Resource estimation,
Cut-off grade
By
Dr. B.S. Choudhary
IIT(ISM) Dhanbad
MINE PLANNING AND DESIGN STEPS
1. A long-term price forecast and maximum practical marketable volume per year is
Established.
2. A geologic reserve assessment is made. A grade versus tonnage curve for the contiguous
portion of the ore body including overburden / waste rock is developed. A typical cut-off
grade for the commodity (gold, copper, iron, etc.), type of deposit (deep, shallow, etc.), and
likely mining/processing system is selected.
3. Block net values and costs for both ore and waste are developed using mining and milling
rates ranging above and below those determined in No.2, incorporating capital costs and
return consideration in the ore and waste block evaluations as feasible. Because timing and
various inter-block interactions cannot be directly addressed, these will be only approximate.
4. Sets of pit ultimate design are developed flexing (varying) prices and/or milling/mining
rates and costs to get logical concentric nests of pits. (A block value of 0 to be used as cutoff).
5. Short-range plans within each ultimate pit are developed using average operating slopes.
Holding costs and rates constant, the price is flexed starting above the price of ultimate pit
and work down in increments. This approach should mine the best ore/waste combinations
first. A set of short-range mining segments will be generated in this process and thereby fix
the feasible mine geometry options for a given ultimate pit.
6. Production, revenue, operating and capital cost schedules over time are developed for each
short-range segment and over full mine life from development through closure. These data
will not normally be derived from the block data directly but they must be related for
consistency.
7. Value of each short-range segment is then optimized by flexing cut off criteria and
mining/ore processing rate being careful not to exceed the marketable maximum volume,
using NPV methods. The production and economic schedules in No.6 will be iterated to
accomplish this. The choice of NPV discount rate will impact the results of the total
evaluation process significantly.
8. The NPV of the total pit plan segment sequence is evaluated to confirm optimum.
What is a Mineral Resource?
A Mineral Resource is an estimate of tonnage and grade for a mineralized
body, based on sampling of that body
The estimate represents a realistic inventory that, under assumed and
justifiable technical and economic conditions, might, in whole or in part,
become economically extractable
Portions of a deposit that do not have reasonable prospects for eventual
economic extraction are NOT Mineral Resources
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What is an Ore (Mineral) Reserve?
An Ore Reserve is an estimate of the tonnage and grade that is expected to
be delivered to the mill or treatment plant
It is the economically mineable part of a Mineral Resource
Realistically assumed Modifying Factors (mining, metallurgical, economic,
marketing, legal, environmental, social and governmental factors) must be
taken into consideration
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Mineral Resource Estimation
Requirements for estimating Mineral Resources:
Confident geological interpretation
High quality, representative samples and assays
Application of appropriate estimation technique
This comes from:
Mapping and sampling the deposit
Ensuring the highest standards of sampling and assaying integrity
Employing experienced, qualified professionals (“Competent Persons”)
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Resource Estimation Techniques
Methods for resource estimation or modeling are
generally divided into
Current Mineral Resource/Reserve Reporting
(1) traditional, geometric methods that are done
Standards
manually on plans or sections and
JORC ( joint ore reserve committee) Code
(2) interpolation methods such as inverse-distance- (Australasia) – translations into South American
weighting and kriging that require the use of a computer. Spanish, Portuguese, Mandarin, Japanese and
Russian (in progress)
UNECE Framework Classification (International) –
These estimates are classified and reported in incorporates JORC style definitions for market-
accordance with one of the accepted international related reporting, but is broader in scope,
covering government inventory reporting
reporting standards (e.g. UNFC, JORC, SAMREC) SAMREC Code (South Africa)
CIM Standards (Canada, in NI 43-101)
The Reporting Code (UK/Western Europe)
SME Guidelines (USA)
Chilean and Peruvian Codes
CRIRSCO definitions and reporting standard
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template (International
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– in progress)
The cut-off grade is the minimum ore
grade that can be mined at a profit
under economic conditions existing at a
particular point in time. The cut-off
grade can vary with time due to
changes in such factors as commodity
prices, operating costs, and taxes. The
cut-off grade used for any reserve
calculation should always be stated.
Grade Calculation
Weighted average grade One of the
most frequent calculations are
weightings, e.g. for the calculation of
the • average grade of a drill hole
from assay intervals of different
lengths or • average grade of a
deposit from the combined grades of
individual, unequal blocks.
METHOD OF VERTICAL SECTIONS
1. Side completion for sections.
2. Development of a final pit outline
including pit ends.
3. Determination of tons and average
grade for a section.
4. Determination of tons and average
grade for the pit.
THE METHOD OF HORIZONTAL SECTIONS
In the triangular method, each hole is taken to be at one corner of a triangle.
If the triangular solid formed is of constant thickness t, its volume is just
equal to the plan area A times this thickness. To obtain tons, the appropriate
tonnage factor is applied. The average grade g is given by
In the polygonal method, each drill hole lies within the center of
a polygon. The polygon is constructed such that its boundary is
always equidistant from the nearest neighboring hole.
Within the polygon, the grade is assumed constant and equal to
that of the hole it includes. The thickness of the polygon is also
constant and equal to the ore intercept/bench thickness
Cross Section Method
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.
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).
The sectional area of ore body is calculated by geometric formula.
AutoCAD software can be used to measure area of irregular ore body.
Tonnage for each sub-block is calculated by multiplication of volume and
specific gravity.
Metal content of each sub-block is calculated by multiplying tonnage and
average grade of that sub-block.
Total tonnage of ore body is summation of sub-block tonnages. Similarly,
total metal content is summation of sub-block metal contents.
Average grade of ore body is total metal content divided by total tonnage
in percentage term.
Constant distance weighting techniques
Block modelling
inverse distance weighting technique.
Basic to application of computer techniques for grade and
tonnage estimation is the visualization of the deposit as a
collection of blocks
Inversely with the square of the distance
If one were to select a different power for
d, the results would change. The general
formula is
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Kriging is the geostatistical estimation method
developed to provide the “best linear, unbiased
estimate” for grade based on a least squares
minimization of the error of estimation, or kriging
error.
The variogram is the fundamental tool used by the geostatistician
and geologist to measure spatial continuity of grade data.
The variogram is a graph of the average variability between
samples vs. the distance between samples. A variogram is computed
by averaging the squared differences between pairs of
samples that are a given distance apart as follows
where N is the number of pairs at distance h, and h is the
distance between the samples
Main Factors affecting Mineral Resource/ Reserve
Estimates
Reliability of geological interpretation
Amount, distribution and quality of resource data
In “nuggety” deposits, treatment of very high grades
Assumptions regarding mining and treatment methods
Assumptions regarding commodity prices and exchange rates
Experience and judgment of Competent Person
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UNFC-Total Initial Resources
The total resources initially in-place of naturally occurring energy and mineral
resources, are described in terms of:
Produced quantities,
Remaining recoverable quantities, and
Additional quantities remaining in-place.
The main focus of the UNFC is on remaining recoverable quantities.
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Total initial in-place resources
For non-renewable resources, the total resources initially in-
place is constant. In inventories, material balance is
ISM therefore maintained. If any change appears, this must be16
explained by a re-evaluation.
Classifications
Total remaining resources are categorized using the three essential criteria
affecting their recoverability:
Economic and commercial viability (E).
Field project status and feasibility (F).
Geological knowledge (G).
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Most of the existing resource classifications recognize these
explicitly or implicitly. By making them explicit, the UNFC
becomes a framework that allows for harmonization of existing
classifications. The three criteria are easily visualized in three
dimensions as shown in Figure
Principal elements of the UNFC
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Three main categories are used to describe economic and commercial
viability,
three to describe field project status and feasibility and
four to describe the level of geological knowledge.
Further subdivision of the main categories is useful for special applications.
Resource quantities are then grouped into classes that are defined by an E a
F and a G category represented by the sub-cubes in Figure . A class of
quantities may be a single sub-cube, i.e. 111, or a collection of sub-cubes.
Total resources are an example of such a class where all sub-cubes are
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included in the class. 19
The three dimensions of categorization are represented by the edges of a
cube. The digits are quoted in the order EFG firstly because the
alphabetical order is easy to memorize, and secondly because the first
digit refers to the economic viability, which is of decisive interest to
producers, investors and host countries. Numbers are used to designate
the different classes. Number 1, in accordance with the usual perception
that the first is the best, refers to the highest degree of economic
viability on the E axis, the most advanced project status on the F axis
and the highest quality assessment on the G axis. The use of categories is
different for fluids and for solids. This is primarily due to the fact that
fluids may flow in a reservoir, irrespective of the level of geological
knowledge. In the case of solids, recovery will normally be restricted to
rock bodies that have been reliably assessed.
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Codification
Due to variation between terminologies
in different systems and languages, it is
recommended to use only three-digit
numeric codes for individual categories,
so that they will be universally
understood. For this to be possible, the
sequence is always fixed, so that the
quantity characterized as E1;F1;G1 may
be written in number form as 111,
independent of languages. In practice,
only a limited number of combinations
(classes) are valid. To illustrate, the
UNFC for coal, uranium and other solid
minerals, shown in Figure
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UN-ECE Framework Classification
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The UNFC in matrix form applied to coal, uranium and other
solid minerals
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cut-off grade and its estimation
The cut-off grade is the minimum ore grade
that can be mined at a profit under economic
conditions existing at a particular point in time.
LANE'S ALGORITHM
cut-off grade is the criterion normally used in
mining to discriminate between ore and waste in
the body of a deposit. Waste may either be left in
place or sent to waste dumps. Ore is sent to the
treatment plant for further processing and eventual
sale.
Quantities: T is the length of the production period being considered (for example 1 year);
Q is the quantity of material to be mined, Qc is the quantity of ore sent to the concentrator
and Qr is the amount of product actually produced over this production period.
The basic equations
Using the definitions given in the preceding section, the basic equations can be
developed. The total costs Tc are
This is the basic profit expression. It can be used to calculate the
profit from the next Qm of material mined.
Cutoff grade for maximum profit
Calculate cutoff grade assuming that the concentrating rate is the governing constraint. If the
concentrator capacity C is the controlling factor in the system, then the time required to mine
and process a Qc block of material (considering that mining continues simultaneously with
processing) is
Calculate cutoff grade assuming that the refining rate is the governing
constraint. If the capacity of the refinery (or the ability to sell the product) is
the controlling factor then the time is given by
Brief-Cutoff grade and Resreves
Cutoff grade could be defined as “any grade that for any specific reasons, is used to
separate two courses of action, e.g. to mine or to dump”.
Where grade of the mineralized material is less than cutoff grade it is classified as waste
and where it is equal to or above cutoff grade it is classified as ore.
The reasons for continuing interest in cutoff grades are obvious. Too high a grade can
reduce the mineral recovered and possibly the life of the deposit (figs 12.3(a) to (d)).Too
low a cutoff would reduce the average grade (and hence profit) below an acceptable
level. In project evaluation it is important to determine a cutoff grade, which is normally
set to achieve the financial objectives for the project.
Studies on cutoff grade theory may fall into two basic categories.
The fixed cutoff grade concept assumes a static cutoff for the life of the mine, while the
variable cutoff grade concept assumes a dynamic cutoff maximizing the mine net present
value.
Lane outlined three distinct stages in a mining operation: ore generation (mining),
concentration (milling) and refining. He demonstrated that in establishing cutoff grades,
consideration of costs, capacities, waste: ore ratios and average grade of different
increments of ore of the orebody as well as the present values of annual cash flows are
essential. For each stage, there is a grade at which the cost of extracting the recoverable
metal equals the revenue from the metal. This is commonly known as break-even grade.
Parameter influencing cutoff grades.
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