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:
 Extent Determination and
 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:
 Polygon Method
 Triangular Method
 Sectional Method
Recommended: SEE WORKED EXAMPLES OF THESE METHODS
 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.
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
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.
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.
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

Recommended: SEE WORKED EXAMPLES OF THESE METHODS
Ore Reserve Estimation  Polygon and Triangular method
Reviewed by CEDRICK KAU
on
May 25, 2017
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