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The mineral reserves & reserves estimation using triangular methods

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It includes the introduction about mineral reserves. It also introducing triangular method to estimate the mineral reserves. Here after solving related problems some relevant problems are introduced for practice.Hope, it will be helpful who wants to estimate ore reserves using triangular methods. Here, the differences between probable and proven reserves also displayed.

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The mineral reserves & reserves estimation using triangular methods

  1. 1. MINERAL RESERVES ESTIMATION BY USING TRIANGULAR METHOD BY MD.NUMAN HOSSAIN DEPT. OF PME ,SUST.
  2. 2. MINERAL RESERVES : • A Mineral Reserve is the economically mineable part of a Measured and/or Indicated Mineral Resource. • It is described as total workable or probable working which depending on thickness of deposit , it’s depth , quality , geological factors etc. • In general mining practice , there are two types of mineral reserves . • These are: (1) probable reserve & (2)proven reserves
  3. 3. :Proven Reserves Probable reserves Proven reserves constitute mining assets with greater confidence than any other mining assets In other word , reserves in fully explored deposits Probable reserves constitute mining assets with lesser confidence than the proven reserves In other word , reserves in estimated and fully explored deposits Mineral recovery :  In mining , the process of valuable mineral extraction in known as mineral recovery  It is the measure of mining or extraction efficiency  For mineral recovery it is very essential to estimate ore reserves,know the mineable reserves , pit limits , cutoff grade etc .  In this slide we will discuss only about different methods for estimating ore reserves.
  4. 4. Methods of ore reserves estimation Triangular method Polygonal methods Method of sections (plans); longitudinal, transverse Regular grid, random stratified grid Inverse distance weighting (1/d, 1/d2, 1/d2.7, 1/d3, etc.) Contouring methods Here we only discuss about triangular method to estimate ore reserves.
  5. 5. Triangular method By using triangular method, the area of the ore body is calculated After that , this calculated area is multiplied with average thickness of the ore to calculate the volume of the ore body The average thickness can be calculated by  Using known thickness of the ore body  Using grade and the length of ore body  Using weight age average thickness After calculating volume , multiplying this value with ore density to estimate the ore reserves.
  6. 6. • Here ,the area of the rectangle abcd = ( X3 – X2) (Y3 –Y1) • Area of triangle A1 = ½ ( X2 - X1)(Y2-Y1) • Area of triangle A2= ½ (X3 –X2) (Y3 –Y1) • Area of triangle A3= ½ (X3 –X1)(Y3 –Y2) • So the area of ore A = area of rectangle abcd – area of triangle (A1+A2+A3)
  7. 7. Calculate A for the following Easting ( x )m northing (y) m 1100 1200 1500 1200 1100 800
  8. 8. Triangular method • Using above equation • The area of rectangle =(1100-1500)(800-1200)=160000 m2 • The area of triangle A1+A2+A3 = 1/2 (( 1500-1100)(1200-1200)+(1500-1100)(1200- 800)+(1100-1100)(800-1200)) =80000 m2 • The area of ore body ,A=160000-80000=80000 m2
  9. 9. Calculation of average thickness of the ore body: 1. If thickness is givenC1= 3 m, C2=5 m,C3= 4 m , then ave. thickness =(C1+C2+C3)/3 =(3+5+4)/3 =4 m 2. If the length of the ore body (m) and the gradient(%) is given then the ave. thickness is calculated by t(ave) = ∑tigi / ∑gi , for example we calculate ave thickness for following case : ymbol
  10. 10. The ave thickness , t(ave) =(0.6*0.59+1.4*0.48+1.4*0.6+1.4*0.56+1.3*0.32)/(0.59+0.48+0.6+0.56+0.32) =0.503 m 3.calculation of reserves using weight age average thickness . For this case the following equ is used: weight age ave. thickness, tw =( (t1Ѳ1+t2Ѳ2+t3Ѳ3)/60 )÷3 = (t1Ѳ1+t2Ѳ2+t3Ѳ3)/ 180 .an example problem related with this is given bellow : where thickness t1=40 m, t2 =60 m ,t3 =50 m. Length of the ore body (m) grade(%) 0.6 0.59 1.4 0.48 1.4 0.6 1.4 0.56 1.3 0.32
  11. 11. Now, ore volume calculation: • Ore volume = area of the ore body * average thickness • For , first case, t(ave)=4 m, so, ore volume = 80000*4 =320000 m3 • For , second case , using length of the ore body and grade, ave thickness = 0.503 So, for this ore volume = 80000*.503 =40240 m3 • For third case, weight age ave thickness , tw =50.77 m then , ore volume = 80000*50.77 =4061600 m3 N.B.here, I use one example problem for several ave thickness ,so don’t be confused with evaluated ore volume .This indicates just calculation procedure . Here, the ave thickness data had not been obtained from same ore reserve but I use here only to show the evaluation procedure ,and so, ore volume can’t be obtained same for all time.
  12. 12. Ore reserve estimation: • Ore reserve(in tons) =ore volume(m3) * density of ore (tons/m3) • For example ,if the density of the ore = 1.35 tons/m3. • Then ,for 1st case, ore reserves =320000*1.35 =432000 tons. • For 2nd case, ore reserves = 40240*1.35 =54324 tons. • For 3rd case, ore reserves =4061600*1.35 =5483160 tons.
  13. 13. Exercise Problem : • For 1st fig the following parameters are given for a ore deposit : • If the thickness for first layer C1=4 m, C2=8m ,C3=3m and for 2nd layer C1=5m,C2=7m,C3=6m .And the density of the ore is 2.5 tons/m3 .Then estimate the reserves for this ore deposit. Easting (x) m Northing (y) m 300 700 600 300 100 0
  14. 14. Exercise Problem : • Estimate the reserves by using triangular method for the following mineral deposit(having density =1.024 tons/m3: Length of ore body (m) grade (%) .9 .62 1.2 .56 1.2 .61 1.8 .49 2.1 .68 2.8 .65 2.8 .61 2.5 .57 2.2 .52 1.9 .48 x (m) y(m) 3500 600 1365 450 350 46 N.B. use fig :1
  15. 15. Exercise Problem : Ѳ2 Ѳ1 Ѳ3 t3(800,1000) t1(200,500) t2(600,1500) Calculate the reserve of the ore shown in above fig having density 2.65 tons/m3 by using the weight average thickness , when t1=80 m, t2 = 125 m, t3 = 98 m.
  16. 16. Exercise Problem • Calculate the reserve of the ore shown in above fig having density 2.65 tons/m3 by using the weight average thickness where others information has give
  17. 17. References : • Open Pit Mine Planning and Design,TwoVolume Set & CD-ROM Pack -William A. Hustrulid, Mark Kuchta, Randall K. Martin • Applied Mineral Inventory Estimation - ByAlastair J. Sinclair & Garston H. Blackwell • Internets & others
  18. 18. THAT’S ALL THANKS……..

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