A bord and pillar panel has 24 developed pillars of size $40\ \text{m} \times 40\ \text{m}$ (centre to centre) under extraction. The following information is given:
Gallery width = $4\ \text{m}$
Extraction height = $3\ \text{m}$
Extraction ratio during depillaring = 80%
Specific gravity of coal = 1.4
Incubation period = 6 months
Average working days per month = 25
In order to extract the panel within the incubation period, the minimum rate of production, in tonne per day, is . (rounded off to one decimal place)

Question

The primary purpose of mine ventilation is to:

Answer 1

Let's approach this by first working out the tonnage locked up in a single pillar, then scaling up to the whole panel, rather than totalling the volume first.

Each pillar's centre to centre spacing is 40 m, but 4 m of that on each pillar's boundary belongs to the surrounding gallery, so the actual coal pillar left standing is $40-4=36\ \text{m}$ on a side.

Volume of coal in one pillar $= 36 \times 36 \times 3 = 3888\ \text{m}^3$, using the 3 m extraction height.

During depillaring only 80% of a pillar's coal is actually recovered, so the recoverable volume per pillar is $0.8 \times 3888 = 3110.4\ \text{m}^3$.

At a specific gravity of 1.4, the mass recoverable from one pillar is $3110.4 \times 1.4 = 4354.56$ tonnes.

With 24 pillars in the panel, the total coal to be extracted is $24 \times 4354.56 = 104509.44$ tonnes.

The incubation period gives the time limit: $6$ months at $25$ working days a month is $150$ days. So the panel must be cleared at a rate of at least $104509.44/150 = 696.7296$ tonne per day.

Let's summarize:

Subtracting the gallery width from the centre to centre spacing gives the true pillar size of 36 m by 36 m.
Only 80% of a pillar's coal is won during depillaring.
Scaling one pillar's recoverable tonnage up to 24 pillars and dividing by the 150 available days gives the same minimum rate.

So the panel needs a minimum production rate of about $696.7$ tonne per day.

Answer 2

Let's approach this by first working out the tonnage locked up in a single pillar, then scaling up to the whole panel, rather than totalling the volume first.

Each pillar's centre to centre spacing is 40 m, but 4 m of that on each pillar's boundary belongs to the surrounding gallery, so the actual coal pillar left standing is $40-4=36\ \text{m}$ on a side.

Volume of coal in one pillar $= 36 \times 36 \times 3 = 3888\ \text{m}^3$, using the 3 m extraction height.

During depillaring only 80% of a pillar's coal is actually recovered, so the recoverable volume per pillar is $0.8 \times 3888 = 3110.4\ \text{m}^3$.

At a specific gravity of 1.4, the mass recoverable from one pillar is $3110.4 \times 1.4 = 4354.56$ tonnes.

With 24 pillars in the panel, the total coal to be extracted is $24 \times 4354.56 = 104509.44$ tonnes.

The incubation period gives the time limit: $6$ months at $25$ working days a month is $150$ days. So the panel must be cleared at a rate of at least $104509.44/150 = 696.7296$ tonne per day.

Let's summarize:

Subtracting the gallery width from the centre to centre spacing gives the true pillar size of 36 m by 36 m.
Only 80% of a pillar's coal is won during depillaring.
Scaling one pillar's recoverable tonnage up to 24 pillars and dividing by the 150 available days gives the same minimum rate.

So the panel needs a minimum production rate of about $696.7$ tonne per day.

Show Hint

Correct Answer: 696.7

Solution and Explanation

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