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Surface Mining
Ore Body Geometry2011 Dr. B. C. Paul
Note- Concepts given here are considered to be common knowledge to thoseinvolved in early stage ore estimation. Geometric concepts used are found in
most books on geometry. Acknowledgement is given to SME for model P.E.exams that guided the choice of some materials chosen for review.
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Need to Define a Size of anOrebody
In more advanced stages of miningorebodies are often modeled as millions of
tiny blocks that are analyzed by computer In early stages approximate magnitude of
orebody size is often determined by
comparison to basic geometric objects.
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Example The Coal Seam
Coalstrip Coalmining Company has obtained therights to 6 sections of coal bearing land
measuring 10,560 ft X 15,840 ft. The coal seamis approximately horizontal and is about 7 feetthick on average. It is bituminous coal with atypical density of 80 lbs/cubic foot. If the
company wants a 20 year reserve and willrecover 90% of the coal, what mining ratewould they use?
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Step #1 Get the Coal volume
This is a big box (but not a very tall one)Volume for a 3D box is
Length*Width*HeightApply 15,840 * 10,560 * 7 =
1,170,892,800 cubic feet
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Step #2 Convert the Volume to aWeight
We know that a cubic foot of coal weighs80 lbs therefore the weight is
1,170,892,800 * 80 = 93,671,424,000 lbs
We also know there are 2000 lbs in ashort ton (the kind used in US coal
mining) therefore the weight in tons is 93,671,424,000 / 2000 = 46,835,712 tons
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Step #3 Adjust for Recovery
Only 90% of the coal in place will actuallybe recovered by mining
46,835,712 tons * 0.9 = 42,152,141 tons
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Step #4 Get the Average MiningRate
The reserve will be mined over 20 yearstime
42,152,141 / 20 = 2,107,607 tons/yearAs a practical matter one would say
mining rate is about 2.1 million tons per
year
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Why is this information Important?
Early in the definition of a deposit you will needto know how you might mine it Knowing how big something is will help you to see
what is practicalA 2.1 million ton per year surface mine makes senseA 50,000 ton per year surface coal mine does not make a lot
of sense
Total amount of recoverable coal may give you anidea of how much profit you could make. Theamount you can invest in the deposit must be lessthan this amount.
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Lets take this coal deposit one stepfurther
Suppose we assume that the coal will pickup about 7% material that is not really
coal (out of seam dilution) Suppose we figure the preparation plantwill have a yield of 70%
How many tons of clean coal will wemarket and how big had the coalpreparation plant better be.
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Feed to the Preparation Plant
The 42,152,141 tons of coal will be dilutedby 7% more out of seam material
42,152,141 * 1.07 = 45,102,791 tons Over 20 years average feed per year is
45,102,791 / 20 = 2,255,140
About 2.25 million tons per year
Incidentally our coal loading equipment at themine better be able to move that tonnage too.
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Size Up the Prep - Plant
About 2,250,000 tons per year A typical coal prep plant will run 250 days per
year, 2 shifts per day, with about 7 hours of realrun time on a shift
250 * 14 = 3500 operating hour per year
Size the Plant 2,250,000 tons/year / 3500 hours/year = 643 tons
per hour
About 650 tons/hour
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More Observations
With the scale of operations approximatedwe can make good guesses on our capital
investment and operating costs We are set up to do early economic
evaluation to determine if we should invest inmore exploration and planning.
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Lets Try a Dipping Vein Next Thismight be a phosphate deposit
We have popped three holes in the deposit on aline every 30 metersA top 30 m bottom 56
B top 68 m bottom 98 C top 106 m bottom 140
What is the thickness of the vein of layer? (Note we cannot really get the dip of the deposit
because we would need to know the holes ranperpendicular to the strike of the depositwhich we do not know).
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Depth to deposit midpoint
A is at 43 meters B is at 83 meters
It went down 40 meters for 30 meters over
C is at 123 meters It went down 40 meters for 30 meters over
We are going down 40 meters for 30 over
40
30
Arctan(40/30) = 53.1 degrees ofApparent dip
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Look at Our Drill Hole InterceptDistance
Hole A 26 meters Hole B 30 meters
Hole C 34 metersAverage Intercept is 30 meters But we Hit it like this
Our intercept isClearly not the seamthickness
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Correcting to Get Seam Thickness
53
30*cos(53) = thickness =18.05 metersAbout 18 meters
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A Dipping Seam Tonnage
The strike of a phosphate bed runs for1000 meters
It dips at 53 degrees for a distance of 500meters
It is 18 meters thick
The density is 2.45 tonnes/cubic meter
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Step #1 Get the Volume
This time the box is dipping 1000 * 500 * 18 = 9,000,000 cubic Meters
Step #2 convert to weight 9,000,000 cubic meters * 2.45 tonnes/cubic
meter
22,050,000 metric tonnes
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