APPLICATION OF NUMERICAL METHODS IN STATISTICA PROCESS CONTROL (SPC)
PT. Freeport Indonesia is a mining company with majority ownership by Freeport-McMoRan Copper & Gold Inc. ie 81.28% and the rest is PT. Indocopper Investama 9.36% and the Indonesian government itself which is only 9.36%. Minerals produced include gold, Silver, Molybdenum and rhenium.The process begins operation of mining activities by applying the technique of open-pit or open cut mining at the Grasberg mine as well as techniques ambrukan or block-caving underground mine in the Deep Ore Zone (DOZ). Then the crushed ore mining results using several different techniques to further destruction of the separation process concentrates containing minerals such as copper, gold and silver. Concentrated in the form of slurry (slurry) is transferred from plant to plant in the port Amamapare drying.The process of drying pulp (slurry) is dried concentrate with 3 units of rotary vacuum disc filters and a new pressure filter unit. Concentrates are hardened (cake) from the rotary vacuum disc filters and then dried with 3 pieces of a rotary kiln burner. Concentrate dry with moisture content of about 9% of the concentrate is stored in the warehouse with a capacity total of approximately 135,000 tons metric. Additional storage space available on the pads next to the dryer plant.
One unit of equipment used in slurry drying process is a pressure filter unit. This unit serves to filter the slurry concentrate with high pressure. The use of very high pressure resulting in possible damage to this unit, causing the drying of concentrate did not meet eligibility standards processed. Therefore it is necessary to test the quality of the process of the unit by using Statistica Process Control (SPC) to monitor, control, analyze, manage and improve products and processes.Statistica Process Control (SPC) in this regard will be applied as a statistical method for monitoring and control process to ensure that the machine working at its full potential and generate the appropriate product. Excess SPC lies in the ability to examine the processes and sources of variation in the process by providing objective analysis allowing each source will be determined numerically.
APPLICATION OF NUMERICAL METHODS IN NUMERICAL GEOLOGYNumerical Geology actually can not be separated by geostatistics. Geology numerically almost equal to the numerical method, namely as a bridge between the mathematics and computer algorithms. Without a numerical method is very difficult to apply the mathematical processes on the computer. Examples are easy, such as to make interpretation of the curve equating method (matching curve) as in the interpretation of geoelectric or groundwater pumping test. The curve of raw / standard (model) can be mathematically calculated and field data can be easily plotted on a graph. The question is how do the equation of curve with a computer? Undeniably, the curve equation can be manually performed by sliding the standard curve (as in the lab geohydrology and geophysical exploration) to nearly exact position of the curve in the vicinity of data points. But in this kind of thing a computer can not be done. To equate the standard curve and pitch curve is usually done by a method of iteration (looping), which will produce a minimum error value from the equation of standard curve with field points.Examples of numerical methods are widely used in geology: Iteration Gauss, Gauss-Siedal, Newton-Raphson, Gauss-Newton.Recent developments have included some mathematical methods:· Fuzzy logic (for modeling porosity and image characterization for petrography)· Fuzzy c-means Cluster Analysis (for the exploration of mineral deposits)· Fractal, FEM (finite element method), FFT (fast Fourier transform), etc.· ANN (artificial neural network) that is widely used for modeling mine
APPLICATION OF NUMERICAL METHODS IN COAL MINE OPEN
Case Example One Dimensional Numerical IntegrationCalculation of Volume and Weight Stone Cover (Overburden)
Problem:An open cut coal mine (pit) is planned with the following quantities:- Equation topographic lines: H (x) = -3 (10-09) x3 + 2 (10-05) x2- 0.0591x + 362.06, with x (m) and H (x) is the position of the reference point and elevation from sea level (m).- The inclination (dip) and highwall coal respectively 6o and 60o.- The coordinates of points A, B and C are (10.361), (1510.100) and (1629.306) With these data required to calculate the total volume of overburden that must be opened from the open coal mine.
UNDERGROUND MINING METHOD SELECTION OF NUMERICA
Parameters in use:1. Deposit geometry and grade distribution2. Rock mass strength for the ore, hangingwall and footwall3. Mining costs and capital required4. The rate of mining5. Type the ability of workers / labor6. Environmental issues7. Other special considerations
Data needed1. GeologyInterpretation of the geological evaluation Dlm mrpkn important bag min. Dr. tsb verifiable interpretations made peta2 geological cross-section and interchangeable pieces shows the main types of bat, alteration zones, veins, etc. fold axis.
2. Deposit geometry and Distribution LevelsFrom the geometry defined retrievable geological interpretation and grade distribution. Geometry CEB stated Dlm:- Form: irregular dimensions, sheets, tubes, irregular.- The thickness of the ore: thin, medium, thick, very thick- Subduction: flat, moderate, steep- The depth of the ore- Distribution of content: uniform, gradual, erratic
3. Characteristics of Mek-BatIncludes:- Strength of rock intack: mrpkn ratio of uniaxial compressive strength against tek cover soil.- Space fracture: is determined based on the number of fragments per meter or RQD (Rock Quality Designation). RQD adl Qty PJG all core pieces reply> or equal 2 times the diameter of the core, divided by the total PJG drilling.- Strong shear fractions (weak, moderate, strong)
Steps in Numerical Mining Method Selection:1. Defining characteristics of geometry and grade distribution and characteristics of the bat Mek2. Assign numeric value to each characteristic geometry and grade distribution3. Set the numeric value of each characteristic Mek-bat for the bjh, HW areas, FW Area4. Summing the numerical value of dr characteristics of geometry and grade distribution, characteristics Mek
bat ore district, regional and local HW FW.5. Develop ranking meth berdsrkan mining large numerical values.
NUMERICAL METHODS IN GeostatisticsGeostatistics is a collection of numerical techniques related to the characterization of spatial attributes, especially applying random models in the same manner as daret time analysis of temporal data (Olea, 1999).Geostatistics is a method that has proven reliable for estimating the various types of mining. Lately various applications successfully applied in the petroleum industry (petroleum), especially for the manufacture of contour as well as modeling and simulation of the internal heterogeneity of the reservoir-reservoir. Applications in other fields including environmental sciences, hydrogeology, agriculture, fisheries and even, where the time component as well as spatial changes become very important. Basic tools in geostatistics, ie variogram, is used to quantify the spatial correlation between observations. Mathematical models have been fit out the experimental variogram, this model can be used to estimate the values at points not sampled (not known). The procedure is referred to as kriging estimation, after Danie Krige (South Africa) and Herbert Sichel developed the Witwatersrand gold mines.Geostatistics was originally developed in the mineral industry to perform the calculation of mineral reserves, such as gold, silver, platinum. D.K. Krige, a South African mining engineer, brought the issue from the point of view of probabilistic later by George Matheron, an engineer from the Ecoles des Mines, Fontainebleau, France, giving attention to the work of Krige and apply probabilistic and statistical theory to formulate the approach in the calculation of reserves Krige ore, known as the kriging method.In further developments many multivariate statistical applications included in geostatistics, such as trend surface analysis, cluster analysis, factor analysis, diskriminant analysis, and principle component analysis. Even today, a method which is not based on probabilistic theory used for analysis in the field of earth science, for example basing on fuzzy logic set theory known as Theory of fuzzy sets as in the method of FCM (Fuzzy c-means cluster analysis). This method is now widely used for petrographic analysis, porosity and permeability modeling, and GIS.Practical application of geostatistics can now be said to infinity. Each experiment was made within the framework of space (such as data in the coordinate space and value) to use geostatistics as a tool to process and interpret. What makes the geostatistical very useful is its ability to characterize in terms of application of spatial structure with a consistent probabilistic model. Spatial structure is characterized by the variogram. Basically, there are two kinds of methods that are based on the variogram and covariance are available, namely:for mapping and estimation, variogram can be used for interpolating between data points (kriging), andto characterize the uncertainty in the estimation (the volume of petroleum, levels above the cut-off, the risk of pollution), the same variogram can be used.As a basic science, there are no limits on the use of geostatistics for a particular field. Geostatistics can be used in the following areas: mining industry (was originally developed), as well as petroleum, environment, meteorology, geophysics, agriculture and fisheries, marine, earth science, physics of heterogeneous media, civil engineering, accounting, and perhaps astrophysics.Some examples of geostatistical applications in mining:Estimate the total reserves,Estimating error,Calculating the optimal sampling distance,Estimating block,Contour mapping and manufacture of the grid,Simulate the deposit for the planning,Estimate the recovery area.
Program 'open source' Geostatistics and numericalCurrently, the development programs based on open source is very fast, even faster than we can say the program proprietary. The meaning of open source programs are the programs provided by the application source code, which the user can be edited, modified for specific purposes. These programs are freely available on the Internet. Source code for earth science application programs can be downloaded from its website the International Association of Mathematical Geology (http://www.iamg.org/). Various open source program that can be used for geological data processing, among others, can be seen in the following table.
Kind of Program Analysis(Licensed GPL) DescriptionNumerical Analysis Root, Scilab, and Rlab program is to process a rather complex data, eg for modeling.Geostatistical R-stat with geo-R, Gstat, Uncert, and Delivery program is to process statistics from univariate to multivariate geostatistical module has been completed.
In addition, among the various programs GIS (Geographic Information System), one of the most popular on the market today for the analysis is the ArcGIS Geostatistical Analyst geostatistikal (see website: www.esri.com / geostatisticalanalyst). ArcgGIS Geostatisticalanalyst is a bridge to connect the geostatistical with GIS analysis, mainly to explore and generate spatial data in a statistical surface. Three main scope of the ability of ArcGIS Geostatistical Analyst is to: (1) exploratory spatial data analysis, (2) Creation of spatial surface information, and (3) Diagnosi and comparative prediction models.
Among the many benefits of ArcGIS Geostatistical Analyst is applied in the following areas.:· Archaeology· Environmental Protection· Geology exploratory· Forestry· Hydrology· Meteorology· Mining
PT. Freeport Indonesia is a mining company with majority ownership by Freeport-McMoRan Copper & Gold Inc. ie 81.28% and the rest is PT. Indocopper Investama 9.36% and the Indonesian government itself which is only 9.36%. Minerals produced include gold, Silver, Molybdenum and rhenium.The process begins operation of mining activities by applying the technique of open-pit or open cut mining at the Grasberg mine as well as techniques ambrukan or block-caving underground mine in the Deep Ore Zone (DOZ). Then the crushed ore mining results using several different techniques to further destruction of the separation process concentrates containing minerals such as copper, gold and silver. Concentrated in the form of slurry (slurry) is transferred from plant to plant in the port Amamapare drying.The process of drying pulp (slurry) is dried concentrate with 3 units of rotary vacuum disc filters and a new pressure filter unit. Concentrates are hardened (cake) from the rotary vacuum disc filters and then dried with 3 pieces of a rotary kiln burner. Concentrate dry with moisture content of about 9% of the concentrate is stored in the warehouse with a capacity total of approximately 135,000 tons metric. Additional storage space available on the pads next to the dryer plant.
One unit of equipment used in slurry drying process is a pressure filter unit. This unit serves to filter the slurry concentrate with high pressure. The use of very high pressure resulting in possible damage to this unit, causing the drying of concentrate did not meet eligibility standards processed. Therefore it is necessary to test the quality of the process of the unit by using Statistica Process Control (SPC) to monitor, control, analyze, manage and improve products and processes.Statistica Process Control (SPC) in this regard will be applied as a statistical method for monitoring and control process to ensure that the machine working at its full potential and generate the appropriate product. Excess SPC lies in the ability to examine the processes and sources of variation in the process by providing objective analysis allowing each source will be determined numerically.
APPLICATION OF NUMERICAL METHODS IN NUMERICAL GEOLOGYNumerical Geology actually can not be separated by geostatistics. Geology numerically almost equal to the numerical method, namely as a bridge between the mathematics and computer algorithms. Without a numerical method is very difficult to apply the mathematical processes on the computer. Examples are easy, such as to make interpretation of the curve equating method (matching curve) as in the interpretation of geoelectric or groundwater pumping test. The curve of raw / standard (model) can be mathematically calculated and field data can be easily plotted on a graph. The question is how do the equation of curve with a computer? Undeniably, the curve equation can be manually performed by sliding the standard curve (as in the lab geohydrology and geophysical exploration) to nearly exact position of the curve in the vicinity of data points. But in this kind of thing a computer can not be done. To equate the standard curve and pitch curve is usually done by a method of iteration (looping), which will produce a minimum error value from the equation of standard curve with field points.Examples of numerical methods are widely used in geology: Iteration Gauss, Gauss-Siedal, Newton-Raphson, Gauss-Newton.Recent developments have included some mathematical methods:· Fuzzy logic (for modeling porosity and image characterization for petrography)· Fuzzy c-means Cluster Analysis (for the exploration of mineral deposits)· Fractal, FEM (finite element method), FFT (fast Fourier transform), etc.· ANN (artificial neural network) that is widely used for modeling mine
APPLICATION OF NUMERICAL METHODS IN COAL MINE OPEN
Case Example One Dimensional Numerical IntegrationCalculation of Volume and Weight Stone Cover (Overburden)
Problem:An open cut coal mine (pit) is planned with the following quantities:- Equation topographic lines: H (x) = -3 (10-09) x3 + 2 (10-05) x2- 0.0591x + 362.06, with x (m) and H (x) is the position of the reference point and elevation from sea level (m).- The inclination (dip) and highwall coal respectively 6o and 60o.- The coordinates of points A, B and C are (10.361), (1510.100) and (1629.306) With these data required to calculate the total volume of overburden that must be opened from the open coal mine.
UNDERGROUND MINING METHOD SELECTION OF NUMERICA
Parameters in use:1. Deposit geometry and grade distribution2. Rock mass strength for the ore, hangingwall and footwall3. Mining costs and capital required4. The rate of mining5. Type the ability of workers / labor6. Environmental issues7. Other special considerations
Data needed1. GeologyInterpretation of the geological evaluation Dlm mrpkn important bag min. Dr. tsb verifiable interpretations made peta2 geological cross-section and interchangeable pieces shows the main types of bat, alteration zones, veins, etc. fold axis.
2. Deposit geometry and Distribution LevelsFrom the geometry defined retrievable geological interpretation and grade distribution. Geometry CEB stated Dlm:- Form: irregular dimensions, sheets, tubes, irregular.- The thickness of the ore: thin, medium, thick, very thick- Subduction: flat, moderate, steep- The depth of the ore- Distribution of content: uniform, gradual, erratic
3. Characteristics of Mek-BatIncludes:- Strength of rock intack: mrpkn ratio of uniaxial compressive strength against tek cover soil.- Space fracture: is determined based on the number of fragments per meter or RQD (Rock Quality Designation). RQD adl Qty PJG all core pieces reply> or equal 2 times the diameter of the core, divided by the total PJG drilling.- Strong shear fractions (weak, moderate, strong)
Steps in Numerical Mining Method Selection:1. Defining characteristics of geometry and grade distribution and characteristics of the bat Mek2. Assign numeric value to each characteristic geometry and grade distribution3. Set the numeric value of each characteristic Mek-bat for the bjh, HW areas, FW Area4. Summing the numerical value of dr characteristics of geometry and grade distribution, characteristics Mek
bat ore district, regional and local HW FW.5. Develop ranking meth berdsrkan mining large numerical values.
NUMERICAL METHODS IN GeostatisticsGeostatistics is a collection of numerical techniques related to the characterization of spatial attributes, especially applying random models in the same manner as daret time analysis of temporal data (Olea, 1999).Geostatistics is a method that has proven reliable for estimating the various types of mining. Lately various applications successfully applied in the petroleum industry (petroleum), especially for the manufacture of contour as well as modeling and simulation of the internal heterogeneity of the reservoir-reservoir. Applications in other fields including environmental sciences, hydrogeology, agriculture, fisheries and even, where the time component as well as spatial changes become very important. Basic tools in geostatistics, ie variogram, is used to quantify the spatial correlation between observations. Mathematical models have been fit out the experimental variogram, this model can be used to estimate the values at points not sampled (not known). The procedure is referred to as kriging estimation, after Danie Krige (South Africa) and Herbert Sichel developed the Witwatersrand gold mines.Geostatistics was originally developed in the mineral industry to perform the calculation of mineral reserves, such as gold, silver, platinum. D.K. Krige, a South African mining engineer, brought the issue from the point of view of probabilistic later by George Matheron, an engineer from the Ecoles des Mines, Fontainebleau, France, giving attention to the work of Krige and apply probabilistic and statistical theory to formulate the approach in the calculation of reserves Krige ore, known as the kriging method.In further developments many multivariate statistical applications included in geostatistics, such as trend surface analysis, cluster analysis, factor analysis, diskriminant analysis, and principle component analysis. Even today, a method which is not based on probabilistic theory used for analysis in the field of earth science, for example basing on fuzzy logic set theory known as Theory of fuzzy sets as in the method of FCM (Fuzzy c-means cluster analysis). This method is now widely used for petrographic analysis, porosity and permeability modeling, and GIS.Practical application of geostatistics can now be said to infinity. Each experiment was made within the framework of space (such as data in the coordinate space and value) to use geostatistics as a tool to process and interpret. What makes the geostatistical very useful is its ability to characterize in terms of application of spatial structure with a consistent probabilistic model. Spatial structure is characterized by the variogram. Basically, there are two kinds of methods that are based on the variogram and covariance are available, namely:for mapping and estimation, variogram can be used for interpolating between data points (kriging), andto characterize the uncertainty in the estimation (the volume of petroleum, levels above the cut-off, the risk of pollution), the same variogram can be used.As a basic science, there are no limits on the use of geostatistics for a particular field. Geostatistics can be used in the following areas: mining industry (was originally developed), as well as petroleum, environment, meteorology, geophysics, agriculture and fisheries, marine, earth science, physics of heterogeneous media, civil engineering, accounting, and perhaps astrophysics.Some examples of geostatistical applications in mining:Estimate the total reserves,Estimating error,Calculating the optimal sampling distance,Estimating block,Contour mapping and manufacture of the grid,Simulate the deposit for the planning,Estimate the recovery area.
Program 'open source' Geostatistics and numericalCurrently, the development programs based on open source is very fast, even faster than we can say the program proprietary. The meaning of open source programs are the programs provided by the application source code, which the user can be edited, modified for specific purposes. These programs are freely available on the Internet. Source code for earth science application programs can be downloaded from its website the International Association of Mathematical Geology (http://www.iamg.org/). Various open source program that can be used for geological data processing, among others, can be seen in the following table.
Kind of Program Analysis(Licensed GPL) DescriptionNumerical Analysis Root, Scilab, and Rlab program is to process a rather complex data, eg for modeling.Geostatistical R-stat with geo-R, Gstat, Uncert, and Delivery program is to process statistics from univariate to multivariate geostatistical module has been completed.
In addition, among the various programs GIS (Geographic Information System), one of the most popular on the market today for the analysis is the ArcGIS Geostatistical Analyst geostatistikal (see website: www.esri.com / geostatisticalanalyst). ArcgGIS Geostatisticalanalyst is a bridge to connect the geostatistical with GIS analysis, mainly to explore and generate spatial data in a statistical surface. Three main scope of the ability of ArcGIS Geostatistical Analyst is to: (1) exploratory spatial data analysis, (2) Creation of spatial surface information, and (3) Diagnosi and comparative prediction models.
Among the many benefits of ArcGIS Geostatistical Analyst is applied in the following areas.:· Archaeology· Environmental Protection· Geology exploratory· Forestry· Hydrology· Meteorology· Mining