Why don't miners get boiled to death at $4$ km deep?

Question

The Mponeng Gold Mine is nearly $4$ km deep. It has the largest elevators in the world and is considered one of the most dangerous mines in the world.

The geothermal gradient is $25$ degrees Celsius per kilometer, which would be $100$ degrees. Therefore, it would be well over boiling temperature at the deepest part of the mine, at least theoretically. Why don't the miners get boiled to death?

Also, I have read that the temperature in the mine is only $150$ °F [$66$ °C] which would seem to conflict with the geothermal gradient. Why is that?

Answer 1

As noted in CountTo10's answer, the main answer is simple - miners don't "boil" because the mines use suitable cooling and ventilation equipment, plain and simple.

That said, there is a contradiction, at least if you go only by Wikipedia and explicitly ignore its caveats. The Wikipedia page for the Mponeng gold mine makes the maximum rock temperature at 66 °C, and if all you read from the Wikipedia page on the geothermal gradient is the stuff in bold, then yes, a 25 °C/km gradient over a 4 km depth would give you 100 °C on top of the surface temperature.

However, the actual text in that page reads

Away from tectonic plate boundaries, it is about 25 °C per km of depth (1 °F per 70 feet of depth) near the surface in most of the world.

and makes it clear that there can be local variations. With that in mind even some very mild digging turns up this map of the geothermal heat flow in South Africa:

(Taken from S. Afr. J. Sci. 110 no. 3-4, p. 1 (2014).) This makes it clear that the Mponeng mine is right on top of a cold spot in the Wits basin.

The stated heat flows are not enough to reconstruct the thermal gradient (you need the thermal conductivity for that), and I'm not going to go on an expedition for fully trustworthy sources for that gradient. However, some more cursory digging unearthed this source, which looks reasonable (if not particularly scientific), and which claims that

mining at these depths is only feasible in South Africa’s Wits Basin due to a relatively low geothermal gradient (nine degrees Celcius/km) and the presence of gold reefs in hard competent country rocks.

This is enough of an agreement to call it a day. Backtracking a 9 °C/km gradient over 4 km gives a ~36 °C difference, and taking that away from the 66 °C (maximal!) rock temperature in the mine gives a ~30 °C average surface temperature. This is relatively high, but it is within a reasonable envelope, and there's plenty of leeway on the numbers (e.g. making the gradient 10 or 11 °C/km) to take away any glaring contradictions.

Answer 2

There is this very short account on Wikipedia, which seems to cover it.

Mponeng Gold Mine

The temperature of the rock reaches 66 °C (151 °F), and the mine pumps slurry ice underground to cool the tunnel air below 30 °C (86 °F). A mixture of concrete, water, and rock is packed into excavated areas, which further acts as an insulator. Tunnel walls are secured by flexible shotcrete reinforced with steel fibers, which is further held in place by diamond-mesh netting.

From Wall Street Journal

It takes 6,000 tons of ice a day to keep Mponeng's deepest levels at a bearable 83 [°F] degrees. They make the ice in a surface plant, then mix it with salt to create a slush that can be pumped down to underground reservoirs. There, giant fans pass air over the coolant and push the chilled air further down, into the mining tunnels. Cool air goes down at a temperature of 37 [°F] and comes back, heated up by the rock, at 86 [°F]. I walked past one of these hot air returns—a black, growling tunnel that exhaled rank air from the bottom levels. (Emphasis Mine)

Answer 3

The gradient you're quoting is an approximate figure that applies to most places. There could be local variations, both in terms of where on the globe the mine is and in terms of the gradient not being exactly constant with depth. It's not so surprising that this one mine is off prediction at a depth of 1 km, which is only about 1% of the lithosphere. One might speculate that having an air pocket (the mine) would passively affect the temperature of the local rock as well before the active cooling system is considered.

From wikipedia:

Geothermal gradient is the rate of increasing temperature with respect to increasing depth in the Earth's interior. Away from tectonic plate boundaries, it is about 25 °C per km of depth (1 °F per 70 feet of depth) near the surface in most of the world.

Answer 4

After doing some more research on this question I have determined, like the other answers, the reason that the miners do not boil to death is that they cool the mine actively. Originally this was done by using chilled service water and ice slurries, a method pioneered scientifically by Wagner (Wagner, H. The management of heat flow in deep mines. Geomechan. Tunn. 2011, 4, 157–163). In more recent years the depth of the mine has become such that it is economic to use hard ice. This is done by conveying hard ice into the bottom of the mine and pumping out the melt water. Here is a picture of the ice as it enters the mine:

The amount of ice needed is computed in the following way:

After the ice melts, the melt water at temperature 25 °C is pumped back to the surface. According to Howden, the company that provides the technology to cool the mine, the virgin rock temperature at the bottom of the mine is 55 °C and the ambient air must be maintained at a temperature of 28 °C or lower. It is important to realize that virgin rock temperatures are only one source of heat. Mining machinery engines, lighting systems and auto-compression of air all add more heat. Auto compression is the term used to describe the way air is compressed by its own weight as it descends into the mine. The heat flow into the mine is mitigated by using thick concrete-based insulation that provides a thermal barrier to the virgin rock. The mine is lined with this insulation, reducing the amount of cooling ice needed.

Low Geothermal Gradient

The reason why the virgin rock temperature of the mine at the deepest levels is only about 55 °C as opposed to the 125 °C we might expect is that the geothermal gradient can differ substantially depending on the kind of rocks in the local area. Different rocks have different heat capacities and insulating qualities, therefore, the thermal flux at different depths and geographic locations will be quite different. Also, tectonic effects like volcanism can increase the heat flux. In addition to this, some rocks, like granites, actually generate heat, so that can affect the heat flux, as well. Yet another factor is the orientation of the country rock. For example, quartz is highly anisotropic so the heat flow through it depends significantly on the direction the quartz crystals are oriented.

In the Witwatersrand Basin, where the Mponeng Mine is located the geothermal gradient is noticeably low and is nominally rated at 9 °C/km. This yields an expected temperature of 4 km × 9 °C/km + 25 °C = 61 °C which is quite near the measured maximums of approximately 55 °C. The apparent reason for this coolness is the presence of a thick, cratonic lithosphere in this region (Jones, M. Q. W. "Heat flow in the Witwatersrand Basin and environs and its significance for the South African shield geotherm and lithosphere thickness." Journal of Geophysical Research: Solid Earth 93.B4 (1988): 3243–3260.) This particular craton is known as the Kaapvaal Craton. The craton shields and insulates the surface layers of the earth from the hot interior of the earth. The map below shows the location of the mine with respect to the Kaapvaal Craton:

The mine is located at the white dot. As you can see it is located right above the center of the craton.