How much fresh water could be produced by pumping warm humid air through a pipeline up to the top of a mountain?

I have been doing a lot of research on the Internet lately about various desalination processes which are being used today and this led me to begin studying about mountain weather and the orographic effect (or orographic lifting).

From studying mountain weather, the thought occurred to me about whether a lot of fresh water could be produced by creating an artificially-produced orographic effect by pumping warm, humid coastal air through a pipeline that would lead to the top of a coastal mountain.

Orographic Effect:

I then used MS Paint to make a conceptual drawing on how this could be done:

Since the temperature of the metal pipe will decrease as it ascends up the coastal mountain, contact with this colder metal should cause the water vapor within the pumped air to condense on the inner wall of the pipeline and forming water droplets. These water droplets should then be pulled down by gravity and should fall into a pipe leading to a water storage tank.

In the case that one air pumping plant cannot produce enough air pressure to push the air all the way up a mountain, then perhaps another air pumping plant could be stationed near the top of the mountain to assist with transporting the air upwards through the pipeline.

These air pumping plants would probably need to have a large volume industrial centrifugal blower fan like the ones built by Elektror Airsystems pictured here:

I am neither a climatologist nor a scientist so I really don't how much fresh water could be produced this way. I am looking for someone in Earth Science.SE to give me just a ballpark figure of how much water may be produced by this process.

Say that this pipeline is 2.5 meters in diameter, the top of the mountain is 2500 meters high, the air temperature at the top of the mountain is 280 Kelvin, the coastal air temperature is 302 Kelvin, and the coastal air humidity is at 70%.

How much fresh water could be produced by pumping warm humid air through a pipeline up to the top of a mountain?

• The volume of air involved in this conduit would be substantial. And as you note, the water would condense as it rose and the temperature declined so you would have substantial condensation within the upward channel, likely diminishing returns at altitude. Commented Jan 21, 2023 at 22:33
• a better way to condense out water from air is to use seawater and a heatpump to cool the air.better in this context does not mean that it is a good way to harvest water from air. Commented Jan 22, 2023 at 6:23
• so just a really complex and inefficient dehumidifier.
– John
Commented Jan 22, 2023 at 14:34
• Note that it isn't colder metal that's would cause condensation... but because air itself cools as it rises and expands. Having the surface would give it a location to quickly condense, but it's the air itself cooling that's causing the condensation Commented Jan 22, 2023 at 23:28
• Solar updraft towers are a variation on this theme - instead of pumping the air up your pipe, you heat the air as it enters the pipe and rely on convection to create an updraft, and use the rising airflow to generate electricity. Potentially these systems can be used to extract moisture from the air. Commented Jan 23, 2023 at 16:57

Using the relative humidity and temperature, the g/kg ratio of water to dry air can be calculated. Using an online rh calculator, a relative humidity of 70% and a temperature of 302 K at 1 atm yields 17.54 grams water/kg air. This is the maximum amount of water that can be extracted.

Using an online calculator, the density of dry air at 302K and 1 atm is 1.16882 kg/cu m.

The total volume of your pipe (2.5 m diameter with a height of 2500 m) = 12,271.85 cu m.

This holds 14,343.58 kg dry air and 251,586.45 grams (251 L) of water or 66.5 gallons of water.

So, the maximum possible is 66.5 gallons/pipe of air. Your design won't extract this much and it's likely to get less than half this.

I haven't calculated is how much time is required to extract all the water from a full pipe of air but I can't imagine this being a fast process and wouldn't be surprised if it took several hours.

Based on this simple analysis, the cost/benefit ratio would be much too high to invest in a project like this. Remember that you are competing with existing technology that according to Texas:

Texas Water Development Board states a good rule of thumb is \$1.10-2.40 per 1,000 gallons for brackish water and$2.46-4.30 per 1,000 gallons for seawater desalination.

• Though I wouldn't think it'd take 3 hours... if it's lifting at just 10 mph, that's just 9 min 18 sec to cycle one tube of air through. The question is how thoroughly it condenses and collects. But I think you may be talking about quite a bit more water in your listed conditions... but a fair bit less in cooler conditions. And still the issue of the fact you're producing water where water is already going to be common. (And the removed moisture tends to mean that much drier the air is downstream... where it is already scarcer [deserts and such]... so if done in large scale... lawsuit?) Commented Jan 22, 2023 at 23:34
• @JeopardyTempest Also, the pipe should be buried to maintain a consistently cool temperature that is not affected by the sun during hot days. Commented Jan 23, 2023 at 0:25
• @SteveSaban ok, fair enough :-p Thanks for the input :-) Commented Jan 23, 2023 at 1:58
• Looks like I accidentally deleted my note that furthermore it won't come close to producing the 17.54 g/kg of water in the air... the air temp will basically be reduced to between the dry adiabatic value of 277.5 K and the 280 K mountaintop temperature, and be saturated-> resulting mixing ratio of 5.16 to 6.14 g/kg... so a maximum production of nearer 12 g/kg. Not a critique on the answer, just an extension to your ideas, that turns out to limit production even more on that aspect :-) Commented Jan 23, 2023 at 3:01
• @JeopardyTempest I agree. I approached this as an investor. What is the maximum I can get? Will this maximum give me an appreciable return on my investment? I never went further than 66 gallons per mile of pipe. Commented Jan 23, 2023 at 3:05

All kinds of additional problems too:

• Your given values equate (RH calc)(dewpoint calc) to a dewpoint of 73°F, rare to find (mostly towards summer in limited areas... for the US: mostly the Plains/Midwest/South). And water content of air drops markedly if cooler... a dewpoint of 50F is only 7 g/kg, a dewpoint of 20F is nearer 2 g/kg. Not much water content at all (and only a fraction is removed by lifting 2.5 km) Take a look at the current dewpoint map for the US or world to see just how low dewpoint values often are.

• You're also extracting the water where there's already plenty of natural water extraction (it's rainy in those orographic locations)... especially those that have the tropical temp/dewpoints you set.

• And then the air needs quite a bit of energy to travel 2.5 km... especially since it's 2.5 km uphill. Just gravitational PE looks like 343 MJ, which if done very slowly (over 3 hours) is 32 kWhr each hour, and at 10 mph would be more like 570 kWhr each hour. Which is roughly 30-600 homes worth. You're talking 150-3000 400W solar panels worth and getting up near a fullscale wind turbine for the 10 mph throughput. Or in the range of \$20000-\$1.25 million (USD) to purchase the power each year, depending on the location and which speed you choose. [Someone feel free to check my math, please!!] And this is if your fans/heaters somehow had 100% efficiency. (You may wind up being better off heating the input air instead, which could make it unstable such that it would rise on its own? And perhaps you can benefit a bit by channeling wind into the ramp when it's from a different direction than the pipeline... but even with both, energy usage is still likely to be significant)

• And if done at scale... there's also an extra concern... the resulting air downstream loses the moisture you took out... meaning spots where moisture is already scarcer [deserts and such] have even less... and may not be too happy... lawsuit?

So unfortunately you're providing water where it usually isn't that needed, and have significant limitations of cost and efficiency if/when you would need to use the device.