idft pasar paper

Philippine Associated Smelting and Refining Corporation

LIDE, Isabel, Leyte

Correlation Between As/Pb Concentration Ratio, As, and Pb Concentration of the Copper

Anodes to the Density of the Slimes Produced After Electrolysis

Ian Dominic F. Tabañag

Bachelor of Science in Chemical Engineering (BS-ChE)

University of San Carlos – Technological Center

In-Plant Trainee 2011


Table of Contents

Acknowledgement ……………………………………………….………………………… i-ii

Abstract…………………………………………………………………………….……….. iii

I.Introduction………………………………………………………………………………… 1

II.Objectives of the Study…………………………………………………………..……… 2

III.Significance of the Study…………………………………………………………..…… 2

IV.Scope and Limitations………………………………………………………………..… 2

V.Review of Related Literature…………………………………………………………… 3-7

Vi.Methodology…………………………………………………………………………….. 8-10

VII.Results and Discussions………………………………………………………………. 11-12

VIII.Conclusions……………………………………………………………………………. 13

IX.Recommendations……………………………………………………………………… 13

X.Bibliography………………………………………………………………………………. 14

XI.Appendices………………………………………………………………………………. 15-22


2011 In-Plant Training i

Acknowledgement

This study would not have been possible without the guidance and the help of several

individuals who in one way or another contributed and extended their valuable assistance in the

preparation and completion of this study.

The researcher would like to thank the following:

To Engr. Severo Andrew B. Lacaba, the main proponent of this study, who shared his

ideas about this study and made the researcher experience the job of being an area manager;

To Engr. Joseph B. Morao, who shared his resources and other literature readings

related this study. Furthermore, he taught the researcher well on how to handle speaking

engagements and for letting the researcher experience a great deal happiness from the small

irrelevant things;

To Ms. Jemmy Liz B. Pohino, who gave the permission for the utilization of the tray oven

and the vacuum pump of the By-Products Plant and also for being the self-proclaimed acting

mom of the researcher in the Tankhouse;

To Mr. Anthony Mark F. Lusica, who enlightened the researcher in the overall idea of

this study and also for being the self-proclaimed acting dad of the researcher;

To Engr. Mark Jun A. Talaban, who gave the researcher an idea on how to conduct the

sampling of the anode slimes;

To Engr. Hercules M. Amson, who gave the permission for the utilization of the former

process mini-lab as a working space for the researcher;

To Kuya Roger, who helped the researcher in the cleaning of the mini-lab;

To Engr. Blessyl Marie Navalatan, who gave the permission to use the laboratory

apparatus and equipment of the process laboratory;

To the tankhouse personnel, who shared good conversations to the researcher during

his free time;

To all the ODT staff, who gave the IPT’s moral support, provided the researcher with

supplies (such as a marker, sticky tape, etc.), provided the IPT’s with free food every time the

ODT department sponsors an activity;

To Ms. Leizel Ponce, for being the acting mother of the researcher during his stay here

in PASAR;


2011 In-Plant Training ii

To the Teaspoon Crew, who served food for the IPT’s during their stay in the

Guesthouse;

To the fellow IPT-mates of the researcher, Kahar (the self-proclaimed best buddy of the

researcher), Mamie, Bhel, Wena, Phebby, Ron, Beth, Irish, Jen, and LAMPY (the best

representative of our school!) for sharing the gift of friendship to the researcher;

To the family of the researcher, for the love and support that they gave to him during his

stay here in PASAR;

To the PASAR Corp., for giving the researcher an opportunity to undergo the In-Plant

Training Program of the company and all the benefits that the researcher experienced as a

trainee;

Lastly, to our Almighty God the Father, for giving us the privilege to enjoy life and it is

through Him that all things are made possible.

Thank you very much!!!


2011 In-Plant Training iii

Abstract

Floating slimes deposition is one of the main problems in electrorefining that greatly

affects the cathode quality. In the present time, the anodes being used in the electrorefining

have high levels of Arsenic and Lead which can be classified a impurities in the electrorefining

process. This primary objective of this study is to establish a relevant correlation between the

As and Pb concentration in the copper anodes to the density of the slimes it produces after

electrolysis. Data of the As and Pb concentration of the anodes were gathered and samples of

slimes were collected, filtered, dried, and the determination of its density. The obtained data

from the experimentation was analyzed and then using regression methods, a relevant

correlation between the As/Pb concentration ratio to the density of slimes was obtained. The

correlation obtained in this study can be used as a basis as to why the As/Pb concentration ratio

can be used as a measure of determining anode slime characteristics. Based from this study,

maintaining the As/Pb concentration ratio of the copper anode in the range of ~0.87-1.12 will

lead to the formation of high density slimes.


2011 In-Plant Training 1

I. Introduction

It is stated in the Quality Policy of PASAR Corp. that the company is committed to

provide Grade A Copper cathode to the satisfaction of the London Metal Exchange (LME) and

other non-ferrous metals market. In producing high quality copper cathodes, the impurity levels

in the copper anodes to be used in the electrorefining process must be maintained at a

minimum level and when not maintained at low levels, it will lead to cathode contamination.

Based from the daily anode charging report by the commercial cells section, it can be

observed that the anodes currently used in the electrorefining process have high levels of

impurities such as As, and Pb. These undesirable elements in the copper cathodes come from

slime occlusions, and co-deposition of dissolved impurities in the electrolyte. Also, it has been

observed by random cathode inspection that most of the nodulations present in the copper

cathodes are due to the entrapment of floating slimes.

This study concerns on establishing a correlation between the impurities present in the

copper anodes (especially As and Pb) to the density of slimes it produces after the

electrorefining process. This study will also find a way to minimize the entrapment of floating

slimesduring the electrolysis process thus, improving cathode quality.



II. Objective of the Study

This study aims to establish a significant correlation between the As and Pb content in

the copper anodes to the density of slimes being produced by these anodes after the

electrolysis.

III. Significance of the Study

Floating slimes deposition is one of the main problems during the electrorefining process

since they decrease the quality of the copper cathodes being produced. Thus, determining the

concentration of the As and Pb, or the optimum As/Pb ratio in the anode that could lead to the

formation of high-density slimes could greatly help in the minimization of the nodulations caused

by the entrapment of floating slimes or floating slimes deposition and ultimately enhance the

cathode quality after electrolysis.

IV. Scope and Limitations

This study focuses mainly on establishing a correlation between and As and Pb content

in the copper anodes to the density of slimes it produces after electrolysis, where the place of

study is limited only to Tankhouse 1 of the Refinery since Tankhouse 1 utilizes the additive

Sanfloc as a flocculant. Samples of slimes being collected depend on the 3rd crop harvesting

schedule since during the 3rd crop harvest, the electrolysis cells are being drained of the

electrolyte solution and which is suitable for the gathering of slime samples. The researcher

intends to gather as many samples as possible to utilize the amount of time given for the study

to be conducted (April 19 to May 11, 2011). Using the available equipment in the laboratory for

the experimentation part of this study, the researcher has seen to it that the uncertainties in

measurement were minimized.



V. Review of Related Literature

Anode Slimes:

Considerable amount of As, Bi, and Sb report in the anode residues as they form

compounds with copper and other impurities in the anode (i.e. 𝐵𝑖2𝑂3, 𝑐𝑜𝑚𝑝𝑙𝑒𝑥 𝐴𝑔 − 𝑃𝑏 −

𝐵𝑖 𝑠𝑢𝑙𝑓𝑖𝑑𝑒). Also, it is believed that to some extent, As, Sb, and Bi combine to form arsenate

precipitates that also report to the anode slimes (Biswas, and Davenport, 1980). The amount of

these three elements in the anode slimes depends not only on their concentration in the anode

but also on the composition of the electrolyte and the composition of other anode impurities.

Origin of this anode slime components include:

1. Compounds existing in the anode and compounds in the anolyte region, or

2. Precipitates which form in the bulk electrolyte due to solubility effects

Kennecott test data have shown that antimony arsenate and bismuth arsenate can

contribute greatly to the presence of As, Sb, and Bi in cathodes, anode slimes and pipelines.

Further tests have shown that an increase in antimony and bismuth content forces an increased

amount of arsenic to report to anode slimes. There is then an increased slime fall that

corresponds to arsenate composition.

Float slimes were found to be amorphous and chemically undefined compounds that

contain Sb(III), Sb(V), Bi(III), and As(V).When antimony concentrations are in excess of 0.5 g/L,

float slime formation occurs.

Slime fall is much greater when electrolyte composition is maintained in a saturated or

supersaturated condition with respect to arsenate solubility than in an unsaturated electrolyte.

Effect of Arsenic in the Anode:

Arsenic is present in the anode and the one hand as a mixed crystal on the other hand

as an oxide. During electrolysis, both the metallic and the oxidic arsenic are for the most part

dissolved in the electrolyte; arsenic goes into the solution in trivalent form and in the course of

electrolysis is oxidized to the pentavalent state by the atmospheric oxygen dissolved in the

electrolyte. A layer of slime forms on the surface of the anode as a function of oxygen content of

the anode and remains loosely adhering through the anode throughout the entire test. At low

arsenic contents, most of this layer consists of copper and copper oxide; at higher contents,

copper arsenide forms on the anode surface from the elemental copper and from the solution

containing As(III). The formation of a covering layer on the anode causes the cell voltage to

increase. The resulting slime becomes more fine-grained, due to the grain refinement, as the



arsenic content of the anode increases. Because of its strong affinity to oxygen, arsenic binds a

large amount of arsenic present in the anode, and as a result, this significantly influences

copper enrichment and acid decomposition during electrolysis. It is found that arsenic goes

almost completely into solution regardless of its oxygen content. (Cornelius, et al., 1997)

Effect of Lead in the anode:

The study of slimes behavior phenomenon that occurs in the electrorefining process is

influenced by variables such as chemical composition of the anode (especially Pb) and the

current density. A high specific weight in the anode slimes can assure a minimum of suspended

solids during the electrorefining process. On the other hand, an increase in the current densities

with anodes of high lead content (~1539ppm Pb based on this study with current densities of

240 − 290 𝐴/𝑚2), produces a synergistic effect to minimize the quantity of suspended slimes in

the cell. Furthermore, it has been estimated that the lead can be the cause for the precipitation

of antimony through the formation of Bindhemite (𝑃𝑏2𝑆𝑏2𝑂7) compounds in the anode slimes. A

specific weight of 4.71g/cm^3 of the anode slimes showed a minimum concentration of

suspended solids. (Cifuentes et al., 1999)

Mean absolute deviation

The mean absolute deviation (MAD) is the mean absolute deviation from the mean. A related

quantity, the mean absolute error (MAE), is a common measure of forecast error in time series

analysis, where this measures the average absolute deviation of observations from their

forecasts.

Although the term mean deviation is used as a synonym for mean absolute deviation, to be

precise it is not the same; in its strict interpretation (namely, omitting the absolute value

operation), the mean deviation of any data set from its mean is always zero.

Grubb’s Test for Detection of Outliers:

Grubbs' test for outliers (Grubbs 1969 and Stefansky 1972 ) checks normally distributed

data for outliers. This implies that one has to check whether the data show a normal distribution

before applying the Grubbs test. The Grubbs test always checks the value which shows the

http://en.wikipedia.org/wiki/Mean_absolute_error

http://en.wikipedia.org/wiki/Forecast_error

http://en.wikipedia.org/wiki/Time_series_analysis



http://www.statistics4u.info/fundstat_eng/cc_outliers.html

http://www.statistics4u.info/fundstat_eng/cc_distri_normal.html



largest absolute deviation from the mean. If an outlier has been indentified and removed, the

test must not be repeated without adapting the critical value.

The application of the test is quite simple and straightforward: one searches the

maximum of the absolute differences between the values xi and the mean . The result is

divided by the standard deviation of the sample. If the resulting test statistic g is greater than the

critical value, the corresponding value can be regarded to be an outlier. An extract of the critical

values is shown in the table shown in the appendix. The formula for getting the statistic g is:

In some other literature data, the test statistic g is sometimes referred to as the Z

statistic. The Z statistic notation was utilized in this study.

Regression or Curve fitting:

Field data is often accompanied by noise. Even though all control parameters (independent

variables) remain constant, the resultant outcomes (dependent variables) vary. A process of

quantitatively estimating the trend of the outcomes, also known as regression or curve fitting,

therefore becomes necessary.

The curve fitting process fits equations of approximating curves to the raw field data.

Nevertheless, for a given set of data, the fitting curves of a given type are generally NOT

unique. Thus, a curve with a minimal deviation from all data points is desired. This best-fitting

curve can be obtained by the method of least squares.

Method of Least Squares Regression:

The method of least squares assumes that the best-fit curve of a given type is the curve

that has the minimal sum of the deviations squared (least square error) from a given set of data.

Suppose that the data points are , , ..., where is the independent

variable and is the dependent variable. The fitting curve has the deviation (error) from

each data point, i.e., , , ..., . According to the

method of least squares, the best fitting curve has the property that:



This states that the sum of the residuals must be kept at minimum.

Polynomial Least Squares Fitting:

When using an mth degree polynomial

to approximate the given set of data, , , ..., , where , the best

fitting curve has the least square error, i.e.,

Please note that , , , ..., and are unknown coefficients while all and are given.

To obtain the least square error, the unknown coefficients , , , ..., and must yield

zero first derivatives.

Expanding the above equations, we have



The unknown coefficients , , , ..., and can hence be obtained by solving the above linear equations.

In this study, an iterative method was used in solving the parameters of the equation with the

aid of MS Excel Solver function in the carrying out of the iterative procedures.



VI. Methodology

1.Data Gathering

Basing from the April and May harvest schedule, blocks to be harvested during 3 rd crop

were noted. From the 3rd crop blocks to be harvested, the anode lot numbers from different cells

were determined from the daily anode charging report and these anode lot numbers were

verified by visual inspection. Those cells with anodes of the same lot numbers were noted for

sample gathering.

2.Experimentation

2.1.Materials and Apparatus:

Materials:

Sampling cups

Distilled or deionized water

Electrolyte

Ashless Filter Paper

Apparatus:

Oven (tray drying)

Top-loading balance (±0.01 g)

Heater (hot plate)

crucibles

Graduated cylinder (15mL, ±0.10 mL )

Thermometer (alcohol)

Erlenmeyer flask (500mL with cork stopper)

Dessicating Cabinet

Vacuum pump

2.2.Procedure:

2.2.1.)Sampling

From the harvested blocks, slimes from cells with anodes of the same lot number were

collected by means of scraping them from the anodes (the locations of the anodes that were

scraped with slime were: near the electrolyte feed, middle, and near the electrolyte outlet). The



block, lot, and cell numbers of the samples taken were recorded. Also, the current densities

were recorded since the current densities were increased during the scope of the sampling time.

2.2.2.)Washing and Filtration

The samples being collected were washed with distilled water until the blue color is

removed (all CuSO4 solution that accompany the slimes are removed to prevent its

crystallization upon drying) and then filtered using an ashless filter paper in a funnel and with

the aid of a vacuum pump, the filtration time was minimized.

2.2.3.)Drying of Slimes

The slimes being collected were placed in crucibles with cover. The samples were dried

in an oven for at least 3 hours at 103-105°𝐶. After 3 hours of drying, the samples are being

cooled inside a desiccating cabinet to prevent the moisture from the air from being entrained in

the dried samples. The cycle of drying, cooling, and weighing was repeated until a constant

weight was obtained or the weight is changed less than 4%.1-3 grams of each sample were

taken and then set aside.

2.2.4.)Density Determination

Electrolyte solution from the feed of the cell was collected and placed in an Erlenmeyer

flask and then heated to 64-68°𝐶 in a hot plate. The graduated cylinder was washed with the

electrolyte solution beforehand then it was filled with ~10mL of the electrolyte solution.After the

preparation of the electrolyte solution, the 1-3 grams of dry sample prepared was placed into the

graduated cylinder with the electrolyte solution and the volume change in the graduated cylinder

was then recorded. The density of the sample was then determined by dividing the mass of the

dry slime sample to the volume of electrolyte solution being displaced. Five runs of density

determination were done to account for the random and systematic errors.

3.Data Treatment

Construction of the Density vs. As, Pb, and As/Pb concentration plots:

After obtaining the density values from all samples, the As, and Pb content of the

anodes were obtained from the daily anode charging report with respect to the anode lot

numbers of the samples. After determining the As and Pb concentrations of the anodes being



charged, the density of the slimes samples obtained are to be plotted correspondingly using a

spreadsheet software (MS Excel) against the As, Pb, and As/Pb ratio where these samples

were taken. The correlation between the As and Pb concentration of the copper anodes to the

density of the slimes being produced after electrolysis was obtained by regression of data using

MS Excel.

4.Statistical Method:

Using the five runs for the density determination, the Mean Absolute Deviation (MAD)

was obtained. The mean average deviation was used in this study due to the limited amount of

samples being obtained. Also, the mean absolute deviation was utilized because the sample run

size is less than 30 and to account for the random and systematic errors that were being

encountered during the experimentation. Grubb’s test was used to detect and remove outliers.



VII. Results and Discussion:

Figure 1: Density vs As and Pb concentration plot

Figure 1 shows the plot of As and Pb anode concentration of the anode to the density of

slimes it produces after electrolysis. It is shown that when Pb concentrations are within the

range of 680 to 800ppm Pb, high density slimes are being produced. On the other hand, As

concentrations within the range of 700 to 900ppm As also produces high density slimes. This

we can attribute to the ability of As and Pb to coprecipitate with other impurities such as Bi, Sb,

and O.

3.00

3.50

4.00

4.50

5.00

5.50

6.00

400 500 600 700 800 900 1000 1100

De

nsi

ty (g

/mL)

concentration (ppm)

As

Pb



Figure 2: Density vs As/Pb ratio

Figures 2shows a relevant correlation between the As/Pb concentration ratio to the

density of slimes being produced. It can be observed from the figure that as the concentration

ratio between As and Pb approaches to 1, high density slimes are formed. But when the ratio is

less than or greater than 1, the density of the slimes tend to decrease. From literature, as the

lead concentration in the anode increases, the density of slimes being formed also increases

due to the fact that Pb can cause the formation of heavy precipitates.However, based from the

data obtained, when Pb concentration exceeds ~800 ppm, the slime density starts to decrease

and conversely for As concentration effect.

In the regression of data, the polynomial least squares fitting method was utilized with

the aid of the MS Excel Solver.

.

0

1

2

3

4

5

6

0.3 0.5 0.7 0.9 1.1 1.3 1.5

De

nsi

ty (g

/mL)

As/Pb

Actual Data

Regressed Data



VIII. Conclusion:

Based on the data gathered, there is a more likely quadratic or parabolic correlation

(with the correlation coefficient R^2 value of 0.910113) between the As/Pb concentration ratio to

the density of slimes it produces after electrolysis for which it can be made as a basis in

characterizing anode slimes and thus helps in minimizing a problem in floating slimes

deposition. As shown Figure 2, Cu anodes with As/Pb ratio of ~0.87-1.12 can result in the

formation of high density slimes. Furthermore, there was no correlation that has been

established between the As concentration to the density of slimes and conversely for Pb

concentration to the density of slimes since both As and Pb vary with each other.

IX. Recommendations:

In establishing a correlation between As concentration to the density of slimes , the Pb

concentration in the anode must be kept constant or vice versa since it has been shown in this

study that As and Pb vary with each other. Also, advanced mathematical modeling methods can

be used to correlate As, Pb, and Density of slimes given that a sufficient period of time is being

allotted in doing this study.

There is a need to minimize further the uncertainty of measurement that was done in this

study since the apparatus used in determining the masses of the slime samples was a top-

loading balance (~0.01 g) due to the unavailability of equipment. This can be achieved by using

an analytical balance (~0.0001 g).

Further experimentation must be done in order to quantify more on the effect of As and

Pb to the formation of composites in slimes or component analysis of slimes. Also, there is a

need in the determination of the standard densities of the slimes at which there is minimum

concentration of suspended solids and relate it to the As and Pb concentration of the copper

anode.



X. Bibliography:

Standard Methods for the Examination of Water and Wastewater, 21st ed., Franson et

al., Port City Press, Baltimore, Maryland, USA, 2005

Anode Slime Characteristics and Behavoiur in Copper Refining, Cifuentes et al.,

Proceedings of Copper 99-Cobre 99 International Conference Vol. 3., 1999

Prevention of Floating Slimes Precipitation, Abe et al., The Electrorefining and Winning

of Copper, Pensylvania, 1987

Extractive Metallurgy of Copper 2nd ed., Pergamon Press, Oxford, 1980

Daily Anode Charging Report, PASAR Corp., revised as of April 29,2010

April and May Harvest Schedule, PASAR Corp.

http://www.statistics4u.info/fundstat_eng/ee_grubbs_outliertest.html

http://www.efunda.com/math/leastsquares/leastsquares.cfm

http://www.statistics4u.info/fundstat_eng/ee_grubbs_outliertest.html



XI. Appendices

Table 1: Data from the Daily Anode Charging Report:

Anode Lot No. As (ppm) Pb (ppm)

115 672 941

116 694 730

117 670 537

114 816 687

121 1042 742

123 905 862

122 765 600

119 483 742

118 779 695

111 577 660

127 776 709

129 712 729

130 534 639

131 496 630

Note:

Red values indicate the concentrations that are within the range of the set point values

used by the company as a standard (600-1000ppm for As and 690-710ppm for Pb).



Table 2: Density Determination:

Trial 1 Trial 2

Anode Lot No.

As (ppm)

Pb (ppm)

As/Pb mass sample (g)

volume change (ml)

Density (g/ml)

mass sample (g)

volume change (ml)

Density (g/ml)

115 672 941 0.71 1.29 0.30 4.30 1.06 0.30 3.53

116 694 730 0.95 1.12 0.20 5.60 1.39 0.30 4.63

117 670 537 1.25 1.07 0.20 5.35 1.02 0.20 5.10

114 816 687 1.19 1.05 0.20 5.25 0.99 0.20 4.95

121 1042 742 1.40 1.02 0.30 3.40 1.29 0.40 3.23

123 905 862 1.05 1.04 0.30 3.47 1.07 0.20 5.35

122 765 600 1.28 1.06 0.30 3.53 1.08 0.30 3.60

119 483 742 0.65 1.25 0.30 4.17 1.07 0.30 3.57

118 779 695 1.12 1.13 0.20 5.65 1.08 0.20 5.40

111 577 660 0.87 2.06 0.40 5.15 3.18 0.65 4.89

127 776 709 1.09 2.28 0.45 5.07 3.05 0.55 5.55

129 712 729 0.98 2.07 0.35 5.91 3.05 0.60 5.08

130 534 639 0.84 2.09 0.40 5.23 3.06 0.55 5.56

131 496 630 0.79 2.03 0.40 5.08 3.01 0.60 5.02



Trial 3 Trial 4 Trial 5

Anode Lot No.

As (ppm)

Pb (ppm)

As/Pb mass sample

(g)

volume change

(ml)

Density (g/ml)

mass sample

(g)

volume change

(ml)

Density (g/ml)

mass sample

(g)

volume change

(ml)

Density (g/ml)

115 672 941 0.71 1.01 0.25 4.04 1.04 0.30 3.47 1.07 0.25 4.28

116 694 730 0.95 1.18 0.25 4.72 0.99 0.20 4.95 1.01 0.20 5.05

117 670 537 1.25 1.05 0.20 5.25 1.17 0.25 4.68 1.16 0.25 4.64

114 816 687 1.19 1.15 0.20 5.75 1.04 0.20 5.20 1.26 0.25 5.04

121 1042 742 1.40 1.18 0.30 3.93 1.07 0.30 3.57 1.09 0.30 3.63

123 905 862 1.05 1.11 0.20 5.55 1.22 0.25 4.88 1.01 0.20 5.05

122 765 600 1.28 1.10 0.30 3.67 1.17 0.30 3.90 1.12 0.30 3.73

119 483 742 0.65 1.10 0.25 4.40 1.14 0.25 4.56 1.22 0.30 4.07

118 779 695 1.12 1.10 0.30 3.67 1.10 0.20 5.50 1.20 0.25 4.80

111 577 660 0.87 3.00 0.60 5.00 3.16 0.65 4.86 3.01 0.60 5.02

127 776 709 1.09 3.18 0.55 5.78 3.23 0.65 4.97 3.07 0.55 5.58

129 712 729 0.98 3.09 0.55 5.62 3.19 0.55 5.80 3.07 0.55 5.58

130 534 639 0.84 3.15 0.60 5.25 3.01 0.55 5.47 3.17 0.60 5.28

131 496 630 0.79 3.07 0.60 5.12 3.17 0.65 4.88 3.12 0.65 4.80



Table 3: Statistical Treatment of Data

Table 3.1: Detection and Elimination of Outliers (Grubb’s Test):

Density (g/mL) Zcrit= 1.71 Detection of Outliers

As (ppm) Pb (ppm) As/Pb Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 D ave D (SD) D(eff) Z1 Z2 Z3 Z4 Z5

672 941 0.71 4.30 3.53 4.04 3.47 4.28 3.92 0.40 3.52 0.94 0.98 0.29 1.13 0.89

694 730 0.95 5.60 4.63 4.72 4.95 5.05 4.99 0.38 4.61 1.60 0.95 0.71 0.11 0.16

670 537 1.25 5.35 5.10 5.25 4.68 4.64 5.00 0.33 4.68 1.06 0.29 0.75 0.99 1.11

816 687 1.19 5.25 4.95 5.75 5.20 5.04 5.24 0.31 4.93 0.04 0.93 1.65 0.12 0.64

1042 742 1.40 3.40 3.23 3.93 3.56 3.63 3.55 0.26 3.29 0.57 1.22 1.45 0.04 0.30

905 862 1.05 5.20 5.35 5.55 4.88 5.05 5.21 0.26 4.95 0.02 0.55 1.32 1.26 0.60

765 600 1.28 3.53 3.60 3.67 3.90 3.73 3.69 0.14 3.54 1.11 0.61 0.11 1.52 0.31

483 742 0.65 4.17 3.57 4.40 4.56 4.07 4.15 0.38 3.78 0.04 1.54 0.65 1.07 0.22

779 695 1.12 5.65 5.40 5.50 5.50 4.80 5.51 0.33 5.18 0.42 0.34 0.04 0.04 2.15

577 660 0.87 5.15 4.89 5.00 4.86 5.00 4.98 0.11 4.87 1.49 0.79 0.18 1.05 0.18

776 709 1.09 5.07 5.08 5.78 4.97 5.44 5.23 0.34 4.89 0.46 0.43 1.65 0.76 0.64

712 729 0.98 5.91 5.56 5.62 5.80 5.58 5.69 0.15 5.54 1.41 0.87 0.48 0.69 0.74

534 639 0.84 5.23 5.13 5.25 5.47 5.28 5.27 0.12 5.15 0.34 1.14 0.18 1.59 0.06

496 630 0.79 5.08 5.02 5.12 4.87 4.80 4.98 0.14 4.84 0.74 0.31 1.03 0.79 1.29



The red value for in the Z5 column is detected as an outlier since its Z is greater than the Zcrit.

The highlighted cell was detected as an outlier since its resulting test statistic Z is greater than the Zcrit for 5% level of error.

The green value represents a calculated mean with the outlier being neglected.



Table 3.2: Mean Average Deviation:

Mean Average Deviation

As (ppm) Pb (ppm) As/Pb D ave T1 T2 T3 T4 T5 DEV AVE

672 941 0.71 3.92 0.38 0.39 0.12 0.45 0.36 0.34

694 730 0.95 4.99 0.61 0.36 0.27 0.04 0.06 0.27

670 537 1.25 5.00 0.35 0.10 0.25 0.32 0.36 0.28

816 687 1.19 5.24 0.01 0.29 0.51 0.04 0.20 0.21

1042 742 1.40 3.55 0.15 0.32 0.38 0.01 0.08 0.19

905 862 1.05 5.21 0.01 0.14 0.34 0.33 0.16 0.20

765 600 1.28 3.69 0.16 0.09 0.02 0.21 0.04 0.10

483 742 0.65 4.15 0.02 0.58 0.25 0.41 0.08 0.27

779 695 1.12 5.51 0.14 0.11 0.01 0.01 0.71 0.07

577 660 0.87 4.98 0.17 0.09 0.02 0.12 0.02 0.08

776 709 1.09 5.23 0.15 0.15 0.56 0.26 0.22 0.27

712 729 0.98 5.69 0.22 0.13 0.07 0.11 0.11 0.13

534 639 0.84 5.27 0.04 0.14 0.02 0.20 0.01 0.08

496 630 0.79 4.98 0.10 0.04 0.14 0.11 0.18 0.11

In the calculation of the mean average deviation, the highlighted red value was not included in the calculation of the average

deviation since this the value for this trial was designated as an outlier



Table 4: Non-Linear Least Squares Regression:

4th order polynomial

n= 3.3625 a= 0.1619 d= 4.5969

b= -0.4608 e= 2.9178

c= -1.5846 0

As (ppm)

Pb (ppm)

As/Pb D ave DEV AVE D app Sr St

672 941 0.71 3.92 0.4 4.199736 0.0782523 0.378551

694 730 0.95 4.99 0.38 5.47078 0.2311491 0.430046

670 537 1.25 5 0.33 4.426885 0.3284603 0.150634

816 687 1.19 5.24 0.31 5.079972 0.025609 0.07021

1042 742 1.4 3.55 0.26 3.167709 0.1461468 2.713572

905 862 1.05 5.21 0.26 5.692639 0.2329406 0.770249

765 600 1.28 3.69 0.14 4.047066 0.1274961 0.589724

483 742 0.65 4.15 0.38 3.904818 0.0601141 0.828432

779 695 1.12 5.51 0.33 5.549568 0.0015656 0.539589

577 660 0.87 4.98 0.11 5.086563 0.0113557 0.073746

776 709 1.09 5.23 0.34 5.64795 0.1746825 0.693805

712 729 0.98 5.69 0.15 5.577117 0.0127427 0.58082

534 639 0.84 5.27 0.12 4.921158 0.1216907 0.011269

496 630 0.79 4.98 0.14 4.638052 0.1169286 0.031311

AVE= 4.815001

SUM= 0.7066912 7.861957

R^2 0.910113

From the results of the least squares method of iteration, the resulting polynomial equation is:

𝑦 = 0.1619 𝑥3.3625 4 − 0.4608 𝑥3.3625 3 − 1.5846 𝑥3.3625 2 + 4.5969 𝑥3.3625 + 2.9178



With the R^2 value of 0.910113

Note:

The green value (sum of residuals) was being minimized using the solver function of excel by changing the parameters a, b,

c, d, e, and n.

Table 5: Critical G or Z Values for the Determination of Outliers

n gcrit

α=0.05

gcrit

α=0.01

n gcrit

α=0.05

gcrit

α=0.01

n gcrit

α=0.05

gcrit

α=0.01

3 1.1543 1.1547 15 2.5483 2.8061 80 3.3061 3.6729

4 1.4812 1.4962 16 2.5857 2.8521 90 3.3477 3.7163

5 1.7150 1.7637 17 2.6200 2.8940 100 3.3841 3.7540

6 1.8871 1.9728 18 2.6516 2.9325 120 3.4451 3.8167

7 2.0200 2.1391 19 2.6809 2.9680 140 3.4951 3.8673

8 2.1266 2.2744 20 2.7082 3.0008 160 3.5373 3.9097

9 2.2150 2.3868 25 2.8217 3.1353 180 3.5736 3.9460

10 2.2900 2.4821 30 2.9085 3.2361 200 3.6055 3.9777

11 2.3547 2.5641 40 3.0361 3.3807 300 3.7236 4.0935

12 2.4116 2.6357 50 3.1282 3.4825 400 3.8032 4.1707

13 2.4620 2.6990 60 3.1997 3.5599 500 3.8631 4.2283

14 2.5073 2.7554 70 3.2576 3.6217 600 3.9109 4.2740

idft pasar paper

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