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/m^{3}.
Figure 1: Drill Plan
and conceptual outline of the minetechpg orebody (green).
Drill Sections:
Section AA’

Section BB’

Section CC’

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) (m^{2})

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) (m^{2})

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.
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