Surface Mining Ore Deposit Grades ©2011 Dr. B. C. Paul Note- The information contained in these slides is considered common knowledge to those schooled in the field and was not collected from any one particular source. Acknowledgement is given to SME for model P.E. exams that provided guidance on subjects that required coverage for students to prepare to pass the P.E.

Ore Grade Realities Very few ore deposits where the mineral or element of interest is only a minor percentage of the total mass have a uniform grade throughout the orebody. Very few ore deposits where the mineral or element of interest is only a minor percentage of the total mass have a uniform grade throughout the orebody. Example – A gold deposit has the following ore grade distribution Example – A gold deposit has the following ore grade distribution –6% is 1 to 4 grams/tonne –12% is 4 to 6 grams/tonne –30% is 6 to 10 grams/tonne –36% is 10 to 12 grams/tonne –16% is 12 to 20 grams/tonne –What is the average grade?

Ore Grade Distributions Most minor element grade distributions are highly skewed with a lot more low grade ore than high grade ore Most minor element grade distributions are highly skewed with a lot more low grade ore than high grade ore Histograms capture that skewness Histograms capture that skewness Average grades can be computed with a weighted average. Average grades can be computed with a weighted average.

Lets Give it a Try Midpoint of each grade category Midpoint of each grade category –6% is about 2.5 grams/tonne –12% is about 5 grams/tonne –30% is about 8 grams/tonne –36% is about 11 grams/tonne –16% is about 16 grams/tonne Weighted Average Weighted Average –(6*2.5+12*5+30*8+36*11+16*16)/100 = 9.67 grams/tonne

Reality #2 Most Ore Deposits are Polymetalic Means there is more than 1 mineral of interest Means there is more than 1 mineral of interest –An orebody contains Cu, Zn, and Pb How do I put a value on the ore How do I put a value on the ore –Best way is to sum the value of the componants

Summing the Value of Components The ore contains 7% zinc, 1% Pb, 0.5% Cu in sulfide - The ore contains 7% zinc, 1% Pb, 0.5% Cu in sulfide - –The zinc will be floated, roasted, leached, electrowon Suppose you have 85% recovery in flotation and then 85% recovery in the roast leach and 99% in electrowin Suppose you have 85% recovery in flotation and then 85% recovery in the roast leach and 99% in electrowin Suppose zinc sells for 80 cents/lb, lead for 60 cents/lb, and copper for $3/lb Suppose zinc sells for 80 cents/lb, lead for 60 cents/lb, and copper for $3/lb Electrowinning costs 5 cents/lb Electrowinning costs 5 cents/lb The roast leach process is about $80/ton of concentrate The roast leach process is about $80/ton of concentrate Flotation process runs about $4.75/ton of ore for 3 products Flotation process runs about $4.75/ton of ore for 3 products

Working on the Value of the Zinc Take the electrowining cost off of the sale price since they are in the same units Take the electrowining cost off of the sale price since they are in the same units –80 cents – 5 cents = 75 cents –But only 99% of the zinc in solution will be recovered for sale 75 * 0.99 = per lb of zinc in solution 75 * 0.99 = per lb of zinc in solution To get the cost for the roast and leach on a lb of zinc basis I will need to know the zinc content of the concentrate To get the cost for the roast and leach on a lb of zinc basis I will need to know the zinc content of the concentrate

Zinc Concentrate Grade In this deposit and most let us suppose the zinc is in sphalerite ZnS. In this deposit and most let us suppose the zinc is in sphalerite ZnS. –Sphalerite is about 64% zinc –Since so stuff that should not float will get into the zinc concentrate let us suppose that 2% of the sulfides are chalcopyrite and 0.5% is pyrite and there is about 4% gangue mineral carry over. Thus 97.5% of the sulfides in the concentrate are sphalerite. Thus 97.5% of the sulfides in the concentrate are sphalerite. And 96% of the concentrate is sulfide And 96% of the concentrate is sulfide 64% * *0.96 = 59.9% zinc 64% * *0.96 = 59.9% zinc

Now lets get the roast leach cost on a recovered zinc basis $80/ton of concentrate that is 59.9% zinc $80/ton of concentrate that is 59.9% zinc –2000 lbs * = 1198 lbs of zinc –But only 85% of that will be recovered 1198 lbs * 0.85 = 1018 lbs 1198 lbs * 0.85 = 1018 lbs –Cost per recovered lb of zinc = 80/1018 = or 7.9 cents per lb Value of zinc in concentrate Value of zinc in concentrate –74.25 cents – 7.9 cents = cents/lb in concentrate

Now Lets Get the Value of Zinc in the Rock Zinc in concentrate is worth cents per lb Zinc in concentrate is worth cents per lb 85% of the zinc in the rock is recovered in concentrate so 85% of the zinc in the rock is recovered in concentrate so –66.35 * 0.85 = 56.4 cents per lb Rock is 7% zinc Rock is 7% zinc –2000 lbs/ton * 0.07 = 140 lbs of zinc –At 56.4 cents/lb –140 * = $78.96 for the zinc

Now Lets Value the Lead Lets assume the lead is in Galena Lets assume the lead is in Galena –PbS is 86.6% lead –Galena will be floated into a concentrate (96.5% recovery) –Smelted in a Blast Furnace $100/ton of concentrate (95% recovery) –Electrorefined for about 10 cents/lb (99% recovery)

Start by getting value of unrefined lead Lead is 60 cents per lb Lead is 60 cents per lb It cost 10 cents per lb to refine It cost 10 cents per lb to refine –That leaves 50 cents per lb But recovery is 99% But recovery is 99% –50 *.99 = 49.5 cents per lb of unrefined lead bullion from the blast furnace

Lets get the Grade of the Concentrate Going to the Blast Furnace Lets assume about 10% impurity in the concentrate – meaning 90% of the concentrate is Galena Lets assume about 10% impurity in the concentrate – meaning 90% of the concentrate is Galena Galena is 86.6% Lead Galena is 86.6% Lead Thus the concentrate has 2000lbs/ton *.9 * = 1559 lbs of lead Thus the concentrate has 2000lbs/ton *.9 * = 1559 lbs of lead –95% will be recovered in the blast furnace –1559 * 0.95 = 1481 lbs of recoverable lead Concentrate Processing is $100/ton / 1481 lbs/ton = or 6.8 cents per lb Concentrate Processing is $100/ton / 1481 lbs/ton = or 6.8 cents per lb Lead in concentrate is thus worth 49.5 cent/lb – 6.8 cents/lb = 42.7 cents/lb Lead in concentrate is thus worth 49.5 cent/lb – 6.8 cents/lb = 42.7 cents/lb

Finding the Value of Lead in Rock 1 Ton of Rock is 1% Lead 1 Ton of Rock is 1% Lead –2000 lbs * 0.01 = 20 lbs of lead 96.5% of that will be recovered in floatation 96.5% of that will be recovered in floatation – 20 lbs * = 19.3 lbs of lead At 42.7 cents/lb At 42.7 cents/lb –19.3 * = $8.24 for the lead in a ton of Ore

Now Lets Get the Copper 0.5% Copper assumed in Chalcopyrite 0.5% Copper assumed in Chalcopyrite –CuFeS2, 34.6% Copper Copper is Floated with about 87% recovery Copper is Floated with about 87% recovery The Concentrate is Smelted with 92% recovery at a cost of $85/ton of concentrate The Concentrate is Smelted with 92% recovery at a cost of $85/ton of concentrate Blister Copper is electrorefined for about 10 cents per lb with about 99% recovery Blister Copper is electrorefined for about 10 cents per lb with about 99% recovery

Get the value of Blister Copper $3/lb market – 10 cents/lb to electrorefine $3/lb market – 10 cents/lb to electrorefine –$2.90/lb as blister –Adjust for 99% recovery –2.90*.99 = 2.87/lb

Getting the Concentrate Grade so the Smelter cost can be converted to a cost/lb Chalcopyrite is 34.6% Cu Chalcopyrite is 34.6% Cu –Assume about 17% impurities –34.6% *.83 = 28.7% Cu A ton of concentrate cost $85 to process to blister copper in the smelter A ton of concentrate cost $85 to process to blister copper in the smelter –2000 lbs *.287 = 574 lbs in concentrate –92% will be recovered 574 *.92 = 528 lbs recovered 574 *.92 = 528 lbs recovered Cost per lb Cost per lb –$85/ton / 528 lbs/ton = or 16.1 cents per lb –$2.87/lb – = $2.71 per lb in concentrate

Working Back to the Rock Rock is 0.5% Copper Rock is 0.5% Copper –2000 lbs *0.005 = 10 lbs of copper –But only 87% of that will be recovered in the concentrator 10 * 0.87 = 8.7 lbs of copper 10 * 0.87 = 8.7 lbs of copper Getting the value Getting the value –8.7 lbs/ton * $2.71/lb = $23.58 for the copper

Totaling Things Up Zinc $78.96 Zinc $78.96 Lead $8.24 Lead $8.24 Copper $23.58 Copper $23.58 $ $ But we still have not charged off the cost of running a 3 product concentrator $4.75 But we still have not charged off the cost of running a 3 product concentrator $4.75 $ $4.75 = $106.03/ton $ $4.75 = $106.03/ton Looks like a nice valuable chunk of ore Looks like a nice valuable chunk of ore

That’s a lot of Calculations – Why Are You Doing This to Us? These types of calculations are on the P.E. exam These types of calculations are on the P.E. exam But Won’t Computer Programs do this for us? But Won’t Computer Programs do this for us? –In mine planning ore grades are kept in blocks and calculations like this are done to get the value per ton of the block –Most programs do not consider all recoveries and costs – you may have to adjust the market price before you feed it to the program If you don’t know what went into the cost you won’t be able to do it. If you don’t know what went into the cost you won’t be able to do it.

What About Early Phase Ore Body Evaluation – Does it have to be this hairy? No No An approximation used for early planning is to assign a polymetalic deposit an equivalent grade An approximation used for early planning is to assign a polymetalic deposit an equivalent grade –Our Zinc Lead Copper deposit might be defined as if all the value came from Zinc

Illustrating What if the entire $ came from Zinc – what grade would do that? What if the entire $ came from Zinc – what grade would do that? 7% zinc = $78.96/ton 7% zinc = $78.96/ton Ratio off Ratio off –($106.03/$78.96) * 7% = 9.4% Equivalent Zinc Grade

Of Course to Do That I Had a Bunch of Calculations Equivalent Grades sometimes use very crude data Equivalent Grades sometimes use very crude data Example of an Equivalent Grade based on market price only Example of an Equivalent Grade based on market price only –Lead was 1% but lead is 60 cents per lb instead of 80 cents/lb 1%*60/80= 0.75% Zinc equivalent 1%*60/80= 0.75% Zinc equivalent –Copper was 0.5% but copper is $3/lb 0.5% * 300/80 = 1.88% zinc equivalent 0.5% * 300/80 = 1.88% zinc equivalent –7%+.75%+1.88% = 9.63% zinc equivalent

Sometimes People include Recovery in Equivalent Grade Zinc 2000 lb/ton * 0.07 (insitu grade) * 0.85 (floatation recovery) * 0.85 (roast leach recovery) * 0.99 (electrorefining recovery) = 100 lbs Zinc 2000 lb/ton * 0.07 (insitu grade) * 0.85 (floatation recovery) * 0.85 (roast leach recovery) * 0.99 (electrorefining recovery) = 100 lbs –Zinc price is 80 cents per lb –Minus 12.9 cents per lb for post concentrate processing –100 *0.671 = $67.1

More Equivalent Grade with Recovery Lead 1% Lead 1% –2000 * 0.01 (lead grade) * (floatation recovery) * 0.95 (blast furnace recovery) * 0.99 (refining recovery) = lbs –60 cents/lb – 16.8 cents/lb for post concentrate processing –18.15 * ( ) = $7.84

More Equivalent Grade with Recovery Copper Copper –2000*.005 (grade) * 0.87 (floatation recovery) * 0.92 (smelter recovery) * 0.99 (refining recovery) = 7.92 lbs –Copper value $3/lb – 0.261/lb (for post concentrate processing) –7.92 * ( ) = $21.7

Get Ratios Value of Lead compared to value of zinc Value of Lead compared to value of zinc –$8.74/67.1 = Value of copper compared to value of zinc Value of copper compared to value of zinc –$21.7/67.1 = Add up the ratios = 1.44 Add up the ratios = % * 1.44 = 10.08% zinc equivalent 7% * 1.44 = 10.08% zinc equivalent

Things to Note About Equivalent Grade People are not totally consistent as to what is and is not included People are not totally consistent as to what is and is not included Equivalent Grade hides a multitude of calculations – many parameters, especially market prices change with time Equivalent Grade hides a multitude of calculations – many parameters, especially market prices change with time –Thus equivalent grade is only good at one point in time and for a specific set of assumptions

Is It Any Good? Yes Yes Early in the life of an orebody discovery our knowledge of ore grades can easily be plus or minus 25% Early in the life of an orebody discovery our knowledge of ore grades can easily be plus or minus 25% –Differences in equivalent grade will usually be well within 10% so the imprecision is within the uncertainty of our orebody The fact that equivalent grade values get bad over time is not important The fact that equivalent grade values get bad over time is not important –Early in the life we want to know whether the orebody merits further attention now – we are not doing a long term plan

Now Its Your Turn Do Assignment #2 on Orebody Sizes and Grades Do Assignment #2 on Orebody Sizes and Grades