minus (-) the aperture size of the screen above
ii) Plus (+) the aperture size of the screen where the material is retained.
Thus, a designation of “-6.80 mm to +4.75 mm,” indicates that the ‘effective’ diameters of the retained particles are in the range of 6.80 mm to 4.75 mm, i.e., 6.80 > D > 4.75 mm.
Use the raw sieve analysis data, measured for a ground ore sample, listed in the table below.
There are several possible ways to represent the data, many of which distort the appearance of the data in some way. Make graphical representations of the data as requested and answer questions 4.1 – 4.5. Also, briefly discuss the merits and shortcomings of each with respect to representation of the different size regions (i.e., fine, and coarse regions of the size distribution). For example, does each way of plotting the data either over-emphasize or under-emphasize a particular feature of the data? Note that the actual screen aperture size for an individual screen is the ‘lower size limit’, i.e., the (+) value in the table below. The (-) number is the aperture size for the screen above it. You may want to construct a data and calculations table (in Excel or other software) to help you answer the questions and construct the plots.
4.1 Fraction (wt.%) retained vs. diameter (aperture lower size limit), linear-linear scale. Use a line plot. Are the points equally spaced on the horizontal axis?
4.2 Fraction (wt.%) retained vs. diameter (aperture lower size limit), linear-log scale. Use a line plot. Are the points equally spaced on the horizontal axis?
4.3 Cumulative fraction (wt.%) retained vs. aperture lower size limit, linear-log scale. Use a line plot.
4.4 Cumulative fraction (wt.%) passing vs. aperture upper size limit, linear-log scale. Use a line plot.
4.5 Cumulative fraction (wt.%) passing vs. aperture upper size limit, log-log scale. Use line plot. This is known as a Gates-Gaudin-Schuhmann plot and is based on the Gaudin-Schuhmann model for the particle size distribution
5. Gates-Gaudin-Schuhmann Model vs Rosin Rammler Model [20 pts]
Use data in Problem 3. Make a Rosin Rammler Plot
Determine if the Rosin-Rammler model is applicable to this data and if it is, determine the two fitting parameters.
Which model fits the dataset better? [hint: you can linearize the equations, plot the data using both models, and compare the regression fitness (R2)]
You can refer to the following for help:
· Djamarani, K. M. and I. M. Clark (1997.). "Characterization of particle size based on fine and coarse fractions." Powder Technology 93(2): 101-108. Section 2
· https://www.sagmilling.com/articles/2/view/RosinRammlerRegression.xls?s=4
· Wills and Finch (2016) Wills’ Mineral Processing Technology: An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery; 8th ed., section 4.3.4
