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Not really anything new...
TLDR: the article discusses a geothermal heat sink, instead of the typical evaporative heat sink.
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Seriously... geothermal has been around for a long time.
Am I missing something? I've never heard of using water for A/C, is using freon and other refrigerants a western thing? Do refrigerants not work as well in India?
Yes, industrial chillers use water. Water is much more efficient at evaporative cooling than just air so you can cool more refrigerant in a much smaller space.

Most skyscrapers will keep the chiller on the roof or in the basement. And that is enough to cool the entire building. The domestic air cooled condenser in most homes and small offices just don't scale.

Oh, cool! Thanks for the info. Is it a closed system? Does the water need to be replenished?
If you use an evaporator tower you do need to replenish that water. The tower is usually used to cool a closed loop of water (or glycol/water mix depending on the climate) that cools the refrigerant in a chiller.

The system in the article uses a pipe loop underground in place of an evaporator. This uses less water/energy but require a higher first cost and very specific location requirements which is why the cooling towers are still more popular.

They are definitely not closed; poorly maintained, the water vapor they output can spread pathogens for miles. Cooling towers were blamed for the recent outbreak of Legionnaires' disease in New York City.
I wouldn't doubt it. Even a small domestic AC can be mold city if not cleaned regularly. It's a warm and moist environment just perfect for all types of bugs.
It depends and yes.

Some systems will have a closed system using water or ammonia as the intermediary medium. The coolant is pumped to an air handler on each floor where it cools a condenser filled with refrigerant.

Most chillers are just a big empty box where water is poured over the coils. The evaporating effect cools the medium inside and vents as steam or water vapour.

"Chillers" are actually direct expansion cooling devices for liquid. They have a condenser and evaporator just like an air cooled air conditioning system. The evaporator will be on the chilled water supply side and the condenser can be cooled by water or air.

The big empty box with water is an evaporative cooling tower used to cool the condenser side water.

Larger systems can use cooling towers which leverage evaporative cooling. Also, arid climates can use swamp coolers to cool a space. They work on the same principal. When water evaporates, it pulls energy from the surrounding medium, causing the temperature to drop.
This article has a nice diagram and some explanation:

http://www.buildings.com/article-details/articleid/5757/titl...

In the discussed example, the water cooled system uses ~1/2 the energy of the air cooled system.

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The systems that use water still use the typical refrigerant-based cooling, the difference is they use water and evaporative cooling to cool the condenser coils(the hot side, usually cooled with just a fan in typical residential units)

This allows the hot/high pressure side to be cooled to lower temperatures than possible with only air cooling, which increases the efficiency of the unit. Since water is evaporated, this required a continuous supply of new water.

Another use of water is in the distribution of the cooling -- basically using the above system to chill a different water supply, then using this chilled water to pipe the cooling to various areas of the building. This is typically a closed loop system and shouldn't require any additional water over the amount required to initially fill the system, unless there is a leak.

Something I haven't yet understood is why is it not possible to pass air underground to cool it and cycle it back into the building, giving air conditioning with the day to day cost of running fans?
It exists, it's called a geothermal heat pump / ground-source heat pump.
That typically refers to cycling water underground and using it to immerse one side of a heat exchanger, does it not?

I am wondering why cycling air directly with no heat pump isn't used more often.

Because air is not very good at moving heat, so it's more efficient to use water or some sort of refrigerant.
In the context of a heat pump yes, but what I'm saying is why not cycle the air of a building underground directly? I would think lots of air would be moved for very little energy and could be put through an underground radiator with lots of surface area.

Even with a heat pump, air has to be passed over the evaporation coils anyway.

If you're trying to cool a building, the goal isn't moving air, it's moving heat. Pushing air around is a convenient way of moving that heat around inside a structure, but it's a lousy way of changing the total amount of heat inside the structure.
But again a heat pump is still running air over the evaporation coils so how does that end up better than having a radiator underground?
The amount of surface area you would need to have underground to expose the air to would be tremendous. The reason heat exchangers work is because they substantially concentrate the heat (or the 'cold'), reducing the surface area needed.