Sampling 2018 Esbensen Keynote Universal Power Of Tos ... 201018.pdf

KHE Consulting

The universal power of the Theory of Sampling (TOS) Why is sampling the critical success factor before analysis?  for the seller; for the buyer ; for the middleman, for the arbiter ?  for the company; for the customer; for the scientist; for the technician?  for science, technology, industry; for compliance; for safety; for society?

Keynote copyright: KHE Consulting

KHE Consulting

Theory and Practice of TOS Representative Sampling A minimum understanding of governing principles and sampling unit operations - all types of materials (all degrees of heterogeneity: low – intermediate – high - at all scales (for all lot sizes: small – intermediate – big – extreme) - unifying principles of representative sampling: field/plant/laboratory/process Keynote copyright: KHE Consulting

Kim H. Esbensen

- who / what / when ….

Geological Surveys of Denmark & Greenland (GEUS) research professor (chemometrics and sampling) 2010

-2 01 5

Aalborg University, prof. (chemometrics & sampling) 2001

19 79

Telemark University of Process Technol. (HIT), prof. 1991 Norwegian Computing Center (NCC) & SINTEF

1985

Terra Swede (exploration)

1982

Technical University of Denmark (DTH), Ph.D.

1981

Århus University, Denmark: M.Sc. (geology),

1979

1991 1981

19 8

0

-2

01 5

2001 2011

1980 – 2015: professor (3 universities/gov. R&D institutions) 2015  consultant, independent researcher (assoc., guest and affiliated professor at 4 universities)

[email protected]

How to take a representative sample of all this XXXX .... ?

Well, one fine day I will know ... hopefully!

Lappeenranta University of Technology (LUT) - 1999

2000  Fast forward ...

Theory of Sampling (TOS) – everything in a glance

The anal ytica l lab orato ry

Incorrect sampling errors (ICS)

Measurement Uncertainty (MU)

IDE IWE IEE

IPE

Theory of Sampling (TOS) FSE

PIE2

”an ya naly tica lm o da lity ”

PIE1 GSE

Correct sampling errors (CSE)

PIE3

Process sampling errors (PSE)

MUtotal = MUsampling + MUanalysis

Representative Sampling: Theory of Sampling (TOS) TOS - Axiomatic exposé Governing principles (GP) – Sampling unit operations (SUO) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

FSP: Fundamental Sampling Principle SSI: Sampling Scale Invariance PSC: Sampling Correctness (bias-free sampling) PSS: Sampling Simplicity (primary sampling + mass-reduction) LDT: Lot Dimensionality Transformation LHC: Lot Heterogeneity Characterization (0-D, 1-D) SUO: Composite Sampling SUO: Comminution SUO: Mixing / Blending SUO: Representative Mass Reduction (Sub-sampling)

Composite sampling employs Q increment extractions with the aim to ‘cover’ the lot volume (only Q = 4 increments shown in this principal illustration). Proportional to the heterogeneity encountered, a higher number of increments will be required. Comp samp. must always respect FSP !!! GP (6) Lot Heterogeneity Characterisation (LHC) guarantees that no sampling plan, sampling procedure nor sampling equipment is employed without a mandatory heterogeneity characterisation of the lot material. Composite sampling is specifically demanding that grab sampling (extraction of one single increment only) is never invoked, unless thoroughly tested and accepted by either a Replication Experiment (RE) or by variographics.

Crushing (comminution) is a sampling unit operation which is only brought to bear when necessary, i.e. when the top particle size is contrasting too much with respect to smaller size ranges in order for sampling to be effective and representative. Comminution is the technical process in which the top particle sizes is preferentially crushed first. A consequence of crushing/comminution is that the majority of particle sizes tend to become more similar, with the further advantage that mixing becomes more effective. Maceration, crushing or shredding in the presense of a facilitating liquid (often used for selective extraction), as applied to biological materials also lead to reduced general particle sizes.

Mixing is a forced mechanical process designed to reduce the distributional heterogeneity (DH) of a material system. It is always advantageous to mix the results of a sampling or a sub-sampling process before further processing (sub-sampling or a next stage mass reduction). Blending is mixing under stoichiometric constraints, i.e. the final mixing product, a blend, must satisfy compositional constraints e.g. tea, tobacco, cement, pharmaceutical drugs. Mixing / blending can be applied to both polyphase dry systems (aggregates) and to slurries (solid – liquid systems).

Representative Mass Reduction (RMR) is the key sampling unit operation connecting all sampling stages. Often the terms mass reduction and sub-sampling are used inter alia. There are very many sub-sampling procedures and types of equipment offered on the market, but far from all deliver representative solutions. For stationary lots, the benchmark study by Petersen et al. (2004) showed conslusively that only the rifflesplitting principle lead to Representative Mass Reduction (RMR). Riffle splitters have different physical manifestations; both stationary and roraty solutions exist. For dynamic lots, lots in movement, the Vezin sampler is by far the most effective, fully representative RMR equipment in existence. The Vezin sampler is also superior regarding slurries a.o.

Representative Sampling: Theory of Sampling (TOS) TOS - Axiomatic exposé Governing principles (GP) – Sampling unit operations (SUO) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

FSP: Fundamental Sampling Principle SSI: Sampling Scale Invariance PSC: Sampling Correctness (bias-free sampling) PSS: Sampling Simplicity (primary sampling + mass-reduction) LDT: Lot Dimensionality Transformation LHC: Lot Heterogeneity Characterization (0-D, 1-D) SUO: Composite Sampling SUO: Comminution SUO: Mixing / Blending SUO: Representative Mass Reduction (Sub-sampling)

Sampling Unit Operations: Composite Sampling

”Grab Sampling” - ”not thinking”

… … vs. Composite Sampling … …

51.02% RSV 07%

47.62% ling p m a ite s s o p m o c t n reme c n i 42

5.95% RSV 17%

4.96%

Concentration

Replication Experiment (10fold) of grab vs. composite sampling Single grab sampling variance

Composite sampling variance aL

True lot concentration

Proper sub-sampling … proper ??

Probably the world’s worst manual ”composite sample”

It so easy to do it WRONG – and so easy to do it RIGHT (representatively)

Teaching TOS by analogy ...

Model photo: with permission

Representative Sampling: Theory of Sampling (TOS) TOS - Axiomatic exposé Governing principles (GP) – Sampling unit operations (SUO) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

FSP: Fundamental Sampling Principle SSI: Sampling Scale Invariance PSC: Sampling Correctness (bias-free sampling) PSS: Sampling Simplicity (primary sampling + mass-reduction) LDT: Lot Dimensionality Transformation LHC: Lot Heterogeneity Characterization (0-D, 1-D) SUO: Composite Sampling SUO: Comminution SUO: Mixing / Blending SUO: Representative Mass Reduction (Sub-sampling)

Representative Sampling: Theory of Sampling (TOS) TOS - Axiomatic exposé Governing principles (GP) – Sampling unit operations (SUO) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

FSP: Fundamental Sampling Principle SSI: Sampling Scale Invariance PSC: Sampling Correctness (bias-free sampling) PSS: Sampling Simplicity (primary sampling + mass-reduction) LDT: Lot Dimensionality Transformation LHC: Lot Heterogeneity Characterization (0-D, 1-D) SUO: Composite Sampling SUO: Comminution SUO: Mixing / Blending SUO: Representative Mass Reduction (Sub-sampling)

A grab sample ...

Fundamental Sampling Error (FSE) [+ GSE]

Several increments ... ...

Trying (very well) to deal with (GSE) [+ FSE]

Heterogeneity (hidden) Lot (1-, 2 & 3-D)

Fundamental Sampling Principle (FSP): All increments must have the same (non-zero) probability of ending up in the sample (non-neg)

FSP

A dve r

se cha racter Heter istic: og e ne ity

Sampling rate (typical)

103 – 106 Primary sample

101 – 102 Secondary sample

101 – 102 Tertiary sample / aliquot

Traditional laboratory domain

103 –3 106 -6 109 9 10 –3 10 -6 10 9 10 – 10 - 10

This is too expensive!

Well, well ...

Fundamental insights - I

 The empowering role of universal principles & SUO’s

Governing principles (GP) & Sampling Unit Operations (SUO))

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

FSP: Fundamental Se Invariance PSC: Sampling Correctness (bias-free sampling) PSS: Sampling Simplicityampling Principle SSI: Sampling Scal (primary sampling + mass-reduction) LDT: Lot Dimensionality Transformation LHC: Lot Heterogeneity Characterization (0-D, 1-D) SUO: Composite Sampling SUO: Comminution SUO: Mixing / Blending SUO: Representative Mass Reduction (sub-sampling/splitting) TOS’ six & Governing how to conduct All GP’s SUO’s are Principles not involveddescribe in all sampling tasks. representative sampling of heterogeneous materials. The analysis & the sampling objective determines which The the only active agents at disposition. GP’sfour andSUO’s SUO’s are to use. The Theory of Sampling (TOS) to the fore ... DS 3077: First horisontal standard (2013)

www.ds.dk

DS-3077

TOS’ six Governing Principles describe how to conduct representative sampling of heterogeneous materials. (for some ..) The four SUO’s are the only active agents at disposition.

An important analogy

Maxwell's Equations describe the world of electromagnetics. The four equations describe how electric and magnetic fields propagate, interact, and how they are influenced by objects

Fundamental insights - II

 The role of statistics – in sampling and analysis

- very difficult to avoid conventional thinking … depend … -statistical because population the analytical results on the sampling procedures used .... !!! !!!

xāavr

Empirical distribution of anal. results

Heterogeneity is different in nature ..... (this is difficult – at first) Heterogeneity is different in nature ..... (this is difficult – at first) The lot: a population of anal. results

The anal ytica l lab orato ry

Theory of Sampling (TOS) All four– SUO’s in action in the laboratory ... everything inanalytical a glance

Work effort considerations vs. REPRESENTATIVITY There is no case – Representativity must come first – always!

12 kg – fully crushed (TOS) compared to 20 g (grab) – ratio 600: 1

Representative mass reduction ---- ??

Alternate shoveling

Rotational dividers

Boerner divider Fractional shoveling

Grab Sampling The “spoon method”

Riffle splitting

The ”Japanese slab cake” approach:

The ”Spoon method”

Open splitter

Closed splitter

A pro pos ”rotating splitters ...” ”subsequent scraping off ...???” ”radial segment”

Coning & quartering is a popular mass reduction approach

A hidden elephant in the room .... VERY in-effcient mixing is the real reason that coning & quartering is one of the worst mass reduction approaches

”Sampling Hall of Shame – BIG TIME ”Coning & Quatering”

An often overlooked factor: HIGHLY INSUFFICIENT lot pre-MIXING !!!

Representativeness (pooled sum for wheat, rape seed and glass) 0,600

0,400

0,300

0,200

0,100

RK

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g d g 5 g er al m m m lin 1: m ho itt lin lin p t m m m l r e e + e o m v v 6 0 0 4 2 Sp N M Sa ho 1: ho f1 f2 1: f3 d 4 n ed e S S o o o b o 3 e o + i o r S ra al Fe te es es 2 es G RK Sp ut ut 1: ut on na Va al i r h h h t o m C C C ri lte ac ni A A Fr 18 10 10 Va RK RK RK

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34

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RK

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qu ar te r in g

0,000

Co ni

Representativeness

0,500

- the analytical result depends on the sampling procedures used ....

NB. Lot sampling & subsampling error can be up to 10-25-50 times higher (dep. heterog.)

GMO lab-sampling and analysis error ~15-20%

Theory of Sampling in to the laboratory Is there an(TOS) alterntive spatula sampling?

Theory of Sampling (TOS) in the laboratory Not just sampling – but HOW TO sample?? ??

?

TOS in the analytical laboratory

The ”Ingamells splitter”

The an alytical laborat o

ry Primary sampling stage ... Secondary ... Tertiary stage ... ...

Primary sampling error ... 10 X 10 X Secondary sampling error ... 10 X Tertiary sampling error ...

Total analytical error ... f.ex. 1% (rel)

Lot

Lot

Primary sampling

Primary sampling

Secondary sampling

Secondary sampling

Tertiary sampling

Tertiary sampling

Laboratory B

Laboratory B - the client’s only guarantee against non-representative analytical results

Laboratory A

Buyer

Seller vs.

Client

Laboratory

Representative sampling Contractual uncertainty interval

Non-representative sampling

Non-representative sampling

Jazz Hall of Fame (Downbeat) Baseball Hall of Fame

Sampling Hall of Fame

Sampling Hall of Shame

”Sample” extraction valves

”On-line” mass reduction equipment ”Inverse flap valve” configuration

Primary sampling collector bin

Flow conduit, toggling Reject outlet i.e. process stream

Sample outlet i.e. mass reduction

It so easy to do it WRONG – and so easy to do it RIGHT (representatively)

Model photo – with permission

All delegates to SAMPLING 2018, Lima have recieved a digital copy of TOS Forum, Issue 8

Teaching by analogy or example

 Barefeet sampling – can be fit-for-purpose

Process engineer: NEED a sample !!

Lightweight Expanded Clay (LECA) production kiln: ~975 C

Sampling Hall of Fame

TOS Forum

Free Sampling Resources from IM Publications impopen.com/tosf

Spectroscopy Europe

Free Sampling Resources from IM Publications spectroscopyeurope.com/sampling

WCSB7 Proceedings

Free Sampling Resources from IM Publications impopen.com/wcsb7

Minerals — Open Access Journal of Mining & Mineral Processing

Special Issue "Sampling across the Mine Value Chain" Minerals (ISSN 2075-163X; CODEN: MBSIBI) is an international peer-reviewed open access journal of natural mineral systems, mineral resources, mining, and mineral processing. Minerals is published monthly online by MDPI. Open Access - free for readers, with article processing charges (APC) paid by authors or their institutions. High visibility: indexed by the Science Citation Index Expanded (Web of Science), Chemical Abstracts, INSPEC and GeoRef. Rapid publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 17 days after submission; acceptance to publication is undertaken in 5.4 days (median values for papers published in the first six months of 2018). Impact Factor: 1.835 (2017) ; 5-Year Impact Factor: 2.037 (2017)

Special Issue "Sampling across the Mine Value Chain" Special Issue Editors Guest Editor

Dr. Simon Dominy

Deadline: December 1.st 2018

Camborne School of Mines, University of Exeter, Penryn, Cornwall TR10 9FE, UK Website | E-Mail Interests: economic geology; sampling/theory of sampling; reserve estimation/evaluation; geometallurgy; mining geology; narrow vein mining; mineral processing Guest Editor

Prof. Hylke Glass Camborne School of Mines, University of Exeter, Penryn, Cornwall TR10 9FE, UK Website | E-Mail Interests: sampling/theory of sampling; geometallurgy; geostatistics; sensor-based mineral sorting; selective leaching; metal bio-accessibility; post-mining revegetation and terragreening

Paper s

Guest Editor

Prof. Kim Esbensen

from S A

MPLIN G

20 18 –

are we lcome in

KHE Consult, Aldersrogade 8, 2. sal, 2100 Copenhagen Ø, Denmark / Geological Survey of Denmark and Greenland (GEUS), Oester Voldgade 10, 1350 Copenhagen C, Denmark Website | E-Mail Interests: sampling/theory of sampling; geochemistry/geoanalysis; process analytical technology; multivariate data analysis; chemometrics

this SI

Novel application: oil pollution monitoring The ”BIOTA GUARD” patented approach

NIR (Near Infra-Red) sensor

Bivalve opening caliper (sensor)

PAT Sampling Hall of Fame

Biosensor time series’ (heart beat & gap opening) 7

6

5

4

3

2

1

0 7 0 5 03 0 1 9 9 97 9 5 93 9 1 89 8 7 85 83 81 7 9 77 75 7 3 71 69 67 65 63 61 59 57 55 53 51 49 47 45 1 2 3 3 4 5 6 7 8 9 10 1 1 12 13 1 4 15 16 17 18 1 9 20 2 1 2 2 23 2 4 25 26 2 7 28 2 9 30

Biosensor time series: ”Let the good times roll ..”

2000 1500 1000 500 0 -500

1 12 23 3 4 45 5 6 67 78 8 9 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 1 1 1 1 1 1 1 1 1 1

-1000 -1500

Measurement variable: Heart beat

Variogram characteristics – no great surprise (yet) 700.000

600.000

500.000

V(j)

400.000

300.000

200.000

100.000

0.000

Lag (j)

Measurement variable: Heart beat

Biosensor time series: ”Let the good times roll ..” 7

6

5

4

3

2

1

0 7 0 5 03 0 1 9 9 97 9 5 93 9 1 89 8 7 85 83 81 7 9 77 75 7 3 71 69 67 65 63 61 59 57 55 53 51 49 47 45 1 2 3 3 4 5 6 7 8 9 10 1 1 12 13 1 4 15 16 17 18 1 9 20 2 1 2 2 23 2 4 25 26 2 7 28 2 9 30

Measurement variable: Bivalve gap opening

Analytical result

Measurement series (blow-up) 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.5

Increment number

Measurement variable:

Bivalve gap opening

Variogram characteristics – no great surprise (yet) 0.000

0.000

0.000

V(j)

0.000

0.000

0.000

0.000

0.000

0.000

Lag (j)

Measurement variable: Bivalve gap opening

Variogram characteristics – sensitivity, specificity Sa mp li

ng

Ha

ll o

fF am e

Bivalve sensors 10,000 more sensitive to trace oil conc. levels NB Dep. upon realistic empirical seawater-oil calibration/validation!

Selective dose-response calibration Interferrant/matrix reponse calib. !!

Multivariate data modelling: chemometrics

X

Y PLS-regression

PLS-regression: Y-data guided projection X-space

Multivariate calibration – powerful, generalized regression: Y-data:

X-data: Geochemistry (descriptors) Spectra (absorption, emission Geophysics (descriptors) Instrumental measurements ... Mineralogy (modal prop.s) Lithology ”Easy-to-measure” data Heavy mineral characteristics Mineralisation/ore charac.s Descriptors …… Variogram ”Input data Geometalurgical X data

Variogram

Geochem. (dependent var.s) Concentration [ppm, %, g/ml] Petrophys. (dependent var.s) ”Wet-chem. Rock mechanicsLaboratory” Mineralisation/ore charac’s ”Difficult, Grindability laborious ...” ... ... Flotability Functional properties Leach recovery …… ”Output data” Spillage – oil concentration

Spectral data

Geometallurgy desc params

Geometallurgy test params

Teaching by analogy or example

 The historical perspective (BIG surprise)

SAMPLING OF MATERIAL OBJECTS Theory and Practice

Pierre M. GY Paris School of Physics & Chemistry, Ph.D Sampling Consultant & Expert E-mail : gy @ pierregy.com --------------Founder & Chairman International Sampling Institute Institut International de L’Echantillonnage (ISI / IIE) E-mail : samp.echant @ wanadoo.fr 97

FIRST PART

PLAN OF THE COURSE STAP 2000 HIT, Porsgrunn, Norway, November 2000

Historical snapshot

HIT, Porsgrunn, Norway, November 2000

FACTORS AT STAKE IN SAMPLING SAMPLING is the first, the most risky, the most neglected and ignored link of … 

QUALITY CONTROL

t IN INDUSTRY and TRADE :

factor at stake is especially the … ECONOMICAL FACTOR

QUALITY IS MONEY

100

the

SAMPLING IN THE LITERATURE Some pertinent, some dubious and some rather surprising remarks … 1930 : Grummel & Dunningham : « Those whose interest in sampling is recent will not easily understand how difficult it has been for the authors to have a new idea adopted » … This sad remark is still valid in 2000 ! 101

SAMPLING AND STANDARDS Standards are usually naïve and written by unqualified people without any regard to scientific considerations. Example of the sampling scoop (ISO) : the handle length alone is optional !

102

Standards impose arbitrary rules to users devoid of any critical formation ! 103

REPRESENTATIVITY All analytical standards state that assays must be carried out on … « REPRESENTATIVE SAMPLES » but these standards …  Fail to give any scientific definition of a « Representative sample »,  Fail to say « what should or should not be done to obtain one ».  A scientific definition of a Representative sample is given in Part 3 « Definitions ». 104

PHILOSOPHY OF STANDARDIZATION According to an ISO officer, the role of the technical committees, ISO/TC, should be « to describe the practices on which trade has been based for a long time ».  No qualification required from TC members  Decisions are taken after a vote !  Practically no standard on sampling is based on scientific considerations. This dubious philosophy encourages lobbying. 

105

ROLE OF UNIVERSITY AND STANDARDS ORGANIZATIONS This role should be major BUT in 2000 University and Standardization go on ignoring the mere existence of a theory which has NEVER been contested by any- one. Exceptions FINLAND and NORWAY 

Equipment manufacturers follow standards that their clients are liable to know. 



Lobbying in ISO Technical Committees ! 106

NINTH PART

BED-BLENDING Theory and Practice

PURPOSE AND PRINCIPLE OF BED-BLENDING Many plants or devices operate much more efficiently or safely when they are fed with a material of quality « as uniform as possible ». This point has been first understood by Lafarge Cements due to the fact that cement kilns are dangerously sensitive to quality fluctuations of their feed. So are metallurgical furnaces. Most transformation processes would benefit from a uniform feed. Bed-blending is the key. 108

The output of the proportioning system has an AVERAGE composition P near the REQUIRED composition C but is absolutely NOT UNIFORM. Its variability is characterized by its variogram… Variograms for CaO

Actual variogram of Proportioning output

Heming Cement Works (France) Flat variogram characterizing a uniform material v(0) >

0

Required variogram of the Bed-blending output

The purpose of Bed-Blending is to transform 10 the RED variogram into a BLUE one (flat). 9

BED-BLENDING SYSTEM TwoSTAGE alternating FROM PROPORTIONING phases

Bed-Blending INPUT

One way

STACKER

2 cm/mn

Stacker reciprocating travel speed

30 m/mn

PHASE 1 t PILE At Phase 1 STACKING

PHASE 2 t PILE B t RECLAIMING Phase 2

UNIFORM COMPOSITION BED-BLENDING OUTPUT

Reclaimer Travel / speed Harrow-type Reclaimer Main Reclaiming Belt

Paddle-chain Conveyor

11

BED-BLENDING t STACKING Stacker speed along the pile  20 / 30 m/mn Photos, courtesy of BMH, Mulhouse, France Feeding belt

Stacker

Pile being built Boom

Reclaimer in idle position

Falling Material

11

BLENDING THEORY t STACKING Reciprocating stacker travel

Stacker

Stacker speed  30 m/mn Future Layer 8 Future Layer 7 Future Layer 6 Future Layer 5 Layer 4 Layer 3 Layer 2

DEAD STOCK

Layer 1

0

Stacking time of one layer Vertical Cross-section of the pile

T0 11

BLENDING THEORY t RECLAIMING Many types of reclaiming devices. After studying the performances of all of them, the « Harrow-type Scraper Reclaimer » appears as the MOST EFFICIENT and can be used as a MODEL FOR THE THEORY OF BED-BLENDING. Its major property is to reclaim a THIN SLICE of the whole pile cross-section SIMULTANEOUSLY (e.g.  2 cm/mn). 113

BLENDING THEORY t RECLAIMING Harrow-type Reclaimer

Slice S reclaimed between t and t + Dt. This slice may be regarded as a … Sample S made of 8 « increments »

8

re

Scraping cycle ½ to 1 mn

Vo lu m e

Pikes

re cl tim aim e t ed b

ef o

7 6 5

4

DEAD STOCK

3 2 1

t

t + Dt

Reclaimer speed  2 cm/mn

Paddle-chain conveyor TO Main reclaiming belt

114

BED-BLENDING t RECLAIMING Harrow-type Reclaimer-Scraper in idle position BMH – Mulhouse, France t Side view Natural angle of repose of the reclaimed material. Can / must be adjusted.

Jig-saw transversal motion Period  ½ to 1 mn

Paddle-chain conveyor. To main reclaiming conveyor (in a trench – not shown here)

Reclaims a thin slice (0.02 – 0.05 m/mn)

115

PROBLEM POSED BY THE PILE ENDS Experiment carried out by BMH, Mulhouse, France

Uniform Composition required

15 to 20 % of the pile must be recycled HAS BEEN IMPROVED BY MANUFACTURERS

Hours

116

VARIOGRAPHIC ANALYSIS OF A BED-BLENDING UNIT The variogram is a mathematical tool that characterizes the variability of a one-dimensional flow. To figure out the efficiency of a bed-blending unit we compare the INPUT and OUTPUT variograms. Variograms for CaO

Heming Cement Works (France)

Input Sill

Input Interval = 90 mn

INPUT Variogram Input Intercept

OUTPUT Variogram Output Interval = 120 mn

vI(0)

Output Intercept and Sill

18 hours

11 7

UNEXPLORED POSSIBILITIES t SCALING DOWN : So far, bed-blending has been implemented only on the scale of heavy industries such as Cement or Metallurgy. But it can very well be scaled down from hundreds of tons to hundreds of kg per hour. t GENERALIZATION : Many industries would increase the quality of their products and their profits if they were fed with a uniform material. t EVEN IN HEAVY INDUSTRIES, the best way to operate a bed-blending system is NOT PROPERLY UNDERSTOOD. 118