Thesis (PhD)--Stellenbosch University, 2008. / ENGLISH ABSTRACT: The growing need to improve accounting accuracy, precision and to standardise
generally accepted measurement methods in the mining and processing industries
has led to the joining of a number of organisations under the AMIRA International
umbrella, with the purpose of fulfilling these objectives. As part of this venture,
Anglo Platinum undertook a project on the material balancing around its largest
smelter, the Waterval Smelter.
The primary objective of the project was to perform a statistical material balance
around the Waterval Smelter using the Maximum Likelihood method with respect
to platinum, rhodium, nickel, sulphur and chrome (III) oxide.
Pt, Rh and Ni were selected for their significant contribution to the company’s profit
margin, whilst S was included because of its environmental importance. Cr2O3 was
included for its importance in as far as the difficulties its presence poses in
smelting of PGMs.
The objective was achieved by performing a series of statistical computations.
These include; quantification of total and analytical uncertainties, detection of
outliers, estimation and modelling of daily and monthly measurement uncertainties,
parameter estimation and data reconciliation. Comparisons were made between
the Maximum Likelihood and Least Squares methods.
Total uncertainties associated with the daily grades were determined by use of
variographic studies. The estimated Pt standard deviations were within 10%
relative to the respective average grades with a few exceptions. The total
uncertainties were split into their respective components by determining analytical variances from analytical replicates. The results indicated that the sampling
components of the total uncertainty were generally larger as compared to their
analytical counterparts. WCM, the platinum rich Waterval smelter product, has an
uncertainty that is worth ~R2 103 000 in its daily Pt grade. This estimated figure
shows that the quality of measurements do not only affect the accuracy of metal
accounting, but can have considerable implications if not quantified and managed.
The daily uncertainties were estimated using Kriging and bootstrapped to obtain
estimates for the monthly uncertainties. Distributions were fitted using MLE on the
distribution fitting tool of the JMP6.0 programme and goodness of fit tests were
performed. The data were fitted with normal and beta distributions, and there was
a notable decrease in the skewness from the daily to the monthly data.
The reconciliation of the data was performed using the Maximum Likelihood and
comparing that with the widely used Least Squares. The Maximum Likelihood and
Least Squares adjustments were performed on simulated data in order to conduct
a test of accuracy and to determine the extent of error reduction after the
reconciliation exercise. The test showed that the two methods had comparable
accuracies and error reduction capabilities. However, it was shown that modelling
of uncertainties with the unbounded normal distribution does lead to the estimation
of adjustments so large that negative adjusted values are the result. The benefit of
modelling the uncertainties with a bounded distribution, which is the beta
distribution in this case, is that the possibility of obtaining negative adjusted values
is annihilated. ML-adjusted values (beta) will always be non-negative, therefore
feasible. In a further comparison of the ML(bounded model) and the LS methods in
the material balancing of the Waterval smelter complex, it was found that for all
those streams whose uncertainties were modelled with a beta distribution, i.e.
those whose distribution possessed some degree of skewness, the ML
adjustments were significantly smaller than the LS counterparts
It is therefore concluded that the Maximum Likelihood (bounded models) is a
rigorous alternative method of data reconciliation to the LS method with the benefits of; -- Better estimates due to the fact that the nature of the data (distribution) is not assumed, but determined through distribution fitting and parameter estimation
-- Adjusted values can never be negative due to the bounded nature of the
distribution
The novel contributions made in this thesis are as follows;
-- The Maximum Likelihood method was for the first time employed in the
material balancing of non-normally distributed data and compared with the
well-known Least Squares method
-- This was an original integration of geostatistical methods with data
reconciliation to quantify and predict measurement uncertainties.
-- For the first time, measurement uncertainties were modeled with a
distribution that was non-normal and bounded in nature, leading to smaller
adjustments / AFRIKAANSE OPSOMMING: Die groeiende behoefte aan rekeningkundige akkuraatheid, en om presisie te
verbeter, en te standardiseer op algemeen aanvaarde meetmetodes in die mynbou
en prosesseringsnywerhede, het gelei tot die samwewerking van 'n aantal van
organisasies onder die AMIRA International sambreel, met die doel om
bogenoemde behoeftes aan te spreek. As deel van hierdie onderneming, het
Anglo Platinum onderneem om 'n projek op die materiaal balansering rondom sy
grootste smelter, die Waterval smelter.
Die primêre doel van die projek was om 'n statistiese materiaal balans rondom die
Waterval smelter uit te voer deur gebruik te maak van die sogenaamde maksimum
waarskynlikheid metode met betrekking tot platinum, rodium, nikkel, swawel en
chroom (iii) oxied.
Pt, Rh en Ni was gekies vir hul beduidende bydrae tot die maatskappy se
winsmarge, terwyl S ingesluit was weens sy belangrike omgewingsimpak. Cr2O3
was ingesluit weens sy impak op die smelting van Platinum groep minerale.
Die doelstelling was bereik deur die uitvoering van 'n reeks van statistiese
berekeninge. Hierdie sluit in: die kwantifisering van die totale en analitiese
variansies, opsporing van uitskieters, beraming en modellering van daaglikse en
maandelikse metingsvariansies, parameter beraming en data rekonsiliasie.
Vergelykings was getref tussen die maksimum waarskynlikheid en kleinste
kwadrate metodes.
Totale onsekerhede of variansies geassosieer met die daaglikse grade was bepaal
deur ’n Variografiese studie. Die beraamde Pt standaard afwykings was binne 10% relatief tot die onderskeie gemiddelde grade met sommige uitsonderings. Die totale
onsekerhede was onderverdeel in hul onderskeie komponente deur bepaling van
die ontledingsvariansies van duplikate. Die uitslae toon dat die monsternemings
komponente van die totale onsekerheid oor die algemeen groter was as hul
bypassende analitiese variansies. WCM, ‘n platinum-ryke Waterval Smelter
produk, het 'n onsekerheid in die orde van ~twee miljoen rand in sy daagliks Pt
graad. Hierdie beraamde waarde toon dat die kwaliteit van metings nie alleen die
akkuraatheid van metaal rekeningkunde affekteer nie, maar aansienlike finansiële
implikasies het indien nie die nie gekwantifiseer en bestuur word nie.
Die daagliks onsekerhede was beraam deur gebruik te maak van “Kriging” en
“Bootstrap” metodes om die maandelikse onsekerhede te beraam. Verspreidings
was gepas deur gebruik te maak van hoogste waarskynlikheid beraming passings
en goedheid–van-pas toetse was uitgevoer. Die data was gepas met Normaal en
Beta verspreidings, en daar was 'n opmerklike vermindering in die skeefheid van
die daaglikse tot die maandeliks data.
Die rekonsiliasies van die massabalans data was uitgevoer deur die gebruik die
maksimum waarskynlikheid metodes en vergelyk daardie met die algemeen
gebruikde kleinste kwadrate metode. Die maksimum waarskynlikheid (ML) en
kleinste kwadrate (LS) aanpassings was uitgevoer op gesimuleerde data ten einde
die akkuraatheid te toets en om die mate van fout vermindering na die rekonsiliasie
te bepaal. Die toets getoon dat die twee metodes het vergelykbare akkuraathede
en foutverminderingsvermoëns. Dit was egter getoon dat modellering van die
onsekerhede met die onbegrensde Normaal verdeling lei tot die beraming van
aanpassings wat so groot is dat negatiewe verstelde waardes kan onstaan na
rekosniliasie. Die voordeel om onsekerhede met 'n begrensde distribusie te
modelleer, soos die beta distribusie in hierdie geval, is dat die moontlikheid om
negatiewe verstelde waardes te verkry uitgelsuit word. ML-verstelde waardes (met
die Beta distribusie funksie) sal altyd nie-negatief wees, en om hierdie rede
uitvoerbaar. In 'n verdere vergelyking van die ML (begrensd) en die LS metodes in
die materiaal balansering van die waterval smelter kompleks, is dit gevind dat vir
almal daardie strome waarvan die onserkerhede gesimuleer was met 'n Beta distribusie, dus daardie strome waarvan die onsekerheidsdistribusie ‘n mate van
skeefheid toon, die ML verstellings altyd beduidend kleiner was as die
ooreenkomstige LS verstellings. Vervolgens word die Maksimum Waarskynlikheid
metode (met begrensde modelle) gesien as 'n beter alternatiewe metode van data
rekosiliasie in vergelyking met die kleinste kwadrate metode met die voordele van:
• Beter beramings te danke aan die feit dat die aard van die
onsekerheidsdistribusie nie aangeneem word nie, maar bepaal is deur die
distribusie te pas en deur van parameter beraming gebruik te maak.
• Die aangepaste waardes kan nooit negatief wees te danke aan die begrensde
aard van die verdeling.
Die volgende oorspronklike bydraes is gelewer in hierdie verhandeling:
• Die Maksimum Waarskynlikheid metode was vir die eerste keer geëvalueer vir
massa balans rekonsiliasie van nie-Normaal verspreide data en vergelyk met die
bekendde kleinste kwadrate metode.
• Dit is die eerste keer geostatistiese metodes geïntegreer is met data rekonsiliasie
om onsekerhede te beraam waarbinne verstellings gemaak word.
• Vir die eerste keer, is meetonsekerhede gemoddelleer met 'n distribusie wat nie-
Normaal en begrensd van aard is, wat lei tot kleiner en meer realistiese verstellings.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/4846 |
| Date | 12 1900 |
| Creators | Mtotywa, Busisiwe Percelia, Lyman, G. J. |
| Contributors | Eksteen, J. J., Lyman, G. J., Stellenbosch University. Faculty of Engineering. Dept. of Process Engineering. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 306 p. : ill. |
| Rights | Stellenbosch University |
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