Dr. SaMeH S. Ahmed

Associate Prof. of Environmental Engineering

Amman

Development of Computer Software for Ore Reserve Estimation O.R.E

(A Case Study of Maghara Coal Mine, Egypt)

M. R. El-Tahlawi(1), M. Z. Rashad(2) and Sameh S. Ahmed(3)

(1) Professor of Mining Geology, Email: [email protected],

Tel.: +20-012 3971550,   Fax: +20-088 336672

(2) Professor of Mining Geostatistics, Email: m.zaki@hotmail.com,

Tel.: +20-088 411212, Fax: +20-088 336672

(3) Assistant Professor, Email: [email protected],

Tel.: +20-012 4785284, Fax: +20-088 365108

Mining and Metallurgical Engineering Department, Faculty of Engineering, Assiut University, Assiut, Egypt.

Abstract

Nowadays, the use of computer facilities has become widely increased in different areas. Mining engineering in general and ore reserve evaluation in particular are among these applications. The main objective of this paper is to develop computer software for the purpose of ore reserve estimation. Several factors have been taken into consideration during the development of the computer software, such as providing robust, accurate, and easy use tool that would assist the mining industry. The software has been developed based on the triangular method, statistical analysis of the raw data and written in C++ language with a facility to work with Windows 98 and above. Given X, Y, Z co-ordinates and one or more variable, for a certain number of sampling points at test area, the software could be used to determine, the total area, volume, tonnage of ore reserves, distribution of the assays, and point estimation for any un-sampled point within the entire area. The results are introduced as tables, contour maps, and three-dimensional representation of the variable. The software has been developed and validated using data from Maghara Coal Mine, Sinai, Egypt. The thickness of the main seam is estimated as 1.2 m and the tonnage of the coal as 26.6 million tons. The software, called “O.R.E. Software”, shows a good, quick, easy implementation and accurate results.


1. Introduction

Development of mining industry is based mainly on the ore reserves and their grades. The higher the accuracy of calculations or estimations the higher is the success of the production plans.

Not far off from now, where mining companies used several traditional methods for ore reserves estimation, based on collecting field sampling data and plotting the locations of the sampling points on geographic maps using the coordinate system and one or more of the known methods to determine the average thickness of the overburden, ore bed(s), to calculate the volumes and reserves.

2. Methods of Ore Reserve Estimation

The methods of ore reserve estimation can be classified into two categories: a) the conventional methods such as polygon method, triangular method,

b) the modern techniques that involve kriging techniques.

The following section describes the principles of the triangular method, on which the software is developed.

2.1 Triangular Method

The triangular method calculates the volume of a triangular-shaped prism formed between three adjacent drill holes (Figure 1). Like the polygonal method, bench levels are specified. The grade is determined by averaging the value at the three corners of each triangle.

The method has proved to be a good tool for determining the tonnage of the ore reserves, however it requires a long-time with high error risk in calculations especially when the case deals with a huge number of sampling points and small scale.

3

8

4

5

7

6

1

2








Results

Area

Average Assay%

Triangle

Assay%

Borehole

Total Area = 178.5 m2

Area x Assay = 49.9

Average Assay = 0.280%

14.5

0.277

1-2-4

0.12

1

21.6

0.223

1-4-6

0.21

2

21.1

0.237

2-3-5

0.17

3

26.2

0.346

2-4-5

0.50

4

14.9

0.217

3-5-8

0.33

5

28.2

0.363

4-5-7

0.05

6

29.7

0.270

4-6-7

0.26

7

22.3

0.247

5-7-8

0.15

8

Figure 1:        Triangular model showing drill hole locations at corners of triangles, and average value for the holes. The grade for each triangular prism-shaped area is found by averaging the three values at the corners.


A) For each triangle:

1) Average thickness ()      = …….………………(1)

2) Average assay () = …………..…..(2)

3) Area (a) = ………(3)

B) For whole area:

1) Average thickness = .(4)

2) Average assay = ………....(5)


3) Volume thickness………………….(6)


4) Tonnage .………….………...…………(7)

Where:

h: thickness of borehole, m;

A: assay of metal, %;

a: area of triangle, m2;

T.F: tonnage factor, t/m3;

L: length of triangle side = ; and

p:       half periphery of triangle         = (L1+L2+L3 )/2

2.2 Kriging Technique

The Kriging technique is named after the South African geostatistician D. J. Krig. It is a technique for determining the best linear unbiased estimator with minimal estimation variance. It can be used on a point as well as on a block (Royle, 1992).


One of the characteristics that distinguish earth science data from most other data is that the data belong to same location in space. Spatial features of the data set such as the location of extreme values, the overall trend, or the degree of continuity are of considerable interest (Isaaks and Srivastava, 1989). These features, in other words the variables Z(x), are functions describing natural phenomena that have geographic distributions, such as the elevation of terrain, the depth of groundwater table, or the ore grade within an ore body.


Swan and Sandilands (1995) studied the difference between Kriging techniques and the other estimation methods and found that Kriging is a different and spatial way of making estimates of spatially distributed values from point value. The following are the key elements involved:

Several Kriging techniques are widely used. According to different requirements of different problems, one refers to simple Kriging when the mean is known and constant; universal Kriging and intrinsic Kriging that allow fluctuations in the mean; log-normal Kriging when processing the logarithms of the original data; or other types of Kriging techniques described in the literature.

The fundamentals and calculations of Kriging techniques are explained in several references such as: David, (1977), Isaaks and Srivastava (1989), Dowd (1992) and in software packages such as; GSLIB, Geo-EAS, ...etc).

3. Development of the Computer Software


This paper introduces a procedure for calculating the ore reserves based on logic and important steps that must be taken into consideration for accurate and certain results. It is not just collect the samples and run the program rather than follow the necessary steps, so the results would reflect a real estimate of the variable(s). Figure (2) shows the necessary steps in the developed Software and the interface between the user and the data.

The procedure is demonstrated through a case study using Maghara coal mine, Sinai, Egypt, where the developed software has been used to estimate the tonnage of the reserves and the thickness of the seam at un-sampled points as well as to map the distribution of the different assays (Isopach maps).

Figure 2:        A flow chart showing the steps for O.R.E. Software.

4. Geology of the Maghara Area

In 1962, coal was recorded among the Jurassic Formations in Sinai Peninsula which occur in two localities: namely Ayun Musa area in western Sinai and Maghara area in northern Sinai.

4.1 Location

Maghara district is of great geological interest and is located in the northern sector of Sinai Peninsula at longitude 33o – 10 to 33o – 40 E and latitude 30o – 25 to 30o – 50 N. Maghara mine in particular, is bounded by latitudes 30o 30 – 30o 45 and longitudes 33o 12, -33o 25, and is located in the northern part of Sinai Peninsula, Figure (3), about 90 km southwest of El-Arish and 120 km east of Ismailia. The area is a regional asymmetrical anticline, whose axis is trending N 55o E.

Figure 3:        Location map of Maghara Coal Mine, Sinai, Egypt.

4.2 General Geology

The geology of the area has been studied by a number of researchers, (El-Far et al., 1966). According to El-Far, who discovered Maghara coalfield in 1959, the boundaries and structures of Jurassic Formations in Gabal Maghara, coal outcrops, locations of exploratory pits, trenches and more than 15 boreholes are displayed in Figure (4).

Figure 4:        Geological map of Maghara area in northern Sinai showing the distribution of Jurassic Formations and boundaries or the Shusha and Safa Formations in which coal seams are localized (After El-Far et. al, 1966).



4. Data and Preliminary Statistical Analysis

The data used throughout this research are collected from 19 boreholes at the Upper Coal Seam (UCS) and 29 boreholes at the Main Coal Seam (MCS) of Maghara coal mine. For each sampling borehole X, Y, Z, thickness of overburden, and thickness of the seam were measured. Most of the borehole samples have a complete analysis for 7 variables: ash, carbon, hydrogen, nitrogen, moisture, oxygen and sulphur that characterise the quality of the coal.

The main statistical parameters such as, measure of location, shape and spread have been tested separately for each set of variables and a summary of the overall data is given in Table (1) for the UCS and in Table (2) for the MCS.

Table 1:           Summary statistics for the (UCS).

Variable

Mean

Variance

Standard Deviation

Min.

Max.

Standard

Skew

Standard

Kurtosis

Ash

9.38053

16.6142

4.07605

4.67

19.4

1.99284

0.945177

Carbon

68.7679

18.6876

4.32292

57.7

75.58

-1.2759

0.784183

Hydrogen

5.84211

0.106718

0.32667

5.17

6.49

-0.33116

0.049751

Moisture

4.27895

0.651721

0.807292

2.8

5.8

-0.32108

-0.349306

Nitrogen

1.38684

0.611634

0.78207

0.8

4.34

5.94596

11.0293

Oxygen

8.27316

3.37975

1.83841

3.35

9.74

-4.01834

4.0223

Sulphur

2.00947

0.55285

0.743539

0.96

3.25

0.346857

-0.903897

Table 2:           Summary statistics for the (MCS).

Variable

Mean

Variance

Standard Deviation

Min.

Max.

Standard

Skew

Standard

Kurtosis

Ash

7.85586

8.6074

2.93384

3.2

16.95

1.9997

2.13463

Carbon

69.5872

5.49326

2.34377

63.85

74

-0.39216

0.025317

Hydrogen

5.78103

0.0744239

0.272807

5.33

6.6

1.7339

1.75027

Moisture

4.31103

1.66156

1.28901

2.8

9.5

5.12851

9.5931

Nitrogen

1.22655

0.0204163

0.142885

0.95

1.43

-0.84904

-0.744281

Oxygen

8.66586

1.93602

1.39141

2.68

10.63

-6.3754

13.3982

Sulphur

2.5831

0.676529

0.822514

1.39

4.85

2.32822

1.03893

Two boreholes have been excluded from the first round of data surveying, namely, BH.Sand and BH.Conc. The reason behind this decision was the expected difficulties in area calculations and misleading results due to very short distance between the boreholes. Statistical analysis of the different variables has shown that the following boreholes (M3, M5, M5a and M13) at the (UCS) do have missing data. In fact, the available data were provided without core thickness at these boreholes. In the case of the (MCS) boreholes K1, K2, and M13 have the same condition, i.e. they are provided with missing data.

The standardised Skewness and standardized Korusis parameters for oxygen and nitrogen variables for the (UCS), are out of the accepted range (-2 to +2). Also, oxygen and moisture variables, from the (MCS), are out of the accepted range; see Tables (1 & 2).

Figure (5) shows a triangulation map of the sampling points of the Upper Coal seam at the area, while Table (3) shows a part of the input data as it appears in the developed software. The thickness of the coal seam at each of the sampling points for the UCS is included in Table (3). Not to mention, the work has been repeated with data for the MCS.


Figure 5:        Triangulation net for calculating the average thickness of the Upper Coal Seam of Maghara mine.

Table 3:           A capture from the "O.R.E. Software" showing the values of the sampling points (UCS).




Figure 6:        A capture from O.R.E Software showing the thickness of the boreholes (UCS).

6. Results and Analysis

Based on the statistical analysis of the chemical variables associated with the borehole sampling at Maghara area, it has been concluded that the actual sampling points that are suitable for estimation and analysis are 42 samples. Also the analysis of the oxygen variable whether from (UCS) or (MCS) has showed a non-linear distribution, and it has been decided to exclude it from further analysis.

Results obtained using Triangular method and Ordinary Kriging for the average thickness, total area, tonnage, and the distribution of the ash%, carbon%, and sulphur%, are obtained and the following is an example.

Number of triangles

73

Total area

26030587.2m2

Volume

12166938.7m3

Average thickness of (UCS)

0.467m

Reserves

17381340.9 ton

Average thickness of overburden

241.096m

Volume of overburden

6275863588m3


The estimation of the thickness of the overburden or the thickness of the coal seam at any un-sampled point within the selected triangulation net can be estimated using the O.R.E. Software. Table (4) includes the results of some random points for thickness estimation.

Table 4:           Estimated sicknesses of the overburden and coal seam (MCS).

Point

X, m

Y, m

h1 (UCS)

(Overburden), m

h2 (UCS), m

1

134718.38

113346.81

328.7

0.576

2

138091.27

1174516.28

247.78

0.58

3

137536.94

1174998.73

300.17

0.65

4

137040.16

1173614.17

154.60

0.72

5

137870.93

1176465.45

358.91

0.15

6

140125.16

1175906.13

099.70

0.39

7

136294.60

1175007.82

342.49

0.39

Point 3 refers to borehole M21b and point 4 refers to borehole M15.

Figures (7) and (8), illustrate the results obtained in the form of contour maps (Isopach) for both the UCS and MCS respectively, and for three of the tested variables.

a) Carbon%

b) Carbon%

a) Ash%

b) Ash%

a) Sulphur%

b) Sulphur%

Figure 7:        Contour maps (isopach) for carbon, ash and sulphur of the (UCS) using the Triangular method a) Plots using SURFER 7        b) Plots using O.R.E. Software.

a) Carbon%

b) Carbon%

a) Ash%

b) Ash%

a) Sulphur%

b) Sulphur%

Figure 8:        Contour maps (isopach) for carbon, ash and sulphur of the MCS), using the Triangular method a) Plots using SURFER b) Plots using O.R.E. Software



Validation of the Developed Software

In order to examine the reliability of the developed Software, the results of ore reserve estimation of the (MCS) have been compared with the last report about the same area and provided by The Ministry of Industry and Mining Projects, Egypt, (Powell Duffryn, ..etc., 1996).

Proved ore reserves of the (MCS) = 27 million tons (report)

Calculated ore reserves using O.R.E Software = 26.62 million tons.

These close results do not mean that the calculations done using the developed software is correct rather than it is just a hint of the correct way. However, it is believed that the difference came from the high precision of the method used in the O.R.E Software. Using the correct coordinates of the sampling points will give more exact determination of the lengths than measuring the lengths from the existing maps (low accuracy especially with a small map scale).

Another way to check the quality of the developed Software is to compare the visual results with one of the known Software’s (SURFER 7.0). Figures (7 and 8) show how close the two results are.



7. Conclusions


The introduced O.R.E. Software has the following facilities:

q estimating the tonnage of ore reserve at acquired area provided that sufficient sampling boreholes are available;

q calculating the area and average thickness or assay within any portion of the entire area;

q determining the lengths between any two sampling points using their X and Y coordinates;

q mapping the boreholes in two- or three- dimensions; and

q link the output data with Surfer Software for contouring the surfaces and conducting a three dimensional representation of the area.

Acknowledgements

The authors would like to thank the people at Maghara Coal Company for their help and cooperation for providing the data and thanks to Engineer Osama El Mokaddem who helped in the computer programming.



REFERENCES

Ahmed, S.S. (2001) “Three-dimensional Characterisation of Groundwater Parameters around Mines and Landfill Sites”. Ph.D., Thesis, Royal School of Mines, Imperial College of Science, Technology & Medicine, London, UK, 230 p.

David, M. (1977) Geostatistical Ore Reserve Estimation”. Elsevier Scientific Publishing, Amsterdam, 364 p.

David, J.K. (1999) “Programming Visual C++”. (5th Edition). Microsoft Press.

Deutsch, C.V. and Journel, A.G. (1998) “GSLIB: Geostatistical Software Library and User’s Guide”. Oxford University Press, New York, 369 p.

Dowd, P.A. (1992) Basic Geostatistics for Mining Industry”. University of Leeds, Leeds, UK, 226 p.

El-Far, D.M. (1966) Geology and Coal Deposits of Gabel El Maghara Egypt”. Geol Survey, Paper No.37, 59 p.

Isaaks, E.H. and Srivastava, R.M. (1989) An Introduction to Applied Geostatistics. Oxford Univ. Press, New York, 561 p.

Microsoft® Visual C++. Release 6.0, Microsoft Corp., (1981-1998) (Software).

Powell Duffryn Technical Services Limited. (1966) Maghara Coal Project”, Unpublished Report on Reserves and Relevant Geology. Geol. Survey, Egypt.

Royle, A. G. (1992) A personal overview of geostatistics. From Annels, A. Ed (ed.), Case Histories and Methods in Mineral Resources Evaluation, Geological Society Special Publication, No. 63, pp 233-241.

Surfer. Release 7.0, Golden® Software, Inc., (1993-1999) (Software).

Swan, A.R.H. and Sandilands, M.H. (1995) Introduction to Geological Data Analysis” Blackwell Science Inc; 446 p.

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