Quiz 2: Chap 3 and 4 Flashcards
Outline the 9 sections of Chapter 3. (Chapter 3)
- Concept and problem description
- Breakeven and marginal cut-off grades
- Grade-tonnage curves
- Balancing cut-off grade
- Cut-off grade optimization
- Loss, dilution, and recovery
- Net smelter return
- Multi-metal deposits
- Production rates and capacity installation
In the literature, this topic appears different names such as. Name 2. (Chapter 3)
- Ore – waste discrimination
- Determination of block destination or route
What are the 2 different cut-off grades?(Chapter 3)
- Break-even cut-off grade
- Marginal cut-off grade
What are the 2 possible destinations for a produced block?(Chapter 3)
Waste dump and Mineral processing plant
What are the 2 parts of the cut-off decision considering each block? (Chapter 3)
Name all of the 6 possible destinations of a block. (Chapter 3)
- Waste dump
- Sub-grade pile
- Marginal grade pile
- Low-grade processing
- High-grade processing
- High-grade stockpile
Describe a block that ends up at the : Waste dump (Chapter 3)
A block, which does not contain any metal, is sent to this destination
Describe a block that ends up at the : Sub-grade pile (Chapter 3)
A block, which contains a small amount of metal, but this is not profitable under current economic conditions (in some cases this is a part of the waste dump/ or not separate from the waste dump)
Describe a block that ends up at the : Marginal grade pile (Chapter 3)
A block, which contains a certain quantity of metal, but this quantity may not be enough for making profit; its profit is close to zero.
Describe a block that ends up at the : Low-grade processing (Chapter 3)
A block, which contains some certain amount of metal (or block belongs to a rock type) and it will result in a small profit.
Describe a block that ends up at the : High-grade processing (Chapter 3)
A block, which contains a high quantity of metal (or block belongs to another rock type) and it will result in a high profit after processing.
Describe a block that ends up at the : High-grade stockpile (Chapter 3)
A block, which contains a high quantity of metal but since high grade process’s capacity is exceeded, it is sent to a stockpile to be used in near future. Note that there will be a cost associated with waiting time in stockpile as well as stockpiling costs.
Breakeven cut-off grade (also called ____ cut-off grade) is associated with which problem. (Chapter 3)
mine If the problem is to decide if a block will be produced or left on the ground (i.e., the inclusion of the block to production block)
marginal cut-off grade (also called ____ cut-off grade) is associated with which problem. (Chapter 3)
mill If the problem is a scheduling problem (i.e., a block will be produced in any case) – marginal cut-off grade (also called mill cut-off grade).
Name the 4 nature of the operations.(Chapter 3)
- mining only;
- mining and mineral processing;
- mining, mineral processing, and net smelter return agreement;
- mining, mineral processing, and metallurgy
Name 3 other factors affecting cut-off grade calculation. (Chapter 3)
- Type of costs (e.g., opportunity cost, fixed cost, etc.)
- Inclusion of loss and dilution makes a difference.
- The number of destinations (waste and processing streams) makes difference.
The costs used in cut-off calculation includes the
following elements for Mining cost: …. (Chapter 3)
Mining cost: Drilling, blasting, loading, and hauling
The costs used in cut-off calculation includes the
following elements for Mineral processing costs: …. (Chapter 3)
Mineral processing costs: Crushing, stockpiling, grinding, screening, classification, filtering and concentration
The costs used in cut-off calculation includes the
following elements for Metallurgical costs: …. (Chapter 3)
Metallurgical costs: Smelting, refining, sales costs, roasting, packaging, freight, and insurance,
When considering Calculations related to the cut-off grade what are the 3 options for a parcel? (Chapter 3)
There are three options, (1) whether produce or not (2) if produced, sent to waste dump (to access to more valuable areas), (3) if produced, sent to mineral processing
To what metallurgical costs are applied to? (Chapter 3)
metallurgical cost are applied to the output of metallurgical process [ $/ metal tonne ]
What is the Breakeven cut-off grade? (Chapter 3)
Breakeven cut-off grade is the grade wherein the revenue obtained from the sale of the metal within the ore blocks is equal to the extraction costs of the blocks.
Where: Extraction costs are all costs that are required to recover metal (mining and mineral processing costs)
What is the revenue formula for the sale of gold within one tonne ore material ? (Chapter 3)
R = (𝑝𝑟𝑖𝑐𝑒 − 𝑚𝑒𝑡𝑎𝑙𝑙𝑢𝑟𝑔𝑖𝑐𝑎𝑙 𝑐𝑜𝑠𝑡) ∗ 𝑔𝑟𝑎𝑑𝑒 ∗ 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 𝑟𝑒𝑐𝑜𝑣𝑒𝑟
What is the production cost formula of gold within one tonne ore material? (Chapter 3)
PC = 𝑚𝑖𝑛𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 + 𝑚𝑖𝑛𝑒𝑟𝑎𝑙 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 𝑐𝑜𝑠t
When is the breakeven cutoff grade achieved?(Chapter 3)
Breakeven cut-off grade is the grade wherein the revenue is equal to production cost.
What is the 𝑏𝑟𝑒𝑎𝑘 − 𝑒𝑣𝑒𝑛 𝑐𝑢𝑡 − 𝑜𝑓𝑓 𝑔𝑟𝑎𝑑e formula? (Chapter 3)
What is the marginal revenue formula? Give 2 Forms.(Chapter 3)
What is the marginal cost formula? Give 2 Forms.(Chapter 3)
What is the marginal cutoff-grade formula for ore and waste, if there is only one mineral processing stream? (Chapter 3)
What is the marginal cutoff-grade formula between processing streams, if If there are more than one mineral processing stream (e.g., heap leaching and flotation) (Chapter 3)
Give every weight equivalent in kg: (Chapter 3)
1 tonne (metric ton) = _____ kg
1 ton (short ton) = ______ kg
1 long ton = _______ kg
1 tonne (metric ton) = 1,000 kg
1 ton (short ton) = 907.18474 kg
1 long ton = 1,016.05 kg
What is the main difficulty in determining a breakeven cut-off grade. (Chapter 3)
The main difficulty in determining a breakeven cut-off grade is to decide which costs should be incorporated into the calculation.
What is a sunk cost? (Chapter 3)
A sunk cost refers to past costs that cannot be recovered. The money associated with sunk costs has already been spent. Sunk costs are not incorporated into cut-off grade decisions
What is a residual cost?(Chapter 3)
A residual cost refers to the future costs, which are incorporated into the future production decisions. Only residual costs are included in the calculation of breakeven cut-off grade.
Draw the curve between:
T(x) is tonnage of material above cut-off grade x
m(x) is average grade of material above cut-off grade x
(Chapter 3)
.
Fill : As seen from the cut-off grade-tonnage curve, if the cut-off grade is changed, ore tonnage will _______.
However, if the operation has a constant processing capacity, the variation in ore tonnage (processing
input) associated with cut-off grades should be considered. One reasonable choice is to increase
processing plant life if the cut-off grade ________. On the other hand, One reasonable choice is to decrease
processing plant life if the cut-off grade ________.(Chapter 3)
As seen from the cut-off grade-tonnage curve, if the cut-off grade is changed, ore tonnage will change.
However, if the operation has a constant processing capacity, the variation in ore tonnage (processing
input) associated with cut-off grades should be considered. One reasonable choice is to increase processing plant life if the cut-off grade decreases. On the other hand, One reasonable choice is to decrease processing plant life if the cut-off grade increases.
Name an aspect that the grade tonnage curves ignore? Why is it important to consider it? (Chapter 3)
Grade tonnage curves also ignore accessibility. This constraint significantly affects relationship between
cut-off grade and processing capacity.
For a given cut-off grade, over- or under-capacity problems may occur. Therefore, in addition to the
maximization of profit, cut-off grades should satisfy the processing capacity to a certain extent.
Since cut-off grades and capacities are not determined simultaneously, marginal cut-off may not be compatible with capacities. In other words, a cut-off grade is the function of: (Name 2) (Chapter 3)
- economic parameters (breakeven grade, marginal cut-off, static cut-off)
- capacities (cut-off grade based on capacities)
Complete: We need to find a balance between capacity and cut-off grade. Otherwise, ….. (Chapter 3)
We need to find a balance between capacity and cut-off grade. Otherwise, opportunity or additional costs occur due to idle or over capacity in ore production.
Each process has its own capacity, and a selected cut-off grade affects downstream capacities that can result in 2 types of problems. (Chapter 3)
- idle problems.
- over-capacity problems.
Describe the solution and issues related to solving the Overcapacity problems. (Chapter 3)
Overcapacity problems may be solved through stockpiling, but it causes stockpiling costs and possible problems such as oxidation of ore or internal combustion.
Describe the idle capacity problems.(Chapter 3)
Idle capacity causes capacity utilization problems that have an opportunity cost.
Give the profit function in 2 forms and list all 11 variable for the second form. (Chapter 3)
Give the Cut-off optimization - Mathematical formulation(Chapter 3)
When the price increases, there will be a positive impact on revenues (positive impact).
However,
If the cut-off grade is lowered, What could happen?
- If the mining and processing capacities do not change, the metal quantity produced per given time will reduce
- Since, grade decreases mine life increases. If ore tonnage increases, but processing capacity remains the same. Then a stockpile is required and the processing plant’s life extends.
- The trade-off between additional mine life and lowering metal quantity per given time is determined by the discount rate.
If discount rate high, the revenue from extension of the mine life will be lost when turned into an NVP.
If discount rate low, the additional revenue from extension of the mine life can be meaningful.
When the price increases, there will be a positive impact on revenues (positive impact).
However,
If the cut-off grade is increased, What could happen?
- If the mining and processing capacities do not change, the metal quantity produced per given time will reduce
- Since, ore quantity decreases, mine life shortens.
- There is a trade-off between disadvantage obtained by shortening mine life and increasing
metal quantity per year determined by the discount rate.
If discount rate high, the disadvantage obtained by shortening life will disappear to
some extent because the contribution of the shortening years to NPV would be very low.
If discount rate low, the disadvantage obtained by shortening life will be furthered
because the contribution of the shortening years to NPV would be lost
What are the 7 main parameters affecting cut-off decision Increase/Decrease
- How much does the price increase?
- What are the initial mining and processing capacities?
- When price increases, will capacities increase or will mine life change?
- When the cut-off grade is changed, what are the new average grades and tonnages?
- What homogeneity level of ore within deposit qualitatively and quantitatively?
- What is the discount rate used in this project?
- What is the future expectation of the price?
What can be said about mining loss?(Chapter 3)
Some ore is mixed with waste and disposed to waste dump. This could be up to 10-30% of total ore tonnage.
Losses is an inevitable phenomenon and can be minimized by selection of production method, equipment sizing, and drilling and blasting design.