SAIMM Journal

The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 107 REFEREED PAPER FEBRUARY 2007

SSuummmmaarryy

One of the most difficult problems in mining

operation is how to determine optimum cut-off

grades of ores at different periods over the

lifespan of the mine that will maximize the net

present value (NPV) of the mine. Maximizing

the NPV of a mining operation, subject to

different constraints is a nonlinear

programming problem. Cut-off grade

optimization is used to arrive at an operating

strategy that maximizes the value of a mine.

Cut-off optimization as a concept has been

known for many years, particularly since

Lane’s latest revolution, but it is still not

widely practised.

Cut-off grade optimization maximizes the

NPV of a project subject to capacity constraints

in the mine, mill and the market. These are

usually expressed as annual limits to the

tonnage mined, tonnage milled and product

sold. At any point in time at least one limit,

and possibly two or all three, will be

constraining the system. For cut-off

optimization to work correctly, capacity

constraints must be independent of the cut-off

grade. The cut-off grade is used to distinguish

ore from waste materials. If the cut-off grade is

too high, much of the mined material will go to

the waste dump area. If the cut-off is too low,

then the input capacity of the entire mining

and mineral processing operations will be fully

stretched, while revenues do not necessarily

increase. The optimal strategy is one that

strikes the correct balance between these two

limits.

This paper describes the determination of a

cut-off grade strategy based on Lane’s (Lane,

1964), algorithm adding an optimization factor

based on the generalized reduced gradient

(GRG) algorithm to maximize the project’s

NPV. In this study, a computer program using

Excel and Visual Basic has been developed to

implement the algorithm. An interactive user-

friendly cut-off grade program was coded

using Visual Basic in a Wwindows based

spreadsheet application (Excel), a well-known

application commonly used by mining profes-

sionals.

The cut-off grade program developed is

used to incorporate the optimization factor (σ)

which is included in the ultimate cut-off grade

equation, which considers the mining (m) cost,

to further maximize the total NPV of the mine

project. σ is the optimization factor and m is

the mining cost per ton. The program solves

cm f F

Psxy

()

++++

−

()

Determination of optimal cut-off grade

policy to optimize NPV using a new

approach with optimization factor

by A. Bascetin,* and A. Nieto

†

SSyynnooppssiiss

One very important aspect of mining is deciding what material in a

deposit is worth mining and processing, versus what material

should be considered waste. This decision is summarized by the cut-

off grade policy. The cut-off grade strategy for an open pit mine

influences the annual cash flows and affects the net present value

of a project. The optimization of cut-off grade strategy requires the

knowledge of detailed operational costs, mining sequence, mining

operation, processing, and product constraints, as well as the grade

distribution of a given deposit defined by pit, phase, and different

material types. Cut-off grade optimization algorithms have been

developed in the past. The most common criteria used in cut-off

grade optimization is to maximize the net present value (NPV). This

paper describes the determination of a cut-off grade strategy based

on Lane’s algorithm adding an optimization factor based on the

generalized reduced gradient (GRG) algorithm to maximize the

project’s NPV. The introduced algorithm is a windows based

program developed at Virginia Tech that is based on a series of

Visual Basic routines within a spreadsheet environment (Excel).

The benefits of the methodology are demonstrated using a

hypothetical case study.

Keywords: Cut-off grade optimization, net present value

maximization, generalized reduced gradient algorithm method.

* Istanbul University, Engineering Faculty, Mining

Engineering Department, Istanbul, Turkey.

† Virginia Polytechnic Institute and State University,

Mining and Minerals Engineering, Blackburg,

Virginia, USA.

Metallurgy, 2007. SA ISSN 0038–223X/3.00 +

0.00. Paper received Mar. 2006; revised paper

received Jan 2007.

▲

Determination of optimal cut-off grade policy to optimize NPV

for the optimization factor (σ), which is a nonlinear problem

(NLP), based on the generalized reduced gradient (GRG)

algorithm by maximizing the project’s NPV.

The algorithm was tested using first the optimization

factor to find the maximum the NPV then it was tested by

removing the optimization factor. The results were examined

and presented in the paper. As a result of the study, the cut-

off grade policy determined by the optimization approach

using the (σ) factor gives a higher NPV than the cut-off

grade policy estimated without the optimization factor. The

results given by the used case study indicate that the impact

of the optimization factor (σ) on the objective function (NPV)

is significant at a $17,889,613.00 increase which is

equivalent to a 5% NPV increment. A NPV sensitivity

analysis, which consisted in varying the optimization factor

(σ) from 0.0 to 12.0 in 1.0 unit increments, indicates—as

calculated by the introduced algorithm—that the maximum

NPV value is at σ = 5.84. This approach provides great

flexibility at the mine planning stage for evaluation of

various economic and grade/ton alternatives.

IInnttrroodduuccttiioonn

Cut-off grade is a geologic/technical measure that embodies

important economic aspects of mineral production within a

mineral deposit. In other words, it is defined not only by the

deposit’s geologic characteristics and the technological limits

of extraction and processing, but also by costs and mineral

prices. Taylor (1972) presents one of the best definitions of

cut-off grade. He defined cut-off grade as any grade that, for

any specific reason, is used to separate two sources of action,

e.g. to mine or to leave, mill or to dump.

Some researchers have developed new optimization

techniques based on Lane’s (Lane, 1964) algorithm to

determine a cut-off grade policy. Cut-off grade optimization

is used to derive an operating strategy that maximizes the

value of a mine. Where the mine’s capacity allows, sacrificing

low-grade material enables the mill to process ore that

delivers a higher cash flow. Hence, the cut-off grade policy

has a significant influence on the overall economics of the

mining operation. The determination of cut-off grade policy,

which maximizes the NPV, is already established in the

industry. It has been realized that, as opposed to constant

breakeven cut-off grade, the optimum/dynamic cut-off

grades, which change due to the declining effect of NPV

during mine life, not only honour the metal price and cash

costs of mining, milling, and refining stages, but also take

into account the limiting capacities of these stages and grade-

tonnage distribution of the deposit (Dagdelen, 1992; Lane,

1988; Dagdelen and Mohammad, 1997). In other words, the

techniques that determine the optimum cut-off grade policy

consider the opportunity cost of not receiving the future cash

flows earlier during the mine life due to limiting capacities

present in the stages of mining, milling, or refining.

The optimization factor indicates the level of optimization

achieved for the cut-off grade strategy calculated by the

algorithm. This paper describes the use of an optimization

factor calculated based on the generalized reduced gradient

(GRG) algorithm to improve optimum cut-off grades.

MMeetthhooddss ooff ccuutt--ooffff ggrraaddee ooppttiimmiizzaattiioonn

As discussed earlier cut-off grade is the criterion normally

used in mining operation to discriminate between ore and

waste within a mineral deposit. Waste may either be left in

place or sent to waste dumps. Ore is sent to the treatment

plant for further processing. Optimizing mine cut-off grades

means to maximize the net present value (NPV) of mining

projects. Cut-off grade directly affects the cash flows of a

mining operation, based on the fact that higher cut-off

grades lead to higher grades per ton of ore; hence, higher

revenues are realized depending upon the grade distribution

of the deposit (Dagdelen, 1993). In any given period, the

allocation of material sent to the mill and the product created

in the refinery for sale are also dependent on the cut-off

grade. It is generally accepted that the cut-off grade policy

that gives higher NPVs is a policy that uses declining cut-off

grades throughout the life of the project. Lane (1964, 1988)

has developed a comprehensive theory of cut-off grade

calculation. Table I shows the notation used in the algorithm.

In his approach K. Lane demonstrates that a cut-off grade

calculation which maximizes NPV has to include the fixed

cost associated with not receiving the future cash flows

quicker due to the cut-off grade decision taken now. The cut-

off grade when the concentrator is the constraint is given

below.

[1]

Where g

(i): milling cut-off grade, f: fixed cost, F

opportunity cost per ton of material milled in Year i, P: profit

($), s: selling price ($/unit of product), y: recovery (%).

The opportunity cost is determined as:

[2]

[3]

Where f

is the annual fixed costs,

NPV

cfF

Psy

−

()

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VVOOLLUUMMEE 110077 RREEFFEERREEEEDD PPAAPPEERR

The Journal of The Southern African Institute of Mining and Metallurgy

Table I

The notations of the algorithm

Notatiton Explanation Unit

i Year —

N Mine life Years

P Metal price $/oz

s Sales cost $/oz

m Mining cost $/ton

c Processing cost $/ton ore

Fixed costs $/year

f Fixed cost $/ton

y Recovery %

d Discount rate %

CC Capital costs $

M Mining capacity Tons/year

C Milling capacity Tons/year

R Refining capacity Tons/year

Material mined Tons/year

Ore processed Tons/year

Concentrate refined Tons/year

d is the discount rate, NPV

is the NPV of the future cash

flows of the years (i) to the end mine life N, and the C is the

total milling capacity in Year i.

The cut-off grade g

(i) depends on the NPV

and NPV

cannot be determined until the optimum cut-off grades have

been decided. The solution to this type of interdependency

problem is obtained by an iterative approach. In this study, a

computer program using Excel and Visual Basic has been

developed to implement the algorithm. An interactive user-

friendly cut-off grade program, based on K. Lane’s algorithm

was coded using Visual Basic in a Windows based

spreadsheet application (Excel), a well-known application

commonly used by mining professionals (Figure 1).

The cut-off grade program developed is used to

incorporate the optimization factor (σ) which is included in

the ultimate cut-off grade equation, which considers the

mining (m) cost,

[4]

to further maximize the total NPV of the mine project. Where

σ is the optimization factor and m is the mining cost per ton

The program solves for the optimization factor (σ), which

is a nonlinear problem (NLP), based on the generalized

reduced gradient (GRG) algorithm by maximizing the

project’s NPV.

A typical difficulty associated with nonlinear optimization

is that in most cases it is only possible to determine a locally

optimal solution but not the global optimum. Loosely

speaking, the global optimum is the best of all possible

values while a local optimum is only the best in the

neighborhood. One of the most powerful nonlinear

optimization algorithms is the generalized reduced gradient

algorithm method. The GRG algorithm was first developed by

Ladson et al. (1978). This procedure is one of a class of

techniques called reduced-gradient or gradient projection

methods, which are based on nonlinear constraints.

The development of the procedure begins with the

nonlinear optimization problem written with equality

constraints. The idea of generalized reduced gradient is to

convert the constrained problem into an unconstrained one

by using direct substitution. If direct substitution were

possible it would reduce the number of independent variables

to (n–m) and eliminate the constraint equations. However,

with nonlinear constraint equations, it is not feasible to solve

the m constraint equations for m of the independent variables

in terms of the remaining (n–m) variables and then to

substitute to these equations into the economic model.

Therefore, the procedures of constrained variation and

Lagrange multipliers in the classical theory of maxima and

minima are required. There, the economic model and

constraint equations were expanded in a Taylor series, and

only the first order terms were retained. Then with these

linear equations, the constraint equations could be used to

reduce the number of independent variables. This led to the

Jacobian determinants of the method of constrained variation

and the definition of the Lagrange multiplier being a ratio of

partial derivatives.

cm f F

Psy

()

++++

−

()

Determination of optimal cut-off grade policy to optimize NPV

The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 107 REFEREED PAPER FEBRUARY 2007

▲

Figure 1—The Windows based program for maximization of NPV

The development of the generalized reduced gradient

method follows that of constrained variation. The case of two

independent variables and one constraint equation will be

used to demonstrate the concept, and then the general case

will be described. Consider the following problem.

[5]

Expanding the above in a Taylor series about a feasible

point xk(x

) gives:

[6]

[7]

Substituting Equation [6] into Equation [7] to eliminate

gives, after some rearrangement:

[8]

In Equation [8] the first two terms are known constants

being evaluated at point xk, and the coefficient of (x

–x

) is

also a known constant and gives the x

the direction to

move. Thus, to compute the stationary point for this

equation, dy/dx

= 0; and the result is the same as for

constrained variation which is the term in the brackets of

Equation [8] that is solved together with the constraint

equation for the stationary point. However, the term in the

bracket also can be viewed as giving the direction to move

away from x

to obtain improved values of the economic

model and satisfy the constraint equation.

For a better explanation consider;

[9]

[10]

Partition variables into two groups x = (y, z) where y has

dimension m and z has dimension n-m. This partition is

formed such that all variables in y are strictly positive.

Now, the original problem can be expressed as:

[11]

[12]

Key notion is that if z is specified (independent

variables), then y (the dependent variables) can be uniquely

solved. NOTE: y and z are dependent. Because of this

dependency, if we move z along the line z + a Dz, then y will

have to move along a corresponding line y + aDy. Dependent

variables y are also referred to as basic variables.

Independent variables z are also referred to as non-basic

variables.

The basic idea of the reduced gradient method is to

consider, at each stage, the problem only in terms of the

indepented variables. Since y can be obtained from z, the

objective function ƒ can be considered as a function of z

only.

The gradient of ƒ with respect to the independent

variables z is found by evaluating the gradient of ƒ

-1

b-B

-1

Cz, z). The resulting gradient

[13]

is called the reduced gradient.

The generalized reduced gradient solves nonlinear

programming problems in the standard form

[14]

[15]

where h(x) is of dimension m.

The generalized reduced gradient is

[16]

GRG algorithm works similarly to linear constraints.

However, it is also plagued with similar problems as gradient

projection methods regarding maintaining feasibility.

Probably, the most important role of this approach is that

it calculates the optimization factor σ in an iterative approach

updating the remaining reserves, thus the mine life, at every

year, in each iteration, in order to maximize the NPV of the

project. This new approach using a variable optimization

factor basis resulted in an improved total NPV as shown later

in this paper. The program solves for the optimization factor

σ by maximizing the project NPV, which is based on the ore

tonnage–grade distribution and economic parameters of the

mine (see Table IV and Figure 4). The program was

developed at Virginia Tech (Nieto and Bascetin, 2006).

The cut-off grade dictates the quantity mined, processed

and refined in a given period ‘i’, and accordingly, the profits

becomes dependent upon the definition of cut-off grade.

Therefore, the solution of the problem is in the determination

of an optimum cut-off grade in a given period, which

ultimately maximizes the objective function (Asad, 2005). In

addition, using the introduced program, the degree of

precision can be determined, the tolerance, and the degree of

convergence of the results. All of these precision parameters

can be reported in the program as an Excel sheet.

Algorithm procedure of the new cut-off grade

optimization method

The cut-off grade g

(i) depends on the NPV

, and the NPV

cannot be determined until the optimum cut-off grades have

been found. The solution to this type of interdependency

problem is obtained by an iterative approach. This iteration

process belongs to the developed package, which is based on

Excell and can be seen as a flowchart demonstrated in

Figure 2.

The steps of the algorithm as mentioned above

(Equation [1]) are as follows:

(i) read the input files:

a. Economic parameters (price, selling cost,

capacities, etc.)

r f y,z f y,z

hy,z hy,z

= ∇

()

−∇

()

∇

()

[]

∇

()

−

subject to h x a ≤ x ≤ b

()

= 0,

minimize

()

R f y,z f y,z B C

= ∇

()

−∇

()

−

s.t. ,

By Cz b y 0, z 0

A B.C

+= ≥≥

[]

()

with, of course

min

y, z

()

s.t. ,

Ax x 0

= ≥

min

()

11 2 2

()

−

()

−

()

df x x x

yyx

xxx

()

−

()

−

()

11 2 2

Optimize

Subjectto

:y x,x

:f x,x 0

()

Determination of optimal cut-off grade policy to optimize NPV

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VVOOLLUUMMEE 110077 RREEFFEERREEEEDD PPAAPPEERR

The Journal of The Southern African Institute of Mining and Metallurgy

b. Grade-tonnage distribution

(ii) determine the COG g

(i) by Equation [1];

Setting V = NPV

, the initial NPV

= 0

(iii) compute the ore tonnage (T

) and waste tonnage

) from the grade-tonnage curve of the deposit:

a. the ore tonnage (T

) and the grade g

above

the COG g

(i)

b. the waste tonnage (T

) that is below the COG

(i)

c. Also, compute the stripping ratio SR where

SR = (T

)/(T

)

(iv) Set Q

= C, if T

is greater than the milling

capacity, otherwise, Q

= T

. Also, set the Q

quantity mined (Q

= Qc(1+SR)) and Q

= Q

avg

(v) determine the annual profit by using the following

equation:

=(S

-r

– Q

( c

+ f) – m

(vi) adjusting the grade tonnage curve of the deposit by

subtracting ore tons Q

from the grade distribution

intervals above optimum COG g

(i) and the waste

tons Q

–Q

from the intervals below optimum

COG g

(i) in proportionate among such that the

distribution is not changed.

(vii) check, if Q

less than the milling capacity (C), then

set mine life N=i and go to step (viii);

otherwise set the year indicator i = i + 1 and go to

step (ii).

(viii) calculate the accumulated future NPV

s based on

the profits P

calculated in step (v) for each year

from i to N by the following equation

for

each year i = 1, N where N is total mine life in years.

Total NPV is calculated at this stage considering a

optimization factor equal to zero.

where σ is the optimization factor equal to zero.

(ix) the first iteration is performed by adjusting the

optimization factor s using the GRG method

maximizing the NPV

computed in step (viii). If the

computed NPV

does not converge, the algorithm

goes to step (ii) and calculates the COG by varying

the embedded optimization factor s. If the

computed NPV converges, the program stops. The

COG gis for years i=1, N is the optimum policy that

maximizes the NPV. Table IV shows COG calculated

for each year using σ.

The algorithm was tested using first the optimization

factor to find the maximum the NPV then it was tested by

removing the optimization factor. The results were examined

and are presented in the next section.

Hypothetical case study and results

Consider the following hypothetical case of an open pit gold

mine (Dagdelen, 1992). The tonnage grade distribution and

cm f F

Psy

()

++++

−

()

NPV

()

− +

∑

Determination of optimal cut-off grade policy to optimize NPV

The Journal of The Southern African Institute of Mining and Metallurgy

VVOOLLUUMMEE 110077 RREEFFEERREEEEDD PPAAPPEERR

FEBRUARY 2007

▲

Figure 2—Flowchart of new algorithm for cut-off grade optimization

mine design parameters are shown in Tables II and Figure 3,

respectively. The values in Table II give assumed capacities

and accepted costs to mine this deposit at 2 857 ton/day

milling rate. The mine will be worked at the rate of seven

days a week for 350 days per year.

Table III presents the optimum cut-off grade policy

without the optimization factor. As indicated in Table III, this

optimizing approach gives a total NPV of $354.6 million and

$676.5 million of non-discounted profit.

On the other hand, Table IV presents the results of the

optimum cut-off grade approach using the optimization factor

(σ=5.84). The cut-off grade policy that is determined by this

optimizing approach using the optimization factor (σ) gives a

total NPV of $372.5 million and $638.9 million of non-

discounted profit.

According to the values that are shown in Tables III–IV,

the cut-off grade policy determined by the optimization

approach using the (σ) factor gives a higher NPV than the

cut-off grade policy estimated without the optimization

factor. The results are given graphically in Figure 4. An NPV

sensitivity analysis, which consisted in varying the

optimization factor (σ) from 0.0 to 12.0 in 1.0 unit

increments, indicates—as calculated by the introduced

algorithm—that the maximum NPV value is at σ = 5.84

which can be seen clearly in Figure 5.

Acknowledgement

This work was supported by the Scientific and Technological

Research Council of Turkey and also by the Research Fund of

Istanbul University (Project number: UDP- 724/26042006).

The software can be requested from: [email protected].

Determination of optimal cut-off grade policy to optimize NPV

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The Journal of The Southern African Institute of Mining and Metallurgy

Table III

Optimum cut-off grade policy of the gold mine (without σ)

Year Optimum cut-off grade (oz/ton) Quantity mined Quantity concentrated Quantity refined Profit ($M) NPV ($M)

1 0.096 12.274.288 1.000.000 209158 61.585.935 354.674.647

2 0.092 11.336.481 1.000.000 199710 58.118.871 293.088.712

3 0.088 10.624.419 1.000.000 192537 55.486.385 242.107.246

4 0.084 10.069.606 1.000.000 186947 53.435.245 199.412.274

5 0.081 9.628.546 1.000.000 182504 51.804.650 163.345.006

6 0.078 9.182.735 1.000.000 177583 49.943.365 132.672.494

7 0.076 8.797.020 1.000.000 173216 48.278.930 106.733.475

8 0.073 8.437.322 1.000.000 168992 46.651.502 84.738.244

9 0.072 8.132.220 1.000.000 165372 45.252.454 66.094.563

10 0.070 7.880.241 1.000.000 162369 44.090.812 50.230.905

11 0.068 7.652.378 1.000.000 159528 42.977.995 36.672.630

12 0.067 7.652.378 1.000.000 159528 42.977.995 25.079.582

13 0.066 7.652.378 1.000.000 159528 42.977.995 14.910.242

14 0.065 7.652.378 809551 129146 32.898.270 5.989.768

Total 126.972.390 13.809.551 2.426.118 676.480.404 354.674.647

Table II

Mine design parameters

Parameters Values

Price 500 $/oz

Sales cost 4 $/oz

Processing cost 17 $/ton

Mining cost 1.3 $/ton

Capital costs $154 M

Fixed costs (f

) $9.2 M/year

Fixed cost (f) 9.2 $/ton

Mining capacity --

Milling capacity 1.00 Mt/year

Discount rate 14%

Recovery 95%

Figure 3—Grade-tonnage distribution of the deposit

Grade category

Tons (in thousands)

Determination of optimal cut-off grade policy to optimize NPV

The Journal of The Southern African Institute of Mining and Metallurgy

VVOOLLUUMMEE 110077 RREEFFEERREEEEDD PPAAPPEERR

FEBRUARY 2007

▲

Table IV

Optimum cut-off grade policy of the gold mine (with σ)

Year Optimum cut-off grade (oz/ton) Quantity mined Quantity concentrated Quantity refined Profit ($M) NPV ($M)

1 0.109 13.568.726 1.000.000 217550 64.065.456 372.564.260

2 0.104 13.317.461 1.000.000 217550 64.392.101 308.498.804

3 0.100 13.094.386 1.000.000 217420 64.617.832 252.014.505

4 0.096 12.261.729 1.000.000 209032 61.539.507 202.293.181

5 0.093 11.613.909 1.000.000 202505 59.144.521 160.755.767

6 0.090 11.099.508 1.000.000 197323 57.242.785 125.737.463

7 0.088 10.684.393 1.000.000 193141 55.708.109 96.007.354

8 0.086 10.345.010 1.000.000 189722 54.453.412 70.627.489

9 0.084 10.064.576 1.000.000 186896 53.416.648 48.865.873

10 0.082 9.830.808 1.000.000 184541 52.552.410 30.140.183

11 0.081 9.634.511 999.998 182563 51.826.583 13.979.900

Total 125.515.017 10.999.998 2.198.243 638.959.363 372.564.260

Figure 4—Comparison of optimization with and without σ, (a) cut-off grade vs. years, (b) profits vs. years

Figure 5—Sensitivity analysis of total NPV vs. different σ values

Years

Cut-off grade ($/oz)

Cut-off grade (with σ) Cut-off grade (without σ)

Years

Optimization factor (σ)

Optimization factor

NPV (M$)

Profits (M$)

Profits (with σ)

Profits (without σ)

Determination of optimal cut-off grade policy to optimize NPV

CCoonncclluussiioonnss

The results given by the case study indicate that the impact

of the optimization factor (σ) on the objective function (NPV)

is significant at a $17,889,613.00 increase, which is

equivalent to a 5% NPV increment. Therefore, the cut-off

grade optimization algorithm presented here is a tool that

improves the cut-off grade policy and serves as a user-

friendly platform for eventual algorithm adaptations such as

the use of cost escalation and simulation for risk analysis.

This approach provides great flexibility at the mine planning

stage for evaluation of various economic and grade/ton

alternatives. The program has been developed within a

Windows environment which is a user-friendly tool, used in

this case, to calculate interactively different mining cut-off

grade scenarios. The other potential benefit of this user-

friendly application is that can be adapted to handle multiple

sources/grades of ore and to incorporate cost escalation

factors based on striping ratios. The research introduced here

uses what we have called the generalized reduced gradient

(GRG) factor, which further maximizes the total project’s

NPV.

RReeffeerreenncceess

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Method to the case of nonlinear constraints in optimization, Gletcher,

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ASAD, M.W.A. Cut-off grade optimization algorithm for open pit mining

operations with consideration of dynamic metal price and cost escalation

during mine life, Application of Computers and Operations Research in

the Mineral Industry, (APCOM 2005), Tuscon, USA. 2005. pp. 273–277.

AGDELEN, K. Cut-off grade optimization, 23rd Application of Computers and

Operations Research in the Mineral Industry, SME, Littleton, Colorado,

USA. 1992. pp. 157–165.

AGDELEN, K. An NPV optimization algorithm for open pit mine design, 24th

Application of Computers and Operations Research in the Mineral

Industry, Montreal, Quebec, Canada. 1993. pp. 257–263.

AGDELEN, K. and MOHAMMAD, W.A. Multi-mineral cut-off grade optimization

with option to stockpile, SME annual meeting, Denver, Colorado, USA.

1997.

ANE, K.F. Choosing the optimum cut-off grade, Colorado School of Mines

Quarterly, vol. 59, 1964. pp. 485–492.

ANE K.F. The economic definition of ore, cut-off grade in theory and practice,

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FEBRUARY 2007

VVOOLLUUMMEE 110077 RREEFFEERREEEEDD PPAAPPEERR

The Journal of The Southern African Institute of Mining and Metallurgy

As part of its research into more cost-effective comminution

technologies, Mintek, specialists in minerals and

metallurgical technology and beneficiation, has commis-

sioned a pilot-scale high pressure grinding roll (HPGR).

The unit, supplied by Polysius, is powered by dual 11

kW motors and can operate at pressures up to 200 bar, with

a nominal throughput of between 0.5 and 2 t/h.

The HPGR is a relatively new technology, which became

commercially available in the mid-1980s. Initially adopted

by the cement industry for replacing a conventional ball mill

for fine grinding, it is now also commonly used in iron ore

processing, for grinding primary ore, as well as in pellet feed

preparation, and for processing diamond ores. Adoption by

the non-ferrous metals sector has been slower, but in recent

years a number of precious- and base-metal producers have

evaluated the HPGR, particularly for ores that are not ideally

suited for semi-autogenous grinding. The technology is now

viewed as having the potential to affect comminution

technology to the same extent as autogenous and semi-

autogenous grinding.

The HPGR uses the principle of interparticle crushing

between two counter-rotating rolls, one of which is fixed

and the other ‘floating’ by means of hydraulic pressure. The

almost pure compressive forces generate a high proportion

of fines, along with extensive micro-cracking in the larger

particles.

‘

As well as being more energy-efficient than conven-

tional technology, the HPGR results in a product with very

favourable characteristics for further downstream

processing,’ explained Jan Lagendijk, Mintek’s Chief

Engineer: Comminution Services. ‘An HPGR in place of

secondary or tertiary crushers can increase the capacity of a

ball mill considerably. Further major benefits are that the

fines produced may result in better liberation, while the

micro-cracking in the coarser product particles may result in

improved mineral and metal recovery in downstream

processes such as flotation and leaching.’

‘The HPGR test work at Mintek will initially focus on

PGM ore processing, and later be extended to other

commodities,’ said Agit Singh, Manager of Mintek’s Mineral

Processing Division. ‘We will be running extensive trials on

different ore types to look at the possibility of reducing the

specific energy consumption in comminution circuits. In

addition, using the HPGR in conjunction with our other

facilities, we will investigate the effect of the process on

downstream unit operations such as dense-media

separation, flotation, and leaching.’

For further information, contact Jan Lagendijk at

Tel.: (011) 709-4550 or e-mail [email protected].

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Mintek commissions new grinding roll for

comminution research