Ore Reserve Estimation - Polygon and Triangular method



As discussed in my previous post, the main objective of ore reserve estimation is to as accurately as possible define the extent (size) and value (grade) of a mineral deposit.

We are confronted with two primary objective in this process and these are:
  1. Extent Determination and 
  2. Value Determination
Value and extent of a mineral deposit can be estimated using classical methods or geostatistical methods.

The simple yet accurate ore reserve estimation technique used are classical methods. Classical methods employ simple geometric function and rules that are easily applied to simple uncomplicated orebodies. The widely used classical methods used are:
    1. Polygon Method
    2. Triangular Method
    3. Sectional Method
  1. Polygon Method
Determining the extent
To determine the extent of the deposit, polygons are developed around each sampling point to establish the area of influence which extends half the distance (d/2) of the sampling distance (d) (distance between two sample points) and in an equidistant manner.

SP - Sample Point (Blue dot); PLY - Polygon (orange Pentagon); d - sampling distance

Proceed by determining the surface are of the polygon by using geometric functions of the resulting polygon. The volume is determined by multiplying the surface area with the average depth.
Tonnage  is then determined by multiplying the volume with the tonnage factor (specific gravity).

1. Area = Area of Resulting polygon
2. Volume = Area x Average depth of drillhole
3. Tonnage = Volume x tonnage factor

Determining the Value
Value is dependent on the ore grade and therefore the average grade of the polygons are then used to establish the grades of each polygon. The average grade of the deposit is determined by taking the arithmetic average of all grades of the individual polygons.

Information is tabulated in the table below for ease of calculation and interpretation.
Polygon ID
Area
Volume
Tonnage
Average Grade
PLY1
Area of PLY1
Area1 X Av.Depth
Volume1 X tonnage factor
Grade of SP1
PLY2
Area of PLY2
Area2 X Av.Depth
Volume2 X tonnage factor
Grade of SP2
PLY3
Area of PLY3
Area3 X Av.Depth
Volume3 X tonnage factor
Grade of SP3
:
:
:
:
:
PLYn
Area of PLYn
Arean X Av.Depth
Volumen X tonnage factor
Grade of SPn
Total

Total Vol
Total Tonnage
Average Grade

     2. Triangular Method
Determining the extent
Triangular method is and extended approach of the polygon method. To determine the extent of the deposit, triangles are developed such that sampling points form the apices of the triangles. The volume and tonnage of the deposit is then determined using simple geometrical equations.  

1. Area = Area of Resulting Triange
2. Volume = Area x Average depth of the apice drillholes
3. Tonnage = Volume x tonnage factor

Determining the Value
The average grade of the deposit is determined by taking the arithmetic average of all grades of the individual triangles.
Information is tabulated in the table below for ease of calculation and interpretation.
Triange ID
Area
Volume
Tonnage
Average Grade
T1
Area of T1
Area1 X Av.Depth
Volume1 X tonnage factor
Average Grade of SP1, SP6 & SP2
T2
Area of T2
Area2 X Av.Depth
Volume2 X tonnage factor
Avergae Grade of SP1, SP4, SP3
T3
Area of T3
Area3 X Av.Depth
Volume3 X tonnage factor
Average Grade of SP1, SP2, and SP3
:
:
:
:
:
Tn
Area of Tn
Arean X Av.Depth
Volumen X tonnage factor
Average Grade of SPmno (Apice Sample Points)
Total

Total Vol
Total Tonnage
Average Grade

Ore Reserve Estimation - Polygon and Triangular method Ore Reserve Estimation - Polygon and Triangular method Reviewed by CEDRICK KAU on May 25, 2017 Rating: 5

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