Tuesday, 5 December 2017

ORE RESERVE ESTIMATION – WORKED EXAMPLE

As requested by some good readers of this blog for numerical examples of ore reserve estimation methods. These examples were put together to broaden the scope of classical (geometrical) methods presented in Classical Methods of Ore Reserve Estimation.

Keeping in mind that the main objective of ore reserve estimation is to as accurately as possible define the extent (size) and value (grade) of a mineral deposit. The two primary concerns confronted are summarized as:
1. Extent (Size) 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 is classical methods. Classical methods employ simple geometric function and rules that are easily applied to simple uncomplicated orebodies.

In the following example, we will be working through the classical methods in determining the tonnage and grade of the Minetechpg Copper Deposit.

It is recommended that these examples are read in line with the post on Classical Methods of Ore ReserveEstimation.

Example

Consider this regular drill pattern spaced 30m by 20m of High Grade at Minetechpg Copper Deposit. There are nine drill holes ranging from DDH 1 to DDH 9. Assuming the surface is flat and faults/discontinuities terminate the continuity of the deposit in which the drill holes define the boundary of the orebody, determine as accurately as possible the tonnage and grade of the deposit using Polygon, Triangular and Sectional Methods of Ore Reserve Estimation. Test indicate that the tonnage factor of ore is 2.15t/m3.
Figure 1: Drill Plan and conceptual outline of the minetechpg orebody (green).

Drill Sections:
Section A-A’
Section B-B’
Section C-C’

Drilling Data

Ore Thickness and Grade:
Drill Hole ID
Thickness (m)
Grade (%)
DDH1
20
10
DDH2
40
6
DDH3
18
7
DDH4
16
9
DDH5
45
5
DDH6
16
6
DDH7
15
5
DDH8
28
7
DDH9
10
8

Solution 

1. Using Polygon Method

Procedure in 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).
Figure 2: Orebody divided into four polygons (P1, P2, P3 and P4 – yellow outline)

Important note: For ease of calculations, polygons were developed around four drill holes but in actual scenarios, polygon must be constructed using set procedures around each drill holes.

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

Procedure in Determining the Value
Value is dependent on the ore grade and therefore the average grades 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(Length x Width) (m2)
Volume (Area x  Thickness) (m3)
Tonnage (2.15m3/t) (tonnes)
Grade (%)
P1
20m x 30 m = 600
600x30.25 = 18150
18150*2.5= 39023
(10+6+9+5)/4 = 7.5
P2
600
17850
38377.5
6
P3
600
15600
33540
6.5
P4
600
14850
31927.5
6.5
Total
2400
66450
142867.5 tons
6.625%

The global resource calculated for the Minetechpg copper deposit using polygon methods is 142867.5 tons (extent/size) ore at an average grade of 6.625% (value) Copper.

     2. Using the Triangular Method

Procedure in 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

Figure 3: Deposit divided into different Triangles

Procedure in 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.
Triangle ID
Area(1/2 Base x Height) (m2)
Volume (Area x  Thickness)
Tonnage (2.15m3/t) (Tonnes)
Grade (%)
T1
20 X 30 X 0.5 = 300
35 X 300 = 10500
10500 X 2.15 = 22575
(10+6+5)/3 =7
T2
300
8100
17415
8
T3
300
10100
21715
5.666667
T4
300
7400
15910
6.333333
T5
300
8900
19135
7
T6
300
5900
12685
7
T7
300
7100
15265
6.333333
T8
300
8300
17845
6.666667
Total
2400
66300
142545 Tonnes
6.75%

The global resource calculated for the Minetechpg copper deposit using triangular method is 142,545 tons (extent/size) ore at an average grade of 6.75% (value) Copper.

In conclusion, the tonnage and grade determined using the two methods is approximately the same. Note that this resource is generic and categorized as opposed of mineral resources and ore reserve definition.

Numerical examples of Sectional Methods will be update in the next post.



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