Sampling of Particulate Materials Theory and Practice - 1st Edition - ISBN: 9780444416094, 9780444601353

Sampling of Particulate Materials Theory and Practice

1st Edition

Authors: Pierre Gy
eBook ISBN: 9780444601353
Imprint: Elsevier
Published Date: 1st January 1979
Page Count: 450
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Description

Developments in Geomathematics 4: Sampling of Particulate Materials: Theory and Practice reviews the theory and practice of sampling particulate solids, such as ores and concentrates. With examples borrowed from the mining, metallurgical, and cement industries, the book examines particulate materials of vegetable and mineral origin, including cereals, oil seeds, sugar beets, granulated drosses or slags, bars, plates, and ingots. Organized into nine parts encompassing 34 chapters, this volume begins with an overview of the theory of sampling and sampling-error generating mechanisms. It then discusses the continuous selection and discrete models of the increment sampling process and the materialization of punctual increments. It explains the splitting process and its practical implementation in sampling. Lot and sample preparation, resolution of sampling problems, and problems associated with commercial sampling are also discussed. The book also describes the detection of measurement or sampling biases and inconspicuous losses of material, and the design of automatic sampling plants. This book is a valuable resource for geologists, mining engineers, metallurgists, and analysts.

Table of Contents


Introduction

Historical Summary

First Part - Analysis of the Problem

Chapter 1: Definition of Basic Terms and Notations

1.1. Definition of basic terms

1.2. Statistical definitions and notations

1.3. Estimators - Estimates - Errors - Biases

1.4. Domains and their extent

1.5. Properties of a selective process

1.6. Specific notations

Chapter 2: Logical Approach

2.1. First part - Analysis of the problem

2.2. Second part - Continuous model of the increment sampling process

2.3. Third part - From the continuous model to the discrete reality

2.4. Fourth part - Discrete model of the increment sampling process

2.5. Fifth part - Splitting processes

2.6. Sixth part - Preparation

2.7. Seventh part - Resolution of sampling problems

2.8. Eighth part - Problems associated with commercial sampling

2.9. Ninth part - Automatic sampling plants

Chapter 3: Part of Sampling in Quality Control

3.1. Introduction

3.2. Possibility of direct estimation of a critical content

3.3. Possibility of direct extraction of the analysis sample

3.4. Preparation stages - Preparation errors

3.5. Successive estimators and eventual estimate of the critical content

3.6. Breaking up of the overall estimation error

Chapter 4: Sampling Processes

4.1. Probabilistic and non-probabilistic sampling processes

4.2. Comments on non-probabilistic sampling processes

4.3. Probabilistic processes - Notion of movable and unmovable batches

4.4. Sampling of unmovable lots

4.5. Sampling of movable lots

4.6. Analysis of the increment sampling process

4.7. Analysis of the splitting process

4.8. Comparison of the increment sampling and splitting processes

4.9. Field of application of the increment sampling and splitting processes

Chapter 5: Models of the Increment Sampling Process

5.1. What is a model and what is the use of it?

5.2. Introduction to a group of models of the sampling processes

5.3. Continuous mode

5.4. Discrete model

5.5. Objectives pursued when developing selection models

5.6. Resolution of sampling problems

Second Part - Continuous Model of the Increment Sampling Process

Chapter 6: Heterogeneity of a Continuous Set

6.1. Introduction

6.2. Definition and properties of a homogeneous material

6.3. Description of a heterogeneous material

6.4. Definition of the variogram

6.5. General properties of the variogram

6.6. Experimental determination of the variogram - Logical approach

6.7. Interpretation of the results of a variographic experiment

6.8. Particular case of zero-dimensional lots

6.9. Conclusions

Chapter 7: Reference Selection Schemes

7.1. Introduction

7.2. Systematic selection with random positioning

7.3. Random stratified selection

7.4. Random selection

7.5. Full description of a selection scheme

7.6. Comparison of the three selection schemes

7.7. Field of application of the three selection schemes

Chapter 8: Development of the Continuous Selection Model Continuous Selection Error CE

8.1. Introduction

8.2. Definition of the model

8.3. Distribution of the weight ΜS of active components in the sample S

8.4. Distribution of the weight ΑS of critical component in the sample S

8.5. Correlation between the distributions of MS and AS

8.6. Distribution of the critical content aS of the sample S - Introduction

8.7. Distribution of the critical content aS of the sample S - Case No. 1

8.8. Distribution of the critical content aS of the sample S - Case No. 2

8.9. Distribution of the critical content aS of the sample S - Case No. 3

8.10. Distribution of the critical content aS of the sample S - Case No. 4

8.11. Distribution of the critical content aS of the sample S - Case No. 5

8.12. Distribution of the critical content aS of the sample S - Case No. 6

Chapter 9: Breaking Up of the Continuous Selection Error CE

9.1. Introduction

9.2. Definition of the weighting error and of the quality fluctuation error

9.3. Analysis of the quality fluctuation error QE

9.4. Moments of the quality fluctuation error QE

9.5. Recapitulation

Chapter 10: Short-Range Quality Fluctuation Error QE₁

10.1. Definition

10.2. Mean of QE₁

10.3. Variance of QE₁

10.4. Cancelling and minimizing of QE₁

10.5. Further analysis of the short-range quality fluctuation error QE₁

Chapter 11: Long-Range Quality Fluctuation Error QE₂

11.1. Definition

11.2. Mean of QE₂

11.3. Variance of QE₂

11.4. Comparison of the three selection schemes

11.5. Cancelling and minimizing of σ² (QE₂ )

Chapter 12: Periodic Quality Fluctuation Error QE₃

12.1. Definition

12.2. Occurrence of periodic fluctuations

12.3. Moments of QE₃

12.4. Comparison of the three selection schemes

12.5. Example

12.6. General conclusion concerning the choice of a selection scheme

Chapter 13: Weighting Error WE

13.1. Definition

13.2. Mean of WE

13.3. Variance of WE

13.4. Constant tonnage sampling systems

13.5. Error resulting from the non-uniformity of the cutter speed from one increment to the next

13.6. Particular rate of flow functions

13.7. Conclusions

Chapter 14: Practical Implementation of the Continuous Model Variographic Experiment

14.1. Introduction

14.2. Organization of a variographic experiment

14.3. Analysis of a simple periodic variogram

14.4. Analysis of a non-periodic variogram

Chapter 15: Practical Implementation of the Continuous Model Error Estimation

15.1. Introduction

15.2. Example No. 1 - Lead ore

15.3. Example No. 2 - Feed to the blending system of a cement plant

Third Part - From the Continuous Model to the Discrete Reality Materialization of the Punctual Increments

Chapter 16: Components of the Materialization Error ME

16.1. Introduction

16.2. Increment sampling of flowing streams

16.3. Recapitulation

16.4. Selection, extraction and sampling probabilities

Chapter 17: Increment Delimitation Error DE

17.1. Definition

17.2. Falling stream sampling - correctness conditions involving the cutter geometry

17.3. Falling stream sampling - Correctness conditions involving the cutter speed

17.4. Falling stream sampling - Correctness conditions involving the general lay-out

17.5. Falling stream sampling - Recapitulation of the conditions of delimitation correctness

17.6. Stopped belt sampling

17.7. Two-dimensional sampling

17.8. Cost of correct delimitation

Chapter 18: Increment Extraction Error EE

18.1. Definition

18.2. Analysis of the rebounding rule

18.3. Conditions of extraction correctness involving the material to be sampled

18.4. Conditions of extraction correctness involving the cutter characteristics

18.5. Cutter width and velocity - Experimental determination of the critical characteristics

18.6. Recapitulation

18.7. Cost of extraction correctness

Fourth Part - Discrete Model of the Increment Sampling Process

Chapter 19: Heterogeneity of a Discrete Set

19.1. Introduction and notations

19.2. Definition and properties of homogeneous and heterogeneous materials

19.3. Characterizing the heterogeneity of a discrete set

19.4. General expression of the distribution heterogeneity

Chapter 20: Development of the Discrete Selection Model

20.1. Introduction and notations

20.2. Distributions of NZm, NSk, MSk and ASk

20.3. Distribution of aS critical content of the sample S - Incorrect selection

20.4. Practical implementation of formulas involving sums Σi

20.5. Moments of NS, MS, AS and aS - Correct selection

20.6. Moments of NS, MS, AS and aS - Correct selection - Uniform weighting

20.7. Practical implementation of the results of the discrete model

Chapter 21: Linking Up of the Continuous and Discrete Models Fundamental Error FE - Grouping and Segregation Error GE

21.1. Introduction and notations

21.2. Moments of SE = QE₁ according to the continuous and discrete models

21.3. Analysis of the short-range quality fluctuation error QE₁

21.4. Cancelling and minimizing of the fundamental error FE

21.5. Cancelling and minimizing of the grouping and segregation error GE

Chapter 22: Practical Implementation of the Theoretical Results - Correct Selection

22.1. Introduction

22.2. Estimation of the moments of the fundamental error FE - Introduction of Y and Z

22.3. Estimation of Y and Z - Method No. 1

22.4. Estimation of Y and Z - Method No. 2

22.5. Estimation of Y and Z - Method No. 3

22.6. Properties and practical estimation of c, ℓ, f , g and d

22.7. Resolution of sampling problems involving the fundamental variance

22.8. Practical application of methods No. 1 , 2 and 3

22.9. Recapitulation and conclusions

Chapter 23: Practical Implementation of the Theoretical Results - Incorrect Selection

23.1. Introduction

23.2. Incorrect extraction curve

23.3. Practical determination of the curve of incorrect extraction

23.4. Examples

23.5. Conclusions

Fifth Part - Splitting Process

Chapter 24: Splitting Methods and Devices

24.1. Introduction

24.2. True and degenerate splitting processes

24.3. Coning and quartering

24.4. Riffling

24.5. Fractional shovelling

24.6. Sectorial splitters

Chapter 25: Model of the Splitting Process - Splitting Errors

25.1. Linking up with the existing models

25.2. Moments of the continuous selection error CE

25.3. Minimizing of σ² (CE)

25.4. Delimitation error DE

25.5. Extraction error EE

Chapter 26: Practical Implementation of Splitting Processes - Example - Reduction of Drill Core Samples

26.1. Introduction

26.2. Core sample reduction methodology

26.3. Selection of a core sample reduction scheme

26.4. Examples

26.5. Recommendations

Sixth Part - Lot and Sample Preparation

Chapter 27: Preparation Errors

27.1. Introduction

27.2. Errors resulting from contamination

27.3. Errors resulting from losses

27.4. Errors resulting from alteration of the chemical composition

27.5. Errors resulting from alteration of the physical composition

27.6. Errors resulting from unintentional mistakes

27.7. Errors resulting from frauding or sabotage

27.8. Conclusions

Seventh Part - Resolution of Sampling Problems

Chapter 28: Recapitulation of the Sampling Error

28.1. Analysis of the overall estimation error

28.2. Fundamental error FE

28.3. Grouping and segregation error GE

28.4. Long-range quality fluctuation error QE₂

28.5. Periodic quality fluctuation error QE₃

28.6. Weighting error WE

28.7. Increment delimitation error DE

28.8. Increment extraction error EE

28.9. Preparation errors PE

28.10. Conclusions

Chapter 29: Solvable and Unsolvable Sampling Problems

29.1. Definitions

29.2. Representativeness and cost

29.3. Sampling of three-dimensional objects

29.4. Sampling of two-dimensional objects

29.5. Sampling of one-dimensional stationary objects

29.6. Sampling of one-dimensional flowing streams

29.7. Sampling of zero-dimensional objects

29.8. Sampling of small or valuable objects

29.9. Conclusions

Eighth Part - Problems Associated With Commercial Sampling

Chapter 30: Notion of Equity

30.1. Introduction - Definition

30.2. Properties of the settlement price assumed to be a linear function of the critical content

30.3. Properties of the settlement price assumed to be a non-linear function of the critical content

30.4. Relative importance of bias and random error in commercial sampling

30.5. Conclusions - Recommendations

30.6. Equity - Louis-le Dēbonnaire's splitting method

Chapter 31: Testing the Agreement Between Two Series of Independent Estimates of a Same Characteristic - Discrepancies Between Seller and Buyer

31.1. Introduction

31.2. Notations and definitions

31.3. Testing the hypothesis H = {D = 0 }

31.4. Testing the hypothesis H' = { D‘ = |D| - DA = 0 }

31.5. Practical implementation of the test

31.6. Graphical implementation of the results of the test

31.7. Examples

31.8. Average number of trials necessary to show up a systematic difference

Chapter 32: Testing the Agreement Between an Estimate and the True Value Check of the Sampling Bias

32.1. Introduction - Notations

32.2. Method No. 1 - Absolute method involving a synthetic lot

32.3. Method No. 2 - Relative method involving a reference method or device

32.4. Method No. 3 - Relative method involving a comparison between sample and sampling reject

32.5. Example of application of method No. 2

32.6. Accuracy vs. reproducibility - Example of application of method No. 3

32.7. Critical inspection of a sampling device vs. experimental testing of accuracy

Ninth Part - Automatic Sampling Plants

Chapter 33: Design of Automatic Sampling Plants

33.1. Introduction

33.2. Achievement of sampling accuracy

33.3. Achievement of sampling reproducibility

33.4. Allotment of the expendable sampling variance

33.5. Sampling large tonnages of coarse materials

33.6. Conclusions

Chapter 34: Typical Flow-Sheets of Automatic Sampling Plants

34.1. Introduction

34.2. Sampling of a bauxite ore

34.3. Sampling of a nickel ore

34.4. Sampling of an iron ore

34.5. Sampling of the raw mix fed to a cement factory

34.6. Commercial sampling of uranium concentrates

References

Index

Details

No. of pages:
450
Language:
English
Copyright:
© Elsevier 1979
Published:
Imprint:
Elsevier
eBook ISBN:
9780444601353

About the Author

Pierre Gy

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