Ore Reserve Estimation Methods – Detailed Tutorial

What is Mineral Reserve / Ore Reserve?

Mineral Resources are defined as the concertation of material of economic interest in earth’s crust. Ore reserves are those part of Resources for which grade and tonnage have been established with reasonable assurance by sub-surface sampling techniques and it can be mined profitably using current technology.

Definition of Reserve Estimation –

The reserve estimation is quantification of economic material present in the ore body with reasonable accuracy. It also involves computation of grade, thickness and different qualitative parameters which are required for commercial exploitation of the ore.

What are the ways of ore reserve estimation?

The ore reserve estimation methods can be grouped in three ways-

1. Geometric Method (Conventional Method)
2. Statistical or Geostatistical Method
3. Computer application or software

What is the basic principle of ore reserve estimation?

The basic principle of ore reserve estimation is utilizing tonnage formula. The unit of estimation is tonne (t) and formula is –

Tonnage (t) = Volume (V) x Specific Gravity (Bulk density)

The above equation can be compared with mass volume formula where –

Mass = Volume x Density

Volume can be calculated as –

Volume (V) = Area (A) x Influence of a third dimension

Area (A) is calculated from borehole plan or sections.

Influence is determined based on the method of estimation.

Basic Assumptions – Several assumptions are taken for reserve estimation. They are –

1. The parameters of an ore body established at one point changes to an adjoining point in accordance with certain principle like rule of gradual changes, rule of nearest points.
2. The projected continuity of ore body based on exploration data is supposed by geological setup.
3. The samples are collected with equal precision at every point and they are representing the ore zone.

In this article we will discuss only Conventional Methods of Ore Reserve Estimation. There are many methods of computation based on anisotropy, drilling grid pattern and stage of exploration.

1. Polygonal method
2. Triangular method
3. Cross section method
4. Inverse Distance method

Polygonal Method

The method is based on area of influence. The area of influence is determined by constructing polygonal blocks around each hole that extends half the distance between two holes. The average grade and thickness of the hole inside the polygon is assigned to the entire polygon in order to provide a volume for the reserve estimate. The volume is computed by multiplying the area of polygons with thickness. Volume is multiplied with specific gravity to get tonnage. Summation of all polygon will get tonnage and metal content of total deposit.

Polygonal method is used for tabular and large lenses ore bodies.

Disadvantages of this methods are –

1. It gives greater weight to isolated hole.
2. The assay values are used only once.

A variant of polygonal method using values of holes at corners of polygons instead of the center. It will be discussed as triangular method.

Triangular Method

This method is slightly advance version of polygonal method. In this method holes are connected to adjacent holes. This divides the ore body into a series of triangles (T₁, T₂, – – – – – -, T_n). Each triangle rests on the plane of the map and represents a base area of an imaginary prism with edges t₁, t₂, t₃ equal to vertical thicknesses of intercepted mineralisation. In this method, the triangle area between three adjacent holes, average grade and thickness of these holes are used to compute tonnage.

Computation steps

Following steps are involved in triangular method-

1. Area of triangle is calculated using geometrical formula. Area (A) is multiplied by average thickness intercepted in holes at three edges of that triangle to get volume (V).
2. Tonnage is computed by multiplying volume (V) with average specific gravity of host rock. This will give tonnage of one triangle.
3. Metal content is estimated by multiplying tonnage (step 2) and average grade.
4. Step 1 & 2 are repeated for all triangles with positive intercepts at their edges.
5. The total tonnage and metal content of deposit are arrived by summation of values calculated for each triangle.

The triangular method is best suitable for flat or gentle dipping ore body having good continuity and correlation.

Different formulas involved in calculation are –

Where s is semi-perimeter of the triangle.

Datasheet of triangular method will look like below-

Cross Section Method

In this method ore body is interpreted on cross-section. The ore body is divided into different segments with the help of transverse section lines. The section line can be spaces at equal or unequal intervals based on grid interval and hole locations.

 Computation steps

1. The total ore body is divided into sub-blocks along section line and a length equal to half of the distance between the adjoining sections.
2. For computation of reserve, volume of each sub-block is required. The volume is calculated by multiplication of sectional area with half the distance of adjoining section on each side (i.e. area of influence).
3. The sectional area of ore body is calculated by geometric formula. AutoCAD software can be used to measure area of irregular ore body.
4. Tonnage for each sub-block is calculated by multiplication of volume and specific gravity.
5. Metal content of each sub-block is calculated by multiplying tonnage and average grade of that sub-block.
6. Total tonnage of ore body is summation of sub-block tonnages. Similarly, total metal content is summation of sub-block metal contents.
7. Average grade of ore body is total metal content divided by total tonnage in percentage term.

Datasheet of cross sectional method will look like below-

Inverse Distance Method

Inverse distance method belongs to the class of moving average methods. It based on repetitive calculations and therefore require the use of computers. In this method weightage of the hole is given according to distance from the block in which computation is to be made. More weightage is given to closer hole compared to the other holes in the region.

It selects only those holes which falls within the influence zone. Inverse distance method utilize the principle that the variable of adjacent boreholes has certain spatial relationship and this relationship is a function of distance.

Unlike polygon method, inverse distance method utilizes the values of all surrounding holes by given certain weights. The weights are determined by the distance between the holes and the center of the block considered for computation. The summation of all weight should be one.

The weighting of the values may be of order one (Inverse to the distance), order two (Inverse to the distance square) etc. This method ignores directional anisotropy in weighting scheme.

Inverse distance method can be applied to deposits with simple to moderate geometry and with low to high variability of grade.

To keep length of the article short, I have discussed only selected conventional methods here. In my other article on this blog, I have discussed Geostatistical Ore Reserve Estimation method.

If you have any doubt or need further clarification on above topic, please do comment below. I will be happy to resolve it.

Suggested Readings

1. Definition of Ore with Example
2. What is the difference between resource and reserve in geology?
3. What is Coral Reefs and types of Coral Reefs?
4. Wilson Cycle: The Cyclical Opening and Closing of Ocean Basins