Wyniki wyszukiwania - Biblioteka Nauki

1

Effect of autocorrelation on the process control charts in monitoring of a coal washing plant

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Tasdemir A.

Physicochemical Problems of Mineral Processing

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2012

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tom Vol. 48, iss. 2

495-512

EN

Traditional statistical process control charts assume that generated process data are normally and independently distributed, i.e. uncorrelated. This research presents the effect of autocorrelation on process control charts to monitor the two quality characteristics of fine coals produced in a coal washing plant for power plant, namely moisture content and ash content. Individual (X) and moving range charts (MR) were constructed to monitor 10 months data. It was determined that even though both data values obey the normal distribution, there is a moderate autocorrelation between their observations. For simulating the autocorrelated data, ARIMA time-series models were used. It was found that X/MR charts showed many false alarms due to the autocorrelation. The ARIMA (1, 0, 1) for moisture content and ARIMA (0, 1, 2) for ash content were determined to be the best models to remove autocorrelation. Compared to large number of false alarms on conventional X/MR charts and on charts applying the Western Electric rules, which assume the data independence, there were much less unusual points on the X/MR charts of residuals (Special Cause Charts). Usage of residual based control charts is suggested when the data are autocorrelated.

2

Analysis of chromite processing plant data by first order autoregressive model

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Tasdemir A.

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tom Vol. 49, iss. 1

157--174

EN

Many mineral processing data can be monitored by a time series model. This research presents results of analysis and simulations of a chromite processing plant data determined by time series model. The plant data obtained by shift to shift include feed grade, concentrate grade, tailing grade, Cr/Fe ratio in concentrate. All the chromite processing data were found stationary over time. The autocorrelation was high for feed grade and Cr/Fe ratio. Weaker autocorrelation was observed for concentrate grade and tailing grade. Autoregressive integrated moving average (ARIMA, 1,0,0) or first order autoregressive (AR, 1) model, was found to fit all data very well. The models obtained have been also shown to be used for the near future estimation of these data. The time constant which is an indicator of sampling frequency of the data sets were determined. It was found that sampling frequency was enough for concentrate and tailing grade and their original values can be used in process control charts for monitoring. On the other hand, the sampling frequency should be reduced for feeding grade and Cr/Fe ratio for the same aims hence ARIMA residual charts were more suitable to monitor their values.

3

Image analysis of narrow size fractions obtained by sieve analysis - an evaluation by log-normal distribution and shape factors

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Tasdemir A. , Özdag H. , Önal G.

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tom Vol. 46

95-106

EN

In this research, a pure quartz sample was subjected to sieve analysis and nine narrow size fractions were obtained. Polished sections were prepared from the representative samples of each fraction and were examined by image analysis (IA) to determine particle size distributions (PSDs) of fractions. Both size and shape measurements were made on individual quartz particles. Mean Feret diameter (dF) and three shape factors measurements, namely chunkiness (Ch), roundness (R) and form factor (FF), were carried out. This study showed that majority of particles in sieved fractions lied outside the nominal openings of the sieves. PSDs in all narrow sieve fractions were found to obey the log-normal distribution function. If number-based distribution of a system is found to be log-normal, the distribution of the derived diameters is also log-normal with the same geometric standard deviation. The number-based means obtained by IA were transformed to the volume (mass)-based means by using this property. The means of number- and volume (mass)-based IA sizes before and after correction by shape factors were compared with their corresponding geometric sieve means. Among the shape factors, FF was found as the most relating factor of sieve and IA sizes. The average of mean FF values of all size fractions was equal to 0.78. Reciprocal of this value (1.29) was very close to the slope of 1.28 obtained from the volume (mass)-based means of IA versus geometric sieve means relation. This result suggests that the slopes of the lines can provide a measure of differences between sieving and IA and this was related to FF values for quartz when dF was used as IA size.

PL

Próbki czystego kwarcu poddano analizie sitowej w celu wydzielenia dziewięciu wąskich klas ziarnowych. Klasy te użyto do przygotowania zgładów, które analizowano za pomocą komputerowej analizy obrazu (IA) w celu wyznaczenia składu ziarnowego (PSDs) każdej klasy. Określano zarówno rozmiar jak i współczynniki kształtu poszczególnych ziarn. Dokonano pomiarów średniej średnicy Fereta (dF) oraz trzech współczynników kształtu (krępość Ch, zaokrąglenie R, wskaźnik kształtu FF). Wykazano, że wymiary większości ziarn frakcji z analizy sitowej znajdowały się poza nominalnymi rozmiarami sit. PSDs wszystkich wąskich klas ziarnowych można było opisać log-normalną funkcją rozkładu. Jeżeli oparta na liczbie ziarn dystrybucja spełnia rozkład log-normalny, wynikająca średnica jest także opisywana funkcją log-normalną z tym samym geometrycznych odchyleniem standardowym. Średnie średnice oparta o liczbę ziarn, otrzymana za pomocą IA, zostały przeliczone na średnią objętościową (masową). Oznacza to, że wymiary oparte o liczbę i objętość (masę) IA przed i po korekcie za pomocą współczynnika kształtu były porównywalne z ich odpowiednimi geometrycznymi średnimi średnicami sitowymi. Stwierdzono, że wśród współczynników kształtu, wskaźnik FF okazał się najlepszy dla powiązania rozmiaru sitowego z rozmiarem z IA. Średnia wartość FF dla wszystkich frakcji wyniosła 0.78. Odwrotność tej liczby (1.29) jest bardzo bliska nachyleniu 1.28 otrzymanemu z średniej średnicy objętościowej IA wykreślonej jako funkcja geometrycznej średniej średnicy sitowej. Sugeruje to, że nachylenie tych zależności może dostarczyć miary różnicy wyników otrzymanych z przesiewania a z IA. Wyjaśniono to wartościami FF kiedy dF jest użyte jako rozmiar oparty o IA.

4

Gas entrainment rate and flow characterization in downcomer of a Jameson cell

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Tasdemir T. , Tasdemir A. , Oteyaka B.

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tom Vol. 47

61-78

EN

The Jameson cell which is a new type of gas-liquid contacting device and can be considered as a type of plunging jet column, has been in use worldwide for the separation of fine minerals, coal particles and wastewater treatment etc. Flow characteristics in the downcomer of a Jameson cell are very important since the hydrodynamics of the cell is largely depends on the flow conditions. The hydrodynamics influences flow regimes in the downcomer and hence the gas holdup and bubble diameter are strongly affected by flow conditions. Depending on the air entrainment rate entered to the system, different flow regimes are observed in the downcomer. Bubbly flow which is observed at less air quantities is desired instead of churn-turbulent flow where the gas entrainment rate increase. In this research, the effect of operating conditions including nozzle diameter, downcomer diameter, jet velocity and jet length on gas entrainment rate, Qg , was evaluated experimentally for an air-water system for the bubbly and churn-turbulent flow. Between these factors, downcomer diameter was found to have very little effect on gas entrainment rate while increasing values of other factors had an increasing effect on it. The results were evaluated by forward stepwise linear regression (MLR) and a piecewise regression with Quasi-Newton estimation of breakpoint (PLR) to estimate the flow conditions and gas entrainment rates. The model by PLR was useful to understand the boundary of the flow characteristics since the two equations were valid in a certain air entrainment ranges, i.e. different flow conditions. The model developed was successful to determine the transition region from bubbly flow to churn-turbulent flow. Experimental data were in good agreement with theoretically predicted value.